Subgroups — #13092689

Order 1472.

100 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	#10625113	C₂	1	2	yes	maximal
3	#10625072	C₂	1	1	yes	maximal, characteristic
4	#10625018	C₂	1	2	yes	maximal, complemented
5	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
7	#67288	C₂²	1	1	yes	characteristic
8	Q₁₆×C₂₃	—	2	1	no	—
9	Q₁₆×C₂₃	—	2	1	no	—
10	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	#67275	—	2	2	no	—
12	#67274	—	2	2	no	—
13	#67267	C₂²	1	1	yes	characteristic
14	#67267	C₂²	1	2	yes	—
15	#67262	—	2	1	no	—
16	C₈×D₂₃	—	2	1	no	—
17	Q₈×C₂₃	—	2	2	no	—
18	Q₈×C₂₃	—	2	2	no	—
19	C₂×C₄×C₂₃	—	2	2	no	—
20	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
21	C₂²⋊D₂₃	—	2	1	no	—
22	D₉₂	D₄	1	1	yes	characteristic
23	C₄×D₂₃	—	2	1	no	—
24	Dic₄₆	D₄	1	1	yes	characteristic
25	C₈×C₂₃	D₄	1	1	yes	characteristic
26	C₈×C₂₃	D₄	1	1	yes	characteristic
27	C₂₃⋊C₈	—	2	1	no	—
28	C₂₃⋊C₈	—	2	2	no	—
29	C₂²×C₂₃	#41	1	1	yes	characteristic
30	C₂×D₂₃	—	2	1	no	—
31	C₄×C₂₃	—	4	2	no	—
32	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
34	Dic₂₃	—	2	1	no	—
35	#473	—	23	1	no	maximal, Sylow
36	C₂×C₂₃	—	2	1	no	—
37	C₂×C₂₃	#121	1	1	yes	characteristic
38	D₂₃	—	4	1	no	—
39	#137	—	23	2	no	—
40	C₂×Q₁₆	D₂₃	1	1	yes	characteristic, complemented
41	#131	—	23	1	no	—
42	#108	—	23	1	no	—
43	#101	—	23	2	no	—
44	C₂₃	#473	1	1	yes	characteristic, complemented, Sylow
45	#41	—	23	1	no	—
46	C₂×Q₈	C₂×D₂₃	1	2	yes	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	2	1	no	—
49	Q₁₆	—	46	2	no	—
50	SD₁₆	—	46	2	no	—
51	M₁₆	—	23	1	no	—
52	M₁₆	—	23	2	no	—
53	M₁₆	—	46	1	no	—
54	C₂×C₈	—	46	1	no	—
55	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	Q₈	—	23	1	no	—
59	D₄	—	23	1	no	—
60	D₄	—	46	1	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	46	1	no	—
63	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
64	C₈	—	46	2	no	—
65	C₈	—	46	1	no	—
66	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
67	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
68	C₂²	—	46	1	no	—
69	C₂²	#67290	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	46	1	no	—
72	C₄	D₄×D₂₃	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	92	1	no	—
76	C₂	#10625109	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10625109
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle	C₂×C₂₃	#121
prime radical	#67288	C₂²
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	#473
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ 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. #10625018	C₂	semidirect
5. #10625001	C₂	semidirect
40. C₂×Q₁₆	D₂₃	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
C₂×Q₁₆×C₂₃	2
#10625113	2
#10625072	2
#10625018	2
#10625001	2
#473	23