Finite Group Databasebeta

← D61×#3444 #30586720

Subgroups — D61×#3444 #30586720

Order 15616.

8518 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C213yesmaximal, complemented
2#21459115C211yesmaximal, characteristic, complemented
3#21459114C213yesmaximal, complemented
4#21459113C2112yesmaximal, complemented
5#21459112C216yesmaximal, complemented
6#21459111C216yesmaximal, complemented
7#533×D61C213yesmaximal, complemented
8#532×D61C213yesmaximal, complemented
9#529×D61C2112yesmaximal, complemented
10#525×D61C216yesmaximal, complemented
11C4×#41×D61C216yesmaximal, complemented
12C22×C42×D61C211yesmaximal, characteristic, complemented
13C61×#3444C211yesmaximal, characteristic, complemented
14C2×#41×D61C2216yes—
15C23×C4×D61C2213yes—
16#16840319C2213yescomplemented
17#16840318C2216yescomplemented
18#16840317C2216yescomplemented
19#16840316C22112yescomplemented
20#16840315C2216yescomplemented
21#16840314C22112yescomplemented
22#16840313C2213yescomplemented
23#16840312C2213yescomplemented
24#16840311C2216yescomplemented
25#16840310C2213yescomplemented
26#16840309C22112yescomplemented
27#16840308C2216yescomplemented
28#16840307C22112yescomplemented
29C4⋊Q8×D61C2213yescomplemented
30#127×D61C2211yescharacteristic, complemented
31#16840299C22112yescomplemented
32#16840298C22112yescomplemented
33#16840297C22112yescomplemented
34#16840296C22112yescomplemented
35#16840295C22124yescomplemented
36#16840294C22112yescomplemented
37#16840293C22112yescomplemented
38#16840292C22124yescomplemented
39#16840291C22112yescomplemented
40#16840290C22124yescomplemented
41#16840289C22124yescomplemented
42#126×D61C2218yescomplemented
43#125×D61C2216yescomplemented
44#124×D61C2216yescomplemented
45#16840275C22112yescomplemented
46#16840274C2216yescomplemented
47#16840273C2216yescomplemented
48#16840272C22112yescomplemented
49#16840271C22124yescomplemented
50#16840270C22112yescomplemented
51#16840269C2216yescomplemented
52#16840268C22112yescomplemented
53#123×D61C22112yes—
54C22⋊Q8×D61C22112yes—
55#121×D61C22112yes—
56#120×D61C2214yes—
57#41×Dic61C2216yescomplemented
58C4×#11758226C22112yescomplemented
59C4×#11758222C2216yescomplemented
60C4×#11758222C22112yescomplemented
61#16840230C2216yescomplemented
62#16840230C22112yescomplemented
63C4×#11758224C22124yescomplemented
64C4×#11758224C22112yescomplemented
65C4×Q8×D61C22112yescomplemented
66C4×D4×D61C22124yes—
67C4×D4×D61C22112yescomplemented
68#117×D61C2216yes—
69#117×D61C22112yescomplemented
70C22×C4×Dic61C2213yescomplemented
71C2×C42×D61C2213yes—
72C2×C42×D61C2216yes—
73C2×C42×D61C2213yes—
74C2×C42×D61C2213yescomplemented
75C2×C42×D61C2216yescomplemented
76C2×C42×D61C2213yescomplemented
