Finite Group Databasebeta

← #29473741

Subgroups — #29473741

Order 15104.

2118 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437935C211yesmaximal, characteristic, complemented
2#21436364C214yesmaximal, complemented
3#21436349C214yesmaximal, complemented
4#21435749C214yesmaximal, complemented
5#21435728C214yesmaximal, complemented
6#21435061C212yesmaximal, complemented
7#21434917C211yesmaximal, characteristic, complemented
8#21434910C212yesmaximal, complemented
9#21434898C211yesmaximal, characteristic, complemented
10#21434176C212yesmaximal, complemented
11#21433356C211yesmaximal, characteristic, complemented
12#21433348C211yesmaximal, characteristic, complemented
13#21433330C212yesmaximal, complemented
14#21433137C211yesmaximal, characteristic, complemented
15C2×C59×#548C211yesmaximal, characteristic, complemented
16C2×#14273758C2214yescomplemented
17C2×#14273757C2212yescomplemented
18C2×#14273752C2212yescomplemented
19#16838101—22no—
20#16838098C2212yescomplemented
21#16838092C2212yescomplemented
22#16838081—22no—
23#16838061C2212yescomplemented
24#16838048C2212yescomplemented
25#16837999—21no—
26#16837990—21no—
27#16837961—21no—
28#16837936C2212yes—
29#16837913C2212yes—
30C2×#14273706C2211yescharacteristic
31C2×#14273701C2211yescharacteristic
32#16837875—21no—
33#16837784C2214yescomplemented
34#16837756C2214yescomplemented
35#16837735C2212yescomplemented
36#16837732C2212yescomplemented
37#16837730C2212yescomplemented
38#16837723C2214yescomplemented
39#16837715C2212yes—
40#16837709C2214yescomplemented
41#16837658C2214yescomplemented
42#16837653C2214yescomplemented
43#16837650C2214yescomplemented
44#16837646C2214yescomplemented
45#16837624C2214yescomplemented
46#16837621C2214yescomplemented
47#16837614C2214yescomplemented
48#16837564C2214yescomplemented
49#16837558C2212yescomplemented
50#16837558C2212yescomplemented
51#16837558C2214yescomplemented
52#16837557C2212yescomplemented
53#16837553C2212yescomplemented
54#16837552C2212yescomplemented
55#16837547C2214yescomplemented
56#16837545C2214yescomplemented
57#16837541C2212yes—
58#16837541C2212yes—
59#16837541C2214yescomplemented
60#16837536C2212yes—
61C4×#11745672C2214yescomplemented
62C4×#11745671C2214yescomplemented
63#16837480C2214yescomplemented
64#16837480C2214yescomplemented
65#16837455C2212yescomplemented
66#16837411C2214yescomplemented
67#16837403C2212yescomplemented
68#16837403C2212yescomplemented
69#16837366C2211yescharacteristic
70#16837366C2211yescharacteristic
71#16837366C2212yescomplemented
72C22×#41×C59C2211yescharacteristic
73C23×Q8×C59C2211yescharacteristic, complemented
74C59×#548—22no—
75C59×#548—22no—
76C59×#548C2214yes—
77C59×#548C2214yescomplemented
78C2×#124×C59—21no—
79C2×#124×C59C2211yescharacteristic, complemented
80C2×C22⋊Q8×C59—21no—
81C2×C22⋊Q8×C59C2211yescharacteristic
82C2×#121×C59—21no—
83C2×#121×C59C2211yescharacteristic, complemented
84C2×C4×Q8×C59C2211yescharacteristic, complemented
85C2×C4×D4×C59—21no—
86C2×C4×D4×C59C2211yescharacteristic
