Finite Group Databasebeta

← #29657562

Subgroups — #29657562

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456994C211yesmaximal, characteristic, complemented
2#21456401C211yesmaximal, characteristic, complemented
3#21455981C211yesmaximal, characteristic, complemented
4#21445061C211yesmaximal, characteristic, complemented
5#21445054C211yesmaximal, characteristic, complemented
6#21445033C211yesmaximal, characteristic, complemented
7#21445026C211yesmaximal, characteristic, complemented
8#21444977C211yesmaximal, characteristic, complemented
9#21444970C211yesmaximal, characteristic, complemented
10#21444953C211yesmaximal, characteristic, complemented
11#21444953C211yesmaximal, characteristic, complemented
12#21444529C211yesmaximal, characteristic, complemented
13#21444279C211yesmaximal, characteristic, complemented
14#21444201C211yesmaximal, characteristic, complemented
15C61×#3515C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840165C2211yescharacteristic
18#16840161—21no—
19#16840141C2211yescharacteristic
20#16840116—21no—
21#16840114C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840103—21no—
24#16840100—21no—
25#16840083—21no—
26#16840057C2211yescharacteristic
27#16840057C2211yescharacteristic
28#16840052C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840042C2211yescharacteristic
32#16840001—22no—
33#16839972C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839924—21no—
36#16839867—21no—
37#16839862—21no—
38C4×#11758202—22no—
39#16839819C2211yescharacteristic
40#16839815C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839511C2211yescharacteristic
43#16839511C2211yescharacteristic
44#16839508C2211yescharacteristic
45#16839508C2211yescharacteristic
46Q8⋊#92418C2211yescharacteristic
47Q8⋊#92418C2211yescharacteristic
48Q8⋊#92418C2211yescharacteristic
49Q8⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54C61×#557C2211yescharacteristic
55C61×#554C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#553—21no—
58C61×#552—21no—
59C61×#552—22no—
60C61×#552—21no—
61C61×#547—21no—
62C61×#547C2211yescharacteristic
63C61×#541—21no—
64C61×#539—22no—
65C61×#533C2211yescharacteristic
66C61×#529—21no—
67C61×#529C2211yescharacteristic
68C2×#125×C61—21no—
69C61×#520—21no—
70C4×#41×C61C2211yescharacteristic
71C2×#11758202—21no—
72C2×#11758202—22no—
73C2×#11758200—21no—
74C22×#92418—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519769—21no—
78#14519756—21no—
79#14519756—21no—
80C4×Dic122—21no—
81C4×Dic122—21no—
82#14519736—21no—
83#14519710—22no—
84#14519710—21no—
85#14519710—21no—
86#14519710—21no—
87#14519708—21no—
88#14519708—21no—
89#14519708—21no—
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519701—22no—
95#14519701—21no—
96#14519701—21no—
97#14519701—21no—
98#14519700—21no—
99#14519700—21no—
100#14519700—22no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106#14519688—21no—
107C4×#92418—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61—21no—
112C2×#41×C61D411yescharacteristic
113C4⋊Q8×C61—21no—
114C4⋊Q8×C61C2311yescharacteristic
115C4⋊Q8×C61C2311yescharacteristic
116#126×C61—22no—
117#126×C61—22no—
118#126×C61—22no—
119#126×C61—21no—
120#125×C61—22no—
121#125×C61—22no—
122#125×C61—22no—
123#125×C61—22no—
124#125×C61—21no—
125#125×C61—21no—
126#125×C61—21no—
127#125×C61—21no—
128#125×C61D411yescharacteristic
