Finite Group Databasebeta

← #30611931

Subgroups — #30611931

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462739C211yesmaximal, characteristic
2#21462466C211yesmaximal, characteristic
3#21461359C211yesmaximal, characteristic, complemented
4#21461358C211yesmaximal, characteristic, complemented
5#21461355C211yesmaximal, characteristic, complemented
6#21461354C211yesmaximal, characteristic, complemented
7#21461341C211yesmaximal, characteristic, complemented
8#21461340C211yesmaximal, characteristic, complemented
9#21461337C211yesmaximal, characteristic, complemented
10#21461337C211yesmaximal, characteristic, complemented
11#21461336C211yesmaximal, characteristic, complemented
12#21461328C211yesmaximal, characteristic, complemented
13#21461321C211yesmaximal, characteristic, complemented
14C2×#16840621C211yesmaximal, characteristic, complemented
15#21459697C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840795—21no—
19#16840793—21no—
20#16840791—21no—
21#16840785C2211yescharacteristic
22#16840782C2211yescharacteristic
23#16840779C2211yescharacteristic
24#16840769—21no—
25#16840768—21no—
26#16840768—21no—
27#16840767C2211yescharacteristic
28#16840767C2211yescharacteristic
29#16840765C2211yescharacteristic
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34C2×#14519844C2211yescharacteristic
35D61⋊(C4⋊C8)C2211yescharacteristic
36#16840622C2211yescharacteristic
37#16840622C2211yescharacteristic
38#16840622C2211yescharacteristic
39#16840622C2211yescharacteristic
40#16840621C2211yescharacteristic
41#16840621C2211yescharacteristic
42#16840621C2211yescharacteristic
43#16840621C2211yescharacteristic
44#16840621C2211yescharacteristic
45#16840621C2211yescharacteristic
46#16840621C2211yescharacteristic
47#16840621C2211yescharacteristic
48#16840621C2211yescharacteristic
49#16840621C2211yescharacteristic
50#16840621C2211yescharacteristic
51#16840621C2211yescharacteristic
52#16840489—21no—
53#16840489C411yescharacteristic
54#16840488C411yescharacteristic
55#16840483C411yescharacteristic
56#16840480C411yescharacteristic
57#16840479—21no—
58#16840454C411yescharacteristic
59#16840452C411yescharacteristic
60#16840449—21no—
61#16840447C411yescharacteristic
62#16840445—21no—
63#16840371—21no—
64#16840369—21no—
65#16840334—21no—
66#16840318C2211yescharacteristic
67#16840316C2211yescharacteristic
68#16840315C2211yescharacteristic
69#16840314C2211yescharacteristic
70#16840314C2211yescharacteristic
71C2×#14519776C2211yescharacteristic
72#16840239—21no—
73C4×#11758224C2211yescharacteristic
74C61×#552C411yescharacteristic
75#14519864—44no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844C2311yescharacteristic
91#14519844C2311yescharacteristic
92#14519844C2311yescharacteristic
93#14519844C2311yescharacteristic
94#14519844C2311yescharacteristic
95#14519844C2311yescharacteristic
96#14519844C2311yescharacteristic
97#14519844C2311yescharacteristic
98C4⋊#92420—21no—
99C4⋊#92420—21no—
100C4⋊#92420—21no—
101C4⋊#92420—21no—
102#14519834—21no—
103C22⋊#92420—21no—
104C22⋊#92420—21no—
105#14519832—21no—
106#14519832—21no—
107C4×#92420—21no—
108C2×#11758224D411yescharacteristic
109C22×Dic122—21no—
110#14519776—21no—
111#14519776—21no—
112#14519776—21no—
113#14519776—21no—
114#14519776C2×C411yescharacteristic
115#14519776C2×C411yescharacteristic
116#14519776C2311yescharacteristic
117#14519776C2311yescharacteristic
118#14519776C2311yescharacteristic
119#14519775C2311yescharacteristic
120#14519772—21no—
121#14519772—21no—
122#14519772—21no—
123#14519771—21no—
124#14519770—21no—
125#14519770—21no—
126#14519770—21no—
127#14519769—21no—
128#14519769C2×C411yescharacteristic
129#14519768—21no—
130#14519768—21no—
131#14519768C2×C411yescharacteristic
