Subgroups — Q₈×#11764049 #22578518

Order 8768.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11764049	C₂	1	3	yes	maximal
2	C₄×#11764049	C₂	1	3	yes	maximal
3	Q₈×#10587739	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764049	C₂²	1	3	yes	—
5	C₂×#11764049	C₂²	1	1	yes	characteristic
6	C₄⋊#10587739	C₄	1	3	yes	—
7	C₄×#10587739	C₂²	1	3	yes	—
8	Q₈×D₁₃₇	C₄	1	1	yes	characteristic
9	#11764049	—	2	3	no	—
10	#11764049	Q₈	1	2	yes	direct product factor
11	C₂×#10587739	C₂×C₄	1	3	yes	—
12	C₂×#10587739	C₂³	1	1	yes	characteristic
13	Dic₂₇₄	C₈	1	3	yes	complemented
14	C₄×D₁₃₇	C₂×C₄	1	3	yes	—
15	Q₈×C₁₃₇	C₈	1	1	yes	characteristic, complemented
16	C₂×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
17	#10587739	—	2	3	no	—
18	#10587739	C₂×Q₈	1	1	yes	characteristic
19	#10587739	#41	1	1	yes	characteristic
20	C₄×C₁₃₇	C₂×C₈	1	3	yes	—
21	Dic₁₃₇	C₂×C₈	1	3	yes	—
22	C₂×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
23	D₁₃₇	C₄×Q₈	1	1	yes	characteristic
24	D₁₃₇	#131	1	1	yes	characteristic
25	C₁₃₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
26	C₈×Q₈	—	137	1	no	maximal, Sylow
27	C₄×Q₈	—	137	1	no	—
28	C₄⋊C₈	—	137	3	no	—
29	C₄×C₈	—	137	3	no	—
30	C₂×Q₈	—	137	1	no	—
31	C₂×C₈	—	137	3	no	—
32	C₂×C₈	—	137	1	no	—
33	C₄⋊C₄	—	137	3	no	—
34	C₄²	—	137	3	no	—
35	Q₈	—	137	3	no	—
36	Q₈	#11764049	1	1	yes	characteristic, direct product factor
37	C₂×C₄	—	137	3	no	—
38	C₂×C₄	—	137	1	no	—
39	C₂×C₄	—	137	3	no	—
40	C₈	—	274	3	no	—
41	C₈	—	137	2	no	—
42	C₂²	—	137	1	no	—
43	C₄	—	274	3	no	—
44	C₄	—	137	1	no	—
45	C₄	—	137	1	no	—
46	C₄	—	137	3	no	—
47	C₄	C₂×#11764049	1	3	yes	—
48	C₂	—	137	1	no	—
49	C₂	—	137	1	no	—
50	C₂	C₂²×#11764049	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
10. #11764049	Q₈	direct (N × H)
13. Dic₂₇₄	C₈	semidirect
15. Q₈×C₁₃₇	C₈	semidirect
25. C₁₃₇	C₈×Q₈	semidirect
36. Q₈	#11764049	direct (N × H)

Subgroups — Q8×#11764049 #22578518

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11764049 #22578518