Subgroups — #15673145

Order 2944.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624985	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	#13092171	C₂	1	4	yes	maximal
4	C₂×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₂₃	C₄	1	4	yes	—
8	C₂×C₄×Dic₂₃	C₂²	1	2	yes	—
9	C₂²×C₂₃⋊C₈	C₂²	1	2	yes	—
10	C₂₃×#97	C₄	1	4	yes	complemented
11	#10624985	C₄	1	4	yes	complemented
12	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
14	C₂²×Dic₂₃	C₂×C₄	1	4	yes	—
15	C₂×C₈×C₂₃	—	2	4	no	—
16	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
17	C₄²×C₂₃	C₂×C₄	1	2	yes	—
18	C₄²×C₂₃	C₂×C₄	1	2	yes	—
19	C₄×Dic₂₃	—	2	4	no	—
20	C₄×Dic₂₃	—	2	8	no	—
21	C₂×C₂₃⋊C₈	—	2	4	no	—
22	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
23	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	—	2	4	no	—
25	C₂×C₄×C₂₃	C₄²	1	4	yes	—
26	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	#41	1	4	yes	—
29	C₂×Dic₂₃	—	2	4	no	—
30	C₂×Dic₂₃	—	2	4	no	—
31	C₂×Dic₂₃	M₁₆	1	8	yes	—
32	C₈×C₂₃	—	2	4	no	—
33	C₂₃⋊C₈	—	2	4	no	—
34	#1745	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
36	C₂²×C₂₃	#117	1	2	yes	—
37	C₂²×C₂₃	C₂×M₁₆	1	4	yes	—
38	C₄×C₂₃	—	2	4	no	—
39	C₄×C₂₃	#117	1	2	yes	—
40	C₄×C₂₃	#117	1	2	yes	—
41	Dic₂₃	—	2	8	no	—
42	C₂×#97	—	23	1	no	—
43	C₂×#97	D₂₃	1	1	yes	characteristic
44	C₄³	—	23	1	no	—
45	#336	—	23	4	no	—
46	C₂×C₂₃	#376	1	1	yes	characteristic
47	C₂×C₂₃	C₄×M₁₆	1	2	yes	—
48	C₂×C₂₃	#432	1	4	yes	—
49	C₂²×C₈	—	23	2	no	—
50	C₂²×C₈	C₂×D₂₃	1	2	yes	—
51	C₂×C₄²	—	23	4	no	—
52	C₂×C₄²	—	23	2	no	—
53	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
54	#97	—	23	4	no	—
55	#97	Dic₂₃	1	4	yes	complemented
56	C₂₃	#1745	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₄	—	23	4	no	—
58	C₂²×C₄	C₄×D₂₃	1	2	yes	—
59	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
60	C₂×C₈	—	2	4	no	—
61	C₂×C₈	—	23	4	no	—
62	C₂×C₈	—	46	4	no	—
63	C₂×C₈	C₂×Dic₂₃	1	4	yes	—
64	C₄²	—	46	8	no	—
65	C₄²	—	46	4	no	—
66	C₄²	C₄×D₂₃	1	2	yes	—
67	C₄²	C₂×Dic₂₃	1	2	yes	—
68	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	23	8	no	—
71	C₂×C₄	—	46	4	no	—
72	C₂×C₄	—	46	4	no	—
73	C₂×C₄	C₄×Dic₂₃	1	4	yes	—
74	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
75	C₂×C₄	#67288	1	4	yes	—
76	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
77	C₈	—	2	4	no	—
78	C₈	—	46	4	no	—
79	C₂²	#10625043	1	2	yes	—
80	C₂²	M₁₆×D₂₃	1	4	yes	—
81	C₂²	C₂×C₄×Dic₂₃	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	—	46	8	no	—
84	C₄	#10625043	1	2	yes	—
85	C₄	#10625097	1	2	yes	—
86	C₂	#13092263	1	1	yes	characteristic
87	C₂	M₁₆×Dic₂₃	1	2	yes	—
88	C₂	#13092472	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₃
commutator	C₂²×C₂₃	C₂×C₄²
Fitting	C₂×C₂₃×#97	C₂
socle, prime radical	C₂³×C₂₃	C₂²×C₄
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	C₂×#97	D₂₃
hypocenter	C₂₃	#1745
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
10. C₂₃×#97	C₄	semidirect
11. #10624985	C₄	semidirect
55. #97	Dic₂₃	semidirect
56. C₂₃	#1745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10624985	2
C₄²×Dic₂₃	2
#13092171	2
C₂×C₂₃×#97	2
#1745	23