Finite Group Databasebeta

← #29648823

Subgroups — #29648823

Order 15616.

862 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459706C211yesmaximal, characteristic
2#21454933C211yesmaximal, characteristic
3#21454486C211yesmaximal, characteristic
4#21444555C211yesmaximal, characteristic, complemented
5#21444546C211yesmaximal, characteristic, complemented
6#21444537C211yesmaximal, characteristic, complemented
7#21444529C211yesmaximal, characteristic, complemented
8#21444528C211yesmaximal, characteristic, complemented
9#21444518C211yesmaximal, characteristic, complemented
10#21444516C211yesmaximal, characteristic, complemented
11#21444506C211yesmaximal, characteristic, complemented
12#21444505C211yesmaximal, characteristic, complemented
13#21444482C211yesmaximal, characteristic, complemented
14#21444473C211yesmaximal, characteristic, complemented
15C61×#1559C211yesmaximal, characteristic, complemented
16#16840491—21no—
17#16840491C412yes—
18#16840485—21no—
19#16840485C412yes—
20#16840454—21no—
21#16840454—21no—
22#16840454C412yes—
23#16840454C412yes—
24#16840375—21no—
25#16840375—21no—
26#16840338—21no—
27#16840317C2211yescharacteristic
28#16840317C2211yescharacteristic
29#16840317C2211yescharacteristic
30#16840317C2211yescharacteristic
31C2×#14519777C2211yescharacteristic
32#16840239—21no—
33C4×#11758222C2211yescharacteristic
34#16839891—21no—
35#16839838—21no—
36#16839832—21no—
37#16839831—21no—
38#16839824—21no—
39#16839820—21no—
40#16839819C2211yescharacteristic
41#16839818C2211yescharacteristic
42#16839818C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839814C2211yescharacteristic
45#16839814C2211yescharacteristic
46#16839784C2211yescharacteristic
47#16839784C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49C4⋊C8×D61C2211yescharacteristic
50#16839727—21no—
51#16839719—21no—
52#16839511C2211yescharacteristic
53#16839511C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839508C2211yescharacteristic
60#16839507C2211yescharacteristic
61#16839507C2211yescharacteristic
62#16839507C2211yescharacteristic
63#16839507C2211yescharacteristic
64C61×#533C2211yescharacteristic
65C61×#432C2211yescharacteristic
66C61×#423C2211yescharacteristic
67C61×#333C2211yescharacteristic
68C61×#333C2211yescharacteristic
69C61×#332C2211yescharacteristic
70C61×#332C2211yescharacteristic
71C2×#11758222D411yescharacteristic
72C22×Dic122—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77#14519777—22no—
78#14519777—21no—
79#14519777—21no—
80#14519777C2×C412yes—
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519772—22no—
84#14519772—22no—
85#14519772—22no—
86#14519772—22no—
87#14519768—22no—
88#14519768—22no—
89#14519768—22no—
90#14519768—22no—
91#14519768—21no—
92#14519768—21no—
93#14519768C2×C412yes—
94#14519768C2×C412yes—
95#14519765—22no—
96#14519761—22no—
97#14519761—22no—
98#14519757—21no—
99#14519757—21no—
100#14519757—21no—
101#14519757—21no—
102#14519753—21no—
103#14519753—21no—
104#14519753C2×C412yes—
105#14519753C2×C412yes—
106Q8×Dic61—21no—
107Q8×Dic61—21no—
