Subgroups — #15671699

Order 2944.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#67262	C₂	1	3	yes	maximal
2	#13092138	C₂	1	3	yes	maximal, complemented
3	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#67262	C₄	1	6	yes	—
5	C₄²×D₂₃	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₂₃	C₂²	1	3	yes	—
7	#10624997	C₄	1	6	yes	—
8	C₄×C₂₃⋊C₈	C₂²	1	3	yes	—
9	C₂×C₄×D₂₃	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₂₃	C₂×C₄	1	6	yes	—
11	C₄²×C₂₃	C₂³	1	1	yes	characteristic
12	C₄×Dic₂₃	C₂×C₄	1	3	yes	—
13	C₂×C₂₃⋊C₈	C₂×C₄	1	6	yes	—
14	#67262	—	2	12	no	—
15	C₂²×D₂₃	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂²×C₄	1	3	yes	—
17	C₂×Dic₂₃	C₄²	1	3	yes	—
18	C₄×D₂₃	—	2	6	no	—
19	C₈×C₂₃	M₁₆	1	12	yes	complemented
20	C₂₃⋊C₈	—	2	6	no	—
21	#1455	—	23	1	no	maximal, Sylow
22	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
23	C₂×D₂₃	—	2	3	no	—
24	C₄×C₂₃	C₂×M₁₆	1	6	yes	—
25	Dic₂₃	—	2	3	no	—
26	C₄×M₁₆	—	23	3	no	—
27	#322	—	23	3	no	—
28	C₈²	D₂₃	1	1	yes	characteristic, complemented
29	C₂×C₂₃	C₄×M₁₆	1	3	yes	—
30	D₂₃	—	4	1	no	—
31	C₂×M₁₆	—	23	6	no	—
32	C₂×C₄²	—	23	1	no	—
33	#97	—	23	6	no	—
34	C₄×C₈	—	23	3	no	—
35	C₄×C₈	C₂×D₂₃	1	3	yes	—
36	C₂₃	#1455	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	—	23	3	no	—
38	M₁₆	—	46	12	no	—
39	C₂×C₈	—	23	6	no	—
40	C₂×C₈	C₄×D₂₃	1	6	yes	—
41	C₄²	—	23	3	no	—
42	C₄²	C₂²×D₂₃	1	1	yes	characteristic
43	C₂³	—	23	1	no	—
44	C₂×C₄	—	23	3	no	—
45	C₂×C₄	—	46	6	no	—
46	C₂×C₄	C₂×C₄×D₂₃	1	3	yes	—
47	C₈	—	46	6	no	—
48	C₈	#67262	1	12	yes	complemented
49	C₂²	—	46	3	no	—
50	C₂²	C₄²×D₂₃	1	1	yes	characteristic
51	C₄	—	46	3	no	—
52	C₄	C₂×#67262	1	6	yes	—
53	C₂	—	92	1	no	—
54	C₂	C₄×#67262	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₃
commutator, socle	C₂²×C₂₃	C₂×C₄²
Fitting	C₈²×C₂₃	C₂
prime radical	C₂²×D₂₃	C₄²
cosocle	C₄²×C₂₃	C₂³
hypercenter	C₈²	D₂₃
hypocenter	C₂₃	#1455
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #13092138	C₂	semidirect
3. C₈²×C₂₃	C₂	semidirect
19. C₈×C₂₃	M₁₆	semidirect
28. C₈²	D₂₃	semidirect
36. C₂₃	#1455	semidirect
48. C₈	#67262	semidirect

Maximal subgroups

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

subgroup	index
C₄×#67262	2
#13092138	2
C₈²×C₂₃	2
#1455	23