Finite Group Databasebeta

← #29453832

Subgroups — #29453832

Order 15104.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437390C211yesmaximal, characteristic
2#21433258C211yesmaximal, characteristic, complemented
3#21433256C211yesmaximal, characteristic, complemented
4#21433252C211yesmaximal, characteristic, complemented
5#21433233C212yesmaximal, complemented
6#21433230C212yesmaximal, complemented
7#21433219C212yesmaximal, complemented
8#21433216C212yesmaximal, complemented
9#21433212C211yesmaximal, characteristic, complemented
10#21433211C211yesmaximal, characteristic, complemented
11#21433206C211yesmaximal, characteristic, complemented
12#21433203C211yesmaximal, characteristic, complemented
13#21433044C211yesmaximal, characteristic, complemented
14#21433038C211yesmaximal, characteristic, complemented
15#21432841C211yesmaximal, characteristic, complemented
16#21432835C211yesmaximal, characteristic, complemented
17#21432787C212yesmaximal, complemented
18#21432785C212yesmaximal, complemented
19#21432759C212yesmaximal, complemented
20#21432724C211yesmaximal, characteristic, complemented
21#21432663C212yesmaximal, complemented
22C2×C4⋊C8×D59C211yesmaximal, characteristic, complemented
23C59×#2994C211yesmaximal, characteristic, complemented
24C2×#14273735C2212yes—
25C2×#14273733C2212yes—
26C22×C8×D59C2212yes—
27#16837958C411yescharacteristic
28#16837956C2211yescharacteristic
29#16837954C411yescharacteristic
30#16837951C411yescharacteristic
31#16837949C2211yescharacteristic
32#16837947C411yescharacteristic
33#16837937C411yescharacteristic
34#16837936C2211yescharacteristic
35#16837935C412yes—
36#16837935C412yes—
37#16837931C411yescharacteristic
38#16837930C2212yes—
39#16837929C412yes—
40#16837915C411yescharacteristic
41#16837912C411yescharacteristic
42#16837911C2212yes—
43#16837910C412yes—
44C4×#11745689C2211yescharacteristic
45#16837870C2212yes—
46C4×#11745687C2211yescharacteristic
47C4×#11745687C2212yes—
48C2×C42×D59C2211yescharacteristic
49#16837533C2211yescharacteristic, complemented
50#16837532C2211yescharacteristic, complemented
51#16837532C2212yescomplemented
52#16837531C2212yescomplemented
53#16837530C2212yescomplemented
54#16837529C2211yescharacteristic, complemented
55#16837529C2212yescomplemented
56Q8×C59⋊C8C2211yescharacteristic, complemented
57C8×Dic118C2211yescharacteristic, complemented
58#16837526C2211yescharacteristic, complemented
59#16837481C2211yescharacteristic, complemented
60#16837480C2211yescharacteristic, complemented
61#16837479C2211yescharacteristic, complemented
62#16837476C2212yes—
63#16837476C2212yescomplemented
64#16837475C2212yes—
65#16837474C2212yes—
66#16837473C2212yes—
67#16837473C2212yescomplemented
68#16837472C2212yes—
69#16837471C2212yes—
70#16837471C2212yescomplemented
71#16837470C2212yes—
72#16837470C2212yescomplemented
73C8×D236C2212yes—
74C8×D236C2211yescharacteristic, complemented
75D4×C59⋊C8C2212yes—
76D4×C59⋊C8C2211yescharacteristic, complemented
77#16837467C2212yes—
78#16837467C2211yescharacteristic, complemented
79C8×C22⋊D59C2212yes—
80C8×C22⋊D59C2212yes—
81(C22⋊D59)⋊C8C2212yes—
82(C22⋊D59)⋊C8C2212yes—
83#16837463C2212yescomplemented
84#16837462C2212yescomplemented
85#16837462C2212yescomplemented
86#16837458C2211yescharacteristic
87#16837458C2211yescharacteristic
88#16837457C2212yescomplemented
89#16837456C2211yescharacteristic
90#16837456C2211yescharacteristic
91#16837456C2212yescomplemented
92#16837455C2211yescharacteristic
93#16837453C2211yescharacteristic
94#16837453C2211yescharacteristic
95#16837453C2212yescomplemented
96#16837452C2212yescomplemented
97#16837429C2212yescomplemented
98#16837427C2212yes—
99#16837427C2212yes—
100#16837427C2212yescomplemented