129#124×C61D411yescharacteristic
130#123×C61—22no—
131#123×C61—22no—
132#123×C61—22no—
133#123×C61—21no—
134#123×C61—22no—
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61—21no—
141C22⋊Q8×C61D412yes—
142C22⋊Q8×C61D411yescharacteristic
143#121×C61—22no—
144#121×C61—21no—
145#121×C61D411yescharacteristic
146C4×Q8×C61—21no—
147C4×Q8×C61—21no—
148C4×Q8×C61—21no—
149C4×Q8×C61D412yes—
150C4×Q8×C61D411yescharacteristic
151C4×Q8×C61C2311yescharacteristic
152C4×Q8×C61C2311yescharacteristic
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61D411yescharacteristic
161C4×D4×C61C2311yescharacteristic
162C4×D4×C61C2311yescharacteristic
163#117×C61—22no—
164#117×C61—22no—
165#117×C61—21no—
166#117×C61—21no—
167#117×C61—21no—
168#117×C61D411yescharacteristic
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61—22no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61C2311yescharacteristic
176#41×C61—22no—
177#41×C61—41no—
178#41×C61—42no—
179#41×C61—42no—
180C2×Q8×C61—21no—
181C2×Q8×C61C2×D411yescharacteristic
182C2×Q8×C61C2×D411yescharacteristic
183C2×Q8×C61C2×D412yes—
184C2×D4×C61—22no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61C2×D411yescharacteristic
188C2×D4×C61C2×D411yescharacteristic
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C2×Dic122—21no—
200C2×Dic122—21no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—22no—
212C4⋊C4×C61—22no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C2×D411yescharacteristic
221C4⋊C4×C61C2×D411yescharacteristic
222C4⋊C4×C61C2×D411yescharacteristic
223C4⋊C4×C61C2×D411yescharacteristic
224C4⋊C4×C61C2×D412yes—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C42×C61—22no—
238C42×C61—21no—
239C42×C61—21no—
240C42×C61—22no—
241C42×C61—21no—
242C42×C61—21no—
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2×D411yescharacteristic
246C42×C61C2411yescharacteristic
247C22⋊Dic61—41no—
248#11758202—44no—
249#11758202—42no—
250#11758200—42no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255#11758196—41no—
256#11758196—41no—
257C4×Dic61—41no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—42no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61#12011yescharacteristic
268Q8×C61—21no—
269Q8×C61—21no—
270Q8×C61—21no—
271Q8×C61—21no—
272Q8×C61—42no—
273Q8×C61—41no—
274Q8×C61—41no—
275D4×C61—21no—
276D4×C61—21no—
277D4×C61—21no—
278D4×C61—42no—
279D4×C61—44no—
280D4×C61—81no—
281D4×C61#13512yes—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—41no—
295C2×C4×C61—42no—
296C2×C4×C61—44no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—81no—
302C2×C4×C61—82no—
303C2×C4×C61—82no—
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12011yescharacteristic
306C2×C4×C61#12011yescharacteristic
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×Dic61—41no—
311C2×Dic61—41no—
312Dic122—42no—
313Dic122—41no—
314Dic122—41no—
315#92418—22no—
316#92418—41no—
317#92418—41no—
318#92418—41no—
319#92418—41no—
320#92418—41no—
321#18661—611nomaximal, Sylow
322C22×C61—21no—
323C22×C61—22no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61C2×#12011yescharacteristic
332C4×C61—21no—
333C4×C61—21no—
334C4×C61—21no—
335C4×C61—21no—
336C4×C61—41no—
337C4×C61—41no—
338C4×C61—42no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—41no—
342C4×C61—41no—
343C4×C61—42no—
344C4×C61C2×#13511yescharacteristic
345C4×C61#57511yescharacteristic