87C2×#11745685C2312yes—
88C22×Dic118C2311yescharacteristic
89C22×D236C2311yescharacteristic
90C22×C22⋊D59—21no—
91#14273758—48no—
92#14273757—44no—
93#14273752—44no—
94C2×#11745672C2314yes—
95C2×#11745672C2314yes—
96C2×#11745670C2314yes—
97C2×#11745671C2314yes—
98C2×#11745671C2314yes—
99C2×#11745669C2314yes—
100C2×#11745664C2314yes—
101C2×#11745664C2312yes—
102C2×#11745664C2312yes—
103#14273722—22no—
104#14273721—22no—
105#14273720—22no—
106#14273719C2312yes—
107#14273717—22no—
108#14273715C2312yes—
109#14273713—22no—
110#14273712—22no—
111#14273710—22no—
112#14273710—22no—
113#14273709—22no—
114#14273708—22no—
115#14273706—21no—
116#14273706—21no—
117#14273706C2312yes—
118#14273706C2312yes—
119#14273706C2312yes—
120#14273705—22no—
121#14273701—21no—
122#14273701—21no—
123#14273701C2312yes—
124#14273701C2312yes—
125#14273701C2312yes—
126#14273700—22no—
127#14273699—22no—
128#14273699—22no—
129#14273696—22no—
130#14273695—22no—
131C4×Dic118C2312yes—
132C4×D236C2312yes—
133C4×C22⋊D59—22no—
134C4×C22⋊D59—22no—
135C4×C22⋊D59—22no—
136(C22⋊D59)⋊C4—22no—
137(C22⋊D59)⋊C4—22no—
138#14273686C2312yes—
139#14273684—22no—
140#14273683—22no—
141C2×C4⋊Dic59C2311yescharacteristic
142C2×C4⋊Dic59C2311yescharacteristic
143C2×Dic59⋊C4—21no—
144C2×C22⋊Dic59—21no—
145C2×(C2×D59)⋊C4—21no—
146C22⋊C4×D59—22no—
147#14273660C2314yes—
148#14273658C2314yes—
149C4⋊(C59⋊C8)C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273651C2314yes—
154#14273650C2314yes—
155#14273648C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158C22⋊(C59⋊C8)C2312yes—
159C22⋊(C59⋊C8)C2312yes—
160C22⋊(C59⋊C8)C2314yes—
161C22⋊(C59⋊C8)C2312yes—
162C22⋊(C59⋊C8)C2312yes—
163C4×C59⋊C8C2314yes—
164C2×#41×C59—21no—
165C2×#41×C59—21no—
166C2×#41×C59—44no—
167C2×#41×C59C2312yes—
168C2×#41×C59C2312yes—
169C22×Q8×C59—21no—
170C22×Q8×C59—22no—
171C22×Q8×C59—44no—
172C22×Q8×C59C2311yescharacteristic
173C22×Q8×C59C2314yes—
174C22×Q8×C59C2311yescharacteristic
175C22×D4×C59—21no—
176C22×D4×C59—21no—
177C22×D4×C59D411yescharacteristic
178C22×D4×C59C2311yescharacteristic
179C23×C4×C59—21no—
180C23×C4×C59—21no—
181C23×C4×C59C2311yescharacteristic
182C23×C4×C59C2311yescharacteristic
183#124×C59—24no—
184#124×C59—24no—
185#124×C59—22no—
186#124×C59C2314yes—
187C22⋊Q8×C59—21no—
188C22⋊Q8×C59—21no—
189C22⋊Q8×C59—24no—
190C22⋊Q8×C59—24no—
191C22⋊Q8×C59C2312yes—
192C22⋊Q8×C59C2312yes—
193#121×C59—24no—
194#121×C59—24no—
195#121×C59—22no—
196#121×C59C2314yes—
197C4×Q8×C59—22no—
198C4×Q8×C59C2314yes—
199C4×D4×C59—24no—
200C4×D4×C59—24no—
201C4×D4×C59D412yes—
202C4×D4×C59D412yes—
203C4×D4×C59C2312yes—
204C4×D4×C59C2312yes—
205C2×C4⋊C4×C59—21no—
206C2×C4⋊C4×C59—21no—
207C2×C4⋊C4×C59D411yescharacteristic
208C2×C4⋊C4×C59C2311yescharacteristic
209C2×C22⋊C4×C59—21no—
210C2×C22⋊C4×C59—21no—
211C2×C22⋊C4×C59—21no—
212C2×C22⋊C4×C59—21no—
213C2×C22⋊C4×C59D411yescharacteristic
214C2×C22⋊C4×C59D411yescharacteristic
215C2×C42×C59—21no—
216C2×C42×C59C2311yescharacteristic
217C24×C59—21no—