101#16837427C2212yescomplemented
102#16837425C2212yescomplemented
103#16837424C2211yescharacteristic
104#16837424C2211yescharacteristic
105#16837424C2212yescomplemented
106C2×C4⋊(C59⋊C8)C2211yescharacteristic
107C2×Dic59⋊C8C2212yes—
108C2×Dic59⋊C8C2212yescomplemented
109C4⋊C8×D59C2211yescharacteristic
110C4⋊C8×D59C2211yescharacteristic
111C4⋊C8×D59C2212yes—
112C4⋊C8×D59C2211yescharacteristic
113C4⋊C8×D59C2211yescharacteristic
114C4⋊C8×D59C2212yes—
115C4⋊C8×D59C2212yescomplemented
116#16837367C2212yes—
117#16837367C2212yes—
118#16837364C2211yescharacteristic
119#16837364C2211yescharacteristic
120#16837359C2212yes—
121#16837356C2212yes—
122C4×#11745659C2211yescharacteristic
123C4×#11745659C2211yescharacteristic
124C59×#529C2211yescharacteristic
125C59×#446C2211yescharacteristic, complemented
126C8×Q8×C59C2211yescharacteristic, complemented
127C59×#436C2211yescharacteristic, complemented
128C59×#435C2212yes—
129C8×D4×C59C2212yes—
130C8×D4×C59C2211yescharacteristic, complemented
131C59×#433C2212yescomplemented
132C59×#431C2211yescharacteristic
133C59×#424C2212yescomplemented
134C2×C4⋊C8×C59C2211yescharacteristic
135C2×#11745689C2×C411yescharacteristic
136C2×#11745685C2312yes—
137C2×#11745687C2×C411yescharacteristic
138C2×#11745687C2×C412yes—
139C22×C4×D59C2×C411yescharacteristic
140C22×C4×D59C2×C411yescharacteristic
141C22×C4×D59C2311yescharacteristic
142#14273735—44no—
143#14273733—44no—
144C2×#11745664C2312yes—
145C2×#11745659C2311yescharacteristic
146C2×#11745659C2311yescharacteristic
147C2×#11745659C2311yescharacteristic
148C2×#11745659C2311yescharacteristic
149C2×#11745659C2312yes—
150C2×#11745659C2312yes—
151C22×C59⋊C8C2312yes—
152C22×C59⋊C8C2312yes—
153C2×C8×D59—44no—
154C2×C8×D59C2312yes—
155C2×C8×D59C2312yes—
156C2×C8×D59C2312yes—
157C2×C8×D59C2312yes—
158C2×C8×D59C2312yes—
159C2×C8×D59C2312yes—
160#14273726C2×C411yescharacteristic
161#14273726C2×C411yescharacteristic
162#14273725C2×C411yescharacteristic
163#14273723C2×C411yescharacteristic
164#14273722C2×C412yes—
165#14273721C2×C412yes—
166#14273720C2×C412yes—
167#14273719C2×C411yescharacteristic
168#14273717C2×C412yes—
169#14273717C2×C412yes—
170#14273715C2×C411yescharacteristic
171#14273713C2×C412yes—
172#14273713C2×C412yes—
173#14273712C2×C412yes—
174#14273712C2×C412yes—
175#14273710C2×C412yes—
176#14273709C2×C412yes—
177#14273709C2×C412yes—
178#14273707C2×C411yescharacteristic
179#14273706C2×C411yescharacteristic
180#14273705C2×C412yes—
181#14273705C2×C412yes—
182#14273705C2×C412yes—
183#14273704C2×C412yes—
184#14273703C2×C411yescharacteristic
185#14273702C2×C411yescharacteristic
186#14273701C2×C411yescharacteristic
187#14273700C2×C412yes—
188#14273700C2×C412yes—
189#14273700C2×C412yes—
190#14273699C2×C412yes—
191#14273698C2×C411yescharacteristic
192#14273697C2×C412yes—
193#14273695C2×C412yes—
194Q8×Dic59C2×C411yescharacteristic
195C4×Dic118C2312yes—
196C4×Dic118C2311yescharacteristic
197#14273692C2×C412yes—
198#14273692C2×C412yes—
199#14273692C2×C412yes—
200#14273692C2×C411yescharacteristic
201C4×D236C2312yes—
202C4×D236C2311yescharacteristic
203D4×Dic59C2×C412yes—
204D4×Dic59C2×C411yescharacteristic
205#14273689C2×C412yes—
206#14273689C2×C412yes—
207#14273689C2×C412yes—
208#14273689C2×C411yescharacteristic
209C4×C22⋊D59C2312yes—
210C4×C22⋊D59C2312yes—
211C4×C22⋊D59C2312yes—
212(C22⋊D59)⋊C4C2×C412yes—
213(C22⋊D59)⋊C4C2×C412yes—
214(C22⋊D59)⋊C4C2×C412yes—
215(C22⋊D59)⋊C4C2×C412yes—
216(C22⋊D59)⋊C4C2×C412yes—
217(C22⋊D59)⋊C4C2×C412yes—
218(C22⋊D59)⋊C4C2×C412yes—
219#14273685C2×C411yescharacteristic
220#14273685C2×C411yescharacteristic
221#14273685C2×C412yes—
222#14273685C2×C412yes—
223#14273684C2312yes—
224#14273684C2312yes—
