Finite Group Databasebeta

← #29647745

Subgroups — #29647745

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459675C211yesmaximal, characteristic
2#21454899C211yesmaximal, characteristic, complemented
3#21448779C211yesmaximal, characteristic, complemented
4#21444395C211yesmaximal, characteristic, complemented
5#21444394C211yesmaximal, characteristic, complemented
6#21444393C211yesmaximal, characteristic, complemented
7#21444381C211yesmaximal, characteristic, complemented
8#21444377C211yesmaximal, characteristic
9#21444316C211yesmaximal, characteristic, complemented
10#21444312C211yesmaximal, characteristic
11#21444306C211yesmaximal, characteristic, complemented
12#21444305C211yesmaximal, characteristic, complemented
13#21444304C211yesmaximal, characteristic, complemented
14#21444302C211yesmaximal, characteristic, complemented
15C61×#1521C211yesmaximal, characteristic, complemented
16#16840495C411yescharacteristic, complemented
17#16840494C411yescharacteristic, complemented
18#16840489C411yescharacteristic, complemented
19#16840488C411yescharacteristic, complemented
20#16840484C411yescharacteristic, complemented
21#16840481C411yescharacteristic, complemented
22#16840480—21no—
23#16840479—21no—
24#16840471C411yescharacteristic, complemented
25#16840468C411yescharacteristic, complemented
26#16840448—21no—
27#16840445—21no—
28#16840356—21no—
29#16840354—21no—
30#16840334—21no—
31#16840314C2211yescharacteristic
32#16840307C2211yescharacteristic
33#16840298C2211yescharacteristic
34#16840296C2211yescharacteristic
35#16840293C2211yescharacteristic
36#16840241—21no—
37C2×C4×Dic122C2211yescharacteristic
38C8×Dic122—21no—
39C8×Dic122—21no—
40#16839886—21no—
41#16839886—21no—
42#16839815C2211yescharacteristic
43#16839812C2211yescharacteristic
44#16839812C2211yescharacteristic
45#16839812C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839666—21no—
48#16839645—21no—
49#16839644—21no—
50#16839629C2211yescharacteristic
51#16839626C2211yescharacteristic
52#16839613—21no—
53#16839613C2211yescharacteristic
54#16839608C2211yescharacteristic
55#16839607C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839499C2211yescharacteristic
59#16839499C2211yescharacteristic
60#16839498C2211yescharacteristic
61#16839498C2211yescharacteristic
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#383C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758224—21no—
76C22×Dic122D411yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519776C2×C411yescharacteristic
80#14519776C2×C411yescharacteristic
81#14519775C2×C411yescharacteristic
82#14519773C2×C411yescharacteristic
83#14519772—21no—
84#14519772—21no—
85#14519771—21no—
86#14519771—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519769—21no—
91#14519769C2×C411yescharacteristic
92#14519768—21no—
93#14519768C2×C411yescharacteristic
94#14519768C2×C411yescharacteristic
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519766C2×C411yescharacteristic
99#14519765C2×C411yescharacteristic
100#14519764C2×C411yescharacteristic
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519761—21no—
105#14519761—21no—
106#14519760—21no—
107#14519760—21no—
108#14519759—21no—
109#14519759—21no—
110#14519758—21no—
111#14519757—21no—
112#14519756—21no—
113#14519756C2311yescharacteristic
114#14519755—21no—
115#14519755—21no—
116#14519755—21no—
117#14519754—21no—
118#14519754—21no—
119#14519754—21no—
120#14519754—21no—
121#14519751C2311yescharacteristic
122#14519749—21no—
123Q8×Dic61C2×C411yescharacteristic
124Q8×Dic61C2×C411yescharacteristic
125C4×Dic122—21no—
126C4×Dic122C2×C411yescharacteristic
127C4×Dic122C2×C411yescharacteristic
128C4×Dic122C2×C411yescharacteristic
129C4×Dic122C2×C411yescharacteristic
