Finite Group Databasebeta

← #29651459

Subgroups — #29651459

Order 15616.

654 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#21454838C211yesmaximal, characteristic, complemented
2#21454832C211yesmaximal, characteristic, complemented
3C4×#14519800C211yesmaximal, characteristic
4#21444709C211yesmaximal, characteristic, complemented
5#21444706C211yesmaximal, characteristic, complemented
6#21444670C211yesmaximal, characteristic, complemented
7#21444650C211yesmaximal, characteristic, complemented
8#21444647C211yesmaximal, characteristic, complemented
9C8×#11758201C211yesmaximal, characteristic, complemented
10#21444616C211yesmaximal, characteristic, complemented
11#21444581C211yesmaximal, characteristic, complemented
12#21444252C211yesmaximal, characteristic, complemented
13#21444252C211yesmaximal, characteristic, complemented
14#21444098C211yesmaximal, characteristic, complemented
15C61×#1584C211yesmaximal, characteristic, complemented
16C2×#14519800C411yescharacteristic
17C4×#11758226C2211yescharacteristic
18C4×#11758226C2211yescharacteristic
19#16839893C2211yescharacteristic
20Q8×#92418C2211yescharacteristic
21Q16×Dic61C411yescharacteristic
22C4×#11758201C2211yescharacteristic
23C4×#11758201C2211yescharacteristic
24#16839847C411yescharacteristic
25#16839847C411yescharacteristic
26C4×D488C2211yescharacteristic
27#16839844C411yescharacteristic
28#16839841—21no—
29#16839841C2211yescharacteristic
30#16839839—21no—
31#16839839C2211yescharacteristic
32#16839835—21no—
33#16839832—21no—
34C8×D244C2211yescharacteristic
35#16839827C2211yescharacteristic
36#16839818—21no—
37#16839818—21no—
38#16839818C2211yescharacteristic
39#16839818C2211yescharacteristic
40#16839813C2211yescharacteristic
41#16839799C411yescharacteristic
42#16839757C411yescharacteristic
43#16839757C411yescharacteristic
44C4×#11758189—21no—
45C4×#11758189C2211yescharacteristic
46#97×D61—21no—
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839491C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758226C2×C411yescharacteristic
68C2×#11758226C2×C411yescharacteristic
69#14519800—24no—
70C2×#11758201C2×C411yescharacteristic
71C2×#11758201C2×C411yescharacteristic
72C2×D488C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189D411yescharacteristic
76C2×#11758189D411yescharacteristic
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61C2×C411yescharacteristic
80C2×C8×D61C2×C411yescharacteristic
81Q8×Dic61C2×C411yescharacteristic
82Q8×Dic61C2×C411yescharacteristic
83C4×D244—21no—
84C4×D244—21no—
85C4×D244C2311yescharacteristic
86C4×D244C2311yescharacteristic
87#14519739—21no—
88#14519739—21no—
89#14519739C2×C411yescharacteristic
90#14519739C2×C411yescharacteristic
91#14519735—21no—
92#14519735—21no—
93#14519735C2×C411yescharacteristic
94#14519735C2×C411yescharacteristic
95C42×D61—21no—
96C42×D61—21no—
97C42×D61C2311yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519708C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519701C2×C411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic
111#14519697C2×C411yescharacteristic
112#14519689—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519688—21no—
120#14519687—21no—
121#14519687—21no—
122#14519687D411yescharacteristic
123#14519687D411yescharacteristic
124C4×#92418—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61C2×C411yescharacteristic
129C8×Dic61C2×C411yescharacteristic
130C2×Q16×C61C2×C411yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#107×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#103×C61C2×C411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147#11758226—22no—
148#11758226—22no—
149#11758226—41no—
150#11758226—41no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244C22×C411yescharacteristic
