Finite Group Databasebeta

← #29656201

Subgroups — #29656201

Order 15616.

922 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456201C211yesmaximal, characteristic, complemented
2#21455634C211yesmaximal, characteristic, complemented
3#21455634C211yesmaximal, characteristic, complemented
4#21444991C212yesmaximal, complemented
5#21444984C212yesmaximal, complemented
6#21444977C212yesmaximal, complemented
7#21444970C212yesmaximal, complemented
8#21444557C211yesmaximal, characteristic, complemented
9#21444258C211yesmaximal, characteristic, complemented
10#21444258C211yesmaximal, characteristic, complemented
11C61×#3482C211yesmaximal, characteristic
12C2×#14519777C2211yescharacteristic
13#16840132—22no—
14#16840114C2212yes—
15#16840114C2212yes—
16#16840057C2212yes—
17#16840057C2212yes—
18#16840052C2212yes—
19#16840052C2212yes—
20#16840047—21no—
21#16840047—21no—
22#16840042—21no—
23#16840042—21no—
24#16839805—21no—
25#16839805—21no—
26#16839786C2211yescharacteristic
27#16839786C2211yescharacteristic
28#16839770—22no—
29#16839763—21no—
30#16839763—21no—
31C4×#11758194C2211yescharacteristic
32#16839508C2212yes—
33#16839508C2212yes—
34Q8⋊#92418C2212yes—
35Q8⋊#92418C2212yes—
36D4⋊#92418C2212yes—
37D4⋊#92418C2212yes—
38C61×#557C2211yescharacteristic
39C61×#556—21no—
40C61×#556C2211yescharacteristic
41C61×#552—22no—
42C61×#552—21no—
43D4×Q8×C61C2211yescharacteristic
44C61×#548—21no—
45C61×#547—21no—
46C61×#547C2211yescharacteristic
47C61×#533—21no—
48C61×#533C2211yescharacteristic
49C61×#529—21no—
50C61×#529—22no—
51C4×#41×C61—21no—
52C4×#41×C61C2211yescharacteristic
53C4×#41×C61C2211yescharacteristic
54C2×C4×Q8×C61—21no—
55C22×Dic122—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59#14519777—21no—
60#14519777—21no—
61#14519777—21no—
62#14519777C2312yes—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65#14519710—22no—
66#14519710—22no—
67#14519708—22no—
68#14519708—22no—
69C4⋊#92418—21no—
70C4⋊#92418—21no—
71C4⋊#92418C2312yes—
72C4⋊#92418C2312yes—
73#14519701—22no—
74#14519701—22no—
75#14519700—24no—
76#14519700—24no—
77#14519698—22no—
78#14519698—22no—
79#14519688—21no—
80C4×#92418C2312yes—
81C2×#41×C61—21no—
82C2×#41×C61D411yescharacteristic
83C2×#41×C61D411yescharacteristic
84C22×Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61C2311yescharacteristic
88C4⋊Q8×C61C2311yescharacteristic
89#126×C61—22no—
90#126×C61—22no—
91#126×C61—22no—
92#125×C61—22no—
93#125×C61—22no—
94#125×C61—21no—
95#125×C61D412yes—
96#124×C61—22no—
97#124×C61—21no—
98#123×C61—22no—
99#123×C61—22no—
100#123×C61—22no—
101C22⋊Q8×C61—22no—
102C22⋊Q8×C61—21no—
103C22⋊Q8×C61—21no—
104C22⋊Q8×C61—21no—
105C22⋊Q8×C61—21no—
106C22⋊Q8×C61—21no—
107C22⋊Q8×C61—22no—
108#121×C61—22no—
109#121×C61—21no—
110C4×Q8×C61—22no—
111C4×Q8×C61—22no—
112C4×Q8×C61—21no—
113C4×Q8×C61—21no—
114C4×Q8×C61—21no—
115C4×Q8×C61—21no—
116C4×Q8×C61—21no—
117C4×Q8×C61D411yescharacteristic
118C4×Q8×C61D411yescharacteristic
119C4×Q8×C61C2311yescharacteristic
120C4×Q8×C61C2311yescharacteristic
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C4×D4×C61—21no—
124C4×D4×C61—21no—
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61D411yescharacteristic
129C4×D4×C61D411yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132#117×C61—22no—
133#117×C61—22no—
134#117×C61—21no—
135#117×C61—21no—
136#117×C61—21no—
137#117×C61D412yes—
138#117×C61D411yescharacteristic
139#117×C61D411yescharacteristic
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—21no—
142C2×C42×C61—22no—
143C2×C42×C61—21no—
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146#41×C61—22no—
147#41×C61—22no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—42no—
151#41×C61—42no—
152C2×Q8×C61—22no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—42no—
156C2×Q8×C61—42no—
157C2×Q8×C61C2×D411yescharacteristic
158C2×Q8×C61C2×D411yescharacteristic
159C2×D4×C61—22no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61C2×D411yescharacteristic
