Finite Group Databasebeta

← #29465813

Subgroups — #29465813

Order 15104.

2124 conjugacy classes of subgroups.

The subgroup lattice has 1824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#552×D59C211yesmaximal, characteristic, complemented
2#21437585C211yesmaximal, characteristic
3#21436369C211yesmaximal, characteristic, complemented
4#21436361C211yesmaximal, characteristic, complemented
5#21436319C211yesmaximal, characteristic, complemented
6#21436311C211yesmaximal, characteristic, complemented
7#21436226C211yesmaximal, characteristic, complemented
8#21436218C211yesmaximal, characteristic, complemented
9#21436198C211yesmaximal, characteristic, complemented
10#21436190C211yesmaximal, characteristic, complemented
11#21436151C211yesmaximal, characteristic, complemented
12#21436143C211yesmaximal, characteristic, complemented
13#21436123C211yesmaximal, characteristic, complemented
14#21436115C211yesmaximal, characteristic, complemented
15#21435983C211yesmaximal, characteristic, complemented
16#21435933C211yesmaximal, characteristic, complemented
17#21435925C211yesmaximal, characteristic, complemented
18#21434493C211yesmaximal, characteristic, complemented
19#21434028C211yesmaximal, characteristic, complemented
20#21434015C211yesmaximal, characteristic, complemented
21#21433915C211yesmaximal, characteristic, complemented
22#21433723C211yesmaximal, characteristic, complemented
23#21433719C211yesmaximal, characteristic, complemented
24#21433566C211yesmaximal, characteristic, complemented
25#21433355C211yesmaximal, characteristic, complemented
26#21433353C211yesmaximal, characteristic, complemented
27C4×#14273759C211yesmaximal, characteristic, complemented
28D4×#11745659C211yesmaximal, characteristic, complemented
29#21432611C211yesmaximal, characteristic, complemented
30C2×#16837402C211yesmaximal, characteristic, complemented
31C59×#3300C211yesmaximal, characteristic, complemented
32C22×#11745689C2211yescharacteristic
33C2×#41×D59C2211yescharacteristic
34C2×#14273759C2211yescharacteristic
35C2×#14273759C2211yescharacteristic, complemented
36C2×#14273756C2211yescharacteristic, complemented
37C22×#11745659C2211yescharacteristic, complemented
38C22×#11745659C2211yescharacteristic, complemented
39#16838094C2211yescharacteristic
40#16838093C2211yescharacteristic, complemented
41#16838092C2211yescharacteristic, complemented
42#16838091C2211yescharacteristic, complemented
43#16838090C2211yescharacteristic, complemented
44#16838089—21no—
45#16838088—21no—
46#16838087C2211yescharacteristic
47#16838086C2211yescharacteristic, complemented
48#16838085—21no—
49#16838084—21no—
50#16838071C2211yescharacteristic
51Q8×C22⋊D59C2211yescharacteristic
52#16838064C2211yescharacteristic
53#16838054—21no—
54#16838054C2211yescharacteristic
55#16838048—21no—
56#16838048C2211yescharacteristic
57#16838045—21no—
58#16838045C2211yescharacteristic
59#16838036—21no—
60#16838036C2211yescharacteristic
61#16837951—21no—
62#16837951C2211yescharacteristic
63#126×D59—21no—
64#125×D59—21no—
65#125×D59C2211yescharacteristic, complemented
66#16837915—21no—
67#16837915C2211yescharacteristic
68#16837912—21no—
69#16837912C2211yescharacteristic
70#123×D59—21no—
71C22⋊Q8×D59C2211yescharacteristic, complemented
72C22⋊Q8×D59C2211yescharacteristic, complemented
73C4×#11745689C2211yescharacteristic
74C4×Q8×D59C2211yescharacteristic, complemented
75C4×D4×D59—21no—
76C4×D4×D59C2211yescharacteristic
77#117×D59—21no—
78#117×D59C2211yescharacteristic, complemented
79C2×C4⋊C4×D59C2211yescharacteristic, complemented
80#16837769C2211yescharacteristic, complemented
81#16837769C2211yescharacteristic, complemented
82#16837765C2211yescharacteristic, complemented
83#16837765C2211yescharacteristic, complemented
84#16837759C2211yescharacteristic, complemented
85#16837757C2211yescharacteristic, complemented
86#16837756C2211yescharacteristic, complemented
87#16837742C2211yescharacteristic, complemented
88#16837741C2211yescharacteristic, complemented
89#16837740C2211yescharacteristic, complemented
90#16837739C2211yescharacteristic, complemented
91#16837739C2211yescharacteristic, complemented
92#16837733C2211yescharacteristic, complemented
93#16837732C2211yescharacteristic, complemented
94#16837729C2211yescharacteristic, complemented
95#16837728C2211yescharacteristic, complemented
96#16837727C2211yescharacteristic, complemented
97#16837726C2211yescharacteristic, complemented
98#16837719C2211yescharacteristic, complemented
99#16837719C2211yescharacteristic, complemented
100#16837713C2211yescharacteristic, complemented
101#16837711C2211yescharacteristic, complemented
102#16837709C2211yescharacteristic, complemented
103#16837707C2211yescharacteristic, complemented
104#16837705C2211yescharacteristic, complemented
105#16837703C2211yescharacteristic, complemented
106#16837701C2211yescharacteristic, complemented
107#16837699C2211yescharacteristic, complemented
108#16837661C2211yescharacteristic, complemented
109#16837659C2211yescharacteristic, complemented
110#16837659C2211yescharacteristic, complemented
111#16837657C2211yescharacteristic, complemented
112#16837651C2211yescharacteristic, complemented
113#16837649C2211yescharacteristic, complemented
114#16837647C2211yescharacteristic, complemented
115#16837645C2211yescharacteristic, complemented
116#16837643C2211yescharacteristic, complemented
117#16837641C2211yescharacteristic, complemented
118#16837641C2211yescharacteristic, complemented
119#16837633C2211yescharacteristic, complemented
120#16837631C2211yescharacteristic, complemented
121#16837629C2211yescharacteristic, complemented
122#16837625C2211yescharacteristic, complemented
123#16837624C2211yescharacteristic, complemented
124#16837621C2211yescharacteristic, complemented
125#16837611C2211yescharacteristic, complemented
126#16837610C2211yescharacteristic, complemented
127#16837601C2211yescharacteristic, complemented
128#16837600C2211yescharacteristic, complemented
129#16837567C2211yescharacteristic, complemented
130#16837567C2211yescharacteristic, complemented
131#16837566C2211yescharacteristic, complemented
132#16837564C2211yescharacteristic, complemented
133#16837563C2211yescharacteristic, complemented
