Subgroups — C₂×#948 #5818

Order 192.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41	C₂	1	1	yes	maximal, characteristic
2	#948	C₂	1	8	yes	maximal, direct product factor
3	C₂×#208	C₂	1	3	yes	maximal, complemented
4	C₂²×C₃⋊C₈	C₂	1	3	yes	maximal, complemented
5	C₂×#131	—	3	1	no	maximal, Sylow
6	C₃×#41	C₄	1	4	yes	—
7	C₃×#41	C₂²	1	4	yes	—
8	C₂×C₃×Q₈	C₄	1	1	yes	characteristic
9	C₂×C₃×D₄	C₄	1	3	yes	—
10	C₂²×C₃×C₄	C₂²	1	3	yes	—
11	#208	C₂²	1	12	yes	complemented
12	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃⋊C₈	C₂²	1	3	yes	—
14	C₂×C₃⋊C₈	C₂²	1	12	yes	complemented
15	C₂×#41	D₃	1	1	yes	characteristic
16	#131	—	3	8	no	—
17	C₂×M₁₆	—	3	3	no	—
18	C₂²×C₈	—	3	3	no	—
19	C₂³×C₃	C₂×C₄	1	3	yes	—
20	C₃×Q₈	C₂×C₄	1	4	yes	—
21	C₃×D₄	C₂×C₄	1	12	yes	—
22	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
23	C₂×C₃×C₄	C₂×C₄	1	6	yes	—
24	C₂×C₃×C₄	C₂³	1	6	yes	—
25	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
26	C₃⋊C₈	C₂³	1	2	yes	—
27	C₃⋊C₈	C₂³	1	6	yes	—
28	#41	Dic₃	1	4	yes	—
29	#41	C₂×D₃	1	4	yes	—
30	C₂×Q₈	Dic₃	1	1	yes	characteristic
31	C₂×D₄	Dic₃	1	3	yes	—
32	C₂²×C₄	C₂×D₃	1	3	yes	—
33	M₁₆	—	3	12	no	—
34	C₂×C₈	—	3	12	no	—
35	C₂×C₈	—	3	1	no	—
36	C₂×C₈	—	3	3	no	—
37	C₂²×C₃	—	2	6	no	—
38	C₂²×C₃	C₂²×C₄	1	6	yes	—
39	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
40	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
41	C₃×C₄	C₂²×C₄	1	6	yes	—
42	C₃×C₄	C₂⁴	1	1	yes	characteristic
43	C₂³	C₂×Dic₃	1	3	yes	—
44	Q₈	C₂×Dic₃	1	4	yes	—
45	D₄	C₂×Dic₃	1	12	yes	—
46	C₂×C₄	C₂×Dic₃	1	3	yes	—
47	C₂×C₄	C₂×Dic₃	1	6	yes	—
48	C₂×C₄	C₂²×D₃	1	6	yes	—
49	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
50	C₈	—	3	2	no	—
51	C₈	—	3	6	no	—
52	C₂×C₃	—	2	6	no	—
53	C₂×C₃	#131	1	2	yes	complemented
54	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
55	C₂²	—	2	6	no	—
56	C₂²	C₂²×Dic₃	1	6	yes	—
57	C₂²	C₂²×Dic₃	1	1	yes	characteristic
58	C₄	C₂²×Dic₃	1	1	yes	characteristic
59	C₄	C₂²×Dic₃	1	6	yes	—
60	C₄	C₂³×D₃	1	1	yes	characteristic
61	C₃	C₂×#131	1	1	yes	characteristic, complemented, Sylow
62	C₂	—	2	6	no	—
63	C₂	#948	1	2	yes	direct product factor
64	C₂	C₂³×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₄	C₂³×D₃
Fitting, prime radical	C₂×C₃×#41	C₂
socle	C₂²×C₃	C₂²×C₄
cosocle	C₃×C₄	C₂⁴
hypercenter	C₂×#41	D₃
hypocenter	C₃	C₂×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #948	C₂	direct (N × H)
3. C₂×#208	C₂	semidirect
4. C₂²×C₃⋊C₈	C₂	semidirect
11. #208	C₂²	semidirect
14. C₂×C₃⋊C₈	C₂²	semidirect
53. C₂×C₃	#131	semidirect
61. C₃	C₂×#131	semidirect
63. C₂	#948	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×#41	2
#948	2
C₂×#208	2
C₂²×C₃⋊C₈	2
C₂×#131	3

Subgroups — C2×#948 #5818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#948 #5818