Subgroups — #49093277

Order 35968.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823581	C₂	1	1	yes	maximal, characteristic
2	#31823284	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈²×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#22582901	C₄	1	1	yes	characteristic
5	#22582885	—	2	1	no	—
6	#22582819	—	2	1	no	—
7	#22582815	C₄	1	1	yes	characteristic
8	#22582807	—	2	1	no	—
9	C₄×C₈×C₂₈₁	—	2	1	no	—
10	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
11	#17985138	—	2	1	no	—
12	Dic₁₁₂₄	C₈	1	1	yes	characteristic, complemented
13	#17985127	—	2	1	no	—
14	D₂₂₄₈	C₈	1	1	yes	characteristic, complemented
15	#17985122	—	2	1	no	—
16	#17985121	—	4	1	no	—
17	C₈×D₂₈₁	—	4	1	no	—
18	#17985113	—	4	1	no	—
19	C₂×C₈×C₂₈₁	—	2	2	no	—
20	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
22	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
23	Dic₅₆₂	—	2	1	no	—
24	D₁₁₂₄	—	2	1	no	—
25	C₂²⋊D₂₈₁	—	4	1	no	—
26	C₄×D₂₈₁	—	4	1	no	—
27	#14555886	—	4	1	no	—
28	C₂×C₄×C₂₈₁	—	2	1	no	—
29	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₈×C₂₈₁	—	2	4	no	—
31	C₈×C₂₈₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₂₈₁	M₁₆	1	1	yes	characteristic
33	C₈×C₂₈₁	D₈	1	1	yes	characteristic
34	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
35	C₂²×C₂₈₁	#104	1	1	yes	characteristic
36	C₂×D₂₈₁	—	4	1	no	—
37	C₄×C₂₈₁	—	2	2	no	—
38	C₄×C₂₈₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₂₈₁	#102	1	1	yes	characteristic
40	Dic₂₈₁	—	4	1	no	—
41	C₂×C₂₈₁	—	2	1	no	—
42	C₂×C₂₈₁	D₄⋊C₈	1	1	yes	characteristic
43	D₂₈₁	—	8	1	no	—
44	C₂₈₁	#1335	1	1	yes	characteristic, complemented, Sylow
45	#1335	—	281	1	no	maximal, Sylow
46	#443	—	281	1	no	—
47	#364	—	281	1	no	—
48	C₈²	D₂₈₁	1	1	yes	characteristic, complemented
49	#135	—	281	1	no	—
50	#131	—	562	1	no	—
51	M₃₂	—	562	1	no	—
52	#108	—	281	1	no	—
53	#104	—	562	1	no	—
54	C₄×C₈	—	2	1	no	—
55	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
56	#41	—	562	1	no	—
57	Q₁₆	—	281	1	no	—
58	SD₁₆	—	562	1	no	—
59	D₈	—	281	1	no	—
60	M₁₆	—	562	1	no	—
61	M₁₆	—	1124	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	1124	1	no	—
64	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
65	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
66	C₄²	C₂²⋊D₂₈₁	1	1	yes	characteristic
67	C₁₆	—	1124	1	no	—
68	Q₈	—	562	1	no	—
69	D₄	—	562	1	no	—
70	D₄	—	1124	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	1124	1	no	—
73	C₂×C₄	#17985115	1	1	yes	characteristic
74	C₈	—	2	4	no	—
75	C₈	—	1124	1	no	—
76	C₈	C₈×D₂₈₁	1	1	yes	characteristic
77	C₈	#17985121	1	1	yes	characteristic
78	C₈	D₂₂₄₈	1	1	yes	characteristic
79	C₈	#17985127	1	1	yes	characteristic
80	C₂²	—	1124	1	no	—
81	C₂²	#22582807	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	1124	1	no	—
84	C₄	#22582791	1	1	yes	characteristic
85	C₄	#22582801	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	2248	1	no	—
88	C₂	#31823192	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₂₂₄₈
commutator	C₈×C₂₈₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	C₈²×C₂₈₁	C₂
socle	C₂×C₂₈₁	D₄⋊C₈
prime radical	#22582901	C₄
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	C₈²	D₂₈₁
hypocenter	C₂₈₁	#1335
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #31823284	C₂	semidirect
3. C₈²×C₂₈₁	C₂	semidirect
12. Dic₁₁₂₄	C₈	semidirect
14. D₂₂₄₈	C₈	semidirect
44. C₂₈₁	#1335	semidirect
48. C₈²	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823581	2
#31823284	2
C₈²×C₂₈₁	2
#1335	281