134#16837563C2211yescharacteristic, complemented
135#16837562C2211yescharacteristic, complemented
136#16837559C2211yescharacteristic, complemented
137#16837558C2211yescharacteristic, complemented
138#16837556C2211yescharacteristic, complemented
139#16837555C2211yescharacteristic, complemented
140#16837554C2211yescharacteristic, complemented
141#16837552C2211yescharacteristic, complemented
142#16837551C2211yescharacteristic, complemented
143#16837509C2211yescharacteristic, complemented
144#16837506C2211yescharacteristic, complemented
145#16837505C2211yescharacteristic, complemented
146#16837501C2211yescharacteristic, complemented
147C4×#11745672C2211yescharacteristic, complemented
148C4×#11745660C2211yescharacteristic, complemented
149C4×#11745671C2211yescharacteristic, complemented
150#16837481C2211yescharacteristic, complemented
151#16837479C2211yescharacteristic, complemented
152#16837473C2211yescharacteristic
153#16837473C2211yescharacteristic, complemented
154#16837470C2211yescharacteristic
155#16837470C2211yescharacteristic, complemented
156D4×C59⋊C8C2211yescharacteristic, complemented
157#16837443C2211yescharacteristic, complemented
158#16837443C2211yescharacteristic, complemented
159#16837441C2211yescharacteristic, complemented
160#16837424C2211yescharacteristic, complemented
161#16837409C2211yescharacteristic, complemented
162#16837409C2211yescharacteristic, complemented
163#16837409C2211yescharacteristic, complemented
164#16837405C2211yescharacteristic, complemented
165#16837405C2211yescharacteristic, complemented
166#16837402C2211yescharacteristic
167#16837402C2211yescharacteristic
168#16837402C2211yescharacteristic
169#16837402C2211yescharacteristic, complemented
170#16837402C2211yescharacteristic, complemented
171#16837402C2211yescharacteristic, complemented
172#16837402C2211yescharacteristic, complemented
173#16837402C2211yescharacteristic, complemented
174#16837402C2211yescharacteristic, complemented
175#16837402C2211yescharacteristic, complemented
176#16837400C2211yescharacteristic, complemented
177#16837400C2211yescharacteristic, complemented
178#16837400C2211yescharacteristic, complemented
179#16837399C2211yescharacteristic, complemented
180#16837398C2211yescharacteristic, complemented
181#16837396C2211yescharacteristic, complemented
182C2×#14273651C2211yescharacteristic, complemented
183C2×#14273649C2211yescharacteristic, complemented
184C2×#14273647C2211yescharacteristic, complemented
185#16837364C2211yescharacteristic, complemented
186#16837364C2211yescharacteristic, complemented
187C4×#11745659C2211yescharacteristic, complemented
188C59×#552C2211yescharacteristic, complemented
189C59×#548C2211yescharacteristic
190C59×#488C2211yescharacteristic, complemented
191C59×#485C2211yescharacteristic, complemented
192C59×#480C2211yescharacteristic, complemented
193C59×#479C2211yescharacteristic, complemented
194C59×#467C2211yescharacteristic, complemented
195C59×#465C2211yescharacteristic, complemented
196C59×#464C2211yescharacteristic, complemented
197C59×#452C2211yescharacteristic, complemented
198C59×#451C2211yescharacteristic, complemented
199C4×Q16×C59C2211yescharacteristic, complemented
200C8×D4×C59C2211yescharacteristic, complemented
201C59×#416C2211yescharacteristic, complemented
202C2×#103×C59C2211yescharacteristic, complemented
203C2×#11745689—21no—
204C2×#11745689—21no—
205C2×#11745689—24no—
206C2×#11745689—42no—
207C2×#11745689C2311yescharacteristic
208C2×#11745689C2311yescharacteristic
209C2×#11745689C2311yescharacteristic
210C2×#11745689C2311yescharacteristic
211C2×#11745685—21no—
212C2×#11745685C2311yescharacteristic
213C2×#11745687—21no—
214C2×#11745687C2311yescharacteristic
215#41×D59—24no—
216#41×D59—42no—
217C2×Q8×D59C2311yescharacteristic
218C2×Q8×D59C2311yescharacteristic
219C22×D236—21no—
220C22×D236C2311yescharacteristic
221C2×D4×D59—21no—
222C2×D4×D59—21no—
223C2×D4×D59D411yescharacteristic
224C2×D4×D59C2311yescharacteristic
225C22×C4×D59—21no—
226C22×C4×D59—21no—
227C22×C4×D59—21no—
228C22×C4×D59C2311yescharacteristic
229C22×C4×D59C2311yescharacteristic
230#14273759—24no—
231#14273759—42no—
232#14273756—42no—
233C2×Dic236C2311yescharacteristic
234C2×#11745672C2311yescharacteristic
235C2×#11745672C2311yescharacteristic
236C2×#11745672C2311yescharacteristic
237C2×#11745660C2311yescharacteristic
238C2×#11745660C2311yescharacteristic
239C2×#11745670C2311yescharacteristic
240C2×#11745671C2311yescharacteristic
241C2×#11745671C2311yescharacteristic
242C2×#11745659—42no—
243C2×#11745659—42no—
244C2×#11745659C2311yescharacteristic
245C2×#11745659C2311yescharacteristic
246C2×#11745659C2311yescharacteristic
247C2×#11745659C2311yescharacteristic
248C2×#11745659C2311yescharacteristic
249C2×#11745659C2311yescharacteristic
250C2×#11745659C2311yescharacteristic
251C2×#11745659C2311yescharacteristic
252C22×C59⋊C8C2311yescharacteristic
253C22×C59⋊C8C2311yescharacteristic
254#14273725—21no—
255#14273725C2311yescharacteristic
256#14273723—21no—
257#14273723C2311yescharacteristic
258#14273722—21no—
259#14273722—21no—
260#14273722—21no—
261#14273721—21no—
262#14273720—21no—
263#14273720—21no—
264#14273720—21no—
265#14273719—21no—
266#14273719C2311yescharacteristic
267#14273718—21no—
268#14273718—21no—
269#14273718C2311yescharacteristic
270#14273718C2311yescharacteristic
271#14273717—21no—
272#14273717—21no—
273#14273717—21no—
274#14273717—21no—
275#14273717—21no—
276#14273717—21no—
277#14273715—21no—
278#14273715C2311yescharacteristic
279#14273712—21no—
280#14273712—21no—
281#14273712—21no—
282#14273712—21no—
283#14273712—21no—
284#14273711—21no—
285#14273710—21no—
286#14273709—21no—
287#14273709—21no—
288#14273709—21no—
289#14273709—21no—
290#14273709—21no—
291#14273708—21no—
292#14273707—21no—
293#14273707C2311yescharacteristic
294#14273707C2311yescharacteristic
295#14273707C2311yescharacteristic
296#14273706—21no—
297#14273706C2311yescharacteristic
298#14273706C2311yescharacteristic
299#14273706C2311yescharacteristic
300#14273705—21no—
301#14273705—21no—
302#14273704—21no—
303#14273704—21no—
304#14273703—21no—
305#14273703C2311yescharacteristic
306#14273703C2311yescharacteristic
307#14273703C2311yescharacteristic