218C24×C59C2×D411yescharacteristic
219C24×C59C2×D411yescharacteristic
220C23×D59—21no—
221#41×C59—24no—
222#41×C59—24no—
223#41×C59—42no—
224#41×C59—42no—
225#41×C59—44no—
226#41×C59—44no—
227C2×Q8×C59—24no—
228C2×Q8×C59—21no—
229C2×Q8×C59—24no—
230C2×Q8×C59—21no—
231C2×Q8×C59—28no—
232C2×Q8×C59—44no—
233C2×Q8×C59—42no—
234C2×Q8×C59—44no—
235C2×Q8×C59—48no—
236C2×Q8×C59C2412yes—
237C2×Q8×C59C2412yes—
238C2×D4×C59—24no—
239C2×D4×C59—22no—
240C2×D4×C59—22no—
241C2×D4×C59—21no—
242C2×D4×C59—42no—
243C2×D4×C59—42no—
244C2×D4×C59—44no—
245C2×D4×C59—44no—
246C2×D4×C59C2×D412yes—
247C2×D4×C59C2×D412yes—
248C2×D4×C59C2412yes—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—24no—
253C22×C4×C59—22no—
254C22×C4×C59—22no—
255C22×C4×C59—42no—
256C22×C4×C59—42no—
257C22×C4×C59—44no—
258C22×C4×C59—44no—
259C22×C4×C59C2×D411yescharacteristic
260C22×C4×C59C2×D411yescharacteristic
261C22×C4×C59C2×D411yescharacteristic
262C22×C4×C59C2×D411yescharacteristic
263C22×C4×C59C2×D412yes—
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2×D411yescharacteristic
266C22×C4×C59C2411yescharacteristic
267C22×C4×C59C2412yes—
268C22×C4×C59C2411yescharacteristic
269C22×C4×C59C2411yescharacteristic
270C2×C22⋊D59—22no—
271C2×C22⋊D59—22no—
272C2×C22⋊D59—22no—
273C2×C22⋊D59—22no—
274C2×C22⋊D59—44no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278#11745685—44no—
279C2×D236—21no—
280C2×D236—42no—
281C2×D236C2412yes—
282C2×C4×D59—22no—
283C2×C4×D59—22no—
284C2×Dic118—21no—
285C2×Dic118—42no—
286C2×Dic118C2412yes—
287C4⋊C4×C59—22no—
288C4⋊C4×C59—22no—
289C4⋊C4×C59—24no—
290C4⋊C4×C59—21no—
291C4⋊C4×C59C2×D412yes—
292C4⋊C4×C59C2×D412yes—
293C4⋊C4×C59C2412yes—
294C22⋊C4×C59—22no—
295C22⋊C4×C59—22no—
296C22⋊C4×C59—24no—
297C22⋊C4×C59—24no—
298C22⋊C4×C59—24no—
299C22⋊C4×C59C2×D412yes—
300C22⋊C4×C59C2×D412yes—
301C22⋊C4×C59C2×D412yes—
302C22⋊C4×C59C2×D412yes—
303C42×C59—24no—
304C42×C59C2×D412yes—
305C42×C59C2412yes—
306C22⋊Dic59—22no—
307C22⋊Dic59—22no—
308C22⋊Dic59—22no—
309C22⋊Dic59—22no—
310#11745672—28no—
311#11745672—44no—
312#11745671—28no—
313#11745671—44no—
314#11745670—44no—
315#11745669—44no—
316(C2×D59)⋊C4—22no—
317(C2×D59)⋊C4—22no—
318(C2×D59)⋊C4—22no—
319(C2×D59)⋊C4—22no—
320(C2×D59)⋊C4—22no—
321(C2×D59)⋊C4—22no—
322C4⋊Dic59—21no—
323C4⋊Dic59—21no—
324C4⋊Dic59C2412yes—
325C4⋊Dic59C2412yes—
326Dic59⋊C4—22no—
327Dic59⋊C4—22no—
328Dic59⋊C4—22no—
329Dic59⋊C4—22no—
330Dic59⋊C4—22no—
331Dic59⋊C4—22no—
332C4×Dic59—22no—
333C4×Dic59—22no—
334#11745664—42no—
335#11745664—42no—
336#11745664—44no—
337C2×C59⋊C8C2414yes—
338C2×C59⋊C8C2414yes—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—42no—
347C23×C59—42no—
348C23×C59—42no—
349C23×C59C22×D411yescharacteristic
350C23×C59C22×D412yes—
351C23×C59C22×D411yescharacteristic
352C23×C59C22×D411yescharacteristic
353C22×D59—22no—
354C22×D59—42no—
355C22×D59—81no—
356C22×D59—81no—
357Q8×C59—24no—
358Q8×C59—22no—
359Q8×C59—24no—
360Q8×C59—48no—
361Q8×C59—42no—
362Q8×C59H(5,𝔽2)14yes—
363D4×C59—22no—
364D4×C59—22no—
365D4×C59—42no—
