Subgroups — #13092142

Order 1472.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₂₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₂²×Dic₂₃	C₄	1	1	yes	characteristic
6	C₂²×Dic₂₃	C₄	1	1	yes	characteristic
7	C₂×C₈×C₂₃	—	2	1	no	—
8	Dic₂₃⋊C₄	—	2	1	no	—
9	Dic₂₃⋊C₄	—	2	1	no	—
10	C₂×C₂₃⋊C₈	—	2	1	no	—
11	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₂₃	—	4	1	no	—
13	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×Dic₂₃	—	2	1	no	—
16	C₂×Dic₂₃	—	2	1	no	—
17	C₂×Dic₂₃	—	2	1	no	—
18	C₂×Dic₂₃	—	4	1	no	—
19	C₂×Dic₂₃	C₈	1	2	yes	complemented
20	C₈×C₂₃	—	4	1	no	—
21	C₂₃⋊C₈	—	4	1	no	—
22	C₂²×C₂₃	—	2	1	no	—
23	C₂²×C₂₃	—	2	1	no	—
24	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₂₃	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₂₃	M₁₆	1	1	yes	characteristic
27	C₄×C₂₃	—	2	1	no	—
28	C₄×C₂₃	—	2	1	no	—
29	Dic₂₃	—	2	2	no	—
30	Dic₂₃	—	4	1	no	—
31	#324	—	23	1	no	maximal, Sylow
32	C₂×C₂₃	—	2	1	no	—
33	C₂×C₂₃	—	2	1	no	—
34	C₂×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
35	C₂×C₂₃	#99	1	1	yes	characteristic
36	C₂×C₂₃	#101	1	1	yes	characteristic
37	C₂×C₄⋊C₄	—	23	1	no	—
38	C₂²⋊C₈	—	23	1	no	—
39	C₂²⋊C₈	D₂₃	1	1	yes	characteristic
40	C₂₃	#324	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	—	23	1	no	—
42	C₂²×C₄	—	23	1	no	—
43	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	—	46	1	no	—
46	C₄⋊C₄	—	46	1	no	—
47	C₄⋊C₄	—	46	1	no	—
48	C₂³	C₄×D₂₃	1	1	yes	characteristic
49	C₂×C₄	—	4	1	no	—
50	C₂×C₄	—	23	2	no	—
51	C₂×C₄	—	46	1	no	—
52	C₂×C₄	—	46	1	no	—
53	C₂×C₄	—	46	1	no	—
54	C₂×C₄	—	92	1	no	—
55	C₂×C₄	D₉₂	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
57	C₈	—	4	1	no	—
58	C₈	—	92	1	no	—
59	C₂²	—	2	1	no	—
60	C₂²	—	2	1	no	—
61	C₂²	C₈×D₂₃	1	1	yes	characteristic
62	C₂²	#67262	1	1	yes	characteristic
63	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	2	1	no	—
66	C₄	—	46	2	no	—
67	C₄	—	92	1	no	—
68	C₂	—	2	1	no	—
69	C₂	—	2	1	no	—
70	C₂	#10624988	1	1	yes	characteristic
71	C₂	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
72	C₂	#10625006	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₂₃)⋊C₄
commutator	C₂²×C₂₃	C₂×C₈
Frattini	C₂²×C₄	C₂×D₂₃
Fitting	C₂₃×C₂²⋊C₈	C₂
socle	C₂²×C₂₃	C₂²⋊C₄
prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂²×C₄×C₂₃	C₂²
hypercenter	C₂²⋊C₈	D₂₃
hypocenter	C₂₃	#324
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
19. C₂×Dic₂₃	C₈	semidirect
40. C₂₃	#324	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₃⋊C₄	2
C₂₃×C₂²⋊C₈	2
C₂²⋊(C₂₃⋊C₈)	2
#324	23