Finite Group Databasebeta

← #29647052

Subgroups — #29647052

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459436C211yesmaximal, characteristic
2#21454940C211yesmaximal, characteristic, complemented
3#21454458C211yesmaximal, characteristic, complemented
4#21444290C211yesmaximal, characteristic, complemented
5#21444285C211yesmaximal, characteristic, complemented
6#21444278C211yesmaximal, characteristic, complemented
7#21444264C211yesmaximal, characteristic, complemented
8#21444252C211yesmaximal, characteristic, complemented
9#21444248C211yesmaximal, characteristic, complemented
10#21444231C211yesmaximal, characteristic, complemented
11#21444225C211yesmaximal, characteristic, complemented
12#21444220C211yesmaximal, characteristic, complemented
13#21444205C211yesmaximal, characteristic, complemented
14Q8⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1479C211yesmaximal, characteristic, complemented
16#16840488C411yescharacteristic
17#16840484—21no—
18#16840484C411yescharacteristic
19#16840453—21no—
20#16840453C411yescharacteristic
21#16840447—21no—
22#16840447C411yescharacteristic
23Q8×C22⋊D61C411yescharacteristic
24#16840424C411yescharacteristic
25#16840423C411yescharacteristic
26#16840413—21no—
27#16840413C411yescharacteristic
28#16840316—21no—
29#16840316C2211yescharacteristic
30#16840299—21no—
31#16840299C2211yescharacteristic
32#16840296—21no—
33#16840296C2211yescharacteristic
34C4×#11758226C2211yescharacteristic
35C4×#11758222—21no—
36C4×#11758222C2211yescharacteristic
37C4×Q8×D61C2211yescharacteristic
38#16839892—21no—
39#16839836—21no—
40#16839836—21no—
41C8×D244—21no—
42#16839822—21no—
43#16839820—21no—
44#16839818C2211yescharacteristic
45#16839818C2211yescharacteristic
46#16839815C2211yescharacteristic
47#16839813C2211yescharacteristic
48#16839813C2211yescharacteristic
49#16839787—21no—
50#16839786C2211yescharacteristic
51C4⋊C8×D61C2211yescharacteristic
52C4⋊C8×D61C2211yescharacteristic
53#16839727—21no—
54C4×#11758189C2211yescharacteristic
55C4×C8×D61C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58Q8⋊#92418C2211yescharacteristic
59Q8⋊#92418C2211yescharacteristic
60Q8⋊#92418C2211yescharacteristic
61Q8⋊#92418C2211yescharacteristic
62#16839492C2211yescharacteristic
63#16839492C2211yescharacteristic
64#16839491C2211yescharacteristic
65#16839491C2211yescharacteristic
66#16839489C2211yescharacteristic
67#16839489C2211yescharacteristic
68C2×C4×Q8×C61C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×Q8⋊C8C2211yescharacteristic
72C61×Q8⋊C8C2211yescharacteristic
73C61×Q8⋊C8C2211yescharacteristic
74C61×Q8⋊C8C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222—21no—
77C2×#11758222D411yescharacteristic
78C2×Q8×D61C2×C411yescharacteristic
79C2×#11758194—21no—
80C2×#11758189—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84#14519776—21no—
85#14519776C2×C411yescharacteristic
86#14519775—21no—
87#14519775C2×C411yescharacteristic
88#14519772—21no—
89#14519772—21no—
90#14519772—21no—
91#14519771—21no—
92#14519771—21no—
93#14519771—21no—
94#14519769—21no—
95#14519769C2×C411yescharacteristic
96#14519768—21no—
97#14519768C2×C411yescharacteristic
98#14519767—21no—
99#14519767—21no—
100#14519767—21no—
101#14519766—21no—
102#14519766C2×C411yescharacteristic
103#14519765—21no—
104#14519765C2×C411yescharacteristic
105#14519762—21no—
106#14519762—21no—
107#14519762—21no—
108#14519760—21no—
109#14519760—21no—
110#14519760—21no—
111#14519757—21no—
112#14519757C2×C411yescharacteristic
113#14519756—21no—
114#14519756C2×C411yescharacteristic
115#14519755—21no—
116#14519755—21no—
117#14519755—21no—
118#14519753—21no—
119#14519753—21no—
120#14519753C2×C411yescharacteristic
121#14519753C2×C411yescharacteristic
122#14519752—21no—
123#14519752C2×C411yescharacteristic
124#14519751—21no—
125#14519751C2×C411yescharacteristic
126Q8×Dic61C2×C411yescharacteristic
127Q8×Dic61C2×C411yescharacteristic
