Subgroups — #13092465

Order 1472.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#67267	C₂	1	1	yes	maximal, characteristic
3	C₂×#67267	C₂	1	1	yes	maximal, characteristic
4	#10625004	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	M₁₆×C₂₃	—	2	1	no	—
7	M₁₆×C₂₃	C₂²	1	2	yes	—
8	C₂×C₈×C₂₃	—	2	1	no	—
9	#67267	—	2	1	no	—
10	#67267	C₄	1	2	yes	—
11	#67267	C₄	1	2	yes	—
12	#67267	C₂²	1	2	yes	—
13	C₂×C₂₃⋊C₈	—	2	1	no	—
14	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₂₃	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₃	Q₈	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
22	C₈×C₂₃	—	2	2	no	—
23	C₂₃⋊C₈	—	2	2	no	—
24	C₂₃⋊C₈	C₂×C₄	1	4	yes	—
25	C₂²×C₂₃	—	4	1	no	—
26	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
33	#430	—	23	1	no	maximal, Sylow
34	C₂×C₂₃	—	2	1	no	—
35	C₂×C₂₃	—	2	1	no	—
36	C₂×C₂₃	—	2	1	no	—
37	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×M₁₆	—	23	1	no	—
39	C₂×M₁₆	—	23	1	no	—
40	C₂×M₁₆	D₂₃	1	1	yes	characteristic
41	#108	—	23	4	no	—
42	C₂₃	#430	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
44	M₁₆	—	2	1	no	—
45	M₁₆	—	23	2	no	—
46	M₁₆	—	23	2	no	—
47	M₁₆	—	23	2	no	—
48	M₁₆	—	46	1	no	—
49	M₁₆	C₂×D₂₃	1	2	yes	—
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	—	23	2	no	—
52	C₂×C₈	—	46	1	no	—
53	C₂³	Dic₄₆	1	1	yes	characteristic
54	C₂×C₄	Dic₄₆	1	1	yes	characteristic
55	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
56	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	23	4	no	—
62	C₈	—	46	2	no	—
63	C₂²	—	4	1	no	—
64	C₂²	Dic₂₃⋊C₄	1	1	yes	characteristic
65	C₂²	Dic₂₃⋊C₄	1	1	yes	characteristic
66	C₂²	C₂×Dic₄₆	1	1	yes	characteristic
67	C₄	Dic₂₃⋊C₄	1	1	yes	characteristic
68	C₄	Dic₂₃⋊C₄	1	1	yes	characteristic
69	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
70	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	C₂×Dic₂₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	Q₈
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	#430
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #10625004	C₂	semidirect
42. C₂₃	#430	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₃	2
C₂×#67267	2
#10625004	2
#430	23