Subgroups — #15673146

Order 2944.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624985	C₂	1	2	yes	maximal
2	#13092172	C₂	1	4	yes	maximal
3	C₄³×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₂₃	C₄	1	4	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₂₃⋊C₈	C₂²	1	4	yes	—
8	#10624985	C₄	1	8	yes	complemented
9	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₂₃	C₂×C₄	1	4	yes	—
11	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
12	C₄²×C₂₃	—	2	8	no	—
13	C₄²×C₂₃	—	2	4	no	—
14	C₄²×C₂₃	C₂×C₄	1	4	yes	—
15	C₂×C₂₃⋊C₈	—	2	8	no	—
16	C₂×C₂₃⋊C₈	C₂×C₄	1	8	yes	—
17	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	2	4	no	—
19	C₂×C₄×C₂₃	—	2	4	no	—
20	C₂×C₄×C₂₃	—	2	4	no	—
21	C₂×C₄×C₂₃	C₄²	1	4	yes	—
22	C₂×C₄×C₂₃	M₁₆	1	8	yes	—
23	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
24	C₂×C₄×C₂₃	#41	1	4	yes	—
25	C₂₃⋊C₈	—	2	8	no	—
26	#1745	—	23	1	no	maximal, Sylow
27	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
28	C₂²×C₂₃	#117	1	2	yes	—
29	C₂²×C₂₃	C₂×M₁₆	1	4	yes	—
30	C₄×C₂₃	—	2	4	no	—
31	C₄×C₂₃	—	2	8	no	—
32	C₄×C₂₃	#117	1	4	yes	—
33	C₂×#97	—	23	2	no	—
34	C₄³	D₂₃	1	1	yes	characteristic
35	#336	—	23	4	no	—
36	C₂×C₂₃	#376	1	1	yes	characteristic
37	C₂×C₂₃	C₄×M₁₆	1	2	yes	—
38	C₂×C₂₃	#432	1	4	yes	—
39	C₂²×C₈	—	23	4	no	—
40	C₂×C₄²	Dic₂₃	1	4	yes	—
41	C₂×C₄²	C₂×D₂₃	1	2	yes	—
42	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
43	#97	—	23	8	no	—
44	C₂₃	#1745	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄	C₂×Dic₂₃	1	4	yes	—
46	C₂²×C₄	C₂×Dic₂₃	1	2	yes	—
47	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
48	C₂×C₈	—	23	8	no	—
49	C₂×C₈	—	46	8	no	—
50	C₄²	—	2	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	C₄×D₂₃	1	4	yes	—
53	C₂³	C₂²×Dic₂₃	1	1	yes	characteristic
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	#67267	1	8	yes	—
58	C₂×C₄	C₄×Dic₂₃	1	4	yes	—
59	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
60	C₂×C₄	#67288	1	4	yes	—
61	C₈	—	46	8	no	—
62	C₂²	C₂×#67267	1	4	yes	—
63	C₂²	C₂×C₄×Dic₂₃	1	1	yes	characteristic
64	C₂²	#10625097	1	2	yes	—
65	C₄	—	2	4	no	—
66	C₄	—	2	8	no	—
67	C₄	#10625043	1	4	yes	—
68	C₂	#13092263	1	1	yes	characteristic
69	C₂	C₄×#67267	1	2	yes	—
70	C₂	#13092474	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₃
commutator	C₂²×C₂₃	C₂×C₄²
Fitting	C₄³×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂²×C₄
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	C₄³	D₂₃
hypocenter	C₂₃	#1745
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
8. #10624985	C₄	semidirect
44. C₂₃	#1745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10624985	2
#13092172	2
C₄³×C₂₃	2
#1745	23