Subgroups — #13092655

Order 1472.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#10625117	C₂	1	2	yes	maximal
3	C₂×C₈×D₂₃	C₂	1	1	yes	maximal, characteristic
4	#10625017	C₂	1	2	yes	maximal, complemented
5	#10625000	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
7	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
8	Q₁₆×C₂₃	—	2	2	no	—
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	(C₂×D₂₃)⋊C₄	—	2	2	no	—
11	C₄⋊Dic₂₃	C₂²	1	2	yes	—
12	Dic₂₃⋊C₄	—	2	2	no	—
13	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₈×D₂₃	—	2	2	no	—
15	C₂²×D₂₃	D₄	1	1	yes	characteristic
16	Q₈×C₂₃	—	2	2	no	—
17	Q₈×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	—	2	2	no	—
19	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₂₃	—	2	2	no	—
21	C₂×Dic₂₃	D₄	1	1	yes	characteristic
22	C₄×D₂₃	—	2	1	no	—
23	C₄×D₂₃	—	2	1	no	—
24	C₈×C₂₃	D₄	1	2	yes	—
25	C₂₃⋊C₈	—	2	1	no	—
26	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
27	C₂×D₂₃	—	2	1	no	—
28	C₂×D₂₃	—	2	1	no	—
29	C₂×D₂₃	Q₁₆	1	2	yes	complemented
30	C₄×C₂₃	—	4	2	no	—
31	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₃	#41	1	1	yes	characteristic
33	Dic₂₃	—	2	1	no	—
34	Dic₂₃	—	4	2	no	—
35	#467	—	23	1	no	maximal, Sylow
36	C₂×C₂₃	#121	1	1	yes	characteristic
37	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
38	C₂×C₂₃	#135	1	1	yes	characteristic
39	D₂₃	—	2	2	no	—
40	C₂×Q₁₆	D₂₃	1	1	yes	characteristic, complemented
41	C₂²×C₈	—	23	1	no	—
42	C₂²⋊Q₈	—	23	2	no	—
43	#107	—	23	1	no	—
44	#103	—	23	2	no	—
45	C₂₃	#467	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₈	C₂×D₂₃	1	2	yes	—
47	C₂²×C₄	—	23	1	no	—
48	Q₁₆	—	2	2	no	—
49	C₂×C₈	—	23	1	no	—
50	C₂×C₈	—	46	2	no	—
51	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
52	C₄⋊C₄	—	23	2	no	—
53	C₄⋊C₄	—	46	2	no	—
54	C₂²⋊C₄	—	46	2	no	—
55	C₂³	—	23	1	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	23	1	no	—
60	C₂×C₄	—	46	1	no	—
61	C₂×C₄	—	46	1	no	—
62	C₂×C₄	—	46	2	no	—
63	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
64	C₈	—	46	1	no	—
65	C₈	C₂²⋊D₂₃	1	2	yes	—
66	C₂²	—	23	2	no	—
67	C₂²	—	46	1	no	—
68	C₂²	—	46	1	no	—
69	C₂²	D₄×D₂₃	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	46	1	no	—
72	C₄	—	92	2	no	—
73	C₄	#67290	1	1	yes	characteristic
74	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
75	C₂	—	46	2	no	—
76	C₂	Q₁₆×D₂₃	1	1	yes	characteristic
77	C₂	#10625090	1	1	yes	characteristic
78	C₂	#10625109	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂²×D₂₃	D₄
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	#467
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₂₃	C₂	semidirect
4. #10625017	C₂	semidirect
5. #10625000	C₂	semidirect
29. C₂×D₂₃	Q₁₆	semidirect
40. C₂×Q₁₆	D₂₃	semidirect
45. C₂₃	#467	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₃	2
#10625117	2
C₂×C₈×D₂₃	2
#10625017	2
#10625000	2
#467	23