Subgroups — Q₈⋊#11764049 #22578491

Order 8768.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11764049	C₂	1	1	yes	maximal, characteristic
2	C₄×#11764049	C₂	1	1	yes	maximal, characteristic
3	Q₈×#10587739	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764049	—	2	1	no	—
5	C₂×#11764049	—	2	1	no	—
6	C₄⋊#10587739	—	2	1	no	—
7	C₄⋊#10587739	C₄	1	1	yes	characteristic
8	C₄×#10587739	—	2	1	no	—
9	C₄×#10587739	C₂²	1	1	yes	characteristic
10	Q₈×D₁₃₇	C₄	1	1	yes	characteristic
11	#11764049	—	2	2	no	—
12	#11764049	—	4	1	no	—
13	C₂×#10587739	—	2	1	no	—
14	C₂×#10587739	D₄	1	1	yes	characteristic
15	C₂×#10587739	D₄	1	1	yes	characteristic
16	Dic₂₇₄	—	2	1	no	—
17	Dic₂₇₄	C₈	1	1	yes	characteristic, complemented
18	C₄×D₁₃₇	—	2	1	no	—
19	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
20	Q₈×C₁₃₇	C₈	1	1	yes	characteristic, complemented
21	C₂×D₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	#10587739	—	2	1	no	—
23	#10587739	—	4	1	no	—
24	#10587739	SD₁₆	1	1	yes	characteristic
25	#10587739	Q₁₆	1	1	yes	characteristic
26	C₄×C₁₃₇	—	2	1	no	—
27	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
28	Dic₁₃₇	—	2	1	no	—
29	Dic₁₃₇	M₁₆	1	1	yes	characteristic
30	C₂×C₁₃₇	C₂²⋊C₈	1	1	yes	characteristic
31	D₁₃₇	#103	1	1	yes	characteristic
32	D₁₃₇	#104	1	1	yes	characteristic
33	C₁₃₇	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
34	Q₈⋊C₈	—	137	1	no	maximal, Sylow
35	C₄×Q₈	—	137	1	no	—
36	C₄⋊C₈	—	137	1	no	—
37	C₄×C₈	—	137	1	no	—
38	C₂×Q₈	—	137	1	no	—
39	C₂×C₈	—	274	1	no	—
40	C₂×C₈	—	274	1	no	—
41	C₄⋊C₄	—	274	1	no	—
42	C₄⋊C₄	—	137	1	no	—
43	C₄²	—	274	1	no	—
44	C₄²	—	137	1	no	—
45	Q₈	—	274	1	no	—
46	Q₈	—	137	1	no	—
47	Q₈	#11764049	1	1	yes	characteristic, complemented
48	C₂×C₄	—	274	1	no	—
49	C₂×C₄	—	274	1	no	—
50	C₂×C₄	—	137	1	no	—
51	C₂×C₄	—	137	1	no	—
52	C₂×C₄	—	137	1	no	—
53	C₈	—	274	2	no	—
54	C₈	—	548	1	no	—
55	C₂²	—	137	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	274	1	no	—
58	C₄	—	274	1	no	—
59	C₄	—	548	1	no	—
60	C₄	—	137	1	no	—
61	C₄	—	137	1	no	—
62	C₄	—	137	1	no	—
63	C₄	C₂×#11764049	1	1	yes	characteristic
64	C₂	—	137	1	no	—
65	C₂	—	137	1	no	—
66	C₂	C₂²⋊#11764049	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#11764049
commutator	C₄×C₁₃₇	C₂×C₈
Frattini	C₄	C₂×#11764049
Fitting	Q₈×C₁₃₇	C₈
socle	C₂×C₁₃₇	C₂²⋊C₈
hypercenter	Q₈	#11764049
hypocenter	C₁₃₇	Q₈⋊C₈
LCS	G ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
17. Dic₂₇₄	C₈	semidirect
20. Q₈×C₁₃₇	C₈	semidirect
33. C₁₃₇	Q₈⋊C₈	semidirect
47. Q₈	#11764049	semidirect

Subgroups — Q8⋊#11764049 #22578491

Conjugacy classes of subgroups

Complements

Subgroups — Q₈⋊#11764049 #22578491