Subgroups — #49093494

Order 35968.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₄₉₆	C₂	1	1	yes	maximal, characteristic
2	#31823293	C₂	1	1	yes	maximal, characteristic, complemented
3	M₆₄×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₂₄₈	—	2	1	no	—
5	D₄₄₉₆	—	2	1	no	—
6	D₄₄₉₆	C₄	1	2	yes	—
7	#22582815	—	2	1	no	—
8	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
9	C₃₂×C₂₈₁	—	2	1	no	—
10	C₂×D₁₁₂₄	—	4	1	no	—
11	D₂₂₄₈	—	2	2	no	—
12	D₂₂₄₈	—	4	1	no	—
13	#17985122	—	4	1	no	—
14	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
15	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₈₁	D₄	1	1	yes	characteristic
17	C₂²×D₂₈₁	—	8	1	no	—
18	D₁₁₂₄	—	4	2	no	—
19	D₁₁₂₄	—	8	1	no	—
20	#14555886	—	8	1	no	—
21	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
22	C₈×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₂₈₁	SD₃₂	1	1	yes	characteristic
25	C₂×D₂₈₁	—	8	2	no	—
26	C₂×D₂₈₁	—	16	2	no	—
27	C₄×C₂₈₁	#102	1	1	yes	characteristic
28	C₄×C₂₈₁	D₁₆	1	1	yes	characteristic
29	C₂×C₂₈₁	—	2	1	no	—
30	C₂×C₂₈₁	#357	1	1	yes	characteristic
31	D₂₈₁	—	16	2	no	—
32	C₂₈₁	#1419	1	1	yes	characteristic, complemented, Sylow
33	#1419	—	281	1	no	maximal, Sylow
34	C₂×D₁₆	—	281	1	no	—
35	M₆₄	D₂₈₁	1	1	yes	characteristic, complemented
36	#368	—	281	1	no	—
37	C₂×D₈	—	562	1	no	—
38	D₁₆	—	281	2	no	—
39	D₁₆	—	562	1	no	—
40	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
41	#108	—	562	1	no	—
42	C₃₂	—	2	1	no	—
43	C₂×D₄	—	1124	1	no	—
44	D₈	—	562	2	no	—
45	D₈	—	1124	1	no	—
46	M₁₆	—	1124	1	no	—
47	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
48	C₁₆	C₄×D₂₈₁	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₂₈₁	1	1	yes	characteristic
50	C₂³	—	2248	1	no	—
51	D₄	—	1124	2	no	—
52	D₄	—	2248	1	no	—
53	C₂×C₄	D₂₂₄₈	1	1	yes	characteristic
54	C₈	—	2248	1	no	—
55	C₈	#17985115	1	1	yes	characteristic
56	C₈	#17985127	1	1	yes	characteristic
57	C₂²	—	4496	2	no	—
58	C₂²	—	2248	2	no	—
59	C₂²	#22582824	1	1	yes	characteristic
60	C₄	#22582801	1	1	yes	characteristic
61	C₄	D₄₄₉₆	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4496	2	no	—
64	C₂	#31823265	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31823265
commutator	C₁₆×C₂₈₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₁
Fitting	M₆₄×C₂₈₁	C₂
socle	C₂×C₂₈₁	#357
prime radical	C₂×D₄₄₉₆	C₂
cosocle	C₂×C₁₆×C₂₈₁	C₂²
hypercenter	M₆₄	D₂₈₁
hypocenter	C₂₈₁	#1419
LCS	G ▷ C₁₆×C₂₈₁ ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #31823293	C₂	semidirect
3. M₆₄×C₂₈₁	C₂	semidirect
32. C₂₈₁	#1419	semidirect
35. 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×D₄₄₉₆	2
#31823293	2
M₆₄×C₂₈₁	2
#1419	281