77C2×C42×D61C2214yescomplemented
78C61×#533C2213yescomplemented
79C61×#532C2213yescomplemented
80C61×#529C22112yescomplemented
81C61×#525C2216yescomplemented
82C4×#41×C61C2216yescomplemented
83C22×C42×C61C2211yescharacteristic, complemented
84C24×D61C2311yescharacteristic
85C2×#11758226C2316yes—
86C2×#11758222C23112yes—
87C2×#11758222C2316yes—
88C2×#11758224C23112yes—
89C2×#11758224C2316yes—
90#41×D61—248no—
91C2×Q8×D61C2316yes—
92C2×D4×D61C23112yes—
93C2×D4×D61C2316yes—
94C23×Dic61C2313yes—
95C22×C4×D61—224no—
96C22×C4×D61C2316yes—
97C22×C4×D61C2316yes—
98C22×C4×D61C2313yes—
99C22×C4×D61C2313yes—
100C22×C4×D61C2313yes—
101C22×C4×D61C2316yes—
102C22×C4×D61C2316yes—
103C22×C4×D61C23112yes—
104C22×C4×D61C2313yes—
105#14519777C2313yescomplemented
106#14519776C23112yescomplemented
107#14519775C2316yescomplemented
108#14519774C2311yescharacteristic, complemented
109#14519773C2316yescomplemented
110#14519772C23124yescomplemented
111#14519771C2318yescomplemented
112#14519770C23124yescomplemented
113#14519769C2316yescomplemented
114#14519768C23112yescomplemented
115#14519767C23124yescomplemented
116#14519766C2316yescomplemented
117#14519765C2316yescomplemented
118#14519764C2316yescomplemented
119#14519763C23124yescomplemented
120#14519762C23124yes—
121#14519761C23112yes—
122#14519760C23112yes—
123#14519759C23124yes—
124#14519758C23112yes—
125#14519757C23112yes—
126#14519756C23112yes—
127#14519755C23124yes—
128#14519754C23124yes—
129#14519753C23112yes—
130#14519752C23112yes—
131#14519751C23112yes—
132#14519750C23124yes—
133#14519749C23124yes—
134#14519748C23112yes—
135#14519747C23112yes—
136#14519746C2314yes—
137#14519745C23112yes—
138Q8×Dic61C23112yescomplemented
139C4×Dic122C23124yescomplemented
140C4×Dic122C23112yescomplemented
141#14519742C23124yescomplemented
142#14519742C23112yescomplemented
143C4×D244C23124yes—
144C4×D244C23112yescomplemented
145D4×Dic61C23124yes—
146D4×Dic61C23112yescomplemented
147#14519739C23124yes—
148#14519739C23112yescomplemented
149C4×C22⋊D61C23124yes—
150C4×C22⋊D61C23124yes—
151C4×C22⋊D61C23124yescomplemented
152#14519737C23124yes—
153#14519737C23124yes—
154#14519737C23124yescomplemented
155#14519736C2316yes—
156#14519736C23112yescomplemented
157#14519735C23112yes—
158#14519735C23124yescomplemented
159#14519734C23112yes—
160#14519734C23112yescomplemented
161#14519734C23112yescomplemented
162#14519733C23112yes—
163#14519733C23124yescomplemented
164C4⋊C4×D61C23112yes—
165C4⋊C4×D61C23124yes—
166C22⋊C4×D61C23112yes—
167C22⋊C4×D61C23124yes—
168C2×C4×Dic61C2316yes—
169C2×C4×Dic61C2313yes—
170C2×C4×Dic61C2316yes—
171C2×C4×Dic61C2316yes—
172C2×C4×Dic61C2316yes—
173C2×C4×Dic61C2316yes—
