Subgroups — #15671566

Order 2944.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092216	C₂	1	2	yes	maximal
2	C₂₃×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₂₃	—	2	2	no	—
4	C₂₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
5	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₂₃	C₄	1	1	yes	characteristic
7	#10625018	—	2	2	no	—
8	C₂×Q₈×C₂₃	—	2	1	no	—
9	C₂×Q₈×C₂₃	D₄	1	2	yes	—
10	Q₁₆×C₂₃	—	4	4	no	—
11	C₂×C₈×C₂₃	—	2	1	no	—
12	C₄⋊C₄×C₂₃	—	4	1	no	—
13	C₄⋊C₄×C₂₃	—	4	1	no	—
14	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
15	#67267	—	4	2	no	—
16	Q₈×C₂₃	—	4	2	no	—
17	Q₈×C₂₃	—	4	2	no	—
18	C₂×C₄×C₂₃	—	2	1	no	—
19	C₂×C₄×C₂₃	—	2	2	no	—
20	C₂×C₄×C₂₃	—	4	1	no	—
21	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₂₃	—	2	2	no	—
23	C₂₃⋊C₈	—	8	2	no	—
24	#1411	—	23	1	no	maximal, Sylow
25	C₂²×C₂₃	#99	1	1	yes	characteristic
26	C₄×C₂₃	—	2	2	no	—
27	C₄×C₂₃	—	2	1	no	—
28	C₄×C₂₃	—	4	2	no	—
29	C₄×C₂₃	—	8	1	no	—
30	#494	D₂₃	1	1	yes	characteristic
31	#356	—	23	2	no	—
32	C₂×C₂₃	—	2	1	no	—
33	C₂×C₂₃	#353	1	1	yes	characteristic
34	C₂×Q₁₆	—	2	2	no	—
35	C₄⋊Q₈	Dic₂₃	1	1	yes	characteristic
36	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
37	#101	—	46	2	no	—
38	C₄×C₈	Dic₂₃	1	1	yes	characteristic
39	C₂₃	#1411	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	C₂²⋊D₂₃	1	2	yes	—
42	Q₁₆	—	4	4	no	—
43	M₁₆	—	92	2	no	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	4	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	184	2	no	—
56	C₂²	#10625016	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	4	2	no	—
60	C₄	—	8	1	no	—
61	C₂	—	2	1	no	—
62	C₂	#13092210	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092210
commutator	C₄²×C₂₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₃
Fitting	C₂₃×#494	C₂
socle	C₂×C₂₃	#353
prime radical	C₂²×C₂₃	#99
cosocle	C₂₃×C₄⋊Q₈	C₂²
hypercenter	#494	D₂₃
hypocenter	C₂₃	#1411
LCS	G ▷ C₄²×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #494

Complements

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

N	H ≅ G/N	type
39. C₂₃	#1411	semidirect

Maximal subgroups

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

subgroup	index
#13092216	2
C₂₃×#494	2
#1411	23