Finite Group Databasebeta

← #30611689

Subgroups — #30611689

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462658C211yesmaximal, characteristic
2#21462658C211yesmaximal, characteristic
3#21461311C211yesmaximal, characteristic, complemented
4#21461302C211yesmaximal, characteristic, complemented
5#21461301C211yesmaximal, characteristic, complemented
6#21461293C211yesmaximal, characteristic, complemented
7#21461292C211yesmaximal, characteristic, complemented
8#21461291C211yesmaximal, characteristic, complemented
9#21461291C211yesmaximal, characteristic, complemented
10#21461282C211yesmaximal, characteristic, complemented
11#21461282C211yesmaximal, characteristic, complemented
12#21461277C211yesmaximal, characteristic, complemented
13D61⋊#330C211yesmaximal, characteristic, complemented
14C2×#16840619C211yesmaximal, characteristic, complemented
15#21459642C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840792—21no—
19#16840792—21no—
20#16840791—21no—
21#16840791—21no—
22#16840789—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic
25#16840785C2211yescharacteristic
26#16840784C2211yescharacteristic
27#16840784C2211yescharacteristic
28#16840782C2211yescharacteristic
29#16840782C2211yescharacteristic
30C4×#11758213C2211yescharacteristic
31C4×#11758213C2211yescharacteristic
32#16840721C2211yescharacteristic
33#16840721C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36#16840619C2211yescharacteristic
37#16840619C2211yescharacteristic
38#16840619C2211yescharacteristic
39#16840619C2211yescharacteristic
40#16840619C2211yescharacteristic
41#16840619C2211yescharacteristic
42#16840619C2211yescharacteristic
43#16840619C2211yescharacteristic
44#16840619C2211yescharacteristic
45#16840619C2211yescharacteristic
46#16840619C2211yescharacteristic
47#16840619C2211yescharacteristic
48#16840619C2211yescharacteristic
49#16840619C2211yescharacteristic
50#16840619C2211yescharacteristic
51#16840619C2211yescharacteristic
52#16840489—21no—
53#16840487—21no—
54#16840473—21no—
55#16840470—21no—
56#16840470—21no—
57#16840468—21no—
58#16840466—21no—
59#16840466—21no—
60#16840392C411yescharacteristic
61#16840392C411yescharacteristic
62#16840390C411yescharacteristic
63#16840389C411yescharacteristic
64#16840389C411yescharacteristic
65#16840317C2211yescharacteristic
66#16840317C2211yescharacteristic
67#16840315C2211yescharacteristic
68C2×#14519768C2211yescharacteristic
69#125×D61C2211yescharacteristic
70#125×D61C2211yescharacteristic
71#16840243C411yescharacteristic
72#16840242C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#544C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—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
108#14519777C2×C411yescharacteristic
109#14519777C2×C411yescharacteristic
110#14519776—21no—
111#14519776—21no—
112#14519776—21no—
113#14519776C2×C411yescharacteristic
114#14519776C2×C411yescharacteristic
115#14519775—21no—
116#14519775—21no—
117#14519769C2×C411yescharacteristic
118#14519769C2×C411yescharacteristic
119#14519768—21no—
120#14519768—21no—
121#14519768—21no—
122#14519768C2×C411yescharacteristic
123#14519768C2×C411yescharacteristic
124#14519768C2311yescharacteristic
125#14519768C2311yescharacteristic
126#14519768C2311yescharacteristic
127#14519768C2311yescharacteristic
128#14519767—21no—
129#14519767—21no—
130#14519767—21no—
131#14519767—21no—
132#14519767—21no—
133#14519767—21no—
134#14519767—21no—
135#14519767—21no—
136#14519757—21no—
137#14519757—21no—
138#14519757—21no—
139#14519757—21no—
140#14519755—21no—
141#14519755—21no—
142#14519755—21no—
143#14519755—21no—
144#14519754—21no—
145#14519754—21no—
146#14519754—21no—
147#14519754—21no—
148#14519753—21no—
149#14519753—21no—
