Finite Group Databasebeta

← #30612986

Subgroups — #30612986

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462765C211yesmaximal, characteristic
2#21462727C211yesmaximal, characteristic, complemented
3#21461465C211yesmaximal, characteristic, complemented
4#21461461C211yesmaximal, characteristic, complemented
5#21461458C211yesmaximal, characteristic, complemented
6#21461454C211yesmaximal, characteristic, complemented
7#21461414C211yesmaximal, characteristic, complemented
8#21461411C211yesmaximal, characteristic, complemented
9#21461407C211yesmaximal, characteristic, complemented
10#21461404C211yesmaximal, characteristic, complemented
11#21461384C211yesmaximal, characteristic, complemented
12#21461173C211yesmaximal, characteristic
13#21461169C211yesmaximal, characteristic, complemented
14#21461017C211yesmaximal, characteristic, complemented
15#21456427C211yesmaximal, characteristic
16#16840813—21no—
17#16840813—21no—
18#16840812C2211yescharacteristic
19#16840812C2211yescharacteristic
20#16840812C2211yescharacteristic
21#16840811C2211yescharacteristic
22#16840811C2211yescharacteristic
23#16840811C2211yescharacteristic
24#16840796—21no—
25#16840796C2211yescharacteristic
26#16840792—21no—
27#16840790C2211yescharacteristic
28#16840787—21no—
29#16840787—21no—
30#16840787—21no—
31#16840784C2211yescharacteristic
32#16840780C2211yescharacteristic
33#16840769—21no—
34#16840766C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36#16840625C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44#16840612C2211yescharacteristic
45#16840612C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#16840603C2211yescharacteristic
49#16840603C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840317C2211yescharacteristic
53#16840297C2211yescharacteristic
54#16840156C411yescharacteristic
55#16840132C411yescharacteristic
56#16840124C411yescharacteristic
57#16840021C411yescharacteristic
58#16840021C411yescharacteristic
59#16840009C411yescharacteristic
60#16840009C411yescharacteristic
61#16839856C2211yescharacteristic
62#16839856C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839849C2211yescharacteristic
65#16839714C2211yescharacteristic
66C61×#501C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×D61⋊C8—21no—
70C2×D61⋊C8—21no—
71#14519844—21no—
72#14519844—21no—
73#14519844—21no—
74#14519844D411yescharacteristic
75#14519844D411yescharacteristic
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834D411yescharacteristic
88#14519834D411yescharacteristic
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92#14519832—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×Dic244C2×C411yescharacteristic
102C2×Dic244C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×#11758190C2×C411yescharacteristic
105C2×#11758189C2×C411yescharacteristic
106C2×#11758189C2×C411yescharacteristic
107#14519777C2×C411yescharacteristic
108#14519772—21no—
109#14519768—21no—
110#14519765C2×C411yescharacteristic
111#14519762—21no—
112#14519757C2×C411yescharacteristic
113#14519757C2×C411yescharacteristic
114#14519757C2×C411yescharacteristic
115#14519753—21no—
116#14519752C2×C411yescharacteristic
117Q8×Dic61—21no—
118#14519742C2311yescharacteristic
119#14519742C2311yescharacteristic
120#14519742C2311yescharacteristic
121#14519739—21no—
122#14519739C2311yescharacteristic
123#14519735—21no—
124#14519735—21no—
125C42×D61C2311yescharacteristic
126#14519700C2×C411yescharacteristic
127#14519700C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519700C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519688C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C4⋊Q8×C61C2×C411yescharacteristic
138#125×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#106×C61C2×C411yescharacteristic
143#97×C61C2×C411yescharacteristic
144C2×Q8×C61—21no—
145C2×D244—21no—
146C2×D244C22×C411yescharacteristic
147C2×C4×D61—21no—
148C2×C4×D61C22×C411yescharacteristic
149C2×C4×D61C2×D411yescharacteristic
150C2×C4×D61#4111yescharacteristic
151C2×Dic122C22×C411yescharacteristic
152C2×Dic122C22×C411yescharacteristic
153C2×Dic122C22×C411yescharacteristic
154C2×#92420—21no—
155C2×#92420—21no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420C2×D411yescharacteristic
161C2×#92420C2×D411yescharacteristic
162C2×#92420C2×D411yescharacteristic
163C2×#92420C2×D411yescharacteristic
164#11758213—81no—
165#11758213—81no—
166D61⋊C8—42no—
167D61⋊C8—81no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C4⋊C4×C61C22×C411yescharacteristic
177C42×C61C22×C411yescharacteristic
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C4×Dic61C2411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201Dic244—22no—
202Dic244—22no—
203#11758190—22no—
204#11758190—22no—
205#11758189—22no—
206#11758189—22no—
207C22×D61—21no—
208C22×D61C4×D411yescharacteristic
209Q8×C61—81no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C23×C411yescharacteristic
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61C4×D411yescharacteristic
221C2×Dic61C22×D411yescharacteristic
222C2×Dic61C2×#4111yescharacteristic
223D244—21no—
224D244—21no—
225D244—81no—
226C4×D61—21no—
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—41no—
233Dic122—21no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239#92420—22no—
240#92420—21no—
241#92420—21no—
242#92420—21no—
243#92420—21no—
244#92420—41no—
245#92420—41no—
246#92420—41no—
