Subgroups — #49119400

Order 36224.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22583549	C₂	1	1	yes	maximal, characteristic
2	#31826299	C₂	1	1	yes	maximal, characteristic, complemented
3	M₆₄×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₂₈₃	C₄	1	1	yes	characteristic
5	#22583549	—	2	1	no	—
6	#22583549	—	2	1	no	—
7	C₂×C₂₈₃⋊C₁₆	C₄	1	1	yes	characteristic
8	C₂₈₃⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₂₈₃	—	2	1	no	—
11	C₂×C₄×D₂₈₃	C₈	1	1	yes	characteristic
12	C₂×C₂₈₃⋊C₈	C₈	1	1	yes	characteristic
13	C₈×D₂₈₃	—	2	1	no	—
14	C₈×D₂₈₃	—	2	1	no	—
15	C₂₈₃⋊C₁₆	—	2	1	no	—
16	C₂×C₈×C₂₈₃	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₂₈₃	D₄	1	1	yes	characteristic
18	C₁₆×C₂₈₃	D₄	1	1	yes	characteristic
19	C₂²×D₂₈₃	C₁₆	1	1	yes	characteristic
20	C₂×Dic₂₈₃	C₁₆	1	1	yes	characteristic
21	C₄×D₂₈₃	—	2	1	no	—
22	C₄×D₂₈₃	—	2	1	no	—
23	C₂₈₃⋊C₈	—	2	1	no	—
24	C₂×C₄×C₂₈₃	C₂×C₈	1	1	yes	characteristic
25	C₈×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₈₃	M₁₆	1	1	yes	characteristic
27	C₂²×C₂₈₃	C₂×C₁₆	1	1	yes	characteristic
28	C₂×D₂₈₃	—	2	1	no	—
29	C₂×D₂₈₃	—	4	1	no	—
30	C₄×C₂₈₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₂₈₃	M₃₂	1	1	yes	characteristic
32	Dic₂₈₃	—	2	1	no	—
33	C₂×C₂₈₃	—	2	1	no	—
34	C₂×C₂₈₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₂₈₃	—	4	1	no	—
36	C₂₈₃	#1400	1	1	yes	characteristic, complemented, Sylow
37	#1400	—	283	1	no	maximal, Sylow
38	C₂×M₃₂	—	283	1	no	—
39	M₆₄	—	283	1	no	—
40	M₆₄	D₂₈₃	1	1	yes	characteristic, complemented
41	C₂²×C₈	—	283	1	no	—
42	M₃₂	—	566	1	no	—
43	M₃₂	—	566	1	no	—
44	C₂×C₁₆	—	283	1	no	—
45	C₂×C₁₆	C₂×D₂₈₃	1	1	yes	characteristic
46	C₃₂	—	2	1	no	—
47	C₃₂	—	566	1	no	—
48	C₂²×C₄	—	283	1	no	—
49	C₂×C₈	—	283	1	no	—
50	C₂×C₈	—	566	1	no	—
51	C₂×C₈	—	566	1	no	—
52	C₂×C₈	C₄×D₂₈₃	1	1	yes	characteristic
53	C₁₆	—	566	1	no	—
54	C₁₆	C₂²⋊D₂₈₃	1	1	yes	characteristic
55	C₁₆	D₁₁₃₂	1	1	yes	characteristic
56	C₂³	—	283	1	no	—
57	C₂×C₄	—	283	1	no	—
58	C₂×C₄	—	566	1	no	—
59	C₂×C₄	—	566	1	no	—
60	C₂×C₄	C₈×D₂₈₃	1	1	yes	characteristic
61	C₈	—	566	1	no	—
62	C₈	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
63	C₈	#17985375	1	1	yes	characteristic
64	C₂²	—	566	1	no	—
65	C₂²	—	1132	1	no	—
66	C₂²	C₁₆×D₂₈₃	1	1	yes	characteristic
67	C₄	—	566	1	no	—
68	C₄	(C₂×D₂₈₃)⋊C₈	1	1	yes	characteristic
69	C₄	#22583549	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	1132	1	no	—
72	C₂	(C₂×D₂₈₃)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×D₂₈₃)⋊C₄
commutator	C₂²×C₂₈₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₂₈₃
Fitting	M₆₄×C₂₈₃	C₂
socle	C₂×C₂₈₃	C₂²⋊C₁₆
prime radical	C₂²×D₂₈₃	C₁₆
cosocle	C₂×C₁₆×C₂₈₃	C₂²
hypercenter	M₆₄	D₂₈₃
hypocenter	C₂₈₃	#1400
LCS	G ▷ C₂²×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #31826299	C₂	semidirect
3. M₆₄×C₂₈₃	C₂	semidirect
36. C₂₈₃	#1400	semidirect
40. M₆₄	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22583549	2
#31826299	2
M₆₄×C₂₈₃	2
#1400	283