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122C2×C411yescharacteristic
132C4×Dic122D411yescharacteristic
133C4×Dic122C2311yescharacteristic
134#14519742—21no—
135#14519742C2×C411yescharacteristic
136C4×D244—21no—
137C4×D244—21no—
138C4×D244—21no—
139C4×D244C2×C411yescharacteristic
140C4×D244D411yescharacteristic
141C4×D244C2311yescharacteristic
142#14519739—21no—
143#14519739C2×C411yescharacteristic
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61C2×C411yescharacteristic
148C4×C22⋊D61C2×C411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151#14519736—21no—
152#14519736D411yescharacteristic
153#14519735—21no—
154#14519735C2×C411yescharacteristic
155#14519734—21no—
156#14519734—21no—
157#14519734—21no—
158#14519734—21no—
159#14519734—21no—
160#14519734D411yescharacteristic
161#14519734D411yescharacteristic
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2×C411yescharacteristic
164C42×D61—21no—
165C42×D61—21no—
166C42×D61C2311yescharacteristic
167C42×D61C2311yescharacteristic
168C4⋊#92418—21no—
169C4⋊#92418—21no—
170C4⋊#92418C2311yescharacteristic
171C4⋊#92418C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174#14519706—21no—
175#14519706—21no—
176C22⋊#92418—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519687—21no—
182#14519687—21no—
183#14519687—21no—
184C4×#92418C2311yescharacteristic
185C4×#92418C2311yescharacteristic
186C8×Dic61—21no—
187C22×Q8×C61C2×C411yescharacteristic
188C4×Q8×C61—21no—
189C4×Q8×C61—21no—
190C4×Q8×C61C2×C411yescharacteristic
191C4×Q8×C61C2×C411yescharacteristic
192C4×Q8×C61C2311yescharacteristic
193C4×Q8×C61C2311yescharacteristic
194C2×C4⋊C4×C61—21no—
195C2×C4⋊C4×C61C2×C411yescharacteristic
196C2×C42×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61C2311yescharacteristic
200C4⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61—21no—
202C22⋊C8×C61—21no—
203C4×C8×C61—21no—
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61—22no—
208C2×Q8×C61—41no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×Q8×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C2×C22⋊D61—21no—
217C2×C22⋊D61C22⋊C411yescharacteristic
218C2×C22⋊D61C22⋊C411yescharacteristic
219#11758226—22no—
220#11758226—41no—
221Q8×D61—22no—
222Q8×D61—41no—
223#11758222—42no—
224#11758222—44no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244C22⋊C411yescharacteristic
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C22×C411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122C22⋊C411yescharacteristic
243C2×Dic122C22×C411yescharacteristic
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C22×C411yescharacteristic
254C4⋊C4×C61C22×C411yescharacteristic
255C42×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61C22×C411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2×D411yescharacteristic
262C42×C61C2411yescharacteristic
263C22⋊Dic61—21no—
264C22⋊Dic61C22⋊C411yescharacteristic
265C22⋊Dic61C22⋊C411yescharacteristic
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198C22⋊C411yescharacteristic
279#11758198C22⋊C411yescharacteristic
280#11758198C22⋊C411yescharacteristic
281#11758198C22⋊C411yescharacteristic
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61C22⋊C411yescharacteristic
287C4⋊Dic61C22⋊C411yescharacteristic
288C4⋊Dic61C22×C411yescharacteristic
289C4⋊Dic61C22×C411yescharacteristic
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61C22×C411yescharacteristic
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317#11758194—81no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322#11758189—42no—
323C8×D61—42no—
324C8×D61—81no—
325C8×D61—81no—
326C23×C61C2×C22⋊C411yescharacteristic
327C22×D61—21no—
328C22×D61C2×C22⋊C411yescharacteristic
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—21no—
333Q8×C61—42no—
334Q8×C61#13112yes—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—41no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C23×C411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C22⋊D61—22no—
