Subgroups — C₂×C₃×#107 #5300

Order 192.

130 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×C₃×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₃×#107	C₂	1	4	yes	maximal, direct product factor
4	C₂×#107	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₄	—	2	2	no	—
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	C₄	1	4	yes	complemented
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₃×C₄⋊C₄	—	2	2	no	—
10	C₃×C₄⋊C₄	C₂²	1	4	yes	—
11	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
12	C₂×C₄⋊C₄	C₂×C₃	1	2	yes	—
13	#107	C₂×C₃	1	4	yes	direct product factor
14	C₂³×C₃	D₄	1	1	yes	characteristic
15	C₂×C₃×C₄	—	2	4	no	—
16	C₂×C₃×C₄	—	4	4	no	—
17	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
18	C₂×C₃×C₄	D₄	1	1	yes	characteristic
19	C₂×C₃×C₄	Q₈	1	2	yes	—
20	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₃×C₈	C₂×C₄	1	4	yes	complemented
22	C₂²×C₄	—	2	2	no	—
23	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
24	C₂×C₈	C₃×C₄	1	4	yes	complemented
25	C₂×C₈	C₂²×C₃	1	2	yes	—
26	C₄⋊C₄	—	2	2	no	—
27	C₄⋊C₄	C₂²×C₃	1	4	yes	—
28	C₂²×C₃	C₄⋊C₄	1	2	yes	—
29	C₂²×C₃	D₈	1	2	yes	—
30	C₂²×C₃	Q₁₆	1	2	yes	—
31	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
32	C₃×C₄	—	4	4	no	—
33	C₃×C₄	C₄⋊C₄	1	2	yes	—
34	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
35	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
36	C₂³	C₃×D₄	1	1	yes	characteristic
37	C₂×C₄	—	2	4	no	—
38	C₂×C₄	—	4	4	no	—
39	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
40	C₂×C₄	C₃×D₄	1	1	yes	characteristic
41	C₂×C₄	C₃×Q₈	1	2	yes	—
42	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
43	C₈	C₂×C₃×C₄	1	4	yes	complemented
44	C₂×C₃	#107	1	4	yes	direct product factor
45	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₃	C₂×D₈	1	1	yes	characteristic
47	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
48	C₂²	C₃×C₄⋊C₄	1	2	yes	—
49	C₂²	C₃×D₈	1	2	yes	—
50	C₂²	C₃×Q₁₆	1	2	yes	—
51	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
52	C₄	—	4	4	no	—
53	C₄	C₃×C₄⋊C₄	1	2	yes	—
54	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
55	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
56	C₃	C₂×#107	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	C₃×#107	1	4	yes	direct product factor
58	C₂	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
59	C₂	C₂×C₃×D₈	1	1	yes	characteristic
60	C₂	C₂×C₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#107	C₂	direct (N × H)
4. C₂×#107	C₃	direct (N × H)
7. C₂×C₃×C₈	C₄	semidirect
13. #107	C₂×C₃	direct (N × H)
21. C₃×C₈	C₂×C₄	semidirect
24. C₂×C₈	C₃×C₄	semidirect
43. C₈	C₂×C₃×C₄	semidirect
44. C₂×C₃	#107	direct (N × H)
56. C₃	C₂×#107	direct (N × H)
57. C₂	C₃×#107	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×C₃×C₄⋊C₄	2
C₃×#107	2
C₂×#107	3

Subgroups — C2×C3×#107 #5300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#107 #5300