308#14273702—21no—
309#14273702C2311yescharacteristic
310#14273701—21no—
311#14273701C2311yescharacteristic
312#14273700—21no—
313#14273700—21no—
314#14273700—21no—
315#14273700—21no—
316#14273700—21no—
317#14273700—21no—
318#14273698—21no—
319#14273698C2311yescharacteristic
320#14273697—21no—
321#14273697—21no—
322#14273697—21no—
323#14273695—21no—
324#14273695—21no—
325#14273695—21no—
326Q8×Dic59C2311yescharacteristic
327Q8×Dic59C2311yescharacteristic
328C4×Dic118—21no—
329C4×Dic118C2311yescharacteristic
330#14273692—21no—
331#14273692C2311yescharacteristic
332C4×D236—21no—
333C4×D236—21no—
334C4×D236C2311yescharacteristic
335C4×D236C2311yescharacteristic
336D4×Dic59—21no—
337D4×Dic59D411yescharacteristic
338#14273689—21no—
339#14273689—21no—
340#14273689D411yescharacteristic
341#14273689C2311yescharacteristic
342C4×C22⋊D59—21no—
343C4×C22⋊D59—21no—
344C4×C22⋊D59C2311yescharacteristic
345C4×C22⋊D59C2311yescharacteristic
346(C22⋊D59)⋊C4—21no—
347(C22⋊D59)⋊C4—21no—
348(C22⋊D59)⋊C4—21no—
349(C22⋊D59)⋊C4—21no—
350(C22⋊D59)⋊C4D411yescharacteristic
351(C22⋊D59)⋊C4D411yescharacteristic
352#14273686—21no—
353#14273686C2311yescharacteristic
354#14273685—21no—
355#14273685—21no—
356#14273685—21no—
357#14273685C2311yescharacteristic
358#14273685C2311yescharacteristic
359#14273685C2311yescharacteristic
360#14273684—21no—
361#14273684—21no—
362#14273684—21no—
363#14273683—21no—
364#14273683—21no—
365#14273683—21no—
366C2×C4⋊Dic59C2311yescharacteristic
367C2×Dic59⋊C4—21no—
368C4⋊C4×D59—21no—
369C4⋊C4×D59—21no—
370C4⋊C4×D59—21no—
371C4⋊C4×D59—21no—
372C4⋊C4×D59—21no—
373C4⋊C4×D59—21no—
374C4⋊C4×D59—21no—
375C4⋊C4×D59—21no—
376C4⋊C4×D59D411yescharacteristic
377C4⋊C4×D59C2311yescharacteristic
378C4⋊C4×D59C2311yescharacteristic
379C4⋊C4×D59C2311yescharacteristic
380C4⋊C4×D59C2311yescharacteristic
381C4⋊C4×D59C2311yescharacteristic
382C22⋊C4×D59—21no—
383C22⋊C4×D59—21no—
384C22⋊C4×D59—21no—
385C22⋊C4×D59—21no—
386C22⋊C4×D59—21no—
387C22⋊C4×D59D411yescharacteristic
388C22⋊C4×D59D411yescharacteristic
389C42×D59—21no—
390C42×D59—21no—
391C42×D59—21no—
392C42×D59C2311yescharacteristic
393#14273661C2311yescharacteristic
394#14273660C2311yescharacteristic
395#14273660C2311yescharacteristic
396#14273660C2311yescharacteristic
397#14273659C2311yescharacteristic
398#14273659C2311yescharacteristic
399#14273658C2311yescharacteristic
400#14273658C2311yescharacteristic
401#14273658C2311yescharacteristic
402C4⋊(C59⋊C8)C2311yescharacteristic
403Dic59⋊C8C2311yescharacteristic
404Dic59⋊C8C2311yescharacteristic
405#14273652C2311yescharacteristic
406#14273652C2311yescharacteristic
407#14273652C2311yescharacteristic
408#14273652C2311yescharacteristic
409#14273651C2311yescharacteristic
410#14273651C2311yescharacteristic
411#14273651C2311yescharacteristic
412#14273651C2311yescharacteristic
413#14273651C2311yescharacteristic
414#14273651C2311yescharacteristic
415#14273651C2311yescharacteristic
416#14273650C2311yescharacteristic
417#14273650C2311yescharacteristic
418#14273650C2311yescharacteristic
419#14273650C2311yescharacteristic
420#14273649C2311yescharacteristic
421#14273649C2311yescharacteristic
422#14273649C2311yescharacteristic
423#14273649C2311yescharacteristic
424#14273649C2311yescharacteristic
425#14273649C2311yescharacteristic
426#14273648C2311yescharacteristic
427#14273648C2311yescharacteristic
428#14273648C2311yescharacteristic
429#14273647C2311yescharacteristic
430#14273647C2311yescharacteristic
431#14273647C2311yescharacteristic
432#14273647C2311yescharacteristic
433#14273647C2311yescharacteristic
434#14273647C2311yescharacteristic
435C22⋊(C59⋊C8)C2311yescharacteristic
436C22⋊(C59⋊C8)C2311yescharacteristic
437(C2×D59)⋊C8C2311yescharacteristic
438(C2×D59)⋊C8C2311yescharacteristic
439(C2×D59)⋊C8C2311yescharacteristic
440(C2×D59)⋊C8C2311yescharacteristic
441#14273637C2311yescharacteristic
442#14273637C2311yescharacteristic
443C4×C59⋊C8C2311yescharacteristic
444C2×#41×C59C2311yescharacteristic
445C22×Q8×C59C2311yescharacteristic
446C2×Q16×C59C2311yescharacteristic
447C2×Q16×C59C2311yescharacteristic
448C2×SD16×C59C2311yescharacteristic
449C22×C8×C59C2311yescharacteristic
450C22×C8×C59C2311yescharacteristic
451#126×C59—21no—
452#125×C59—21no—
453#125×C59C2311yescharacteristic
454#124×C59—21no—
455#124×C59C2311yescharacteristic
456#123×C59—21no—
457C22⋊Q8×C59—21no—
458C22⋊Q8×C59C2311yescharacteristic
459C22⋊Q8×C59C2311yescharacteristic
460C22⋊Q8×C59C2311yescharacteristic
461#121×C59—21no—
462#121×C59C2311yescharacteristic
463C4×Q8×C59C2311yescharacteristic
464C4×Q8×C59C2311yescharacteristic
465C4×D4×C59—21no—
466C4×D4×C59C2311yescharacteristic
467#117×C59—21no—
468#117×C59C2311yescharacteristic
469C2×C4⋊C4×C59C2311yescharacteristic
470#107×C59C2311yescharacteristic
471#107×C59C2311yescharacteristic
472#106×C59C2311yescharacteristic
473C4⋊C8×C59C2311yescharacteristic
474#103×C59C2311yescharacteristic
475#103×C59C2311yescharacteristic
476#103×C59C2311yescharacteristic
477#103×C59C2311yescharacteristic
478#103×C59C2311yescharacteristic
479#103×C59C2311yescharacteristic
480#103×C59C2311yescharacteristic
481#102×C59C2311yescharacteristic
482#102×C59C2311yescharacteristic
483#102×C59C2311yescharacteristic
484C22⋊C8×C59C2311yescharacteristic
485C22⋊C8×C59C2311yescharacteristic
486C4×C8×C59C2311yescharacteristic
487C23×D59—21no—
488C23×D59—21no—
489C23×D59C2×D411yescharacteristic
490C23×D59C2×D411yescharacteristic
491#41×C59—22no—
492#41×C59—41no—
493C2×Q8×C59—21no—
494C2×Q8×C59—22no—
495C2×Q8×C59—41no—
496C2×Q8×C59C2411yescharacteristic
497C2×Q8×C59C2411yescharacteristic
498C2×Q8×C59C2411yescharacteristic
499C2×D4×C59—21no—
500C2×D4×C59—21no—
501C2×D4×C59C2×D411yescharacteristic
502C2×D4×C59C2411yescharacteristic
503C22×C4×C59—21no—
504C22×C4×C59—21no—
505C22×C4×C59—21no—
506C22×C4×C59C2411yescharacteristic
507C22×C4×C59C2411yescharacteristic
508C2×C22⋊D59—21no—
509C2×C22⋊D59—21no—
510C2×C22⋊D59—21no—
511C2×C22⋊D59—21no—
512C2×C22⋊D59—21no—
513C2×C22⋊D59—21no—
514C2×C22⋊D59—21no—
515C2×C22⋊D59C2×D411yescharacteristic
516C2×C22⋊D59C2×D411yescharacteristic
517C22×Dic59—21no—
518C22×Dic59—21no—
519C22×Dic59C2×D411yescharacteristic
520C22×Dic59C2×D411yescharacteristic
521#11745689—22no—