108Q8×Dic61C2×C412yes—
109Q8×Dic61C2×C412yes—
110C4×Dic122—22no—
111C4×Dic122—22no—
112C4×Dic122C2×C411yescharacteristic
113C4×Dic122D411yescharacteristic
114#14519742—21no—
115#14519742—21no—
116#14519742—21no—
117#14519742—21no—
118C4×D244C2×C411yescharacteristic
119C4×D244D411yescharacteristic
120C4×C22⋊D61C2×C411yescharacteristic
121C4×C22⋊D61C2×C411yescharacteristic
122C4×C22⋊D61D411yescharacteristic
123C4×C22⋊D61D411yescharacteristic
124#14519736D411yescharacteristic
125#14519735—21no—
126#14519735—21no—
127#14519735C2×C412yes—
128#14519735C2×C412yes—
129#14519734D411yescharacteristic
130#14519734D411yescharacteristic
131#14519733—22no—
132#14519733—22no—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61C2×C412yes—
135C42×D61C2311yescharacteristic
136C42×D61C2311yescharacteristic
137C4⋊#92418C2311yescharacteristic
138C4⋊#92418C2311yescharacteristic
139C4⋊#92418C2311yescharacteristic
140C4⋊#92418C2311yescharacteristic
141#14519706—21no—
142#14519706—21no—
143#14519706—21no—
144#14519706—21no—
145C22⋊#92418—21no—
146C22⋊#92418—21no—
147#14519689—21no—
148#14519689—21no—
149#14519689—21no—
150#14519689—21no—
151#14519688—21no—
152#14519687—21no—
153#14519687—21no—
154C4×#92418—21no—
155C8×Dic61—21no—
156C8×Dic61—21no—
157C2×M16×C61—21no—
158C4⋊Q8×C61C2311yescharacteristic
159C4⋊Q8×C61C2311yescharacteristic
160#125×C61—21no—
161C22⋊Q8×C61—21no—
162C22⋊Q8×C61C2×C412yes—
163C4×Q8×C61—21no—
164C4×Q8×C61C2×C412yes—
165#117×C61—21no—
166C2×C42×C61C2311yescharacteristic
167C4⋊C8×C61—21no—
168C4⋊C8×C61C2311yescharacteristic
169C4⋊C8×C61C2311yescharacteristic
170C4⋊C8×C61C2311yescharacteristic
171C4⋊C8×C61C2311yescharacteristic
172C22⋊C8×C61—21no—
173#97×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61C22×C412yes—
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C2×C22⋊D61C22⋊C411yescharacteristic
180C2×C22⋊D61C22⋊C411yescharacteristic
181C22×Dic61—22no—
182#11758222—41no—
183#11758222—41no—
184C2×D244C22⋊C411yescharacteristic
185C2×C4×D61C22×C411yescharacteristic
186C2×C4×D61C22×C411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×Dic122—22no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—42no—
195C2×Dic122—42no—
196C2×Dic122C22⋊C411yescharacteristic
197M16×C61—81no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C22×C412yes—
208C22⋊C4×C61—22no—
209C42×C61—22no—
210C42×C61C22×C411yescharacteristic
211C42×C61C2×D411yescharacteristic
212C42×C61C2×D411yescharacteristic
213C42×C61C2411yescharacteristic
214C22⋊Dic61C22⋊C411yescharacteristic
215C22⋊Dic61C22⋊C411yescharacteristic
216#11758198—22no—
217#11758198—22no—
218#11758198—22no—
219#11758198—22no—
220#11758198C22⋊C411yescharacteristic
221#11758198C22⋊C411yescharacteristic
222#11758198C22⋊C411yescharacteristic
223#11758198C22⋊C411yescharacteristic
224C4⋊Dic61—22no—
225C4⋊Dic61—22no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—22no—
229C4⋊Dic61—22no—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61C22⋊C411yescharacteristic
233C4⋊Dic61C22⋊C411yescharacteristic
234C4⋊Dic61C22×C412yes—