174C2×C4×Dic61C2313yes—
175C2×C4×Dic61C23112yescomplemented
176C42×D61C2311yescharacteristic
177C42×D61C2313yes—
178C42×D61C2316yes—
179C42×D61C2313yes—
180C42×D61C2312yes—
181C42×D61C2311yescharacteristic
182C42×D61C2316yes—
183C42×D61C2313yes—
184C42×D61C2313yes—
185C42×D61C2316yes—
186C42×D61C2316yes—
187C42×D61C2316yes—
188C42×D61C2316yes—
189C42×D61C2316yes—
190C42×D61C2313yes—
191C42×D61C2313yes—
192C42×D61C23112yes—
193C42×D61C23112yescomplemented
194C42×D61C2314yescomplemented
195C2×#41×C61C2316yes—
196C23×C4×C61C2313yes—
197C4⋊Q8×C61C2313yescomplemented
198#127×C61C2311yescharacteristic, complemented
199#126×C61C2318yescomplemented
200#125×C61C2316yescomplemented
201#124×C61C2316yescomplemented
202#123×C61C23112yes—
203C22⋊Q8×C61C23112yes—
204#121×C61C23112yes—
205#120×C61C2314yes—
206C4×Q8×C61C23112yescomplemented
207C4×D4×C61C23124yes—
208C4×D4×C61C23112yescomplemented
209#117×C61C2316yes—
210#117×C61C23112yescomplemented
211C2×C42×C61C2313yes—
212C2×C42×C61C2313yes—
213C2×C42×C61C2316yes—
214C2×C42×C61C2314yescomplemented
215C24×C61C2411yescharacteristic
216C23×D61—212no—
217C23×D61C2413yes—
218C23×D61C2414yes—
219C23×D61C2413yes—
220#41×C61—224no—
221C2×Q8×C61C2416yes—
222C2×D4×C61C24112yes—
223C2×D4×C61C2416yes—
224C22×C4×C61—212no—
225C22×C4×C61C2416yes—
226C22×C4×C61C2416yes—
227C22×C4×C61C2413yes—
228C22×C4×C61C24112yes—
229C22×C4×C61C2413yes—
230C2×C22⋊D61C24112yes—
231C2×C22⋊D61C24112yes—
232C2×C22⋊D61C24112yes—
233C22×Dic61—212no—
234C22×Dic61C2416yes—
235C22×Dic61C2416yes—
236C22×Dic61C2413yes—
237C22×Dic61C24112yes—
238C22×Dic61C2413yes—
239#11758226—224no—
240Q8×D61—224no—
241#11758224—248no—
242#11758224—224no—
243D4×D61—248no—
244D4×D61—224no—
245#11758222—224no—
246#11758222—248no—
247C2×D244C24112yes—
248C2×D244C2416yes—
249C2×C4×D61—212no—
250C2×C4×D61—212no—
251C2×C4×D61—212no—
252C2×C4×D61—224no—
253C2×C4×D61—224no—
254C2×C4×D61—248no—
255C2×C4×D61—224no—
256C2×C4×D61—224no—
257C2×C4×D61#41124yescomplemented
258C2×C4×D61C2416yes—
259C2×C4×D61C2416yes—
260C2×C4×D61C2416yes—
261C2×C4×D61C2416yes—
262C2×C4×D61C2416yes—
263C2×C4×D61C2416yes—
264C2×C4×D61C24112yes—
265C2×C4×D61C24112yes—
266C2×C4×D61C24112yes—
267C2×C4×D61C2413yes—
268C2×C4×D61C2413yes—
269C2×C4×D61C2413yes—
270C2×C4×D61C2413yes—
271C2×Dic122C24112yes—
272C2×Dic122C2416yes—
273C4⋊C4×C61C24112yes—
274C4⋊C4×C61C24124yes—
275C22⋊C4×C61C24112yes—
276C22⋊C4×C61C24124yes—
277C42×C61C2413yes—
278C42×C61C2416yes—
279C42×C61C2413yes—
280C42×C61C2412yes—
281C42×C61C2411yescharacteristic
282C42×C61C24112yes—
283C42×C61C2411yescharacteristic
284C22⋊Dic61C24112yes—
285C22⋊Dic61C24124yes—
286#11758198C24124yes—
