Finite Group Databasebeta

← #30611673

Subgroups — #30611673

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462660C211yesmaximal, characteristic, complemented
2#21462658C211yesmaximal, characteristic, complemented
3#21461304C211yesmaximal, characteristic, complemented
4#21461303C211yesmaximal, characteristic, complemented
5#21461299C211yesmaximal, characteristic, complemented
6#21461297C211yesmaximal, characteristic, complemented
7#21461296C211yesmaximal, characteristic, complemented
8#21461293C211yesmaximal, characteristic, complemented
9#21461292C211yesmaximal, characteristic, complemented
10#21461287C211yesmaximal, characteristic, complemented
11#21461286C211yesmaximal, characteristic, complemented
12#21461270C211yesmaximal, characteristic, complemented
13#21461269C211yesmaximal, characteristic, complemented
14D61⋊#329C211yesmaximal, characteristic, complemented
15#21459711C211yesmaximal, characteristic
16#16840814—21no—
17#16840812—21no—
18#16840794—21no—
19#16840794—21no—
20#16840792—21no—
21#16840791—21no—
22#16840790—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic, complemented
25#16840784C2211yescharacteristic
26#16840784C2211yescharacteristic
27#16840784C2211yescharacteristic, complemented
28#16840783C2211yescharacteristic, complemented
29#16840782C2211yescharacteristic, complemented
30C4×#11758213C2211yescharacteristic, complemented
31C4×#11758217C2211yescharacteristic, complemented
32#16840721C2211yescharacteristic
33#16840721C2211yescharacteristic
34#16840721C2211yescharacteristic, complemented
35C2×#14519832C2211yescharacteristic, complemented
36#16840619C2211yescharacteristic, complemented
37#16840619C2211yescharacteristic, complemented
38#16840619C2211yescharacteristic, complemented
39#16840619C2211yescharacteristic, complemented
40#16840619C2211yescharacteristic, complemented
41#16840619C2211yescharacteristic, complemented
42#16840619C2211yescharacteristic, complemented
43#16840619C2211yescharacteristic, complemented
44#16840618C2211yescharacteristic
45#16840618C2211yescharacteristic
46#16840618C2211yescharacteristic
47#16840618C2211yescharacteristic
48#16840617C2211yescharacteristic
49#16840617C2211yescharacteristic
50#16840617C2211yescharacteristic
51#16840617C2211yescharacteristic
52#16840496—21no—
53#16840494—21no—
54#16840483—21no—
55#16840479—21no—
56#16840442—21no—
57#16840439—21no—
58#16840437—21no—
59#16840435—21no—
60#16840386C411yescharacteristic
61#16840383C411yescharacteristic
62#16840381C411yescharacteristic
63#16840335C411yescharacteristic
64#16840328C411yescharacteristic
65#16840317C2211yescharacteristic
66#16840299C2211yescharacteristic
67#16840298C2211yescharacteristic
68#16840294C2211yescharacteristic
69#16840293C2211yescharacteristic
70#124×D61C2211yescharacteristic
71#16840238C411yescharacteristic
72#16840234C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#542C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103#14519832C2311yescharacteristic
104#14519832C2311yescharacteristic
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222C2×C411yescharacteristic
108C2×Q8×D61C2×C411yescharacteristic
109C2×D4×D61C2×C411yescharacteristic
110#14519777C2×C411yescharacteristic
111#14519776—21no—
112#14519773—21no—
113#14519772—21no—
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519768C2311yescharacteristic
121#14519768C2311yescharacteristic
122#14519766—21no—
123#14519766C2311yescharacteristic
124#14519765C2×C411yescharacteristic
125#14519764C2311yescharacteristic
126#14519763—21no—
127#14519763—21no—
128#14519763—21no—
129#14519763—21no—
130#14519763—21no—
131#14519763—21no—
132#14519762—21no—
133#14519762—21no—
134#14519762—21no—
135#14519761—21no—
136#14519761—21no—
137#14519759—21no—
138#14519759—21no—
139#14519759—21no—
