Subgroups — C₂×#810 #4969

Order 192.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#810	C₂	1	4	yes	maximal, direct product factor
5	C₂×#103	—	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	C₂×Dic₆	—	2	2	no	—
10	C₂×Dic₆	—	2	1	no	—
11	C₂×Dic₆	C₄	1	4	yes	complemented
12	C₂×Dic₆	C₂²	1	2	yes	—
13	C₃×C₄⋊C₄	—	2	1	no	—
14	C₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃⋊C₈	—	2	2	no	—
16	C₂×C₃⋊C₈	C₂²	1	2	yes	—
17	C₂²×Q₈	—	3	1	no	—
18	C₂²×C₈	—	3	1	no	—
19	C₂×C₄⋊C₄	D₃	1	1	yes	characteristic
20	#103	—	3	4	no	—
21	C₂³×C₃	D₄	1	1	yes	characteristic
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	—	4	2	no	—
24	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
25	C₂×C₃×C₄	D₄	1	2	yes	—
26	C₂×C₃×C₄	D₄	1	1	yes	characteristic
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₂×Dic₃	—	2	4	no	—
29	C₂×Dic₃	—	2	2	no	—
30	Dic₆	—	2	4	no	—
31	Dic₆	—	2	2	no	—
32	Dic₆	C₂×C₄	1	4	yes	complemented
33	C₃⋊C₈	—	2	2	no	—
34	C₂×Q₈	—	3	4	no	—
35	C₂×Q₈	—	3	2	no	—
36	C₂×Q₈	—	6	2	no	—
37	C₂×Q₈	—	6	1	no	—
38	C₂²×C₄	—	2	1	no	—
39	C₂²×C₄	—	6	1	no	—
40	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
41	C₂×C₈	—	3	2	no	—
42	C₂×C₈	—	6	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	C₂×D₃	1	2	yes	—
45	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₃	SD₁₆	1	2	yes	—
47	C₂²×C₃	Q₁₆	1	2	yes	—
48	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
49	C₃×C₄	—	4	2	no	—
50	C₃×C₄	C₂²⋊C₄	1	2	yes	—
51	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
52	C₃×C₄	C₂×D₄	1	1	yes	characteristic
53	Dic₃	—	2	4	no	—
54	C₂³	#67	1	1	yes	characteristic
55	Q₈	—	3	4	no	—
56	Q₈	—	6	4	no	—
57	Q₈	—	6	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	—	6	4	no	—
61	C₂×C₄	—	6	2	no	—
62	C₂×C₄	C₄×D₃	1	2	yes	—
63	C₂×C₄	D₁₂	1	2	yes	—
64	C₂×C₄	#67	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
66	C₈	—	6	2	no	—
67	C₂×C₃	#103	1	4	yes	complemented
68	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
70	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
71	C₂²	(C₂×D₃)⋊C₄	1	2	yes	—
72	C₂²	#214	1	2	yes	—
73	C₂²	#216	1	2	yes	—
74	C₂²	C₂×#67	1	1	yes	characteristic
75	C₄	—	4	2	no	—
76	C₄	—	6	4	no	—
77	C₄	(C₂×D₃)⋊C₄	1	2	yes	—
78	C₄	C₂×C₄×D₃	1	1	yes	characteristic
79	C₄	C₂×D₁₂	1	1	yes	characteristic
80	C₃	C₂×#103	1	1	yes	characteristic, complemented, Sylow
81	C₂	#810	1	4	yes	direct product factor
82	C₂	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
83	C₂	C₂×#214	1	1	yes	characteristic
84	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×#103
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. #810	C₂	direct (N × H)
11. C₂×Dic₆	C₄	semidirect
32. Dic₆	C₂×C₄	semidirect
67. C₂×C₃	#103	semidirect
80. C₃	C₂×#103	semidirect
81. C₂	#810	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×Dic₆	2
C₂×C₃×C₄⋊C₄	2
C₂²×C₃⋊C₈	2
#810	2
C₂×#103	3

Subgroups — C2×#810 #4969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#810 #4969