Subgroups — C₂×#875 #5476

Order 192.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
5	#875	C₂	1	8	yes	maximal, direct product factor
6	C₂×#124	—	3	1	no	maximal, Sylow
7	C₂³×D₃	C₂²	1	2	yes	—
8	C₂²×C₃×C₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃	C₂²	1	2	yes	—
11	C₂×D₁₂	—	2	4	no	—
12	C₂×D₁₂	C₂²	1	4	yes	—
13	C₂×Dic₆	—	2	4	no	—
14	C₂×Dic₆	C₂²	1	4	yes	complemented
15	C₃×C₄²	C₂²	1	4	yes	complemented
16	(C₂×D₃)⋊C₄	C₂²	1	16	yes	complemented
17	C₂²×Q₈	—	3	1	no	—
18	C₂²×D₄	—	3	1	no	—
19	#124	—	3	8	no	—
20	C₂×C₂²⋊C₄	—	3	4	no	—
21	C₂×C₄²	D₃	1	1	yes	characteristic, complemented
22	C₂³×C₃	C₂³	1	1	yes	characteristic
23	C₂²×D₃	—	2	4	no	—
24	C₂²×D₃	—	2	8	no	—
25	C₂²×D₃	C₂³	1	4	yes	—
26	C₂×C₃×C₄	—	2	4	no	—
27	C₂×C₃×C₄	D₄	1	4	yes	—
28	C₂×C₃×C₄	C₂³	1	4	yes	—
29	C₂×C₃×C₄	C₂³	1	2	yes	—
30	C₂×Dic₃	—	2	4	no	—
31	C₂×Dic₃	C₂³	1	4	yes	—
32	D₁₂	—	2	8	no	—
33	Dic₆	—	2	8	no	—
34	C₂⁴	—	3	2	no	—
35	C₂×Q₈	—	3	4	no	—
36	C₂×Q₈	—	6	4	no	—
37	C₂×D₄	—	3	4	no	—
38	C₂×D₄	—	6	4	no	—
39	C₂²×C₄	—	3	2	no	—
40	C₂²×C₄	C₂×D₃	1	2	yes	—
41	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂²⋊C₄	—	3	16	no	—
43	C₄²	C₂×D₃	1	4	yes	complemented
44	C₂²×C₃	C₂×D₄	1	2	yes	—
45	C₂²×C₃	#41	1	4	yes	—
46	C₂²×C₃	C₂⁴	1	1	yes	characteristic
47	C₂×D₃	—	2	4	no	—
48	C₂×D₃	—	2	8	no	—
49	C₂×D₃	—	4	8	no	—
50	C₃×C₄	—	2	4	no	—
51	C₃×C₄	C₂×D₄	1	4	yes	—
52	Dic₃	—	2	4	no	—
53	C₂³	—	3	4	no	—
54	C₂³	—	6	4	no	—
55	C₂³	—	6	8	no	—
56	C₂³	C₂²×D₃	1	1	yes	characteristic
57	Q₈	—	6	8	no	—
58	D₄	—	6	8	no	—
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	3	4	no	—
61	C₂×C₄	—	6	4	no	—
62	C₂×C₄	D₁₂	1	4	yes	—
63	C₂×C₄	C₂²×D₃	1	4	yes	—
64	C₂×C₄	C₂²×D₃	1	2	yes	—
65	C₂×C₃	#124	1	4	yes	complemented
66	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
67	C₂×C₃	C₂×#41	1	2	yes	—
68	D₃	—	4	4	no	—
69	C₂²	—	6	4	no	—
70	C₂²	—	6	8	no	—
71	C₂²	—	12	8	no	—
72	C₂²	C₂×D₁₂	1	2	yes	—
73	C₂²	#235	1	4	yes	—
74	C₂²	C₂³×D₃	1	1	yes	characteristic
75	C₄	—	2	4	no	—
76	C₄	—	6	4	no	—
77	C₄	C₂×D₁₂	1	4	yes	—
78	C₃	C₂×#124	1	1	yes	characteristic, complemented, Sylow
79	C₂	—	12	4	no	—
80	C₂	#875	1	4	yes	direct product factor
81	C₂	C₂²×D₁₂	1	1	yes	characteristic
82	C₂	C₂×#235	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴
Frattini	C₂²	C₂³×D₃
Fitting	C₂×C₃×C₄²	C₂
socle	C₂³×C₃	C₂³
prime radical	C₂²×D₁₂	C₂
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₂×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₆	C₂	semidirect
3. C₂×C₃×C₄²	C₂	semidirect
4. C₂×(C₂×D₃)⋊C₄	C₂	semidirect
5. #875	C₂	direct (N × H)
14. C₂×Dic₆	C₂²	semidirect
15. C₃×C₄²	C₂²	semidirect
16. (C₂×D₃)⋊C₄	C₂²	semidirect
21. C₂×C₄²	D₃	semidirect
43. C₄²	C₂×D₃	semidirect
65. C₂×C₃	#124	semidirect
78. C₃	C₂×#124	semidirect
80. C₂	#875	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×D₁₂	2
C₂²×Dic₆	2
C₂×C₃×C₄²	2
C₂×(C₂×D₃)⋊C₄	2
#875	2
C₂×#124	3

Subgroups — C2×#875 #5476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#875 #5476