287#11758198C24124yes—
288#11758198C24124yes—
289C4⋊Dic61C24112yes—
290C4⋊Dic61C24124yes—
291#11758196C24124yes—
292#11758196C24124yes—
293#11758196C24124yes—
294C4×Dic61C2413yes—
295C4×Dic61C2416yes—
296C4×Dic61C2413yes—
297C4×Dic61C2416yes—
298C4×Dic61C2416yes—
299C4×Dic61C2416yes—
300C4×Dic61C2416yes—
301C4×Dic61C2413yes—
302C4×Dic61C2416yes—
303C4×Dic61C2413yes—
304C4×Dic61C24124yes—
305C4×Dic61C24112yes—
306C23×C61—26no—
307C23×C61C2514yes—
308C23×C61C2513yes—
309C22×D61—232no—
310C22×D61—26no—
311C22×D61—212no—
312C22×D61—212no—
313C22×D61—224no—
314C22×D61C2×#41112yes—
315C22×D61C2514yes—
316C22×D61C2513yes—
317C22×D61C2511yescharacteristic
318Q8×C61—212no—
319D4×C61—224no—
320D4×C61—212no—
321C2×C4×C61—26no—
322C2×C4×C61—212no—
323C2×C4×C61—212no—
324C2×C4×C61—224no—
325C2×C4×C61C2×#41112yescomplemented
326C2×C4×C61C2516yes—
327C2×C4×C61C25112yes—
328C2×C4×C61C2513yes—
329C2×C4×C61C2513yes—
330C22⋊D61—224no—
331C22⋊D61—224no—
332C22⋊D61—224no—
333C2×Dic61—26no—
334C2×Dic61—212no—
335C2×Dic61—212no—
336C2×Dic61—224no—
337C2×Dic61C2×#41112yescomplemented
338C2×Dic61C2516yes—
339C2×Dic61C25112yes—
340C2×Dic61C2513yes—
341C2×Dic61C2513yes—
342D244—224no—
343D244—212no—
344C4×D61—212no—
345C4×D61—212no—
346C4×D61—224no—
347C4×D61—212no—
348C4×D61—212no—
349C4×D61—224no—
350C4×D61—212no—
351C4×D61—212no—
352C4×D61—224no—
353C4×D61C2×#41112yes—
354C4×D61C2×#41112yes—
355C4×D61C2×#41112yescomplemented
356C4×D61C2×#41112yescomplemented
357Dic122—212no—
358Dic122—224no—
359C2×#3444—611nomaximal, Sylow
360C22×C61—28no—
361C22×C61—26no—
362C22×C61—212no—
363C22×C61C22×#4116yes—
364C22×C61C2611yescharacteristic
365C2×D61—224no—
366C2×D61—26no—
367C2×D61—224no—
368C2×D61—212no—
369C2×D61—416no—
370C2×D61C22×#4116yes—
371C2×D61C22×#4116yes—
372C4×C61—212no—
373C4×C61—26no—
374C4×C61C22×#4116yes—
375C4×C61C22×#4116yes—
376Dic61—212no—
377Dic61—26no—
378Dic61C22×#4116yes—
379Dic61C22×#4116yes—
380#3444—611no—
381#3444—613no—
382#3444—613no—
383#3444—6112no—
384#3444—616no—
385#3444—616no—
386#3444D6111yescharacteristic, direct product factor
387C2×#533—613no—
388C2×#532—613no—
389C2×#529—6112no—
390C2×#525—616no—
391C2×C4×#41—616no—
392C23×C42—611no—
393C2×C61—26no—
394C2×C61—44no—
395C2×C61C23×#4113yes—
396D61—26no—
397D61—44no—
398D61#344414yesdirect product factor
399C22×#41—616no—
400C24×C4—613no—
401#533—616no—
402#533—616no—
403#533—6112no—
404#533—6112no—
405#533—616no—
406#533—613no—
407#533C2×D6113yescomplemented
408#532—616no—
409#532—613no—
410#532—613no—
411#532—616no—
412#532—6112no—
413#532—6112no—
414#532—613no—
415#532C2×D6113yescomplemented
416C2×C4⋊Q8—613no—
417C2×#127—611no—
418#529—6124no—
419#529—6112no—