225#14273683C2×C412yes—
226#14273683C2×C412yes—
227#14273683C2×C412yes—
228C2×C4×Dic59C2×C411yescharacteristic
229C2×C4×Dic59C2×C411yescharacteristic
230C2×C4×Dic59C2311yescharacteristic
231C2×C4×Dic59C2312yes—
232C42×D59C2×C411yescharacteristic
233C42×D59C2×C411yescharacteristic
234C42×D59C2×C411yescharacteristic
235C42×D59C2×C411yescharacteristic
236C42×D59C2311yescharacteristic
237C42×D59C2311yescharacteristic
238C42×D59C2311yescharacteristic
239C42×D59C2311yescharacteristic
240C42×D59C2312yes—
241C4⋊(C59⋊C8)C2312yes—
242C4⋊(C59⋊C8)C2311yescharacteristic
243C4⋊(C59⋊C8)C2311yescharacteristic
244C4⋊(C59⋊C8)C2312yes—
245C4⋊(C59⋊C8)C2311yescharacteristic
246C4⋊(C59⋊C8)C2311yescharacteristic
247C4⋊(C59⋊C8)C2312yes—
248Dic59⋊C8C2312yes—
249Dic59⋊C8C2312yes—
250Dic59⋊C8C2312yes—
251Dic59⋊C8C2312yes—
252Dic59⋊C8C2311yescharacteristic
253Dic59⋊C8C2311yescharacteristic
254Dic59⋊C8C2312yes—
255Dic59⋊C8C2312yes—
256Dic59⋊C8C2311yescharacteristic
257Dic59⋊C8C2311yescharacteristic
258Dic59⋊C8C2312yes—
259Dic59⋊C8C2312yes—
260C22⋊(C59⋊C8)C2312yes—
261C22⋊(C59⋊C8)C2311yescharacteristic
262C22⋊(C59⋊C8)C2311yescharacteristic
263C22⋊(C59⋊C8)C2312yes—
264(C2×D59)⋊C8C2311yescharacteristic
265(C2×D59)⋊C8C2311yescharacteristic
266(C2×D59)⋊C8C2311yescharacteristic
267(C2×D59)⋊C8C2311yescharacteristic
268(C2×D59)⋊C8C2312yes—
269(C2×D59)⋊C8C2312yes—
270(C2×D59)⋊C8C2312yes—
271(C2×D59)⋊C8C2312yes—
272#14273638C2312yes—
273#14273637C2311yescharacteristic
274#14273637C2311yescharacteristic
275#14273637C2311yescharacteristic
276#14273637C2311yescharacteristic
277#14273637C2312yes—
278#14273637C2312yes—
279C4×C59⋊C8C2311yescharacteristic
280C4×C59⋊C8C2311yescharacteristic
281C4×C59⋊C8C2312yes—
282C8×Dic59C2312yes—
283C8×Dic59C2312yes—
284C2×M16×C59C2312yes—
285C22×C8×C59C2312yes—
286C22×C8×C59C2312yes—
287#126×C59C2×C412yes—
288#125×C59C2×C411yescharacteristic
289#124×C59C2×C411yescharacteristic
290#123×C59C2×C412yes—
291C22⋊Q8×C59C2×C411yescharacteristic
292#121×C59C2×C411yescharacteristic
293C4×Q8×C59C2311yescharacteristic
294C4×D4×C59C2312yes—
295C4×D4×C59C2311yescharacteristic
296#117×C59C2312yes—
297C2×C42×C59C2311yescharacteristic
298C4⋊C8×C59C2312yes—
299C4⋊C8×C59C2311yescharacteristic
300C4⋊C8×C59C2311yescharacteristic
301C4⋊C8×C59C2312yes—
302C4⋊C8×C59C2311yescharacteristic
303C4⋊C8×C59C2311yescharacteristic
304C4⋊C8×C59C2312yes—
305C22⋊C8×C59C2312yes—
306C22⋊C8×C59C2311yescharacteristic
307C22⋊C8×C59C2311yescharacteristic
308C22⋊C8×C59C2312yes—
309#97×C59C2312yes—
310C4×C8×C59C2311yescharacteristic
311C4×C8×C59C2311yescharacteristic
312C4×C8×C59C2312yes—
313C23×D59C22×C411yescharacteristic
314C2×Q8×C59C22×C411yescharacteristic
315C2×D4×C59C22×C412yes—
316C2×D4×C59C22×C411yescharacteristic
317C22×C4×C59C22×C411yescharacteristic
318C22×C4×C59C22×C411yescharacteristic
319C22×C4×C59C2411yescharacteristic
320C22×C4×C59C2412yes—
321C2×C22⋊D59C22×C412yes—
322C2×C22⋊D59C22×C412yes—
323C2×C22⋊D59C22×C412yes—
324C2×C22⋊D59C22×C412yes—
325C2×C22⋊D59C22×C412yes—
326C22×Dic59C22×C411yescharacteristic
327C22×Dic59C22×C411yescharacteristic
328C22×Dic59C22×C411yescharacteristic
329C22×Dic59C22×C412yes—
330C22×Dic59C22×C412yes—
331#11745689—24no—
332#11745687—24no—
333#11745687—44no—
334#11745685—24no—
335#11745685—24no—
336C2×D236C22×C412yes—
337C2×D236C22×C412yes—
338C2×D236C22×C411yescharacteristic
339C2×C4×D59—24no—
340C2×C4×D59—22no—
341C2×C4×D59—22no—
342C2×C4×D59—42no—
343C2×C4×D59C22×C411yescharacteristic
344C2×C4×D59C22×C411yescharacteristic
345C2×C4×D59C22×C411yescharacteristic
346C2×C4×D59C22×C411yescharacteristic
347C2×C4×D59C22×C411yescharacteristic
348C2×C4×D59C22×C412yes—
349C2×C4×D59C22×C411yescharacteristic
