Subgroups — C₂×C₃×#103 #5289

Order 192.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Subgroups — C2×C3×#103 #5289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#103 #5289