366D4×C59—42no—
367D4×C59—44no—
368D4×C59—44no—
369D4×C59—42no—
370D4×C59—48no—
371C2×C4×C59—24no—
372C2×C4×C59—22no—
373C2×C4×C59—22no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—24no—
377C2×C4×C59—22no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—42no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—44no—
387C2×C4×C59—44no—
388C2×C4×C59—48no—
389C2×C4×C59—42no—
390C2×C4×C59—42no—
391C2×C4×C59C22×D412yes—
392C2×C4×C59C22×D412yes—
393C2×C4×C59C22×D411yescharacteristic
394C2×C4×C59C22×D411yescharacteristic
395C2×C4×C59C22×D412yes—
396C2×C4×C59C22×D411yescharacteristic
397C2×C4×C59C2511yescharacteristic
398C22⋊D59—44no—
399C22⋊D59—44no—
400C22⋊D59—82no—
401C22⋊D59—82no—
402C2×Dic59—22no—
403C2×Dic59—22no—
404C2×Dic59—22no—
405C2×Dic59—42no—
406C2×Dic59—81no—
407C2×Dic59—81no—
408D236—24no—
409D236—81no—
410C4×D59—82no—
411C4×D59—82no—
412Dic118—24no—
413Dic118—81no—
414C59⋊C8—24no—
415C59⋊C8—24no—
416#61583—591nomaximal, Sylow
417C22×C59—21no—
418C22×C59—21no—
419C22×C59—21no—
420C22×C59—22no—
421C22×C59—21no—
422C22×C59—21no—
423C22×C59—22no—
424C22×C59—21no—
425C22×C59—21no—
426C22×C59—21no—
427C22×C59—22no—
428C22×C59—44no—
429C22×C59—42no—
430C22×C59—42no—
431C22×C59—42no—
432C22×C59—82no—
433C22×C59—84no—
434C22×C59#57512yes—
435C22×C59C23×D411yescharacteristic
436C2×D59—42no—
437C2×D59—42no—
438C2×D59—42no—
439C2×D59—162no—
440C4×C59—22no—
441C4×C59—21no—
442C4×C59—22no—
443C4×C59—21no—
444C4×C59—24no—
445C4×C59—21no—
446C4×C59—22no—
447C4×C59—42no—
448C4×C59—42no—
449C4×C59C2×H(5,𝔽2)12yes—
450Dic59—42no—
451Dic59—42no—
452Dic59—42no—
453#3505—591no—
454C2×#548D5911yescharacteristic, complemented
455#3327—594no—
456#3326—594no—
457#3277—594no—
458#3275—594no—
459#3211—592no—
460#3195—591no—
461#3194—592no—
462#3193—591no—
463#3108—592no—
464#3007—591no—
465#3006—591no—
466#3004—592no—
467#2975—591no—
468C2×C59—22no—
469C2×C59—41no—
470C2×C59—42no—
471C2×C59—41no—
472C2×C59—82no—
473C2×C59#348411yescharacteristic
474C2×C59C2×#57511yescharacteristic
475C2×C59#358611yescharacteristic
476D59—82no—
477C22×#41C2×D5911yescharacteristic
478C23×Q8C2×D5911yescharacteristic, complemented
479C2×#137—592no—
480C2×#137—594no—
481C2×AGL(1,ℤ/8)—592no—
482#553—592no—
483#553—1182no—
484#552—592no—
485#551—1182no—
486#548—22no—
487#548—22no—
488#548—592no—
489#548C2×D5914yes—
490#548C2×D5914yescomplemented
491#546—592no—
492#539—1181no—
493#538—1181no—
494#534—1181no—
495#529—592no—
496C2×#124—21no—
497C2×#124C2×D5911yescharacteristic, complemented
498#525—592no—
499C2×C22⋊Q8—21no—
500C2×C22⋊Q8—591no—
501C2×C22⋊Q8C2×D5911yescharacteristic
502C2×#121—21no—
503C2×#121—591no—
504C2×#121C2×D5911yescharacteristic, complemented
505#518—1181no—
506C2×C4×Q8C2×D5911yescharacteristic, complemented
507C2×C4×D4—21no—
508C2×C4×D4C2×D5911yescharacteristic
509#495—594no—
510#488—594no—
511#484—592no—
512#483—592no—
513#483—592no—
514#482—594no—
515#480—592no—
516#479—594no—
517#470—594no—
518#469—594no—
519#468—594no—