132#14519768C2×C411yescharacteristic
133#14519767—21no—
134#14519767—21no—
135#14519767—21no—
136#14519767—21no—
137#14519767—21no—
138#14519767—21no—
139#14519767—21no—
140#14519763—21no—
141#14519763—21no—
142#14519761—21no—
143#14519760—21no—
144#14519758—21no—
145#14519757C2×C411yescharacteristic
146#14519756C2×C411yescharacteristic
147#14519756C2×C411yescharacteristic
148#14519755—21no—
149#14519755—21no—
150#14519755—21no—
151#14519754—21no—
152#14519754—21no—
153#14519754—21no—
154#14519754—21no—
155#14519753C2×C411yescharacteristic
156Q8×Dic61C2×C411yescharacteristic
157Q8×Dic61C2×C411yescharacteristic
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122—21no—
161C4×Dic122—21no—
162C4×Dic122—21no—
163C4×Dic122C2×C411yescharacteristic
164C4×Dic122C2×C411yescharacteristic
165#14519742—21no—
166#14519742—21no—
167#14519742—21no—
168#14519742—21no—
169#14519742—21no—
170#14519742—21no—
171#14519742C2×C411yescharacteristic
172#14519742C2×C411yescharacteristic
173#14519742D411yescharacteristic
174D4×Dic61D411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519736—21no—
180#14519736C2×C411yescharacteristic
181#14519735C2×C411yescharacteristic
182#14519735C2×C411yescharacteristic
183#14519735D411yescharacteristic
184#14519734—21no—
185#14519733—21no—
186#14519733—21no—
187#14519733—21no—
188#14519733—21no—
189#14519733D411yescharacteristic
190#14519733D411yescharacteristic
191C2×C4⋊Dic61C2×C411yescharacteristic
192C2×#11758196—21no—
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61—21no—
198#125×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201C22⋊Q8×C61C2×C411yescharacteristic
202C4×Q8×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204#117×C61—21no—
205#117×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C2×C22⋊D61C22⋊C411yescharacteristic
213C2×C22⋊D61C22⋊C411yescharacteristic
214C22×Dic61—21no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758224—22no—
220#11758224—22no—
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—42no—
230C2×Dic122—42no—
231C2×Dic122C22⋊C411yescharacteristic
232C2×Dic122C22×C411yescharacteristic
233#11758217—42no—
234#11758217—42no—
235#11758217—81no—
236C2×#92420—21no—
237C2×#92420—21no—
238C2×#92420—21no—
239C2×#92420—21no—
240C2×#92420—21no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—42no—
245C2×#92420—42no—
246C2×#92420—81no—
247#11758213—42no—
248#11758213—81no—
249D61⋊C8—42no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C22⋊C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61C22⋊C411yescharacteristic
264C22⋊C4×C61C22⋊C411yescharacteristic
265C42×C61—21no—
266C42×C61—21no—
267C42×C61C22×C411yescharacteristic
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61C22⋊C411yescharacteristic
272C22⋊Dic61C22⋊C411yescharacteristic
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198C22⋊C411yescharacteristic
278#11758198C22⋊C411yescharacteristic
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
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—21no—
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2411yescharacteristic
327C23×C61C2×C22⋊C411yescharacteristic
328C23×C61C2×C22⋊C411yescharacteristic
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—41no—
331D4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—42no—
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C23×C411yescharacteristic
344C22⋊D61—22no—
345C22⋊D61—22no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—42no—
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61AGL(1,ℤ/8)12yes—
363C2×Dic61#13712yes—
364C2×Dic61C22×D411yescharacteristic
365C2×Dic61C22×D411yescharacteristic
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—41no—
371Dic122—22no—
