Subgroups — C₂²×Q₈×D₂₃ #13093240

Order 1472.

850 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Q₈×D₂₃	C₂	1	24	yes	maximal, direct product factor
3	C₂²×C₄×D₂₃	C₂	1	3	yes	maximal
4	C₂²×Dic₄₆	C₂	1	3	yes	maximal, complemented
5	C₂³×D₂₃	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₂₃	C₂²	1	12	yes	complemented
7	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
8	C₂²×Dic₂₃	C₂²	1	3	yes	—
9	Q₈×D₂₃	C₂²	1	64	yes	direct product factor
10	C₂×C₄×D₂₃	C₂²	1	36	yes	—
11	C₂×Dic₄₆	C₂²	1	36	yes	complemented
12	C₂³×C₂₃	C₂³	1	1	yes	characteristic
13	C₂²×D₂₃	Q₈	1	8	yes	direct product factor
14	C₂²×D₂₃	C₂³	1	6	yes	—
15	Q₈×C₂₃	C₂³	1	16	yes	complemented
16	C₂×C₄×C₂₃	C₂³	1	18	yes	—
17	C₂×Dic₂₃	C₂³	1	18	yes	—
18	C₄×D₂₃	C₂³	1	48	yes	—
19	Dic₄₆	C₂³	1	48	yes	complemented
20	C₂²×C₂₃	C₂×Q₈	1	4	yes	complemented
21	C₂²×C₂₃	C₂⁴	1	3	yes	—
22	C₂×D₂₃	C₂×Q₈	1	24	yes	direct product factor
23	C₂×D₂₃	C₂⁴	1	4	yes	—
24	C₄×C₂₃	C₂⁴	1	12	yes	—
25	Dic₂₃	C₂⁴	1	12	yes	—
26	C₂³×Q₈	—	23	1	no	maximal, Sylow
27	C₂×C₂₃	C₂²×Q₈	1	6	yes	complemented
28	C₂×C₂₃	C₂⁵	1	1	yes	characteristic
29	D₂₃	C₂²×Q₈	1	8	yes	direct product factor
30	C₂²×Q₈	—	23	24	no	—
31	C₂²×Q₈	—	23	3	no	—
32	C₂²×Q₈	D₂₃	1	1	yes	characteristic, direct product factor
33	C₂³×C₄	—	23	3	no	—
34	C₂₃	C₂³×Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	23	1	no	—
36	C₂×Q₈	—	23	64	no	—
37	C₂×Q₈	—	23	36	no	—
38	C₂×Q₈	C₂×D₂₃	1	12	yes	direct product factor
39	C₂²×C₄	—	23	3	no	—
40	C₂²×C₄	—	23	36	no	—
41	C₂²×C₄	C₂×D₂₃	1	3	yes	—
42	C₂³	—	23	8	no	—
43	C₂³	—	23	6	no	—
44	C₂³	C₂²×D₂₃	1	1	yes	characteristic
45	Q₈	—	23	48	no	—
46	Q₈	C₂²×D₂₃	1	16	yes	direct product factor
47	C₂×C₄	—	23	18	no	—
48	C₂×C₄	—	23	48	no	—
49	C₂×C₄	C₂²×D₂₃	1	18	yes	—
50	C₂²	—	23	24	no	—
51	C₂²	—	23	4	no	—
52	C₂²	Q₈×D₂₃	1	4	yes	direct product factor
53	C₂²	C₂³×D₂₃	1	3	yes	—
54	C₄	—	23	12	no	—
55	C₄	C₂³×D₂₃	1	12	yes	—
56	C₂	—	23	8	no	—
57	C₂	C₂×Q₈×D₂₃	1	6	yes	direct product factor
58	C₂	C₂⁴×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator, cosocle	C₂×C₂₃	C₂⁵
Frattini	C₂	C₂⁴×D₂₃
Fitting	C₂²×Q₈×C₂₃	C₂
socle	C₂³×C₂₃	C₂³
prime radical	C₂³×D₂₃	C₂²
hypercenter	C₂²×Q₈	D₂₃
hypocenter	C₂₃	C₂³×Q₈
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×C₂₃	C₂	semidirect
2. C₂×Q₈×D₂₃	C₂	direct (N × H)
4. C₂²×Dic₄₆	C₂	semidirect
6. C₂×Q₈×C₂₃	C₂²	semidirect
9. Q₈×D₂₃	C₂²	direct (N × H)
11. C₂×Dic₄₆	C₂²	semidirect
13. C₂²×D₂₃	Q₈	direct (N × H)
15. Q₈×C₂₃	C₂³	semidirect
19. Dic₄₆	C₂³	semidirect
20. C₂²×C₂₃	C₂×Q₈	semidirect
22. C₂×D₂₃	C₂×Q₈	direct (N × H)
27. C₂×C₂₃	C₂²×Q₈	semidirect
29. D₂₃	C₂²×Q₈	direct (N × H)
32. C₂²×Q₈	D₂₃	direct (N × H)
34. C₂₃	C₂³×Q₈	semidirect
38. C₂×Q₈	C₂×D₂₃	direct (N × H)
46. Q₈	C₂²×D₂₃	direct (N × H)
52. C₂²	Q₈×D₂₃	direct (N × H)
57. C₂	C₂×Q₈×D₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₂₃	2
C₂×Q₈×D₂₃	2
C₂²×C₄×D₂₃	2
C₂²×Dic₄₆	2
C₂³×Q₈	23

Subgroups — C22×Q8×D23 #13093240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Q₈×D₂₃ #13093240