Subgroups — #14580772

Order 2624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050186	C₂	1	1	yes	maximal, characteristic, complemented
2	#13050108	C₂	1	2	yes	maximal, complemented
3	#13050105	C₂	1	2	yes	maximal, complemented
4	#13050104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₄₁	—	2	1	no	—
7	#10620306	—	2	1	no	—
8	D₈×C₄₁	—	2	1	no	—
9	D₈×C₄₁	C₂²	1	2	yes	—
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	Dic₁₆₄	C₂²	1	1	yes	characteristic, complemented
12	D₃₂₈	C₂²	1	1	yes	characteristic, complemented
13	#10620273	—	2	1	no	—
14	#10620268	C₂²	1	2	yes	complemented
15	C₂³×C₄₁	—	4	1	no	—
16	D₄×C₄₁	—	2	2	no	—
17	D₄×C₄₁	—	4	1	no	—
18	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
19	C₂²⋊D₄₁	—	4	1	no	—
20	D₁₆₄	—	2	1	no	—
21	C₄×D₄₁	—	4	1	no	—
22	Dic₈₂	—	2	1	no	—
23	C₈×C₄₁	D₄	1	1	yes	characteristic
24	C₈×C₄₁	C₂³	1	1	yes	characteristic
25	C₂²×C₄₁	—	4	2	no	—
26	C₂²×C₄₁	—	8	2	no	—
27	C₂²×C₄₁	D₈	1	1	yes	characteristic
28	C₂×D₄₁	—	4	1	no	—
29	C₄×C₄₁	D₈	1	1	yes	characteristic
30	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
31	Dic₄₁	—	4	1	no	—
32	C₂×C₄₁	—	2	1	no	—
33	C₂×C₄₁	—	8	2	no	—
34	C₂×C₄₁	C₂×D₈	1	1	yes	characteristic
35	D₄₁	—	8	1	no	—
36	#509	—	41	1	no	maximal, Sylow
37	C₄₁	#509	1	1	yes	characteristic, complemented, Sylow
38	#135	—	41	1	no	—
39	C₂×D₈	D₄₁	1	1	yes	characteristic, complemented
40	SD₃₂	—	41	2	no	—
41	D₁₆	—	41	2	no	—
42	M₃₂	—	41	1	no	—
43	#41	—	82	1	no	—
44	C₂×D₄	—	2	1	no	—
45	Q₁₆	—	41	1	no	—
46	SD₁₆	—	82	1	no	—
47	D₈	—	2	1	no	—
48	D₈	—	41	1	no	—
49	D₈	C₂×D₄₁	1	2	yes	—
50	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
51	C₁₆	—	41	2	no	—
52	C₂³	—	4	1	no	—
53	Q₈	—	82	1	no	—
54	D₄	—	2	2	no	—
55	D₄	—	4	1	no	—
56	D₄	—	82	1	no	—
57	D₄	—	164	1	no	—
58	C₂×C₄	—	164	1	no	—
59	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
60	C₈	C₂²⋊D₄₁	1	1	yes	characteristic
61	C₈	C₂²×D₄₁	1	1	yes	characteristic
62	C₂²	—	4	2	no	—
63	C₂²	—	8	2	no	—
64	C₂²	—	164	1	no	—
65	C₂²	#10620282	1	1	yes	characteristic
66	C₄	—	164	1	no	—
67	C₄	#10620282	1	1	yes	characteristic
68	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	8	2	no	—
71	C₂	—	328	1	no	—
72	C₂	C₂×#10620282	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#10620282
commutator, cosocle	C₈×C₄₁	C₂³
Frattini	C₈	C₂²×D₄₁
Fitting	C₂×D₈×C₄₁	C₂
socle	C₂×C₄₁	C₂×D₈
hypercenter	C₂×D₈	D₄₁
hypocenter	C₄₁	#509
LCS	G ▷ C₈×C₄₁ ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. #13050186	C₂	semidirect
2. #13050108	C₂	semidirect
3. #13050105	C₂	semidirect
4. #13050104	C₂	semidirect
5. C₂×D₈×C₄₁	C₂	semidirect
11. Dic₁₆₄	C₂²	semidirect
12. D₃₂₈	C₂²	semidirect
14. #10620268	C₂²	semidirect
37. C₄₁	#509	semidirect
39. C₂×D₈	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050186	2
#13050108	2
#13050105	2
#13050104	2
C₂×D₈×C₄₁	2
#509	41