Subgroups — #13092658

Order 1472.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625095	C₂	1	2	yes	maximal
3	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625000	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624998	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₄₆	C₂²	1	2	yes	—
8	C₂×C₈×C₂₃	—	2	2	no	—
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₂₃	—	2	2	no	—
12	C₄⋊Dic₂₃	C₂²	1	2	yes	—
13	Dic₂₃⋊C₄	—	2	2	no	—
14	Dic₉₂	—	2	2	no	—
15	C₂³×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	—	2	1	no	—
18	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₂₃	—	2	2	no	—
21	C₂×Dic₂₃	—	2	2	no	—
22	Dic₄₆	—	2	2	no	—
23	Dic₄₆	—	2	2	no	—
24	C₈×C₂₃	—	2	1	no	—
25	C₈×C₂₃	D₄	1	2	yes	—
26	C₂²×C₂₃	—	2	1	no	—
27	C₂²×C₂₃	—	2	1	no	—
28	C₂²×C₂₃	Q₁₆	1	2	yes	complemented
29	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₃	—	2	1	no	—
31	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₃	#41	1	1	yes	characteristic
33	Dic₂₃	—	4	2	no	—
34	Dic₂₃	—	4	2	no	—
35	#467	—	23	1	no	maximal, Sylow
36	C₂×C₂₃	—	2	2	no	—
37	C₂×C₂₃	#121	1	1	yes	characteristic
38	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
39	C₂×C₂₃	#135	1	1	yes	characteristic
40	C₂×Q₁₆	—	23	1	no	—
41	C₂²×C₈	D₂₃	1	1	yes	characteristic
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	—	23	2	no	—
47	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
48	Q₁₆	—	46	2	no	—
49	C₂×C₈	—	2	2	no	—
50	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
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	D₉₂	1	1	yes	characteristic
56	Q₈	—	46	2	no	—
57	Q₈	—	46	2	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	46	2	no	—
61	C₂×C₄	—	46	2	no	—
62	C₂×C₄	D₉₂	1	1	yes	characteristic
63	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	C₂²⋊D₂₃	1	2	yes	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	1	no	—
68	C₂²	Dic₉₂	1	2	yes	complemented
69	C₂²	C₂×D₉₂	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	92	2	no	—
72	C₄	—	92	2	no	—
73	C₄	#67288	1	1	yes	characteristic
74	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
75	C₂	—	2	2	no	—
76	C₂	#10625075	1	1	yes	characteristic
77	C₂	C₂×Dic₉₂	1	1	yes	characteristic
78	C₂	#10625101	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂³×C₂₃	D₄
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	#467
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
3. C₂×Dic₉₂	C₂	semidirect
4. #10625000	C₂	semidirect
5. #10624998	C₂	semidirect
28. C₂²×C₂₃	Q₁₆	semidirect
45. C₂₃	#467	semidirect
68. C₂²	Dic₉₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₃	2
#10625095	2
C₂×Dic₉₂	2
#10625000	2
#10624998	2
#467	23