Subgroups — C₂²×#67272 #13093186

Order 1472.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#67272	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×C₂₃	—	2	1	no	—
6	C₂³×D₂₃	—	2	1	no	—
7	C₂×D₄×C₂₃	—	2	3	no	—
8	C₂×D₄×C₂₃	C₂²	1	6	yes	complemented
9	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×D₉₂	—	2	3	no	—
11	C₂×D₉₂	C₂²	1	6	yes	complemented
12	#67272	C₂²	1	16	yes	direct product factor
13	C₂×C₂₃⋊C₈	C₂²	1	6	yes	complemented
14	C₂³×C₂₃	—	2	6	no	—
15	C₂³×C₂₃	—	4	4	no	—
16	C₂³×C₂₃	D₄	1	1	yes	characteristic
17	C₂²×D₂₃	—	2	6	no	—
18	C₂²×D₂₃	—	4	4	no	—
19	D₄×C₂₃	—	2	6	no	—
20	D₄×C₂₃	C₂³	1	4	yes	complemented
21	C₂×C₄×C₂₃	D₄	1	3	yes	—
22	C₂×C₄×C₂₃	C₂³	1	3	yes	—
23	D₉₂	—	2	6	no	—
24	D₉₂	C₂³	1	4	yes	complemented
25	C₂₃⋊C₈	C₂³	1	4	yes	complemented
26	C₂²×C₂₃	—	2	4	no	—
27	C₂²×C₂₃	—	4	12	no	—
28	C₂²×C₂₃	D₈	1	4	yes	complemented
29	C₂²×C₂₃	C₂×D₄	1	3	yes	—
30	C₂×D₂₃	—	2	4	no	—
31	C₂×D₂₃	—	4	12	no	—
32	C₄×C₂₃	C₂×D₄	1	3	yes	—
33	C₄×C₂₃	C₂⁴	1	1	yes	characteristic
34	C₂²×D₈	—	23	1	no	maximal, Sylow
35	C₂×C₂₃	—	4	4	no	—
36	C₂×C₂₃	C₂×D₈	1	6	yes	complemented
37	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
38	D₂₃	—	4	4	no	—
39	C₂²×D₄	—	23	1	no	—
40	C₂²×D₄	D₂₃	1	1	yes	characteristic, complemented
41	C₂×D₈	—	23	12	no	—
42	C₂²×C₈	—	23	1	no	—
43	C₂₃	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
44	C₂⁴	—	2	1	no	—
45	C₂⁴	—	46	1	no	—
46	C₂×D₄	—	2	3	no	—
47	C₂×D₄	—	23	6	no	—
48	C₂×D₄	—	46	3	no	—
49	C₂×D₄	C₂×D₂₃	1	6	yes	complemented
50	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
51	D₈	—	23	16	no	—
52	C₂×C₈	—	23	6	no	—
53	C₂³	—	2	6	no	—
54	C₂³	—	4	4	no	—
55	C₂³	—	46	6	no	—
56	C₂³	—	92	4	no	—
57	C₂³	C₂²⋊D₂₃	1	1	yes	characteristic
58	D₄	—	2	6	no	—
59	D₄	—	23	4	no	—
60	D₄	—	46	6	no	—
61	D₄	C₂²×D₂₃	1	4	yes	complemented
62	C₂×C₄	C₂²⋊D₂₃	1	3	yes	—
63	C₂×C₄	C₂²×D₂₃	1	3	yes	—
64	C₈	—	23	4	no	—
65	C₂²	—	2	4	no	—
66	C₂²	—	4	12	no	—
67	C₂²	—	46	4	no	—
68	C₂²	—	92	12	no	—
69	C₂²	#67272	1	4	yes	direct product factor
70	C₂²	C₂×C₂²⋊D₂₃	1	3	yes	—
71	C₄	C₂×C₂²⋊D₂₃	1	3	yes	—
72	C₄	C₂³×D₂₃	1	1	yes	characteristic
73	C₂	—	4	4	no	—
74	C₂	—	92	4	no	—
75	C₂	C₂×#67272	1	6	yes	direct product factor
76	C₂	C₂²×C₂²⋊D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₂₃
commutator, cosocle	C₄×C₂₃	C₂⁴
Frattini	C₄	C₂³×D₂₃
Fitting	C₂²×D₄×C₂₃	C₂
socle	C₂³×C₂₃	D₄
hypercenter	C₂²×D₄	D₂₃
hypocenter	C₂₃	C₂²×D₈
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×C₂₃	C₂	semidirect
2. C₂²×D₉₂	C₂	semidirect
3. C₂×#67272	C₂	direct (N × H)
4. C₂²×C₂₃⋊C₈	C₂	semidirect
8. C₂×D₄×C₂₃	C₂²	semidirect
11. C₂×D₉₂	C₂²	semidirect
12. #67272	C₂²	direct (N × H)
13. C₂×C₂₃⋊C₈	C₂²	semidirect
20. D₄×C₂₃	C₂³	semidirect
24. D₉₂	C₂³	semidirect
25. C₂₃⋊C₈	C₂³	semidirect
28. C₂²×C₂₃	D₈	semidirect
36. C₂×C₂₃	C₂×D₈	semidirect
40. C₂²×D₄	D₂₃	semidirect
43. C₂₃	C₂²×D₈	semidirect
49. C₂×D₄	C₂×D₂₃	semidirect
61. D₄	C₂²×D₂₃	semidirect
69. C₂²	#67272	direct (N × H)
75. C₂	C₂×#67272	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×D₄×C₂₃	2
C₂²×D₉₂	2
C₂×#67272	2
C₂²×C₂₃⋊C₈	2
C₂²×D₈	23

Subgroups — C22×#67272 #13093186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#67272 #13093186