372Dic122—41no—
373Dic122—41no—
374Dic122—41no—
375Dic122—41no—
376Dic122—41no—
377Dic122—41no—
378Dic122—42no—
379Dic122—42no—
380Dic122—41no—
381#92420—41no—
382#92420—41no—
383#92420—41no—
384#92420—41no—
385#92420—41no—
386#92420—41no—
387#92420—41no—
388#92420—41no—
389#17763—611nomaximal, Sylow
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61#41712yes—
396C22×C61C22×C22⋊C411yescharacteristic
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—41no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—41no—
414Dic61—41no—
415Dic61—41no—
416Dic61—41no—
417Dic61#41712yes—
418Dic61C2×AGL(1,ℤ/8)11yescharacteristic
419Dic61C2×#13711yescharacteristic
420Dic61#57711yescharacteristic
421Dic61#57811yescharacteristic
422#3509—611no—
423#2989—611no—
424#2906—611no—
425#1561—611no—
426#1561—611no—
427#1559—611no—
428#1559—611no—
429#1552—611no—
430#1552—611no—
431#1550—611no—
432#1550—611no—
433#1550—611no—
434#1546—611no—
435#1542—611no—
436C2×#332—611no—
437C2×C61—22no—
438C2×C61—41no—
439C2×C61#288911yescharacteristic
440C2×C61C2×#41711yescharacteristic
441C2×C61#289811yescharacteristic
442D61—41no—
443C2×#131—1221no—
444#557—611no—
445#557—611no—
446#557—1221no—
447#556—611no—
448#556—611no—
449#556—1221no—
450#552—611no—
451#552—611no—
452#552—611no—
453#552—1221no—
454#552—1221no—
455#552#692311yescharacteristic
456#541—1221no—
457#541—1221no—
458#536—1221no—
459#533—611no—
460#533—611no—
461#533—611no—
462#533—611no—
463#533—611no—
464C2×C4⋊Q8—611no—
465#519—1221no—
466C4×#41—611no—
467#446—1221no—
468#436—1221no—
469#435—1221no—
470#435—1221no—
471#432—611no—
472#432—611no—
473#431—611no—
474#424—1221no—
475#424—1221no—
476#424—1221no—
477#423—611no—
478#423—611no—
479#423—611no—
480#423—611no—
481#423—611no—
482C2×C4⋊C8—611no—
483C2×C4⋊C8—611no—
484C2×C4⋊C8—611no—
485C2×C4⋊C8—611no—
486#333—611no—
487#333—611no—
488#333—611no—
489#333—611no—
490#332—611no—
491#332—611no—
492#332—611no—
493#332—611no—
494#332—611no—
495#332—611no—
496#332—611no—
497#332—611no—
498#332—611no—
499#332—611no—
500#332—611no—
501#332—611no—
502C61#1776311yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C22×Q8—1221no—
505#131—2444no—
506C2×M16—1221no—
507C2×M16—1221no—
508C2×M16—1221no—
509C2×M16—1221no—
510C2×M16—1221no—
511C22×C8—1221no—
512C22×C8—1221no—
513C22×C8—1221no—
514C22×C8—1221no—
515C4⋊Q8—611no—
516C4⋊Q8—611no—
517C4⋊Q8—611no—
518C4⋊Q8—611no—
519C4⋊Q8—611no—
520C4⋊Q8—611no—
521C4⋊Q8—1221no—
522C4⋊Q8—1221no—
523C4⋊Q8—1221no—
524C4⋊Q8—1221no—
525#126—21no—
526#126—1221no—
527#126—1221no—
528#126—1221no—
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#126—1221no—
533#125—21no—
534#125—611no—
535#125—611no—
536#125—611no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125—1221no—
541#125—1221no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125—1221no—
547#125C2×#692311yescharacteristic
548#124—1221no—
549#124—1221no—
550#123—21no—
551#123—1221no—
552#123—1221no—
553#123—1221no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—611no—
557C22⋊Q8—611no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563C22⋊Q8—1221no—
564C22⋊Q8—1221no—
565C22⋊Q8C2×#692311yescharacteristic
566C22⋊Q8C2×#692311yescharacteristic
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×Q8—1221no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×Q8C2×#692311yescharacteristic
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4C2×#692311yescharacteristic
592#117—21no—
593#117—611no—
594#117—611no—
595#117—611no—
596#117—611no—
597#117—611no—
598#117—611no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117C2×#692311yescharacteristic
606C2×C4⋊C4—611no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4C2×#692311yescharacteristic