522#11745689—22no—
523#11745689—22no—
524#11745689—22no—
525#11745689—22no—
526#11745689—44no—
527#11745689—41no—
528#11745689—41no—
529#11745689—44no—
530#11745689#4114yes—
531Q8×D59—22no—
532Q8×D59—22no—
533Q8×D59—22no—
534Q8×D59—41no—
535#11745687—22no—
536#11745687—22no—
537#11745687—44no—
538D4×D59—22no—
539D4×D59—41no—
540D4×D59—44no—
541D4×D59—42no—
542D4×D59—44no—
543#11745685—22no—
544#11745685—41no—
545#11745685—44no—
546C2×D236—21no—
547C2×D236—22no—
548C2×D236—21no—
549C2×D236—21no—
550C2×D236—21no—
551C2×D236—21no—
552C2×D236—21no—
553C2×D236—41no—
554C2×D236—44no—
555C2×D236C2×D411yescharacteristic
556C2×D236C2411yescharacteristic
557C2×D236C2411yescharacteristic
558C2×C4×D59—21no—
559C2×C4×D59—22no—
560C2×C4×D59—22no—
561C2×C4×D59—22no—
562C2×C4×D59—22no—
563C2×C4×D59—21no—
564C2×C4×D59—21no—
565C2×C4×D59—21no—
566C2×C4×D59—21no—
567C2×C4×D59—21no—
568C2×C4×D59—21no—
569C2×C4×D59—21no—
570C2×C4×D59—21no—
571C2×C4×D59—21no—
572C2×C4×D59—21no—
573C2×C4×D59—21no—
574C2×C4×D59—21no—
575C2×C4×D59—21no—
576C2×C4×D59—44no—
577C2×C4×D59—44no—
578C2×C4×D59—44no—
579C2×C4×D59C2×D411yescharacteristic
580C2×C4×D59C2×D411yescharacteristic
581C2×C4×D59C2×D411yescharacteristic
582C2×C4×D59C2×D411yescharacteristic
583C2×C4×D59C2×D411yescharacteristic
584C2×C4×D59C2×D411yescharacteristic
585C2×C4×D59C2411yescharacteristic
586C2×C4×D59C2411yescharacteristic
587C2×C4×D59C2411yescharacteristic
588C2×Dic118—21no—
589C2×Dic118—21no—
590C2×Dic118C2411yescharacteristic
591C2×Dic118C2411yescharacteristic
592Q16×C59—22no—
593Q16×C59—41no—
594SD16×C59—41no—
595C2×C8×C59—41no—
596C2×C8×C59—41no—
597C2×C8×C59C2411yescharacteristic
598C2×C8×C59C2411yescharacteristic
599C2×C8×C59C2411yescharacteristic
600C2×C8×C59C2411yescharacteristic
601C4⋊C4×C59—21no—
602C4⋊C4×C59—21no—
603C4⋊C4×C59—21no—
604C4⋊C4×C59—21no—
605C4⋊C4×C59—21no—
606C4⋊C4×C59—21no—
607C4⋊C4×C59—21no—
608C4⋊C4×C59—21no—
609C4⋊C4×C59C2×D411yescharacteristic
610C4⋊C4×C59C2411yescharacteristic
611C4⋊C4×C59C2411yescharacteristic
612C4⋊C4×C59C2411yescharacteristic
613C4⋊C4×C59C2411yescharacteristic
614C22⋊C4×C59—21no—
615C22⋊C4×C59—21no—
616C22⋊C4×C59—21no—
617C22⋊C4×C59—21no—
618C22⋊C4×C59—21no—
619C22⋊C4×C59—21no—
620C22⋊C4×C59—21no—
621C22⋊C4×C59C2×D411yescharacteristic
622C22⋊C4×C59C2×D411yescharacteristic
623C42×C59—21no—
624C42×C59—21no—
625C42×C59—21no—
626C42×C59C2411yescharacteristic
627C22⋊Dic59—21no—
628C22⋊Dic59—21no—
629C22⋊Dic59—21no—
630C22⋊Dic59—21no—
631C22⋊Dic59—21no—
632C22⋊Dic59C2×D411yescharacteristic
633C22⋊Dic59C2×D411yescharacteristic
634#11745672—22no—
635#11745672—41no—
636#11745672—41no—
637#11745671—22no—
638#11745671—41no—
639#11745670—41no—
640(C2×D59)⋊C4—21no—
641(C2×D59)⋊C4—21no—
642(C2×D59)⋊C4—21no—
643(C2×D59)⋊C4—21no—
644(C2×D59)⋊C4—21no—
645(C2×D59)⋊C4—21no—
646(C2×D59)⋊C4—21no—
647(C2×D59)⋊C4—21no—
648(C2×D59)⋊C4—21no—
649(C2×D59)⋊C4—21no—
650(C2×D59)⋊C4—21no—
651(C2×D59)⋊C4—21no—
652(C2×D59)⋊C4—21no—
653(C2×D59)⋊C4—21no—
654(C2×D59)⋊C4—21no—
655(C2×D59)⋊C4C2×D411yescharacteristic
656(C2×D59)⋊C4C2×D411yescharacteristic
657(C2×D59)⋊C4C2×D411yescharacteristic
658(C2×D59)⋊C4C2×D411yescharacteristic
659C4⋊Dic59—21no—
660C4⋊Dic59—21no—
661C4⋊Dic59—21no—
662C4⋊Dic59—21no—
663C4⋊Dic59—21no—
664C4⋊Dic59—21no—
665C4⋊Dic59—21no—
666C4⋊Dic59—21no—
667C4⋊Dic59C2×D411yescharacteristic
668C4⋊Dic59C2411yescharacteristic
669C4⋊Dic59C2411yescharacteristic
670C4⋊Dic59C2411yescharacteristic
671C4⋊Dic59C2411yescharacteristic
672Dic59⋊C4—21no—
673Dic59⋊C4—21no—
674Dic59⋊C4—21no—
675Dic59⋊C4—21no—
676Dic59⋊C4—21no—
677Dic59⋊C4—21no—
678Dic59⋊C4—21no—
679Dic59⋊C4—21no—
680Dic59⋊C4—21no—
681Dic59⋊C4—21no—
682Dic59⋊C4—21no—
683Dic59⋊C4—21no—
684Dic59⋊C4—21no—
685Dic59⋊C4—21no—
686Dic59⋊C4—21no—
687Dic59⋊C4—21no—
688Dic59⋊C4—21no—
689Dic59⋊C4—21no—
690Dic59⋊C4—21no—
691Dic59⋊C4C2×D411yescharacteristic
692Dic59⋊C4C2×D411yescharacteristic
693C4×Dic59—21no—
694C4×Dic59—21no—
695C4×Dic59—21no—
696C4×Dic59—21no—
697C4×Dic59—21no—
698C4×Dic59—21no—
699C4×Dic59—21no—
700C4×Dic59—21no—
701C4×Dic59C2×D411yescharacteristic
702C4×Dic59C2×D411yescharacteristic
703C4×Dic59C2411yescharacteristic
704C2×C59⋊C8—41no—
705C2×C59⋊C8—41no—
706C2×C59⋊C8C2411yescharacteristic
707C2×C59⋊C8C2411yescharacteristic
708C2×C59⋊C8C2411yescharacteristic
709C2×C59⋊C8C2411yescharacteristic
710Dic236—41no—
711#11745660—22no—
712#11745660—41no—
713#11745659—22no—
714#11745659—22no—
715#11745659—22no—
716#11745659—22no—
717#11745659—41no—
718#11745659—41no—
719#11745659—41no—
720#11745659—41no—
721C23×C59—21no—
722C23×C59C22×D411yescharacteristic
723C23×C59C22×D411yescharacteristic
724C22×D59—22no—
725C22×D59—21no—
726C22×D59—22no—
727C22×D59—22no—
728C22×D59—21no—
729C22×D59—41no—
730C22×D59—41no—
731C22×D59—41no—
732C22×D59—42no—
733C22×D59—42no—
734C22×D59—42no—
735C22×D59—42no—
736C22×D59—81no—
737C22×D59—81no—
738C22×D59C22×D411yescharacteristic
739C22×D59C22×D411yescharacteristic
740C22×D59C22×D411yescharacteristic
741Q8×C59—21no—
742Q8×C59—21no—
743Q8×C59—21no—
744Q8×C59—21no—
745Q8×C59—21no—
746Q8×C59—42no—
747Q8×C59C2×#4112yes—
748D4×C59—22no—
749D4×C59—21no—
750D4×C59—21no—
751D4×C59—42no—
752D4×C59—42no—
753C2×C4×C59—21no—
754C2×C4×C59—21no—
755C2×C4×C59—21no—
756C2×C4×C59—21no—
757C2×C4×C59—21no—
758C2×C4×C59—21no—
759C2×C4×C59—21no—
760C2×C4×C59—21no—
761C2×C4×C59—21no—
762C2×C4×C59—21no—
763C2×C4×C59—21no—
764C2×C4×C59—42no—
765C2×C4×C59—42no—
766C2×C4×C59—42no—
767C2×C4×C59C22×D411yescharacteristic
768C2×C4×C59C22×D411yescharacteristic
769C2×C4×C59C22×D411yescharacteristic
770C2×C4×C59C22×D411yescharacteristic
771C2×C4×C59C2511yescharacteristic
772C22⋊D59—22no—
773C22⋊D59—41no—
774C22⋊D59—42no—
775C22⋊D59—42no—
776C22⋊D59—42no—
777C22⋊D59—42no—
778C22⋊D59—81no—
779C22⋊D59—81no—
780C22⋊D59—81no—
781C2×Dic59—22no—
782C2×Dic59—22no—
783C2×Dic59—21no—
784C2×Dic59—21no—
785C2×Dic59—21no—
786C2×Dic59—21no—
787C2×Dic59—21no—
788C2×Dic59—21no—
789C2×Dic59—42no—
790C2×Dic59—42no—
791C2×Dic59C22×D411yescharacteristic
792C2×Dic59C22×D411yescharacteristic
793C2×Dic59C22×D411yescharacteristic
794C2×Dic59C22×D411yescharacteristic
795C2×Dic59C22×D411yescharacteristic
796D236—24no—
797D236—21no—
798D236—21no—