130C4×Dic122C2×C411yescharacteristic
131C4×Dic122D411yescharacteristic
132C4×Dic122D411yescharacteristic
133C4×Dic122D411yescharacteristic
134C4×Dic122D411yescharacteristic
135#14519742—21no—
136#14519742—21no—
137#14519742C2×C411yescharacteristic
138#14519742C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140D4×Dic61—21no—
141D4×Dic61C2×C411yescharacteristic
142D4×Dic61C2×C411yescharacteristic
143#14519739C2×C411yescharacteristic
144#14519739C2×C411yescharacteristic
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147#14519737—21no—
148#14519737—21no—
149#14519737—21no—
150#14519735—21no—
151#14519734—21no—
152#14519734—21no—
153#14519733—21no—
154#14519733—21no—
155#14519733—21no—
156C2×C4⋊Dic61D411yescharacteristic
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—21no—
163C2×C4×Dic61—21no—
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61C2311yescharacteristic
167C2×C4×Dic61C2311yescharacteristic
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C4×#92418—21no—
176C8×Dic61—21no—
177C8×Dic61—21no—
178C8×Dic61—21no—
179C8×Dic61—21no—
180#14519684—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic
189#124×C61C2×C411yescharacteristic
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic
196#117×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C22⋊C8×C61C2311yescharacteristic
200C22⋊C8×C61C2311yescharacteristic
201C4×C8×C61—21no—
202#95×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C2×Q8×C61C22×C411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226#11758224—42no—
227#11758224—42no—
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22⋊C411yescharacteristic
237C2×Dic122C22⋊C411yescharacteristic
238C2×Dic122C22⋊C411yescharacteristic
239C2×Dic122C22⋊C411yescharacteristic
240C2×Dic122C22×C411yescharacteristic
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C22×C411yescharacteristic
248C4⋊C4×C61C22×C411yescharacteristic
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C42×C61—21no—
255C42×C61C22×C411yescharacteristic
256C42×C61C22×C411yescharacteristic
257C42×C61C2×D411yescharacteristic
258C42×C61C2×D411yescharacteristic
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61C22⋊C411yescharacteristic
277C4⋊Dic61C22⋊C411yescharacteristic
278C4⋊Dic61C22⋊C411yescharacteristic
279C4⋊Dic61C22⋊C411yescharacteristic
280C4⋊Dic61C22×C411yescharacteristic
281C4⋊Dic61C22×C411yescharacteristic
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—42no—
295#11758196—42no—
296#11758196C22⋊C411yescharacteristic
297#11758196C22⋊C411yescharacteristic
298#11758196C22⋊C411yescharacteristic
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301#11758196C22⋊C411yescharacteristic
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304C4×Dic61—21no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—42no—
310C4×Dic61—42no—
311C4×Dic61—42no—
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C22×C411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C2×#92418—21no—
321C2×#92418—21no—
322C23×C61—21no—
323C23×C61C22×D411yescharacteristic
324C22×D61—21no—
325Q8×C61—41no—
326D4×C61—41no—
327D4×C61—41no—
328D4×C61—41no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—81no—
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C22⋊D61—41no—
350C22⋊D61—41no—
351C22⋊D61—42no—
352C22⋊D61—81no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—22no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—42no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—81no—
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61#13512yes—
377C2×Dic61#13512yes—
378D244—41no—
379C4×D61—42no—
380C4×D61—81no—
381C4×D61—81no—
382Dic122—22no—
383Dic122—22no—
384Dic122—22no—
385Dic122—22no—