520#468—594no—
521#464—594no—
522#464—594no—
523#463—594no—
524#452—594no—
525#451—592no—
526#451—592no—
527#451—594no—
528#451—592no—
529#450—592no—
530#450—592no—
531#449—594no—
532#449—594no—
533#448—592no—
534#448—592no—
535#448—594no—
536#447—592no—
537C4×Q16—594no—
538C4×SD16—594no—
539#436—594no—
540#436—594no—
541#431—592no—
542#419—594no—
543#417—592no—
544#417—592no—
545#407—591no—
546#407—592no—
547#407—591no—
548C59#6158311yescharacteristic, complemented, Sylow
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—44no—
552C2×#41—592no—
553C2×#41C22×D5912yes—
554C2×#41C22×D5912yes—
555C22×Q8—21no—
556C22×Q8—22no—
557C22×Q8—44no—
558C22×Q8—591no—
559C22×Q8C22×D5911yescharacteristic
560C22×Q8C22×D5914yes—
561C22×Q8C22×D5911yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—591no—
565C22×D4—1181no—
566C22×D4C22⋊D5911yescharacteristic
567C22×D4C22×D5911yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C22×D5911yescharacteristic
571C23×C4C22×D5911yescharacteristic
572#137—2368no—
573#137—2364no—
574AGL(1,ℤ/8)—2364no—
575C2×Q16—594no—
576C2×Q16—594no—
577C2×SD16—594no—
578C2×SD16—594no—
579C2×SD16—594no—
580C2×D8—594no—
581C2×M16—592no—
582C2×M16—592no—
583C2×M16—594no—
584#126—1182no—
585#126—1182no—
586#126—1182no—
587#125—592no—
588#125—1182no—
589#124—24no—
590#124—24no—
591#124—22no—
592#124—592no—
593#124—1182no—
594#124C22×D5914yes—
595#123—1182no—
596#123—1182no—
597#123—1182no—
598#123—1182no—
599#123—1182no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—24no—
603C22⋊Q8—24no—
604C22⋊Q8—592no—
605C22⋊Q8—592no—
606C22⋊Q8—592no—
607C22⋊Q8—1181no—
608C22⋊Q8—1181no—
609C22⋊Q8—1182no—
610C22⋊Q8C22×D5912yes—
611C22⋊Q8C22×D5912yes—
612#121—24no—
613#121—24no—
614#121—22no—
615#121—592no—
616#121—592no—
617#121—592no—
618#121—1182no—
619#121—1182no—
620#121—1181no—
621#121—1181no—
622#121—1182no—
623#121C22×D5914yes—
624#120—1182no—
625#120—1182no—
626C4×Q8—22no—
627C4×Q8—592no—
628C4×Q8C22×D5914yes—
629C4×D4—24no—
630C4×D4—24no—
631C4×D4—592no—
632C4×D4—1182no—
633C4×D4—1182no—
634C4×D4—1182no—
635C4×D4—1182no—
636C4×D4—1182no—
637C4×D4C22⋊D5912yes—
638C4×D4C22⋊D5912yes—
639C4×D4C22×D5912yes—
640C4×D4C22×D5912yes—
641#117—592no—
642#117—1182no—
643#117—1182no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—591no—
647C2×C4⋊C4—591no—
648C2×C4⋊C4—1181no—
649C2×C4⋊C4C22⋊D5911yescharacteristic
650C2×C4⋊C4C22×D5911yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—1181no—
656C2×C22⋊C4—1181no—
657C2×C22⋊C4—1182no—
658C2×C22⋊C4C22⋊D5911yescharacteristic
659C2×C22⋊C4C22⋊D5911yescharacteristic
660C2×C42—21no—
661C2×C42C22×D5911yescharacteristic
662#107—594no—
663#106—594no—
664C4⋊C8—594no—
665#103—594no—
666#103—594no—
667#103—594no—
668#103—594no—
669#103—594no—
670#102—594no—
671#102—594no—
672#102—594no—
673C22⋊C8—592no—
674C22⋊C8—592no—
675C22⋊C8—594no—
676C22⋊C8—592no—
677C22⋊C8—592no—
678C4×C8—594no—
679C24—21no—
680C24—1181no—
681C24C2×C22⋊D5911yescharacteristic
682C24C2×C22⋊D5911yescharacteristic
