Finite Group Databasebeta

← #30611925

Subgroups — #30611925

Order 15616.

896 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462739C211yesmaximal, characteristic
2#21462517C211yesmaximal, characteristic
3#21461355C211yesmaximal, characteristic, complemented
4#21461354C211yesmaximal, characteristic, complemented
5#21461349C211yesmaximal, characteristic, complemented
6#21461348C211yesmaximal, characteristic, complemented
7#21461345C211yesmaximal, characteristic, complemented
8#21461344C211yesmaximal, characteristic, complemented
9#21461337C211yesmaximal, characteristic, complemented
10#21461334C211yesmaximal, characteristic, complemented
11#21461329C211yesmaximal, characteristic, complemented
12#21461328C211yesmaximal, characteristic, complemented
13#21461321C211yesmaximal, characteristic, complemented
14C2×#16840621C211yesmaximal, characteristic, complemented
15#21459633C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic
23#16840785C2211yescharacteristic
24#16840782C2211yescharacteristic
25#16840782C2211yescharacteristic
26#16840780C2211yescharacteristic
27#16840779C2211yescharacteristic
28#16840779C2211yescharacteristic
29#16840767C2211yescharacteristic
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34#16840735—21no—
35#16840726—21no—
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
52Q8×Dic122C411yescharacteristic
53#16840492C411yescharacteristic
54#16840489—21no—
55#16840470C411yescharacteristic
56#16840470C411yescharacteristic
57#16840469C411yescharacteristic
58#16840467C411yescharacteristic
59#16840467C411yescharacteristic
60D4×Dic122—21no—
61#16840425—21no—
62#16840425—21no—
63#16840392—21no—
64#16840391—21no—
65#16840391—21no—
66#16840316C2211yescharacteristic
67#16840314C2211yescharacteristic
68#16840314C2211yescharacteristic
69C2×#14519776C2211yescharacteristic
70C2×#14519776C2211yescharacteristic
71C4⋊Q8×D61C2211yescharacteristic
72#16840241—21no—
73C4×#11758224C2211yescharacteristic
74C61×#554C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844C2311yescharacteristic
84#14519844C2311yescharacteristic
85#14519844C2311yescharacteristic
86#14519844C2311yescharacteristic
87#14519844C2311yescharacteristic
88#14519844C2311yescharacteristic
89#14519844C2311yescharacteristic
90#14519844C2311yescharacteristic
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93#14519834—21no—
94#14519834—21no—
95#14519834—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99C22⋊#92420—21no—
100#14519832—21no—
101#14519832—21no—
102#14519832—21no—
103#14519832—21no—
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758224D411yescharacteristic
108C22×Dic122—21no—
109C22×Dic122—21no—
110C2×Q8×D61—21no—
111#14519777—21no—
112#14519777C2×C411yescharacteristic
113#14519776—21no—
114#14519776—21no—
115#14519776—21no—
116#14519776—21no—
117#14519776—21no—
118#14519776—21no—
119#14519776—21no—
120#14519776—21no—
121#14519776C2×C411yescharacteristic
122#14519776C2×C411yescharacteristic
123#14519776C2×C411yescharacteristic
124#14519776C2×C411yescharacteristic
125#14519776C2311yescharacteristic
126#14519776C2311yescharacteristic
127#14519776C2311yescharacteristic
128#14519775—21no—
129#14519775—21no—
130#14519775—21no—
131#14519775C2311yescharacteristic
132#14519768—21no—
133#14519767—21no—
134#14519767—21no—
135#14519767—21no—
136#14519767—21no—
137#14519767—21no—
138#14519767—21no—
139#14519767—21no—
140#14519757—21no—
141#14519757—21no—
142#14519757C2×C411yescharacteristic
143#14519756—21no—
144#14519756—21no—
145#14519756C2×C411yescharacteristic
146#14519756C2×C411yescharacteristic
147#14519755—21no—
148#14519755—21no—
