Subgroups — C₂×#926 #5786

Order 192.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#217	C₂	1	2	yes	maximal
3	#926	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×Dic₃	C₂	1	2	yes	maximal, complemented
6	C₂×#117	—	3	1	no	maximal, Sylow
7	C₂⁴×C₃	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄	C₄	1	8	yes	complemented
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄	C₂²	1	4	yes	—
11	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃	C₂²	1	4	yes	—
13	#217	C₂²	1	8	yes	—
14	C₄⋊Dic₃	C₂²	1	8	yes	complemented
15	C₄×Dic₃	C₂²	1	8	yes	complemented
16	C₂³×C₄	D₃	1	1	yes	characteristic
17	#117	—	3	8	no	—
18	C₂×C₄⋊C₄	—	3	2	no	—
19	C₂×C₂²⋊C₄	—	3	2	no	—
20	C₂×C₄²	—	3	2	no	—
21	C₂³×C₃	—	2	4	no	—
22	C₂³×C₃	C₂×C₄	1	4	yes	—
23	C₂³×C₃	C₂³	1	2	yes	—
24	C₂³×C₃	C₂³	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
26	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
27	C₂×C₃×C₄	C₂×C₄	1	16	yes	complemented
28	C₂×C₃×C₄	C₂³	1	2	yes	—
29	C₂×C₃×C₄	C₂³	1	2	yes	—
30	C₂×Dic₃	—	2	8	no	—
31	C₂×Dic₃	C₂³	1	8	yes	—
32	C₂⁴	C₂×D₃	1	1	yes	characteristic
33	C₂²×C₄	—	3	4	no	—
34	C₂²×C₄	Dic₃	1	8	yes	complemented
35	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
36	C₂²×C₄	C₂×D₃	1	4	yes	—
37	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
38	C₄⋊C₄	—	3	8	no	—
39	C₂²⋊C₄	—	3	8	no	—
40	C₄²	—	3	8	no	—
41	C₂²×C₃	—	2	8	no	—
42	C₂²×C₃	—	2	4	no	—
43	C₂²×C₃	C₂²×C₄	1	4	yes	—
44	C₂²×C₃	C₂²×C₄	1	2	yes	—
45	C₂²×C₃	#41	1	4	yes	—
46	C₂²×C₃	C₂⁴	1	1	yes	characteristic
47	C₃×C₄	C₂²×C₄	1	4	yes	—
48	C₃×C₄	C₂²×C₄	1	4	yes	—
49	Dic₃	—	2	8	no	—
50	C₂³	—	2	4	no	—
51	C₂³	C₂×Dic₃	1	4	yes	—
52	C₂³	C₂²×D₃	1	2	yes	—
53	C₂³	C₂²×D₃	1	1	yes	characteristic
54	C₂×C₄	—	3	8	no	—
55	C₂×C₄	—	6	8	no	—
56	C₂×C₄	C₂×Dic₃	1	4	yes	—
57	C₂×C₄	C₂×Dic₃	1	4	yes	—
58	C₂×C₄	C₂×Dic₃	1	16	yes	complemented
59	C₂×C₄	C₂²×D₃	1	2	yes	—
60	C₂×C₄	C₂²×D₃	1	2	yes	—
61	C₂×C₃	—	2	4	no	—
62	C₂×C₃	#117	1	4	yes	complemented
63	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
64	C₂×C₃	C₂×#41	1	2	yes	—
65	C₂²	—	2	8	no	—
66	C₂²	—	2	4	no	—
67	C₂²	#235	1	4	yes	—
68	C₂²	C₂²×Dic₃	1	4	yes	—
69	C₂²	C₂²×Dic₃	1	2	yes	—
70	C₂²	C₂³×D₃	1	1	yes	characteristic
71	C₄	—	6	8	no	—
72	C₄	C₂²×Dic₃	1	4	yes	—
73	C₄	C₂²×Dic₃	1	4	yes	—
74	C₃	C₂×#117	1	1	yes	characteristic, complemented, Sylow
75	C₂	—	2	4	no	—
76	C₂	#926	1	4	yes	direct product factor
77	C₂	C₂×#235	1	2	yes	—
78	C₂	C₂³×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₂²	C₂³×D₃
Fitting	C₂³×C₃×C₄	C₂
socle	C₂³×C₃	C₂³
prime radical	C₂⁴×C₃	C₂²
cosocle	C₂²×C₃	C₂⁴
hypercenter	C₂³×C₄	D₃
hypocenter	C₃	C₂×#117
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. #926	C₂	direct (N × H)
4. C₂×C₄⋊Dic₃	C₂	semidirect
5. C₂×C₄×Dic₃	C₂	semidirect
8. C₂²×C₃×C₄	C₄	semidirect
14. C₄⋊Dic₃	C₂²	semidirect
15. C₄×Dic₃	C₂²	semidirect
27. C₂×C₃×C₄	C₂×C₄	semidirect
34. C₂²×C₄	Dic₃	semidirect
58. C₂×C₄	C₂×Dic₃	semidirect
62. C₂×C₃	#117	semidirect
74. C₃	C₂×#117	semidirect
76. C₂	#926	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄	2
C₂×#217	2
#926	2
C₂×C₄⋊Dic₃	2
C₂×C₄×Dic₃	2
C₂×#117	3

Subgroups — C2×#926 #5786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#926 #5786