Subgroups — #14580310

Order 2624.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050123	C₂	1	2	yes	maximal, complemented
2	#13050079	C₂	1	4	yes	maximal, complemented
3	C₂×#41×C₄₁	C₂	1	1	yes	maximal, characteristic
4	#41×C₄₁	—	2	2	no	—
5	#41×C₄₁	—	2	2	no	—
6	C₂×Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
7	C₂×D₄×C₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂×D₄×C₄₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₄₁	C₄	1	2	yes	complemented
10	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₄₁	C₂²	1	4	yes	—
12	C₄⋊Dic₄₁	—	2	2	no	—
13	C₄×Dic₄₁	—	2	2	no	—
14	C₂³×C₄₁	C₂×C₄	1	2	yes	—
15	C₂³×C₄₁	C₂³	1	1	yes	characteristic
16	Q₈×C₄₁	—	2	2	no	—
17	D₄×C₄₁	—	2	4	no	—
18	D₄×C₄₁	—	2	2	no	—
19	C₂×C₄×C₄₁	—	2	2	no	—
20	C₂×C₄×C₄₁	—	2	2	no	—
21	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₁	D₄	1	2	yes	—
25	C₂×C₄×C₄₁	D₄	1	2	yes	—
26	C₂×Dic₄₁	—	2	4	no	—
27	C₂²×C₄₁	—	2	2	no	—
28	C₂²×C₄₁	—	4	1	no	—
29	C₂²×C₄₁	—	4	2	no	—
30	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄₁	C₂×D₄	1	2	yes	—
32	C₄×C₄₁	—	2	2	no	—
33	C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
35	C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₄₁	—	4	4	no	—
37	C₂×C₄₁	—	2	2	no	—
38	C₂×C₄₁	—	2	1	no	—
39	C₂×C₄₁	—	4	2	no	—
40	C₂×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	#410	—	41	1	no	maximal, Sylow
42	C₄₁	#410	1	1	yes	characteristic, complemented, Sylow
43	C₂×#41	D₄₁	1	1	yes	characteristic
44	#117	—	41	2	no	—
45	#99	—	41	4	no	—
46	#41	—	2	2	no	—
47	#41	—	2	2	no	—
48	C₂×Q₈	Dic₄₁	1	1	yes	characteristic, complemented
49	C₂×D₄	Dic₄₁	1	1	yes	characteristic, complemented
50	C₂×D₄	C₂×D₄₁	1	2	yes	—
51	C₂²×C₄	Dic₄₁	1	2	yes	complemented
52	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
53	C₄⋊C₄	—	82	2	no	—
54	C₂²⋊C₄	—	41	4	no	—
55	C₄²	—	82	2	no	—
56	C₂³	C₂×Dic₄₁	1	2	yes	—
57	C₂³	C₂²×D₄₁	1	1	yes	characteristic
58	Q₈	—	2	2	no	—
59	D₄	—	2	4	no	—
60	D₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	82	4	no	—
64	C₂×C₄	C₂×Dic₄₁	1	2	yes	—
65	C₂×C₄	C₂×Dic₄₁	1	1	yes	characteristic
66	C₂×C₄	C₂×Dic₄₁	1	1	yes	characteristic
67	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
68	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
69	C₂²	—	2	2	no	—
70	C₂²	—	4	1	no	—
71	C₂²	—	4	2	no	—
72	C₂²	C₂²×Dic₄₁	1	1	yes	characteristic
73	C₂²	C₂×C₂²⋊D₄₁	1	2	yes	—
74	C₄	—	2	2	no	—
75	C₄	—	164	4	no	—
76	C₄	C₂²⋊Dic₄₁	1	1	yes	characteristic
77	C₄	C₂²⋊Dic₄₁	1	2	yes	—
78	C₄	C₂²⋊Dic₄₁	1	1	yes	characteristic
79	C₂	—	2	2	no	—
80	C₂	—	2	1	no	—
81	C₂	—	4	2	no	—
82	C₂	C₂×C₂²⋊Dic₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₄₁
commutator	C₂²×C₄₁	C₂²×C₄
Frattini	C₂³	C₂²×D₄₁
Fitting, prime radical	C₂×#41×C₄₁	C₂
socle	C₂×C₄₁	C₂×C₂²⋊C₄
cosocle	C₂³×C₄₁	C₂³
hypercenter	C₂×#41	D₄₁
hypocenter	C₄₁	#410
LCS	G ▷ C₂²×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #13050123	C₂	semidirect
2. #13050079	C₂	semidirect
6. C₂×Q₈×C₄₁	C₄	semidirect
7. C₂×D₄×C₄₁	C₄	semidirect
9. C₂²×C₄×C₄₁	C₄	semidirect
42. C₄₁	#410	semidirect
48. C₂×Q₈	Dic₄₁	semidirect
49. C₂×D₄	Dic₄₁	semidirect
51. C₂²×C₄	Dic₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050123	2
#13050079	2
C₂×#41×C₄₁	2
#410	41