Finite Group Databasebeta

← #29647684

Subgroups — #29647684

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459573C211yesmaximal, characteristic
2#21454473C211yesmaximal, characteristic, complemented
3#21448681C211yesmaximal, characteristic, complemented
4#21444393C211yesmaximal, characteristic, complemented
5#21444381C211yesmaximal, characteristic, complemented
6#21444368C211yesmaximal, characteristic, complemented
7#21444354C211yesmaximal, characteristic, complemented
8#21444351C211yesmaximal, characteristic, complemented
9#21444341C211yesmaximal, characteristic, complemented
10#21444329C211yesmaximal, characteristic, complemented
11#21444323C211yesmaximal, characteristic
12#21444316C211yesmaximal, characteristic, complemented
13#21444302C211yesmaximal, characteristic, complemented
14C2×#16839500C211yesmaximal, characteristic, complemented
15C61×#1516C211yesmaximal, characteristic
16#16840482—21no—
17#16840469—21no—
18#16840452—21no—
19#16840452—21no—
20#16840449—21no—
21#16840449—21no—
22#16840443—21no—
23#16840443—21no—
24#16840390C411yescharacteristic, complemented
25#16840379C411yescharacteristic, complemented
26#16840379C411yescharacteristic, complemented
27#16840372C411yescharacteristic, complemented
28#16840372C411yescharacteristic, complemented
29#16840333C411yescharacteristic, complemented
30#16840314C2211yescharacteristic
31#16840314C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840293C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35#16840245C411yescharacteristic, complemented
36#16840239C411yescharacteristic, complemented
37C2×#14519736C2211yescharacteristic
38#16839820—21no—
39#16839820—21no—
40#16839816C2211yescharacteristic
41#16839816C2211yescharacteristic
42#16839812C2211yescharacteristic
43#16839812C2211yescharacteristic
44#16839788—21no—
45#16839726C2211yescharacteristic
46#16839717—21no—
47#16839647—21no—
48#16839645—21no—
49#16839634—21no—
50#16839629C2211yescharacteristic
51#16839626C2211yescharacteristic
52#16839613C2211yescharacteristic
53C22⋊C4×Dic61—21no—
54#16839607C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839498C2211yescharacteristic
65#16839498C2211yescharacteristic
66#16839496C2211yescharacteristic
67#16839496C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic
70C61×#381C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic
76C23×Dic61—21no—
77C2×#11758194—21no—
78#14519777—21no—
79#14519776C2×C411yescharacteristic, complemented
80#14519776C2×C411yescharacteristic, complemented
81#14519775C2×C411yescharacteristic, complemented
82#14519775C2×C411yescharacteristic, complemented
83#14519770—21no—
84#14519770—21no—
85#14519770—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519769—21no—
92#14519768—21no—
93#14519768—21no—
94#14519768C2×C411yescharacteristic, complemented
95#14519768C2×C411yescharacteristic, complemented
96#14519767—21no—
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519764—21no—
101#14519764—21no—
102#14519764C2×C411yescharacteristic, complemented
103#14519764C2×C411yescharacteristic, complemented
104#14519758—21no—
105#14519758—21no—
106#14519758—21no—
107#14519758—21no—
108#14519758—21no—
109#14519758—21no—
110#14519756—21no—
111#14519756—21no—
112#14519756—21no—
113#14519756—21no—
114#14519756C2×C411yescharacteristic
115#14519756C2×C411yescharacteristic
116#14519756C2311yescharacteristic
117#14519756C2311yescharacteristic
118#14519754—21no—
119#14519754—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519754—21no—
124Q8×Dic61C2×C411yescharacteristic, complemented
125Q8×Dic61C2×C411yescharacteristic, complemented
126C4×Dic122—21no—
127C4×Dic122—21no—
128#14519742—21no—
129#14519742—21no—
130#14519742C2×C411yescharacteristic, complemented
131#14519742C2×C411yescharacteristic, complemented
132#14519742C2×C411yescharacteristic, complemented
133#14519742C2×C411yescharacteristic, complemented
134D4×Dic61—21no—
135D4×Dic61—21no—
136D4×Dic61—21no—
137D4×Dic61—21no—
138D4×Dic61C2×C411yescharacteristic, complemented
