Subgroups — C₂×#815 #5100

Order 192.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈	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	#815	C₂	1	4	yes	maximal, direct product factor
5	C₂×#97	—	3	1	no	maximal, Sylow
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃	C₄	1	2	yes	—
8	C₂×C₃×C₈	C₄	1	4	yes	complemented
9	C₂×C₃×C₈	C₂²	1	2	yes	—
10	C₄×Dic₃	C₄	1	2	yes	—
11	C₄×Dic₃	C₂²	1	2	yes	—
12	C₂×C₃⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₃⋊C₈	C₂²	1	2	yes	—
14	C₂²×C₈	—	3	1	no	—
15	C₂²×C₈	D₃	1	1	yes	characteristic
16	C₂×C₄²	—	3	1	no	—
17	#97	—	3	4	no	—
18	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
21	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
22	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
23	C₂×Dic₃	—	2	4	no	—
24	C₂×Dic₃	C₂×C₄	1	4	yes	—
25	C₃×C₈	C₂×C₄	1	4	yes	complemented
26	C₃⋊C₈	C₂×C₄	1	4	yes	complemented
27	C₂²×C₄	—	3	2	no	—
28	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
29	C₂×C₈	—	3	4	no	—
30	C₂×C₈	—	3	2	no	—
31	C₂×C₈	Dic₃	1	4	yes	complemented
32	C₂×C₈	C₂×D₃	1	2	yes	—
33	C₄²	—	3	2	no	—
34	C₄²	—	3	2	no	—
35	C₂²×C₃	C₄²	1	2	yes	—
36	C₂²×C₃	M₁₆	1	4	yes	—
37	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
38	C₃×C₄	C₄²	1	2	yes	—
39	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
40	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
41	Dic₃	—	2	4	no	—
42	C₂³	C₄×D₃	1	1	yes	characteristic
43	C₂×C₄	—	3	4	no	—
44	C₂×C₄	—	6	4	no	—
45	C₂×C₄	C₄×D₃	1	1	yes	characteristic
46	C₂×C₄	C₄×D₃	1	2	yes	—
47	C₂×C₄	C₂×Dic₃	1	2	yes	—
48	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
49	C₈	—	3	4	no	—
50	C₈	C₂×Dic₃	1	4	yes	complemented
51	C₂×C₃	#97	1	4	yes	complemented
52	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₃	C₂×M₁₆	1	2	yes	—
54	C₂²	ΓL(1,𝔽₂₅)	1	4	yes	—
55	C₂²	C₄×Dic₃	1	2	yes	—
56	C₂²	C₂×C₄×D₃	1	1	yes	characteristic
57	C₄	—	6	4	no	—
58	C₄	C₄×Dic₃	1	2	yes	—
59	C₄	C₂×C₄×D₃	1	1	yes	characteristic
60	C₄	C₂²×Dic₃	1	1	yes	characteristic
61	C₃	C₂×#97	1	1	yes	characteristic, complemented, Sylow
62	C₂	#815	1	4	yes	direct product factor
63	C₂	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
64	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₂²×C₃×C₈	C₂
socle, prime radical	C₂³×C₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₂²×C₈	D₃
hypocenter	C₃	C₂×#97
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #815	C₂	direct (N × H)
8. C₂×C₃×C₈	C₄	semidirect
12. C₂×C₃⋊C₈	C₄	semidirect
25. C₃×C₈	C₂×C₄	semidirect
26. C₃⋊C₈	C₂×C₄	semidirect
31. C₂×C₈	Dic₃	semidirect
50. C₈	C₂×Dic₃	semidirect
51. C₂×C₃	#97	semidirect
61. C₃	C₂×#97	semidirect
62. C₂	#815	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×C₃×C₈	2
C₂×C₄×Dic₃	2
C₂²×C₃⋊C₈	2
#815	2
C₂×#97	3

Subgroups — C2×#815 #5100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#815 #5100