Subgroups — #13092155

Order 1472.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625095	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂₃⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₂²×Dic₂₃	—	2	1	no	—
6	C₂×Dic₄₆	C₄	1	1	yes	characteristic, complemented
7	C₂×C₈×C₂₃	—	2	1	no	—
8	C₂²⋊Dic₂₃	—	2	1	no	—
9	C₄⋊Dic₂₃	C₄	1	1	yes	characteristic, complemented
10	Dic₂₃⋊C₄	—	2	1	no	—
11	C₂³×C₂₃	D₄	1	1	yes	characteristic
12	C₂×C₄×C₂₃	—	4	1	no	—
13	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×Dic₂₃	—	2	2	no	—
16	C₂×Dic₂₃	—	2	1	no	—
17	C₂×Dic₂₃	—	2	1	no	—
18	C₂×Dic₂₃	—	4	1	no	—
19	C₂×Dic₂₃	—	4	1	no	—
20	Dic₄₆	—	4	1	no	—
21	C₈×C₂₃	—	4	1	no	—
22	C₂²×C₂₃	—	2	1	no	—
23	C₂²×C₂₃	—	2	1	no	—
24	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₂₃	SD₁₆	1	1	yes	characteristic
26	C₂²×C₂₃	Q₁₆	1	1	yes	characteristic
27	C₄×C₂₃	—	2	1	no	—
28	C₄×C₂₃	—	2	1	no	—
29	Dic₂₃	—	4	2	no	—
30	Dic₂₃	—	4	1	no	—
31	Dic₂₃	—	4	1	no	—
32	#328	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	—	2	1	no	—
34	C₂×C₂₃	—	2	1	no	—
35	C₂×C₂₃	#99	1	1	yes	characteristic
36	C₂×C₂₃	#103	1	1	yes	characteristic
37	C₂×C₂₃	#104	1	1	yes	characteristic
38	C₂²⋊Q₈	—	23	1	no	—
39	C₂²⋊C₈	D₂₃	1	1	yes	characteristic
40	#95	—	23	1	no	—
41	C₂₃	#328	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	23	1	no	—
43	C₂²×C₄	—	46	1	no	—
44	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
45	C₂×C₈	—	2	1	no	—
46	C₄⋊C₄	—	23	1	no	—
47	C₄⋊C₄	—	46	1	no	—
48	C₂²⋊C₄	—	46	1	no	—
49	C₂³	D₉₂	1	1	yes	characteristic
50	Q₈	—	92	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	—	46	2	no	—
53	C₂×C₄	—	46	1	no	—
54	C₂×C₄	—	46	1	no	—
55	C₂×C₄	—	92	1	no	—
56	C₂×C₄	—	92	1	no	—
57	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
59	C₈	—	4	1	no	—
60	C₂²	—	2	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	#67263	1	1	yes	characteristic
63	C₂²	Dic₉₂	1	1	yes	characteristic
64	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	2	1	no	—
67	C₄	—	92	2	no	—
68	C₄	—	92	1	no	—
69	C₄	—	92	1	no	—
70	C₂	—	2	1	no	—
71	C₂	—	2	1	no	—
72	C₂	#10624988	1	1	yes	characteristic
73	C₂	#10624998	1	1	yes	characteristic
74	C₂	#10625007	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₂₃)⋊C₄
commutator	C₂×C₄×C₂₃	C₂×C₄
Frattini	C₂²×C₄	C₂×D₂₃
Fitting	C₂₃×C₂²⋊C₈	C₂
socle	C₂²×C₂₃	C₂²⋊C₄
prime radical	C₂³×C₂₃	D₄
cosocle	C₂²×C₄×C₂₃	C₂²
hypercenter	C₂²⋊C₈	D₂₃
hypocenter	C₂₃	#328
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×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
6. C₂×Dic₄₆	C₄	semidirect
9. C₄⋊Dic₂₃	C₄	semidirect
41. C₂₃	#328	semidirect

Maximal subgroups

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

subgroup	index
#10625095	2
C₂₃×C₂²⋊C₈	2
C₂₃⋊#95	2
#328	23