Subgroups — Q₈×#11764047 #22578451

Order 8768.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11764047	C₂	1	3	yes	maximal
2	C₄×#11764047	C₂	1	3	yes	maximal
3	Q₈×Dic₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764047	C₂²	1	3	yes	—
5	C₂×#11764047	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₁₃₇	C₄	1	3	yes	—
7	C₄×Dic₁₃₇	C₂²	1	3	yes	—
8	C₂×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
9	#11764047	—	2	3	no	—
10	#11764047	Q₈	1	2	yes	direct product factor
11	C₂×Dic₁₃₇	C₂×C₄	1	3	yes	—
12	C₂×Dic₁₃₇	C₂³	1	1	yes	characteristic
13	Q₈×C₁₃₇	C₈	1	4	yes	complemented
14	C₂×C₄×C₁₃₇	C₂×C₄	1	3	yes	—
15	C₂²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₁₃₇	C₂×C₈	1	6	yes	—
17	Dic₁₃₇	—	2	3	no	—
18	Dic₁₃₇	C₂×Q₈	1	1	yes	characteristic
19	Dic₁₃₇	#41	1	1	yes	characteristic
20	C₂×C₁₃₇	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₃₇	#131	1	1	yes	characteristic
23	C₁₃₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	137	1	no	maximal, Sylow
25	C₄×Q₈	—	137	1	no	—
26	C₄⋊C₈	—	137	3	no	—
27	C₄×C₈	—	137	3	no	—
28	C₂×Q₈	#10587739	1	1	yes	characteristic
29	C₂×C₈	—	137	3	no	—
30	C₂×C₈	—	137	1	no	—
31	C₄⋊C₄	—	137	3	no	—
32	C₄²	—	137	3	no	—
33	Q₈	#11764047	1	4	yes	direct product factor
34	C₂×C₄	—	137	3	no	—
35	C₂×C₄	—	137	1	no	—
36	C₂×C₄	C₂×#10587739	1	3	yes	—
37	C₈	—	274	3	no	—
38	C₈	—	137	2	no	—
39	C₂²	C₂²×#10587739	1	1	yes	characteristic
40	C₄	—	274	3	no	—
41	C₄	—	137	1	no	—
42	C₄	—	137	1	no	—
43	C₄	C₂×#11764047	1	6	yes	—
44	C₂	Q₈×#10587739	1	1	yes	characteristic
45	C₂	C₂²×#11764047	1	1	yes	characteristic
46	C₂	#17984176	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10587739
commutator	C₂×C₁₃₇	C₂²×C₈
Fitting	C₂×Q₈×C₁₃₇	C₄
socle	C₂²×C₁₃₇	C₂²×C₄
hypercenter	C₂×Q₈	#10587739
hypocenter	C₁₃₇	C₈×Q₈
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
10. #11764047	Q₈	direct (N × H)
13. Q₈×C₁₃₇	C₈	semidirect
23. C₁₃₇	C₈×Q₈	semidirect
33. Q₈	#11764047	direct (N × H)

Subgroups — Q8×#11764047 #22578451

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11764047 #22578451