Subgroups — C₄×Dic₃⋊C₄ #4931

Order 192.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₃⋊#95	C₂	1	2	yes	maximal
6	C₄×C₄⋊C₄	—	3	1	no	maximal, Sylow
7	C₂²×C₃×C₄	C₂²	1	2	yes	—
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃	C₂²	1	2	yes	—
11	C₂²×Dic₃	C₂²	1	1	yes	characteristic
12	C₃×C₄²	—	2	2	no	—
13	Dic₃⋊C₄	C₄	1	8	yes	direct product factor
14	C₄×Dic₃	—	2	2	no	—
15	C₄×Dic₃	C₄	1	4	yes	complemented
16	C₂×C₄⋊C₄	—	3	2	no	—
17	C₂×C₄²	—	3	1	no	—
18	C₂×C₄²	—	3	1	no	—
19	C₂×C₄²	D₃	1	1	yes	characteristic
20	#95	—	3	2	no	—
21	C₂³×C₃	C₂³	1	1	yes	characteristic
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
25	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
26	C₂×C₃×C₄	D₄	1	2	yes	—
27	C₂×C₃×C₄	Q₈	1	2	yes	—
28	C₂×Dic₃	—	2	2	no	—
29	C₂×Dic₃	—	2	2	no	—
30	C₂×Dic₃	—	2	2	no	—
31	C₂×Dic₃	C₂×C₄	1	2	yes	—
32	C₂×Dic₃	C₂×C₄	1	4	yes	—
33	C₂×Dic₃	C₂×C₄	1	2	yes	—
34	C₂×Dic₃	C₂×C₄	1	4	yes	—
35	C₂²×C₄	—	3	1	no	—
36	C₂²×C₄	—	3	1	no	—
37	C₂²×C₄	—	3	2	no	—
38	C₂²×C₄	C₂×D₃	1	2	yes	—
39	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
40	C₄⋊C₄	—	3	8	no	—
41	C₄²	—	2	2	no	—
42	C₄²	—	3	4	no	—
43	C₄²	—	6	2	no	—
44	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₃	C₂²×C₄	1	2	yes	—
46	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
48	C₂²×C₃	#41	1	2	yes	—
49	C₃×C₄	—	2	4	no	—
50	C₃×C₄	C₄⋊C₄	1	4	yes	complemented
51	Dic₃	—	2	2	no	—
52	Dic₃	—	2	4	no	—
53	Dic₃	C₄²	1	4	yes	complemented
54	C₂³	C₂²×D₃	1	1	yes	characteristic
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	3	2	no	—
58	C₂×C₄	—	3	4	no	—
59	C₂×C₄	—	3	2	no	—
60	C₂×C₄	—	3	4	no	—
61	C₂×C₄	—	6	2	no	—
62	C₂×C₄	—	6	2	no	—
63	C₂×C₄	—	6	2	no	—
64	C₂×C₄	Dic₆	1	2	yes	—
65	C₂×C₄	C₄×D₃	1	4	yes	—
66	C₂×C₄	C₄×D₃	1	2	yes	—
67	C₂×C₄	#67	1	2	yes	—
68	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₃	#117	1	1	yes	characteristic
71	C₂×C₃	C₄×D₄	1	2	yes	—
72	C₂×C₃	C₄×Q₈	1	2	yes	—
73	C₂²	C₂×Dic₆	1	1	yes	characteristic
74	C₂²	C₂×C₄×D₃	1	2	yes	—
75	C₂²	C₂×C₄×D₃	1	1	yes	characteristic
76	C₂²	#235	1	2	yes	—
77	C₂²	C₂×#67	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	3	4	no	—
80	C₄	—	6	2	no	—
81	C₄	—	6	4	no	—
82	C₄	Dic₃⋊C₄	1	4	yes	direct product factor
83	C₃	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
84	C₂	C₄×Dic₆	1	2	yes	—
85	C₂	C₄²×D₃	1	1	yes	characteristic
86	C₂	#872	1	1	yes	characteristic
87	C₂	C₂×Dic₃⋊C₄	1	1	yes	characteristic
88	C₂	C₄×#67	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂×C₄²
Frattini	C₂³	C₂²×D₃
Fitting	C₂×C₃×C₄²	C₂
socle, prime radical, cosocle	C₂³×C₃	C₂³
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
13. Dic₃⋊C₄	C₄	direct (N × H)
15. C₄×Dic₃	C₄	semidirect
50. C₃×C₄	C₄⋊C₄	semidirect
53. Dic₃	C₄²	semidirect
82. C₄	Dic₃⋊C₄	direct (N × H)
83. C₃	C₄×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²	2
C₂×Dic₃⋊C₄	2
C₂×C₄×Dic₃	2
C₃⋊#95	2
C₄×C₄⋊C₄	3

Subgroups — C4×Dic3⋊C4 #4931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₃⋊C₄ #4931