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—611no—
612C4⋊C8—611no—
613C4⋊C8—611no—
614C4⋊C8—611no—
615C4⋊C8—611no—
616C4⋊C8—611no—
617C4⋊C8—611no—
618C4⋊C8—611no—
619C4⋊C8—611no—
620C4⋊C8—1221no—
621C4⋊C8—1221no—
622C4⋊C8—1221no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C22⋊C8—1221no—
630C22⋊C8—1221no—
631C22⋊C8—1221no—
632#97—1221no—
633#97—1221no—
634C4×C8—1221no—
635#41—1222no—
636#41—1222no—
637C2×Q8—611no—
638C2×Q8—611no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8—1221no—
644C2×Q8—2442no—
645C2×Q8—2442no—
646C2×Q8C22×#692311yescharacteristic
647C2×D4—611no—
648C2×D4—611no—
649C2×D4C22⋊#692311yescharacteristic
650C22×C4—21no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—1221no—
659C22×C4C22×#692311yescharacteristic
660C22×C4C22×#692311yescharacteristic
661M16—4881no—
662M16—4881no—
663M16—2442no—
664M16—2442no—
665M16—2442no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—4881no—
675C2×C8—2442no—
676C2×C8—2442no—
677C2×C8—2442no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—1221no—
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⋊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⋊C4C22⋊#692311yescharacteristic
716C4⋊C4C22×#692311yescharacteristic
717C4⋊C4C22×#692311yescharacteristic
718C4⋊C4C22×#692311yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—611no—
723C22⋊C4—611no—
724C22⋊C4—611no—
725C22⋊C4—611no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4C22⋊#692311yescharacteristic
734C22⋊C4C22⋊#692311yescharacteristic
735C42—21no—
736C42—21no—
737C42—611no—
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—1221no—
752C42—1221no—
753C42—1221no—
754C42C22×#692311yescharacteristic
755C23—611no—
756C23C2×C22⋊#692311yescharacteristic
757C23C2×C22⋊#692311yescharacteristic
758Q8—41no—
759Q8—1222no—
760Q8—2441no—
761Q8—2441no—
762Q8—2441no—
763Q8—2441no—
764Q8—2441no—
765Q8—2441no—
766Q8—2441no—
767Q8—2442no—
768Q8—2442no—
769D4—22no—
770D4—1222no—
771D4—1222no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—611no—
786C2×C4—611no—
787C2×C4—611no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—2441no—
803C2×C4—2442no—
804C2×C4C2×C22⋊#692311yescharacteristic
805C2×C4C2×C22⋊#692311yescharacteristic
806C2×C4C2×C22⋊#692311yescharacteristic
807C2×C4C2×C22⋊#692311yescharacteristic
808C2×C4C23×#692311yescharacteristic
809C8—2441no—
810C8—2441no—
811C8—2441no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C8—2441no—
816C8—2441no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—1221no—
823C22—1221no—
824C22—1221no—
825C22#1684075312yes—
826C22C22×C22⋊#692311yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—611no—
837C4—611no—
838C4—612no—
839C4—611no—
840C4—611no—
841C4—1221no—
842C4—1221no—
843C4—1221no—
844C4—1221no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C2—22no—
850C2—41no—
851C2—2441no—
852C2#2146243111yescharacteristic
853C2C2×#1684075311yescharacteristic
854C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#552C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758224D4
cosocleC4×Dic61C24
hypercenter#552#6923
hypocenterC61#17763
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
3. #21461359C2semidirect
4. #21461358C2semidirect
5. #21461355C2semidirect
6. #21461354C2semidirect
7. #21461341C2semidirect
8. #21461340C2semidirect
9. #21461337C2semidirect
10. #21461337C2semidirect
11. #21461336C2semidirect
12. #21461328C2semidirect
13. #21461321C2semidirect
14. C2×#16840621C2semidirect
502. C61#17763semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214624662
#214613592
#214613582
#214613552
#214613542
#214613412
#214613402
#214613372
#214613362
#214613282
#214613212
C2×#168406212
#214596972
#1776361