353C22⋊D61—41no—
354C22⋊D61—42no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364D244—22no—
365D244—21no—
366D244—21no—
367D244—42no—
368D244—42no—
369C4×D61—22no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—41no—
379C4×D61—42no—
380C4×D61—42no—
381C4×D61—42no—
382C4×D61—42no—
383C4×D61—41no—
384C4×D61—41no—
385Dic122—21no—
386Dic122—21no—
387Dic122—41no—
388Dic122—42no—
389Dic122—42no—
390C8×C61—41no—
391C8×C61—41no—
392C8×C61—41no—
393C8×C61—41no—
394#92418—41no—
395#92418—41no—
396#92418—41no—
397#92418—41no—
398#17524—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61C22×C22⋊C411yescharacteristic
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61#42112yes—
412C4×C61—22no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61—41no—
420C4×C61C2×#13111yescharacteristic
421C4×C61#56811yescharacteristic
422C4×C61#57711yescharacteristic
423C4×C61#57811yescharacteristic
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—41no—
431Dic61—41no—
432Dic61—41no—
433#3482—611no—
434#2990—611no—
435#2922—611no—
436#1497—611no—
437#1495—611no—
438#1494—611no—
439#1491—611no—
440#1488—611no—
441#1487—611no—
442#1483—611no—
443#1482—611no—
444#1481—611no—
445#1479D6111yescharacteristic, complemented
446#1477—611no—
447C2×Q8⋊C8—611no—
448C2×C61—41no—
449C2×C61#288011yescharacteristic
450C2×C61#289811yescharacteristic
451C2×C61C2×#42111yescharacteristic
452D61—22no—
453D61—41no—
454D61—81no—
455#557—611no—
456#556—611no—
457#556—1221no—
458#552—611no—
459#552—611no—
460#552—1221no—
461#552—1221no—
462D4×Q8—611no—
463#548—611no—
464#548—611no—
465#547—611no—
466#547—1221no—
467#533—611no—
468#533—1221no—
469#529—611no—
470#529—611no—
471#529—1221no—
472#529—1221no—
473C4×#41—611no—
474C4×#41—611no—
475C4×#41—1221no—
476C2×C4×Q8—611no—
477C2×C4×Q8C2×D6111yescharacteristic
478#446—1221no—
479#435—1221no—
480#435—1221no—
481C8×D4—1221no—
482#433—1221no—
483#433—1221no—
484#432—611no—
485#432—611no—
486#431—611no—
487#431—611no—
488#431—611no—
489#431C2×D6111yescharacteristic
490#431C2×D6111yescharacteristic
491#424—1221no—
492#423—611no—
493C2×C4⋊C8—611no—
494C2×C4⋊C8—611no—
495#408—1221no—
496C4×M16—611no—
497C2×C4×C8—611no—
498Q8⋊C8—611no—
499Q8⋊C8—611no—
500Q8⋊C8—611no—
501Q8⋊C8—611no—
502Q8⋊C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8C2×D6111yescharacteristic
507Q8⋊C8C2×D6111yescharacteristic
508Q8⋊C8C2×D6111yescharacteristic
509Q8⋊C8C2×D6111yescharacteristic
510D4⋊C8—611no—
511D4⋊C8—611no—
512D4⋊C8—611no—
513D4⋊C8—611no—
514C61#1752411yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C2×#41—611no—
517C2×#41—1221no—
518C22×Q8—611no—
519C22×Q8C4×D6111yescharacteristic
520C2×M16—1221no—
521C2×M16—1221no—
522C22×C8—1221no—
523C22×C8—1221no—
524C22×C8—1221no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—1221no—
528C4⋊Q8—1221no—
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#125—611no—
536#125—611no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125—1221no—
541#125—1221no—
542#124—611no—
543#124—611no—
544#124—1221no—
545#124—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551#123—1221no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563#121—611no—
564#121—611no—
565#121—1221no—
566#121—1221no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—611no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8C4×D6111yescharacteristic
580C4×Q8C4×D6111yescharacteristic
581C4×Q8C22×D6111yescharacteristic
582C4×Q8C22×D6111yescharacteristic
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117—1221no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4C4×D6111yescharacteristic
613C2×C42—21no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42C22×D6111yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—611no—
621C4⋊C8—611no—
622C4⋊C8—1221no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8C22×D6111yescharacteristic
629C4⋊C8C22×D6111yescharacteristic