350C2×C4×D59C22×C411yescharacteristic
351C2×C4×D59C22×C411yescharacteristic
352C2×C4×D59C22×C411yescharacteristic
353C2×C4×D59C22×C412yes—
354C2×C4×D59C22×C411yescharacteristic
355C2×C4×D59C2411yescharacteristic
356C2×C4×D59C2412yes—
357C2×C4×D59C2411yescharacteristic
358C2×Dic118C22×C412yes—
359C2×Dic118C22×C411yescharacteristic
360C2×Dic118C22×C412yes—
361M16×C59—42no—
362C2×C8×C59—42no—
363C2×C8×C59—42no—
364C2×C8×C59C2411yescharacteristic
365C2×C8×C59C2411yescharacteristic
366C2×C8×C59C2412yes—
367C2×C8×C59C2411yescharacteristic
368C2×C8×C59C2411yescharacteristic
369C2×C8×C59C2412yes—
370C4⋊C4×C59C22×C412yes—
371C4⋊C4×C59C22×C412yes—
372C4⋊C4×C59C22×C411yescharacteristic
373C4⋊C4×C59C22×C412yes—
374C4⋊C4×C59C22×C411yescharacteristic
375C4⋊C4×C59C22×C412yes—
376C22⋊C4×C59C22×C412yes—
377C22⋊C4×C59C22×C412yes—
378C22⋊C4×C59C22×C412yes—
379C22⋊C4×C59C22×C412yes—
380C22⋊C4×C59C22×C412yes—
381C42×C59C22×C411yescharacteristic
382C42×C59C22×C411yescharacteristic
383C42×C59C2411yescharacteristic
384C42×C59C2412yes—
385C42×C59C2411yescharacteristic
386C22⋊Dic59C22×C412yes—
387C22⋊Dic59C22×C412yes—
388C22⋊Dic59C22×C412yes—
389(C2×D59)⋊C4C22×C412yes—
390(C2×D59)⋊C4C22×C412yes—
391(C2×D59)⋊C4C22×C412yes—
392(C2×D59)⋊C4C22×C412yes—
393(C2×D59)⋊C4C22×C412yes—
394(C2×D59)⋊C4C22×C412yes—
395(C2×D59)⋊C4C22×C412yes—
396(C2×D59)⋊C4C22×C412yes—
397(C2×D59)⋊C4C22×C412yes—
398(C2×D59)⋊C4C22×C412yes—
399C4⋊Dic59C22×C411yescharacteristic
400C4⋊Dic59C22×C412yes—
401C4⋊Dic59C22×C411yescharacteristic
402C4⋊Dic59C22×C412yes—
403Dic59⋊C4C22×C412yes—
404Dic59⋊C4C22×C412yes—
405Dic59⋊C4C22×C412yes—
406Dic59⋊C4C22×C412yes—
407Dic59⋊C4C22×C412yes—
408Dic59⋊C4C22×C412yes—
409Dic59⋊C4C22×C412yes—
410Dic59⋊C4C22×C412yes—
411Dic59⋊C4C22×C412yes—
412Dic59⋊C4C22×C412yes—
413C4×Dic59C22×C411yescharacteristic
414C4×Dic59C22×C411yescharacteristic
415C4×Dic59C22×C411yescharacteristic
416C4×Dic59C22×C411yescharacteristic
417C4×Dic59C22×C411yescharacteristic
418C4×Dic59C22×C411yescharacteristic
419C4×Dic59C22×C411yescharacteristic
420C4×Dic59C22×C411yescharacteristic
421C4×Dic59C22×C411yescharacteristic
422C4×Dic59C22×C411yescharacteristic
423C4×Dic59C22×C412yes—
424C4×Dic59C22×C412yes—
425C4×Dic59C22×C412yes—
426C4×Dic59C22×C412yes—
427C4×Dic59C2412yes—
428C4×Dic59C2411yescharacteristic
429C4×Dic59C2411yescharacteristic
430#11745664—42no—
431C2×C59⋊C8—42no—
432C2×C59⋊C8—42no—
433C2×C59⋊C8C2411yescharacteristic
434C2×C59⋊C8C2412yes—
435C2×C59⋊C8C2411yescharacteristic
436C2×C59⋊C8C2411yescharacteristic
437C2×C59⋊C8C2411yescharacteristic
438C2×C59⋊C8C2412yes—
439#11745659—22no—
440#11745659—22no—
441#11745659—22no—
442#11745659—22no—
443#11745659—42no—
444#11745659—42no—
445C8×D59—24no—
446C8×D59—24no—
447C8×D59—42no—
448C8×D59—42no—
449C8×D59—42no—
450C8×D59—42no—
451C23×C59C23×C412yes—
452C23×C59C23×C411yescharacteristic
453C22×D59—22no—
454C22×D59—22no—
455C22×D59—22no—
456C22×D59C23×C412yes—
457C22×D59C23×C411yescharacteristic
458C22×D59C23×C411yescharacteristic
459Q8×C59—22no—
460D4×C59—24no—
461D4×C59—22no—
462C2×C4×C59—22no—
463C2×C4×C59—22no—
464C2×C4×C59—21no—
465C2×C4×C59—22no—
466C2×C4×C59—21no—
467C2×C4×C59—22no—
468C2×C4×C59C23×C411yescharacteristic
469C2×C4×C59C23×C411yescharacteristic
470C2×C4×C59C23×C411yescharacteristic
471C2×C4×C59C23×C411yescharacteristic
472C2×C4×C59C23×C412yes—
473C2×C4×C59C23×C412yes—
474C2×C4×C59C23×C412yes—
475C2×C4×C59C23×C411yescharacteristic
476C2×C4×C59C2511yescharacteristic
477C22⋊D59—24no—
478C22⋊D59—24no—
479C22⋊D59—24no—
480C22⋊D59—24no—
481C22⋊D59—42no—
482C2×Dic59—22no—
483C2×Dic59—22no—
484C2×Dic59—22no—
485C2×Dic59—24no—
486C2×Dic59—42no—
487C2×Dic59C23×C411yescharacteristic
488C2×Dic59C23×C411yescharacteristic