149#14519755—21no—
150#14519754—21no—
151#14519754—21no—
152#14519754—21no—
153#14519754—21no—
154#14519754—21no—
155#14519754—21no—
156#14519753C2×C411yescharacteristic
157Q8×Dic61C2×C411yescharacteristic
158Q8×Dic61C2×C411yescharacteristic
159C4×Dic122—21no—
160C4×Dic122—21no—
161C4×Dic122C2×C411yescharacteristic
162C4×Dic122C2×C411yescharacteristic
163#14519742—21no—
164#14519742—21no—
165#14519742—21no—
166#14519742C2×C411yescharacteristic
167#14519742C2×C411yescharacteristic
168#14519742D411yescharacteristic
169D4×Dic61—21no—
170D4×Dic61D411yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61C2×C411yescharacteristic
174C4×C22⋊D61C2×C411yescharacteristic
175#14519737—21no—
176#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519735D411yescharacteristic
180#14519734—21no—
181#14519733—21no—
182#14519733—21no—
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C2×C4⋊Dic61C2×C411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic
187C2×#11758196—21no—
188C2×#11758196—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61C2×C411yescharacteristic
191C4⋊C4×D61C2×C411yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#125×C61—21no—
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic
201C4×Q8×C61C2×C411yescharacteristic
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C2×C4⋊C4×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C2×C22⋊D61C22⋊C411yescharacteristic
214C2×C22⋊D61C22⋊C411yescharacteristic
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221Q8×D61—81no—
222Q8×D61—81no—
223#11758224—22no—
224#11758224—22no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—81no—
239C2×Dic122—81no—
240C2×Dic122—81no—
241C2×Dic122—81no—
242C2×Dic122C22⋊C411yescharacteristic
243C2×Dic122C22×C411yescharacteristic
244#11758217—42no—
245#11758217—81no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—21no—
252C2×#92420—21no—
253C2×#92420—21no—
254C2×#92420—42no—
255C2×#92420—81no—
256#11758213—81no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C22⋊C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C4⋊C4×C61C22×C411yescharacteristic
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61C22⋊C411yescharacteristic
270C22⋊C4×C61C22⋊C411yescharacteristic
271C42×C61—21no—
272C42×C61C22×C411yescharacteristic
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61C22⋊C411yescharacteristic
276C22⋊Dic61C22⋊C411yescharacteristic
277#11758198—21no—
278#11758198—21no—
279#11758198C22⋊C411yescharacteristic
280#11758198C22⋊C411yescharacteristic
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61C22⋊C411yescharacteristic
288C4⋊Dic61C22×C411yescharacteristic
289C4⋊Dic61C22×C411yescharacteristic
290C4⋊Dic61C22×C411yescharacteristic
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#11758196—21no—
307#11758196—21no—
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2411yescharacteristic
326C23×C61C2×C22⋊C411yescharacteristic
327C23×C61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329Q8×C61—41no—
330Q8×C61—81no—
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—81no—
339C2×C4×C61—81no—
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—22no—
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—21no—
357C2×Dic61—81no—
358C2×Dic61—81no—
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61#13712yes—
365C2×Dic61#13712yes—
366C2×Dic61C22×D411yescharacteristic
367C2×Dic61C22×D411yescharacteristic
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—41no—
373C4×D61—81no—
374C4×D61—81no—
375Dic122—22no—
376Dic122—41no—
377Dic122—41no—
378Dic122—41no—
379Dic122—41no—
380Dic122—41no—
381Dic122—41no—
382Dic122—41no—