139D4×Dic61C2×C411yescharacteristic, complemented
140#14519736—21no—
141#14519736C2×C411yescharacteristic
142#14519736C2×C411yescharacteristic
143#14519736C2×C411yescharacteristic
144#14519736C2×C411yescharacteristic
145#14519736D411yescharacteristic
146#14519736D411yescharacteristic
147#14519736D411yescharacteristic
148#14519736D411yescharacteristic
149#14519733—21no—
150#14519733—21no—
151#14519733—21no—
152#14519733—21no—
153#14519733—21no—
154#14519733—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61C2×C411yescharacteristic
157C2×C4⋊Dic61D411yescharacteristic
158C2×C4⋊Dic61D411yescharacteristic
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196—21no—
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61D411yescharacteristic
164C2×C22⋊Dic61D411yescharacteristic
165C2×C4×Dic61—21no—
166C2×C4×Dic61—21no—
167C2×C4×Dic61C2311yescharacteristic
168C2×C4×Dic61C2311yescharacteristic
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519687—21no—
177#14519687—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
187C2×#41×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C22×C8×C61—21no—
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2×C411yescharacteristic
194#121×C61C2311yescharacteristic
195#120×C61—21no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207#41×C61—42no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61C22×C411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—42no—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—42no—
230C22×Dic61—42no—
231C22×Dic61—81no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—42no—
240C2×Dic122C22×C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—42no—
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—
254C22⋊C4×C61—42no—
255C42×C61—21no—
256C22⋊Dic61—21no—
257C22⋊Dic61—21no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266C22⋊Dic61C22⋊C411yescharacteristic
267C22⋊Dic61C22⋊C411yescharacteristic
268C22⋊Dic61C22⋊C411yescharacteristic
269C22⋊Dic61C22⋊C411yescharacteristic
270C22⋊Dic61C22⋊C411yescharacteristic
271C22⋊Dic61C22⋊C411yescharacteristic
272C22⋊Dic61C22⋊C411yescharacteristic
273C22⋊Dic61C22⋊C411yescharacteristic
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61C22⋊C411yescharacteristic
280C4⋊Dic61C22⋊C411yescharacteristic
281C4⋊Dic61C22⋊C411yescharacteristic
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22⋊C411yescharacteristic
284C4⋊Dic61C22⋊C411yescharacteristic
285C4⋊Dic61C22⋊C411yescharacteristic
286C4⋊Dic61C22⋊C411yescharacteristic
287C4⋊Dic61C22×C411yescharacteristic
288C4⋊Dic61C22×C411yescharacteristic
289#11758196—21no—
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#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—42no—
306#11758196—81no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—42no—
314C4×Dic61—81no—
315C4×Dic61C22×C411yescharacteristic
316C4×Dic61C22×C411yescharacteristic
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323#11758194—42no—
324C2×#92418—21no—
325C2×#92418—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—22no—
329C23×C61—21no—
330C23×C61—41no—
331C23×C61C2×C22⋊C411yescharacteristic
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C22×D411yescharacteristic
334Q8×C61—41no—
335D4×C61—41no—
336D4×C61—41no—
337D4×C61—41no—
338D4×C61—42no—
339D4×C61—81no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—42no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C23×C411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—42no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—81no—
378C2×Dic61—81no—
379C2×Dic61—81no—
380C2×Dic61—84no—
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389Dic122—42no—
390Dic122—41no—
391Dic122—41no—
392Dic122—81no—
393Dic122—81no—
394C8×C61—41no—
395C8×C61—41no—
396#92418—41no—
397#92418—41no—
398#17609—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61#41012yes—
412C22×C61C22×C22⋊C411yescharacteristic
413C22×C61#57711yescharacteristic
414C22×C61#57811yescharacteristic
