Subgroups — #15673013

Order 2944.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092820	C₂	1	4	yes	maximal
2	#13092797	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₂₃	—	2	2	no	—
6	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×Dic₉₂	—	2	2	no	—
8	#10625040	C₂²	1	2	yes	—
9	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	#10624989	—	2	8	no	—
11	C₄×C₂₃⋊C₈	C₂²	1	2	yes	—
12	C₂×Q₈×C₂₃	—	2	2	no	—
13	C₂×Dic₄₆	—	2	2	no	—
14	Q₁₆×C₂₃	—	4	4	no	—
15	C₂×C₈×C₂₃	D₄	1	2	yes	—
16	C₄⋊C₄×C₂₃	—	2	4	no	—
17	C₄²×C₂₃	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₂₃	—	2	4	no	—
19	C₂×C₂₃⋊C₈	D₄	1	4	yes	—
20	Dic₉₂	—	4	4	no	—
21	Q₈×C₂₃	—	4	4	no	—
22	C₂×C₄×C₂₃	—	4	2	no	—
23	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
24	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₂₃	—	4	2	no	—
26	Dic₄₆	—	4	4	no	—
27	C₈×C₂₃	D₈	1	4	yes	—
28	C₂₃⋊C₈	Q₁₆	1	8	yes	complemented
29	#1713	—	23	1	no	maximal, Sylow
30	C₂²×C₂₃	#127	1	1	yes	characteristic
31	C₄×C₂₃	—	8	2	no	—
32	C₄×C₂₃	C₂×D₈	1	2	yes	—
33	C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
34	Dic₂₃	—	8	2	no	—
35	#500	—	23	4	no	—
36	#494	—	23	1	no	—
37	#494	D₂₃	1	1	yes	characteristic
38	C₈²	—	23	1	no	—
39	C₂×C₂₃	#493	1	1	yes	characteristic
40	C₂×C₂₃	#494	1	2	yes	—
41	C₂×Q₁₆	—	2	2	no	—
42	C₂×Q₁₆	—	46	2	no	—
43	C₄⋊Q₈	—	23	2	no	—
44	C₄⋊Q₈	C₂×D₂₃	1	2	yes	—
45	#107	—	46	8	no	—
46	C₄×C₈	—	23	2	no	—
47	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
48	C₂₃	#1713	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₈	—	2	2	no	—
50	C₂×Q₈	—	46	2	no	—
51	Q₁₆	—	4	4	no	—
52	Q₁₆	—	92	4	no	—
53	C₂×C₈	—	23	4	no	—
54	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	—	46	4	no	—
57	C₄²	C₂²×D₂₃	1	1	yes	characteristic
58	Q₈	—	4	4	no	—
59	Q₈	—	92	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	92	2	no	—
62	C₂×C₄	D₄×D₂₃	1	2	yes	—
63	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
64	C₈	—	23	8	no	—
65	C₈	#67272	1	4	yes	—
66	C₂²	#10625111	1	1	yes	characteristic
67	C₄	—	8	2	no	—
68	C₄	—	184	2	no	—
69	C₄	Q₁₆×D₂₃	1	4	yes	—
70	C₄	C₂×#67272	1	2	yes	—
71	C₂	#13092793	1	1	yes	characteristic
72	C₂	#13092795	1	2	yes	—

	subgroup	G/H
center	C₂²	#10625111
commutator, cosocle	C₄²×C₂₃	C₂³
Frattini	C₄²	C₂²×D₂₃
Fitting	C₂₃×#494	C₂
socle, prime radical	C₂²×C₂₃	#127
hypercenter	#494	D₂₃
hypocenter	C₂₃	#1713
LCS	G ▷ C₄²×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
28. C₂₃⋊C₈	Q₁₆	semidirect
48. C₂₃	#1713	semidirect

Maximal subgroups

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

subgroup	index
#13092820	2
#13092797	2
C₈×C₂₃⋊C₈	2
C₂₃×#494	2
#1713	23