Subgroups — #49093442

Order 35968.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22582818	C₂	1	1	yes	maximal, characteristic
2	#31823297	C₂	1	1	yes	maximal, characteristic, complemented
3	M₆₄×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₂₈₁	C₄	1	1	yes	characteristic
5	#22582818	—	2	1	no	—
6	#22582818	—	2	1	no	—
7	C₂×#17985113	C₄	1	1	yes	characteristic
8	#22582785	—	2	1	no	—
9	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₃₂×C₂₈₁	—	2	1	no	—
11	C₂×C₄×D₂₈₁	C₈	1	1	yes	characteristic
12	C₂×#14555886	C₈	1	1	yes	characteristic
13	C₈×D₂₈₁	—	2	1	no	—
14	C₈×D₂₈₁	—	2	1	no	—
15	#17985113	—	2	1	no	—
16	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₂₈₁	D₄	1	1	yes	characteristic
18	C₁₆×C₂₈₁	D₄	1	1	yes	characteristic
19	C₂²×D₂₈₁	C₁₆	1	1	yes	characteristic
20	C₂×Dic₂₈₁	C₁₆	1	1	yes	characteristic
21	C₄×D₂₈₁	—	2	1	no	—
22	C₄×D₂₈₁	—	2	1	no	—
23	#14555886	—	2	1	no	—
24	C₂×C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
25	C₈×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₈₁	M₁₆	1	1	yes	characteristic
27	C₂²×C₂₈₁	C₂×C₁₆	1	1	yes	characteristic
28	C₂×D₂₈₁	—	2	1	no	—
29	C₂×D₂₈₁	—	4	1	no	—
30	C₄×C₂₈₁	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₂₈₁	M₃₂	1	1	yes	characteristic
32	Dic₂₈₁	—	2	1	no	—
33	C₂×C₂₈₁	—	2	1	no	—
34	C₂×C₂₈₁	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₂₈₁	—	4	1	no	—
36	C₂₈₁	#1400	1	1	yes	characteristic, complemented, Sylow
37	#1400	—	281	1	no	maximal, Sylow
38	C₂×M₃₂	—	281	1	no	—
39	M₆₄	—	281	1	no	—
40	M₆₄	D₂₈₁	1	1	yes	characteristic, complemented
41	C₂²×C₈	—	281	1	no	—
42	M₃₂	—	562	1	no	—
43	M₃₂	—	562	1	no	—
44	C₂×C₁₆	—	281	1	no	—
45	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
46	C₃₂	—	2	1	no	—
47	C₃₂	—	562	1	no	—
48	C₂²×C₄	—	281	1	no	—
49	C₂×C₈	—	281	1	no	—
50	C₂×C₈	—	562	1	no	—
51	C₂×C₈	—	562	1	no	—
52	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
53	C₁₆	—	562	1	no	—
54	C₁₆	C₂²⋊D₂₈₁	1	1	yes	characteristic
55	C₁₆	D₁₁₂₄	1	1	yes	characteristic
56	C₂³	—	281	1	no	—
57	C₂×C₄	—	281	1	no	—
58	C₂×C₄	—	562	1	no	—
59	C₂×C₄	—	562	1	no	—
60	C₂×C₄	C₈×D₂₈₁	1	1	yes	characteristic
61	C₈	—	562	1	no	—
62	C₈	#17985115	1	1	yes	characteristic
63	C₈	#17985121	1	1	yes	characteristic
64	C₂²	—	562	1	no	—
65	C₂²	—	1124	1	no	—
66	C₂²	C₁₆×D₂₈₁	1	1	yes	characteristic
67	C₄	—	562	1	no	—
68	C₄	#22582791	1	1	yes	characteristic
69	C₄	#22582818	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	1124	1	no	—
72	C₂	#31823242	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#17985115
commutator	C₂²×C₂₈₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₂₈₁
Fitting	M₆₄×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₂²⋊C₁₆
prime radical	C₂²×D₂₈₁	C₁₆
cosocle	C₂×C₁₆×C₂₈₁	C₂²
hypercenter	M₆₄	D₂₈₁
hypocenter	C₂₈₁	#1400
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #31823297	C₂	semidirect
3. M₆₄×C₂₈₁	C₂	semidirect
36. C₂₈₁	#1400	semidirect
40. M₆₄	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22582818	2
#31823297	2
M₆₄×C₂₈₁	2
#1400	281