235C4⋊Dic61C22×C412yes—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196C22⋊C411yescharacteristic
241#11758196C22⋊C411yescharacteristic
242#11758196C22⋊C411yescharacteristic
243#11758196C22⋊C411yescharacteristic
244C4×Dic61—22no—
245C4×Dic61—22no—
246C4×Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61C22×C411yescharacteristic
249C4×Dic61C22×C411yescharacteristic
250C4×Dic61C2×D411yescharacteristic
251C4×Dic61C2×D411yescharacteristic
252C4×Dic61C2×D411yescharacteristic
253C4×Dic61C2×D411yescharacteristic
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258#11758189—42no—
259#11758189—81no—
260C8×D61—42no—
261C8×D61—81no—
262C23×C61C2×C22⋊C411yescharacteristic
263C22×D61C2×C22⋊C411yescharacteristic
264C22×D61C2×C22⋊C411yescharacteristic
265Q8×C61—42no—
266Q8×C61—41no—
267Q8×C61—41no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—41no—
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C23×C411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C22⋊D61—41no—
282C22⋊D61—41no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—44no—
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292D244—41no—
293C4×D61—21no—
294C4×D61—21no—
295C4×D61—21no—
296C4×D61—21no—
297C4×D61—21no—
298C4×D61—21no—
299C4×D61—21no—
300C4×D61—21no—
301C4×D61—41no—
302C4×D61—41no—
303Dic122—41no—
304Dic122—44no—
305Dic122—41no—
306Dic122—41no—
307Dic122—41no—
308Dic122—41no—
309C8×C61—41no—
310C8×C61—41no—
311C8×C61—41no—
312C8×C61—41no—
313#92418—41no—
314#92418—41no—
315#92418—41no—
316#92418—41no—
317#17767—611nomaximal, Sylow
318C22×C61—21no—
319C22×C61—21no—
320C22×C61—21no—
321C22×C61C22×C22⋊C411yescharacteristic
322C2×D61—21no—
323C2×D61—21no—
324C2×D61—21no—
325C2×D61—21no—
326C2×D61—21no—
327C2×D61—21no—
328C4×C61—21no—
329C4×C61—21no—
330C4×C61—21no—
331C4×C61—21no—
332C4×C61—42no—
333C4×C61—42no—
334C4×C61#57511yescharacteristic
335C4×C61#57511yescharacteristic
336C4×C61#57711yescharacteristic
337C4×C61#57811yescharacteristic
338Dic61—21no—
339Dic61—21no—
340Dic61—21no—
341Dic61—21no—
342Dic61—21no—
343Dic61—21no—
344Dic61—42no—
345Dic61—42no—
346#3509—611no—
347#2989—611no—
348#2925—611no—
349#1561—611no—
350#1559—611no—
351#1559D6111yescharacteristic, complemented
352#1556—611no—
353#1554—611no—
354#1554—611no—
355#1552—611no—
356#1552—611no—
357#1550—611no—
358#1549—611no—
359#1544—611no—
360#1542—611no—
361C2×C61—41no—
362C2×C61#288911yescharacteristic
363C2×C61#289611yescharacteristic
364C2×C61#289811yescharacteristic
365D61—41no—
366D61—41no—
367#557—612no—
368#557—1221no—
369#556—612no—
370#556—1221no—
371#552—612no—
372#552—612no—
373#552—1221no—
374#552—1221no—
375#541—1221no—
376#541—1221no—
377#536—1221no—
378#533—611no—
379#533—611no—
380#533—611no—
381#533—611no—
382#533C2×D6111yescharacteristic
383C2×C4⋊Q8—611no—
384#519—1221no—
385C4×#41—611no—
386#446—1221no—
387#436—1221no—
388#435—1221no—
389#435—1221no—
390#433—1221no—
391#433—1221no—
392#432—611no—
393#432—611no—
394#432—611no—
395#432C2×D6111yescharacteristic
396#431—611no—
397#431—611no—