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—41no—
420C4×C61—41no—
421C4×C61—41no—
422C4×C61—81no—
423C4×C61—81no—
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—21no—
431Dic61—21no—
432Dic61—42no—
433Dic61—41no—
434Dic61—41no—
435Dic61—41no—
436Dic61—41no—
437Dic61—81no—
438#3495—611no—
439#2924—611no—
440#2343—611no—
441#1521—611no—
442#1518—611no—
443#1516D6111yescharacteristic
444#1515—611no—
445#1512—611no—
446#1511—611no—
447#1509—611no—
448#1506—611no—
449#1504—611no—
450#1503—611no—
451#1500—611no—
452C2×#328—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—22no—
456C2×C61—41no—
457C2×C61—81no—
458C2×C61C2×#41011yescharacteristic
459C2×C61#289811yescharacteristic
460C2×C61#290111yescharacteristic
461#556—1221no—
462#554—1221no—
463#552—1221no—
464#552—1221no—
465#552—1221no—
466#552—1221no—
467#551—1221no—
468#551—1221no—
469#544—611no—
470#542—611no—
471#542—611no—
472#541—611no—
473#541—611no—
474#536—611no—
475#533—611no—
476#533—611no—
477#529—611no—
478#529—611no—
479#525C2×D6111yescharacteristic
480C2×C22⋊Q8—611no—
481#520—611no—
482#519—611no—
483C2×#117—611no—
484#433—1221no—
485#433—1221no—
486#432—611no—
487#432—611no—
488#431—611no—
489#431—611no—
490#424—1221no—
491#407—611no—
492C2×C22⋊C8C2×D6111yescharacteristic
493#405—1221no—
494#387—1221no—
495#387—1221no—
496#385—1221no—
497#383—611no—
498#382—611no—
499#381C2×D6111yescharacteristic
500C4×C4⋊C4—611no—
501C4×C22⋊C4—1221no—
502#376—611no—
503C2×#95—611no—
504#328—611no—
505#328—611no—
506#328—611no—
507#328—611no—
508#328—611no—
509#328—611no—
510#328—611no—
511#328—611no—
512#328—611no—
513#328—611no—
514#328C2×D6111yescharacteristic
515#328C2×D6111yescharacteristic
516#327—611no—
517#327—611no—
518#327C2×D6111yescharacteristic
519#327C2×D6111yescharacteristic
520C61#1760911yescharacteristic, complemented, Sylow
521C2×#41C4×D6111yescharacteristic
522C22×Q8—611no—
523C23×C4—1221no—
524C23×C4C22×D6111yescharacteristic
525C2×M16—1221no—
526C22×C8—21no—
527C4⋊Q8—611no—
528C4⋊Q8—611no—
529C4⋊Q8—611no—
530C4⋊Q8—611no—
531C4⋊Q8—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#126—1221no—
537#126—1221no—
538#126—1221no—
539#126—1221no—
540#125—611no—
541#125—611no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125—1221no—
547#125—1221no—
548#125—1221no—
549#124—611no—
550#124—611no—
551#124—1221no—
552#124—1221no—
553#123—21no—
554#123—1221no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560C22⋊Q8—611no—
561C22⋊Q8—611no—
562C22⋊Q8—611no—
563C22⋊Q8—611no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8C4×D6111yescharacteristic
575C22⋊Q8C22×D6111yescharacteristic
576#121C4×D6111yescharacteristic
577#121C22×D6111yescharacteristic
578#120—21no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—1221no—
586C4×Q8—1221no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—611no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—611no—
603#117—611no—
604#117—611no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117—1221no—
609#117—1221no—
610#117—1221no—
611#117—1221no—
612#117C4×D6111yescharacteristic
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4—1221no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C22⋊C8—21no—
633C22⋊C8—611no—
634C22⋊C8—611no—
635C22⋊C8—1221no—
636C22⋊C8C22×D6111yescharacteristic
637C22⋊C8C22×D6111yescharacteristic
638#97—1221no—
639#97—1221no—
640C4×C8—1221no—
641C4×C8—1221no—
642#95—21no—
643#95—611no—
644#95—611no—
645#95—1221no—
646#95—1221no—
647#95—1221no—
648#95—1221no—
649#95—1221no—
650#95C22×D6111yescharacteristic
651#95C22×D6111yescharacteristic
652C24D4×D6111yescharacteristic
653#41—42no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1221no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8—2442no—
660C2×Q8C2×C4×D6111yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C2×C4×D6111yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—42no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—4881no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6111yescharacteristic
