Subgroups — #15671433

Order 2944.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092794	C₂	1	1	yes	maximal, characteristic
2	#13092238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₈₄	—	2	1	no	—
5	C₂×D₁₈₄	—	2	1	no	—
6	#10625045	C₄	1	2	yes	—
7	C₂₃×M₃₂	—	2	1	no	—
8	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	#10624994	—	2	1	no	—
10	C₂×D₉₂	—	2	2	no	—
11	C₂×D₉₂	—	4	2	no	—
12	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
15	D₁₈₄	—	4	1	no	—
16	D₁₈₄	—	4	1	no	—
17	D₁₈₄	—	4	1	no	—
18	D₁₈₄	—	4	1	no	—
19	C₁₆×C₂₃	—	4	1	no	—
20	C₂₃⋊C₁₆	—	4	1	no	—
21	C₂²×D₂₃	—	4	2	no	—
22	C₂×C₄×C₂₃	—	2	1	no	—
23	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
24	D₉₂	—	4	2	no	—
25	D₉₂	—	4	2	no	—
26	D₉₂	—	8	4	no	—
27	C₈×C₂₃	D₈	1	1	yes	characteristic
28	C₈×C₂₃	D₈	1	1	yes	characteristic
29	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
31	#1357	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	#100	1	1	yes	characteristic
33	C₂×D₂₃	—	8	4	no	—
34	C₂×D₂₃	—	8	2	no	—
35	C₄×C₂₃	—	2	2	no	—
36	C₄×C₂₃	#102	1	1	yes	characteristic
37	C₄×C₂₃	#102	1	1	yes	characteristic
38	#493	—	23	1	no	—
39	#364	—	23	1	no	—
40	#364	D₂₃	1	1	yes	characteristic, complemented
41	C₂×C₂₃	—	2	1	no	—
42	C₂×C₂₃	#331	1	1	yes	characteristic
43	D₂₃	—	16	2	no	—
44	C₂×D₈	—	46	1	no	—
45	C₂×D₈	—	46	1	no	—
46	#127	—	23	2	no	—
47	M₃₂	—	2	1	no	—
48	M₃₂	—	46	1	no	—
49	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
50	C₂₃	#1357	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₄	—	46	2	no	—
52	C₂×D₄	—	92	2	no	—
53	D₈	—	92	1	no	—
54	D₈	—	92	1	no	—
55	D₈	—	92	1	no	—
56	D₈	—	92	1	no	—
57	C₂×C₈	D₉₂	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
59	C₄²	C₄×D₂₃	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	92	1	no	—
62	C₂³	—	92	2	no	—
63	D₄	—	92	2	no	—
64	D₄	—	92	2	no	—
65	D₄	—	184	4	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
68	C₈	#67263	1	1	yes	characteristic
69	C₈	D₁₈₄	1	1	yes	characteristic
70	C₈	#67272	1	1	yes	characteristic
71	C₈	#67274	1	1	yes	characteristic
72	C₂²	—	184	4	no	—
73	C₂²	—	184	2	no	—
74	C₂²	#10625005	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#10624991	1	1	yes	characteristic
77	C₄	#10625003	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	368	2	no	—
80	C₂	#13092160	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092160
commutator	C₄²×C₂₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×#364	C₂
socle	C₂×C₂₃	#331
prime radical	#13092794	C₂
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	#364	D₂₃
hypocenter	C₂₃	#1357
LCS	G ▷ C₄²×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #13092238	C₂	semidirect
3. C₂₃×#364	C₂	semidirect
40. #364	D₂₃	semidirect
50. C₂₃	#1357	semidirect

Maximal subgroups

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

subgroup	index
#13092794	2
#13092238	2
C₂₃×#364	2
#1357	23