420#529—6112no—
421#529—6124no—
422#529—6112no—
423#529—6112no—
424#529—6112no—
425#529—6124no—
426#529—6112no—
427#529—6124no—
428#529—6112no—
429#529C2×D61112yescomplemented
430C2×#126—618no—
431C2×#125—616no—
432C2×#124—616no—
433#525—616no—
434#525—616no—
435#525—6112no—
436#525—6112no—
437#525—6112no—
438#525—6112no—
439#525—6124no—
440#525—616no—
441#525C2×D6116yescomplemented
442C2×#123—6112no—
443C2×C22⋊Q8—6112no—
444C2×#121—6112no—
445C2×#120—614no—
446C4×#41—616no—
447C4×#41—6112no—
448C4×#41—6124no—
449C4×#41—6112no—
450C4×#41—616no—
451C4×#41—6112no—
452C4×#41—616no—
453C4×#41—6112no—
454C4×#41C2×D6116yescomplemented
455C2×C4×Q8—6112no—
456C2×C4×D4—6124no—
457C2×C4×D4—6112no—
458C2×#117—616no—
459C2×#117—6112no—
460C22×C42—613no—
461C22×C42—613no—
462C22×C42—616no—
463C22×C42—613no—
464C22×C42—613no—
465C22×C42—616no—
466C22×C42—613no—
467C22×C42—614no—
468C22×C42C2×D6111yescharacteristic, complemented
469C61C2×#344411yescharacteristic, complemented, Sylow
470C25—611no—
471C2×#41—616no—
472C2×#41—6112no—
473C2×#41—616no—
474C2×#41—6112no—
475C2×#41—616no—
476C2×#41—12248no—
477C2×#41C22×D6116yes—
478C22×Q8—616no—
479C22×D4—6112no—
480C22×D4—616no—
481C23×C4—613no—
482C23×C4—613no—
483C23×C4—6112no—
484C23×C4—616no—
485C23×C4—616no—
486C23×C4—613no—
487C23×C4—613no—
488C23×C4—616no—
489C23×C4—616no—
490C23×C4—613no—
491C23×C4—12224no—
492C23×C4C22×D6113yes—
493C4⋊Q8—616no—
494C4⋊Q8—6112no—
495C4⋊Q8—613no—
496C4⋊Q8C22×D6113yescomplemented
497#127—616no—
498#127—611no—
499#127C22×D6111yescharacteristic, complemented
500#126—6124no—
501#126—6124no—
502#126—618no—
503#126C22×D6118yescomplemented
504#125—6124no—
505#125—6112no—
506#125—616no—
507#125C22×D6116yescomplemented
508#124—616no—
509#124—616no—
510#124—6124no—
511#124—616no—
512#124C22×D6116yescomplemented
513#123—6112no—
514#123—6112no—
515#123—6124no—
516#123—6124no—
517#123—6112no—
518#123C22×D61112yes—
519C22⋊Q8—6112no—
520C22⋊Q8—6112no—
521C22⋊Q8—6124no—
522C22⋊Q8—6112no—
523C22⋊Q8—6124no—
524C22⋊Q8C22×D61112yes—
525#121—6112no—
526#121—6124no—
527#121—6112no—
528#121—6112no—
529#121—6124no—
530#121C22×D61112yes—
531#120—614no—
532#120—6112no—
533#120—6112no—
534#120C22×D6114yes—
535C4×Q8—6112no—
536C4×Q8—6124no—
537C4×Q8—6112no—
538C4×Q8—6124no—
539C4×Q8—6112no—
540C4×Q8C22×D61112yescomplemented
541C4×D4—6124no—
542C4×D4—6112no—
543C4×D4—6124no—
544C4×D4—6124no—
545C4×D4—6124no—
546C4×D4—6124no—
547C4×D4—6112no—
548C4×D4—6124no—
549C4×D4—6124no—
550C4×D4—6124no—
551C4×D4—6124no—
552C4×D4—6112no—
553C4×D4C22×D61124yes—
554C4×D4C22×D61112yescomplemented
555#117—616no—
556#117—6112no—
557#117—6112no—
558#117—6124no—
559#117—6112no—
