Subgroups — (C₂×#87938)⋊C₈ #20266042

Order 6464.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₀₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#87938	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#87938	C₄	1	2	yes	—
5	D₁₀₁⋊C₈	—	2	1	no	—
6	D₁₀₁⋊C₈	—	2	1	no	—
7	C₂×#11717581	C₄	1	2	yes	complemented
8	C₄×#87938	—	2	1	no	—
9	C₄×#87938	—	2	1	no	—
10	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×#11717579	C₄	1	1	yes	characteristic, complemented
12	C₈×D₁₀₁	—	2	1	no	—
13	C₈×D₁₀₁	—	2	1	no	—
14	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×D₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×#87938	—	2	2	no	—
17	C₂×#87938	—	2	2	no	—
18	C₂×#87938	C₈	1	4	yes	complemented
19	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₄×D₁₀₁	D₄	1	1	yes	characteristic
22	C₄×D₁₀₁	D₄	1	1	yes	characteristic
23	C₄×D₁₀₁	D₄	1	1	yes	characteristic
24	C₄×D₁₀₁	Q₈	1	1	yes	characteristic
25	#11717581	—	2	2	no	—
26	C₈×C₁₀₁	—	2	1	no	—
27	#11717579	—	2	1	no	—
28	C₂²×C₁₀₁	C₄²	1	1	yes	characteristic
29	C₂×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₁₀₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₁₀₁	C₂×C₈	1	2	yes	—
32	C₂×D₁₀₁	M₁₆	1	2	yes	—
33	#87938	—	2	4	no	—
34	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
36	Dic₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
37	Dic₁₀₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₁₀₁	#95	1	1	yes	characteristic
39	C₂×C₁₀₁	C₄×C₈	1	1	yes	characteristic
40	C₂×C₁₀₁	#97	1	1	yes	characteristic
41	D₁₀₁	C₂²⋊C₈	1	2	yes	—
42	D₁₀₁	C₄⋊C₈	1	2	yes	—
43	C₁₀₁	#336	1	1	yes	characteristic, complemented, Sylow
44	#336	—	101	1	no	maximal, Sylow
45	C₂²×C₈	—	101	1	no	—
46	C₂²×C₈	—	101	1	no	—
47	C₂×C₄²	—	101	1	no	—
48	C₂²×C₄	—	101	1	no	—
49	C₂²×C₄	—	101	2	no	—
50	C₂×C₈	—	101	2	no	—
51	C₂×C₈	—	101	1	no	—
52	C₂×C₈	—	202	1	no	—
53	C₂×C₈	—	202	1	no	—
54	C₂×C₈	—	202	1	no	—
55	C₂×C₈	—	202	1	no	—
56	C₂×C₈	#87938	1	1	yes	characteristic, complemented
57	C₄²	—	202	1	no	—
58	C₄²	—	202	1	no	—
59	C₂³	—	101	1	no	—
60	C₂×C₄	—	101	1	no	—
61	C₂×C₄	—	101	1	no	—
62	C₂×C₄	—	101	1	no	—
63	C₂×C₄	—	101	1	no	—
64	C₂×C₄	—	101	1	no	—
65	C₂×C₄	—	101	4	no	—
66	C₂×C₄	—	202	2	no	—
67	C₂×C₄	—	202	2	no	—
68	C₂×C₄	C₂×#87938	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	202	2	no	—
71	C₈	—	202	1	no	—
72	C₂²	—	101	1	no	—
73	C₂²	—	101	1	no	—
74	C₂²	—	101	2	no	—
75	C₂²	—	101	2	no	—
76	C₂²	C₄×#87938	1	1	yes	characteristic
77	C₄	—	101	1	no	—
78	C₄	—	101	1	no	—
79	C₄	—	202	4	no	—
80	C₄	C₂²⋊#87938	1	1	yes	characteristic
81	C₄	C₄⋊#87938	1	1	yes	characteristic
82	C₂	—	101	2	no	—
83	C₂	—	101	2	no	—
84	C₂	(C₂×#87938)⋊C₄	1	1	yes	characteristic
85	C₂	C₈×#87938	1	1	yes	characteristic
86	C₂	#15692309	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#87938
commutator	C₂×C₁₀₁	C₄×C₈
Fitting	C₂×C₈×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₄²
hypercenter	C₂×C₈	#87938
hypocenter	C₁₀₁	#336
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₂×#11717581	C₄	semidirect
11. C₂×#11717579	C₄	semidirect
14. C₂×C₈×C₁₀₁	C₄	semidirect
18. C₂×#87938	C₈	semidirect
43. C₁₀₁	#336	semidirect
56. C₂×C₈	#87938	semidirect

Subgroups — (C2×#87938)⋊C8 #20266042

Conjugacy classes of subgroups

Complements

Subgroups — (C₂×#87938)⋊C₈ #20266042