Subgroups — (C₂×#11929639)⋊C₈ #35204088

Order 20288.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₁₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11929639	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₃₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11929639	C₄	1	2	yes	—
5	D₃₁₇⋊C₈	—	2	1	no	—
6	D₃₁₇⋊C₈	—	2	1	no	—
7	C₂×#14579268	C₄	1	2	yes	complemented
8	C₄×#11929639	—	2	1	no	—
9	C₄×#11929639	—	2	1	no	—
10	C₂×C₄×D₃₁₇	C₂²	1	1	yes	characteristic
11	C₂×#14579261	C₄	1	1	yes	characteristic, complemented
12	C₈×D₃₁₇	—	2	1	no	—
13	C₈×D₃₁₇	—	2	1	no	—
14	C₂×C₈×C₃₁₇	C₄	1	1	yes	characteristic, complemented
15	C₂×#11929639	—	2	2	no	—
16	C₂×#11929639	—	2	2	no	—
17	C₂×#11929639	C₈	1	4	yes	complemented
18	#14579268	—	2	2	no	—
19	C₂²×D₃₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₁₇	C₂×C₄	1	1	yes	characteristic
21	C₄×D₃₁₇	D₄	1	1	yes	characteristic
22	C₄×D₃₁₇	D₄	1	1	yes	characteristic
23	C₄×D₃₁₇	D₄	1	1	yes	characteristic
24	C₄×D₃₁₇	Q₈	1	1	yes	characteristic
25	#14579261	—	2	1	no	—
26	C₂×C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic
27	C₈×C₃₁₇	—	2	1	no	—
28	C₂²×C₃₁₇	C₄²	1	1	yes	characteristic
29	C₂×D₃₁₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₃₁₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₃₁₇	C₂×C₈	1	2	yes	—
32	C₂×D₃₁₇	M₁₆	1	2	yes	—
33	#11929639	—	2	4	no	—
34	C₄×C₃₁₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₃₁₇	C₄⋊C₄	1	1	yes	characteristic
36	Dic₃₁₇	C₂²⋊C₄	1	1	yes	characteristic
37	Dic₃₁₇	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₃₁₇	#95	1	1	yes	characteristic
39	C₂×C₃₁₇	C₄×C₈	1	1	yes	characteristic
40	C₂×C₃₁₇	#97	1	1	yes	characteristic
41	D₃₁₇	C₂²⋊C₈	1	2	yes	—
42	D₃₁₇	C₄⋊C₈	1	2	yes	—
43	C₃₁₇	#336	1	1	yes	characteristic, complemented, Sylow
44	#336	—	317	1	no	maximal, Sylow
45	C₂²×C₈	—	317	1	no	—
46	C₂²×C₈	—	317	1	no	—
47	C₂×C₄²	—	317	1	no	—
48	C₂²×C₄	—	317	1	no	—
49	C₂²×C₄	—	317	2	no	—
50	C₂×C₈	—	317	2	no	—
51	C₂×C₈	—	317	1	no	—
52	C₂×C₈	—	634	1	no	—
53	C₂×C₈	—	634	1	no	—
54	C₂×C₈	—	634	1	no	—
55	C₂×C₈	—	634	1	no	—
56	C₂×C₈	#11929639	1	1	yes	characteristic, complemented
57	C₄²	—	634	1	no	—
58	C₄²	—	634	1	no	—
59	C₂³	—	317	1	no	—
60	C₂×C₄	—	317	1	no	—
61	C₂×C₄	—	317	1	no	—
62	C₂×C₄	—	317	1	no	—
63	C₂×C₄	—	317	1	no	—
64	C₂×C₄	—	317	1	no	—
65	C₂×C₄	—	317	4	no	—
66	C₂×C₄	—	634	2	no	—
67	C₂×C₄	—	634	2	no	—
68	C₂×C₄	C₂×#11929639	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	634	2	no	—
71	C₈	—	634	1	no	—
72	C₂²	—	317	1	no	—
73	C₂²	—	317	1	no	—
74	C₂²	—	317	2	no	—
75	C₂²	—	317	2	no	—
76	C₂²	C₄×#11929639	1	1	yes	characteristic
77	C₄	—	317	1	no	—
78	C₄	—	317	1	no	—
79	C₄	—	634	4	no	—
80	C₄	C₂²⋊#11929639	1	1	yes	characteristic
81	C₄	C₄⋊#11929639	1	1	yes	characteristic
82	C₂	—	317	2	no	—
83	C₂	—	317	2	no	—
84	C₂	(C₂×#11929639)⋊C₄	1	1	yes	characteristic
85	C₂	C₈×#11929639	1	1	yes	characteristic
86	C₂	#23778834	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11929639
commutator	C₂×C₃₁₇	C₄×C₈
Fitting	C₂×C₈×C₃₁₇	C₄
socle	C₂²×C₃₁₇	C₄²
prime radical	C₂²×D₃₁₇	C₂×C₄
cosocle	C₂×C₄×D₃₁₇	C₂²
hypercenter	C₂×C₈	#11929639
hypocenter	C₃₁₇	#336
LCS	G ▷ C₂×C₃₁₇ ▷ C₃₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₂×#14579268	C₄	semidirect
11. C₂×#14579261	C₄	semidirect
14. C₂×C₈×C₃₁₇	C₄	semidirect
17. C₂×#11929639	C₈	semidirect
43. C₃₁₇	#336	semidirect
56. C₂×C₈	#11929639	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₃₁₇⋊C₈	2
C₂×C₄×#11929639	2
C₂×C₈×D₃₁₇	2
#336	317

Subgroups — (C2×#11929639)⋊C8 #35204088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#11929639)⋊C₈ #35204088