247#92420—41no—
248#92420—41no—
249C8×C61#13112yes—
250C8×C61#13112yes—
251#92418—21no—
252#92418—21no—
253#17969—611nomaximal, Sylow
254C22×C61C2×C4×D411yescharacteristic
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61C2×#13111yescharacteristic
268C4×C61C2×#13111yescharacteristic
269Dic61—21no—
270Dic61—21no—
271Dic61—41no—
272Dic61—41no—
273Dic61—41no—
274Dic61#57711yescharacteristic
275Dic61#57811yescharacteristic
276#3172—611no—
277#2993—611no—
278#2985—611no—
279#1593—611no—
280#1592—611no—
281#1591—611no—
282#1590—611no—
283#1579—611no—
284SD16⋊C8—611no—
285C8×Q16—611no—
286C8×SD16—611no—
287#1569—611no—
288#1494—611no—
289#1493—611no—
290C8×M16—611no—
291C2×C61#293111yescharacteristic
292C2×C61#294711yescharacteristic
293C2×C61#295611yescharacteristic
294D61—41no—
295D61—81no—
296#533—611no—
297#529—611no—
298#501#692311yescharacteristic
299#497—611no—
300#491—611no—
301#489—611no—
302#470—611no—
303#470—611no—
304#468—611no—
305#468—611no—
306#446—611no—
307#446—611no—
308#446—611no—
309#446—1221no—
310#446—1221no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C4×Q16—611no—
315C4×Q16—611no—
316C4×SD16—611no—
317C4×SD16—611no—
318#436—611no—
319#436—1221no—
320#435—1221no—
321C8×D4—611no—
322#433—1221no—
323#433—1221no—
324#433—1221no—
325#432—611no—
326#431—611no—
327#424—1221no—
328#423—611no—
329C4×M16—611no—
330C2×C4×C8—611no—
331#335—611no—
332#335—611no—
333#334—611no—
334#334—611no—
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341D4⋊C8—611no—
342D4⋊C8—611no—
343#322—611no—
344#322—611no—
345C82—611no—
346C82—611no—
347C61#1796911yescharacteristic, complemented, Sylow
348C2×Q16—611no—
349C2×Q16—611no—
350C2×SD16—611no—
351C2×SD16—611no—
352C2×M16—611no—
353C2×M16—611no—
354C2×M16—1221no—
355C2×M16—1221no—
356C22×C8—1221no—
357C22×C8—1221no—
358C4⋊Q8—611no—
359C4⋊Q8C2×#692311yescharacteristic
360#126—1221no—
361#125—1221no—
362#125C2×#692311yescharacteristic
363#124—611no—
364#123—1221no—
365C22⋊Q8—611no—
366C22⋊Q8—611no—
367C22⋊Q8—611no—
368C22⋊Q8—1221no—
369#121—611no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×D4—611no—
375C4×D4—1221no—
376#117—1221no—
377#117—1221no—
378C2×C42—611no—
379#107C2×#692311yescharacteristic
380#107C2×#692311yescharacteristic
381#106C2×#692311yescharacteristic
382#106C2×#692311yescharacteristic
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#102—611no—
403#102—611no—
404C22⋊C8—611no—
405C22⋊C8—611no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409#97—611no—
410#97—1221no—
411#97—1221no—
412#97—1221no—
413#97—1221no—
414#97C2×#692311yescharacteristic
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8—1221no—
425C2×Q8—21no—
426C2×Q8—611no—
427C2×Q8—611no—
428C2×Q8—611no—
429C2×D4—611no—
430C2×D4—1221no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—1221no—
435Q16—1222no—
436Q16—1222no—
437SD16—1222no—
438SD16—1222no—
439M16—1222no—
440M16—1222no—
441M16—4881no—
442M16—4881no—
443C2×C8—611no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—4881no—
456C2×C8—2442no—
457C2×C8C22×#692311yescharacteristic
458C2×C8C22×#692311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
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⋊C4C22×#692311yescharacteristic
471C4⋊C4C22×#692311yescharacteristic
472C4⋊C4C22×#692311yescharacteristic
473C4⋊C4C22×#692311yescharacteristic
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—611no—
482C42—611no—
483C42—611no—
484C42—1221no—
485C42—1221no—
486C42—1221no—
487C42C22×#692311yescharacteristic
488C23—611no—
489C23—1221no—
490Q8—81no—
491Q8—1221no—
492Q8—1221no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—1221no—
497D4—1221no—
498D4—1221no—
499D4—4881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—611no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4D4×#692311yescharacteristic
518C2×C4D4×#692311yescharacteristic
519C2×C4C23×#692311yescharacteristic
520C8—1221no—
521C8—1221no—
522C8—1221no—
523C8—1221no—
524C8—1222no—
525C8—1221no—
526C8—1221no—
527C8—2441no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C8#1451986512yes—
533C8#1451986512yes—
534C22—1221no—
535C22—1221no—
536C22—1221no—
537C22—2441no—
538C22—2441no—
539C22—2441no—
540C22C2×D4×#692311yescharacteristic
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—611no—
548C4—611no—
549C4—1221no—
550C4—1221no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4C2×#1451986511yescharacteristic
555C4C2×#1451986511yescharacteristic
556C2—4881no—
557C2—2441no—
558C2#2146254411yescharacteristic
559C2#2146257711yescharacteristic
560C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#501C4
socleC22×C61C2×C4×D4
prime radical#14519752C2×C4
cosocleC4×Dic61C24
hypercenter#501#6923
hypocenterC61#17969
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #21462727C2semidirect
3. #21461465C2semidirect
4. #21461461C2semidirect
5. #21461458C2semidirect
6. #21461454C2semidirect
7. #21461414C2semidirect
8. #21461411C2semidirect
9. #21461407C2semidirect
10. #21461404C2semidirect
11. #21461384C2semidirect
13. #21461169C2semidirect
14. #21461017C2semidirect
347. C61#17969semidirect

Maximal subgroups

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

subgroupindex
#214627652
#214627272
#214614652
#214614612
#214614582
#214614542
#214614142
#214614112
#214614072
#214614042
#214613842
#214611732
#214611692
#214610172
#214564272
#1796961