Subgroups — 2₋¹⁺⁴×D₂₃ #13093249

Order 1472.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	#10625161	C₂	1	10	yes	maximal, complemented
3	#41×D₂₃	C₂	1	10	yes	maximal, complemented
4	#10625158	C₂	1	5	yes	maximal, complemented
5	C₂×Q₈×D₂₃	C₂	1	5	yes	maximal, complemented
6	#41×C₂₃	C₂²	1	10	yes	complemented
7	C₂×Q₈×C₂₃	C₂²	1	5	yes	complemented
8	#67292	C₂²	1	10	yes	complemented
9	Q₈×D₂₃	C₂²	1	10	yes	—
10	Q₈×D₂₃	C₂²	1	20	yes	complemented
11	#67290	C₂²	1	30	yes	complemented
12	D₄×D₂₃	C₂²	1	10	yes	—
13	#67288	C₂²	1	30	yes	complemented
14	C₂×C₄×D₂₃	C₂²	1	15	yes	—
15	C₂×Dic₄₆	C₂²	1	15	yes	complemented
16	C₂²×D₂₃	C₂³	1	5	yes	—
17	Q₈×C₂₃	C₂³	1	10	yes	—
18	D₄×C₂₃	C₂³	1	10	yes	—
19	C₂×C₄×C₂₃	C₂³	1	15	yes	—
20	C₂²⋊D₂₃	C₂³	1	20	yes	—
21	C₂×Dic₂₃	C₂³	1	15	yes	—
22	D₉₂	C₂³	1	10	yes	—
23	C₄×D₂₃	C₂³	1	10	yes	—
24	C₄×D₂₃	C₂³	1	30	yes	—
25	Dic₄₆	C₂³	1	30	yes	—
26	C₂²×C₂₃	C₂⁴	1	5	yes	—
27	C₂×D₂₃	—	2	10	no	—
28	C₂×D₂₃	C₂⁴	1	5	yes	—
29	C₂×D₂₃	C₂⁴	1	1	yes	characteristic
30	C₄×C₂₃	C₂⁴	1	10	yes	—
31	Dic₂₃	C₂⁴	1	10	yes	—
32	C₂×2₋¹⁺⁴	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	—	2	5	no	—
34	C₂×C₂₃	C₂⁵	1	1	yes	characteristic
35	D₂₃	—	2	5	no	—
36	D₂₃	2₋¹⁺⁴	1	2	yes	direct product factor
37	2₋¹⁺⁴	—	23	10	no	—
38	2₋¹⁺⁴	—	23	5	no	—
39	2₋¹⁺⁴	D₂₃	1	1	yes	characteristic, direct product factor
40	C₂×#41	—	23	10	no	—
41	C₂²×Q₈	—	23	5	no	—
42	C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
43	#41	—	23	10	no	—
44	#41	—	23	30	no	—
45	#41	—	23	30	no	—
46	#41	C₂×D₂₃	1	10	yes	complemented
47	C₂×Q₈	—	23	10	no	—
48	C₂×Q₈	—	23	20	no	—
49	C₂×Q₈	—	23	15	no	—
50	C₂×Q₈	C₂×D₂₃	1	5	yes	complemented
51	C₂×D₄	—	23	10	no	—
52	C₂²×C₄	—	23	15	no	—
53	C₂³	—	23	5	no	—
54	Q₈	—	23	30	no	—
55	Q₈	C₂²×D₂₃	1	10	yes	—
56	D₄	—	23	20	no	—
57	D₄	—	23	10	no	—
58	D₄	C₂²×D₂₃	1	10	yes	—
59	C₂×C₄	—	23	15	no	—
60	C₂×C₄	—	23	10	no	—
61	C₂×C₄	—	23	30	no	—
62	C₂×C₄	C₂²×D₂₃	1	15	yes	—
63	C₂²	—	23	1	no	—
64	C₂²	—	23	5	no	—
65	C₂²	—	46	10	no	—
66	C₂²	C₂³×D₂₃	1	5	yes	—
67	C₄	—	23	10	no	—
68	C₄	C₂³×D₂₃	1	10	yes	—
69	C₂	—	2	5	no	—
70	C₂	—	23	2	no	—
71	C₂	—	46	5	no	—
72	C₂	C₂⁴×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂⁴×D₂₃
commutator, socle, cosocle	C₂×C₂₃	C₂⁵
Fitting	C₂₃×2₋¹⁺⁴	C₂
hypercenter	2₋¹⁺⁴	D₂₃
hypocenter	C₂₃	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ 2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂₃×2₋¹⁺⁴	C₂	semidirect
2. #10625161	C₂	semidirect
3. #41×D₂₃	C₂	semidirect
4. #10625158	C₂	semidirect
5. C₂×Q₈×D₂₃	C₂	semidirect
6. #41×C₂₃	C₂²	semidirect
7. C₂×Q₈×C₂₃	C₂²	semidirect
8. #67292	C₂²	semidirect
10. Q₈×D₂₃	C₂²	semidirect
11. #67290	C₂²	semidirect
13. #67288	C₂²	semidirect
15. C₂×Dic₄₆	C₂²	semidirect
36. D₂₃	2₋¹⁺⁴	direct (N × H)
39. 2₋¹⁺⁴	D₂₃	direct (N × H)
42. C₂₃	C₂×2₋¹⁺⁴	semidirect
46. #41	C₂×D₂₃	semidirect
50. C₂×Q₈	C₂×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×2₋¹⁺⁴	2
#10625161	2
#41×D₂₃	2
#10625158	2
C₂×Q₈×D₂₃	2
C₂×2₋¹⁺⁴	23

Subgroups — 2−1+4×D23 #13093249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 2₋¹⁺⁴×D₂₃ #13093249