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164Q16×C61—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C42×C61—21no—
177C42×C61—21no—
178C42×C61C2411yescharacteristic
179#11758201—22no—
180#11758201M1614yescomplemented
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205D488—22no—
206#11758189—22no—
207#11758189—22no—
208#11758189—42no—
209#11758189—42no—
210C8×D61—22no—
211C8×D61—41no—
212C8×D61—42no—
213C8×D61—42no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61C4×D411yescharacteristic
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—21no—
220Q8×C61C2×M1612yes—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61C4×D411yescharacteristic
231C2×Dic61C4×D411yescharacteristic
232C2×Dic61C4×D411yescharacteristic
233D244—21no—
234D244—21no—
235D244—21no—
236D244—42no—
237D244—42no—
238D244C2×M1612yes—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—41no—
244C4×D61—42no—
245C4×D61—42no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—81no—
251C4×D61—81no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61#13512yescomplemented
259#92418—21no—
260#92418—21no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#92418C2×M1612yes—
265#92418#13512yescomplemented
266#18037—611nomaximal, Sylow
267C22×C61C2×C4×D411yescharacteristic
268C2×D61—21no—
269C2×D61—22no—
270C2×D61—21no—
271C2×D61—21no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C4×C61—22no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61C22×M1611yescharacteristic
283C4×C61#56811yescharacteristic
284C4×C61C2×#13511yescharacteristic
285C4×C61C2×#13511yescharacteristic
286Dic61—21no—
287Dic61—21no—
288Dic61—21no—
289Dic61—41no—
290Dic61—41no—
291#2971—611no—
292#2970—611no—
293C4×#135—611no—
294#1590—611no—
295#1590—611no—
296#1584—611no—
297#1584D6111yescharacteristic, complemented
298#1581—611no—
299#1581—611no—
300C8×SD16—611no—
301C8×SD16—611no—
302#1568—611no—
303#1488—611no—
304#1488—611no—
305C8×M16—611no—
306C2×C61D4×M1611yescharacteristic
307C2×C61C4×#13511yescharacteristic
308C2×C61#295711yescharacteristic
309D61—41no—
310D61—42no—
311D61—81no—
312C2×#135—611no—
313C4×#41—611no—
314C4×#41—611no—
315#446—611no—
316#446C2×D6111yescharacteristic
317C8×Q8—611no—
318C8×Q8C2×D6111yescharacteristic
319C4×Q16—611no—
320C4×Q16C2×D6111yescharacteristic
321C4×SD16—611no—
322C4×SD16—611no—
323C4×SD16—611no—
324C4×SD16—611no—
325C4×D8—611no—
326C4×D8—611no—
327#436—611no—
328#436—611no—
329#436—1221no—
330#436—1221no—
331#435—1221no—
332#435—1221no—
333C8×D4—611no—
334C8×D4—611no—
335#432—611no—
336#432—611no—
337#432—1221no—
338#432—1221no—
339#431—611no—
340#427—611no—
341#416—611no—
342#416—611no—
343C4×M16—611no—
344C4×M16—1221no—
345C2×#97—1221no—
346C2×C4×C8—611no—
347#335—611no—
348#335C2×D6111yescharacteristic
349#334—611no—
350#334—611no—
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353Q8⋊C8C2×D6111yescharacteristic
354Q8⋊C8C2×D6111yescharacteristic
355D4⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359#322—611no—
360#322C2×D6111yescharacteristic
361C82—611no—
362C82—611no—
363C61#1803711yescharacteristic, complemented, Sylow
364C2×#41—611no—
365C2×#41—611no—
366#135—1224no—
367C2×Q16C4×D6111yescharacteristic
368C2×SD16—611no—
369C2×SD16—611no—
370C2×D8—611no—
371C2×M16—611no—
372C2×M16—611no—
373C2×M16—1221no—
374C2×M16—1221no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—1221no—
378C22×C8—1221no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×Q8C22×D6111yescharacteristic
382C4×Q8C22×D6111yescharacteristic
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—611no—
386C4×D4—611no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4—1221no—
390C4×D4—1221no—
391#117—611no—
392#117—611no—
393#117—1221no—
394#117—1221no—
395C2×C42—611no—
396C2×C42—1221no—
397C2×C42—1221no—
398#107—611no—
