Subgroups — #15671435

Order 2944.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092797	C₂	1	1	yes	maximal, characteristic
2	#13092238	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₂	—	2	1	no	—
5	C₂×Dic₉₂	—	2	1	no	—
6	#10625040	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×Dic₄₆	—	2	2	no	—
11	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
13	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₂₃	—	4	2	no	—
15	Dic₉₂	—	4	1	no	—
16	Dic₉₂	—	4	1	no	—
17	Dic₉₂	—	4	1	no	—
18	Dic₉₂	—	4	1	no	—
19	C₁₆×C₂₃	—	4	1	no	—
20	C₂₃⋊C₁₆	—	4	1	no	—
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₂₃	—	4	2	no	—
24	Dic₄₆	—	4	2	no	—
25	Dic₄₆	—	4	2	no	—
26	C₈×C₂₃	D₈	1	1	yes	characteristic
27	C₈×C₂₃	D₈	1	1	yes	characteristic
28	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
29	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
30	#1358	—	23	1	no	maximal, Sylow
31	C₂²×C₂₃	#100	1	1	yes	characteristic
32	C₄×C₂₃	—	2	2	no	—
33	C₄×C₂₃	#102	1	1	yes	characteristic
34	C₄×C₂₃	#102	1	1	yes	characteristic
35	Dic₂₃	—	8	2	no	—
36	#494	—	23	1	no	—
37	#364	—	23	1	no	—
38	#364	D₂₃	1	1	yes	characteristic
39	C₂×C₂₃	—	2	1	no	—
40	C₂×C₂₃	#331	1	1	yes	characteristic
41	C₂×Q₁₆	—	46	1	no	—
42	C₂×Q₁₆	—	46	1	no	—
43	C₄⋊Q₈	—	23	2	no	—
44	M₃₂	—	2	1	no	—
45	M₃₂	—	46	1	no	—
46	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
47	C₂₃	#1358	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	46	2	no	—
49	Q₁₆	—	92	1	no	—
50	Q₁₆	—	92	1	no	—
51	Q₁₆	—	92	1	no	—
52	Q₁₆	—	92	1	no	—
53	C₂×C₈	D₉₂	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
55	C₄⋊C₄	—	92	2	no	—
56	C₄²	C₄×D₂₃	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	92	1	no	—
59	Q₈	—	92	2	no	—
60	Q₈	—	92	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	92	2	no	—
63	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
64	C₈	#67263	1	1	yes	characteristic
65	C₈	D₁₈₄	1	1	yes	characteristic
66	C₈	#67272	1	1	yes	characteristic
67	C₈	#67274	1	1	yes	characteristic
68	C₂²	#10625005	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	184	2	no	—
71	C₄	#10624991	1	1	yes	characteristic
72	C₄	#10625003	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	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	C₂²×C₂₃	#100
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	#364	D₂₃
hypocenter	C₂₃	#1358
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
47. C₂₃	#1358	semidirect

Maximal subgroups

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

subgroup	index
#13092797	2
#13092238	2
C₂₃×#364	2
#1358	23