Subgroups — C₂×SD₃₂×C₂₂₃ #28383218

Order 14272.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	SD₃₂×C₂₂₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₂₂₃	—	2	1	no	—
6	C₂×D₄×C₂₂₃	—	2	1	no	—
7	Q₁₆×C₂₂₃	—	2	1	no	—
8	Q₁₆×C₂₂₃	C₂²	1	2	yes	complemented
9	D₈×C₂₂₃	—	2	1	no	—
10	D₈×C₂₂₃	C₂²	1	2	yes	—
11	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
12	C₁₆×C₂₂₃	C₂²	1	2	yes	complemented
13	C₂³×C₂₂₃	—	4	1	no	—
14	Q₈×C₂₂₃	—	2	2	no	—
15	Q₈×C₂₂₃	—	4	1	no	—
16	D₄×C₂₂₃	—	2	2	no	—
17	D₄×C₂₂₃	—	4	1	no	—
18	C₂×C₄×C₂₂₃	—	4	1	no	—
19	C₂×C₄×C₂₂₃	D₄	1	1	yes	characteristic
20	C₈×C₂₂₃	D₄	1	1	yes	characteristic
21	C₈×C₂₂₃	C₂³	1	1	yes	characteristic
22	C₂²×C₂₂₃	—	4	2	no	—
23	C₂²×C₂₂₃	—	8	2	no	—
24	C₂²×C₂₂₃	D₈	1	1	yes	characteristic
25	C₄×C₂₂₃	—	4	2	no	—
26	C₄×C₂₂₃	D₈	1	1	yes	characteristic
27	C₄×C₂₂₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₂₂₃	—	8	2	no	—
29	C₂×C₂₂₃	SD₃₂	1	2	yes	direct product factor
30	C₂×C₂₂₃	C₂×D₈	1	1	yes	characteristic
31	C₂₂₃	C₂×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×SD₃₂	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×Q₁₆	C₂×C₂₂₃	1	1	yes	characteristic, complemented
34	C₂×D₈	C₂×C₂₂₃	1	1	yes	characteristic
35	SD₃₂	C₂×C₂₂₃	1	4	yes	direct product factor
36	C₂×C₁₆	C₂×C₂₂₃	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	2	1	no	—
38	C₂×D₄	—	2	1	no	—
39	Q₁₆	—	2	1	no	—
40	Q₁₆	C₂²×C₂₂₃	1	2	yes	complemented
41	D₈	—	2	1	no	—
42	D₈	C₂²×C₂₂₃	1	2	yes	—
43	C₂×C₈	C₂²×C₂₂₃	1	1	yes	characteristic
44	C₁₆	C₂²×C₂₂₃	1	2	yes	complemented
45	C₂³	—	4	1	no	—
46	Q₈	—	2	2	no	—
47	Q₈	—	4	1	no	—
48	D₄	—	2	2	no	—
49	D₄	—	4	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	D₄×C₂₂₃	1	1	yes	characteristic
52	C₈	D₄×C₂₂₃	1	1	yes	characteristic
53	C₈	C₂³×C₂₂₃	1	1	yes	characteristic
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	D₈×C₂₂₃	1	1	yes	characteristic
57	C₄	—	4	2	no	—
58	C₄	D₈×C₂₂₃	1	1	yes	characteristic
59	C₄	C₂×D₄×C₂₂₃	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	SD₃₂×C₂₂₃	1	2	yes	direct product factor
62	C₂	C₂×D₈×C₂₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₂₃	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₂₂₃
prime radical	C₂×D₈×C₂₂₃	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₂₃ ◁ C₂×C₄×C₂₂₃ ◁ C₂×C₈×C₂₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₂₂₃	C₂	semidirect
3. SD₃₂×C₂₂₃	C₂	direct (N × H)
4. C₂×C₁₆×C₂₂₃	C₂	semidirect
8. Q₁₆×C₂₂₃	C₂²	semidirect
12. C₁₆×C₂₂₃	C₂²	semidirect
29. C₂×C₂₂₃	SD₃₂	direct (N × H)
31. C₂₂₃	C₂×SD₃₂	direct (N × H)
32. C₂×SD₃₂	C₂₂₃	direct (N × H)
33. C₂×Q₁₆	C₂×C₂₂₃	semidirect
35. SD₃₂	C₂×C₂₂₃	direct (N × H)
36. C₂×C₁₆	C₂×C₂₂₃	semidirect
40. Q₁₆	C₂²×C₂₂₃	semidirect
44. C₁₆	C₂²×C₂₂₃	semidirect
61. C₂	SD₃₂×C₂₂₃	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×C₂₂₃	2
C₂×D₈×C₂₂₃	2
SD₃₂×C₂₂₃	2
C₂×C₁₆×C₂₂₃	2
C₂×SD₃₂	223

Subgroups — C2×SD32×C223 #28383218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×SD₃₂×C₂₂₃ #28383218