Subgroups — C₂×Q₈×Dic₂₃ #13092883

Order 1472.

298 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
2	Q₈×Dic₂₃	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊Dic₂₃	C₂	1	3	yes	maximal
4	C₂×C₄×Dic₂₃	C₂	1	3	yes	maximal
5	C₂×Q₈×C₂₃	C₄	1	8	yes	complemented
6	C₂×Q₈×C₂₃	C₂²	1	4	yes	—
7	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
8	C₂²×Dic₂₃	C₂²	1	3	yes	—
9	C₂²×Dic₂₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₃	C₂²	1	12	yes	—
11	C₄×Dic₂₃	C₂²	1	12	yes	—
12	C₂³×C₂₃	C₂³	1	1	yes	characteristic
13	Q₈×C₂₃	C₂×C₄	1	16	yes	complemented
14	C₂×C₄×C₂₃	C₂×C₄	1	12	yes	—
15	C₂×C₄×C₂₃	C₂³	1	6	yes	—
16	C₂×Dic₂₃	—	2	6	no	—
17	C₂×Dic₂₃	Q₈	1	4	yes	direct product factor
18	C₂×Dic₂₃	C₂³	1	6	yes	—
19	C₂×Dic₂₃	C₂³	1	2	yes	—
20	C₂²×C₂₃	C₂²×C₄	1	2	yes	—
21	C₂²×C₂₃	C₂×Q₈	1	2	yes	—
22	C₂²×C₂₃	#41	1	2	yes	—
23	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
24	C₄×C₂₃	C₂²×C₄	1	12	yes	—
25	Dic₂₃	—	2	6	no	—
26	Dic₂₃	C₂×Q₈	1	4	yes	direct product factor
27	C₂×C₄×Q₈	—	23	1	no	maximal, Sylow
28	C₂×C₂₃	C₄×Q₈	1	4	yes	complemented
29	C₂×C₂₃	C₂³×C₄	1	1	yes	characteristic
30	C₂×C₂₃	C₂²×Q₈	1	1	yes	characteristic
31	C₂×C₂₃	C₂×#41	1	1	yes	characteristic
32	C₂²×Q₈	D₂₃	1	1	yes	characteristic
33	C₄×Q₈	—	23	8	no	—
34	C₂×C₄⋊C₄	—	23	3	no	—
35	C₂×C₄²	—	23	3	no	—
36	C₂₃	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	Dic₂₃	1	8	yes	direct product factor
38	C₂×Q₈	C₂×D₂₃	1	4	yes	—
39	C₂²×C₄	—	23	1	no	—
40	C₂²×C₄	—	23	3	no	—
41	C₂²×C₄	C₂×D₂₃	1	3	yes	—
42	C₄⋊C₄	—	23	12	no	—
43	C₄²	—	23	12	no	—
44	C₂³	C₂²×D₂₃	1	1	yes	characteristic
45	Q₈	C₂×Dic₂₃	1	16	yes	direct product factor
46	C₂×C₄	—	23	4	no	—
47	C₂×C₄	—	23	2	no	—
48	C₂×C₄	—	23	6	no	—
49	C₂×C₄	—	46	6	no	—
50	C₂×C₄	C₂×Dic₂₃	1	12	yes	—
51	C₂×C₄	C₂²×D₂₃	1	6	yes	—
52	C₂²	Q₈×D₂₃	1	2	yes	—
53	C₂²	#67292	1	2	yes	—
54	C₂²	C₂²×Dic₂₃	1	2	yes	—
55	C₂²	C₂³×D₂₃	1	1	yes	characteristic
56	C₄	—	23	4	no	—
57	C₄	—	46	6	no	—
58	C₄	C₂²×Dic₂₃	1	12	yes	—
59	C₂	Q₈×Dic₂₃	1	4	yes	direct product factor
60	C₂	C₂×Q₈×D₂₃	1	1	yes	characteristic
61	C₂	C₂×#67292	1	1	yes	characteristic
62	C₂	C₂³×Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator	C₂×C₂₃	C₂³×C₄
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂²×Q₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂³
cosocle	C₂²×C₂₃	C₂⁴
hypercenter	C₂²×Q₈	D₂₃
hypocenter	C₂₃	C₂×C₄×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
2. Q₈×Dic₂₃	C₂	direct (N × H)
5. C₂×Q₈×C₂₃	C₄	semidirect
13. Q₈×C₂₃	C₂×C₄	semidirect
17. C₂×Dic₂₃	Q₈	direct (N × H)
26. Dic₂₃	C₂×Q₈	direct (N × H)
28. C₂×C₂₃	C₄×Q₈	semidirect
36. C₂₃	C₂×C₄×Q₈	semidirect
37. C₂×Q₈	Dic₂₃	direct (N × H)
45. Q₈	C₂×Dic₂₃	direct (N × H)
59. C₂	Q₈×Dic₂₃	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
Q₈×Dic₂₃	2
C₂×C₄⋊Dic₂₃	2
C₂×C₄×Dic₂₃	2
C₂×C₄×Q₈	23

Subgroups — C2×Q8×Dic23 #13092883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×Dic₂₃ #13092883