Finite Group Databasebeta

← #30612322

Subgroups — #30612322

Order 15616.

702 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462735C211yesmaximal, characteristic
2#21462713C211yesmaximal, characteristic, complemented
3#21461414C211yesmaximal, characteristic, complemented
4#21461413C211yesmaximal, characteristic, complemented
5#21461410C211yesmaximal, characteristic, complemented
6SD16⋊#92420C211yesmaximal, characteristic, complemented
7#21461407C211yesmaximal, characteristic, complemented
8#21461406C211yesmaximal, characteristic, complemented
9#21461402C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461371C211yesmaximal, characteristic, complemented
12#21461111C211yesmaximal, characteristic
13D61⋊(Q8⋊C8)C211yesmaximal, characteristic, complemented
14#21461017C211yesmaximal, characteristic, complemented
15#21454641C211yesmaximal, characteristic
16#16840811—21no—
17#16840811—21no—
18#16840811C2211yescharacteristic
19#16840811C2211yescharacteristic
20#16840811C2211yescharacteristic
21#16840811C2211yescharacteristic
22Q8×#92420C2211yescharacteristic
23Q8×#92420C2211yescharacteristic
24#16840789—21no—
25#16840789—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840781—21no—
29#16840781C2211yescharacteristic
30#16840780—21no—
31#16840780C2211yescharacteristic
32#16840779—21no—
33C2×#14519844—21no—
34D61⋊(C4⋊C8)C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#16840603C2211yescharacteristic
49#16840603C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52C2×#14519806C411yescharacteristic
53C4×#11758224C2211yescharacteristic
54C4×Q8×D61C2211yescharacteristic
55#16839870C411yescharacteristic
56#16839867C411yescharacteristic
57#16839862C411yescharacteristic
58#16839856C2211yescharacteristic
59#16839854C2211yescharacteristic
60#16839853C2211yescharacteristic
61SD16×Dic61C2211yescharacteristic
62#16839803C411yescharacteristic
63#16839769C411yescharacteristic
64#16839760C411yescharacteristic
65#16839714C2211yescharacteristic
66C61×#440C411yescharacteristic
67C2×D61⋊C8—21no—
68C2×D61⋊C8—21no—
69C22×#92420—21no—
70C22×#92420—21no—
71#14519844—21no—
72#14519844—21no—
73#14519844—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834D411yescharacteristic
86#14519834D411yescharacteristic
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C4×#92420—21no—
90C4×#92420—21no—
91C4×#92420—21no—
92C4×#92420—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224C2×C411yescharacteristic
102C2×Q8×D61C2×C411yescharacteristic
103#14519806C818yescomplemented
104C2×Dic244C2×C411yescharacteristic
105C2×#11758202C2×C411yescharacteristic
106C2×#11758200C2×C411yescharacteristic
107C2×#11758189C2×C411yescharacteristic
108C2×#11758189C2×C411yescharacteristic
109Q8×Dic61C2311yescharacteristic
110C4×Dic122—21no—
111C4×Dic122C2×C411yescharacteristic
112C4×Dic122C2×C411yescharacteristic
113#14519742—21no—
114#14519742C2311yescharacteristic
115#14519742C2311yescharacteristic
116D4×Dic61C2311yescharacteristic
117C4×C22⋊D61—21no—
118#14519737—21no—
119#14519735C2×C411yescharacteristic
120#14519733—21no—
121C4⋊C4×D61—21no—
122C4⋊C4×D61C2×C411yescharacteristic
123C2×C4×Dic61—21no—
124C42×D61—21no—
125C42×D61C2311yescharacteristic
126#14519710C2×C411yescharacteristic
127#14519709C2×C411yescharacteristic
128#14519708C2×C411yescharacteristic
129#14519702C2×C411yescharacteristic
130#14519702C2×C411yescharacteristic
131#14519701C2×C411yescharacteristic
132#14519700C2×C411yescharacteristic
133#14519700C2×C411yescharacteristic
134#14519698C2×C411yescharacteristic
135#14519688C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C4×Q8×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141#107×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#97×C61C2×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151Q8×D61—22no—
152Q8×D61C2×C814yescomplemented
153#11758224—22no—
