Finite Group Databasebeta

← #29648956

Subgroups — #29648956

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459706C211yesmaximal, characteristic
2#21454946C211yesmaximal, characteristic
3#21454941C211yesmaximal, characteristic
4#21444548C211yesmaximal, characteristic, complemented
5#21444548C211yesmaximal, characteristic, complemented
6#21444544C211yesmaximal, characteristic, complemented
7#21444526C211yesmaximal, characteristic, complemented
8#21444526C211yesmaximal, characteristic, complemented
9#21444519C211yesmaximal, characteristic, complemented
10#21444508C211yesmaximal, characteristic, complemented
11#21444508C211yesmaximal, characteristic, complemented
12#21444475C211yesmaximal, characteristic, complemented
13#21444475C211yesmaximal, characteristic, complemented
14C2×#16839510C211yesmaximal, characteristic, complemented
15C61×#1552C211yesmaximal, characteristic, complemented
16#16840491—21no—
17#16840491—21no—
18#16840485—21no—
19#16840485—21no—
20#16840454—21no—
21#16840454—21no—
22#16840454—21no—
23#16840454—21no—
24#16840375C412yes—
25#16840375C412yes—
26#16840338C412yes—
27#16840317C2211yescharacteristic
28#16840317C2211yescharacteristic
29#16840317C2211yescharacteristic
30#16840317C2211yescharacteristic
31C2×#14519777C2211yescharacteristic
32#16840239C412yes—
33C4×#11758222C2211yescharacteristic
34#16839891—21no—
35#16839890—21no—
36#16839835—21no—
37#16839833—21no—
38#16839832—21no—
39#16839830—21no—
40C8×C22⋊D61—21no—
41#16839825—21no—
42#16839819C2211yescharacteristic
43#16839818C2211yescharacteristic
44#16839818C2211yescharacteristic
45#16839814C2211yescharacteristic
46#16839814C2211yescharacteristic
47#16839784C2211yescharacteristic
48#16839784C2211yescharacteristic
49C2×C4⋊#92418C2211yescharacteristic
50C4⋊C8×D61C2211yescharacteristic
51C4⋊C8×D61C2211yescharacteristic
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839510C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839510C2211yescharacteristic
59#16839510C2211yescharacteristic
60#16839508C2211yescharacteristic
61#16839508C2211yescharacteristic
62#16839508C2211yescharacteristic
63#16839508C2211yescharacteristic
64C61×#533C2211yescharacteristic
65C61×#432C2211yescharacteristic
66C2×C4⋊C8×C61C2211yescharacteristic
67C61×#332C2211yescharacteristic
68C61×#332C2211yescharacteristic
69C61×#332C2211yescharacteristic
70C61×#332C2211yescharacteristic
71C2×#11758222C2×C411yescharacteristic
72C22×Dic122C2×C412yes—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78#14519777—22no—
79#14519777—21no—
80#14519777—21no—
81#14519777C2×C412yes—
82#14519777C2311yescharacteristic
83#14519777C2311yescharacteristic
84#14519772—22no—
85#14519772—22no—
86#14519772—22no—
87#14519772—22no—
88#14519768—22no—
89#14519768—22no—
90#14519768—22no—
91#14519768—22no—
92#14519768—21no—
93#14519768—21no—
94#14519768—21no—
95#14519768—21no—
96#14519765—22no—
97#14519761—22no—
98#14519761—22no—
99#14519757C2×C412yes—
100#14519757C2×C412yes—
101#14519757C2×C412yes—
102#14519757C2×C412yes—
103#14519753—21no—
104#14519753—21no—
105#14519753—21no—
106#14519753—21no—
107Q8×Dic61—21no—
108Q8×Dic61—21no—
109Q8×Dic61—21no—
110Q8×Dic61—21no—
111C4×Dic122—22no—
112C4×Dic122—22no—
113C4×Dic122D411yescharacteristic
114C4×Dic122D411yescharacteristic
115#14519742C2×C412yes—
116#14519742C2×C412yes—
117#14519742C2×C412yes—
118#14519742C2×C412yes—
119C4×D244D411yescharacteristic
120C4×D244D411yescharacteristic
121C4×C22⋊D61D411yescharacteristic
122C4×C22⋊D61D411yescharacteristic
