Subgroups — C₂×#10625047 #13092942

Order 1472.

246 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, complemented
2	C₂×(C₂×D₂₃)⋊C₄	C₂	1	3	yes	maximal
3	C₂×Dic₂₃⋊C₄	C₂	1	3	yes	maximal, complemented
4	#10625047	C₂	1	8	yes	maximal, direct product factor
5	C₂³×D₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
7	C₂²×Dic₂₃	C₂²	1	3	yes	—
8	C₄²×C₂₃	C₂²	1	4	yes	complemented
9	(C₂×D₂₃)⋊C₄	C₂²	1	12	yes	—
10	Dic₂₃⋊C₄	C₂²	1	12	yes	complemented
11	C₂³×C₂₃	C₂³	1	1	yes	characteristic
12	C₂²×D₂₃	—	2	6	no	—
13	C₂²×D₂₃	C₂³	1	2	yes	—
14	C₂×C₄×C₂₃	—	2	6	no	—
15	C₂×C₄×C₂₃	C₂³	1	6	yes	—
16	C₂×Dic₂₃	—	2	6	no	—
17	C₂×Dic₂₃	C₂³	1	6	yes	—
18	C₂²×C₂₃	#41	1	6	yes	—
19	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
20	C₂×D₂₃	—	2	6	no	—
21	C₂×D₂₃	—	4	4	no	—
22	C₄×C₂₃	—	2	6	no	—
23	Dic₂₃	—	2	6	no	—
24	C₂×#126	—	23	1	no	maximal, Sylow
25	C₂×C₂₃	#126	1	4	yes	complemented
26	C₂×C₂₃	C₂×#41	1	3	yes	—
27	D₂₃	—	4	2	no	—
28	#126	—	23	8	no	—
29	C₂×C₄⋊C₄	—	23	3	no	—
30	C₂×C₂²⋊C₄	—	23	3	no	—
31	C₂×C₄²	D₂₃	1	1	yes	characteristic, complemented
32	C₂₃	C₂×#126	1	1	yes	characteristic, complemented, Sylow
33	C₂⁴	—	23	1	no	—
34	C₂²×C₄	—	23	3	no	—
35	C₂²×C₄	C₂×D₂₃	1	3	yes	—
36	C₄⋊C₄	—	23	12	no	—
37	C₂²⋊C₄	—	23	12	no	—
38	C₄²	C₂×D₂₃	1	4	yes	complemented
39	C₂³	—	23	2	no	—
40	C₂³	—	46	6	no	—
41	C₂³	C₂²×D₂₃	1	1	yes	characteristic
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	—	23	6	no	—
44	C₂×C₄	—	46	6	no	—
45	C₂×C₄	C₂²×D₂₃	1	6	yes	—
46	C₂²	—	46	6	no	—
47	C₂²	—	92	4	no	—
48	C₂²	#67288	1	6	yes	—
49	C₂²	C₂³×D₂₃	1	1	yes	characteristic
50	C₄	—	2	6	no	—
51	C₄	—	46	6	no	—
52	C₂	—	92	2	no	—
53	C₂	#10625047	1	4	yes	direct product factor
54	C₂	C₂×#67288	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁴
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂×C₄²×C₂₃	C₂
socle	C₂³×C₂₃	C₂³
prime radical	C₂³×D₂₃	C₂²
hypercenter	C₂×C₄²	D₂₃
hypocenter	C₂₃	C₂×#126
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
1. C₂×C₄²×C₂₃	C₂	semidirect
3. C₂×Dic₂₃⋊C₄	C₂	semidirect
4. #10625047	C₂	direct (N × H)
8. C₄²×C₂₃	C₂²	semidirect
10. Dic₂₃⋊C₄	C₂²	semidirect
25. C₂×C₂₃	#126	semidirect
31. C₂×C₄²	D₂₃	semidirect
32. C₂₃	C₂×#126	semidirect
38. C₄²	C₂×D₂₃	semidirect
53. C₂	#10625047	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×(C₂×D₂₃)⋊C₄	2
C₂×Dic₂₃⋊C₄	2
#10625047	2
C₂×#126	23

Subgroups — C2×#10625047 #13092942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625047 #13092942