Subgroups — C₂×#10625041 #13092939

Order 1472.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₃	C₂	1	2	yes	maximal
3	C₂×Dic₂₃⋊C₄	C₂	1	4	yes	maximal
4	#10625041	C₂	1	8	yes	maximal, direct product factor
5	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₃	C₂²	1	4	yes	—
8	C₄²×C₂₃	C₂²	1	4	yes	—
9	C₄⋊Dic₂₃	C₂²	1	8	yes	—
10	Dic₂₃⋊C₄	C₂²	1	16	yes	—
11	C₂³×C₂₃	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₂₃	—	2	4	no	—
13	C₂×C₄×C₂₃	Q₈	1	4	yes	—
14	C₂×C₄×C₂₃	C₂³	1	4	yes	—
15	C₂×C₄×C₂₃	C₂³	1	2	yes	—
16	C₂×Dic₂₃	—	2	8	no	—
17	C₂×Dic₂₃	C₂³	1	8	yes	—
18	C₂²×C₂₃	C₂×Q₈	1	2	yes	—
19	C₂²×C₂₃	#41	1	4	yes	—
20	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
21	C₄×C₂₃	—	2	4	no	—
22	C₄×C₂₃	C₂×Q₈	1	4	yes	—
23	Dic₂₃	—	2	8	no	—
24	C₂×#125	—	23	1	no	maximal, Sylow
25	C₂×C₂₃	#125	1	4	yes	complemented
26	C₂×C₂₃	C₂²×Q₈	1	1	yes	characteristic
27	C₂×C₂₃	C₂×#41	1	2	yes	—
28	#125	—	23	8	no	—
29	C₂×C₄⋊C₄	—	23	4	no	—
30	C₂×C₄⋊C₄	—	23	2	no	—
31	C₂×C₄²	D₂₃	1	1	yes	characteristic
32	C₂₃	C₂×#125	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄	—	23	4	no	—
34	C₂²×C₄	C₂×D₂₃	1	2	yes	—
35	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
36	C₄⋊C₄	—	23	16	no	—
37	C₄⋊C₄	—	23	8	no	—
38	C₄²	C₂×D₂₃	1	4	yes	—
39	C₂³	C₂²×D₂₃	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	23	8	no	—
42	C₂×C₄	—	46	8	no	—
43	C₂×C₄	Dic₄₆	1	4	yes	—
44	C₂×C₄	C₂²×D₂₃	1	4	yes	—
45	C₂×C₄	C₂²×D₂₃	1	2	yes	—
46	C₂²	C₂×Dic₄₆	1	2	yes	—
47	C₂²	#67288	1	4	yes	—
48	C₂²	C₂³×D₂₃	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	46	8	no	—
51	C₄	C₂×Dic₄₆	1	4	yes	—
52	C₂	#10625041	1	4	yes	direct product factor
53	C₂	C₂²×Dic₄₆	1	1	yes	characteristic
54	C₂	C₂×#67288	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁴
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂×C₄²×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂³
hypercenter	C₂×C₄²	D₂₃
hypocenter	C₂₃	C₂×#125
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #10625041	C₂	direct (N × H)
25. C₂×C₂₃	#125	semidirect
32. C₂₃	C₂×#125	semidirect
52. C₂	#10625041	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₂₃	2
C₂×C₄⋊Dic₂₃	2
C₂×Dic₂₃⋊C₄	2
#10625041	2
C₂×#125	23

Subgroups — C2×#10625041 #13092939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625041 #13092939