Subgroups — C₄×#67267 #13092370

Order 1472.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#67267	C₂	1	2	yes	maximal
3	#10624985	C₂	1	2	yes	maximal, complemented
4	C₄×C₂₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₂₃	C₄	1	2	yes	—
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₄²×C₂₃	C₄	1	2	yes	—
8	C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₄²×C₂₃	C₂²	1	1	yes	characteristic
10	#67267	C₄	1	8	yes	direct product factor
11	C₂×C₂₃⋊C₈	C₂²	1	4	yes	—
12	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	—	2	4	no	—
14	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂₃⋊C₈	C₂×C₄	1	8	yes	complemented
20	C₂²×C₂₃	—	2	2	no	—
21	C₂²×C₂₃	C₄²	1	2	yes	—
22	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₂₃	—	2	2	no	—
24	C₄×C₂₃	C₄²	1	2	yes	—
25	C₄×C₂₃	M₁₆	1	4	yes	complemented
26	C₄×C₂₃	C₂²×C₄	1	2	yes	—
27	C₄×M₁₆	—	23	1	no	maximal, Sylow
28	C₂×C₂₃	—	2	2	no	—
29	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₂₃	C₂×M₁₆	1	2	yes	—
31	C₂×M₁₆	—	23	2	no	—
32	C₂×C₄²	D₂₃	1	1	yes	characteristic
33	#97	—	23	2	no	—
34	C₄×C₈	—	23	2	no	—
35	C₂₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₄	Dic₂₃	1	2	yes	—
37	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
38	M₁₆	—	23	8	no	—
39	C₂×C₈	—	23	4	no	—
40	C₄²	Dic₂₃	1	2	yes	—
41	C₄²	C₂×D₂₃	1	1	yes	characteristic
42	C₄²	C₂×D₂₃	1	1	yes	characteristic
43	C₂³	C₂×Dic₂₃	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	C₄×D₂₃	1	4	yes	—
46	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
47	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
48	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
49	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
50	C₈	—	23	8	no	—
51	C₂²	—	2	2	no	—
52	C₂²	C₄×Dic₂₃	1	2	yes	—
53	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#67267	1	4	yes	direct product factor
56	C₄	C₄×Dic₂₃	1	2	yes	—
57	C₄	C₂×C₄×D₂₃	1	2	yes	—
58	C₂	—	2	2	no	—
59	C₂	C₂×#67267	1	2	yes	—
60	C₂	C₂×C₄×Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×C₄²×C₂₃	C₂
socle	C₂²×C₂₃	C₂²×C₄
prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×C₄²	D₂₃
hypocenter	C₂₃	C₄×M₁₆
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #10624985	C₂	semidirect
4. C₄×C₂₃⋊C₈	C₂	semidirect
10. #67267	C₄	direct (N × H)
19. C₂₃⋊C₈	C₂×C₄	semidirect
25. C₄×C₂₃	M₁₆	semidirect
35. C₂₃	C₄×M₁₆	semidirect
55. C₄	#67267	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×C₄²×C₂₃	2
C₂×#67267	2
#10624985	2
C₄×C₂₃⋊C₈	2
C₄×M₁₆	23

Subgroups — C4×#67267 #13092370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#67267 #13092370