399#107C4×D6111yescharacteristic
400#106—611no—
401#106—611no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411#103—611no—
412#103—611no—
413#103C4×D6111yescharacteristic
414#103C4×D6111yescharacteristic
415#102—611no—
416#102—611no—
417#102—611no—
418#102—611no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426#97—21no—
427#97—611no—
428#97—611no—
429#97—1221no—
430#97—1221no—
431#97—1221no—
432C4×C8—21no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8—1221no—
439C4×C8C22×D6111yescharacteristic
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442#41—1222no—
443#41—1222no—
444#41—2441no—
445#41—2441no—
446C2×Q8C2×C4×D6111yescharacteristic
447C2×Q8C2×C4×D6111yescharacteristic
448C2×D4—611no—
449C2×D4—611no—
450C2×D4—1221no—
451C2×D4—1221no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461Q16—22no—
462SD16—614no—
463SD16—1222no—
464D8—1222no—
465M16—1222no—
466M16—1222no—
467M16—2442no—
468M16—2442no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—1222no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—2441no—
481C2×C8—2442no—
482C2×C8—2442no—
483C2×C8C2×C4×D6111yescharacteristic
484C2×C8C2×C4×D6111yescharacteristic
485C2×C8D4×D6111yescharacteristic
486C2×C8D4×D6111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—611no—
490C4⋊C4—611no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4C2×C4×D6111yescharacteristic
494C4⋊C4C2×C4×D6111yescharacteristic
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C42—21no—
502C42—21no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42C23×D6111yescharacteristic
511C23—611no—
512C23—1221no—
513C23—1221no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8M16×D6112yes—
518D4—612no—
519D4—1221no—
520D4—1221no—
521D4—1221no—
522D4—2442no—
523D4—2442no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—611no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—4881no—
538C2×C4—4881no—
539C2×C4—2441no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4C22×C4×D6111yescharacteristic
547C2×C4C2×D4×D6111yescharacteristic
548C2×C4#41×D6111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—612no—
556C8—612no—
557C8—1221no—
558C8—1221no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C8#1451980012yescomplemented
563C22—1221no—
564C22—1221no—
565C22—1222no—
566C22—1221no—
567C22—2441no—
568C22—2441no—
569C22—2441no—
570C22—2441no—
571C22—2441no—
572C22C4×D4×D6111yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—1221no—
579C4—1221no—
580C4—1221no—
581C4—2441no—
582C4—2441no—
583C4C2×M16×D6111yescharacteristic
584C4#1684052711yescharacteristic
585C4#135×D6111yescharacteristic
586C4C2×#1451980011yescharacteristic
587C2—4881no—
588C2—2441no—
589C2—2442no—
590C2#2145455211yescharacteristic
591C2C4×#1451980011yescharacteristic
592C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1584C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519800C4
cosocleC42×C61C24
hypercenter#1584D61
hypocenterC61#18037
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
1. #21454838C2semidirect
2. #21454832C2semidirect
4. #21444709C2semidirect
5. #21444706C2semidirect
6. #21444670C2semidirect
7. #21444650C2semidirect
8. #21444647C2semidirect
9. C8×#11758201C2semidirect
10. #21444616C2semidirect
11. #21444581C2semidirect
12. #21444252C2semidirect
13. #21444252C2semidirect
14. #21444098C2semidirect
15. C61×#1584C2semidirect
180. #11758201M16semidirect
258. C8×C61#135semidirect
265. #92418#135semidirect
297. #1584D61semidirect
363. C61#18037semidirect
562. C8#14519800semidirect

Maximal subgroups

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

subgroupindex
#214548382
#214548322
C4×#145198002
#214447092
#214447062
#214446702
#214446502
#214446472
C8×#117582012
#214446162
#214445812
#214442522
#214440982
C61×#15842
#1803761