Subgroups — C₂×#10625010 #13092840

Order 1472.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₈₄	C₂	1	1	yes	maximal, characteristic
3	#10625010	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₂₃	—	2	1	no	—
6	C₂×D₉₂	—	2	1	no	—
7	Q₁₆×C₂₃	—	2	1	no	—
8	Q₁₆×C₂₃	C₂²	1	2	yes	complemented
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	D₁₈₄	—	2	1	no	—
11	D₁₈₄	C₂²	1	2	yes	—
12	C₂₃⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂²×D₂₃	—	4	1	no	—
14	Q₈×C₂₃	—	2	2	no	—
15	Q₈×C₂₃	—	4	1	no	—
16	C₂×C₄×C₂₃	—	4	1	no	—
17	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
18	D₉₂	—	2	2	no	—
19	D₉₂	—	4	1	no	—
20	C₈×C₂₃	D₄	1	1	yes	characteristic
21	C₈×C₂₃	C₂³	1	1	yes	characteristic
22	C₂²×C₂₃	D₈	1	1	yes	characteristic
23	C₂×D₂₃	—	4	2	no	—
24	C₂×D₂₃	—	8	2	no	—
25	C₄×C₂₃	—	4	2	no	—
26	C₄×C₂₃	D₈	1	1	yes	characteristic
27	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₂×SD₃₂	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	SD₃₂	1	2	yes	complemented
30	C₂×C₂₃	C₂×D₈	1	1	yes	characteristic
31	D₂₃	—	8	2	no	—
32	C₂×Q₁₆	D₂₃	1	1	yes	characteristic, complemented
33	C₂×D₈	—	23	1	no	—
34	SD₃₂	—	23	4	no	—
35	C₂×C₁₆	—	23	1	no	—
36	C₂₃	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	2	1	no	—
38	C₂×D₄	—	46	1	no	—
39	Q₁₆	—	2	1	no	—
40	Q₁₆	C₂×D₂₃	1	2	yes	complemented
41	D₈	—	23	2	no	—
42	D₈	—	46	1	no	—
43	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
44	C₁₆	—	23	2	no	—
45	C₂³	—	92	1	no	—
46	Q₈	—	2	2	no	—
47	Q₈	—	4	1	no	—
48	D₄	—	46	2	no	—
49	D₄	—	92	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
52	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
53	C₈	C₂²×D₂₃	1	1	yes	characteristic
54	C₂²	—	92	2	no	—
55	C₂²	—	184	2	no	—
56	C₂²	#67272	1	1	yes	characteristic
57	C₄	—	4	2	no	—
58	C₄	#67272	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
60	C₂	—	184	2	no	—
61	C₂	#10625010	1	2	yes	direct product factor
62	C₂	C₂×#67272	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#67272
commutator, cosocle	C₈×C₂₃	C₂³
Frattini	C₈	C₂²×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle	C₂²×C₂₃	D₈
prime radical	C₂×D₁₈₄	C₂
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	C₂×SD₃₂
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₂₃	C₂	semidirect
3. #10625010	C₂	direct (N × H)
4. C₂×C₂₃⋊C₁₆	C₂	semidirect
8. Q₁₆×C₂₃	C₂²	semidirect
12. C₂₃⋊C₁₆	C₂²	semidirect
29. C₂×C₂₃	SD₃₂	semidirect
32. C₂×Q₁₆	D₂₃	semidirect
36. C₂₃	C₂×SD₃₂	semidirect
40. Q₁₆	C₂×D₂₃	semidirect
61. C₂	#10625010	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×Q₁₆×C₂₃	2
C₂×D₁₈₄	2
#10625010	2
C₂×C₂₃⋊C₁₆	2
C₂×SD₃₂	23

Subgroups — C2×#10625010 #13092840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625010 #13092840