Subgroups — Q₈×#3771 #11798007

Order 1152.

169 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#622	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3771	C₂	1	3	yes	maximal
3	C₄×#3771	C₂	1	3	yes	maximal
4	C₂×#3771	C₂²	1	3	yes	—
5	C₂×#3771	C₂²	1	1	yes	characteristic
6	Q₈×C₃⋊Dic₃	C₄	1	1	yes	characteristic
7	C₄⋊#622	C₄	1	3	yes	—
8	C₄×#622	C₂²	1	3	yes	—
9	C₂×C₃²×Q₈	C₈	1	1	yes	characteristic
10	C₂×#622	C₂×C₄	1	3	yes	—
11	C₂×#622	C₂³	1	1	yes	characteristic
12	#3771	—	2	3	no	—
13	#3771	Q₈	1	2	yes	direct product factor
14	C₄⋊(C₃⋊Dic₃)	C₈	1	3	yes	—
15	C₄×C₃⋊Dic₃	C₂×C₄	1	3	yes	—
16	Q₈×C₁₆	—	9	1	no	maximal, Sylow
17	Q₈×Dic₃	—	12	1	no	—
18	C₃²×Q₈	C₁₆	1	4	yes	complemented
19	C₂×C₃²×C₄	C₂×C₈	1	3	yes	—
20	C₂×C₃⋊Dic₃	C₂×C₈	1	3	yes	—
21	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
22	#622	—	2	3	no	—
23	#622	C₂×Q₈	1	1	yes	characteristic
24	#622	#41	1	1	yes	characteristic
25	C₈×Q₈	—	9	1	no	—
26	C₄⋊C₁₆	—	9	3	no	—
27	C₄×C₁₆	—	9	3	no	—
28	C₂×C₃×Q₈	—	4	1	no	—
29	C₄⋊Dic₃	—	12	3	no	—
30	C₄×Dic₃	—	12	3	no	—
31	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
32	C₃²×C₄	C₂×C₁₆	1	6	yes	—
33	C₃⋊Dic₃	—	2	3	no	—
34	C₃⋊Dic₃	C₄×Q₈	1	1	yes	characteristic
35	C₃⋊Dic₃	#131	1	1	yes	characteristic
36	C₄×Q₈	—	9	1	no	—
37	C₂×C₁₆	—	9	1	no	—
38	C₂×C₁₆	—	9	3	no	—
39	C₄⋊C₈	—	9	3	no	—
40	C₄×C₈	—	9	3	no	—
41	C₃×Q₈	—	4	4	no	—
42	C₂×C₃×C₄	—	4	3	no	—
43	C₂×Dic₃	—	12	1	no	—
44	C₂×Dic₃	—	12	3	no	—
45	C₂×C₃²	C₈×Q₈	1	1	yes	characteristic
46	C₂×C₃²	C₂²×C₁₆	1	1	yes	characteristic
47	C₂×C₃²	#504	1	1	yes	characteristic
48	C₂×Q₈	AGL(1,𝔽₉)	1	1	yes	characteristic
49	C₂×C₈	—	9	1	no	—
50	C₂×C₈	—	9	3	no	—
51	C₄⋊C₄	—	9	3	no	—
52	C₄²	—	9	3	no	—
53	C₁₆	—	9	2	no	—
54	C₁₆	—	18	3	no	—
55	C₂²×C₃	—	4	1	no	—
56	C₃×C₄	—	4	6	no	—
57	Dic₃	—	12	1	no	—
58	Dic₃	—	12	1	no	—
59	Dic₃	—	24	3	no	—
60	C₃²	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
61	Q₈	#3771	1	4	yes	direct product factor
62	C₂×C₄	—	9	1	no	—
63	C₂×C₄	—	9	3	no	—
64	C₂×C₄	C₂×AGL(1,𝔽₉)	1	3	yes	—
65	C₈	—	9	1	no	—
66	C₈	—	9	1	no	—
67	C₈	—	18	3	no	—
68	C₂×C₃	—	4	1	no	—
69	C₂×C₃	—	4	1	no	—
70	C₂×C₃	—	4	1	no	—
71	C₂²	C₂²×AGL(1,𝔽₉)	1	1	yes	characteristic
72	C₄	—	9	1	no	—
73	C₄	—	9	1	no	—
74	C₄	—	18	3	no	—
75	C₄	C₂×#3771	1	6	yes	—
76	C₃	—	4	1	no	—
77	C₂	#10596487	1	1	yes	characteristic
78	C₂	Q₈×AGL(1,𝔽₉)	1	1	yes	characteristic
79	C₂	C₂²×#3771	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×AGL(1,𝔽₉)
commutator	C₂×C₃²	C₂²×C₁₆
Fitting	C₂×C₃²×Q₈	C₈
socle, prime radical	C₂²×C₃²	C₂²×C₈
cosocle	C₂×#622	C₂³
hypercenter	C₂×Q₈	AGL(1,𝔽₉)
hypocenter	C₃²	Q₈×C₁₆
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
13. #3771	Q₈	direct (N × H)
18. C₃²×Q₈	C₁₆	semidirect
60. C₃²	Q₈×C₁₆	semidirect
61. Q₈	#3771	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×#622	2
C₄⋊#3771	2
C₄×#3771	2
Q₈×C₁₆	9

Subgroups — Q8×#3771 #11798007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#3771 #11798007