560#117—6124no—
561#117—6112no—
562#117—6112no—
563#117—6112no—
564#117C22×D6116yes—
565#117C22×D61112yescomplemented
566C2×C4⋊C4—6112no—
567C2×C4⋊C4—6124no—
568C2×C22⋊C4—6112no—
569C2×C22⋊C4—6124no—
570C2×C42—6112no—
571C2×C42—616no—
572C2×C42—613no—
573C2×C42—616no—
574C2×C42—616no—
575C2×C42—616no—
576C2×C42—616no—
577C2×C42—613no—
578C2×C42—613no—
579C2×C42—6112no—
580C2×C42—616no—
581C2×C42—6112no—
582C2×C42—616no—
583C2×C42—613no—
584C2×C42—613no—
585C2×C42—612no—
586C2×C42—616no—
587C2×C42—616no—
588C2×C42—616no—
589C2×C42—616no—
590C2×C42—611no—
591C2×C42—613no—
592C2×C42—613no—
593C2×C42—616no—
594C2×C42—614no—
595C2×C42—613no—
596C2×C42—611no—
597C2×C42C22×D6116yes—
598C2×C42C22×D6113yes—
599C2×C42C22×D6113yes—
600C2×C42C22×D6114yescomplemented
601C24—613no—
602C24—614no—
603C24—613no—
604C24—12212no—
605C24C23×D6111yescharacteristic
606#41—224no—
607#41—12248no—
608#41—12248no—
609#41—12224no—
610#41—12224no—
611#41—12224no—
612C2×Q8—6112no—
613C2×Q8—616no—
614C2×Q8—12224no—
615C2×Q8C23×D6116yes—
616C2×D4—6112no—
617C2×D4—6112no—
618C2×D4—6112no—
619C2×D4—6112no—
620C2×D4—616no—
621C2×D4—12224no—
622C2×D4—12248no—
623C2×D4C23×D61112yes—
624C2×D4C23×D6116yes—
625C22×C4—212no—
626C22×C4—613no—
627C22×C4—6124no—
628C22×C4—613no—
629C22×C4—613no—
630C22×C4—613no—
631C22×C4—613no—
632C22×C4—616no—
633C22×C4—616no—
634C22×C4—613no—
635C22×C4—6112no—
636C22×C4—616no—
637C22×C4—616no—
638C22×C4—616no—
639C22×C4—616no—
640C22×C4—616no—
641C22×C4—616no—
642C22×C4—6112no—
643C22×C4—6112no—
644C22×C4—6112no—
645C22×C4—12212no—
646C22×C4—12224no—
647C22×C4—12224no—
648C22×C4—12224no—
649C22×C4—12224no—
650C22×C4—12248no—
651C22×C4—12212no—
652C22×C4—12212no—
653C22×C4—12212no—
654C22×C4C23×D6116yes—
655C22×C4C23×D6116yes—
656C22×C4C23×D6113yes—
657C22×C4C23×D61112yes—
658C22×C4C23×D6113yes—
659C4⋊C4—6124no—
660C4⋊C4—6124no—
661C4⋊C4—6124no—
662C4⋊C4—6112no—
663C4⋊C4—6124no—
664C4⋊C4C23×D61112yes—
665C4⋊C4C23×D61124yes—
666C22⋊C4—6112no—
667C22⋊C4—6124no—
668C22⋊C4—6124no—
669C22⋊C4—6124no—
670C22⋊C4—6124no—
671C22⋊C4C23×D61112yes—
672C22⋊C4C23×D61124yes—
673C42—613no—
674C42—616no—
675C42—613no—
676C42—616no—
677C42—616no—
678C42—616no—
679C42—616no—
680C42—613no—
681C42—616no—
682C42—613no—
683C42—6124no—
684C42—6112no—
685C42C23×D6113yes—
686C42C23×D6116yes—
687C42C23×D6113yes—
688C42C23×D6112yes—
689C42C23×D6111yescharacteristic
690C42C23×D61112yes—
691C42C23×D6111yescharacteristic
692C23—26no—
693C23—611no—
694C23—6112no—
695C23—613no—
696C23—614no—
697C23—12212no—
698C23—12212no—
699C23—12224no—
700C23—12232no—
701C23—1226no—
702C23C24×D6114yes—
703C23C24×D6113yes—
704Q8—212no—
705Q8—12224no—
706Q8—12212no—