346C4×C61#57811yescharacteristic
347C4×C61#57811yescharacteristic
348Dic61—81no—
349Dic61—81no—
350#3515D6111yescharacteristic
351#3233—611no—
352#3170—611no—
353#3116—611no—
354#1648—611no—
355#1647—611no—
356#1644—611no—
357#1643—611no—
358#1636—611no—
359#1635—611no—
360#1632—611no—
361#1632—611no—
362#1554—611no—
363#1494—611no—
364#1476—611no—
365C2×C61—41no—
366C2×C61—42no—
367C2×C61—81no—
368C2×C61#300211yescharacteristic
369C2×C61#301111yescharacteristic
370C2×C61#301811yescharacteristic
371#557C2×D6111yescharacteristic
372#554C2×D6111yescharacteristic
373#554C2×D6111yescharacteristic
374#553—21no—
375#552—21no—
376#552—22no—
377#552—21no—
378#547—21no—
379#547C2×D6111yescharacteristic
380#541—21no—
381#539—22no—
382#533—611no—
383#533C2×D6111yescharacteristic
384#529—21no—
385#529C2×D6111yescharacteristic
386C2×#125—21no—
387#520—21no—
388C4×#41C2×D6111yescharacteristic
389#500—611no—
390#499—1221no—
391#494—611no—
392#488—1221no—
393#487—611no—
394#487—611no—
395#485—1221no—
396#485—1221no—
397#482—1221no—
398#477—611no—
399#477—611no—
400#476—611no—
401#476—611no—
402#475—611no—
403#474—611no—
404#467—1222no—
405#462—611no—
406#461—611no—
407#452—1221no—
408#441—1221no—
409#440—1221no—
410C4×Q16—1222no—
411#432—611no—
412#431—611no—
413C2×C4×C8—611no—
414#333—611no—
415#333—611no—
416#332—611no—
417#332—611no—
418Q8⋊C8—611no—
419Q8⋊C8—611no—
420Q8⋊C8—611no—
421Q8⋊C8—611no—
422D4⋊C8—611no—
423D4⋊C8—611no—
424D4⋊C8—611no—
425D4⋊C8—611no—
426C61#1866111yescharacteristic, complemented, Sylow
427C2×#41—21no—
428C2×#41C22⋊D6111yescharacteristic
429C2×Q16—1222no—
430C2×Q16—1221no—
431C2×SD16—1221no—
432C22×C8—1221no—
433C4⋊Q8—21no—
434C4⋊Q8—611no—
435C4⋊Q8—611no—
436C4⋊Q8C22×D6111yescharacteristic
437C4⋊Q8C22×D6111yescharacteristic
438#126—22no—
439#126—22no—
440#126—22no—
441#126—21no—
442#125—22no—
443#125—22no—
444#125—22no—
445#125—21no—
446#125—21no—
447#125—22no—
448#125—21no—
449#125—21no—
450#125—1221no—
451#125C22⋊D6111yescharacteristic
452#124C22⋊D6111yescharacteristic
453#123—22no—
454#123—22no—
455#123—22no—
456#123—21no—
457#123—22no—
458C22⋊Q8—21no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—1221no—
465C22⋊Q8—1221no—
466C22⋊Q8C22⋊D6111yescharacteristic
467C22⋊Q8C22⋊D6112yes—
468#121—22no—
469#121—21no—
470#121C22⋊D6111yescharacteristic
471C4×Q8—21no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—1221no—
475C4×Q8—1221no—
476C4×Q8C22⋊D6111yescharacteristic
477C4×Q8C22⋊D6112yes—
478C4×Q8C22×D6111yescharacteristic
479C4×Q8C22×D6111yescharacteristic
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4C22⋊D6111yescharacteristic
488C4×D4C22×D6111yescharacteristic
489C4×D4C22×D6111yescharacteristic
490#117—22no—
491#117—22no—
492#117—21no—
493#117—21no—
494#117—21no—
495#117—1221no—
496#117C22⋊D6111yescharacteristic
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C42—21no—
503C2×C42C22×D6111yescharacteristic
504#107—1222no—
505#107—1221no—
506#107—1221no—
507#107—1221no—
508#106—1221no—
509#106—1221no—
510#106—1221no—
511C4⋊C8—611no—
512C4⋊C8—611no—
513C4⋊C8—611no—
514C4⋊C8—611no—
515#103—1222no—
516#103—1221no—
517#103—1221no—
518#103—1221no—
519#103—1222no—
520#103—1221no—
521#103—1221no—
522#102—1221no—
523#102—1221no—
524#102—1221no—
525C22⋊C8—1221no—
526C22⋊C8—1221no—
527#97—1221no—
528C4×C8—611no—
529C4×C8—611no—
