Finite Group Databasebeta

← #29753133

Subgroups — #29753133

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450219C211yesmaximal, characteristic
2#21448844C211yesmaximal, characteristic
3#21447239C211yesmaximal, characteristic, complemented
4#21447199C211yesmaximal, characteristic, complemented
5#21447023C211yesmaximal, characteristic
6#21447016C211yesmaximal, characteristic
7#21446589C211yesmaximal, characteristic, complemented
8#21446557C211yesmaximal, characteristic, complemented
9#21446412C211yesmaximal, characteristic, complemented
10#21446405C211yesmaximal, characteristic, complemented
11#21446076C211yesmaximal, characteristic, complemented
12#21446020C211yesmaximal, characteristic
13#21445915C211yesmaximal, characteristic
14#21445650C211yesmaximal, characteristic, complemented
15C61×#1924C211yesmaximal, characteristic
16C2×#14519756C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519709C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C61⋊#401—21no—
28#16839690—21no—
29#16839668C2211yescharacteristic
30#16839660C2211yescharacteristic
31#16839660C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839656—21no—
34#16839656—21no—
35#16839650—21no—
36#16839644—21no—
37#16839644—21no—
38#16839628C2211yescharacteristic
39#16839622C2211yescharacteristic
40#16839622C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43#16839613—21no—
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60#14519756—22no—
61#14519756—22no—
62C4×Dic122—22no—
63C4×Dic122—41no—
64#14519736—22no—
65#14519736—41no—
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86#14519711—22no—
87#14519711—22no—
88#14519709—22no—
89#14519709—41no—
90#14519702—22no—
91#14519702—22no—
92#14519702—22no—
93#14519702—41no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C23×C4×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114C4⋊C8×C61—22no—
115C22⋊C8×C61—22no—
116C22⋊C8×C61—41no—
117#97×C61—41no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C24×C61C2×D411yescharacteristic
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C2×Dic122—21no—
142C2×Dic122—21no—
143C2×Dic122—21no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122#4112yes—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61#4112yes—
159C22⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—21no—
164C42×C61—21no—
165C22⋊Dic61—24no—
166C22⋊Dic61—42no—
167C22⋊Dic61—42no—
168C22⋊Dic61—81no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61#4112yes—
182C4⋊Dic61#4112yes—
183#11758196—24no—
184#11758196—42no—
185#11758196—42no—
186#11758196—42no—
187#11758196—81no—
188C4×Dic61—42no—
189C4×Dic61—42no—
190C4×Dic61—42no—
191C4×Dic61—81no—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61—21no—
195C23×C61—21no—
196C23×C61—21no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61C22×D411yescharacteristic
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61H(5,𝔽2)11yescharacteristic
224C2×C4×C612−1+411yescharacteristic
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249Dic122—22no—
250Dic122—22no—
251Dic122—41no—
252Dic122—41no—
253C8×C61—22no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61—41no—
257#27061—611nomaximal, Sylow
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61#52511yescharacteristic
266C22×C61#54611yescharacteristic
267C22×C61#54711yescharacteristic
268C22×C61#57511yescharacteristic
269C22×C61#57511yescharacteristic
270C22×C61#57711yescharacteristic
271C22×C61#57811yescharacteristic
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61#52911yescharacteristic
278C4×C61#53911yescharacteristic
279C4×C61#55311yescharacteristic
280C4×C61#55611yescharacteristic
281Dic61—42no—
282Dic61—42no—
283Dic61—42no—
284Dic61—81no—
285Dic61—81no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289#2494—611no—
290#2362—611no—
291#2074—611no—
292#2066—611no—
293#2036—611no—
294#2035—611no—
295#1949—611no—
296#1943—611no—
297#1924D6111yescharacteristic
298#1921—611no—
299#1920—611no—
300#1863—611no—
301#1854—611no—
302#1825—611no—
303#1763—611no—
304C2×C61—81no—
305C2×C61#246611yescharacteristic
306C2×C61#311111yescharacteristic
307C2×C61#312111yescharacteristic
308C2×C61#330711yescharacteristic
309C2×C61#332711yescharacteristic
310C2×C61#334911yescharacteristic
311C2×C61#335011yescharacteristic
312C2×C22⋊Q8—611no—
313C2×C4×Q8—611no—