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—1221no—
633C22⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637#97—1221no—
638#97—1221no—
639#97—1221no—
640C4×C8—21no—
641C4×C8—611no—
642C4×C8—611no—
643C4×C8—1221no—
644C4×C8C22×D6111yescharacteristic
645C4×C8C22×D6111yescharacteristic
646#41—1222no—
647#41—2442no—
648#41—2444no—
649#41—2441no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—41no—
653C2×Q8—611no—
654C2×Q8—611no—
655C2×Q8—1221no—
656C2×Q8—1221no—
657C2×Q8—1222no—
658C2×Q8—2441no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×Q8C2×C4×D6111yescharacteristic
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—611no—
664C2×D4—611no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4C2×C4×D6111yescharacteristic
682C22×C4D4×D6111yescharacteristic
683C22×C4D4×D6111yescharacteristic
684M16—4881no—
685M16—2442no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—4881no—
695C2×C8—4881no—
696C2×C8—2442no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
706C4⋊C4—611no—
707C4⋊C4—611no—
708C4⋊C4—611no—
709C4⋊C4—611no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4C2×C4×D6111yescharacteristic
727C4⋊C4C2×C4×D6111yescharacteristic
728C22⋊C4—611no—
729C22⋊C4—611no—
730C22⋊C4—611no—
731C22⋊C4—611no—
732C22⋊C4—611no—
733C22⋊C4—611no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42C2×C4×D6111yescharacteristic
763C42D4×D6111yescharacteristic
764C42D4×D6111yescharacteristic
765C42C23×D6111yescharacteristic
766C23—611no—
767C23—611no—
768C23—1221no—
769C23C22⋊C4×D6111yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—42no—
774Q8—1221no—
775Q8—1221no—
776Q8—2441no—
777Q8—2442no—
778Q8—2442no—
779Q8#1451978312yes—
780D4—1222no—
781D4—1222no—
782D4—1221no—
783D4—1221no—
784D4—2442no—
785D4—2442no—
786D4—2441no—
787D4—2442no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—1222no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—2441no—
818C2×C4—2442no—
819C2×C4—2442no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4C22⋊C4×D6111yescharacteristic
825C2×C4C22⋊C4×D6111yescharacteristic
826C2×C4C22⋊C4×D6111yescharacteristic
827C2×C4C22×C4×D6111yescharacteristic
828C2×C4C2×D4×D6111yescharacteristic
829C2×C4C2×D4×D6111yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—2441no—
835C8—2441no—
836C8—2441no—
837C8—2441no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—612no—
842C22—1221no—
843C22—1221no—
844C22—1221no—
845C22—1221no—
846C22—1221no—
847C22—2441no—
848C22—2441no—
849C22—2441no—
850C22C2×C22⋊C4×D6111yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—22no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—1221no—
860C4—1221no—
861C4—1221no—
862C4—1221no—
863C4—1221no—
864C4—1221no—
865C4—2441no—
866C4—2441no—
867C4—2441no—
868C4C2×#1451978311yescharacteristic
869C4#1684052811yescharacteristic
870C4#1684057111yescharacteristic
871C4#1684057811yescharacteristic
872C2—41no—
873C2—1222no—
874C2—4881no—
875C2—2441no—
876C2#2145426511yescharacteristic
877C2#2145435111yescharacteristic
878C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1479C2
socleC22×C61C22×C22⋊C4
prime radical#21459436C2
cosocleC42×C61C24
hypercenter#1479D61
hypocenterC61#17524
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #21454940C2semidirect
3. #21454458C2semidirect
4. #21444290C2semidirect
5. #21444285C2semidirect
6. #21444278C2semidirect
7. #21444264C2semidirect
8. #21444252C2semidirect
9. #21444248C2semidirect
10. #21444231C2semidirect
11. #21444225C2semidirect
12. #21444220C2semidirect
13. #21444205C2semidirect
14. Q8⋊C8×D61C2semidirect
15. C61×#1479C2semidirect
445. #1479D61semidirect
514. C61#17524semidirect

Maximal subgroups

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

subgroupindex
#214594362
#214549402
#214544582
#214442902
#214442852
#214442782
#214442642
#214442522
#214442482
#214442312
#214442252
#214442202
#214442052
Q8⋊C8×D612
C61×#14792
#1752461