799D236—21no—
800D236—41no—
801D236—42no—
802D236—42no—
803D236—42no—
804D236—42no—
805D236—42no—
806D236C2×#4112yes—
807C4×D59—22no—
808C4×D59—22no—
809C4×D59—21no—
810C4×D59—21no—
811C4×D59—21no—
812C4×D59—21no—
813C4×D59—22no—
814C4×D59—22no—
815C4×D59—24no—
816C4×D59—41no—
817C4×D59—41no—
818C4×D59—42no—
819C4×D59—42no—
820C4×D59—42no—
821C4×D59—42no—
822C4×D59—42no—
823C4×D59—42no—
824C4×D59—42no—
825C4×D59—42no—
826C4×D59—42no—
827C4×D59—42no—
828C4×D59—42no—
829C4×D59—42no—
830C4×D59—81no—
831C4×D59C2×#4112yes—
832C4×D59H(5,𝔽2)12yes—
833Dic118—21no—
834Dic118—21no—
835Dic118—21no—
836Dic118—21no—
837Dic118—42no—
838Dic118—42no—
839C8×C59—21no—
840C8×C59—21no—
841C8×C59—21no—
842C8×C59—21no—
843C59⋊C8—21no—
844C59⋊C8—21no—
845C59⋊C8—21no—
846C59⋊C8—21no—
847#61163—591nomaximal, Sylow
848C22×C59—21no—
849C22×C59—21no—
850C22×C59—21no—
851C22×C59—21no—
852C22×C59—21no—
853C22×C59—41no—
854C22×C59—41no—
855C22×C59—41no—
856C22×C59#57512yes—
857C22×C59C23×D411yescharacteristic
858C2×D59—21no—
859C2×D59—21no—
860C2×D59—21no—
861C2×D59—21no—
862C2×D59—21no—
863C2×D59—21no—
864C2×D59—22no—
865C2×D59—21no—
866C2×D59—21no—
867C2×D59—44no—
868C2×D59—41no—
869C2×D59—41no—
870C2×D59—41no—
871C2×D59—41no—
872C2×D59—41no—
873C2×D59—82no—
874C2×D59—84no—
875C2×D59—84no—
876C2×D59#54612yes—
877C4×C59—21no—
878C4×C59—22no—
879C4×C59—21no—
880C4×C59—21no—
881C4×C59—21no—
882C4×C59—41no—
883C4×C59—41no—
884C4×C59—41no—
885C4×C59—41no—
886C4×C59—41no—
887C4×C59—41no—
888C4×C59C22×#4111yescharacteristic
889C4×C59C2×H(5,𝔽2)11yescharacteristic
890Dic59—21no—
891Dic59—21no—
892Dic59—21no—
893Dic59—21no—
894Dic59—41no—
895Dic59—41no—
896Dic59—41no—
897Dic59—41no—
898Dic59—41no—
899Dic59—41no—
900Dic59#54612yes—
901C2×#552—591no—
902D4×#41—591no—
903#3327—591no—
904#3327—591no—
905#3323—591no—
906#3323—591no—
907#3317—591no—
908#3317—591no—
909#3315—591no—
910#3315—591no—
911#3312—591no—
912#3312—591no—
913#3310—591no—
914#3310—591no—
915#3300—591no—
916#3300D5911yescharacteristic, complemented
917#3296—591no—
918#3296—591no—
919#3142—591no—
920#3093—591no—
921#3092—591no—
922#3080—591no—
923#3056—591no—
924#3056—591no—
925#3037—591no—
926#3007—591no—
927#3007—591no—
928C4×#137—591no—
929D4×M16—591no—
930#2896—591no—
931C2×#417—591no—
932C2×C59—22no—
933C2×C59—41no—
934C2×C59—81no—
935C2×C59C2×#54611yescharacteristic
936C2×C59C2×#57511yescharacteristic
937C2×C59#358611yescharacteristic
938D59—22no—
939D59—41no—
940D59—41no—
941D59—42no—
942D59—81no—
943C22×#41—591no—
944C22×#41—591no—
945C2×#137—591no—
946C2×#137—591no—
947C2×#137—591no—
948C22×M16—591no—
949C22×M16—591no—
950#552—591no—
951#552—591no—
952#552—591no—
953#552—591no—
954#552—591no—
955#552—591no—
956#552—591no—
957#552—1181no—
958#552—1181no—
959#552—1181no—
960#552—1181no—
961#552C2×D5911yescharacteristic, complemented
962#550—591no—
963D4×Q8—591no—
964#548—591no—
965#548C2×D5911yescharacteristic
966#547—591no—
967#547—1181no—
968#546—591no—
969#546—591no—
970#546—1181no—
971#546—1181no—
972D42—591no—
973D42—1181no—
974#532—591no—
975#532—1181no—
976C2×#126—1181no—
977C2×#125—591no—
978C2×#125—1181no—
979#525—591no—
980#525—591no—
981#525—1181no—
982#525—1181no—
983C2×#123—1181no—
984C2×C22⋊Q8—591no—
985C2×C22⋊Q8—591no—
986C4×#41—591no—
987C2×C4×Q8—591no—
988C2×C4×D4—591no—
989C2×C4×D4—1181no—
990C2×#117—591no—
991C2×#117—1181no—
992C22×C4⋊C4—591no—
993#491—591no—
994#491—591no—
995#490—591no—
996#490—591no—
997#488—591no—
998#488—591no—
999#488—591no—
1000#488C2×D5911yescharacteristic, complemented
1001#485—591no—
1002#485—591no—
1003#485—591no—
1004#485C2×D5911yescharacteristic, complemented
1005#484—591no—
1006#484—591no—
1007#483—591no—
1008#483—591no—
1009#482—591no—
1010#482—591no—
1011#482—591no—
1012#482—591no—
1013#481—591no—
1014#481—591no—
1015#480—591no—
1016#480C2×D5911yescharacteristic, complemented
1017#479—591no—
1018#479—591no—
1019#479—591no—
1020#479C2×D5911yescharacteristic, complemented
1021#478—591no—
1022#478—591no—
1023#478—591no—
1024#478—591no—
1025#470—591no—
1026#470—591no—
1027#470—591no—
1028#470—591no—
1029#468—591no—
1030#468—591no—
1031#468—591no—
1032#468—591no—
1033#467—591no—
1034#467—591no—
1035#467—591no—
1036#467C2×D5911yescharacteristic, complemented
1037#465—591no—
1038#465—591no—
1039#465—591no—
1040#465C2×D5911yescharacteristic, complemented
1041#464—591no—
1042#464—591no—
1043#464—591no—
1044#464C2×D5911yescharacteristic, complemented
1045#462—591no—
1046#462—591no—
1047#460—591no—
1048#460—591no—
1049#452—591no—
1050#452—591no—
1051#452—591no—
1052#452—591no—
1053#452—591no—
1054#452—591no—
1055#452—591no—
1056#452C2×D5911yescharacteristic, complemented
1057#451—591no—
1058#451—591no—
1059#451—591no—
1060#451C2×D5911yescharacteristic, complemented
1061#450—591no—
1062#450—591no—
1063#450—591no—
1064#450—591no—
1065#441—591no—
1066#441—591no—
1067#440—591no—
1068#440—591no—
1069C4×Q16—591no—
1070C4×Q16C2×D5911yescharacteristic, complemented
1071C4×SD16—591no—
1072C4×SD16—591no—
1073#436—591no—
1074#436—591no—
1075#435—591no—
1076#435—591no—
1077#435—591no—
1078#435—591no—
1079C8×D4—591no—
1080C8×D4C2×D5911yescharacteristic, complemented
1081#428—591no—
1082#428—591no—
1083#428—591no—
1084#423—591no—
1085#419—591no—
1086#419—591no—
1087#419—591no—
1088#418—591no—
1089#418—591no—
1090#417—591no—
1091#417—591no—
1092#417—591no—
1093#417—591no—
1094#417—591no—
1095#417—591no—
1096#417—591no—
1097#417—591no—
1098#417—591no—
1099#417—591no—
1100#417—591no—
1101#417—591no—
1102#417—591no—
1103#416—591no—
1104#416—591no—
1105#416—591no—
1106#416C2×D5911yescharacteristic, complemented
1107C2×#103—591no—
1108C2×#103C2×D5911yescharacteristic, complemented
1109C2×#102—591no—
1110C2×#102—591no—
1111#407—591no—
1112#407—591no—
1113C4×M16—591no—
1114C59#6116311yescharacteristic, complemented, Sylow
1115C2×#41—591no—
1116C2×#41—591no—
1117C2×#41—591no—
1118C2×#41—591no—
1119C2×#41—591no—
1120C2×#41—591no—
1121C2×#41—1181no—
1122C2×#41—1181no—
1123C2×#41—1181no—
1124C2×#41—1181no—
1125C2×#41—1184no—
1126C2×#41—1184no—
1127C2×#41—2362no—
1128C2×#41—2362no—
1129C2×#41C22×D5911yescharacteristic
1130C22×Q8—591no—
1131C22×Q8—591no—
1132C22×Q8C22×D5911yescharacteristic
