Subgroups — #49094908

Order 35968.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823843	C₂	1	1	yes	maximal, characteristic, complemented
2	#31823809	C₂	1	4	yes	maximal, complemented
3	C₈×#14555886	C₂	1	1	yes	maximal, characteristic, complemented
4	#493×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₁₂₄	—	2	2	no	—
6	#22582879	C₂²	1	2	yes	—
7	#22582800	—	2	8	no	—
8	C₄×#14555886	C₂²	1	2	yes	—
9	C₂×D₈×C₂₈₁	—	2	2	no	—
10	#127×C₂₈₁	C₂²	1	2	yes	—
11	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
12	C₂×Dic₅₆₂	—	2	2	no	—
13	Dic₁₁₂₄	—	4	4	no	—
14	C₂×#14555886	D₄	1	4	yes	—
15	C₄⋊Dic₂₈₁	—	2	4	no	—
16	C₂×D₄×C₂₈₁	—	2	4	no	—
17	C₂×D₄×C₂₈₁	—	2	2	no	—
18	D₈×C₂₈₁	—	4	4	no	—
19	C₂×C₈×C₂₈₁	D₄	1	2	yes	—
20	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
21	Dic₅₆₂	—	4	4	no	—
22	C₂×Dic₂₈₁	—	4	2	no	—
23	#14555886	—	2	4	no	—
24	C₂³×C₂₈₁	—	4	2	no	—
25	D₄×C₂₈₁	—	4	4	no	—
26	D₄×C₂₈₁	—	4	8	no	—
27	C₂×C₄×C₂₈₁	C₂×D₄	1	2	yes	—
28	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₈₁	D₈	1	4	yes	—
30	C₂²×C₂₈₁	—	8	2	no	—
31	C₂²×C₂₈₁	—	8	4	no	—
32	C₂²×C₂₈₁	#127	1	1	yes	characteristic
33	C₄×C₂₈₁	C₂×D₈	1	2	yes	—
34	C₄×C₂₈₁	#135	1	4	yes	—
35	Dic₂₈₁	—	8	2	no	—
36	C₂×C₂₈₁	—	16	2	no	—
37	C₂×C₂₈₁	#493	1	1	yes	characteristic
38	C₂×C₂₈₁	#495	1	2	yes	—
39	C₂₈₁	#1709	1	1	yes	characteristic, complemented, Sylow
40	#1709	—	281	1	no	maximal, Sylow
41	#494	—	281	1	no	—
42	#493	D₂₈₁	1	1	yes	characteristic
43	#486	—	281	4	no	—
44	C₈²	—	281	1	no	—
45	C₂×Q₁₆	—	562	2	no	—
46	C₂×D₈	—	2	2	no	—
47	C₄⋊Q₈	—	281	2	no	—
48	#127	C₂×D₂₈₁	1	2	yes	—
49	#102	—	562	8	no	—
50	C₄×C₈	—	281	2	no	—
51	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
52	C₂×Q₈	—	562	2	no	—
53	C₂×D₄	—	2	4	no	—
54	C₂×D₄	—	2	2	no	—
55	Q₁₆	—	1124	4	no	—
56	D₈	—	4	4	no	—
57	C₂×C₈	—	281	4	no	—
58	C₂×C₈	C₂²⋊D₂₈₁	1	2	yes	—
59	C₄⋊C₄	—	562	4	no	—
60	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
61	C₂³	—	4	2	no	—
62	Q₈	—	1124	4	no	—
63	D₄	—	4	4	no	—
64	D₄	—	4	8	no	—
65	C₂×C₄	—	1124	2	no	—
66	C₂×C₄	D₄×D₂₈₁	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
68	C₈	—	562	4	no	—
69	C₈	#17985123	1	4	yes	—
70	C₂²	—	8	2	no	—
71	C₂²	—	8	4	no	—
72	C₂²	#22582875	1	1	yes	characteristic
73	C₄	—	2248	2	no	—
74	C₄	C₂×#17985123	1	2	yes	—
75	C₄	#22582898	1	4	yes	—
76	C₂	—	16	2	no	—
77	C₂	#31823839	1	1	yes	characteristic
78	C₂	#31823846	1	2	yes	—

	subgroup	G/H
center	C₂²	#22582875
commutator, cosocle	C₄²×C₂₈₁	C₂³
Frattini	C₄²	C₂²×D₂₈₁
Fitting, prime radical	#493×C₂₈₁	C₂
socle	C₂²×C₂₈₁	#127
hypercenter	#493	D₂₈₁
hypocenter	C₂₈₁	#1709
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

Complements

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

N	H ≅ G/N	type
1. #31823843	C₂	semidirect
2. #31823809	C₂	semidirect
3. C₈×#14555886	C₂	semidirect
39. C₂₈₁	#1709	semidirect

Maximal subgroups

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

subgroup	index
#31823843	2
#31823809	2
C₈×#14555886	2
#493×C₂₈₁	2
#1709	281