683C22×C4C2×C4×D6111yescharacteristic
684C22×C4D4×D6111yescharacteristic
685C22×C4D4×D6111yescharacteristic
686C22×C4D4×D6111yescharacteristic
687C22×C4C23×D6111yescharacteristic
688M16—2442no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—42no—
692C2×C8—1221no—
693C2×C8—1221no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—611no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
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—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⋊C4—1221no—
727C4⋊C4—4881no—
728C4⋊C4—2442no—
729C4⋊C4C2×C4×D6111yescharacteristic
730C4⋊C4C2×C4×D6111yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—42no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—611no—
740C22⋊C4—611no—
741C22⋊C4—611no—
742C22⋊C4—611no—
743C22⋊C4—611no—
744C22⋊C4—611no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C42—21no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—611no—
761C42—611no—
762C42—611no—
763C42—611no—
764C42—1221no—
765C42—1221no—
766C42—1221no—
767C42—1221no—
768C42—1221no—
769C42—1221no—
770C42—4881no—
771C42—2442no—
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—41no—
777C23C22⋊C4×D6111yescharacteristic
778C23C22⋊C4×D6111yescharacteristic
779C23C2×D4×D6111yescharacteristic
780Q8—41no—
781Q8—4881no—
782Q8—4881no—
783Q8—2441no—
784Q8—2441no—
785Q8—2442no—
786D4—41no—
787D4—42no—
788D4—41no—
789D4—41no—
790D4—81no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—611no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1222no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—4881no—
825C2×C4—4881no—
826C2×C4—4884no—
827C2×C4—4881no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2442no—
835C2×C4—2441no—
836C2×C4C22⋊C4×D6111yescharacteristic
837C2×C4C22⋊C4×D6111yescharacteristic
838C2×C4C22×C4×D6111yescharacteristic
839C2×C4C2×D4×D6111yescharacteristic
840C8—41no—
841C8—41no—
842C8—2441no—
843C8—2441no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22#1683973412yes—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22#1684056911yescharacteristic
859C22#1684057611yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—81no—
868C4—81no—
869C4—1221no—
870C4—1221no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—1221no—
875C4—1221no—
876C4—1221no—
877C4—4881no—
878C4—2442no—
879C4—2441no—
880C4—2441no—
881C4—2441no—
882C4—2441no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—81no—
888C2C2×#1683973411yescharacteristic
889C2#2145434811yescharacteristic
890C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1516C2
socleC22×C61C22×C22⋊C4
prime radicalC61×#525C22
cosocleC22×C4×C61C24
hypercenter#1516D61
hypocenterC61#17609
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #21454473C2semidirect
3. #21448681C2semidirect
4. #21444393C2semidirect
5. #21444381C2semidirect
6. #21444368C2semidirect
7. #21444354C2semidirect
8. #21444351C2semidirect
9. #21444341C2semidirect
10. #21444329C2semidirect
12. #21444316C2semidirect
13. #21444302C2semidirect
14. C2×#16839500C2semidirect
24. #16840390C4semidirect
25. #16840379C4semidirect
26. #16840379C4semidirect
27. #16840372C4semidirect
28. #16840372C4semidirect
29. #16840333C4semidirect
35. #16840245C4semidirect
36. #16840239C4semidirect
79. #14519776C2×C4semidirect
80. #14519776C2×C4semidirect
81. #14519775C2×C4semidirect
82. #14519775C2×C4semidirect
94. #14519768C2×C4semidirect
95. #14519768C2×C4semidirect
102. #14519764C2×C4semidirect
103. #14519764C2×C4semidirect
124. Q8×Dic61C2×C4semidirect
125. Q8×Dic61C2×C4semidirect
130. #14519742C2×C4semidirect
131. #14519742C2×C4semidirect
132. #14519742C2×C4semidirect
133. #14519742C2×C4semidirect
138. D4×Dic61C2×C4semidirect
139. D4×Dic61C2×C4semidirect
520. C61#17609semidirect

Maximal subgroups

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

subgroupindex
#214595732
#214544732
#214486812
#214443932
#214443812
#214443682
#214443542
#214443512
#214443412
#214443292
#214443232
#214443162
#214443022
C2×#168395002
C61×#15162
#1760961