1133C22×D4—591no—
1134C22×D4—591no—
1135C22×D4—591no—
1136C22×D4—1181no—
1137C22×D4—1181no—
1138C22×D4—1181no—
1139C23×C4—591no—
1140C23×C4—591no—
1141C23×C4—1181no—
1142C23×C4—1181no—
1143C23×C4—1181no—
1144#137—1184no—
1145#137—2362no—
1146#137—2362no—
1147C2×Q16—591no—
1148C2×Q16—591no—
1149C2×Q16—591no—
1150C2×Q16—591no—
1151C2×Q16C22×D5911yescharacteristic
1152C2×Q16C22×D5911yescharacteristic
1153C2×SD16—591no—
1154C2×SD16—591no—
1155C2×SD16—591no—
1156C2×SD16—591no—
1157C2×SD16—591no—
1158C2×SD16C22×D5911yescharacteristic
1159C2×M16—591no—
1160C2×M16—591no—
1161C2×M16—591no—
1162C2×M16—591no—
1163C2×M16—591no—
1164C2×M16—591no—
1165C2×M16—591no—
1166C2×M16—591no—
1167C2×M16—2362no—
1168C2×M16—2362no—
1169C22×C8—591no—
1170C22×C8—591no—
1171C22×C8C22×D5911yescharacteristic
1172C22×C8C22×D5911yescharacteristic
1173C4⋊Q8—591no—
1174C4⋊Q8—1181no—
1175#127—591no—
1176#127—1181no—
1177#126—21no—
1178#126—1181no—
1179#126—1181no—
1180#126—1181no—
1181#126—1181no—
1182#126—1181no—
1183#126—1181no—
1184#126—1181no—
1185#125—21no—
1186#125—591no—
1187#125—591no—
1188#125—591no—
1189#125—1181no—
1190#125—1181no—
1191#125—1181no—
1192#125—1181no—
1193#125—1181no—
1194#125—1181no—
1195#125—1181no—
1196#125—1181no—
1197#125—1181no—
1198#125C22×D5911yescharacteristic
1199#124—21no—
1200#124—591no—
1201#124—1181no—
1202#124C22×D5911yescharacteristic
1203#123—21no—
1204#123—1181no—
1205#123—1181no—
1206#123—1181no—
1207#123—1181no—
1208#123—1181no—
1209#123—1181no—
1210#123—1181no—
1211#123—1181no—
1212#123—1181no—
1213#123—1181no—
1214#123—1181no—
1215#123—1181no—
1216#123—1181no—
1217C22⋊Q8—21no—
1218C22⋊Q8—591no—
1219C22⋊Q8—591no—
1220C22⋊Q8—591no—
1221C22⋊Q8—591no—
1222C22⋊Q8—591no—
1223C22⋊Q8—591no—
1224C22⋊Q8—591no—
1225C22⋊Q8—591no—
1226C22⋊Q8—591no—
1227C22⋊Q8—1181no—
1228C22⋊Q8—1181no—
1229C22⋊Q8—1181no—
1230C22⋊Q8—1181no—
1231C22⋊Q8—1181no—
1232C22⋊Q8—1181no—
1233C22⋊Q8—1181no—
1234C22⋊Q8C22×D5911yescharacteristic
1235C22⋊Q8C22×D5911yescharacteristic
1236C22⋊Q8C22×D5911yescharacteristic
1237#121—21no—
1238#121—591no—
1239#121—591no—
1240#121—591no—
1241#121—1181no—
1242#121—1181no—
1243#121—1181no—
1244#121—1181no—
1245#121—1181no—
1246#121—1181no—
1247#121—1181no—
1248#121—1181no—
1249#121—1181no—
1250#121C22×D5911yescharacteristic
1251#120—1181no—
1252#120—1181no—
1253#120—1181no—
1254#120—1181no—
1255#120—1181no—
1256#120—1181no—
1257C4×Q8—591no—
1258C4×Q8—591no—
1259C4×Q8—591no—
1260C4×Q8—591no—
1261C4×Q8—1181no—
1262C4×Q8—1181no—
1263C4×Q8C22×D5911yescharacteristic
1264C4×Q8C22×D5911yescharacteristic
1265C4×D4—21no—
1266C4×D4—591no—
1267C4×D4—591no—
1268C4×D4—591no—
1269C4×D4—591no—
1270C4×D4—591no—
1271C4×D4—591no—
1272C4×D4—591no—
1273C4×D4—591no—
1274C4×D4—591no—
1275C4×D4—1181no—
1276C4×D4—1181no—
1277C4×D4—1181no—
1278C4×D4—1181no—
1279C4×D4—1181no—
1280C4×D4—1181no—
1281C4×D4—1181no—
1282C4×D4—1181no—
1283C4×D4—1181no—
1284C4×D4—1181no—
1285C4×D4—1181no—
1286C4×D4C22×D5911yescharacteristic
1287#117—21no—
1288#117—591no—
1289#117—591no—
1290#117—591no—
1291#117—591no—
1292#117—1181no—
1293#117—1181no—
1294#117—1181no—
1295#117—1181no—
1296#117—1181no—
1297#117—1181no—
1298#117—1181no—
1299#117—1181no—
1300#117—1181no—
1301#117—1181no—
1302#117C22×D5911yescharacteristic
1303C2×C4⋊C4—591no—
1304C2×C4⋊C4—591no—
1305C2×C4⋊C4—591no—
1306C2×C4⋊C4—591no—
1307C2×C4⋊C4—591no—
1308C2×C4⋊C4—591no—
1309C2×C4⋊C4—591no—
1310C2×C4⋊C4—1181no—
1311C2×C4⋊C4—1181no—
1312C2×C4⋊C4—1181no—
1313C2×C4⋊C4—1181no—
1314C2×C4⋊C4—1181no—
1315C2×C4⋊C4—1181no—
1316C2×C4⋊C4—1181no—
1317C2×C4⋊C4—1181no—
1318C2×C4⋊C4—1181no—
1319C2×C4⋊C4C22×D5911yescharacteristic
1320C2×C22⋊C4—591no—
1321C2×C22⋊C4—591no—
1322C2×C22⋊C4—1181no—
1323C2×C22⋊C4—1181no—
1324C2×C22⋊C4—1181no—
1325C2×C22⋊C4—1181no—
1326C2×C22⋊C4—1181no—
1327C2×C42—591no—
1328C2×C42—1181no—
1329C2×C42—1181no—
1330C2×C42—1181no—
1331#107—591no—
1332#107—591no—
1333#107—591no—
1334#107—591no—
1335#107C22×D5911yescharacteristic
1336#107C22×D5911yescharacteristic
1337#106—591no—
1338#106—591no—
1339#106—591no—
1340#106—591no—
1341#106—591no—
1342#106C22×D5911yescharacteristic
1343C4⋊C8—591no—
1344C4⋊C8—591no—
1345C4⋊C8—591no—
1346C4⋊C8C22×D5911yescharacteristic
1347#103—591no—
1348#103—591no—
1349#103—591no—
1350#103—591no—
1351#103—591no—
1352#103—591no—
1353#103—591no—
1354#103—591no—
1355#103—591no—
1356#103—591no—
1357#103—591no—
1358#103—591no—
1359#103—591no—
1360#103—591no—
1361#103—591no—
1362#103C22×D5911yescharacteristic
1363#103C22×D5911yescharacteristic
1364#103C22×D5911yescharacteristic
1365#103C22×D5911yescharacteristic
1366#103C22×D5911yescharacteristic
1367#103C22×D5911yescharacteristic
1368#103C22×D5911yescharacteristic
1369#102—591no—
1370#102—591no—
1371#102—591no—
1372#102—591no—
1373#102—591no—
1374#102—591no—
1375#102—591no—
1376#102—591no—
1377#102—591no—
1378#102—591no—
1379#102—591no—
1380#102—591no—
1381#102—591no—
1382#102—591no—
1383#102—591no—
1384#102C22×D5911yescharacteristic
1385#102C22×D5911yescharacteristic
1386#102C22×D5911yescharacteristic
1387C22⋊C8—591no—
1388C22⋊C8—591no—
1389C22⋊C8—591no—
1390C22⋊C8—591no—
1391C22⋊C8—591no—
1392C22⋊C8—591no—
1393C22⋊C8C22×D5911yescharacteristic
1394C22⋊C8C22×D5911yescharacteristic
1395#97—591no—
1396#97—591no—
1397C4×C8—591no—
1398C4×C8C22×D5911yescharacteristic
1399C24—591no—
1400C24—591no—
1401C24—1181no—
1402C24—1181no—
1403#41—22no—
1404#41—41no—
1405#41—594no—
1406#41—1182no—
1407#41—1182no—
1408#41—1182no—
1409#41—1182no—
1410#41—1182no—
1411#41—1182no—
1412#41—1182no—
1413#41—1182no—
1414#41—2361no—
1415#41—2364no—
1416#41—2364no—
1417#41—2364no—
1418#41—2361no—
1419#41—2361no—
1420#41—2364no—
1421C2×Q8—21no—
1422C2×Q8—22no—
1423C2×Q8—41no—
1424C2×Q8—591no—
1425C2×Q8—591no—
1426C2×Q8—1181no—
1427C2×Q8—1181no—
1428C2×Q8—1182no—
1429C2×Q8—1182no—
1430C2×Q8—1182no—
1431C2×Q8—2361no—
1432C2×Q8C23×D5911yescharacteristic
1433C2×Q8C23×D5911yescharacteristic
1434C2×Q8C23×D5911yescharacteristic
1435C2×D4—21no—
1436C2×D4—21no—
1437C2×D4—591no—
1438C2×D4—591no—
1439C2×D4—591no—
1440C2×D4—591no—
1441C2×D4—591no—
1442C2×D4—1182no—
1443C2×D4—1181no—
1444C2×D4—1181no—
1445C2×D4—1181no—
1446C2×D4—1181no—
1447C2×D4—1181no—
1448C2×D4—1181no—