163C2×D4×C61C2×D411yescharacteristic
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×Dic61—41no—
176C2×Dic122—22no—
177C2×Dic122—44no—
178C2×Dic122—41no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C4⋊C4×C61C2×D411yescharacteristic
196C4⋊C4×C61C2×D411yescharacteristic
197C4⋊C4×C61C2×D412yes—
198C4⋊C4×C61C2×D412yes—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—21no—
207C22⋊C4×C61—21no—
208C22⋊C4×C61—21no—
209C22⋊C4×C61—21no—
210C42×C61—22no—
211C42×C61—22no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—22no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61C2×D411yescharacteristic
220C42×C61C2×D411yescharacteristic
221C42×C61C2×D411yescharacteristic
222C42×C61C2411yescharacteristic
223C4⋊Dic61—22no—
224C4⋊Dic61—22no—
225C4⋊Dic61—41no—
226C4⋊Dic61—41no—
227#11758194—42no—
228#11758194—42no—
229#11758194—42no—
230C2×#92418—22no—
231C2×#92418—22no—
232C2×#92418—22no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61#12011yescharacteristic
236Q8×C61—21no—
237Q8×C61—21no—
238Q8×C61—21no—
239Q8×C61—44no—
240Q8×C61—41no—
241Q8×C61—41no—
242Q8×C61—41no—
243Q8×C61—41no—
244Q8×C61#13712yes—
245D4×C61—21no—
246D4×C61—21no—
247D4×C61—21no—
248D4×C61—42no—
249D4×C61—42no—
250D4×C61—44no—
251D4×C61#13712yes—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—22no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—44no—
268C2×C4×C61—44no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61#12011yescharacteristic
276C2×C4×C61#12011yescharacteristic
277C2×C4×C61#12011yescharacteristic
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×Dic61—42no—
282C2×Dic61—82no—
283Dic122—44no—
284Dic122—82no—
285#92418—42no—
286#92418—42no—
287#92418—42no—
288#18538—611nomaximal, Sylow
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—22no—
292C22×C61—21no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61C2×#12011yescharacteristic
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—22no—
302C4×C61—21no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—42no—
306C4×C61—42no—
307C4×C61—41no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61#45412yes—
311C4×C61C2×#13711yescharacteristic
312C4×C61C2×#13711yescharacteristic
313C4×C61#57511yescharacteristic
314C4×C61#57511yescharacteristic
315Dic61—82no—
316#3482D6111yescharacteristic
317#3139—611no—
318#3079—611no—
319#3079—611no—
320#1638—612no—
321#1637—612no—
322#1636—612no—
323#1635—612no—
324#1561—611no—
325#1489—611no—
326#1489—611no—
327C2×C61—41no—
328C2×C61—42no—
329C2×C61—81no—
330C2×C61#300711yescharacteristic
331C2×C61#300711yescharacteristic
332C2×C61C2×#45411yescharacteristic
333#557C2×D6111yescharacteristic
334#556—21no—
335#556C2×D6111yescharacteristic
336#552—22no—
337#552—21no—
338D4×Q8C2×D6111yescharacteristic
339#548—21no—
340#547—21no—
341#547C2×D6111yescharacteristic
342#533—21no—
343#533C2×D6111yescharacteristic
344C2×C4⋊Q8—611no—
345#529—21no—
346#529—22no—
347C4×#41—21no—
348C4×#41C2×D6111yescharacteristic
349C4×#41C2×D6111yescharacteristic
350C2×C4×Q8—21no—
351#491—1222no—
352#487—612no—
353#487—612no—
354#477—612no—
355#477—612no—
356#476—612no—
357#476—612no—
358#475—1221no—
359#475—1221no—
360#474—1221no—
361#474—1221no—
362#428—1221no—
363#428—1221no—
364#423—611no—
365#423—611no—
366#419—1222no—
367#417—1221no—
368#417—1221no—
369C4×M16—611no—
370#332—612no—
371#332—612no—
372Q8⋊C8—612no—
373Q8⋊C8—612no—
374D4⋊C8—612no—
375D4⋊C8—612no—
376C61#1853811yescharacteristic, complemented, Sylow
377C2×#41—21no—
378C2×#41C22⋊D6111yescharacteristic
379C2×#41C22⋊D6111yescharacteristic
380C22×Q8—21no—
381C22×Q8—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—612no—
388C4⋊Q8—1221no—
389C4⋊Q8—1221no—
390C4⋊Q8—1221no—
391C4⋊Q8C22×D6111yescharacteristic
392C4⋊Q8C22×D6111yescharacteristic
393#126—22no—
394#126—22no—
395#126—22no—
396#125—22no—
397#125—22no—
398#125—21no—
399#125C22⋊D6112yes—
400#124—22no—
401#124—21no—
402#123—22no—
403#123—22no—
404#123—22no—
405C22⋊Q8—22no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—22no—