398#431—611no—
399#423—611no—
400#423—611no—
401#423C2×D6111yescharacteristic
402C2×C4⋊C8—611no—
403C2×C4⋊C8—611no—
404#408—1221no—
405#405—1221no—
406#333—611no—
407#333—611no—
408#333C2×D6111yescharacteristic
409#333C2×D6111yescharacteristic
410#332—611no—
411#332—611no—
412#332—611no—
413#332—611no—
414#332—611no—
415#332—611no—
416#332—611no—
417#332—611no—
418#332—611no—
419#332—611no—
420#332C2×D6111yescharacteristic
421#332C2×D6111yescharacteristic
422C61#1776711yescharacteristic, complemented, Sylow
423C2×#41—611no—
424C22×Q8—1221no—
425C2×M16—21no—
426C2×M16—1221no—
427C2×M16—1221no—
428C22×C8—1221no—
429C22×C8—1221no—
430C4⋊Q8—612no—
431C4⋊Q8—611no—
432C4⋊Q8—611no—
433C4⋊Q8—1222no—
434C4⋊Q8—1221no—
435C4⋊Q8—1221no—
436C4⋊Q8C22×D6111yescharacteristic
437C4⋊Q8C22×D6111yescharacteristic
438#126—1222no—
439#126—1222no—
440#126—1222no—
441#126—1222no—
442#125—21no—
443#125—612no—
444#125—612no—
445#125—1221no—
446#125—1221no—
447#125—1222no—
448#125—1222no—
449#125—1222no—
450#125—1222no—
451#124—1222no—
452#123—1222no—
453#123—1222no—
454C22⋊Q8—21no—
455C22⋊Q8—612no—
456C22⋊Q8—612no—
457C22⋊Q8—1221no—
458C22⋊Q8—1221no—
459C22⋊Q8—1221no—
460C22⋊Q8—1221no—
461C22⋊Q8—1221no—
462C22⋊Q8—1221no—
463C22⋊Q8C4×D6112yes—
464C4×Q8—21no—
465C4×Q8—611no—
466C4×Q8—611no—
467C4×Q8—612no—
468C4×Q8—612no—
469C4×Q8—1222no—
470C4×Q8—1222no—
471C4×Q8—1221no—
472C4×Q8—1221no—
473C4×Q8—1221no—
474C4×Q8—1221no—
475C4×Q8—1221no—
476C4×Q8—1221no—
477C4×Q8C4×D6112yes—
478C4×D4—611no—
479C4×D4—611no—
480C4×D4—611no—
481C4×D4—611no—
482C4×D4—611no—
483C4×D4—611no—
484#117—21no—
485#117—611no—
486#117—611no—
487#117—611no—
488#117—612no—
489#117—612no—
490#117—1222no—
491#117—1222no—
492#117—1221no—
493#117—1221no—
494C2×C4⋊C4—612no—
495C2×C4⋊C4—1221no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—21no—
500C4⋊C8—611no—
501C4⋊C8—611no—
502C4⋊C8—611no—
503C4⋊C8—611no—
504C4⋊C8—1221no—
505C4⋊C8—1221no—
506C4⋊C8—1221no—
507C4⋊C8—1221no—
508C4⋊C8C22×D6111yescharacteristic
509C4⋊C8C22×D6111yescharacteristic
510C4⋊C8C22×D6111yescharacteristic
511C4⋊C8C22×D6111yescharacteristic
512C22⋊C8—21no—
513C22⋊C8—1221no—
514C22⋊C8—1221no—
515C22⋊C8—1221no—
516C22⋊C8—1221no—
517C22⋊C8—1221no—
518C22⋊C8—1221no—
519#97—21no—
520#97—1221no—
521#97—1221no—
522#97—1221no—
523C4×C8—1221no—
524C4×C8—1221no—
525C4×C8—1221no—
526#41—2441no—
527#41—2441no—
528C2×Q8—21no—
529C2×Q8—611no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1222no—
533C2×Q8—2442no—
534C2×Q8—2442no—
535C2×Q8C2×C4×D6112yes—
536C2×D4—611no—
537C2×D4—611no—
538C2×D4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—1222no—
546C22×C4C2×C4×D6111yescharacteristic
547C22×C4D4×D6111yescharacteristic
548C22×C4D4×D6111yescharacteristic
549M16—81no—
550M16—4881no—
551M16—2442no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—4881no—
561C2×C8—2442no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—611no—
568C4⋊C4—611no—
569C4⋊C4—611no—
570C4⋊C4—611no—
571C4⋊C4—611no—
572C4⋊C4—611no—
573C4⋊C4—612no—