140#14519758—21no—
141#14519757—21no—
142#14519757C2×C411yescharacteristic
143#14519756C2×C411yescharacteristic
144#14519755—21no—
145#14519754—21no—
146#14519753—21no—
147#14519753—21no—
148#14519753C2×C411yescharacteristic
149#14519752C2×C411yescharacteristic
150#14519751C2×C411yescharacteristic
151#14519748C2×C411yescharacteristic
152#14519747—21no—
153#14519745—21no—
154Q8×Dic61—21no—
155Q8×Dic61C2×C411yescharacteristic
156C4×Dic122—21no—
157C4×Dic122C2×C411yescharacteristic
158#14519742—21no—
159#14519742—21no—
160#14519742C2×C411yescharacteristic
161#14519742D411yescharacteristic
162#14519742D411yescharacteristic
163C4×D244—21no—
164C4×D244C2×C411yescharacteristic
165D4×Dic61—21no—
166D4×Dic61C2×C411yescharacteristic
167#14519739C2×C411yescharacteristic
168#14519739D411yescharacteristic
169#14519739D411yescharacteristic
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172#14519737—21no—
173#14519737—21no—
174#14519737D411yescharacteristic
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519737D411yescharacteristic
178#14519736—21no—
179#14519735—21no—
180#14519735—21no—
181#14519735C2×C411yescharacteristic
182#14519735C2×C411yescharacteristic
183#14519734—21no—
184#14519734—21no—
185#14519734C2×C411yescharacteristic
186#14519734C2×C411yescharacteristic
187#14519733—21no—
188C2×#11758198—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#124×C61—21no—
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C23×D61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61C22×C411yescharacteristic
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61C22⋊C411yescharacteristic
217C2×C22⋊D61C22⋊C411yescharacteristic
218C22×Dic61—21no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221Q8×D61—42no—
222D4×D61—42no—
223#11758222—42no—
224C2×D244—21no—
225C2×D244C22⋊C411yescharacteristic
226C2×D244C22×C411yescharacteristic
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122C22⋊C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240#11758217—42no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—42no—
250#11758213—42no—
251D61⋊C8—42no—
252D61⋊C8—42no—
253D61⋊C8—42no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C22⋊C411yescharacteristic
258C4⋊C4×C61C22⋊C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61C22⋊C411yescharacteristic
267C22⋊C4×C61C22⋊C411yescharacteristic
268C42×C61—21no—
269C42×C61C22×C411yescharacteristic
270C42×C61C22×C411yescharacteristic
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198C22⋊C411yescharacteristic
289#11758198C22⋊C411yescharacteristic
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C411yescharacteristic
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61C22×C411yescharacteristic
298C4⋊Dic61C22×C411yescharacteristic
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2411yescharacteristic
322C23×C61—21no—
323C23×C61C2×C22⋊C411yescharacteristic
324C22×D61—21no—
325C22×D61—42no—
326C22×D61—81no—
327C22×D61—81no—
328C22×D61C2×C22⋊C411yescharacteristic
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—41no—
331Q8×C61—81no—
332D4×C61—41no—
333D4×C61—81no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—41no—
338C2×C4×C61—81no—
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C23×C411yescharacteristic
345C22⋊D61—22no—
346C22⋊D61—41no—
347C22⋊D61—42no—
348C22⋊D61—81no—
349C22⋊D61—81no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—81no—
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C22×D411yescharacteristic
361C2×Dic61C22×D411yescharacteristic
362D244—22no—
363D244—41no—
364D244—81no—
365C4×D61—22no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—42no—
372C4×D61—81no—
373C4×D61—81no—
374Dic122—41no—
375Dic122—42no—
376Dic122—41no—
377Dic122—81no—
378#92420—22no—
