Subgroups — C₂₃⋊#1273 #15671224

Order 2944.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₃⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₄	1	2	yes	—
4	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
5	C₂²×C₂₃⋊C₈	C₄	1	4	yes	—
6	C₄×C₈×C₂₃	—	2	2	no	—
7	C₄×C₂₃⋊C₈	—	2	2	no	—
8	C₄×C₂₃⋊C₈	—	2	2	no	—
9	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₂₃	—	2	2	no	—
12	C₂×C₈×C₂₃	—	2	2	no	—
13	C₂×C₈×C₂₃	C₈	1	4	yes	complemented
14	C₄²×C₂₃	D₄	1	1	yes	characteristic
15	C₄²×C₂₃	D₄	1	2	yes	—
16	C₄²×C₂₃	Q₈	1	1	yes	characteristic
17	C₂×C₂₃⋊C₈	—	2	4	no	—
18	C₂×C₂₃⋊C₈	—	2	4	no	—
19	C₂×C₂₃⋊C₈	C₈	1	8	yes	complemented
20	C₂³×C₂₃	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	C₂×C₈	1	4	yes	—
26	C₂×C₄×C₂₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₃	M₁₆	1	4	yes	—
28	C₂×C₄×C₂₃	M₁₆	1	2	yes	—
29	C₈×C₂₃	—	2	4	no	—
30	C₂₃⋊C₈	—	2	8	no	—
31	#1273	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	#95	1	1	yes	characteristic
33	C₂²×C₂₃	C₄×C₈	1	1	yes	characteristic
34	C₂²×C₂₃	C₄×C₈	1	2	yes	—
35	C₂²×C₂₃	#97	1	1	yes	characteristic
36	C₂²×C₂₃	#97	1	2	yes	—
37	C₄×C₂₃	C₂²⋊C₈	1	4	yes	—
38	C₄×C₂₃	C₂²⋊C₈	1	2	yes	—
39	C₄×C₂₃	C₄⋊C₈	1	2	yes	—
40	C₄×C₂₃	C₄⋊C₈	1	4	yes	—
41	C₂×C₄×C₈	—	23	2	no	—
42	C₂×C₄×C₈	D₂₃	1	1	yes	characteristic
43	C₂×C₂₃	C₈²	1	1	yes	characteristic
44	C₂×C₂₃	#322	1	1	yes	characteristic
45	C₂×C₂₃	#322	1	2	yes	—
46	C₂×C₂₃	#336	1	2	yes	—
47	C₂×C₂₃	#336	1	1	yes	characteristic
48	C₂²×C₈	—	23	4	no	—
49	C₂²×C₈	Dic₂₃	1	2	yes	—
50	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
51	C₄×C₈	—	2	2	no	—
52	C₄×C₈	—	46	2	no	—
53	C₄×C₈	—	46	2	no	—
54	C₂₃	#1273	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₄	C₄×D₂₃	1	2	yes	—
56	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	—	2	2	no	—
59	C₂×C₈	—	23	8	no	—
60	C₂×C₈	—	46	4	no	—
61	C₂×C₈	—	46	4	no	—
62	C₂×C₈	C₂₃⋊C₈	1	4	yes	complemented
63	C₄²	Dic₄₆	1	1	yes	characteristic
64	C₄²	D₉₂	1	1	yes	characteristic
65	C₄²	C₂²⋊D₂₃	1	2	yes	—
66	C₂³	C₄×Dic₂₃	1	1	yes	characteristic
67	C₂×C₄	C₈×D₂₃	1	4	yes	—
68	C₂×C₄	#67262	1	4	yes	—
69	C₂×C₄	C₂×C₂₃⋊C₈	1	2	yes	—
70	C₂×C₄	#67267	1	2	yes	—
71	C₂×C₄	Dic₂₃⋊C₄	1	2	yes	—
72	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
73	C₂×C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
74	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
75	C₈	—	2	4	no	—
76	C₈	—	46	8	no	—
77	C₂²	C₄×C₂₃⋊C₈	1	1	yes	characteristic
78	C₂²	#10624985	1	1	yes	characteristic
79	C₂²	C₈×Dic₂₃	1	2	yes	—
80	C₂²	#10624997	1	2	yes	—
81	C₂²	C₂₃⋊#95	1	1	yes	characteristic
82	C₄	C₄⋊(C₂₃⋊C₈)	1	2	yes	—
83	C₄	Dic₂₃⋊C₈	1	4	yes	—
84	C₄	(C₂×D₂₃)⋊C₈	1	4	yes	—
85	C₄	C₂²⋊(C₂₃⋊C₈)	1	2	yes	—
86	C₂	C₈×C₂₃⋊C₈	1	1	yes	characteristic
87	C₂	#13092138	1	1	yes	characteristic
88	C₂	#13092139	1	2	yes	—
89	C₂	#13092171	1	2	yes	—
90	C₂	#13092172	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂×D₂₃
commutator	C₂×C₂₃	C₈²
Fitting	C₂×C₄×C₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₄²
cosocle	C₂×C₄²×C₂₃	C₂²
hypercenter	C₂×C₄×C₈	D₂₃
hypocenter	C₂₃	#1273
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
13. C₂×C₈×C₂₃	C₈	semidirect
19. C₂×C₂₃⋊C₈	C₈	semidirect
54. C₂₃	#1273	semidirect
62. C₂×C₈	C₂₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₂₃⋊C₈	2
C₂×C₄×C₈×C₂₃	2
#1273	23

Subgroups — C23⋊#1273 #15671224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃⋊#1273 #15671224