683#41—24no—
684#41—24no—
685#41—42no—
686#41—42no—
687#41—44no—
688#41—44no—
689#41—2364no—
690C2×Q8—24no—
691C2×Q8—21no—
692C2×Q8—24no—
693C2×Q8—21no—
694C2×Q8—28no—
695C2×Q8—44no—
696C2×Q8—42no—
697C2×Q8—44no—
698C2×Q8—48no—
699C2×Q8—592no—
700C2×Q8—1181no—
701C2×Q8—2362no—
702C2×Q8C23×D5912yes—
703C2×Q8C23×D5912yes—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—21no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—592no—
713C2×D4—1182no—
714C2×D4—1182no—
715C2×D4—1182no—
716C2×D4—1182no—
717C2×D4—1181no—
718C2×D4—2362no—
719C2×D4—2364no—
720C2×D4C2×C22⋊D5912yes—
721C2×D4C2×C22⋊D5912yes—
722C2×D4C23×D5912yes—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—24no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—1181no—
734C22×C4—1181no—
735C22×C4—1181no—
736C22×C4—1182no—
737C22×C4—1182no—
738C22×C4C2×C22⋊D5911yescharacteristic
739C22×C4C2×C22⋊D5911yescharacteristic
740C22×C4C2×C22⋊D5911yescharacteristic
741C22×C4C2×C22⋊D5911yescharacteristic
742C22×C4C2×C22⋊D5911yescharacteristic
743C22×C4C2×C22⋊D5911yescharacteristic
744C22×C4C2×C22⋊D5912yes—
745C22×C4C23×D5911yescharacteristic
746C22×C4C23×D5911yescharacteristic
747C22×C4C23×D5911yescharacteristic
748C22×C4C23×D5912yes—
749Q16—1188no—
750Q16—2364no—
751SD16—1188no—
752SD16—2364no—
753SD16—2364no—
754D8—2364no—
755M16—2362no—
756M16—2364no—
757M16—2362no—
758C2×C8—594no—
759C2×C8—594no—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—592no—
765C4⋊C4—592no—
766C4⋊C4—1181no—
767C4⋊C4—1181no—
768C4⋊C4—1182no—
769C4⋊C4—1182no—
770C4⋊C4—1182no—
771C4⋊C4—1182no—
772C4⋊C4—1182no—
773C4⋊C4—1182no—
774C4⋊C4C2×C22⋊D5912yes—
775C4⋊C4C2×C22⋊D5912yes—
776C4⋊C4C23×D5912yes—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—1182no—
783C22⋊C4—1182no—
784C22⋊C4—1182no—
785C22⋊C4—1182no—
786C22⋊C4—1182no—
787C22⋊C4—1182no—
788C22⋊C4—1182no—
789C22⋊C4—1182no—
790C22⋊C4—1182no—
791C22⋊C4—1182no—
792C22⋊C4C2×C22⋊D5912yes—
793C22⋊C4C2×C22⋊D5912yes—
794C22⋊C4C2×C22⋊D5912yes—
795C22⋊C4C2×C22⋊D5912yes—
796C42—24no—
797C42—1182no—
798C42—1182no—
799C42C2×C22⋊D5912yes—
800C42C23×D5912yes—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—1182no—
812C23—4721no—
813C23—4721no—
814C23—2362no—
815C23C22×C22⋊D5911yescharacteristic
816C23C22×C22⋊D5911yescharacteristic
817C23C22×C22⋊D5912yes—
818C23C22×C22⋊D5911yescharacteristic
819Q8—24no—
820Q8—22no—
821Q8—24no—
822Q8—48no—
823Q8—42no—
824Q8—1184no—
825Q8—4721no—
826Q8#1427377214yes—
827D4—22no—
828D4—22no—
829D4—42no—
830D4—42no—
831D4—44no—
832D4—44no—
833D4—42no—
834D4—48no—
835D4—1184no—
836D4—4721no—
837D4—4722no—
838D4—4722no—
839D4—2364no—
840D4—2364no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—48no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—1182no—
862C2×C4—1182no—
863C2×C4—1182no—
864C2×C4—4722no—
865C2×C4—4722no—
866C2×C4—4721no—
867C2×C4—4721no—
868C2×C4—2362no—
869C2×C4C22×C22⋊D5912yes—
870C2×C4C22×C22⋊D5912yes—
871C2×C4C22×C22⋊D5911yescharacteristic
872C2×C4C22×C22⋊D5912yes—
873C2×C4C22×C22⋊D5911yescharacteristic
