Subgroups — Q₈×#622 #10593833

Order 576.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#622	C₂	1	3	yes	maximal
3	C₄×#622	C₂	1	3	yes	maximal
4	C₂×C₃²×Q₈	C₄	1	1	yes	characteristic
5	C₂×#622	C₂²	1	3	yes	—
6	C₂×#622	C₂²	1	1	yes	characteristic
7	C₄⋊(C₃⋊Dic₃)	C₄	1	3	yes	—
8	C₄×C₃⋊Dic₃	C₂²	1	3	yes	—
9	Q₈×Dic₃	—	6	2	no	—
10	C₃²×Q₈	C₈	1	4	yes	complemented
11	C₂×C₃²×C₄	C₂×C₄	1	3	yes	—
12	C₂×C₃⋊Dic₃	C₂×C₄	1	3	yes	—
13	C₂×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
14	#622	—	2	3	no	—
15	#622	Q₈	1	2	yes	direct product factor
16	C₈×Q₈	—	9	1	no	maximal, Sylow
17	C₂×C₃×Q₈	—	2	2	no	—
18	C₄⋊Dic₃	—	6	6	no	—
19	C₄×Dic₃	—	6	6	no	—
20	C₂²×C₃²	C₂²×C₄	1	1	yes	characteristic
21	C₃²×C₄	C₂×C₈	1	6	yes	—
22	C₃⋊Dic₃	—	2	3	no	—
23	C₃⋊Dic₃	C₂×Q₈	1	1	yes	characteristic
24	C₃⋊Dic₃	#41	1	1	yes	characteristic
25	C₄×Q₈	—	9	1	no	—
26	C₄⋊C₈	—	9	3	no	—
27	C₄×C₈	—	9	3	no	—
28	C₃×Q₈	—	2	8	no	—
29	C₂×C₃×C₄	—	2	6	no	—
30	C₂×Dic₃	—	6	2	no	—
31	C₂×Dic₃	—	6	6	no	—
32	C₂×C₃²	C₄×Q₈	1	1	yes	characteristic
33	C₂×C₃²	C₂²×C₈	1	1	yes	characteristic
34	C₂×C₃²	#131	1	1	yes	characteristic
35	C₂×Q₈	#157	1	1	yes	characteristic
36	C₂×C₈	—	9	1	no	—
37	C₂×C₈	—	9	3	no	—
38	C₄⋊C₄	—	9	3	no	—
39	C₄²	—	9	3	no	—
40	C₂²×C₃	—	2	2	no	—
41	C₃×C₄	—	2	12	no	—
42	Dic₃	—	6	2	no	—
43	Dic₃	—	6	2	no	—
44	Dic₃	—	12	6	no	—
45	C₃²	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
46	Q₈	#622	1	4	yes	direct product factor
47	C₂×C₄	—	9	1	no	—
48	C₂×C₄	—	9	3	no	—
49	C₂×C₄	C₂×#157	1	3	yes	—
50	C₈	—	9	2	no	—
51	C₈	—	18	3	no	—
52	C₂×C₃	—	2	2	no	—
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	—	2	2	no	—
55	C₂²	C₂²×#157	1	1	yes	characteristic
56	C₄	—	9	1	no	—
57	C₄	—	9	1	no	—
58	C₄	—	18	3	no	—
59	C₄	C₂×#622	1	6	yes	—
60	C₃	—	2	2	no	—
61	C₂	#64289	1	1	yes	characteristic
62	C₂	Q₈×#157	1	1	yes	characteristic
63	C₂	C₂²×#622	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#157
commutator	C₂×C₃²	C₂²×C₈
Fitting	C₂×C₃²×Q₈	C₄
socle, prime radical	C₂²×C₃²	C₂²×C₄
cosocle	C₂×C₃⋊Dic₃	C₂³
hypercenter	C₂×Q₈	#157
hypocenter	C₃²	C₈×Q₈
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
10. C₃²×Q₈	C₈	semidirect
15. #622	Q₈	direct (N × H)
45. C₃²	C₈×Q₈	semidirect
46. Q₈	#622	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×C₃⋊Dic₃	2
C₄⋊#622	2
C₄×#622	2
C₈×Q₈	9

Subgroups — Q8×#622 #10593833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#622 #10593833