Subgroups — #13092181

Order 1472.

90 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	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
5	M₁₆×C₂₃	—	2	1	no	—
6	M₁₆×C₂₃	C₄	1	2	yes	—
7	C₂×C₈×C₂₃	—	2	1	no	—
8	#67267	—	2	1	no	—
9	#67267	C₄	1	2	yes	—
10	C₂×C₂₃⋊C₈	—	2	1	no	—
11	C₂×C₂₃⋊C₈	—	2	1	no	—
12	C₂×C₂₃⋊C₈	—	2	1	no	—
13	C₂×C₂₃⋊C₈	C₄	1	2	yes	—
14	C₂³×C₂₃	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₂₃	C₂×C₄	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	D₄	1	1	yes	characteristic
21	C₈×C₂₃	—	2	2	no	—
22	C₂₃⋊C₈	—	2	2	no	—
23	C₂₃⋊C₈	—	2	2	no	—
24	C₂²×C₂₃	—	2	2	no	—
25	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₂₃	C₄²	1	1	yes	characteristic
29	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
32	#341	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	—	2	1	no	—
34	C₂×C₂₃	—	2	1	no	—
35	C₂×C₂₃	#95	1	1	yes	characteristic
36	C₂×C₂₃	#108	1	2	yes	—
37	C₂×M₁₆	—	23	1	no	—
38	C₂×M₁₆	D₂₃	1	1	yes	characteristic
39	C₂²×C₈	—	23	1	no	—
40	C₂₃	#341	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
42	M₁₆	—	2	1	no	—
43	M₁₆	—	23	2	no	—
44	M₁₆	—	46	1	no	—
45	M₁₆	Dic₂₃	1	2	yes	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	23	2	no	—
48	C₂×C₈	—	46	1	no	—
49	C₂×C₈	—	46	1	no	—
50	C₂×C₈	—	46	1	no	—
51	C₂³	Dic₄₆	1	1	yes	characteristic
52	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
53	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
54	C₂×C₄	D₉₂	1	1	yes	characteristic
55	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	46	2	no	—
60	C₈	—	46	2	no	—
61	C₂²	—	2	2	no	—
62	C₂²	Dic₂₃⋊C₄	1	1	yes	characteristic
63	C₂²	Dic₂₃⋊C₄	1	1	yes	characteristic
64	C₂²	C₄⋊Dic₂₃	1	1	yes	characteristic
65	C₄	C₄×Dic₂₃	1	1	yes	characteristic
66	C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
67	C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
68	C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	2	1	no	—
71	C₂	#10625004	1	2	yes	—
72	C₂	C₂₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₂₃
commutator	C₄×C₂₃	C₄²
Frattini	C₂²×C₄	C₂×D₂₃
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₄⋊C₄
prime radical	C₂³×C₂₃	Q₈
cosocle	C₂²×C₄×C₂₃	C₂²
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	#341
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
40. C₂₃	#341	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
C₂²×C₂₃⋊C₈	2
#341	23