Subgroups — C₂²×(C₂×D₃)⋊C₄ #5787

Order 192.

674 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₂×D₃)⋊C₄	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₂²⋊C₄	—	3	1	no	maximal, Sylow
6	C₂⁴×C₃	C₂²	1	1	yes	characteristic
7	C₂³×D₃	—	2	4	no	—
8	C₂³×D₃	—	2	4	no	—
9	C₂³×D₃	C₄	1	8	yes	complemented
10	C₂³×D₃	C₂²	1	6	yes	—
11	C₂²×C₃×C₄	—	2	4	no	—
12	C₂²×C₃×C₄	C₂²	1	6	yes	complemented
13	C₂²×Dic₃	—	2	4	no	—
14	C₂²×Dic₃	C₂²	1	6	yes	complemented
15	(C₂×D₃)⋊C₄	C₂²	1	16	yes	direct product factor
16	C₂⁵	—	3	1	no	—
17	C₂³×C₄	—	3	1	no	—
18	C₂³×C₄	D₃	1	1	yes	characteristic, complemented
19	C₂×C₂²⋊C₄	—	3	12	no	—
20	C₂³×C₃	C₂×C₄	1	4	yes	—
21	C₂³×C₃	D₄	1	4	yes	—
22	C₂³×C₃	D₄	1	4	yes	—
23	C₂³×C₃	C₂³	1	3	yes	—
24	C₂²×D₃	—	2	32	no	—
25	C₂²×D₃	—	2	12	no	—
26	C₂²×D₃	—	2	12	no	—
27	C₂²×D₃	C₂×C₄	1	24	yes	complemented
28	C₂²×D₃	C₂³	1	4	yes	—
29	C₂×C₃×C₄	—	2	12	no	—
30	C₂×C₃×C₄	C₂³	1	4	yes	complemented
31	C₂×Dic₃	—	2	12	no	—
32	C₂×Dic₃	C₂³	1	4	yes	complemented
33	C₂⁴	—	3	8	no	—
34	C₂⁴	—	3	6	no	—
35	C₂⁴	—	6	4	no	—
36	C₂⁴	—	6	4	no	—
37	C₂⁴	C₂×D₃	1	1	yes	characteristic
38	C₂²×C₄	—	2	4	no	—
39	C₂²×C₄	—	3	6	no	—
40	C₂²×C₄	—	6	4	no	—
41	C₂²×C₄	C₂×D₃	1	6	yes	complemented
42	C₂²⋊C₄	—	3	16	no	—
43	C₂²×C₃	C₂²⋊C₄	1	16	yes	complemented
44	C₂²×C₃	C₂²×C₄	1	6	yes	—
45	C₂²×C₃	C₂×D₄	1	6	yes	—
46	C₂²×C₃	C₂×D₄	1	6	yes	—
47	C₂²×C₃	C₂⁴	1	1	yes	characteristic
48	C₂×D₃	—	2	48	no	—
49	C₂×D₃	—	2	4	no	—
50	C₂×D₃	—	2	4	no	—
51	C₂×D₃	C₂²×C₄	1	8	yes	complemented
52	C₃×C₄	—	2	4	no	—
53	Dic₃	—	2	4	no	—
54	C₂³	—	3	24	no	—
55	C₂³	—	3	4	no	—
56	C₂³	—	6	32	no	—
57	C₂³	—	6	12	no	—
58	C₂³	—	6	12	no	—
59	C₂³	C₄×D₃	1	4	yes	—
60	C₂³	D₁₂	1	4	yes	—
61	C₂³	#67	1	4	yes	—
62	C₂³	C₂²×D₃	1	3	yes	—
63	C₂×C₄	—	2	12	no	—
64	C₂×C₄	—	3	4	no	—
65	C₂×C₄	—	6	12	no	—
66	C₂×C₄	C₂²×D₃	1	4	yes	complemented
67	C₂×C₃	C₂×C₂²⋊C₄	1	12	yes	complemented
68	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
69	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
70	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
71	D₃	—	2	8	no	—
72	C₂²	—	3	8	no	—
73	C₂²	—	6	48	no	—
74	C₂²	—	6	4	no	—
75	C₂²	—	6	4	no	—
76	C₂²	(C₂×D₃)⋊C₄	1	16	yes	direct product factor
77	C₂²	C₂×C₄×D₃	1	6	yes	—
78	C₂²	C₂×D₁₂	1	6	yes	—
79	C₂²	C₂×#67	1	6	yes	—
80	C₂²	C₂³×D₃	1	1	yes	characteristic
81	C₄	—	2	4	no	—
82	C₄	—	6	4	no	—
83	C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	6	8	no	—
85	C₂	C₂×(C₂×D₃)⋊C₄	1	12	yes	direct product factor
86	C₂	C₂²×C₄×D₃	1	1	yes	characteristic
87	C₂	C₂²×D₁₂	1	1	yes	characteristic
88	C₂	C₂²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₂²	C₂³×D₃
Fitting	C₂³×C₃×C₄	C₂
socle	C₂⁴×C₃	C₂²
prime radical	C₂⁴×D₃	C₂
cosocle	C₂²×C₃	C₂⁴
hypercenter	C₂³×C₄	D₃
hypocenter	C₃	C₂²×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×C₄	C₂	semidirect
3. C₂³×Dic₃	C₂	semidirect
4. C₂×(C₂×D₃)⋊C₄	C₂	direct (N × H)
9. C₂³×D₃	C₄	semidirect
12. C₂²×C₃×C₄	C₂²	semidirect
14. C₂²×Dic₃	C₂²	semidirect
15. (C₂×D₃)⋊C₄	C₂²	direct (N × H)
18. C₂³×C₄	D₃	semidirect
27. C₂²×D₃	C₂×C₄	semidirect
30. C₂×C₃×C₄	C₂³	semidirect
32. C₂×Dic₃	C₂³	semidirect
41. C₂²×C₄	C₂×D₃	semidirect
43. C₂²×C₃	C₂²⋊C₄	semidirect
51. C₂×D₃	C₂²×C₄	semidirect
66. C₂×C₄	C₂²×D₃	semidirect
67. C₂×C₃	C₂×C₂²⋊C₄	semidirect
76. C₂²	(C₂×D₃)⋊C₄	direct (N × H)
83. C₃	C₂²×C₂²⋊C₄	semidirect
85. C₂	C₂×(C₂×D₃)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃	2
C₂³×C₃×C₄	2
C₂³×Dic₃	2
C₂×(C₂×D₃)⋊C₄	2
C₂²×C₂²⋊C₄	3

Subgroups — C22×(C2×D3)⋊C4 #5787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×(C₂×D₃)⋊C₄ #5787