574C4⋊C4—612no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1222no—
578C4⋊C4—1222no—
579C4⋊C4—1222no—
580C4⋊C4—1222no—
581C4⋊C4—1222no—
582C4⋊C4—1222no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—1222no—
586C4⋊C4—1222no—
587C4⋊C4C2×C4×D6112yes—
588C22⋊C4—22no—
589C22⋊C4—611no—
590C22⋊C4—611no—
591C22⋊C4—611no—
592C22⋊C4—611no—
593C22⋊C4—611no—
594C22⋊C4—611no—
595C22⋊C4—1222no—
596C22⋊C4—1222no—
597C22⋊C4—1222no—
598C22⋊C4—1222no—
599C42—22no—
600C42—611no—
601C42—611no—
602C42—611no—
603C42—611no—
604C42—611no—
605C42—611no—
606C42—1222no—
607C42—1222no—
608C42—1222no—
609C42—1222no—
610C42C2×C4×D6111yescharacteristic
611C42D4×D6111yescharacteristic
612C42D4×D6111yescharacteristic
613C42C23×D6111yescharacteristic
614C23—611no—
615C23—611no—
616C23C22⋊C4×D6111yescharacteristic
617Q8—42no—
618Q8—41no—
619Q8—41no—
620Q8—2441no—
621Q8—2444no—
622Q8—2441no—
623Q8—2441no—
624Q8—2441no—
625Q8—2441no—
626D4—2441no—
627D4—2441no—
628D4—2441no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—611no—
637C2×C4—611no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—611no—
641C2×C4—611no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2444no—
655C2×C4C22⋊C4×D6111yescharacteristic
656C2×C4C22⋊C4×D6111yescharacteristic
657C2×C4C22⋊C4×D6111yescharacteristic
658C2×C4C22×C4×D6111yescharacteristic
659C2×C4C2×D4×D6111yescharacteristic
660C2×C4C2×D4×D6111yescharacteristic
661C8—41no—
662C8—41no—
663C8—41no—
664C8—41no—
665C8—2441no—
666C8—2441no—
667C8—2441no—
668C8—2441no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—1221no—
673C22—1221no—
674C22—1221no—
675C22—1221no—
676C22—1221no—
677C22—1221no—
678C22C2×C22⋊C4×D6111yescharacteristic
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—42no—
684C4—42no—
685C4—1221no—
686C4—1221no—
687C4—1221no—
688C4—1221no—
689C4—1221no—
690C4—1221no—
691C4—2442no—
692C4—2442no—
693C4#1684056111yescharacteristic
694C4#1684056111yescharacteristic
695C4#1684057211yescharacteristic
696C4#1684057811yescharacteristic
697C2—41no—
698C2—2441no—
699C2—2441no—
700C2#2145430011yescharacteristic
701C2#2145433711yescharacteristic
702C2#2145435011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1559C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222D4
cosocleC42×C61C24
hypercenter#1559D61
hypocenterC61#17767
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1559

Complements

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

NH ≅ G/Ntype
4. #21444555C2semidirect
5. #21444546C2semidirect
6. #21444537C2semidirect
7. #21444529C2semidirect
8. #21444528C2semidirect
9. #21444518C2semidirect
10. #21444516C2semidirect
11. #21444506C2semidirect
12. #21444505C2semidirect
13. #21444482C2semidirect
14. #21444473C2semidirect
15. C61×#1559C2semidirect
351. #1559D61semidirect
422. C61#17767semidirect

Maximal subgroups

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

subgroupindex
#214597062
#214549332
#214544862
#214445552
#214445462
#214445372
#214445292
#214445282
#214445182
#214445162
#214445062
#214445052
#214444822
#214444732
C61×#15592
#1776761