386Dic122—42no—
387Dic122—41no—
388Dic122—81no—
389C8×C61—41no—
390C8×C61—41no—
391#92418—41no—
392#92418—41no—
393#17616—611nomaximal, Sylow
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61C22×C22⋊C411yescharacteristic
400C22×C61C2×#13511yescharacteristic
401C22×C61C2×#13511yescharacteristic
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—81no—
415C4×C61—81no—
416Dic61—21no—
417Dic61—21no—
418Dic61—21no—
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—42no—
423Dic61—41no—
424Dic61—41no—
425Dic61—41no—
426Dic61—81no—
427Dic61#41612yes—
428Dic61#41612yes—
429#3507—611no—
430#2982—611no—
431#2356—611no—
432#1521—611no—
433#1521—611no—
434#1521—611no—
435#1521D6111yescharacteristic, complemented
436#1518—611no—
437#1517—611no—
438#1503—611no—
439#1502—611no—
440#1500—611no—
441#1500—611no—
442#1500—611no—
443#1500—611no—
444C2×C61—21no—
445C2×C61—21no—
446C2×C61—81no—
447C2×C61#288411yescharacteristic
448C2×C61C2×#41611yescharacteristic
449C2×C61#290111yescharacteristic
450D61—81no—
451#559—611no—
452#559—611no—
453#557—611no—
454#557—611no—
455#556—611no—
456#556—611no—
457#556—1221no—
458#556—1221no—
459#554—611no—
460#554—611no—
461#552—1221no—
462#552—1221no—
463#539—1221no—
464#539—1221no—
465#536—1221no—
466#533—611no—
467#532—611no—
468#529—611no—
469#529—611no—
470#529—611no—
471#529C2×D6111yescharacteristic
472#520—1221no—
473C2×C4×Q8—611no—
474C8×Q8—1221no—
475C8×Q8—1221no—
476C8×Q8—1221no—
477C8×Q8—1221no—
478#431—611no—
479#431—611no—
480#431—611no—
481#431—611no—
482#431—611no—
483#431C2×D6111yescharacteristic
484#391—1221no—
485#387—1221no—
486#387—1221no—
487#383—611no—
488#383C2×D6111yescharacteristic
489#382—611no—
490C4×C4⋊C4—611no—
491C4×C4⋊C4—1221no—
492#376—611no—
493#376—611no—
494#328—611no—
495#328—611no—
496#328—611no—
497#328—611no—
498#328—611no—
499#328—611no—
500#328C2×D6111yescharacteristic
501#328C2×D6111yescharacteristic
502#327—611no—
503#327—611no—
504#327—611no—
505#327—611no—
506#327—611no—
507#327—611no—
508#327C2×D6111yescharacteristic
509#327C2×D6111yescharacteristic
510C61#1761611yescharacteristic, complemented, Sylow
511C2×#41—1221no—
512C22×Q8—611no—
513C4⋊Q8—611no—
514C4⋊Q8—611no—
515C4⋊Q8—611no—
516C4⋊Q8—1221no—
517C4⋊Q8—1221no—
518#127—611no—
519#126—21no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#126—1221no—
526#126—1221no—
527#125—611no—
528#125—611no—
529#125—611no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#125C4×D6111yescharacteristic
536#124—611no—
537#124—611no—
538#124—611no—
539#124—1221no—
540#124—1221no—
541#124—1221no—
542#124C4×D6111yescharacteristic
543#123—21no—
544#123—1221no—
545#123—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551C22⋊Q8—611no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8C22×D6111yescharacteristic
562#121—611no—
563#121—1221no—
564#121C22×D6111yescharacteristic
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—611no—
575C4×Q8—611no—
576C4×Q8—611no—
577C4×Q8—611no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8C4×D6111yescharacteristic
582C4×D4—21no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4C4×D6111yescharacteristic
595#117—21no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—1221no—
614C2×C42C22×D6111yescharacteristic
615C4⋊C8—21no—
616C4⋊C8—1221no—
617C4⋊C8—1221no—
618C4⋊C8—1221no—
619C4⋊C8—1221no—
620C4⋊C8—1221no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8C22×D6111yescharacteristic
624C22⋊C8C22×D6111yescharacteristic
625C4×C8—21no—
626C4×C8—1221no—
627C4×C8—1221no—
628C4×C8—1221no—
629C4×C8—1221no—
630C4×C8—1221no—
631#95—21no—
632#95—21no—
633#95—611no—
634#95—611no—
635#95—1221no—
636#95—1221no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95C22×D6111yescharacteristic