150#14519753—21no—
151#14519753—21no—
152Q8×Dic61—21no—
153Q8×Dic61—21no—
154C4×Dic122—21no—
155C4×Dic122—21no—
156C4×Dic122—21no—
157#14519742—21no—
158#14519742—21no—
159#14519742—21no—
160#14519742D411yescharacteristic
161#14519742D411yescharacteristic
162C4×D244—21no—
163#14519739—21no—
164#14519739D411yescharacteristic
165#14519739D411yescharacteristic
166C4×C22⋊D61—21no—
167C4×C22⋊D61—21no—
168#14519737—21no—
169#14519737—21no—
170#14519737D411yescharacteristic
171#14519737D411yescharacteristic
172#14519737D411yescharacteristic
173#14519737D411yescharacteristic
174#14519736C2×C411yescharacteristic
175#14519735C2×C411yescharacteristic
176#14519735C2×C411yescharacteristic
177#14519735C2×C411yescharacteristic
178#14519735C2×C411yescharacteristic
179#14519734C2×C411yescharacteristic
180#14519734C2×C411yescharacteristic
181C2×C4⋊Dic61—21no—
182C2×C4⋊Dic61C2×C411yescharacteristic
183C2×#11758196—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61C2×C411yescharacteristic
189C4⋊C4×D61C2×C411yescharacteristic
190C4⋊C4×D61C2×C411yescharacteristic
191C4⋊C4×D61C2×C411yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic
197C4⋊Q8×C61C2×C411yescharacteristic
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic
200#125×C61C2×C411yescharacteristic
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203#117×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61C22×C411yescharacteristic
210C2×C22⋊D61C22⋊C411yescharacteristic
211C2×C22⋊D61C22⋊C411yescharacteristic
212C22×Dic61—21no—
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215#11758222—24no—
216C2×D244C22⋊C411yescharacteristic
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C22×C411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122C22⋊C411yescharacteristic
232C2×#92420—21no—
233C2×#92420—21no—
234C2×#92420—21no—
235C2×#92420—21no—
236C2×#92420—21no—
237C2×#92420—21no—
238C2×#92420—21no—
239C2×#92420—21no—
240C2×#92420—42no—
241C2×#92420—42no—
242#11758213—42no—
243#11758213—42no—
244D61⋊C8—42no—
245D61⋊C8—42no—
246C4⋊C4×C61—21no—
247C4⋊C4×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
255C4⋊C4×C61C22×C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C22⋊C4×C61—21no—
260C22⋊C4×C61C22⋊C411yescharacteristic
261C22⋊C4×C61C22⋊C411yescharacteristic
262C42×C61—21no—
263C42×C61C22×C411yescharacteristic
264C42×C61C22×C411yescharacteristic
265C22⋊Dic61—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198C22⋊C411yescharacteristic
271#11758198C22⋊C411yescharacteristic
272#11758198C22⋊C411yescharacteristic
273#11758198C22⋊C411yescharacteristic
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C22×C411yescharacteristic
284C4⋊Dic61C22×C411yescharacteristic
285C4⋊Dic61C22×C411yescharacteristic
286C4⋊Dic61C22×C411yescharacteristic
287#11758196—21no—
288#11758196—21no—
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#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2411yescharacteristic
320C23×C61C2×C22⋊C411yescharacteristic
321C22×D61C2×C22⋊C411yescharacteristic
322C22×D61C2×C22⋊C411yescharacteristic
323Q8×C61—81no—
324Q8×C61—81no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—81no—
331C2×C4×C61C2×C22⋊C411yescharacteristic
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C23×C411yescharacteristic
337C22⋊D61—22no—
338C22⋊D61#10114yes—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—81no—
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C22×D411yescharacteristic
351C2×Dic61C22×D411yescharacteristic
352D244—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—81no—
360C4×D61—81no—
361C4×D61—81no—
362C4×D61—81no—
363Dic122—22no—
364Dic122—81no—
365Dic122—81no—
366Dic122—81no—
367Dic122—81no—
368#92420—22no—
369#92420—22no—
