Subgroups — C₂×C₃×#102 #5288

Order 192.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#102	C₂	1	4	yes	maximal, direct product factor
5	C₂×#102	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂⁴×C₃	—	2	1	no	—
7	C₂×C₃×D₄	—	2	1	no	—
8	C₂×C₃×D₄	—	2	2	no	—
9	C₂×C₃×D₄	C₄	1	4	yes	complemented
10	C₂×C₃×D₄	C₂²	1	2	yes	—
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	complemented
15	C₃×C₄⋊C₄	—	2	1	no	—
16	C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
17	C₂²×D₄	C₂×C₃	1	1	yes	characteristic
18	C₂²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
20	#102	C₂×C₃	1	4	yes	direct product factor
21	C₂³×C₃	—	2	4	no	—
22	C₂³×C₃	—	2	2	no	—
23	C₂³×C₃	—	4	2	no	—
24	C₂³×C₃	—	4	2	no	—
25	C₂³×C₃	D₄	1	1	yes	characteristic
26	C₃×D₄	—	2	4	no	—
27	C₃×D₄	—	2	2	no	—
28	C₃×D₄	C₂×C₄	1	4	yes	complemented
29	C₂×C₃×C₄	—	2	2	no	—
30	C₂×C₃×C₄	—	4	2	no	—
31	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
32	C₂×C₃×C₄	D₄	1	1	yes	characteristic
33	C₂×C₃×C₄	D₄	1	2	yes	—
34	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
35	C₃×C₈	—	2	2	no	—
36	C₂⁴	—	2	1	no	—
37	C₂×D₄	—	2	1	no	—
38	C₂×D₄	—	2	2	no	—
39	C₂×D₄	C₃×C₄	1	4	yes	complemented
40	C₂×D₄	C₂²×C₃	1	2	yes	—
41	C₂²×C₄	—	2	1	no	—
42	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
43	C₂×C₈	—	2	2	no	—
44	C₂×C₈	C₂²×C₃	1	2	yes	complemented
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
47	C₂²×C₃	—	2	4	no	—
48	C₂²×C₃	—	4	8	no	—
49	C₂²×C₃	—	4	2	no	—
50	C₂²×C₃	—	4	2	no	—
51	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₃	D₈	1	2	yes	—
53	C₂²×C₃	SD₁₆	1	2	yes	—
54	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
55	C₃×C₄	—	4	2	no	—
56	C₃×C₄	C₂²⋊C₄	1	2	yes	—
57	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
58	C₃×C₄	C₂×D₄	1	1	yes	characteristic
59	C₂³	—	2	4	no	—
60	C₂³	—	2	2	no	—
61	C₂³	—	4	2	no	—
62	C₂³	—	4	2	no	—
63	C₂³	C₃×D₄	1	1	yes	characteristic
64	D₄	—	2	4	no	—
65	D₄	—	2	2	no	—
66	D₄	C₂×C₃×C₄	1	4	yes	complemented
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
70	C₂×C₄	C₃×D₄	1	1	yes	characteristic
71	C₂×C₄	C₃×D₄	1	2	yes	—
72	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₂×C₃	—	4	4	no	—
75	C₂×C₃	#102	1	4	yes	direct product factor
76	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₃	C₂×D₈	1	1	yes	characteristic
78	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
79	C₂²	—	2	4	no	—
80	C₂²	—	4	8	no	—
81	C₂²	—	4	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	C₃×C₂²⋊C₄	1	2	yes	—
84	C₂²	C₃×D₈	1	2	yes	—
85	C₂²	C₃×SD₁₆	1	2	yes	—
86	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
87	C₄	—	4	2	no	—
88	C₄	C₃×C₂²⋊C₄	1	2	yes	—
89	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
90	C₄	C₂×C₃×D₄	1	1	yes	characteristic
91	C₃	C₂×#102	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	—	4	4	no	—
93	C₂	C₃×#102	1	4	yes	direct product factor
94	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
95	C₂	C₂×C₃×D₈	1	1	yes	characteristic
96	C₂	C₂×C₃×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂²×C₃×D₄	C₂
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
2. C₂²×C₃×C₈	C₂	semidirect
3. C₂×C₃×C₄⋊C₄	C₂	semidirect
4. C₃×#102	C₂	direct (N × H)
5. C₂×#102	C₃	direct (N × H)
9. C₂×C₃×D₄	C₄	semidirect
14. C₂×C₃×C₈	C₂²	semidirect
16. C₃×C₄⋊C₄	C₂²	semidirect
18. C₂²×C₈	C₂×C₃	semidirect
19. C₂×C₄⋊C₄	C₂×C₃	semidirect
20. #102	C₂×C₃	direct (N × H)
28. C₃×D₄	C₂×C₄	semidirect
39. C₂×D₄	C₃×C₄	semidirect
44. C₂×C₈	C₂²×C₃	semidirect
46. C₄⋊C₄	C₂²×C₃	semidirect
66. D₄	C₂×C₃×C₄	semidirect
75. C₂×C₃	#102	direct (N × H)
91. C₃	C₂×#102	direct (N × H)
93. C₂	C₃×#102	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×D₄	2
C₂²×C₃×C₈	2
C₂×C₃×C₄⋊C₄	2
C₃×#102	2
C₂×#102	3

Subgroups — C2×C3×#102 #5288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#102 #5288