Subgroups — C₄×D₁₈₄ #13092501

Order 1472.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₈₄	C₂	1	1	yes	maximal, characteristic
2	C₄×D₉₂	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625003	C₂	1	2	yes	maximal, complemented
5	#10625000	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₉₂	C₂²	1	2	yes	—
7	C₂×C₄×D₂₃	—	2	2	no	—
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₄²×C₂₃	C₂²	1	1	yes	characteristic
11	(C₂×D₂₃)⋊C₄	—	2	2	no	—
12	C₄⋊Dic₂₃	C₂²	1	2	yes	—
13	D₁₈₄	C₄	1	4	yes	direct product factor
14	C₂²×D₂₃	—	2	2	no	—
15	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₃	—	2	2	no	—
19	D₉₂	—	2	2	no	—
20	D₉₂	C₂×C₄	1	4	yes	complemented
21	C₄×D₂₃	—	4	4	no	—
22	C₈×C₂₃	—	2	1	no	—
23	C₈×C₂₃	C₂×C₄	1	2	yes	complemented
24	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
25	C₂×D₂₃	—	2	4	no	—
26	C₂×D₂₃	—	4	2	no	—
27	C₂×D₂₃	—	4	2	no	—
28	C₄×C₂₃	—	2	1	no	—
29	C₄×C₂₃	D₈	1	2	yes	complemented
30	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₃	#41	1	1	yes	characteristic
32	Dic₂₃	—	4	2	no	—
33	C₄×D₈	—	23	1	no	maximal, Sylow
34	C₂×C₂₃	C₄×D₄	1	1	yes	characteristic
35	C₂×C₂₃	C₂×D₈	1	1	yes	characteristic
36	C₂×C₂₃	#135	1	1	yes	characteristic
37	D₂₃	—	4	4	no	—
38	C₂×D₈	—	23	1	no	—
39	C₄×D₄	—	23	2	no	—
40	#107	—	23	1	no	—
41	#102	—	23	2	no	—
42	C₄×C₈	D₂₃	1	1	yes	characteristic, complemented
43	C₂₃	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₄	—	23	2	no	—
45	C₂²×C₄	—	46	2	no	—
46	D₈	—	23	4	no	—
47	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
48	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
49	C₄⋊C₄	—	23	2	no	—
50	C₂²⋊C₄	—	46	2	no	—
51	C₄²	C₂×D₂₃	1	1	yes	characteristic
52	C₂³	—	46	2	no	—
53	D₄	—	23	4	no	—
54	D₄	—	46	2	no	—
55	C₂×C₄	—	46	2	no	—
56	C₂×C₄	—	92	4	no	—
57	C₂×C₄	D₉₂	1	1	yes	characteristic
58	C₂×C₄	D₉₂	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	C₄×D₂₃	1	2	yes	complemented
62	C₂²	—	46	4	no	—
63	C₂²	—	92	2	no	—
64	C₂²	—	92	2	no	—
65	C₂²	C₂×D₉₂	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	92	2	no	—
68	C₄	D₁₈₄	1	2	yes	direct product factor
69	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
70	C₄	#67288	1	1	yes	characteristic
71	C₂	—	92	4	no	—
72	C₂	C₄×D₉₂	1	1	yes	characteristic
73	C₂	C₂×D₁₈₄	1	1	yes	characteristic
74	C₂	#10625075	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	C₂²×C₂₃	C₂×D₄
prime radical	C₂×D₁₈₄	C₂
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₄×C₈	D₂₃
hypocenter	C₂₃	C₄×D₈
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
2. C₄×D₉₂	C₂	semidirect
3. C₄×C₈×C₂₃	C₂	semidirect
4. #10625003	C₂	semidirect
5. #10625000	C₂	semidirect
13. D₁₈₄	C₄	direct (N × H)
20. D₉₂	C₂×C₄	semidirect
23. C₈×C₂₃	C₂×C₄	semidirect
29. C₄×C₂₃	D₈	semidirect
42. C₄×C₈	D₂₃	semidirect
43. C₂₃	C₄×D₈	semidirect
61. C₈	C₄×D₂₃	semidirect
68. C₄	D₁₈₄	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×D₁₈₄	2
C₄×D₉₂	2
C₄×C₈×C₂₃	2
#10625003	2
#10625000	2
C₄×D₈	23

Subgroups — C4×D184 #13092501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₈₄ #13092501