707D4—224no—
708D4—212no—
709D4—12224no—
710D4—12224no—
711D4—12224no—
712D4—12224no—
713D4—12212no—
714C2×C4—26no—
715C2×C4—212no—
716C2×C4—212no—
717C2×C4—224no—
718C2×C4—6112no—
719C2×C4—613no—
720C2×C4—613no—
721C2×C4—6112no—
722C2×C4—6112no—
723C2×C4—6112no—
724C2×C4—6112no—
725C2×C4—616no—
726C2×C4—6112no—
727C2×C4—12212no—
728C2×C4—12212no—
729C2×C4—12224no—
730C2×C4—12212no—
731C2×C4—12212no—
732C2×C4—12224no—
733C2×C4—12212no—
734C2×C4—12212no—
735C2×C4—12224no—
736C2×C4—1226no—
737C2×C4—12212no—
738C2×C4—12212no—
739C2×C4—12224no—
740C2×C4#41×D61112yescomplemented
741C2×C4C24×D6116yes—
742C2×C4C24×D61112yes—
743C2×C4C24×D6113yes—
744C2×C4C24×D6113yes—
745C22—28no—
746C22—26no—
747C22—212no—
748C22—616no—
749C22—616no—
750C22—12224no—
751C22—12224no—
752C22—1226no—
753C22—12212no—
754C22—24416no—
755C22C2×#41×D6116yes—
756C22C25×D6111yescharacteristic
757C4—26no—
758C4—212no—
759C4—616no—
760C4—616no—
761C4—1226no—
762C4—12212no—
763C4C2×#41×D6116yes—
764C4C2×#41×D6116yes—
765C2—26no—
766C2—44no—
767C2—614no—
768C2—1226no—
769C2—2444no—
770C2C22×#41×D6113yes—
subgroupG/H
centerC42C23×D61
commutator, socle, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC61×#3444C2
hypercenter#3444D61
hypocenterC61C2×#3444
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #21459116C2semidirect
2. #21459115C2semidirect
3. #21459114C2semidirect
4. #21459113C2semidirect
5. #21459112C2semidirect
6. #21459111C2semidirect
7. #533×D61C2semidirect
8. #532×D61C2semidirect
9. #529×D61C2semidirect
10. #525×D61C2semidirect
11. C4×#41×D61C2semidirect
12. C22×C42×D61C2semidirect
13. C61×#3444C2semidirect
16. #16840319C22semidirect
17. #16840318C22semidirect
18. #16840317C22semidirect
19. #16840316C22semidirect
20. #16840315C22semidirect
21. #16840314C22semidirect
22. #16840313C22semidirect
23. #16840312C22semidirect
24. #16840311C22semidirect
25. #16840310C22semidirect
26. #16840309C22semidirect
27. #16840308C22semidirect
28. #16840307C22semidirect
29. C4⋊Q8×D61C22semidirect
30. #127×D61C22semidirect
31. #16840299C22semidirect
32. #16840298C22semidirect
33. #16840297C22semidirect
34. #16840296C22semidirect
35. #16840295C22semidirect
36. #16840294C22semidirect
37. #16840293C22semidirect
38. #16840292C22semidirect
39. #16840291C22semidirect
40. #16840290C22semidirect
41. #16840289C22semidirect
42. #126×D61C22semidirect
43. #125×D61C22semidirect
44. #124×D61C22semidirect
45. #16840275C22semidirect
46. #16840274C22semidirect
47. #16840273C22semidirect
48. #16840272C22semidirect
49. #16840271C22semidirect
50. #16840270C22semidirect
51. #16840269C22semidirect
52. #16840268C22semidirect
57. #41×Dic61C22semidirect