489C2×Dic59C23×C411yescharacteristic
490C2×Dic59C23×C411yescharacteristic
491C2×Dic59C23×C412yes—
492C2×Dic59C23×C412yes—
493C2×Dic59C23×C412yes—
494C2×Dic59C23×C411yescharacteristic
495C2×Dic59C23×C411yescharacteristic
496D236—24no—
497D236—24no—
498D236—22no—
499C4×D59—22no—
500C4×D59—22no—
501C4×D59—22no—
502C4×D59—21no—
503C4×D59—22no—
504C4×D59—21no—
505C4×D59—22no—
506C4×D59—22no—
507C4×D59—22no—
508C4×D59—24no—
509C4×D59—41no—
510C4×D59—41no—
511C4×D59—41no—
512C4×D59—41no—
513C4×D59—42no—
514C4×D59#13114yescomplemented
515C4×D59H(5,𝔽2)12yes—
516C4×D592−1+412yes—
517Dic118—22no—
518Dic118—24no—
519Dic118—42no—
520C8×C59—22no—
521C8×C59—22no—
522C8×C59—21no—
523C8×C59—21no—
524C8×C59—21no—
525C8×C59—21no—
526C59⋊C8—22no—
527C59⋊C8—22no—
528C59⋊C8—21no—
529C59⋊C8—21no—
530C59⋊C8—21no—
531C59⋊C8—21no—
532#60265—591nomaximal, Sylow
533C22×C59—21no—
534C22×C59—21no—
535C22×C59—22no—
536C22×C59—22no—
537C22×C59—22no—
538C22×C59#56812yes—
539C22×C59C24×C411yescharacteristic
540C2×D59—28no—
541C2×D59—21no—
542C2×D59—21no—
543C2×D59—21no—
544C2×D59—21no—
545C2×D59—22no—
546C2×D59—22no—
547C2×D59—22no—
548C2×D59#52012yes—
549C2×D59C2×#13112yes—
550C4×C59—22no—
551C4×C59—21no—
552C4×C59—21no—
553C4×C59—22no—
554C4×C59—22no—
555C4×C59—21no—
556C4×C59—21no—
557C4×C59C2×#13112yes—
558C4×C59C2×H(5,𝔽2)11yescharacteristic
559C4×C59C2×2−1+411yescharacteristic
560Dic59—22no—
561Dic59—21no—
562Dic59—22no—
563Dic59—21no—
564Dic59—21no—
565Dic59—22no—
566Dic59—21no—
567Dic59#52012yes—
568Dic59C2×#13112yes—
569#3444—591no—
570#2994—591no—
571#2994—591no—
572#2994—591no—
573#2994D5911yescharacteristic, complemented
574#2992—592no—
575#2992—592no—
576#2990—592no—
577#2990—592no—
578#2989—591no—
579#2989—591no—
580#2988—591no—
581#2988—591no—
582#2962—591no—
583#2962—591no—
584#2935—591no—
585#2935—591no—
586#2929—592no—
587#2929—592no—
588#2925—592no—
589#2920—591no—
590#2906—592no—
591C22×C4⋊C8—591no—
592C2×C59—22no—
593C2×C59—42no—
594C2×C59C2×#52011yescharacteristic
595C2×C59C22×#13111yescharacteristic
596C2×C59C2×#56811yescharacteristic
597D59—22no—
598D59—22no—
599D59—42no—
600C2×#131—592no—
601C2×#131—592no—
602C23×C8—592no—
603#533—591no—
604#533—591no—
605#533—591no—
606#532—591no—
607#532—591no—
608#532—591no—
609#529—592no—
610#529—592no—
611#529—591no—
612#529—591no—
613#529—592no—
614#529—592no—
615#529—591no—
616#529C2×D5911yescharacteristic
617#525—592no—
618#525—591no—
619#525—591no—
620#525—592no—
621C4×#41—591no—
622C4×#41—591no—
623C4×#41—592no—
624C4×#41—592no—
625C22×C42—591no—
626#446—591no—
627#446—591no—
628#446—592no—
629#446—592no—
630#446—592no—
631#446—591no—
632#446—592no—
633#446C2×D5911yescharacteristic, complemented
634C8×Q8—591no—
635C8×Q8—591no—
636C8×Q8—591no—
637C8×Q8C2×D5911yescharacteristic, complemented
638#436—591no—
639#436—591no—
640#436—591no—
641#436C2×D5911yescharacteristic, complemented
642#435—592no—
643#435—592no—
644#435—592no—
645#435—592no—
646#435—592no—
647#435—592no—
648#435—592no—
649#435—592no—
650#435—592no—
651#435—592no—
652#435—592no—
653#435C2×D5912yes—
654C8×D4—592no—
655C8×D4—592no—
656C8×D4—592no—
657C8×D4—591no—
658C8×D4—592no—
659C8×D4—591no—
660C8×D4—592no—
661C8×D4—592no—
662C8×D4—592no—
663C8×D4—591no—
664C8×D4C2×D5912yes—
665C8×D4C2×D5911yescharacteristic, complemented
666#433—592no—
667#433—592no—
668#433—592no—
669#433C2×D5912yescomplemented
670#432—591no—
671#432—591no—
672#432—591no—
673#432—591no—
674#432—592no—
675#432—592no—
676#431—591no—
677#431—592no—
678#431—591no—
679#431—591no—
680#431—592no—
681#431C2×D5911yescharacteristic
682#424—592no—
683#424—592no—
684#424—592no—
685#424—592no—
686#424—592no—
687#424C2×D5912yescomplemented
