Subgroups — C₄×Dic₉₂ #13092513

Order 1472.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₄₆	C₂	1	2	yes	maximal
3	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	#10625000	C₂	1	1	yes	maximal, characteristic
5	#10624998	C₂	1	2	yes	maximal
6	C₂×Dic₄₆	C₂²	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₄²×C₂₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₃	C₂²	1	2	yes	—
11	Dic₂₃⋊C₄	—	2	2	no	—
12	C₄×Dic₂₃	—	2	2	no	—
13	Dic₉₂	C₄	1	4	yes	direct product factor
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₃	—	2	2	no	—
18	C₂×Dic₂₃	—	2	2	no	—
19	Dic₄₆	—	2	2	no	—
20	Dic₄₆	C₂×C₄	1	4	yes	—
21	C₈×C₂₃	—	2	1	no	—
22	C₈×C₂₃	C₂×C₄	1	2	yes	—
23	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₂₃	—	2	1	no	—
25	C₄×C₂₃	Q₁₆	1	2	yes	complemented
26	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₃	#41	1	1	yes	characteristic
28	Dic₂₃	—	2	4	no	—
29	Dic₂₃	—	4	2	no	—
30	C₄×Q₁₆	—	23	1	no	maximal, Sylow
31	C₂×C₂₃	C₄×D₄	1	1	yes	characteristic
32	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
33	C₂×C₂₃	#135	1	1	yes	characteristic
34	C₂×Q₁₆	—	23	1	no	—
35	C₄×Q₈	—	23	2	no	—
36	#107	—	23	1	no	—
37	#103	—	23	2	no	—
38	C₄×C₈	D₂₃	1	1	yes	characteristic
39	C₂₃	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	23	2	no	—
41	Q₁₆	—	23	4	no	—
42	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
43	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
44	C₄⋊C₄	—	23	2	no	—
45	C₄⋊C₄	—	46	2	no	—
46	C₄²	—	46	2	no	—
47	C₄²	C₂×D₂₃	1	1	yes	characteristic
48	Q₈	—	23	4	no	—
49	Q₈	—	46	2	no	—
50	C₂×C₄	—	46	2	no	—
51	C₂×C₄	—	46	2	no	—
52	C₂×C₄	D₉₂	1	1	yes	characteristic
53	C₂×C₄	D₉₂	1	1	yes	characteristic
54	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₄×D₂₃	1	2	yes	—
57	C₂²	C₂×D₉₂	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	46	4	no	—
60	C₄	—	92	2	no	—
61	C₄	Dic₉₂	1	2	yes	direct product factor
62	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
63	C₄	#67288	1	1	yes	characteristic
64	C₂	C₄×D₉₂	1	1	yes	characteristic
65	C₂	#10625075	1	1	yes	characteristic
66	C₂	C₂×Dic₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₄×C₈×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₄×C₈	D₂₃
hypocenter	C₂₃	C₄×Q₁₆
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
13. Dic₉₂	C₄	direct (N × H)
25. C₄×C₂₃	Q₁₆	semidirect
39. C₂₃	C₄×Q₁₆	semidirect
61. C₄	Dic₉₂	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×Dic₉₂	2
C₄×Dic₄₆	2
C₄×C₈×C₂₃	2
#10625000	2
#10624998	2
C₄×Q₁₆	23

Subgroups — C4×Dic92 #13092513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₉₂ #13092513