Subgroups — C₂×#872 #5472

Order 192.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
4	C₂×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#872	C₂	1	8	yes	maximal, direct product factor
7	C₂×#117	—	3	1	no	maximal, Sylow
8	C₂³×D₃	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃	C₂²	1	2	yes	—
12	C₂²×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃	C₄	1	8	yes	complemented
14	C₂×C₄×D₃	C₂²	1	4	yes	—
15	C₃×C₄²	C₂²	1	4	yes	complemented
16	(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
17	Dic₃⋊C₄	C₂²	1	8	yes	complemented
18	C₄×Dic₃	C₂²	1	4	yes	complemented
19	C₂³×C₄	—	3	1	no	—
20	#117	—	3	8	no	—
21	C₂×C₄⋊C₄	—	3	2	no	—
22	C₂×C₂²⋊C₄	—	3	2	no	—
23	C₂×C₄²	—	3	1	no	—
24	C₂×C₄²	D₃	1	1	yes	characteristic, complemented
25	C₂³×C₃	C₂³	1	1	yes	characteristic
26	C₂²×D₃	—	2	4	no	—
27	C₂²×D₃	C₂×C₄	1	4	yes	—
28	C₂²×D₃	C₂³	1	2	yes	—
29	C₂×C₃×C₄	—	2	4	no	—
30	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
31	C₂×C₃×C₄	C₂³	1	4	yes	—
32	C₂×C₃×C₄	C₂³	1	2	yes	—
33	C₂×Dic₃	—	2	4	no	—
34	C₂×Dic₃	C₂×C₄	1	4	yes	—
35	C₂×Dic₃	C₂³	1	4	yes	—
36	C₂×Dic₃	C₂³	1	2	yes	—
37	C₄×D₃	C₂×C₄	1	16	yes	complemented
38	C₂⁴	—	3	1	no	—
39	C₂²×C₄	—	3	1	no	—
40	C₂²×C₄	—	3	8	no	—
41	C₂²×C₄	—	3	4	no	—
42	C₂²×C₄	—	3	2	no	—
43	C₂²×C₄	C₂×D₃	1	2	yes	—
44	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
45	C₄⋊C₄	—	3	8	no	—
46	C₂²⋊C₄	—	3	8	no	—
47	C₄²	—	3	4	no	—
48	C₄²	C₂×D₃	1	4	yes	complemented
49	C₂²×C₃	C₂²×C₄	1	2	yes	—
50	C₂²×C₃	#41	1	4	yes	—
51	C₂²×C₃	C₂⁴	1	1	yes	characteristic
52	C₂×D₃	—	2	8	no	—
53	C₂×D₃	—	2	4	no	—
54	C₂×D₃	C₂²×C₄	1	4	yes	—
55	C₃×C₄	—	2	4	no	—
56	C₃×C₄	C₂²×C₄	1	4	yes	—
57	Dic₃	—	2	4	no	—
58	Dic₃	C₂²×C₄	1	4	yes	—
59	C₂³	—	3	4	no	—
60	C₂³	—	3	2	no	—
61	C₂³	—	6	4	no	—
62	C₂³	C₂²×D₃	1	1	yes	characteristic
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	—	3	4	no	—
65	C₂×C₄	—	3	2	no	—
66	C₂×C₄	—	3	16	no	—
67	C₂×C₄	—	3	4	no	—
68	C₂×C₄	—	6	4	no	—
69	C₂×C₄	C₄×D₃	1	4	yes	—
70	C₂×C₄	C₂²×D₃	1	4	yes	—
71	C₂×C₄	C₂²×D₃	1	2	yes	—
72	C₂×C₃	#117	1	4	yes	complemented
73	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
74	C₂×C₃	C₂×#41	1	2	yes	—
75	D₃	—	2	4	no	—
76	C₂²	—	3	4	no	—
77	C₂²	—	6	8	no	—
78	C₂²	—	6	4	no	—
79	C₂²	C₂×C₄×D₃	1	2	yes	—
80	C₂²	#235	1	4	yes	—
81	C₂²	C₂³×D₃	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	—	3	4	no	—
84	C₄	—	6	4	no	—
85	C₄	C₂×C₄×D₃	1	4	yes	—
86	C₃	C₂×#117	1	1	yes	characteristic, complemented, Sylow
87	C₂	—	6	4	no	—
88	C₂	#872	1	4	yes	direct product factor
89	C₂	C₂²×C₄×D₃	1	1	yes	characteristic
90	C₂	C₂×#235	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₂²	C₂³×D₃
Fitting	C₂×C₃×C₄²	C₂
socle	C₂³×C₃	C₂³
prime radical	C₂³×D₃	C₂²
cosocle	C₂²×C₃	C₂⁴
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₂×#117
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
2. C₂×C₃×C₄²	C₂	semidirect
4. C₂×Dic₃⋊C₄	C₂	semidirect
5. C₂×C₄×Dic₃	C₂	semidirect
6. #872	C₂	direct (N × H)
13. C₂×C₄×D₃	C₄	semidirect
15. C₃×C₄²	C₂²	semidirect
17. Dic₃⋊C₄	C₂²	semidirect
18. C₄×Dic₃	C₂²	semidirect
24. C₂×C₄²	D₃	semidirect
37. C₄×D₃	C₂×C₄	semidirect
48. C₄²	C₂×D₃	semidirect
72. C₂×C₃	#117	semidirect
86. C₃	C₂×#117	semidirect
88. C₂	#872	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃	2
C₂×C₃×C₄²	2
C₂×(C₂×D₃)⋊C₄	2
C₂×Dic₃⋊C₄	2
C₂×C₄×Dic₃	2
#872	2
C₂×#117	3

Subgroups — C2×#872 #5472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#872 #5472