688#423—592no—
689#423—591no—
690#423—591no—
691#423—592no—
692C2×C4⋊C8—592no—
693C2×C4⋊C8—592no—
694C2×C4⋊C8—591no—
695C2×C4⋊C8—592no—
696C2×C4⋊C8—591no—
697C2×C4⋊C8—591no—
698C2×C4⋊C8—591no—
699C2×C4⋊C8—591no—
700C2×C4⋊C8—592no—
701C2×C4⋊C8—592no—
702C2×C4⋊C8C2×D5911yescharacteristic
703#408—592no—
704#408—592no—
705#407—591no—
706#407—591no—
707#405—592no—
708#405—592no—
709C4×M16—591no—
710C4×M16—591no—
711C59#6026511yescharacteristic, complemented, Sylow
712C2×#41—591no—
713C2×#41—591no—
714C2×#41—592no—
715C2×#41—592no—
716C23×C4—591no—
717C23×C4—591no—
718C23×C4—591no—
719#131—2364no—
720#131—2364no—
721C2×M16—592no—
722C2×M16—591no—
723C2×M16—591no—
724C2×M16—591no—
725C2×M16—591no—
726C2×M16—592no—
727C2×M16—592no—
728C2×M16C22×D5912yes—
729C22×C8—592no—
730C22×C8—592no—
731C22×C8—592no—
732C22×C8—592no—
733C22×C8—592no—
734C22×C8—592no—
735C22×C8—592no—
736C22×C8—592no—
737C22×C8—2364no—
738C22×C8C22×D5912yes—
739C22×C8C22×D5912yes—
740C4⋊Q8—591no—
741C4⋊Q8—591no—
742C4⋊Q8—591no—
743#127—591no—
744#126—592no—
745#126—592no—
746#126—592no—
747#126C4×D5912yes—
748#125—592no—
749#125—592no—
750#125—591no—
751#125C4×D5911yescharacteristic
752#124—592no—
753#124—592no—
754#124—591no—
755#124C4×D5911yescharacteristic
756#123—592no—
757#123—592no—
758#123—592no—
759#123—592no—
760#123—592no—
761#123C4×D5912yes—
762C22⋊Q8—591no—
763C22⋊Q8—591no—
764C22⋊Q8—592no—
765C22⋊Q8—592no—
766C22⋊Q8—592no—
767C22⋊Q8—591no—
768C22⋊Q8—592no—
769C22⋊Q8C4×D5911yescharacteristic
770#121—591no—
771#121—592no—
772#121—591no—
773#121—591no—
774#121—592no—
775#121—592no—
776#121—592no—
777#121C4×D5911yescharacteristic
778#120—592no—
779#120—592no—
780C4×Q8—591no—
781C4×Q8—592no—
782C4×Q8—592no—
783C4×Q8—592no—
784C4×Q8—591no—
785C4×Q8—591no—
786C4×Q8—592no—
787C4×Q8C22×D5911yescharacteristic
788C4×D4—592no—
789C4×D4—591no—
790C4×D4—592no—
791C4×D4—592no—
792C4×D4—592no—
793C4×D4—592no—
794C4×D4—592no—
795C4×D4—592no—
796C4×D4—591no—
797C4×D4—592no—
798C4×D4—592no—
799C4×D4—592no—
800C4×D4—592no—
801C4×D4—592no—
802C4×D4—592no—
803C4×D4—592no—
804C4×D4—592no—
805C4×D4—591no—
806C4×D4C22×D5912yes—
807C4×D4C22×D5911yescharacteristic
808#117—591no—
809#117—591no—
810#117—592no—
811#117—592no—
812#117—592no—
813#117—592no—
814#117—592no—
815#117—592no—
816#117—592no—
817#117C22×D5912yes—
818C2×C42—591no—
819C2×C42—591no—
820C2×C42—592no—
821C2×C42—591no—
822C2×C42—591no—
823C2×C42—591no—
824C2×C42—591no—
825C2×C42—591no—
826C2×C42—592no—
827C2×C42—591no—
828C2×C42—591no—
829C2×C42—591no—
830C2×C42—591no—
831C2×C42C22×D5911yescharacteristic
832C4⋊C8—592no—
833C4⋊C8—592no—
834C4⋊C8—592no—
835C4⋊C8—592no—
836C4⋊C8—591no—
837C4⋊C8—591no—
838C4⋊C8—592no—
839C4⋊C8—592no—
840C4⋊C8—592no—
841C4⋊C8—592no—
842C4⋊C8—591no—
843C4⋊C8—591no—
844C4⋊C8—592no—
845C4⋊C8—591no—
846C4⋊C8—591no—
847C4⋊C8—592no—
848C4⋊C8—591no—
849C4⋊C8—592no—
850C4⋊C8—591no—
851C4⋊C8C22×D5912yes—
852C4⋊C8C22×D5911yescharacteristic
853C4⋊C8C22×D5911yescharacteristic
854C4⋊C8C22×D5912yes—
855C4⋊C8C22×D5911yescharacteristic
856C4⋊C8C22×D5912yes—
857C4⋊C8C22×D5911yescharacteristic
858C22⋊C8—591no—
859C22⋊C8—591no—
860C22⋊C8—592no—
861C22⋊C8—592no—
862C22⋊C8—591no—
863C22⋊C8—591no—
864C22⋊C8—591no—
865C22⋊C8—591no—
866C22⋊C8—592no—
867C22⋊C8—592no—
868C22⋊C8—592no—
869C22⋊C8—592no—
870C22⋊C8C22×D5911yescharacteristic
871C22⋊C8C22×D5911yescharacteristic
872C22⋊C8C22×D5912yes—
873C22⋊C8C22×D5912yes—
874#97—591no—
875#97—591no—
876#97—591no—
877#97—591no—
878#97—592no—
879#97—592no—
880#97—592no—
881#97C22×D5912yes—
882C4×C8—592no—
883C4×C8—592no—
884C4×C8—591no—
885C4×C8—591no—
886C4×C8—592no—
887C4×C8C22×D5911yescharacteristic
888C4×C8C22×D5911yescharacteristic
