Subgroups — Q₈×#11715906 #20261850

Order 6208.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715906	C₂	1	3	yes	maximal
2	C₄×#11715906	C₂	1	3	yes	maximal
3	Q₈×#87604	C₂	1	1	yes	maximal, characteristic
4	C₂×#11715906	C₂²	1	3	yes	—
5	C₂×#11715906	C₂²	1	1	yes	characteristic
6	C₄⋊#87604	C₄	1	3	yes	—
7	C₄×#87604	C₂²	1	3	yes	—
8	Q₈×D₉₇	C₄	1	1	yes	characteristic
9	C₂×#87604	C₂×C₄	1	3	yes	—
10	C₂×#87604	C₂³	1	1	yes	characteristic
11	#11715906	—	2	3	no	—
12	#11715906	Q₈	1	2	yes	direct product factor
13	Q₈×C₉₇	C₈	1	1	yes	characteristic, complemented
14	C₄×D₉₇	C₂×C₄	1	3	yes	—
15	Dic₁₉₄	C₈	1	3	yes	complemented
16	C₂×D₉₇	C₂²×C₄	1	1	yes	characteristic
17	#87604	—	2	3	no	—
18	#87604	C₂×Q₈	1	1	yes	characteristic
19	#87604	#41	1	1	yes	characteristic
20	C₄×C₉₇	C₂×C₈	1	3	yes	—
21	Dic₉₇	C₂×C₈	1	3	yes	—
22	C₂×C₉₇	C₂²×C₈	1	1	yes	characteristic
23	D₉₇	C₄×Q₈	1	1	yes	characteristic
24	D₉₇	#131	1	1	yes	characteristic
25	C₉₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
26	C₈×Q₈	—	97	1	no	maximal, Sylow
27	C₄×Q₈	—	97	1	no	—
28	C₄⋊C₈	—	97	3	no	—
29	C₄×C₈	—	97	3	no	—
30	C₂×Q₈	—	97	1	no	—
31	C₂×C₈	—	97	1	no	—
32	C₂×C₈	—	97	3	no	—
33	C₄⋊C₄	—	97	3	no	—
34	C₄²	—	97	3	no	—
35	Q₈	—	97	3	no	—
36	Q₈	#11715906	1	1	yes	characteristic, direct product factor
37	C₂×C₄	—	97	1	no	—
38	C₂×C₄	—	97	3	no	—
39	C₂×C₄	—	97	3	no	—
40	C₈	—	97	2	no	—
41	C₈	—	194	3	no	—
42	C₂²	—	97	1	no	—
43	C₄	—	97	1	no	—
44	C₄	—	97	1	no	—
45	C₄	—	97	3	no	—
46	C₄	—	194	3	no	—
47	C₄	C₂×#11715906	1	3	yes	—
48	C₂	—	97	1	no	—
49	C₂	—	97	1	no	—
50	C₂	C₂²×#11715906	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#11715906
commutator, socle	C₂×C₉₇	C₂²×C₈
Fitting	Q₈×C₉₇	C₈
hypercenter	Q₈	#11715906
hypocenter	C₉₇	C₈×Q₈
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
12. #11715906	Q₈	direct (N × H)
13. Q₈×C₉₇	C₈	semidirect
15. Dic₁₉₄	C₈	semidirect
25. C₉₇	C₈×Q₈	semidirect
36. Q₈	#11715906	direct (N × H)

Subgroups — Q8×#11715906 #20261850

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11715906 #20261850