Subgroups — #13093184

Order 1472.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625119	C₂	1	8	yes	maximal, complemented
3	C₂×#67267	C₂	1	6	yes	maximal, complemented
4	#41×C₂₃	C₄	1	4	yes	—
5	#41×C₂₃	C₂²	1	4	yes	—
6	C₂×Q₈×C₂₃	C₄	1	1	yes	characteristic
7	C₂×D₄×C₂₃	C₄	1	3	yes	—
8	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
9	#67267	C₂²	1	4	yes	—
10	#67267	C₂²	1	12	yes	complemented
11	C₂×C₂₃⋊C₈	C₂²	1	12	yes	complemented
12	C₂³×C₂₃	C₂×C₄	1	3	yes	—
13	Q₈×C₂₃	C₂×C₄	1	4	yes	—
14	D₄×C₂₃	C₂×C₄	1	12	yes	—
15	C₂×C₄×C₂₃	C₂×C₄	1	3	yes	—
16	C₂×C₄×C₂₃	C₂×C₄	1	6	yes	—
17	C₂×C₄×C₂₃	C₂³	1	6	yes	—
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂₃⋊C₈	C₂³	1	8	yes	—
20	C₂²×C₂₃	—	4	3	no	—
21	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₂₃	C₂²×C₄	1	6	yes	—
23	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₃	C₂²×C₄	1	6	yes	—
25	C₄×C₂₃	C₂⁴	1	1	yes	characteristic
26	#568	—	23	1	no	maximal, Sylow
27	C₂×C₂₃	—	2	1	no	—
28	C₂×C₂₃	—	2	6	no	—
29	C₂×C₂₃	C₂³×C₄	1	1	yes	characteristic
30	C₂×#41	D₂₃	1	1	yes	characteristic
31	#131	—	23	8	no	—
32	C₂×M₁₆	—	23	6	no	—
33	C₂₃	#568	1	1	yes	characteristic, complemented, Sylow
34	#41	Dic₂₃	1	4	yes	—
35	#41	C₂×D₂₃	1	4	yes	—
36	C₂×Q₈	Dic₂₃	1	1	yes	characteristic
37	C₂×D₄	Dic₂₃	1	3	yes	—
38	C₂²×C₄	C₂×D₂₃	1	3	yes	—
39	M₁₆	—	23	4	no	—
40	M₁₆	—	23	12	no	—
41	C₂×C₈	—	23	12	no	—
42	C₂³	C₂×Dic₂₃	1	3	yes	—
43	Q₈	C₂×Dic₂₃	1	4	yes	—
44	D₄	C₂×Dic₂₃	1	12	yes	—
45	C₂×C₄	C₂×Dic₂₃	1	3	yes	—
46	C₂×C₄	C₂×Dic₂₃	1	6	yes	—
47	C₂×C₄	C₂²×D₂₃	1	6	yes	—
48	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
49	C₈	—	23	8	no	—
50	C₂²	—	4	3	no	—
51	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
52	C₂²	C₂²×Dic₂₃	1	6	yes	—
53	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
54	C₄	C₂²×Dic₂₃	1	6	yes	—
55	C₄	C₂³×D₂₃	1	1	yes	characteristic
56	C₂	—	2	1	no	—
57	C₂	—	2	6	no	—
58	C₂	C₂³×Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂³×D₂₃
commutator, socle	C₂×C₂₃	C₂³×C₄
Fitting, prime radical	C₂×#41×C₂₃	C₂
cosocle	C₄×C₂₃	C₂⁴
hypercenter	C₂×#41	D₂₃
hypocenter	C₂₃	#568
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #10625119	C₂	semidirect
3. C₂×#67267	C₂	semidirect
10. #67267	C₂²	semidirect
11. C₂×C₂₃⋊C₈	C₂²	semidirect
33. C₂₃	#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×C₂₃	2
#10625119	2
C₂×#67267	2
#568	23