383Dic122—81no—
384Dic122—81no—
385Dic122—81no—
386Dic122—81no—
387Dic122—81no—
388#92420—41no—
389#92420—41no—
390#92420—41no—
391#92420—41no—
392#92420—41no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#17761—611nomaximal, Sylow
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61#41912yes—
403C22×C61C22×C22⋊C411yescharacteristic
404C2×D61—21no—
405C2×D61—21no—
406C2×D61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—41no—
416Dic61—21no—
417Dic61—21no—
418Dic61—21no—
419Dic61—21no—
420Dic61—41no—
421Dic61—41no—
422Dic61—41no—
423Dic61—41no—
424Dic61#41912yes—
425Dic61C2×#13711yescharacteristic
426Dic61C2×#13711yescharacteristic
427Dic61#57611yescharacteristic
428Dic61#57711yescharacteristic
429#3503—611no—
430#2989—611no—
431#2925—611no—
432#1559—611no—
433#1559—611no—
434#1556—611no—
435#1556—611no—
436#1554—611no—
437#1554—611no—
438#1550—611no—
439#1549—611no—
440#1546—611no—
441#1546—611no—
442#1542—611no—
443C2×#332—611no—
444C2×C61—22no—
445C2×C61—41no—
446C2×C61#288911yescharacteristic
447C2×C61C2×#41911yescharacteristic
448C2×C61#289711yescharacteristic
449D61—41no—
450Q82—611no—
451Q82—611no—
452#557—1221no—
453#554—611no—
454#554—611no—
455#554—611no—
456#554—611no—
457#554—611no—
458#554#692311yescharacteristic
459D4×Q8—1221no—
460D4×Q8—1221no—
461D4×Q8—1221no—
462#544—1221no—
463#544—1221no—
464#544—1221no—
465#533—611no—
466#533—611no—
467#533—611no—
468C2×C4⋊Q8—611no—
469C2×C4⋊Q8—611no—
470C2×C4⋊Q8—611no—
471#520—1221no—
472C4×#41—611no—
473#446—1221no—
474#436—1221no—
475#435—1221no—
476#435—1221no—
477#433—1221no—
478#433—1221no—
479#432—611no—
480#432—611no—
481#432—611no—
482#432—611no—
483#431—611no—
484#431—611no—
485#431—611no—
486#423—611no—
487#423—611no—
488#423—611no—
489C2×C4⋊C8—611no—
490C2×C4⋊C8—611no—
491#408—1221no—
492#405—1221no—
493#333—611no—
494#333—611no—
495#333—611no—
496#333—611no—
497#332—611no—
498#332—611no—
499#332—611no—
500#332—611no—
501#332—611no—
502#332—611no—
503#332—611no—
504#332—611no—
505#332—611no—
506#332—611no—
507#332—611no—
508#332—611no—
509C61#1776111yescharacteristic, complemented, Sylow
510C2×#41—611no—
511C22×Q8—1221no—
512C22×Q8—1221no—
513C22×Q8—1221no—
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16—1221no—
517C22×C8—1221no—
518C22×C8—1221no—
519C4⋊Q8—611no—
520C4⋊Q8—611no—
521C4⋊Q8—611no—
522C4⋊Q8—611no—
523C4⋊Q8—611no—
524C4⋊Q8—611no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—611no—
528C4⋊Q8—1221no—
529C4⋊Q8—1221no—
530C4⋊Q8—1221no—
531C4⋊Q8—1221no—
532C4⋊Q8—1221no—
533C4⋊Q8—1221no—
534C4⋊Q8—1221no—
535C4⋊Q8—1221no—
536C4⋊Q8—1221no—
537C4⋊Q8—1221no—
538C4⋊Q8—1221no—
539C4⋊Q8—1221no—
540C4⋊Q8C2×#692311yescharacteristic
541#125—21no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125—1221no—
547#125—1221no—
548#125—1221no—
549#125—1221no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
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—
563C22⋊Q8—1221no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8C2×#692311yescharacteristic
570C22⋊Q8C2×#692311yescharacteristic
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×Q8—1221no—
582C4×Q8—1221no—
583C4×Q8C2×#692311yescharacteristic
584C4×D4—21no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4C2×#692311yescharacteristic
596#117—611no—
597#117—611no—
598#117—611no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4C2×#692311yescharacteristic
610C2×C4⋊C4C2×#692311yescharacteristic
611C2×C42—611no—
612C2×C42—611no—
613C2×C42—611no—
614C4⋊C8—611no—
615C4⋊C8—611no—
616C4⋊C8—611no—
617C4⋊C8—611no—
618C4⋊C8—611no—
619C4⋊C8—611no—
620C4⋊C8—611no—
621C4⋊C8—611no—