874C2×C4C22×C22⋊D5911yescharacteristic
875C2×C4C24×D5911yescharacteristic
876C8—1184no—
877C8—1184no—
878C22—21no—
879C22—21no—
880C22—22no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—44no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—84no—
895C22—9442no—
896C22—2362no—
897C22—2362no—
898C22—2362no—
899C22#1683820012yes—
900C22C23×C22⋊D5911yescharacteristic
901C4—24no—
902C4—21no—
903C4—21no—
904C4—21no—
905C4—22no—
906C4—22no—
907C4—22no—
908C4—42no—
909C4—42no—
910C4—2362no—
911C4—2362no—
912C4—2362no—
913C4C2×#1427377212yes—
914C2—22no—
915C2—42no—
916C2—41no—
917C2—41no—
918C2—82no—
919C2—4722no—
920C2#2143773111yescharacteristic
921C2C2×#1683820011yescharacteristic
922C2#2143888311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#548C2
socleC22×C59C23×D4
hypercenterC2×#548D59
hypocenterC59#61583
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #21437935C2semidirect
2. #21436364C2semidirect
3. #21436349C2semidirect
4. #21435749C2semidirect
5. #21435728C2semidirect
6. #21435061C2semidirect
7. #21434917C2semidirect
8. #21434910C2semidirect
9. #21434898C2semidirect
10. #21434176C2semidirect
11. #21433356C2semidirect
12. #21433348C2semidirect
13. #21433330C2semidirect
14. #21433137C2semidirect
15. C2×C59×#548C2semidirect
16. C2×#14273758C22semidirect
17. C2×#14273757C22semidirect
18. C2×#14273752C22semidirect
20. #16838098C22semidirect
21. #16838092C22semidirect
23. #16838061C22semidirect
24. #16838048C22semidirect
33. #16837784C22semidirect
34. #16837756C22semidirect
35. #16837735C22semidirect
36. #16837732C22semidirect
37. #16837730C22semidirect
38. #16837723C22semidirect
40. #16837709C22semidirect
41. #16837658C22semidirect
42. #16837653C22semidirect
43. #16837650C22semidirect
44. #16837646C22semidirect
45. #16837624C22semidirect
46. #16837621C22semidirect
47. #16837614C22semidirect
48. #16837564C22semidirect
49. #16837558C22semidirect
50. #16837558C22semidirect
51. #16837558C22semidirect
52. #16837557C22semidirect
53. #16837553C22semidirect
54. #16837552C22semidirect
55. #16837547C22semidirect
56. #16837545C22semidirect
59. #16837541C22semidirect
61. C4×#11745672C22semidirect
62. C4×#11745671C22semidirect
63. #16837480C22semidirect
64. #16837480C22semidirect
65. #16837455C22semidirect
66. #16837411C22semidirect
67. #16837403C22semidirect
68. #16837403C22semidirect
71. #16837366C22semidirect
73. C23×Q8×C59C22semidirect
77. C59×#548C22semidirect
79. C2×#124×C59C22semidirect
83. C2×#121×C59C22semidirect
84. C2×C4×Q8×C59C22semidirect
454. C2×#548D59semidirect
478. C23×Q8C2×D59semidirect
490. #548C2×D59semidirect
497. C2×#124C2×D59semidirect
504. C2×#121C2×D59semidirect
506. C2×C4×Q8C2×D59semidirect
548. C59#61583semidirect

Maximal subgroups

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

subgroupindex
#214379352
#214363642
#214363492
#214357492
#214357282
#214350612
#214349172
#214349102
#214348982
#214341762
#214333562
#214333482
#214333302
#214331372
C2×C59×#5482
#6158359