1449C2×D4—1181no—
1450C2×D4—1181no—
1451C2×D4—1182no—
1452C2×D4—1181no—
1453C2×D4—1181no—
1454C2×D4—1181no—
1455C2×D4—1181no—
1456C2×D4—1181no—
1457C2×D4—2361no—
1458C2×D4—2364no—
1459C2×D4—2361no—
1460C2×D4—2362no—
1461C2×D4—2364no—
1462C2×D4—2364no—
1463C2×D4D4×D5911yescharacteristic
1464C2×D4C23×D5911yescharacteristic
1465C22×C4—21no—
1466C22×C4—21no—
1467C22×C4—21no—
1468C22×C4—591no—
1469C22×C4—591no—
1470C22×C4—591no—
1471C22×C4—591no—
1472C22×C4—591no—
1473C22×C4—591no—
1474C22×C4—591no—
1475C22×C4—591no—
1476C22×C4—591no—
1477C22×C4—591no—
1478C22×C4—591no—
1479C22×C4—1181no—
1480C22×C4—1182no—
1481C22×C4—1182no—
1482C22×C4—1182no—
1483C22×C4—1182no—
1484C22×C4—1181no—
1485C22×C4—1181no—
1486C22×C4—1181no—
1487C22×C4—1181no—
1488C22×C4—1181no—
1489C22×C4—1181no—
1490C22×C4—1181no—
1491C22×C4—1181no—
1492C22×C4—1181no—
1493C22×C4—1181no—
1494C22×C4—1181no—
1495C22×C4—1181no—
1496C22×C4—1181no—
1497C22×C4—1181no—
1498C22×C4—1181no—
1499C22×C4—2364no—
1500C22×C4—2364no—
1501C22×C4—2364no—
1502C22×C4C23×D5911yescharacteristic
1503C22×C4C23×D5911yescharacteristic
1504Q16—22no—
1505Q16—41no—
1506Q16—1182no—
1507Q16—2361no—
1508Q16—2361no—
1509Q16—2361no—
1510SD16—41no—
1511SD16—1182no—
1512SD16—1182no—
1513SD16—2361no—
1514SD16—2361no—
1515SD16—2361no—
1516M16—1182no—
1517M16—1182no—
1518M16—1182no—
1519M16—1182no—
1520M16—2361no—
1521M16—2361no—
1522M16—2361no—
1523M16—2361no—
1524C2×C8—41no—
1525C2×C8—41no—
1526C2×C8—591no—
1527C2×C8—591no—
1528C2×C8—591no—
1529C2×C8—591no—
1530C2×C8—2361no—
1531C2×C8—2361no—
1532C2×C8C23×D5911yescharacteristic
1533C2×C8C23×D5911yescharacteristic
1534C2×C8C23×D5911yescharacteristic
1535C2×C8C23×D5911yescharacteristic
1536C4⋊C4—21no—
1537C4⋊C4—21no—
1538C4⋊C4—21no—
1539C4⋊C4—21no—
1540C4⋊C4—21no—
1541C4⋊C4—21no—
1542C4⋊C4—21no—
1543C4⋊C4—21no—
1544C4⋊C4—591no—
1545C4⋊C4—591no—
1546C4⋊C4—591no—
1547C4⋊C4—591no—
1548C4⋊C4—591no—
1549C4⋊C4—591no—
1550C4⋊C4—591no—
1551C4⋊C4—1181no—
1552C4⋊C4—1181no—
1553C4⋊C4—1181no—
1554C4⋊C4—1181no—
1555C4⋊C4—1181no—
1556C4⋊C4—1181no—
1557C4⋊C4—1181no—
1558C4⋊C4—1181no—
1559C4⋊C4—1181no—
1560C4⋊C4—1181no—
1561C4⋊C4—1181no—
1562C4⋊C4—1181no—
1563C4⋊C4—1181no—
1564C4⋊C4—1181no—
1565C4⋊C4—1181no—
1566C4⋊C4—1181no—
1567C4⋊C4—1181no—
1568C4⋊C4—1181no—
1569C4⋊C4—1181no—
1570C4⋊C4—1181no—
1571C4⋊C4—1181no—
1572C4⋊C4—1181no—
1573C4⋊C4—1181no—
1574C4⋊C4—1181no—
1575C4⋊C4—1181no—
1576C4⋊C4—1181no—
1577C4⋊C4—1181no—
1578C4⋊C4D4×D5911yescharacteristic
1579C4⋊C4C23×D5911yescharacteristic
1580C4⋊C4C23×D5911yescharacteristic
1581C4⋊C4C23×D5911yescharacteristic
1582C4⋊C4C23×D5911yescharacteristic
1583C22⋊C4—21no—
1584C22⋊C4—21no—
1585C22⋊C4—21no—
1586C22⋊C4—21no—
1587C22⋊C4—21no—
1588C22⋊C4—21no—
1589C22⋊C4—21no—
1590C22⋊C4—591no—
1591C22⋊C4—591no—
1592C22⋊C4—591no—
1593C22⋊C4—591no—
1594C22⋊C4—591no—
1595C22⋊C4—591no—
1596C22⋊C4—1181no—
1597C22⋊C4—1181no—
1598C22⋊C4—1181no—
1599C22⋊C4—1181no—
1600C22⋊C4—1181no—
1601C22⋊C4—1181no—
1602C22⋊C4—1181no—
1603C22⋊C4—1181no—
1604C22⋊C4—1181no—
1605C22⋊C4—1181no—
1606C22⋊C4—1181no—
1607C22⋊C4—1181no—
1608C22⋊C4—1181no—
1609C22⋊C4—1181no—
1610C22⋊C4—1181no—
1611C22⋊C4—1181no—
1612C22⋊C4—1181no—
1613C22⋊C4—1181no—
1614C22⋊C4—1181no—
1615C22⋊C4—1181no—
1616C22⋊C4D4×D5911yescharacteristic
1617C22⋊C4D4×D5911yescharacteristic
1618C42—21no—
1619C42—21no—
1620C42—21no—
1621C42—591no—
1622C42—591no—
1623C42—591no—
1624C42—1181no—
1625C42—1181no—
1626C42—1181no—
1627C42—1181no—
1628C42—1181no—
1629C42—1181no—
1630C42—1181no—
1631C42—1181no—
1632C42C23×D5911yescharacteristic
1633C23—21no—
1634C23—591no—
1635C23—591no—
1636C23—591no—
1637C23—1182no—
1638C23—1182no—
1639C23—1182no—
1640C23—1181no—
1641C23—1181no—
1642C23—4721no—
1643C23—4721no—
1644C23—2361no—
1645C23—2361no—
1646C23—2361no—
1647C23—2362no—
1648C23—2362no—
1649C23—2362no—
1650C23—2362no—
1651C23C2×D4×D5911yescharacteristic
1652C23C2×D4×D5911yescharacteristic
1653Q8—21no—
1654Q8—21no—
1655Q8—21no—
1656Q8—21no—
1657Q8—21no—
1658Q8—42no—
1659Q8—1181no—
1660Q8—1181no—
1661Q8—1181no—
1662Q8—1181no—
1663Q8—2362no—
1664Q8—2362no—
1665Q8#41×D5912yes—
1666D4—22no—
1667D4—21no—
1668D4—21no—
1669D4—42no—
1670D4—42no—
1671D4—592no—
1672D4—1184no—
1673D4—1182no—
1674D4—1181no—
1675D4—1181no—
1676D4—1181no—
1677D4—4721no—
1678D4—4721no—
1679D4—4721no—
1680D4—2361no—
1681D4—2362no—
1682D4—2362no—
1683D4—2362no—
1684D4—2362no—
1685D4—2362no—
1686D4—2361no—
1687D4—2362no—
1688D4—2362no—
1689D4—2362no—
1690D4—2362no—
1691C2×C4—21no—
1692C2×C4—21no—
1693C2×C4—21no—
1694C2×C4—21no—
1695C2×C4—21no—
1696C2×C4—21no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—21no—
1702C2×C4—42no—
1703C2×C4—42no—
1704C2×C4—42no—
1705C2×C4—591no—
1706C2×C4—592no—
1707C2×C4—592no—
1708C2×C4—591no—
1709C2×C4—591no—
1710C2×C4—591no—
1711C2×C4—591no—
1712C2×C4—1182no—
1713C2×C4—1182no—
1714C2×C4—1184no—
1715C2×C4—1182no—
1716C2×C4—1182no—
1717C2×C4—1182no—
1718C2×C4—1182no—
1719C2×C4—1181no—
1720C2×C4—1181no—
1721C2×C4—1181no—
1722C2×C4—1181no—
1723C2×C4—1181no—
1724C2×C4—1181no—
1725C2×C4—1181no—
1726C2×C4—1181no—
1727C2×C4—1181no—
1728C2×C4—1181no—
1729C2×C4—4721no—
1730C2×C4—2361no—
1731C2×C4—2361no—
1732C2×C4—2362no—
1733C2×C4—2362no—
1734C2×C4—2362no—
1735C2×C4—2362no—
1736C2×C4—2362no—
1737C2×C4—2362no—
1738C2×C4—2362no—
1739C2×C4—2362no—
1740C2×C4—2362no—
1741C2×C4—2362no—
1742C2×C4—2362no—
1743C2×C4—2362no—
1744C2×C4—2362no—
1745C2×C4—2362no—
1746C2×C4C2×D4×D5911yescharacteristic
1747C2×C4C2×D4×D5911yescharacteristic
1748C2×C4C2×D4×D5911yescharacteristic
1749C2×C4C2×D4×D5911yescharacteristic
1750C2×C4C24×D5911yescharacteristic
1751C8—21no—
1752C8—21no—
1753C8—21no—
1754C8—21no—
1755C8—1181no—
1756C8—1181no—
1757C8—1181no—
1758C8—1181no—
1759C22—21no—
1760C22—21no—
1761C22—21no—
1762C22—21no—
1763C22—21no—
1764C22—41no—
1765C22—41no—
1766C22—41no—
1767C22—592no—
1768C22—1181no—
1769C22—1181no—
1770C22—1181no—
1771C22—1181no—
1772C22—1182no—
1773C22—1181no—
1774C22—1181no—
1775C22—1181no—
1776C22—1181no—
1777C22—4724no—
1778C22—4722no—
1779C22—4724no—
1780C22—2364no—
1781C22—2361no—
1782C22—2361no—
1783C22—2361no—
1784C22—2361no—
1785C22—2361no—
1786C22#1683819912yes—
1787C22C22×D4×D5911yescharacteristic
1788C4—21no—