123C4×C22⋊D61D411yescharacteristic
124C4×C22⋊D61D411yescharacteristic
125#14519736C2×C411yescharacteristic
126#14519735—21no—
127#14519735—21no—
128#14519735—21no—
129#14519735—21no—
130#14519734C2×C411yescharacteristic
131#14519734C2×C411yescharacteristic
132#14519733—22no—
133#14519733—22no—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61—21no—
136C42×D61C2311yescharacteristic
137C42×D61C2311yescharacteristic
138C4⋊#92418—21no—
139C4⋊#92418C2311yescharacteristic
140C4⋊#92418C2311yescharacteristic
141C4⋊#92418C2311yescharacteristic
142C4⋊#92418C2311yescharacteristic
143#14519706—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147C22⋊#92418—21no—
148#14519689—21no—
149#14519689—21no—
150#14519689—21no—
151#14519689—21no—
152#14519688—21no—
153#14519687—21no—
154#14519687—21no—
155C8×Dic61—21no—
156C8×Dic61—21no—
157C22×C8×C61—21no—
158C4⋊Q8×C61C2311yescharacteristic
159C4⋊Q8×C61C2311yescharacteristic
160#125×C61C2×C412yes—
161C22⋊Q8×C61—21no—
162C22⋊Q8×C61—21no—
163C4×Q8×C61—21no—
164C4×Q8×C61—21no—
165#117×C61C2×C412yes—
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×C61—21no—
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—42no—
183C2×D244C22⋊C411yescharacteristic
184C2×C4×D61C22×C411yescharacteristic
185C2×C4×D61C22×C411yescharacteristic
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×Dic122—22no—
191C2×Dic122—44no—
192C2×Dic122C22⋊C411yescharacteristic
193C2×Dic122C22×C412yes—
194C2×Dic122C22×C412yes—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—81no—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C22×C412yes—
205C4⋊C4×C61C22×C412yes—
206C22⋊C4×C61—22no—
207C42×C61—22no—
208C42×C61C22×C411yescharacteristic
209C42×C61C2×D411yescharacteristic
210C42×C61C2×D411yescharacteristic
211C42×C61C2411yescharacteristic
212C22⋊Dic61C22⋊C411yescharacteristic
213C22⋊Dic61C22⋊C411yescharacteristic
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758198—22no—
218#11758198C22⋊C411yescharacteristic
219#11758198C22⋊C411yescharacteristic
220#11758198C22⋊C411yescharacteristic
221#11758198C22⋊C411yescharacteristic
222C4⋊Dic61—22no—
223C4⋊Dic61—22no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—22no—
229C4⋊Dic61—22no—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61C22⋊C411yescharacteristic
233C4⋊Dic61C22⋊C411yescharacteristic
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238#11758196C22⋊C411yescharacteristic
239#11758196C22⋊C411yescharacteristic
240#11758196C22⋊C411yescharacteristic
241#11758196C22⋊C411yescharacteristic
242C4×Dic61—22no—
243C4×Dic61—22no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246C4×Dic61C22×C411yescharacteristic
247C4×Dic61C22×C411yescharacteristic
248C4×Dic61C2×D411yescharacteristic
249C4×Dic61C2×D411yescharacteristic
250C4×Dic61C2×D411yescharacteristic
251C4×Dic61C2×D411yescharacteristic
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—81no—
257#11758189—81no—
258#11758189—81no—
259C8×D61—81no—
260C8×D61—81no—
261C23×C61C2×C22⋊C411yescharacteristic
262C22×D61C2×C22⋊C411yescharacteristic
263C22×D61C2×C22⋊C411yescharacteristic
264Q8×C61—41no—
265Q8×C61—41no—
266Q8×C61—41no—
267Q8×C61—41no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
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—22no—
282C22⋊D61—22no—
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—42no—
306Dic122—42no—
307C8×C61—41no—
308C8×C61—41no—
309C8×C61—41no—
310C8×C61—41no—
311#92418—41no—
312#92418—41no—
313#92418—41no—
314#92418—41no—
315#17780—611nomaximal, Sylow