889C4×C8C22×D5912yes—
890C24—591no—
891#41—1184no—
892#41—1184no—
893#41—1184no—
894#41—1184no—
895#41—2364no—
896C2×Q8—592no—
897C2×Q8—591no—
898C2×Q8—592no—
899C2×Q8C2×C4×D5911yescharacteristic
900C2×D4—592no—
901C2×D4—592no—
902C2×D4—592no—
903C2×D4—592no—
904C2×D4—592no—
905C2×D4—592no—
906C2×D4—592no—
907C2×D4—591no—
908C2×D4C2×C4×D5912yes—
909C2×D4C2×C4×D5911yescharacteristic
910C22×C4—591no—
911C22×C4—591no—
912C22×C4—591no—
913C22×C4—591no—
914C22×C4—591no—
915C22×C4—592no—
916C22×C4—592no—
917C22×C4—591no—
918C22×C4—591no—
919C22×C4—591no—
920C22×C4—591no—
921C22×C4—591no—
922C22×C4—592no—
923C22×C4—591no—
924C22×C4—592no—
925C22×C4—591no—
926C22×C4—591no—
927C22×C4—591no—
928C22×C4—591no—
929C22×C4—592no—
930C22×C4—1182no—
931C22×C4—1184no—
932C22×C4—1182no—
933C22×C4—2362no—
934C22×C4C2×C4×D5911yescharacteristic
935C22×C4C2×C4×D5911yescharacteristic
936C22×C4C23×D5911yescharacteristic
937C22×C4C23×D5912yes—
938M16—42no—
939M16—1182no—
940M16—1182no—
941M16—1182no—
942M16—1182no—
943M16—2362no—
944M16—2362no—
945M16—2362no—
946C2×C8—42no—
947C2×C8—42no—
948C2×C8—591no—
949C2×C8—591no—
950C2×C8—592no—
951C2×C8—591no—
952C2×C8—591no—
953C2×C8—592no—
954C2×C8—1184no—
955C2×C8—1184no—
956C2×C8—2362no—
957C2×C8—2362no—
958C2×C8—2362no—
959C2×C8—2362no—
960C2×C8—2362no—
961C2×C8—2362no—
962C2×C8C23×D5911yescharacteristic
963C2×C8C23×D5912yes—
964C2×C8C23×D5911yescharacteristic
965C2×C8C23×D5911yescharacteristic
966C2×C8C23×D5911yescharacteristic
967C2×C8C23×D5912yes—
968C4⋊C4—592no—
969C4⋊C4—592no—
970C4⋊C4—592no—
971C4⋊C4—592no—
972C4⋊C4—591no—
973C4⋊C4—591no—
974C4⋊C4—592no—
975C4⋊C4—592no—
976C4⋊C4—592no—
977C4⋊C4—592no—
978C4⋊C4—592no—
979C4⋊C4—592no—
980C4⋊C4—592no—
981C4⋊C4—592no—
982C4⋊C4C2×C4×D5911yescharacteristic
983C4⋊C4C2×C4×D5912yes—
984C4⋊C4C2×C4×D5911yescharacteristic
985C4⋊C4C2×C4×D5912yes—
986C4⋊C4C2×C4×D5912yes—
987C4⋊C4C2×C4×D5912yes—
988C22⋊C4—592no—
989C22⋊C4—592no—
990C22⋊C4—592no—
991C22⋊C4—592no—
992C22⋊C4—592no—
993C22⋊C4—592no—
994C22⋊C4—592no—
995C22⋊C4—592no—
996C22⋊C4—592no—
997C22⋊C4—592no—
998C22⋊C4—592no—
999C22⋊C4—592no—
1000C22⋊C4—592no—
1001C22⋊C4C2×C4×D5912yes—
1002C22⋊C4C2×C4×D5912yes—
1003C22⋊C4C2×C4×D5912yes—
1004C22⋊C4C2×C4×D5912yes—
1005C22⋊C4C2×C4×D5912yes—
1006C42—591no—
1007C42—591no—
1008C42—591no—
1009C42—591no—
1010C42—591no—
1011C42—591no—
1012C42—591no—
1013C42—591no—
1014C42—591no—
1015C42—591no—
1016C42—592no—
1017C42—592no—
1018C42—592no—
1019C42—592no—
1020C42—592no—
1021C42—591no—
1022C42—591no—
1023C42C2×C4×D5911yescharacteristic
1024C42C2×C4×D5911yescharacteristic
1025C42C23×D5911yescharacteristic
1026C42C23×D5912yes—
1027C42C23×D5911yescharacteristic
1028C23—591no—
1029C23—591no—
1030C23—592no—
1031C23—1182no—
1032C23—1182no—
1033C23—1182no—
1034C23C22×C4×D5912yes—
1035C23C22×C4×D5911yescharacteristic
1036Q8—22no—
1037Q8—1184no—
1038Q8—1182no—
1039Q8—2362no—
1040D4—24no—
1041D4—22no—
1042D4—1184no—
1043D4—1184no—
1044D4—1184no—
1045D4—1184no—
1046D4—1184no—
1047D4—1184no—
1048D4—1182no—
1049D4—2362no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—591no—
1057C2×C4—591no—
1058C2×C4—594no—
1059C2×C4—592no—
1060C2×C4—592no—
1061C2×C4—591no—
1062C2×C4—591no—
1063C2×C4—591no—
1064C2×C4—591no—
1065C2×C4—592no—
1066C2×C4—592no—
1067C2×C4—592no—
1068C2×C4—1182no—
1069C2×C4—1182no—
1070C2×C4—1184no—
1071C2×C4—1182no—
1072C2×C4—1182no—
1073C2×C4—1182no—
1074C2×C4—1182no—
1075C2×C4—1184no—
1076C2×C4—1182no—
1077C2×C4—1182no—
1078C2×C4—1181no—
1079C2×C4—1182no—
1080C2×C4—1181no—
1081C2×C4—1182no—
1082C2×C4—2361no—
1083C2×C4—2361no—
1084C2×C4—2361no—
1085C2×C4—2361no—
1086C2×C4—2362no—
1087C2×C4—2362no—
1088C2×C4C22×C4×D5911yescharacteristic