530C4×C8—1221no—
531C4×C8—1221no—
532#41—22no—
533#41—41no—
534#41—42no—
535#41—42no—
536C2×Q8—21no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8C2×C22⋊D6111yescharacteristic
540C2×Q8C2×C22⋊D6111yescharacteristic
541C2×Q8C2×C22⋊D6112yes—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4C2×C22⋊D6111yescharacteristic
546C2×D4C2×C22⋊D6111yescharacteristic
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4C2×C22⋊D6111yescharacteristic
555C22×C4C2×C22⋊D6111yescharacteristic
556C22×C4C2×C22⋊D6111yescharacteristic
557Q16—2444no—
558Q16—2442no—
559SD16—2442no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—2442no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—2441no—
591C4⋊C4—2441no—
592C4⋊C4C2×C22⋊D6111yescharacteristic
593C4⋊C4C2×C22⋊D6111yescharacteristic
594C4⋊C4C2×C22⋊D6112yes—
595C4⋊C4C2×C22⋊D6111yescharacteristic
596C4⋊C4C2×C22⋊D6111yescharacteristic
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—2441no—
610C42—22no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—22no—
616C42—2441no—
617C42C2×C22⋊D6111yescharacteristic
618C42C2×C22⋊D6111yescharacteristic
619C42C2×C22⋊D6111yescharacteristic
620C42C23×D6111yescharacteristic
621C23—21no—
622C23—21no—
623C23#1451974611yescharacteristic
624Q8—21no—
625Q8—21no—
626Q8—21no—
627Q8—21no—
628Q8—42no—
629Q8—41no—
630Q8—41no—
631Q8—2442no—
632Q8—2441no—
633Q8—2441no—
634D4—21no—
635D4—21no—
636D4—21no—
637D4—42no—
638D4—44no—
639D4—81no—
640D4#1451979712yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—44no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—81no—
661C2×C4—82no—
662C2×C4—82no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4#1451974611yescharacteristic
666C2×C4#1451974611yescharacteristic
667C2×C4#1451974611yescharacteristic
668C2×C4C22×C22⋊D6111yescharacteristic
669C2×C4C22×C22⋊D6111yescharacteristic
670C2×C4C22×C22⋊D6111yescharacteristic
671C8—1222no—
672C8—2441no—
673C8—2441no—
674C8—2441no—
675C8—2441no—
676C8—2441no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22C2×#1451974611yescharacteristic
687C4—21no—
688C4—21no—
689C4—21no—
690C4—21no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—41no—
698C4—42no—
699C4—4881no—
700C4—4881no—
701C4C2×#1451979711yescharacteristic
702C4#1684056011yescharacteristic
703C4#1684057711yescharacteristic
704C4#1684057711yescharacteristic
705C2—41no—
706C2—42no—
707C2—81no—
708C2#2145503711yescharacteristic
709C2#2145511411yescharacteristic
710C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3515C2
socleC22×C61C2×#120
hypercenter#3515D61
hypocenterC61#18661
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3515

Complements

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

NH ≅ G/Ntype
1. #21456994C2semidirect
2. #21456401C2semidirect
3. #21455981C2semidirect
4. #21445061C2semidirect
5. #21445054C2semidirect
6. #21445033C2semidirect
7. #21445026C2semidirect
8. #21444977C2semidirect
9. #21444970C2semidirect
10. #21444953C2semidirect
11. #21444953C2semidirect
12. #21444529C2semidirect
13. #21444279C2semidirect
14. #21444201C2semidirect
426. C61#18661semidirect

Maximal subgroups

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

subgroupindex
#214569942
#214564012
#214559812
#214450612
#214450542
#214450332
#214450262
#214449772
#214449702
#214449532
#214445292
#214442792
#214442012
C61×#35152
#1866161