Subgroups — #13092369

Order 1472.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67262	C₂	1	2	yes	maximal
2	C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×Dic₂₃	C₂	1	2	yes	maximal, complemented
5	#10624985	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₃	C₄	1	2	yes	—
7	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂²	1	2	yes	—
9	C₄²×C₂₃	C₂²	1	1	yes	characteristic
10	C₄×Dic₂₃	C₄	1	2	yes	—
11	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
13	#67262	C₄	1	8	yes	complemented
14	C₂²×D₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
19	C₄×D₂₃	—	2	4	no	—
20	C₄×D₂₃	C₂×C₄	1	4	yes	—
21	C₈×C₂₃	C₂×C₄	1	4	yes	complemented
22	C₂₃⋊C₈	C₂×C₄	1	4	yes	complemented
23	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₂₃	—	2	2	no	—
25	C₂×D₂₃	C₄²	1	2	yes	—
26	C₄×C₂₃	—	2	2	no	—
27	C₄×C₂₃	C₂²×C₄	1	2	yes	—
28	Dic₂₃	C₄²	1	2	yes	—
29	Dic₂₃	M₁₆	1	4	yes	complemented
30	C₄×M₁₆	—	23	1	no	maximal, Sylow
31	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
32	C₂×C₂₃	C₂×M₁₆	1	2	yes	—
33	D₂₃	—	2	2	no	—
34	C₂×M₁₆	—	23	2	no	—
35	C₂×C₄²	—	23	1	no	—
36	#97	—	23	1	no	—
37	#97	D₂₃	1	1	yes	characteristic, complemented
38	C₄×C₈	—	23	2	no	—
39	C₂₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₄	—	23	1	no	—
41	C₂²×C₄	—	23	2	no	—
42	M₁₆	—	23	8	no	—
43	C₂×C₈	—	23	2	no	—
44	C₂×C₈	C₂×D₂₃	1	2	yes	—
45	C₄²	—	23	2	no	—
46	C₄²	—	23	1	no	—
47	C₄²	C₂×D₂₃	1	1	yes	characteristic
48	C₂³	—	23	1	no	—
49	C₂×C₄	—	23	1	no	—
50	C₂×C₄	—	23	2	no	—
51	C₂×C₄	—	23	4	no	—
52	C₂×C₄	—	46	4	no	—
53	C₂×C₄	C₄×D₂₃	1	2	yes	—
54	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
55	C₈	—	23	4	no	—
56	C₈	C₄×D₂₃	1	4	yes	complemented
57	C₂²	—	23	2	no	—
58	C₂²	—	46	2	no	—
59	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	23	2	no	—
62	C₄	—	23	4	no	—
63	C₄	C₂×C₄×D₂₃	1	2	yes	—
64	C₂	—	46	2	no	—
65	C₂	C₄²×D₂₃	1	1	yes	characteristic
66	C₂	M₁₆×D₂₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₃
commutator	C₂×C₂₃	C₂×C₄²
Fitting	C₂₃×#97	C₂
socle	C₂²×C₂₃	C₂²×C₄
prime radical	C₂²×D₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#97	D₂₃
hypocenter	C₂₃	C₄×M₁₆
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
3. C₂₃×#97	C₂	semidirect
4. C₈×Dic₂₃	C₂	semidirect
5. #10624985	C₂	semidirect
13. #67262	C₄	semidirect
21. C₈×C₂₃	C₂×C₄	semidirect
22. C₂₃⋊C₈	C₂×C₄	semidirect
29. Dic₂₃	M₁₆	semidirect
37. #97	D₂₃	semidirect
39. C₂₃	C₄×M₁₆	semidirect
56. C₈	C₄×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#67262	2
C₄²×D₂₃	2
C₂₃×#97	2
C₈×Dic₂₃	2
#10624985	2
C₄×M₁₆	23