316C22×C61—21no—
317C22×C61—21no—
318C22×C61#41312yes—
319C22×C61C22×C22⋊C411yescharacteristic
320C2×D61—21no—
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—21no—
324C2×D61—21no—
325C2×D61—21no—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—21no—
330C4×C61—42no—
331C4×C61—42no—
332C4×C61#57711yescharacteristic
333C4×C61#57711yescharacteristic
334C4×C61#57811yescharacteristic
335C4×C61#57811yescharacteristic
336Dic61—21no—
337Dic61—21no—
338Dic61—21no—
339Dic61—21no—
340Dic61—21no—
341Dic61—21no—
342Dic61—42no—
343Dic61—42no—
344#3509—611no—
345#2990—611no—
346#2990—611no—
347#1559—611no—
348#1559—611no—
349#1558—611no—
350#1554—611no—
351#1554—611no—
352#1552—611no—
353#1552D6111yescharacteristic, complemented
354#1550—611no—
355#1550—611no—
356#1542—611no—
357#1542—611no—
358C2×#333—611no—
359C2×C61—22no—
360C2×C61C2×#41311yescharacteristic
361C2×C61#289811yescharacteristic
362C2×C61#289811yescharacteristic
363D61—41no—
364D61—41no—
365#557—1221no—
366#557—1221no—
367#556—1221no—
368#556—1221no—
369#552—1221no—
370#552—1221no—
371#552—1221no—
372#552—1221no—
373#541—612no—
374#541—612no—
375#536—612no—
376#533—611no—
377#533—611no—
378#533—611no—
379#533—611no—
380#533C2×D6111yescharacteristic
381C2×C4⋊Q8—611no—
382#519—612no—
383C4×#41—611no—
384#446—1221no—
385#446—1221no—
386#435—1221no—
387#435—1221no—
388#435—1221no—
389#435—1221no—
390C8×D4—1221no—
391C8×D4—1221no—
392#432—611no—
393#432—611no—
394#432—611no—
395#432C2×D6111yescharacteristic
396#431—611no—
397#431—611no—
398#423—611no—
399#423—611no—
400C2×C4⋊C8—611no—
401C2×C4⋊C8—611no—
402C2×C4⋊C8—611no—
403C2×C4⋊C8C2×D6111yescharacteristic
404#333—611no—
405#333—611no—
406#333—611no—
407#333—611no—
408#333—611no—
409#333—611no—
410#333—611no—
411#333—611no—
412#332—611no—
413#332—611no—
414#332—611no—
415#332—611no—
416#332C2×D6111yescharacteristic
417#332C2×D6111yescharacteristic
418#332C2×D6111yescharacteristic
419#332C2×D6111yescharacteristic
420C61#1778011yescharacteristic, complemented, Sylow
421C2×#41—611no—
422C22×Q8—612no—
423C2×M16—1221no—
424C2×M16—1221no—
425C22×C8—21no—
426C22×C8—1221no—
427C22×C8—1221no—
428C22×C8—1221no—
429C4⋊Q8—612no—
430C4⋊Q8—611no—
431C4⋊Q8—611no—
432C4⋊Q8—1222no—
433C4⋊Q8—1221no—
434C4⋊Q8—1221no—
435C4⋊Q8C22×D6111yescharacteristic
436C4⋊Q8C22×D6111yescharacteristic
437#126—1222no—
438#126—1222no—
439#126—1222no—
440#126—1222no—
441#125—1221no—
442#125—1221no—
443#125—1221no—
444#125—1221no—
445#125—1222no—
446#125—1222no—
447#125—1222no—
448#125—1222no—
449#125C4×D6112yes—
450#124—1222no—
451#123—1222no—
452#123—1222no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—612no—
456C22⋊Q8—612no—
457C22⋊Q8—612no—
458C22⋊Q8—612no—
459C22⋊Q8—1221no—
460C22⋊Q8—1221no—
461C22⋊Q8—1221no—
462C22⋊Q8—1221no—
463C4×Q8—21no—
464C4×Q8—21no—
465C4×Q8—611no—
466C4×Q8—611no—
467C4×Q8—612no—
468C4×Q8—612no—
469C4×Q8—612no—
470C4×Q8—612no—
471C4×Q8—1222no—
472C4×Q8—1222no—
473C4×Q8—1221no—
474C4×Q8—1221no—
475C4×Q8—1221no—
476C4×Q8—1221no—
477C4×D4—611no—
478C4×D4—611no—
479C4×D4—611no—
480C4×D4—611no—
481C4×D4—611no—
482C4×D4—611no—
483#117—611no—
484#117—611no—
485#117—611no—
486#117—1222no—
487#117—1222no—
488#117—1221no—
489#117—1221no—
490#117—1221no—
491#117—1221no—
492#117C4×D6112yes—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42C22×D6111yescharacteristic
498C4⋊C8—21no—
499C4⋊C8—611no—
500C4⋊C8—611no—
501C4⋊C8—611no—
502C4⋊C8—611no—
503C4⋊C8—1221no—
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—
518#97—21no—
