Subgroups — D₄×#11929639 #23778860

Order 10144.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11929639	C₂	1	2	yes	maximal, complemented
2	C₄⋊#11929639	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#11929639	C₂	1	2	yes	maximal, complemented
4	C₄×#11929639	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₃₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929639	—	2	4	no	—
7	C₂×#11929639	C₂²	1	1	yes	characteristic
8	C₂×#11929639	C₂²	1	2	yes	—
9	C₂×#11929639	C₂²	1	1	yes	characteristic
10	C₂²×D₃₁₇	C₂²	1	2	yes	—
11	D₁₂₆₈	C₄	1	1	yes	characteristic, complemented
12	C₂²⋊D₃₁₇	C₄	1	2	yes	complemented
13	C₄×D₃₁₇	C₂²	1	1	yes	characteristic
14	D₄×C₃₁₇	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₃₁₇	C₂×C₄	1	2	yes	complemented
16	C₂×D₃₁₇	—	2	2	no	—
17	C₂×D₃₁₇	—	2	2	no	—
18	C₂×D₃₁₇	C₂×C₄	1	2	yes	complemented
19	C₂×D₃₁₇	C₂³	1	1	yes	characteristic
20	#11929639	—	2	2	no	—
21	#11929639	—	2	1	no	—
22	#11929639	D₄	1	2	yes	direct product factor
23	C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic, complemented
24	Dic₃₁₇	C₂×C₄	1	1	yes	characteristic, complemented
25	C₂×C₃₁₇	—	2	2	no	—
26	C₂×C₃₁₇	C₂²×C₄	1	1	yes	characteristic
27	D₃₁₇	—	2	2	no	—
28	D₃₁₇	C₂×D₄	1	1	yes	characteristic
29	D₃₁₇	#41	1	1	yes	characteristic
30	C₃₁₇	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
31	C₄×D₄	—	317	1	no	maximal, Sylow
32	C₂×D₄	—	317	1	no	—
33	C₂²×C₄	—	317	2	no	—
34	C₄⋊C₄	—	317	1	no	—
35	C₂²⋊C₄	—	317	2	no	—
36	C₄²	—	317	1	no	—
37	C₂³	—	317	2	no	—
38	D₄	—	317	2	no	—
39	D₄	—	317	1	no	—
40	D₄	#11929639	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	317	1	no	—
42	C₂×C₄	—	317	1	no	—
43	C₂×C₄	—	317	1	no	—
44	C₂×C₄	—	317	2	no	—
45	C₂×C₄	—	634	4	no	—
46	C₂²	—	317	1	no	—
47	C₂²	—	317	2	no	—
48	C₂²	—	634	2	no	—
49	C₂²	—	634	2	no	—
50	C₂²	C₂×#11929639	1	2	yes	complemented
51	C₄	—	317	2	no	—
52	C₄	—	317	1	no	—
53	C₄	—	634	2	no	—
54	C₄	—	634	1	no	—
55	C₄	C₂×#11929639	1	1	yes	characteristic, complemented
56	C₂	—	2	2	no	—
57	C₂	—	317	1	no	—
58	C₂	—	317	1	no	—
59	C₂	—	634	2	no	—
60	C₂	C₂²×#11929639	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#11929639
commutator, socle	C₂×C₃₁₇	C₂²×C₄
Fitting	D₄×C₃₁₇	C₄
prime radical	D₄×D₃₁₇	C₂
cosocle	C₂×D₃₁₇	C₂³
hypercenter	D₄	#11929639
hypocenter	C₃₁₇	C₄×D₄
LCS	G ▷ C₂×C₃₁₇ ▷ C₃₁₇
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#11929639	C₂	semidirect
2. C₄⋊#11929639	C₂	semidirect
3. C₂²⋊#11929639	C₂	semidirect
4. C₄×#11929639	C₂	semidirect
11. D₁₂₆₈	C₄	semidirect
12. C₂²⋊D₃₁₇	C₄	semidirect
14. D₄×C₃₁₇	C₄	semidirect
15. C₂²×C₃₁₇	C₂×C₄	semidirect
18. C₂×D₃₁₇	C₂×C₄	semidirect
22. #11929639	D₄	direct (N × H)
23. C₄×C₃₁₇	C₂×C₄	semidirect
24. Dic₃₁₇	C₂×C₄	semidirect
30. C₃₁₇	C₄×D₄	semidirect
40. D₄	#11929639	direct (N × H)
50. C₂²	C₂×#11929639	semidirect
55. C₄	C₂×#11929639	semidirect

Subgroups — D4×#11929639 #23778860

Conjugacy classes of subgroups

Complements

Subgroups — D₄×#11929639 #23778860