Subgroups — #13092425

Order 1472.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₆	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×#67267	C₂	1	1	yes	maximal, characteristic
4	#10624992	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₃	—	2	1	no	—
7	C₂×Dic₄₆	—	2	2	no	—
8	C₂×Dic₄₆	—	2	1	no	—
9	C₂×Dic₄₆	C₄	1	4	yes	complemented
10	C₂×Dic₄₆	C₂²	1	2	yes	—
11	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
12	C₂²⋊C₄×C₂₃	—	2	1	no	—
13	C₄²×C₂₃	—	2	1	no	—
14	#67267	—	2	2	no	—
15	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₃	D₄	1	2	yes	—
20	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₂₃	—	2	4	no	—
23	C₂×Dic₂₃	—	2	2	no	—
24	Dic₄₆	—	2	4	no	—
25	Dic₄₆	—	2	2	no	—
26	Dic₄₆	C₂×C₄	1	4	yes	—
27	C₂₃⋊C₈	—	2	2	no	—
28	C₂²×C₂₃	—	2	2	no	—
29	C₂²×C₂₃	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₃	—	4	2	no	—
32	C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
33	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
35	Dic₂₃	—	2	4	no	—
36	#419	—	23	1	no	maximal, Sylow
37	C₂×C₂₃	—	2	2	no	—
38	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₂₃	#137	1	2	yes	—
40	C₂²×Q₈	—	23	1	no	—
41	C₂×M₁₆	—	23	1	no	—
42	#117	D₂₃	1	1	yes	characteristic
43	#103	—	23	4	no	—
44	C₂₃	#419	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	23	4	no	—
46	C₂×Q₈	—	23	2	no	—
47	C₂×Q₈	—	46	2	no	—
48	C₂×Q₈	—	46	1	no	—
49	C₂²×C₄	—	46	1	no	—
50	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
51	M₁₆	—	46	2	no	—
52	C₂×C₈	—	23	2	no	—
53	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
54	C₂²⋊C₄	—	2	1	no	—
55	C₄²	—	2	1	no	—
56	C₂³	C₂²⋊D₂₃	1	1	yes	characteristic
57	Q₈	—	23	4	no	—
58	Q₈	—	46	4	no	—
59	Q₈	—	46	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	46	4	no	—
62	C₂×C₄	—	46	2	no	—
63	C₂×C₄	C₄×D₂₃	1	2	yes	—
64	C₂×C₄	D₉₂	1	2	yes	—
65	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
67	C₈	—	46	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	(C₂×D₂₃)⋊C₄	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	46	4	no	—
73	C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
74	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
75	C₄	C₂×D₉₂	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	C₂×(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
78	C₂	#10625122	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#117	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂³×C₂₃	D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#117	D₂₃
hypocenter	C₂₃	#419
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
4. #10624992	C₂	semidirect
9. C₂×Dic₄₆	C₄	semidirect
44. C₂₃	#419	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₄₆	2
C₂₃×#117	2
C₂×#67267	2
#10624992	2
#419	23