154#11758224C2×C814yes—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61C22×C411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61#4111yescharacteristic
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162C2×Dic122C22×C411yescharacteristic
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—81no—
170C2×#92420—81no—
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175D61⋊C8—42no—
176D61⋊C8—81no—
177SD16×C61C2×C814yescomplemented
178C2×C8×C61C22×C411yescharacteristic
179C2×C8×C61C22×C411yescharacteristic
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—21no—
184C42×C61—21no—
185C42×C61C22×C411yescharacteristic
186C22⋊Dic61—21no—
187#11758202C2×C814yescomplemented
188#11758200C2×C814yescomplemented
189#11758198—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C22×C411yescharacteristic
192C4⋊Dic61C22×C411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C4×Dic61C2411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209Dic244C2×C814yescomplemented
210#11758189—22no—
211#11758189C2×C814yescomplemented
212C23×C61—21no—
213C22×D61C4×D411yescharacteristic
214Q8×C61—21no—
215Q8×C61C22×C812yes—
216D4×C61—21no—
217D4×C61C22×C812yes—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—81no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C22⋊D61—24no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—24no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61C4×D411yescharacteristic
234C2×Dic61C22×D411yescharacteristic
235C2×Dic61C2×#4111yescharacteristic
236C4×D61—24no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—41no—
240C4×D61—81no—
241C4×D61C22×C812yes—
242C4×D61#13112yes—
243Dic122—21no—
244Dic122—21no—
245Dic122—24no—
246Dic122C22×C812yes—
247Dic122C22×C812yes—
248#92420—22no—
249#92420—21no—
250#92420—21no—
251#92420—21no—
252#92420—21no—
253#92420—41no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258C8×C61—21no—
259C8×C61C22×C812yes—
260#92418—21no—
261#92418C22×C812yes—
262#17853—611nomaximal, Sylow
263C22×C61—22no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61C8×D412yes—
270C4×C61—22no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61C23×C811yescharacteristic
276C4×C61C2×#13111yescharacteristic
277Dic61—22no—
278Dic61—22no—
279Dic61—21no—
280Dic61—41no—
281Dic61—41no—
282Dic61C8×D412yes—
283Dic61#57711yescharacteristic
284Dic61#57811yescharacteristic
285#2988—611no—
286#2982—611no—
287C4×#137—611no—
288#1579—611no—
289#1579—611no—
290SD16⋊C8—611no—
291SD16⋊C8—611no—
292C8×Q16—611no—
293C8×Q16—611no—
294C8×SD16—611no—
295C8×SD16—611no—
296#1565—611no—
297#1476—611no—
298C2×Q8⋊C8—611no—
299C8×M16—611no—
300C2×C61—42no—
301C2×C61C2×C8×D411yescharacteristic
302C2×C61#294711yescharacteristic
303C2×C61#295611yescharacteristic
304D61—22no—
305C2×#137—611no—
306C4×#41—611no—
307C2×C4×Q8—611no—
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—1221no—
315C8×Q8—1221no—
316#441—611no—
317#441—611no—
318#440—611no—
319#440#692311yescharacteristic
320C4×Q16—611no—
321C4×Q16—611no—
322C4×SD16—611no—
323C4×SD16—611no—
324C8×D4—611no—
325C8×D4—611no—
326C8×D4—1221no—
327C8×D4—1221no—
328#431—611no—
329#431—611no—
330#431—1221no—
331#431—1221no—
332#431—1221no—
333#428—611no—
334C2×C4⋊C8—611no—
335C2×C4⋊C8—1221no—
336#419—611no—
337#417—611no—
338C4×M16—611no—
339C2×C4×C8—611no—
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352#322—611no—
353#322—611no—
354C82—611no—
355C82—611no—
356C61#1785311yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C22×Q8—611no—
359#137—618no—
360C2×Q16—611no—
361C2×Q16—611no—
362C2×SD16—611no—
363C2×SD16C2×#692311yescharacteristic
364C2×M16—611no—
365C2×M16—611no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—611no—
374C4×Q8—611no—
375C4×Q8—1221no—
376C4×Q8—1221no—
377C4×Q8C2×#692311yescharacteristic
378C4×D4—611no—
379C4×D4—1221no—
380C4×D4—1221no—
