Finite Group Databasebeta

← #29656858

Subgroups — #29656858

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457192C211yesmaximal, characteristic, complemented
2#21456560C211yesmaximal, characteristic, complemented
3#21455607C211yesmaximal, characteristic, complemented
4#21445103C211yesmaximal, characteristic, complemented
5#21445096C211yesmaximal, 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#21444509C211yesmaximal, characteristic, complemented
13#21444258C211yesmaximal, characteristic, complemented
14#21444232C211yesmaximal, characteristic, complemented
15C61×#3515C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840158C2211yescharacteristic
18#16840141C2211yescharacteristic
19#16840114C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840069—21no—
22#16840066—21no—
23#16840062—21no—
24#16840057C2211yescharacteristic
25#16840057C2211yescharacteristic
26#16840052C2211yescharacteristic
27#16840052C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840018—21no—
31#16840018—22no—
32#16840006—21no—
33#16839981—21no—
34#16839972C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839867—22no—
37#16839798—21no—
38#16839786C2211yescharacteristic
39C2×C4⋊#92418C2211yescharacteristic
40#16839758—21no—
41C4×#11758194C2211yescharacteristic
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—22no—
72C2×#11758202—21no—
73C2×#11758200—21no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C22×#92418—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519769—21no—
80#14519756—21no—
81#14519756—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84#14519736—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—21no—
89#14519708—22no—
90#14519708—21no—
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—22no—
102#14519700—21no—
103#14519700—21no—
104#14519700—22no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519688—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—81no—
250#11758200—81no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255#11758196—41no—
256#11758196—41no—
257C4×Dic61—41no—
258#11758194—42no—
259#11758194—81no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—42no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61#12011yescharacteristic
270Q8×C61—21no—
271Q8×C61—21no—
272Q8×C61—21no—
273Q8×C61—21no—
274Q8×C61—42no—
275Q8×C61—41no—
276Q8×C61—41no—
277D4×C61—21no—
278D4×C61—21no—
279D4×C61—21no—
280D4×C61—42no—
281D4×C61—44no—
282D4×C61—81no—
283D4×C61#13712yes—
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—21no—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—41no—
297C2×C4×C61—42no—
298C2×C4×C61—44no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—81no—
304C2×C4×C61—82no—
305C2×C4×C61—82no—
306C2×C4×C61#12011yescharacteristic
307C2×C4×C61#12011yescharacteristic
308C2×C4×C61#12011yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×Dic61—41no—
313C2×Dic61—41no—
314Dic122—42no—
315Dic122—41no—
316Dic122—41no—
317#92418—22no—
318#92418—41no—
319#92418—41no—
320#92418—41no—
321#92418—41no—
322#92418—41no—
323#18597—611nomaximal, Sylow
324C22×C61—21no—
325C22×C61—22no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C2×#12011yescharacteristic
334C4×C61—21no—
335C4×C61—21no—
336C4×C61—21no—
337C4×C61—21no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—42no—
341C4×C61—41no—
342C4×C61—41no—
343C4×C61—41no—
344C4×C61—41no—
345C4×C61—42no—
346C4×C61C2×#13711yescharacteristic
347C4×C61#57511yescharacteristic
348C4×C61#57711yescharacteristic
349C4×C61#57811yescharacteristic
350Dic61—81no—
351Dic61—81no—
352#3515D6111yescharacteristic
353#3252—611no—
354#3185—611no—
355#3076—611no—
356#1654—611no—
357#1653—611no—
358#1644—611no—
359#1643—611no—
360#1636—611no—
361#1635—611no—
362#1632—611no—
363#1632—611no—
364#1550—611no—
365#1489—611no—
366#1483—611no—
367C2×C61—41no—
368C2×C61—42no—
369C2×C61—81no—
370C2×C61#300711yescharacteristic
371C2×C61#301311yescharacteristic
372C2×C61#301811yescharacteristic
373#557C2×D6111yescharacteristic
374#554C2×D6111yescharacteristic
375#554C2×D6111yescharacteristic
376#553—21no—
377#552—21no—
378#552—22no—
379#552—21no—
380#547—21no—
381#547C2×D6111yescharacteristic
382#541—21no—
383#539—22no—
384#533—611no—
385#533C2×D6111yescharacteristic
386#529—21no—
387#529C2×D6111yescharacteristic
388C2×#125—21no—
389#520—21no—
390C4×#41C2×D6111yescharacteristic
391#498—611no—
392#494—611no—
393#487—611no—
394#487—611no—
395#479—1221no—
396#479—1221no—
397#478—1221no—
398#477—611no—
399#477—611no—
400#476—611no—
401#476—611no—
402#475—611no—
403#474—611no—
404#470—1222no—
405#470—1221no—
406#468—1221no—
407#464—1221no—
408#462—611no—
409#461—611no—
410#441—1222no—
411#427—1221no—
412#423—611no—
413C2×C4⋊C8—611no—
414#416—1221no—
415C4×M16—611no—
416#333—611no—
417#333—611no—
418#332—611no—
419#332—611no—
420Q8⋊C8—611no—
421Q8⋊C8—611no—
422Q8⋊C8—611no—
423Q8⋊C8—611no—
424D4⋊C8—611no—
425D4⋊C8—611no—
426D4⋊C8—611no—
427D4⋊C8—611no—
428C61#1859711yescharacteristic, complemented, Sylow
429C2×#41—21no—
430C2×#41C22⋊D6111yescharacteristic