379#92420—22no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383#92420—41no—
384#92420—41no—
385#92420—41no—
386#17686—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61C22×C22⋊C411yescharacteristic
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—162no—
403C2×D61#41312yes—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413Dic61—21no—
414Dic61—21no—
415Dic61—21no—
416Dic61—21no—
417Dic61—21no—
418Dic61—21no—
419Dic61—41no—
420Dic61—41no—
421Dic61—41no—
422#3510—611no—
423#2970—611no—
424#2970—611no—
425#1535—611no—
426#1535—611no—
427#1533—611no—
428#1532—611no—
429#1532—611no—
430#1531—611no—
431#1531—611no—
432#1529—611no—
433#1529—611no—
434#1524—611no—
435#1524—611no—
436C2×#329—611no—
437C2×C61—41no—
438C2×C61—81no—
439C2×C61C2×#41311yescharacteristic
440C2×C61#290111yescharacteristic
441C2×C61#290111yescharacteristic
442D61—22no—
443D61—41no—
444D61—81no—
445#559—1221no—
446#559—1221no—
447#556—1221no—
448#556—1221no—
449#551—1221no—
450#551—1221no—
451#551—1221no—
452#551—1221no—
453#542—611no—
454#542—611no—
455#542—611no—
456#542#692311yescharacteristic
457#536—611no—
458#535—611no—
459#533—611no—
460#529—611no—
461#529—611no—
462#529—611no—
463#529—611no—
464C2×#124—611no—
465#519—611no—
466#518—611no—
467C4×#41—611no—
468#446—1221no—
469#446—1221no—
470#435—1221no—
471#435—1221no—
472#435—1221no—
473#435—1221no—
474C8×D4—1221no—
475C8×D4—1221no—
476#432—611no—
477#432—611no—
478#432—611no—
479#432—611no—
480#432—611no—
481#432—611no—
482C4×M16—611no—
483C4×M16—611no—
484C2×#97—611no—
485C2×#97—611no—
486C2×#97—611no—
487C2×#97—611no—
488#330—611no—
489#330—611no—
490#330—611no—
491#330—611no—
492#330—611no—
493#330—611no—
494#330—611no—
495#330—611no—
496#329—611no—
497#329—611no—
498#329—611no—
499#329—611no—
500#329—611no—
501#329—611no—
502#329—611no—
503#329—611no—
504C61#1768611yescharacteristic, complemented, Sylow
505C2×#41—611no—
506C22×Q8—611no—
507C22×D4—611no—
508C2×M16—1221no—
509C2×M16—1221no—
510C22×C8—1221no—
511C22×C8—1221no—
512C22×C8—1221no—
513C22×C8—1221no—
514C4⋊Q8—611no—
515C4⋊Q8—1221no—
516C4⋊Q8C2×#692311yescharacteristic
517#127—1221no—
518#126—21no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#126—1221no—
526#125—611no—
527#125—611no—
528#124—21no—
529#124—611no—
530#124—611no—
531#124—611no—
532#124—1221no—
533#124—1221no—
534#124—1221no—
535#124—1221no—
536#124—1221no—
537#124—1221no—
538#124—1221no—
539#124C2×#692311yescharacteristic
540#123—21no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550C22⋊Q8—21no—
551C22⋊Q8—611no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8C2×#692311yescharacteristic
560#121—611no—
561#121—611no—
562#121—611no—
563#121C2×#692311yescharacteristic
564#120—1221no—
565#120—1221no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8C2×#692311yescharacteristic
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4C2×#692311yescharacteristic
592#117—611no—
593#117—611no—
594#117—611no—
595#117—611no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602#117C2×#692311yescharacteristic
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42—611no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C22⋊C8—1221no—
617C22⋊C8—1221no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622#97—611no—
623#97—611no—
624#97—611no—
625#97—611no—
626#97—611no—
627#97—611no—
628#97—611no—
629#97—611no—
630#97—1221no—
631#97—1221no—
632#97—1221no—
633#97—1221no—
634C4×C8—1221no—
635C4×C8—1221no—
636C24—1221no—
637#41—2442no—
638C2×Q8—21no—
639C2×Q8—611no—
640C2×Q8—611no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8—2442no—
644C2×Q8C22×#692311yescharacteristic
645C2×D4—21no—
646C2×D4—611no—
647C2×D4—611no—
648C2×D4—611no—
649C2×D4—611no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—2442no—