1089C2×C4C22×C4×D5911yescharacteristic
1090C2×C4C22×C4×D5911yescharacteristic
1091C2×C4C22×C4×D5911yescharacteristic
1092C2×C4C22×C4×D5912yes—
1093C2×C4C22×C4×D5912yes—
1094C2×C4C22×C4×D5912yes—
1095C2×C4C22×C4×D5911yescharacteristic
1096C2×C4C24×D5911yescharacteristic
1097C8—22no—
1098C8—21no—
1099C8—22no—
1100C8—21no—
1101C8—21no—
1102C8—21no—
1103C8—1182no—
1104C8—1182no—
1105C8—1181no—
1106C8—1181no—
1107C8—1181no—
1108C8—1181no—
1109C22—21no—
1110C22—21no—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—592no—
1115C22—592no—
1116C22—1188no—
1117C22—1181no—
1118C22—1181no—
1119C22—1181no—
1120C22—1181no—
1121C22—1182no—
1122C22—1182no—
1123C22—1182no—
1124C22#1683816712yes—
1125C22C23×C4×D5911yescharacteristic
1126C4—21no—
1127C4—22no—
1128C4—21no—
1129C4—21no—
1130C4—22no—
1131C4—21no—
1132C4—22no—
1133C4—592no—
1134C4—592no—
1135C4—1181no—
1136C4—1182no—
1137C4—1181no—
1138C4—1181no—
1139C4—1182no—
1140C4—1181no—
1141C4—1182no—
1142C4#131×D5912yes—
1143C4H(5,𝔽2)×D5911yescharacteristic
1144C42−1+4×D5911yescharacteristic
1145C2—22no—
1146C2—42no—
1147C2—1182no—
1148C2—1182no—
1149C2—2362no—
1150C2#520×D5911yescharacteristic
1151C2C2×#131×D5911yescharacteristic
1152C2C2×#1683816711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
FittingC59×#2994C2
prime radical#21437390C2
cosocleC2×C4×C59C25
hypercenter#2994D59
hypocenterC59#60265
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #21433258C2semidirect
3. #21433256C2semidirect
4. #21433252C2semidirect
5. #21433233C2semidirect
6. #21433230C2semidirect
7. #21433219C2semidirect
8. #21433216C2semidirect
9. #21433212C2semidirect
10. #21433211C2semidirect
11. #21433206C2semidirect
12. #21433203C2semidirect
13. #21433044C2semidirect
14. #21433038C2semidirect
15. #21432841C2semidirect
16. #21432835C2semidirect
17. #21432787C2semidirect
18. #21432785C2semidirect
19. #21432759C2semidirect
20. #21432724C2semidirect
21. #21432663C2semidirect
22. C2×C4⋊C8×D59C2semidirect
23. C59×#2994C2semidirect
49. #16837533C22semidirect
50. #16837532C22semidirect
51. #16837532C22semidirect
52. #16837531C22semidirect
53. #16837530C22semidirect
54. #16837529C22semidirect
55. #16837529C22semidirect
56. Q8×C59⋊C8C22semidirect
57. C8×Dic118C22semidirect
58. #16837526C22semidirect
59. #16837481C22semidirect
60. #16837480C22semidirect
61. #16837479C22semidirect
63. #16837476C22semidirect
67. #16837473C22semidirect
70. #16837471C22semidirect
72. #16837470C22semidirect
74. C8×D236C22semidirect
76. D4×C59⋊C8C22semidirect
78. #16837467C22semidirect
83. #16837463C22semidirect
84. #16837462C22semidirect
85. #16837462C22semidirect
88. #16837457C22semidirect
91. #16837456C22semidirect
95. #16837453C22semidirect
96. #16837452C22semidirect
97. #16837429C22semidirect
100. #16837427C22semidirect
101. #16837427C22semidirect
102. #16837425C22semidirect
105. #16837424C22semidirect
108. C2×Dic59⋊C8C22semidirect
115. C4⋊C8×D59C22semidirect
125. C59×#446C22semidirect
126. C8×Q8×C59C22semidirect
127. C59×#436C22semidirect
130. C8×D4×C59C22semidirect
131. C59×#433C22semidirect
133. C59×#424C22semidirect
514. C4×D59#131semidirect
573. #2994D59semidirect
633. #446C2×D59semidirect
637. C8×Q8C2×D59semidirect
641. #436C2×D59semidirect
665. C8×D4C2×D59semidirect
669. #433C2×D59semidirect
687. #424C2×D59semidirect
711. C59#60265semidirect

Maximal subgroups

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

subgroupindex
#214373902
#214332582
#214332562
#214332522
#214332332
#214332302
#214332192
#214332162
#214332122
#214332112
#214332062
#214332032
#214330442
#214330382
#214328412
#214328352
#214327872
#214327852
#214327592
#214327242
#214326632
C2×C4⋊C8×D592
C59×#29942
#6026559