411C22⋊Q8—21no—
412#121—22no—
413#121—21no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8C22⋊D6111yescharacteristic
422C4×Q8C22⋊D6111yescharacteristic
423C4×Q8C22×D6111yescharacteristic
424C4×Q8C22×D6111yescharacteristic
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4C22⋊D6111yescharacteristic
433C4×D4C22⋊D6111yescharacteristic
434C4×D4C22×D6111yescharacteristic
435C4×D4C22×D6111yescharacteristic
436#117—22no—
437#117—22no—
438#117—21no—
439#117—21no—
440#117—21no—
441#117C22⋊D6111yescharacteristic
442#117C22⋊D6111yescharacteristic
443#117C22⋊D6112yes—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C42—22no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C22×D6111yescharacteristic
452#107—1222no—
453#107—1222no—
454#106—1222no—
455#106—1222no—
456C4⋊C8—612no—
457C4⋊C8—612no—
458C4⋊C8—1221no—
459C4⋊C8—1221no—
460#103—1222no—
461#103—1222no—
462#103—1224no—
463#103—1224no—
464#102—1222no—
465#102—1222no—
466#97—1221no—
467C4×C8—612no—
468#41—22no—
469#41—22no—
470#41—41no—
471#41—41no—
472#41—42no—
473#41—42no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—1222no—
480C2×Q8—2444no—
481C2×Q8—2441no—
482C2×Q8C2×C22⋊D6111yescharacteristic
483C2×Q8C2×C22⋊D6111yescharacteristic
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×C22⋊D6111yescharacteristic
488C2×D4C2×C22⋊D6111yescharacteristic
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—2441no—
498C22×C4C2×C22⋊D6111yescharacteristic
499C22×C4C2×C22⋊D6111yescharacteristic
500C22×C4C2×C22⋊D6111yescharacteristic
501M16—2442no—
502M16—2442no—
503M16—2442no—
504C2×C8—1222no—
505C2×C8—1222no—
506C2×C8—1222no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—2441no—
524C4⋊C4—2441no—
525C4⋊C4C2×C22⋊D6112yes—
526C4⋊C4C2×C22⋊D6112yes—
527C4⋊C4C2×C22⋊D6111yescharacteristic
528C4⋊C4C2×C22⋊D6111yescharacteristic
529C4⋊C4C2×C22⋊D6111yescharacteristic
530C4⋊C4C2×C22⋊D6111yescharacteristic
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C42—22no—
543C42—22no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—22no—
550C42—21no—
551C42C2×C22⋊D6111yescharacteristic
552C42C2×C22⋊D6111yescharacteristic
553C42C2×C22⋊D6111yescharacteristic
554C42C23×D6111yescharacteristic
555C23—21no—
556C23—21no—
557C23#1451974611yescharacteristic
558Q8—21no—
559Q8—21no—
560Q8—21no—
561Q8—44no—
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—4882no—
567Q8—2444no—
568Q8#1451980712yes—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—42no—
573D4—42no—
574D4—44no—
575D4#1451980712yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—4882no—
600C2×C4—2442no—
601C2×C4#1451974611yescharacteristic
602C2×C4#1451974611yescharacteristic
603C2×C4#1451974611yescharacteristic
604C2×C4C22×C22⋊D6111yescharacteristic
605C2×C4C22×C22⋊D6111yescharacteristic
606C2×C4C22×C22⋊D6111yescharacteristic
607C8—2442no—
608C8—2442no—
609C8—2442no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22C2×#1451974611yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—42no—
630C4—41no—
631C4—4882no—
632C4#1683993512yes—
633C4C2×#1451980711yescharacteristic
634C4C2×#1451980711yescharacteristic
635C4#1684056011yescharacteristic
636C4#1684056011yescharacteristic
637C2—41no—
638C2—42no—
639C2—81no—
640C2#2145507911yescharacteristic
641C2#2145507911yescharacteristic
642C2C2×#1683993511yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3482C2
socleC22×C61C2×#120
hypercenter#3482D61
hypocenterC61#18538
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #21456201C2semidirect
2. #21455634C2semidirect
3. #21455634C2semidirect
4. #21444991C2semidirect
5. #21444984C2semidirect
6. #21444977C2semidirect
7. #21444970C2semidirect
8. #21444557C2semidirect
9. #21444258C2semidirect
10. #21444258C2semidirect
376. C61#18538semidirect

Maximal subgroups

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

subgroupindex
#214562012
#214556342
#214449912
#214449842
#214449772
#214449702
#214445572
#214442582
C61×#34822
#1853861