641#95C22×D6111yescharacteristic
642#41—2442no—
643#41—2442no—
644C2×Q8—611no—
645C2×Q8—611no—
646C2×Q8—611no—
647C2×Q8—611no—
648C2×Q8—611no—
649C2×Q8—1222no—
650C2×Q8—1222no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8C2×C4×D6111yescharacteristic
654C2×D4—21no—
655C2×D4—611no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4C2×C4×D6111yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4D4×D6111yescharacteristic
675C22×C4D4×D6111yescharacteristic
676C22×C4C23×D6111yescharacteristic
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—1221no—
680C2×C8—1221no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—611no—
694C4⋊C4—611no—
695C4⋊C4—611no—
696C4⋊C4—611no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—2442no—
716C4⋊C4—2442no—
717C4⋊C4C2×C4×D6111yescharacteristic
718C4⋊C4C2×C4×D6111yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C42—21no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—1221no—
747C42—1221no—
748C42—1221no—
749C42—1221no—
750C42—1221no—
751C42—2442no—
752C42—2442no—
753C42—2442no—
754C42C2×C4×D6111yescharacteristic
755C42C2×C4×D6111yescharacteristic
756C42D4×D6111yescharacteristic
757C42D4×D6111yescharacteristic
758C23—21no—
759C23—1221no—
760C23C2×D4×D6111yescharacteristic
761Q8—41no—
762Q8—1222no—
763Q8—1222no—
764Q8—1222no—
765Q8—1222no—
766Q8—4881no—
767Q8—2441no—
768Q8—2442no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—4881no—
773D4—2441no—
774D4—2442no—
775D4—2441no—
776D4—2441no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—81no—
791C2×C4—611no—
792C2×C4—611no—
793C2×C4—612no—
794C2×C4—612no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—4881no—
808C2×C4—4881no—
809C2×C4—4881no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22⋊C4×D6111yescharacteristic
820C2×C4C22⋊C4×D6111yescharacteristic
821C2×C4C22⋊C4×D6111yescharacteristic
822C2×C4C22⋊C4×D6111yescharacteristic
823C2×C4C22×C4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C8—41no—
826C8—41no—
827C8—2441no—
828C8—2441no—
829C22—21no—
830C22—21no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—2441no—
835C22—2441no—
836C22—2441no—
837C22C2×C22⋊C4×D6111yescharacteristic
838C22#135×D6111yescharacteristic
839C22#135×D6111yescharacteristic
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—81no—
850C4—81no—
851C4—612no—
852C4—612no—
853C4—1221no—
854C4—1221no—
855C4—1221no—
856C4—1221no—
857C4—1221no—
858C4—1221no—
859C4—4881no—
860C4—2442no—
861C4—2441no—
862C4—2441no—
863C4—2441no—
864C2—21no—
865C2—21no—
866C2—81no—
867C2—4881no—
868C2#2145428111yescharacteristic
869C2#416×D6111yescharacteristic
870C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1521C2
socleC22×C61C22×C22⋊C4
prime radical#16840307C22
cosocleC22×C4×C61C24
hypercenter#1521D61
hypocenterC61#17616
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #21454899C2semidirect
3. #21448779C2semidirect
4. #21444395C2semidirect
5. #21444394C2semidirect
6. #21444393C2semidirect
7. #21444381C2semidirect
9. #21444316C2semidirect
11. #21444306C2semidirect
12. #21444305C2semidirect
13. #21444304C2semidirect
14. #21444302C2semidirect
15. C61×#1521C2semidirect
16. #16840495C4semidirect
17. #16840494C4semidirect
18. #16840489C4semidirect
19. #16840488C4semidirect
20. #16840484C4semidirect
21. #16840481C4semidirect
24. #16840471C4semidirect
25. #16840468C4semidirect
435. #1521D61semidirect
510. C61#17616semidirect

Maximal subgroups

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

subgroupindex
#214596752
#214548992
#214487792
#214443952
#214443942
#214443932
#214443812
#214443772
#214443162
#214443122
#214443062
#214443052
#214443042
#214443022
C61×#15212
#1761661