370#92420—41no—
371#92420—41no—
372#92420—41no—
373#92420—41no—
374#92420—41no—
375#92420—41no—
376#17689—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61C2×#10112yes—
380C22×C61C22×C22⋊C411yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61C2×#10112yes—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—41no—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—41no—
403Dic61—41no—
404Dic61—41no—
405Dic61—41no—
406Dic61C2×#10112yes—
407#3504—611no—
408#2970—611no—
409#2970—611no—
410#1537—611no—
411#1534—611no—
412#1534—611no—
413#1531—611no—
414#1531—611no—
415#1531—611no—
416#1531—611no—
417#1528—611no—
418#1528—611no—
419#1526—611no—
420C2×#330—611no—
421C2×#330—611no—
422C2×C61—22no—
423C2×C61C22×#10111yescharacteristic
424C2×C61#290111yescharacteristic
425C2×C61#290111yescharacteristic
426D61—22no—
427D61—41no—
428#557—1221no—
429#557—1221no—
430#554—1221no—
431#554—1221no—
432#554—1221no—
433#554—1221no—
434#554—1221no—
435#554—1221no—
436#544—611no—
437#544—611no—
438#544—611no—
439#544—611no—
440#544—611no—
441#544#692311yescharacteristic
442#533—611no—
443#533—611no—
444#533—611no—
445C2×#125—611no—
446C2×#125—611no—
447C2×#125—611no—
448#520—611no—
449#520—611no—
450C4×#41—611no—
451#446—1221no—
452#446—1221no—
453#435—1221no—
454#435—1221no—
455#435—1221no—
456#435—1221no—
457C8×D4—1221no—
458C8×D4—1221no—
459#432—611no—
460#432—611no—
461#432—611no—
462#432—611no—
463#432—611no—
464#432—611no—
465C4×M16—611no—
466C4×M16—611no—
467C2×#97—611no—
468C2×#97—611no—
469C2×#97—611no—
470C2×#97—611no—
471#330—611no—
472#330—611no—
473#330—611no—
474#330—611no—
475#330—611no—
476#330—611no—
477#330—611no—
478#330—611no—
479#330—611no—
480#330—611no—
481#330—611no—
482#330—611no—
483#330—611no—
484#330—611no—
485#330—611no—
486#330—611no—
487C61#1768911yescharacteristic, complemented, Sylow
488C2×#41—611no—
489C2×M16—1221no—
490C2×M16—1221no—
491C22×C8—1221no—
492C22×C8—1221no—
493C22×C8—1221no—
494C22×C8—1221no—
495C4⋊Q8—21no—
496C4⋊Q8—611no—
497C4⋊Q8—611no—
498C4⋊Q8—611no—
499C4⋊Q8—611no—
500C4⋊Q8—1221no—
501C4⋊Q8—1221no—
502C4⋊Q8—1221no—
503C4⋊Q8—1221no—
504C4⋊Q8—1221no—
505C4⋊Q8C2×#692311yescharacteristic
506C4⋊Q8C2×#692311yescharacteristic
507#125—21no—
508#125—611no—
509#125—611no—
510#125—611no—
511#125—611no—
512#125—611no—
513#125—611no—
514#125—611no—
515#125—611no—
516#125—1221no—
517#125—1221no—
518#125—1221no—
519#125—1221no—
520#125—1221no—
521#125—1221no—
522#125—1221no—
523#125—1221no—
524#125—1221no—
525#125—1221no—
526#125—1221no—
527#125C2×#692311yescharacteristic
528#125C2×#692311yescharacteristic
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—1221no—
532C22⋊Q8—1221no—
533C22⋊Q8—1221no—
534C22⋊Q8—1221no—
535C22⋊Q8—1221no—
536C22⋊Q8—1221no—
537C22⋊Q8—1221no—
538C22⋊Q8—1221no—
539C22⋊Q8—1221no—
540C22⋊Q8—1221no—
541C22⋊Q8—1221no—
542C22⋊Q8—1221no—
543C22⋊Q8—1221no—
544C22⋊Q8—1221no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547C4×Q8—611no—
548C4×Q8—611no—
549C4×Q8—1221no—
550C4×Q8—1221no—
551C4×Q8—1221no—
552C4×Q8—1221no—
553C4×Q8—1221no—
554C4×Q8—1221no—
555C4×Q8—1221no—
556C4×Q8—1221no—
557C4×D4—611no—
558C4×D4—611no—
559C4×D4—611no—
560C4×D4—611no—
561C4×D4—611no—
562C4×D4—611no—
563C4×D4—1221no—
564C4×D4—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569#117—611no—
570#117—611no—
571#117—611no—
572#117—611no—
573#117—611no—
574#117—611no—
575#117—611no—
576#117C2×#692311yescharacteristic
577#117C2×#692311yescharacteristic
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—1221no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4—1221no—
586C2×C4⋊C4—1221no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4C2×#692311yescharacteristic
