Subgroups — #15671536

Order 2944.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624980	C₂	1	1	yes	maximal, characteristic
2	#13092251	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₂₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃⋊C₁₆	C₄	1	1	yes	characteristic
7	#10624980	—	2	1	no	—
8	#10624980	—	2	1	no	—
9	C₂₃×C₃₂	—	2	1	no	—
10	C₂₃⋊C₃₂	—	2	1	no	—
11	C₂×C₄×D₂₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₂₃⋊C₈	C₈	1	1	yes	characteristic
14	C₈×D₂₃	—	2	1	no	—
15	C₈×D₂₃	—	2	1	no	—
16	C₁₆×C₂₃	D₄	1	1	yes	characteristic
17	C₁₆×C₂₃	D₄	1	1	yes	characteristic
18	C₂₃⋊C₁₆	—	2	1	no	—
19	C₂²×D₂₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₂₃	C₁₆	1	1	yes	characteristic
22	C₄×D₂₃	—	2	1	no	—
23	C₄×D₂₃	—	2	1	no	—
24	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₂₃	M₁₆	1	1	yes	characteristic
26	C₂₃⋊C₈	—	2	1	no	—
27	#1400	—	23	1	no	maximal, Sylow
28	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
29	C₂×D₂₃	—	2	1	no	—
30	C₂×D₂₃	—	4	1	no	—
31	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₂₃	M₃₂	1	1	yes	characteristic
33	Dic₂₃	—	2	1	no	—
34	C₂×M₃₂	—	23	1	no	—
35	M₆₄	—	23	1	no	—
36	M₆₄	D₂₃	1	1	yes	characteristic, complemented
37	C₂×C₂₃	—	2	1	no	—
38	C₂×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
39	D₂₃	—	4	1	no	—
40	C₂²×C₈	—	23	1	no	—
41	M₃₂	—	46	1	no	—
42	M₃₂	—	46	1	no	—
43	C₂×C₁₆	—	23	1	no	—
44	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	46	1	no	—
47	C₂₃	#1400	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	23	1	no	—
49	C₂×C₈	—	23	1	no	—
50	C₂×C₈	—	46	1	no	—
51	C₂×C₈	—	46	1	no	—
52	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
53	C₁₆	—	46	1	no	—
54	C₁₆	D₉₂	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
56	C₂³	—	23	1	no	—
57	C₂×C₄	—	23	1	no	—
58	C₂×C₄	—	46	1	no	—
59	C₂×C₄	—	46	1	no	—
60	C₂×C₄	C₈×D₂₃	1	1	yes	characteristic
61	C₈	—	46	1	no	—
62	C₈	#67262	1	1	yes	characteristic
63	C₈	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
64	C₂²	—	46	1	no	—
65	C₂²	—	92	1	no	—
66	C₂²	C₁₆×D₂₃	1	1	yes	characteristic
67	C₄	—	46	1	no	—
68	C₄	#10624980	1	1	yes	characteristic
69	C₄	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	92	1	no	—
72	C₂	(C₂×D₂₃)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×D₂₃)⋊C₄
commutator	C₂²×C₂₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₂₃
Fitting	C₂₃×M₆₄	C₂
socle	C₂×C₂₃	C₂²⋊C₁₆
prime radical	C₂²×D₂₃	C₁₆
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	M₆₄	D₂₃
hypocenter	C₂₃	#1400
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #13092251	C₂	semidirect
3. C₂₃×M₆₄	C₂	semidirect
36. M₆₄	D₂₃	semidirect
47. C₂₃	#1400	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10624980	2
#13092251	2
C₂₃×M₆₄	2
#1400	23