655C2×D4C22×#692311yescharacteristic
656C22×C4—21no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4C22×#692311yescharacteristic
670M16—2442no—
671M16—2442no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—2442no—
681C2×C8—2442no—
682C2×C8—2442no—
683C2×C8—2442no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4C22⋊#692311yescharacteristic
705C4⋊C4C22⋊#692311yescharacteristic
706C4⋊C4C22×#692311yescharacteristic
707C4⋊C4C22×#692311yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—611no—
714C22⋊C4—611no—
715C22⋊C4—611no—
716C22⋊C4—611no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
735C22⋊C4C22⋊#692311yescharacteristic
736C42—21no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—1221no—
746C42—1221no—
747C42—1221no—
748C42—1221no—
749C42—1221no—
750C42C22×#692311yescharacteristic
751C42C22×#692311yescharacteristic
752C23—21no—
753C23—611no—
754C23—611no—
755C23—1221no—
756C23—4881no—
757C23—4881no—
758C23—2442no—
759C23C2×C22⋊#692311yescharacteristic
760Q8—41no—
761Q8—81no—
762Q8—4881no—
763Q8—2441no—
764Q8—2441no—
765Q8—2442no—
766D4—41no—
767D4—81no—
768D4—1222no—
769D4—1222no—
770D4—4881no—
771D4—4881no—
772D4—4881no—
773D4—2441no—
774D4—2441no—
775D4—2442no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—81no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—611no—
786C2×C4—611no—
787C2×C4—1222no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—4881no—
792C2×C4—4881no—
793C2×C4—4881no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2442no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4C2×C22⋊#692311yescharacteristic
803C2×C4C2×C22⋊#692311yescharacteristic
804C2×C4C2×C22⋊#692311yescharacteristic
805C2×C4C2×C22⋊#692311yescharacteristic
806C2×C4C2×C22⋊#692311yescharacteristic
807C2×C4C23×#692311yescharacteristic
808C8—1222no—
809C8—1222no—
810C8—2441no—
811C8—2441no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C8—2441no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—612no—
823C22—1221no—
824C22—1221no—
825C22—1221no—
826C22—1221no—
827C22—1221no—
828C22—9762no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22C22×C22⋊#692311yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—1221no—
843C4—1221no—
844C4—1221no—
845C4—1221no—
846C4—1221no—
847C4—1221no—
848C4—2441no—
849C4—2441no—
850C4—2441no—
851C2—41no—
852C2—81no—
853C2—1222no—
854C2—4881no—
855C2—2441no—
856C2D61⋊#41311yescharacteristic
857C2#2146244911yescharacteristic
858C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#542C4
socleC22×C61C22×C22⋊C4
prime radical#16840328C4
cosocleC4×Dic61C24
hypercenter#542#6923
hypocenterC61#17686
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #21462660C2semidirect
2. #21462658C2semidirect
3. #21461304C2semidirect
4. #21461303C2semidirect
5. #21461299C2semidirect
6. #21461297C2semidirect
7. #21461296C2semidirect
8. #21461293C2semidirect
9. #21461292C2semidirect
10. #21461287C2semidirect
11. #21461286C2semidirect
12. #21461270C2semidirect
13. #21461269C2semidirect
14. D61⋊#329C2semidirect
24. #16840785C22semidirect
27. #16840784C22semidirect
28. #16840783C22semidirect
29. #16840782C22semidirect
30. C4×#11758213C22semidirect
31. C4×#11758217C22semidirect
34. #16840721C22semidirect
35. C2×#14519832C22semidirect
36. #16840619C22semidirect
37. #16840619C22semidirect
38. #16840619C22semidirect
39. #16840619C22semidirect
40. #16840619C22semidirect
41. #16840619C22semidirect
42. #16840619C22semidirect
43. #16840619C22semidirect
504. C61#17686semidirect

Maximal subgroups

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

subgroupindex
#214626602
#214626582
#214613042
#214613032
#214612992
#214612972
#214612962
#214612932
#214612922
#214612872
#214612862
#214612702
#214612692
D61⋊#3292
#214597112
#1768661