590C2×C42—611no—
591C2×C42—611no—
592C2×C42—611no—
593C4⋊C8—1221no—
594C4⋊C8—1221no—
595C4⋊C8—1221no—
596C4⋊C8—1221no—
597C4⋊C8—1221no—
598C4⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604C22⋊C8—1221no—
605#97—611no—
606#97—611no—
607#97—611no—
608#97—611no—
609#97—611no—
610#97—611no—
611#97—611no—
612#97—611no—
613#97—1221no—
614#97—1221no—
615#97—1221no—
616#97—1221no—
617C4×C8—1221no—
618C4×C8—1221no—
619#41—1224no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—611no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×D4—611no—
628C2×D4—611no—
629C2×D4—611no—
630C22×C4—21no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4C22×#692311yescharacteristic
645M16—2442no—
646M16—2442no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—2442no—
656C2×C8—2442no—
657C2×C8—2442no—
658C2×C8—2442no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—611no—
667C4⋊C4—611no—
668C4⋊C4—611no—
669C4⋊C4—611no—
670C4⋊C4—611no—
671C4⋊C4—611no—
672C4⋊C4—611no—
673C4⋊C4—611no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4C22⋊#692311yescharacteristic
700C4⋊C4C22⋊#692311yescharacteristic
701C4⋊C4C22×#692311yescharacteristic
702C4⋊C4C22×#692311yescharacteristic
703C4⋊C4C22×#692311yescharacteristic
704C4⋊C4C22×#692311yescharacteristic
705C22⋊C4—21no—
706C22⋊C4—611no—
707C22⋊C4—611no—
708C22⋊C4—611no—
709C22⋊C4—611no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
715C22⋊C4C22⋊#692311yescharacteristic
716C22⋊C4C22⋊#692311yescharacteristic
717C42—21no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—611no—
723C42—611no—
724C42—611no—
725C42—611no—
726C42—1221no—
727C42—1221no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42C22×#692311yescharacteristic
732C42C22×#692311yescharacteristic
733C23—611no—
734C23—611no—
735C23C2×C22⋊#692311yescharacteristic
736Q8—81no—
737Q8—81no—
738Q8—1222no—
739Q8—4881no—
740Q8—4881no—
741Q8—4881no—
742Q8—4881no—
743D4—614no—
744D4—1222no—
745D4—1222no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—81no—
752C2×C4—611no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—4881no—
765C2×C4—4881no—
766C2×C4—4881no—
767C2×C4—4881no—
768C2×C4—4881no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C2×C22⋊#692311yescharacteristic
776C2×C4C2×C22⋊#692311yescharacteristic
777C2×C4C2×C22⋊#692311yescharacteristic
778C2×C4C2×C22⋊#692311yescharacteristic
779C2×C4C2×C22⋊#692311yescharacteristic
780C2×C4C23×#692311yescharacteristic
781C8—1222no—
782C8—1222no—
783C8—2441no—
784C8—2441no—
785C8—2441no—
786C8—2441no—
787C8—2441no—
788C8—2441no—
789C22—21no—
790C22—21no—
791C22—612no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22D61⋊#10112yes—
798C22C22×C22⋊#692311yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—612no—
810C4—1221no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—1221no—
815C4—2441no—
816C4—2441no—
817C4—2441no—
818C4—2441no—
819C2—22no—
820C2—1222no—
821C2—2441no—
822C2C2×D61⋊#10111yescharacteristic
823C2#2146244911yescharacteristic
824C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC4×Dic61C24
hypercenter#544#6923
hypocenterC61#17689
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #21461311C2semidirect
4. #21461302C2semidirect
5. #21461301C2semidirect
6. #21461293C2semidirect
7. #21461292C2semidirect
8. #21461291C2semidirect
9. #21461291C2semidirect
10. #21461282C2semidirect
11. #21461282C2semidirect
12. #21461277C2semidirect
13. D61⋊#330C2semidirect
14. C2×#16840619C2semidirect
487. C61#17689semidirect

Maximal subgroups

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

subgroupindex
#214626582
#214613112
#214613022
#214613012
#214612932
#214612922
#214612912
#214612822
#214612772
D61⋊#3302
C2×#168406192
#214596422
#1768961