314C2×#117—611no—
315C2×#107—611no—
316C2×#107—611no—
317C2×#106—611no—
318C2×#106—611no—
319C2×C4⋊C8C2×D6111yescharacteristic
320C2×#103—611no—
321C2×#103—611no—
322C2×#103—611no—
323C2×#103—611no—
324C2×C22⋊C8C2×D6111yescharacteristic
325C2×C22⋊C8C2×D6111yescharacteristic
326C2×#97C2×D6111yescharacteristic
327#401—1221no—
328#397—1221no—
329#391—611no—
330#389—611no—
331#389—611no—
332#389—611no—
333#388—1221no—
334#388—1221no—
335#388—1221no—
336#387—1221no—
337#387—1221no—
338#382—611no—
339#380—611no—
340#380—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4—1221no—
344C4×C22⋊C4C2×D6111yescharacteristic
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#336C2×D6111yescharacteristic
354#336C2×D6111yescharacteristic
355C61#2706111yescharacteristic, complemented, Sylow
356C22×Q8—611no—
357C23×C4C22×D6111yescharacteristic
358C22×C8C22×D6111yescharacteristic
359C22×C8C22×D6111yescharacteristic
360C22×C8C22×D6111yescharacteristic
361C22×C8C22×D6111yescharacteristic
362C22⋊Q8—1222no—
363C22⋊Q8—1222no—
364C4×Q8—1222no—
365C4×Q8—2441no—
366#117—1222no—
367#117—2441no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4D24411yescharacteristic
385C2×C22⋊C4D24411yescharacteristic
386C2×C42—1221no—
387C2×C42—1221no—
388C2×C42—1221no—
389C2×C42—1221no—
390C2×C42C22×D6111yescharacteristic
391C2×C42C22×D6111yescharacteristic
392#107—1222no—
393#107—1222no—
394#106—1222no—
395#106—2441no—
396C4⋊C8—22no—
397#103—1222no—
398#103—1222no—
399#103—1222no—
400#103—2441no—
401C22⋊C8—22no—
402C22⋊C8—41no—
403#97—41no—
404#95—1221no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95D24411yescharacteristic
416#95D24411yescharacteristic
417C24C2×D24411yescharacteristic
418C2×Q8—612no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4C2×D24411yescharacteristic
439C22×C4C2×D24411yescharacteristic
440C22×C4C2×D24411yescharacteristic
441C22×C4C2×D24411yescharacteristic
442C22×C4C2×D24411yescharacteristic
443C22×C4C23×D6111yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8#1175822412yes—
456C4⋊C4—612no—
457C4⋊C4—612no—
458C4⋊C4—1224no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—4881no—
472C4⋊C4—2442no—
473C4⋊C4—2442no—
474C4⋊C4—2442no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—1224no—
478C22⋊C4—4881no—
479C22⋊C4—2442no—
480C22⋊C4—2442no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—4881no—
486C42—2442no—
487C42—2442no—
488C42—2442no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×D24411yescharacteristic
497Q8—1222no—
498Q8—1222no—
499Q8—2441no—
500Q8—2441no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4#41×D6111yescharacteristic
545C2×C4#41×D6111yescharacteristic
546C2×C4#41×D6111yescharacteristic
547C2×C4C2×#1175822411yescharacteristic
548C2×C4#1451982211yescharacteristic
549C2×C4#1451982411yescharacteristic
550C8—22no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1684027411yescharacteristic
562C22#1684040711yescharacteristic
563C22#1684041611yescharacteristic
564C22#1684056211yescharacteristic
565C22#1684056211yescharacteristic
566C22#1684057411yescharacteristic
567C22#1684057911yescharacteristic
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—4881no—
574C4—4881no—
575C4—4881no—
576C4—4881no—
577C4—4881no—
578C4—2442no—
579C4—2442no—
580C4—2442no—
581C4#1684029111yescharacteristic
582C4#1684035511yescharacteristic
583C4#1684045511yescharacteristic
584C4#1684047911yescharacteristic
585C2—81no—
586C2#2144985311yescharacteristic
587C2#2145593011yescharacteristic
588C2#2145605011yescharacteristic
589C2#2145779711yescharacteristic
590C2#2145808911yescharacteristic
591C2#2145835111yescharacteristic
592C2#2145836611yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1924C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#1924D61
hypocenterC61#27061
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
3. #21447239C2semidirect
4. #21447199C2semidirect
7. #21446589C2semidirect
8. #21446557C2semidirect
9. #21446412C2semidirect
10. #21446405C2semidirect
11. #21446076C2semidirect
14. #21445650C2semidirect
355. C61#27061semidirect

Maximal subgroups

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

subgroupindex
#214502192
#214488442
#214472392
#214471992
#214470232
#214470162
#214465892
#214465572
#214464122
#214464052
#214460762
#214460202
#214459152
#214456502
C61×#19242
#2706161