519#97—1221no—
520#97—1221no—
521#97—1221no—
522C4×C8—1221no—
523C4×C8—1221no—
524#41—2442no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—611no—
528C2×Q8—612no—
529C2×Q8—612no—
530C2×Q8—1222no—
531C2×Q8—2444no—
532C2×D4—611no—
533C2×D4—611no—
534C2×D4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—1222no—
542C22×C4C2×C4×D6111yescharacteristic
543C22×C4D4×D6111yescharacteristic
544C22×C4D4×D6111yescharacteristic
545M16—4881no—
546M16—4881no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—81no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—4881no—
557C2×C8—4881no—
558C2×C8—4881no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—611no—
564C4⋊C4—611no—
565C4⋊C4—611no—
566C4⋊C4—611no—
567C4⋊C4—611no—
568C4⋊C4—611no—
569C4⋊C4—1222no—
570C4⋊C4—1222no—
571C4⋊C4—1222no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1222no—
582C4⋊C4—1222no—
583C4⋊C4C2×C4×D6112yes—
584C4⋊C4C2×C4×D6112yes—
585C22⋊C4—22no—
586C22⋊C4—611no—
587C22⋊C4—611no—
588C22⋊C4—611no—
589C22⋊C4—611no—
590C22⋊C4—611no—
591C22⋊C4—611no—
592C22⋊C4—1222no—
593C22⋊C4—1222no—
594C22⋊C4—1222no—
595C22⋊C4—1222no—
596C42—22no—
597C42—611no—
598C42—611no—
599C42—611no—
600C42—611no—
601C42—611no—
602C42—611no—
603C42—1222no—
604C42—1222no—
605C42—1222no—
606C42—1222no—
607C42C2×C4×D6111yescharacteristic
608C42D4×D6111yescharacteristic
609C42D4×D6111yescharacteristic
610C42C23×D6111yescharacteristic
611C23—611no—
612C23—611no—
613C23C22⋊C4×D6111yescharacteristic
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—2441no—
619Q8—2442no—
620Q8—2442no—
621Q8—2444no—
622D4—1222no—
623D4—1222no—
624D4—2441no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—611no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—611no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2444no—
651C2×C4C22⋊C4×D6111yescharacteristic
652C2×C4C22⋊C4×D6111yescharacteristic
653C2×C4C22⋊C4×D6111yescharacteristic
654C2×C4C22×C4×D6111yescharacteristic
655C2×C4C2×D4×D6111yescharacteristic
656C2×C4C2×D4×D6111yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C8—2441no—
662C8—2441no—
663C8—2441no—
664C8—2441no—
665C22—21no—
666C22—21no—
667C22—1221no—
668C22—1221no—
669C22—1221no—
670C22—1221no—
671C22—1221no—
672C22—1221no—
673C22#1683974512yes—
674C22C2×C22⋊C4×D6111yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—42no—
680C4—42no—
681C4—1221no—
682C4—1221no—
683C4—1221no—
684C4—1221no—
685C4—1221no—
686C4—1221no—
687C4—2442no—
688C4—2442no—
689C4#1684056911yescharacteristic
690C4#1684057211yescharacteristic
691C4#1684057611yescharacteristic
692C4#1684057811yescharacteristic
693C2—22no—
694C2—2441no—
695C2—2441no—
696C2C2×#1683974511yescharacteristic
697C2#2145434811yescharacteristic
698C2#2145435011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1552C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1552D61
hypocenterC61#17780
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
4. #21444548C2semidirect
5. #21444548C2semidirect
6. #21444544C2semidirect
7. #21444526C2semidirect
8. #21444526C2semidirect
9. #21444519C2semidirect
10. #21444508C2semidirect
11. #21444508C2semidirect
12. #21444475C2semidirect
13. #21444475C2semidirect
14. C2×#16839510C2semidirect
15. C61×#1552C2semidirect
353. #1552D61semidirect
420. C61#17780semidirect

Maximal subgroups

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

subgroupindex
#214597062
#214549462
#214549412
#214445482
#214445442
#214445262
#214445192
#214445082
#214444752
C2×#168395102
C61×#15522
#1778061