Finite Group Databasebeta

← #30613290

Subgroups — #30613290

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462771C211yesmaximal, characteristic
2#21462721C211yesmaximal, characteristic, complemented
3#21461458C211yesmaximal, characteristic, complemented
4#21461454C211yesmaximal, characteristic, complemented
5#21461446C211yesmaximal, characteristic, complemented
6#21461443C211yesmaximal, characteristic, complemented
7#21461442C211yesmaximal, characteristic, complemented
8#21461435C211yesmaximal, characteristic, complemented
9#21461406C211yesmaximal, characteristic, complemented
10#21461403C211yesmaximal, characteristic, complemented
11#21461393C211yesmaximal, characteristic, complemented
12#21461173C211yesmaximal, characteristic
13D61⋊(Q8⋊C8)C211yesmaximal, characteristic, complemented
14#21461025C211yesmaximal, characteristic, complemented
15#21455904C211yesmaximal, characteristic
16#16840812—21no—
17#16840812—21no—
18#16840812C2211yescharacteristic
19#16840812C2211yescharacteristic
20#16840812C2211yescharacteristic
21#16840811C2211yescharacteristic
22Q8×#92420C2211yescharacteristic
23Q8×#92420C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840792—21no—
26#16840790—21no—
27#16840790C2211yescharacteristic
28#16840787—21no—
29#16840784—21no—
30#16840784C2211yescharacteristic
31#16840781—21no—
32#16840781C2211yescharacteristic
33#16840769—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
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840297C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840094C411yescharacteristic
55#16840077C411yescharacteristic
56#16840066C411yescharacteristic
57#16839985C411yescharacteristic
58#16839984C411yescharacteristic
59#16839919C411yescharacteristic
60#16839902C411yescharacteristic
61#16839856C2211yescharacteristic
62#16839854C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839847C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#479C411yescharacteristic
67C2×#11758213—21no—
68C2×D61⋊C8—21no—
69C2×D61⋊C8—21no—
70C2×D61⋊C8—21no—
71#14519844—21no—
72#14519844—21no—
73C4⋊#92420—21no—
74C4⋊#92420—21no—
75C4⋊#92420—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420D411yescharacteristic
79C4⋊#92420D411yescharacteristic
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×Q8×D61C2×C411yescharacteristic
102C2×Dic244C2×C411yescharacteristic
103C2×#11758202C2×C411yescharacteristic
104C2×#11758190C2×C411yescharacteristic
105C2×#11758201C2×C411yescharacteristic
106#14519772—21no—
107#14519765C2×C411yescharacteristic
108#14519762—21no—
109#14519757C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111Q8×Dic61C2311yescharacteristic
112C4×Dic122—21no—
113C4×Dic122C2×C411yescharacteristic
114#14519742—21no—
115#14519742C2311yescharacteristic
116#14519742C2311yescharacteristic
117#14519739—21no—
118#14519739C2311yescharacteristic
119#14519735—21no—
120C4⋊C4×D61—21no—
121C4⋊C4×D61C2×C411yescharacteristic
122C42×D61—21no—
123C42×D61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#125×C61C2×C411yescharacteristic
138C4×Q8×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145Q8×D61—22no—
146Q8×D61—41no—
147C2×D244—21no—
148C2×D244C22×C411yescharacteristic
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420C2×D411yescharacteristic
165C2×#92420C2×D411yescharacteristic
166C2×#92420C2×D411yescharacteristic
167C2×#92420C2×D411yescharacteristic
168#11758213—81no—
169D61⋊C8—24no—
170D61⋊C8—81no—
171D61⋊C8—81no—
172C2×C8×C61C22×C411yescharacteristic
173C2×C8×C61C22×C411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C42×C61—21no—
181C42×C61C22×C411yescharacteristic
182#11758202—22no—
183#11758201—22no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61#4111yescharacteristic
202C4×Dic61C2411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205Dic244—41no—
206#11758190—41no—
207C22×D61—21no—
208C22×D61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61#13112yes—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C23×C411yescharacteristic
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61C4×D411yescharacteristic
222C2×Dic61C22×D411yescharacteristic
223C2×Dic61C2×#4111yescharacteristic
224D244—21no—
225D244—21no—
226D244—42no—
227C4×D61—22no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—42no—
233C4×D61—42no—
234C4×D61—41no—
235C4×D61—41no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239Dic122—21no—
240Dic122—42no—
241#92420—22no—
242#92420—22no—
243#92420—21no—
244#92420—21no—
245#92420—21no—
246#92420—21no—
247#92420—41no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251C8×C61—21no—
252C8×C61—21no—
253#92418—21no—
254#92418—21no—
255#18017—611nomaximal, Sylow
256C22×C61C2×C4×D411yescharacteristic
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61#44312yes—
263C4×C61—22no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61C2×#13111yescharacteristic
270C4×C61#56811yescharacteristic
271Dic61—21no—
272Dic61—21no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276Dic61#57711yescharacteristic
