Subgroups — C₂×#807 #4962

Order 192.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#807	C₂	1	4	yes	maximal, direct product factor
5	C₂×#107	—	3	1	no	maximal, Sylow
6	C₂²×C₃×C₄	—	2	1	no	—
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃	—	2	1	no	—
9	C₃×C₄⋊C₄	—	2	1	no	—
10	C₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₄⋊Dic₃	—	2	1	no	—
12	C₄⋊Dic₃	C₂²	1	2	yes	—
13	C₂×C₃⋊C₈	C₄	1	4	yes	complemented
14	C₂×C₃⋊C₈	C₂²	1	2	yes	—
15	C₂²×C₈	—	3	1	no	—
16	C₂×C₄⋊C₄	—	3	1	no	—
17	C₂×C₄⋊C₄	D₃	1	1	yes	characteristic
18	#107	—	3	4	no	—
19	C₂³×C₃	D₄	1	1	yes	characteristic
20	C₂×C₃×C₄	—	2	2	no	—
21	C₂×C₃×C₄	—	4	2	no	—
22	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₄	D₄	1	1	yes	characteristic
24	C₂×C₃×C₄	Q₈	1	2	yes	—
25	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
26	C₂×Dic₃	—	2	2	no	—
27	C₂×Dic₃	—	4	2	no	—
28	C₃⋊C₈	C₂×C₄	1	4	yes	complemented
29	C₂²×C₄	—	2	1	no	—
30	C₂²×C₄	—	6	1	no	—
31	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
32	C₂×C₈	—	3	4	no	—
33	C₂×C₈	—	3	2	no	—
34	C₄⋊C₄	—	2	1	no	—
35	C₄⋊C₄	—	3	2	no	—
36	C₄⋊C₄	—	6	1	no	—
37	C₄⋊C₄	C₂×D₃	1	2	yes	—
38	C₂²×C₃	C₄⋊C₄	1	2	yes	—
39	C₂²×C₃	D₈	1	2	yes	—
40	C₂²×C₃	Q₁₆	1	2	yes	—
41	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
42	C₃×C₄	—	4	2	no	—
43	C₃×C₄	C₄⋊C₄	1	2	yes	—
44	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
45	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
46	Dic₃	—	4	2	no	—
47	C₂³	#67	1	1	yes	characteristic
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	4	2	no	—
50	C₂×C₄	—	6	2	no	—
51	C₂×C₄	—	12	2	no	—
52	C₂×C₄	Dic₆	1	2	yes	—
53	C₂×C₄	C₄×D₃	1	2	yes	—
54	C₂×C₄	#67	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
56	C₈	—	3	4	no	—
57	C₂×C₃	#107	1	4	yes	complemented
58	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₃	C₂×D₈	1	1	yes	characteristic
60	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
61	C₂²	Dic₃⋊C₄	1	2	yes	—
62	C₂²	#213	1	2	yes	—
63	C₂²	#216	1	2	yes	—
64	C₂²	C₂×#67	1	1	yes	characteristic
65	C₄	—	4	2	no	—
66	C₄	—	12	2	no	—
67	C₄	Dic₃⋊C₄	1	2	yes	—
68	C₄	C₂×Dic₆	1	1	yes	characteristic
69	C₄	C₂×C₄×D₃	1	1	yes	characteristic
70	C₃	C₂×#107	1	1	yes	characteristic, complemented, Sylow
71	C₂	#807	1	4	yes	direct product factor
72	C₂	C₂×Dic₃⋊C₄	1	1	yes	characteristic
73	C₂	C₂×#213	1	1	yes	characteristic
74	C₂	C₂×#216	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#67
commutator	C₃×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₂×C₃×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃	D₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₂×C₄⋊C₄	D₃
hypocenter	C₃	C₂×#107
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #807	C₂	direct (N × H)
13. C₂×C₃⋊C₈	C₄	semidirect
28. C₃⋊C₈	C₂×C₄	semidirect
57. C₂×C₃	#107	semidirect
70. C₃	C₂×#107	semidirect
71. C₂	#807	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄⋊C₄	2
C₂×C₄⋊Dic₃	2
C₂²×C₃⋊C₈	2
#807	2
C₂×#107	3

Subgroups — C2×#807 #4962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#807 #4962