1789C4—21no—
1790C4—22no—
1791C4—21no—
1792C4—21no—
1793C4—41no—
1794C4—41no—
1795C4—41no—
1796C4—41no—
1797C4—41no—
1798C4—41no—
1799C4—592no—
1800C4—1181no—
1801C4—1181no—
1802C4—1181no—
1803C4—1181no—
1804C4—2361no—
1805C4—2361no—
1806C4—2361no—
1807C4—2361no—
1808C4—2361no—
1809C4—2361no—
1810C4C2×#41×D5911yescharacteristic
1811C4H(5,𝔽2)×D5911yescharacteristic
1812C2—22no—
1813C2—41no—
1814C2—81no—
1815C2—1182no—
1816C2—4721no—
1817C2—2361no—
1818C2—2361no—
1819C2—2362no—
1820C2#546×D5911yescharacteristic
1821C2C2×#1683819911yescharacteristic
1822C2#2143888111yescharacteristic
subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3300C2
socleC22×C59C23×D4
prime radical#21437585C2
hypercenter#3300D59
hypocenterC59#61163
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3300

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #552×D59C2semidirect
3. #21436369C2semidirect
4. #21436361C2semidirect
5. #21436319C2semidirect
6. #21436311C2semidirect
7. #21436226C2semidirect
8. #21436218C2semidirect
9. #21436198C2semidirect
10. #21436190C2semidirect
11. #21436151C2semidirect
12. #21436143C2semidirect
13. #21436123C2semidirect
14. #21436115C2semidirect
15. #21435983C2semidirect
16. #21435933C2semidirect
17. #21435925C2semidirect
18. #21434493C2semidirect
19. #21434028C2semidirect
20. #21434015C2semidirect
21. #21433915C2semidirect
22. #21433723C2semidirect
23. #21433719C2semidirect
24. #21433566C2semidirect
25. #21433355C2semidirect
26. #21433353C2semidirect
27. C4×#14273759C2semidirect
28. D4×#11745659C2semidirect
29. #21432611C2semidirect
30. C2×#16837402C2semidirect
31. C59×#3300C2semidirect
35. C2×#14273759C22semidirect
36. C2×#14273756C22semidirect
37. C22×#11745659C22semidirect
38. C22×#11745659C22semidirect
40. #16838093C22semidirect
41. #16838092C22semidirect
42. #16838091C22semidirect
43. #16838090C22semidirect
47. #16838086C22semidirect
65. #125×D59C22semidirect
71. C22⋊Q8×D59C22semidirect
72. C22⋊Q8×D59C22semidirect
74. C4×Q8×D59C22semidirect
78. #117×D59C22semidirect
79. C2×C4⋊C4×D59C22semidirect
80. #16837769C22semidirect
81. #16837769C22semidirect
82. #16837765C22semidirect
83. #16837765C22semidirect
84. #16837759C22semidirect
85. #16837757C22semidirect
86. #16837756C22semidirect
87. #16837742C22semidirect
88. #16837741C22semidirect
89. #16837740C22semidirect
90. #16837739C22semidirect
91. #16837739C22semidirect
92. #16837733C22semidirect
93. #16837732C22semidirect
94. #16837729C22semidirect
95. #16837728C22semidirect
96. #16837727C22semidirect
97. #16837726C22semidirect
98. #16837719C22semidirect
99. #16837719C22semidirect
100. #16837713C22semidirect
101. #16837711C22semidirect
102. #16837709C22semidirect
103. #16837707C22semidirect
104. #16837705C22semidirect
105. #16837703C22semidirect
106. #16837701C22semidirect
107. #16837699C22semidirect
108. #16837661C22semidirect
109. #16837659C22semidirect
110. #16837659C22semidirect
111. #16837657C22semidirect
112. #16837651C22semidirect
113. #16837649C22semidirect
114. #16837647C22semidirect
115. #16837645C22semidirect
116. #16837643C22semidirect
117. #16837641C22semidirect
118. #16837641C22semidirect
119. #16837633C22semidirect
120. #16837631C22semidirect
121. #16837629C22semidirect
122. #16837625C22semidirect
123. #16837624C22semidirect
124. #16837621C22semidirect
125. #16837611C22semidirect
126. #16837610C22semidirect
127. #16837601C22semidirect
128. #16837600C22semidirect
129. #16837567C22semidirect
130. #16837567C22semidirect
131. #16837566C22semidirect
132. #16837564C22semidirect
133. #16837563C22semidirect
134. #16837563C22semidirect
135. #16837562C22semidirect
136. #16837559C22semidirect
137. #16837558C22semidirect
138. #16837556C22semidirect
139. #16837555C22semidirect
140. #16837554C22semidirect
141. #16837552C22semidirect
142. #16837551C22semidirect
143. #16837509C22semidirect
144. #16837506C22semidirect
145. #16837505C22semidirect
146. #16837501C22semidirect
147. C4×#11745672C22semidirect
148. C4×#11745660C22semidirect
149. C4×#11745671C22semidirect
150. #16837481C22semidirect
151. #16837479C22semidirect
153. #16837473C22semidirect
155. #16837470C22semidirect
156. D4×C59⋊C8C22semidirect
157. #16837443C22semidirect
158. #16837443C22semidirect
159. #16837441C22semidirect
160. #16837424C22semidirect
161. #16837409C22semidirect
162. #16837409C22semidirect
163. #16837409C22semidirect
164. #16837405C22semidirect
165. #16837405C22semidirect
169. #16837402C22semidirect
170. #16837402C22semidirect
171. #16837402C22semidirect
172. #16837402C22semidirect
173. #16837402C22semidirect
174. #16837402C22semidirect
175. #16837402C22semidirect
176. #16837400C22semidirect
177. #16837400C22semidirect
178. #16837400C22semidirect
179. #16837399C22semidirect
180. #16837398C22semidirect
181. #16837396C22semidirect
182. C2×#14273651C22semidirect
183. C2×#14273649C22semidirect
184. C2×#14273647C22semidirect
185. #16837364C22semidirect
186. #16837364C22semidirect
187. C4×#11745659C22semidirect
188. C59×#552C22semidirect
190. C59×#488C22semidirect
191. C59×#485C22semidirect
192. C59×#480C22semidirect
193. C59×#479C22semidirect
194. C59×#467C22semidirect
195. C59×#465C22semidirect
196. C59×#464C22semidirect
197. C59×#452C22semidirect
198. C59×#451C22semidirect
199. C4×Q16×C59C22semidirect
200. C8×D4×C59C22semidirect
201. C59×#416C22semidirect
202. C2×#103×C59C22semidirect
916. #3300D59semidirect
961. #552C2×D59semidirect
1000. #488C2×D59semidirect
1004. #485C2×D59semidirect
1016. #480C2×D59semidirect
1020. #479C2×D59semidirect
1036. #467C2×D59semidirect
1040. #465C2×D59semidirect
1044. #464C2×D59semidirect
1056. #452C2×D59semidirect
1060. #451C2×D59semidirect
1070. C4×Q16C2×D59semidirect
1080. C8×D4C2×D59semidirect
1106. #416C2×D59semidirect
1108. C2×#103C2×D59semidirect
1114. C59#61163semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#552×D592
#214375852
#214363692
#214363612
#214363192
#214363112
#214362262
#214362182
#214361982
#214361902
#214361512
#214361432
#214361232
#214361152
#214359832
#214359332
#214359252
#214344932
#214340282
#214340152
#214339152
#214337232
#214337192
#214335662
#214333552
#214333532
C4×#142737592
D4×#117456592
#214326112
C2×#168374022
C59×#33002
#6116359