277Dic61#57811yescharacteristic
278#3108—611no—
279#2994—611no—
280#2984—611no—
281#1591—611no—
282#1590—611no—
283#1588—611no—
284#1587—611no—
285#1587—611no—
286#1585—611no—
287C8×Q16—611no—
288C8×SD16—611no—
289#1573—611no—
290#1494—611no—
291C2×Q8⋊C8—611no—
292#1450—611no—
293C2×C61#293311yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61C2×#44311yescharacteristic
296D61—22no—
297D61—81no—
298#529—611no—
299C2×C4×Q8—611no—
300#483—611no—
301#480—611no—
302#479—611no—
303#479#692311yescharacteristic
304#464—611no—
305#464—611no—
306#451—611no—
307#448—611no—
308#446—611no—
309#446—611no—
310#446—611no—
311#446—1221no—
312#446—1221no—
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8—611no—
316C4×Q16—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320#436—611no—
321#435—1221no—
322C8×D4—611no—
323C8×D4—1221no—
324#433—1221no—
325#432—611no—
326#432—1221no—
327#431—611no—
328#431—611no—
329#431—1221no—
330#424—1221no—
331C2×C4⋊C8—611no—
332C2×C4×C8—611no—
333#335—611no—
334#335—611no—
335#334—611no—
336#334—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343D4⋊C8—611no—
344D4⋊C8—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C82—611no—
349C61#1801711yescharacteristic, complemented, Sylow
350C22×Q8—611no—
351C2×Q16—611no—
352C2×Q16—611no—
353C2×SD16—611no—
354C2×SD16—611no—
355C2×M16—1221no—
356C22×C8—1221no—
357C22×C8—1221no—
358C22×C8—1221no—
359#126—1221no—
360#125C2×#692311yescharacteristic
361#124—611no—
362#123—1221no—
363C22⋊Q8—611no—
364#121—611no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×Q8C2×#692311yescharacteristic
372C4×D4—611no—
373C4×D4—1221no—
374#117—1221no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C42—611no—
378C2×C42—1221no—
379#107—611no—
380#107C2×#692311yescharacteristic
381#106—611no—
382#106C2×#692311yescharacteristic
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C2×#692311yescharacteristic
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103C2×#692311yescharacteristic
403#103C2×#692311yescharacteristic
404#102—611no—
405#102—611no—
406C22⋊C8—611no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416#97—1221no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8—1221no—
427C2×Q8—611no—
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—1222no—
431C2×Q8—2441no—
432C2×Q8C22×#692311yescharacteristic
433C2×D4—611no—
434C2×D4—1221no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441Q16—1222no—
442Q16—2441no—
443SD16—1222no—
444SD16—2441no—
445M16—4881no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1224no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—4881no—
460C2×C8—4881no—
461C2×C8C22×#692311yescharacteristic
462C2×C8C22×#692311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—611no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4C22×#692311yescharacteristic
474C4⋊C4C22×#692311yescharacteristic
475C4⋊C4C22×#692311yescharacteristic
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—21no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C42C22×#692311yescharacteristic
490C23—611no—
491C23—1221no—
492Q8—21no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—1221no—
497Q8—2442no—
498Q8#1451986512yes—
499D4—1221no—
500D4—1221no—
501D4—2442no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1222no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—2442no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2442no—
521C2×C4D4×#692311yescharacteristic
522C2×C4D4×#692311yescharacteristic
523C2×C4C23×#692311yescharacteristic
524C8—21no—
525C8—21no—
526C8—1221no—
527C8—1221no—
528C8—1221no—
529C8—1221no—
530C8—1222no—
531C8—1222no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C22—612no—
539C22—1221no—
540C22—1221no—
541C22—2441no—
542C22—2441no—
543C22—2441no—
544C22C2×D4×#692311yescharacteristic
545C4—22no—
546C4—21no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—611no—
552C4—611no—
553C4—1221no—
554C4—1221no—
555C4—2441no—
556C4—2441no—
557C4—2441no—
558C4C2×#1451986511yescharacteristic
559C4#1684084111yescharacteristic
560C2—1222no—
561C2—4881no—
562C2#2146255211yescharacteristic
563C2#2146257711yescharacteristic
564C2D61⋊#44311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#479C4
socleC22×C61C2×C4×D4
prime radical#14519752C2×C4
cosocleC4×Dic61C24
hypercenter#479#6923
hypocenterC61#18017
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #21462721C2semidirect
3. #21461458C2semidirect
4. #21461454C2semidirect
5. #21461446C2semidirect
6. #21461443C2semidirect
7. #21461442C2semidirect
8. #21461435C2semidirect
9. #21461406C2semidirect
10. #21461403C2semidirect
11. #21461393C2semidirect
13. D61⋊(Q8⋊C8)C2semidirect
14. #21461025C2semidirect
349. C61#18017semidirect

Maximal subgroups

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

subgroupindex
#214627712
#214627212
#214614582
#214614542
#214614462
#214614432
#214614422
#214614352
#214614062
#214614032
#214613932
#214611732
D61⋊(Q8⋊C8)2
#214610252
#214559042
#1801761