58. C4×#11758226C22semidirect
59. C4×#11758222C22semidirect
60. C4×#11758222C22semidirect
61. #16840230C22semidirect
62. #16840230C22semidirect
63. C4×#11758224C22semidirect
64. C4×#11758224C22semidirect
65. C4×Q8×D61C22semidirect
67. C4×D4×D61C22semidirect
69. #117×D61C22semidirect
70. C22×C4×Dic61C22semidirect
74. C2×C42×D61C22semidirect
75. C2×C42×D61C22semidirect
76. C2×C42×D61C22semidirect
77. C2×C42×D61C22semidirect
78. C61×#533C22semidirect
79. C61×#532C22semidirect
80. C61×#529C22semidirect
81. C61×#525C22semidirect
82. C4×#41×C61C22semidirect
83. C22×C42×C61C22semidirect
105. #14519777C23semidirect
106. #14519776C23semidirect
107. #14519775C23semidirect
108. #14519774C23semidirect
109. #14519773C23semidirect
110. #14519772C23semidirect
111. #14519771C23semidirect
112. #14519770C23semidirect
113. #14519769C23semidirect
114. #14519768C23semidirect
115. #14519767C23semidirect
116. #14519766C23semidirect
117. #14519765C23semidirect
118. #14519764C23semidirect
119. #14519763C23semidirect
138. Q8×Dic61C23semidirect
139. C4×Dic122C23semidirect
140. C4×Dic122C23semidirect
141. #14519742C23semidirect
142. #14519742C23semidirect
144. C4×D244C23semidirect
146. D4×Dic61C23semidirect
148. #14519739C23semidirect
151. C4×C22⋊D61C23semidirect
154. #14519737C23semidirect
156. #14519736C23semidirect
158. #14519735C23semidirect
160. #14519734C23semidirect
161. #14519734C23semidirect
163. #14519733C23semidirect
175. C2×C4×Dic61C23semidirect
193. C42×D61C23semidirect
194. C42×D61C23semidirect
197. C4⋊Q8×C61C23semidirect
198. #127×C61C23semidirect
199. #126×C61C23semidirect
200. #125×C61C23semidirect
201. #124×C61C23semidirect
206. C4×Q8×C61C23semidirect
208. C4×D4×C61C23semidirect
210. #117×C61C23semidirect
214. C2×C42×C61C23semidirect
257. C2×C4×D61#41semidirect
325. C2×C4×C61C2×#41semidirect
337. C2×Dic61C2×#41semidirect
355. C4×D61C2×#41semidirect
356. C4×D61C2×#41semidirect
386. #3444D61direct (N × H)
398. D61#3444direct (N × H)
407. #533C2×D61semidirect
415. #532C2×D61semidirect
429. #529C2×D61semidirect
441. #525C2×D61semidirect
454. C4×#41C2×D61semidirect
468. C22×C42C2×D61semidirect
469. C61C2×#3444semidirect
496. C4⋊Q8C22×D61semidirect
499. #127C22×D61semidirect
503. #126C22×D61semidirect
507. #125C22×D61semidirect
512. #124C22×D61semidirect
540. C4×Q8C22×D61semidirect
554. C4×D4C22×D61semidirect
565. #117C22×D61semidirect
600. C2×C42C22×D61semidirect
740. C2×C4#41×D61semidirect

Maximal subgroups

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

subgroupindex
#214591162
#214591152
#214591142
#214591132
#214591122
#214591112
#533×D612
#532×D612
#529×D612
#525×D612
C4×#41×D612
C22×C42×D612
C61×#34442
C2×#344461