431C2×Q16—1221no—
432C2×Q16—1222no—
433C2×SD16—1221no—
434C2×M16—1221no—
435C2×M16—1221no—
436C22×C8—1221no—
437C4⋊Q8—21no—
438C4⋊Q8—611no—
439C4⋊Q8—611no—
440C4⋊Q8C22×D6111yescharacteristic
441C4⋊Q8C22×D6111yescharacteristic
442#126—22no—
443#126—22no—
444#126—22no—
445#126—21no—
446#125—22no—
447#125—22no—
448#125—22no—
449#125—21no—
450#125—21no—
451#125—22no—
452#125—21no—
453#125—21no—
454#125—1221no—
455#125C22⋊D6111yescharacteristic
456#124C22⋊D6111yescharacteristic
457#123—22no—
458#123—22no—
459#123—22no—
460#123—21no—
461#123—22no—
462C22⋊Q8—21no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—1221no—
469C22⋊Q8—1221no—
470C22⋊Q8C22⋊D6111yescharacteristic
471C22⋊Q8C22⋊D6112yes—
472#121—22no—
473#121—21no—
474#121C22⋊D6111yescharacteristic
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—1221no—
479C4×Q8—1221no—
480C4×Q8C22⋊D6111yescharacteristic
481C4×Q8C22⋊D6112yes—
482C4×Q8C22×D6111yescharacteristic
483C4×Q8C22×D6111yescharacteristic
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4C22⋊D6111yescharacteristic
492C4×D4C22×D6111yescharacteristic
493C4×D4C22×D6111yescharacteristic
494#117—22no—
495#117—22no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—1221no—
500#117C22⋊D6111yescharacteristic
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C42—21no—
507C2×C42C22×D6111yescharacteristic
508#107—1221no—
509#107—1221no—
510#107—1221no—
511#106—1221no—
512#106—1221no—
513#106—1222no—
514#106—1221no—
515C4⋊C8—611no—
516C4⋊C8—611no—
517C4⋊C8—611no—
518C4⋊C8—611no—
519C4⋊C8—1221no—
520C4⋊C8—1221no—
521#103—1221no—
522#103—1221no—
523#103—1222no—
524#103—1221no—
525#103—1222no—
526#103—1221no—
527#103—1221no—
528#102—1221no—
529#102—1221no—
530#102—1221no—
531#97—1221no—
532C4×C8—611no—
533C4×C8—611no—
534#41—22no—
535#41—41no—
536#41—42no—
537#41—42no—
538C2×Q8—21no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8C2×C22⋊D6111yescharacteristic
542C2×Q8C2×C22⋊D6111yescharacteristic
543C2×Q8C2×C22⋊D6112yes—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4C2×C22⋊D6111yescharacteristic
548C2×D4C2×C22⋊D6111yescharacteristic
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4C2×C22⋊D6111yescharacteristic
557C22×C4C2×C22⋊D6111yescharacteristic
558C22×C4C2×C22⋊D6111yescharacteristic
559Q16—4881no—
560Q16—2444no—
561SD16—4881no—
562M16—4881no—
563M16—2442no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—2442no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—2441no—
595C4⋊C4—2441no—
596C4⋊C4C2×C22⋊D6111yescharacteristic
597C4⋊C4C2×C22⋊D6112yes—
598C4⋊C4C2×C22⋊D6111yescharacteristic
599C4⋊C4C2×C22⋊D6111yescharacteristic
600C4⋊C4C2×C22⋊D6111yescharacteristic
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—2441no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—22no—
620C42—2441no—
621C42C2×C22⋊D6111yescharacteristic
622C42C2×C22⋊D6111yescharacteristic
623C42C2×C22⋊D6111yescharacteristic
624C42C23×D6111yescharacteristic
625C23—21no—
626C23—21no—
627C23#1451974611yescharacteristic
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—21no—
632Q8—42no—
633Q8—41no—
634Q8—41no—
635Q8—2442no—
636Q8—2441no—
637Q8—2441no—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—42no—
642D4—44no—
643D4—81no—
644D4#1451980712yes—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—44no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—81no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4#1451974611yescharacteristic
670C2×C4#1451974611yescharacteristic
671C2×C4#1451974611yescharacteristic
672C2×C4C22×C22⋊D6111yescharacteristic
673C2×C4C22×C22⋊D6111yescharacteristic
674C2×C4C22×C22⋊D6111yescharacteristic
675C8—1222no—
676C8—2441no—
677C8—2441no—
678C8—2441no—
679C8—2441no—
680C8—2441no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C2×#1451974611yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—21no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—42no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—4881no—
704C4—4881no—
705C4C2×#1451980711yescharacteristic
706C4#1684056011yescharacteristic
707C4#1684057011yescharacteristic
708C4#1684057711yescharacteristic
709C2—41no—
710C2—42no—
711C2—81no—
712C2#2145507911yescharacteristic
713C2#2145513411yescharacteristic
714C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3515C2
socleC22×C61C2×#120
hypercenter#3515D61
hypocenterC61#18597
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. #21457192C2semidirect
2. #21456560C2semidirect
3. #21455607C2semidirect
4. #21445103C2semidirect
5. #21445096C2semidirect
6. #21445033C2semidirect
7. #21445026C2semidirect
8. #21444977C2semidirect
9. #21444970C2semidirect
10. #21444953C2semidirect
11. #21444953C2semidirect
12. #21444509C2semidirect
13. #21444258C2semidirect
14. #21444232C2semidirect
428. C61#18597semidirect

Maximal subgroups

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

subgroupindex
#214571922
#214565602
#214556072
#214451032
#214450962
#214450332
#214450262
#214449772
#214449702
#214449532
#214445092
#214442582
#214442322
C61×#35152
#1859761