622C4⋊C8—1221no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C22⋊C8—1221no—
628C22⋊C8—1221no—
629C22⋊C8—1221no—
630C22⋊C8—1221no—
631C22⋊C8—1221no—
632C22⋊C8—1221no—
633C22⋊C8—1221no—
634#97—1221no—
635#97—1221no—
636#97—1221no—
637#97—1221no—
638C4×C8—1221no—
639C4×C8—1221no—
640C4×C8—1221no—
641#41—1222no—
642#41—1222no—
643C2×Q8—21no—
644C2×Q8—611no—
645C2×Q8—611no—
646C2×Q8—1221no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—4881no—
655C2×Q8—4881no—
656C2×Q8—4881no—
657C2×Q8—4881no—
658C2×Q8—4881no—
659C2×Q8—4881no—
660C2×Q8C22×#692311yescharacteristic
661C2×D4—611no—
662C2×D4—611no—
663C2×D4C22⋊#692311yescharacteristic
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
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×C4C22×#692311yescharacteristic
678C22×C4C22×#692311yescharacteristic
679M16—4881no—
680M16—4881no—
681M16—2442no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—4881no—
691C2×C8—2442no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
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—1221no—
728C4⋊C4—1221no—
729C4⋊C4C22⋊#692311yescharacteristic
730C4⋊C4C22×#692311yescharacteristic
731C4⋊C4C22×#692311yescharacteristic
732C4⋊C4C22×#692311yescharacteristic
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—611no—
736C22⋊C4—611no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4C22⋊#692311yescharacteristic
744C22⋊C4C22⋊#692311yescharacteristic
745C42—21no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—1221no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42C22×#692311yescharacteristic
761C23—611no—
762C23C2×C22⋊#692311yescharacteristic
763C23C2×C22⋊#692311yescharacteristic
764Q8—41no—
765Q8—81no—
766Q8—1222no—
767Q8—4881no—
768Q8—4881no—
769Q8—4881no—
770Q8—4881no—
771Q8—4881no—
772Q8—2441no—
773Q8—2441no—
774Q8—2441no—
775Q8—2441no—
776Q8—2441no—
777Q8—2441no—
778Q8—2441no—
779D4—22no—
780D4—1222no—
781D4—1222no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—612no—
791C2×C4—612no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—4881no—
814C2×C4—4881no—
815C2×C4—4881no—
816C2×C4—4881no—
817C2×C4—2441no—
818C2×C4C2×C22⋊#692311yescharacteristic
819C2×C4C2×C22⋊#692311yescharacteristic
820C2×C4C2×C22⋊#692311yescharacteristic
821C2×C4C2×C22⋊#692311yescharacteristic
822C2×C4C23×#692311yescharacteristic
823C8—2441no—
824C8—2441no—
825C8—2441no—
826C8—2441no—
827C8—2441no—
828C8—2441no—
829C8—2441no—
830C8—2441no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—1221no—
837C22—1221no—
838C22—1221no—
839C22#1684075512yes—
840C22C22×C22⋊#692311yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—611no—
851C4—611no—
852C4—612no—
853C4—611no—
854C4—611no—
855C4—1221no—
856C4—1221no—
857C4—1221no—
858C4—1221no—
859C4—2441no—
860C4—2441no—
861C4—2441no—
862C4—2441no—
863C2—22no—
864C2—41no—
865C2—2441no—
866C2#2146243111yescharacteristic
867C2C2×#1684075511yescharacteristic
868C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758224D4
cosocleC4×Dic61C24
hypercenter#554#6923
hypocenterC61#17761
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
3. #21461355C2semidirect
4. #21461354C2semidirect
5. #21461349C2semidirect
6. #21461348C2semidirect
7. #21461345C2semidirect
8. #21461344C2semidirect
9. #21461337C2semidirect
10. #21461334C2semidirect
11. #21461329C2semidirect
12. #21461328C2semidirect
13. #21461321C2semidirect
14. C2×#16840621C2semidirect
509. C61#17761semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214625172
#214613552
#214613542
#214613492
#214613482
#214613452
#214613442
#214613372
#214613342
#214613292
#214613282
#214613212
C2×#168406212
#214596332
#1776161