Subgroups — #13092748

Order 1472.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625095	C₂	1	1	yes	maximal, characteristic
3	C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10624999	C₂	1	2	yes	maximal, complemented
5	#10624998	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₃	—	2	1	no	—
8	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₃	C₂²	1	2	yes	—
10	C₂²⋊Dic₂₃	—	2	1	no	—
11	C₄⋊Dic₂₃	—	2	1	no	—
12	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₂₃	C₂²	1	2	yes	—
14	Dic₂₃⋊C₄	—	2	1	no	—
15	C₂³×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	—	2	2	no	—
17	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₃	—	2	1	no	—
20	C₂×Dic₂₃	—	2	1	no	—
21	C₂×Dic₂₃	—	2	2	no	—
22	C₂×Dic₂₃	—	4	2	no	—
23	Dic₄₆	—	2	2	no	—
24	C₈×C₂₃	—	2	2	no	—
25	C₂²×C₂₃	—	2	1	no	—
26	C₂²×C₂₃	—	2	1	no	—
27	C₂²×C₂₃	SD₁₆	1	2	yes	—
28	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₃	—	2	1	no	—
30	C₄×C₂₃	#41	1	2	yes	—
31	Dic₂₃	—	4	1	no	—
32	Dic₂₃	—	4	2	no	—
33	Dic₂₃	—	4	1	no	—
34	#483	—	23	1	no	maximal, Sylow
35	C₂×C₂₃	—	2	2	no	—
36	C₂×C₂₃	#123	1	1	yes	characteristic
37	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
38	C₂×C₂₃	#137	1	1	yes	characteristic
39	C₂²⋊Q₈	—	23	1	no	—
40	C₂×C₄⋊C₄	—	23	1	no	—
41	#106	—	23	2	no	—
42	#103	—	23	2	no	—
43	C₂²⋊C₈	D₂₃	1	1	yes	characteristic
44	C₂₃	#483	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	23	1	no	—
46	C₂²×C₄	—	46	1	no	—
47	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
48	C₂×C₈	C₂×D₂₃	1	2	yes	—
49	C₄⋊C₄	—	23	2	no	—
50	C₄⋊C₄	—	23	1	no	—
51	C₄⋊C₄	—	46	1	no	—
52	C₄⋊C₄	—	46	1	no	—
53	C₂²⋊C₄	—	46	1	no	—
54	C₂³	D₉₂	1	1	yes	characteristic
55	Q₈	—	46	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	46	1	no	—
58	C₂×C₄	—	46	1	no	—
59	C₂×C₄	—	46	2	no	—
60	C₂×C₄	—	92	2	no	—
61	C₂×C₄	D₉₂	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	#67263	1	2	yes	—
67	C₂²	C₂×D₉₂	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	92	1	no	—
70	C₄	—	92	2	no	—
71	C₄	—	92	1	no	—
72	C₄	#67290	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	#10625057	1	1	yes	characteristic
75	C₂	C₂×#67263	1	1	yes	characteristic
76	C₂	#10625080	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×C₂²⋊C₈	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂³×C₂₃	D₄
hypercenter	C₂²⋊C₈	D₂₃
hypocenter	C₂₃	#483
LCS	G ▷ C₂×C₄×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
4. #10624999	C₂	semidirect
5. #10624998	C₂	semidirect
44. C₂₃	#483	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₂₃	2
#10625095	2
C₂₃×C₂²⋊C₈	2
#10624999	2
#10624998	2
#483	23