381C4×D4C2×#692311yescharacteristic
382#117—611no—
383#117—1221no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1221no—
386C2×C42—611no—
387C2×C42—1221no—
388C2×C42—1221no—
389#107—611no—
390#107C2×#692311yescharacteristic
391#106—611no—
392#106—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406#103—611no—
407#103—611no—
408#103—611no—
409#103—611no—
410#103—611no—
411#103C2×#692311yescharacteristic
412#102—611no—
413#102C2×#692311yescharacteristic
414C22⋊C8—611no—
415C22⋊C8—611no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419#97—611no—
420#97C2×#692311yescharacteristic
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8—1221no—
433C4×C8—1221no—
434C4×C8—1221no—
435#41—614no—
436#41—1222no—
437C2×Q8—614no—
438C2×Q8—611no—
439C2×Q8—611no—
440C2×Q8—1221no—
441C2×Q8—1222no—
442C2×Q8C22×#692311yescharacteristic
443C2×D4—1221no—
444C2×D4C22×#692311yescharacteristic
445C22×C4—21no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453Q16—614no—
454Q16—614no—
455SD16—614no—
456SD16D61⋊C814yescomplemented
457M16—614no—
458M16—1222no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—4881no—
472C2×C8—4881no—
473C2×C8—4881no—
474C2×C8—2442no—
475C2×C8C22×#692311yescharacteristic
476C2×C8C22×#692311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—611no—
479C4⋊C4—611no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4C22×#692311yescharacteristic
487C4⋊C4C22×#692311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—21no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C42—1221no—
501C42C22×#692311yescharacteristic
502C23—21no—
503C23—611no—
504Q8—21no—
505Q8—612no—
506Q8—612no—
507Q8—1224no—
508Q8—1221no—
509Q8—1221no—
510Q8C2×D61⋊C812yes—
511D4—21no—
512D4—1224no—
513D4C2×D61⋊C812yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—81no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—611no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1224no—
526C2×C4—1224no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—4881no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4D4×#692311yescharacteristic
536C2×C4D4×#692311yescharacteristic
537C2×C4C23×#692311yescharacteristic
538C8—21no—
539C8—612no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—1221no—
544C8—1222no—
545C8—1221no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8C2×D61⋊C812yes—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—612no—
556C22—1221no—
557C22—1221no—
558C22C2×D4×#692311yescharacteristic
559C4—21no—
560C4—21no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—611no—
565C4—611no—
566C4—612no—
567C4—1221no—
568C4—1222no—
569C4—1222no—
570C4—2441no—
571C4—2441no—
572C4C22×D61⋊C811yescharacteristic
573C4D61⋊#13111yescharacteristic
574C2—42no—
575C2—1222no—
576C2D4×D61⋊C811yescharacteristic
577C2#2146257711yescharacteristic
578C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC4×C61C23×C8
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C2×C4
cosocleC4×Dic61C24
hypercenter#440#6923
hypocenterC61#17853
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #21462713C2semidirect
3. #21461414C2semidirect
4. #21461413C2semidirect
5. #21461410C2semidirect
6. SD16⋊#92420C2semidirect
7. #21461407C2semidirect
8. #21461406C2semidirect
9. #21461402C2semidirect
10. SD16×#92420C2semidirect
11. #21461371C2semidirect
13. D61⋊(Q8⋊C8)C2semidirect
14. #21461017C2semidirect
103. #14519806C8semidirect
152. Q8×D61C2×C8semidirect
177. SD16×C61C2×C8semidirect
187. #11758202C2×C8semidirect
188. #11758200C2×C8semidirect
209. Dic244C2×C8semidirect
211. #11758189C2×C8semidirect
356. C61#17853semidirect
456. SD16D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214627352
#214627132
#214614142
#214614132
#214614102
SD16⋊#924202
#214614072
#214614062
#214614022
SD16×#924202
#214613712
#214611112
D61⋊(Q8⋊C8)2
#214610172
#214546412
#1785361