Subgroups — #13092692

Order 1472.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#131	C₂	1	1	yes	maximal, characteristic
2	#10625122	C₂	1	2	yes	maximal
3	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625006	C₂	1	2	yes	maximal, complemented
5	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₄₆	C₂²	1	2	yes	—
8	M₁₆×C₂₃	—	2	1	no	—
9	M₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₃	—	2	1	no	—
11	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	#67275	—	2	2	no	—
13	#67273	—	2	2	no	—
14	#67267	C₂²	1	2	yes	—
15	Dic₉₂	—	2	1	no	—
16	Dic₉₂	—	2	1	no	—
17	Q₈×C₂₃	D₄	1	1	yes	characteristic
18	D₄×C₂₃	—	2	1	no	—
19	D₄×C₂₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₂₃	—	2	2	no	—
23	Dic₄₆	—	2	2	no	—
24	Dic₄₆	—	2	2	no	—
25	C₈×C₂₃	—	2	1	no	—
26	C₈×C₂₃	D₄	1	1	yes	characteristic
27	C₈×C₂₃	D₄	1	1	yes	characteristic
28	C₂₃⋊C₈	—	2	2	no	—
29	C₂²×C₂₃	—	2	1	no	—
30	C₂²×C₂₃	#41	1	1	yes	characteristic
31	C₄×C₂₃	—	2	1	no	—
32	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
34	Dic₂₃	—	4	2	no	—
35	#473	—	23	1	no	maximal, Sylow
36	C₂×C₂₃	—	2	1	no	—
37	C₂×C₂₃	—	4	1	no	—
38	C₂×C₂₃	#121	1	1	yes	characteristic
39	#137	—	23	2	no	—
40	C₂×Q₁₆	—	23	1	no	—
41	#131	D₂₃	1	1	yes	characteristic
42	#108	—	23	1	no	—
43	#101	—	23	2	no	—
44	C₂₃	#473	1	1	yes	characteristic, complemented, Sylow
45	#41	C₂×D₂₃	1	1	yes	characteristic
46	C₂×Q₈	—	23	2	no	—
47	Q₁₆	—	46	2	no	—
48	Q₁₆	—	46	1	no	—
49	Q₁₆	—	46	1	no	—
50	SD₁₆	—	46	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	—	23	2	no	—
53	M₁₆	C₂×D₂₃	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
56	Q₈	—	46	2	no	—
57	Q₈	—	46	2	no	—
58	Q₈	D₉₂	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₉₂	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	46	2	no	—
63	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	46	2	no	—
66	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
67	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#67288	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	92	2	no	—
72	C₄	C₂×D₉₂	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#10625101	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10625101
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#131	C₂
socle	C₂×C₂₃	#121
prime radical	#41×C₂₃	C₂²
hypercenter	#131	D₂₃
hypocenter	C₂₃	#473
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₉₂	C₂	semidirect
4. #10625006	C₂	semidirect
5. #10625001	C₂	semidirect
44. C₂₃	#473	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#131	2
#10625122	2
C₂×Dic₉₂	2
#10625006	2
#10625001	2
#473	23