Subgroups — C₃×#478 #5352

Order 192.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#102	C₂	1	1	yes	maximal, characteristic
7	C₃×#102	C₂	1	1	yes	maximal, characteristic
8	#478	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄	—	2	1	no	—
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	—	2	1	no	—
14	C₃×C₄⋊C₄	—	2	1	no	—
15	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×C₂²⋊C₄	—	2	1	no	—
19	C₃×C₄²	C₂²	1	1	yes	characteristic
20	#125	C₂×C₃	1	1	yes	characteristic, complemented
21	C₄×D₄	C₂×C₃	1	1	yes	characteristic
22	#107	C₂×C₃	1	1	yes	characteristic, complemented
23	#106	C₂×C₃	1	1	yes	characteristic, complemented
24	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
25	#102	C₂×C₃	1	1	yes	characteristic
26	#102	C₂×C₃	1	1	yes	characteristic
27	C₂³×C₃	—	2	1	no	—
28	C₃×D₄	—	2	1	no	—
29	C₃×D₄	Q₈	1	2	yes	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	1	no	—
33	C₂×C₃×C₄	—	4	2	no	—
34	C₂×C₃×C₄	D₄	1	1	yes	characteristic
35	C₂×C₃×C₄	D₄	1	1	yes	characteristic
36	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
37	C₃×C₈	—	2	1	no	—
38	C₃×C₈	—	2	1	no	—
39	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
40	C₂²×C₄	—	2	1	no	—
41	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
42	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
46	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
47	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
48	C₂²⋊C₄	—	2	1	no	—
49	C₄²	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₃	—	2	2	no	—
51	C₂²×C₃	—	4	1	no	—
52	C₂²×C₃	—	4	1	no	—
53	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
54	C₃×C₄	—	2	1	no	—
55	C₃×C₄	—	2	1	no	—
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	—	4	1	no	—
58	C₃×C₄	—	4	1	no	—
59	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
60	C₃×C₄	#41	1	1	yes	characteristic
61	C₂³	—	2	1	no	—
62	D₄	—	2	1	no	—
63	D₄	C₃×Q₈	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	4	2	no	—
68	C₂×C₄	C₃×D₄	1	1	yes	characteristic
69	C₂×C₄	C₃×D₄	1	1	yes	characteristic
70	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₂×C₃	—	4	2	no	—
74	C₂×C₃	C₂²⋊Q₈	1	1	yes	characteristic
75	C₂×C₃	#135	1	1	yes	characteristic
76	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
77	C₂²	—	2	2	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	1	no	—
80	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
87	C₄	C₃×#41	1	1	yes	characteristic
88	C₃	#478	1	1	yes	characteristic, direct product factor, Sylow
89	C₂	—	4	2	no	—
90	C₂	C₃×C₂²⋊Q₈	1	1	yes	characteristic
91	C₂	C₃×#135	1	1	yes	characteristic
92	C₂	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#125	C₂	semidirect
3. C₃×#107	C₂	semidirect
4. C₃×#106	C₂	semidirect
5. C₃×C₄⋊C₈	C₂	semidirect
8. #478	C₃	direct (N × H)
20. #125	C₂×C₃	semidirect
22. #107	C₂×C₃	semidirect
23. #106	C₂×C₃	semidirect
24. C₄⋊C₈	C₂×C₃	semidirect
88. C₃	#478	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#125	2
C₃×C₄×D₄	2
C₃×#107	2
C₃×#106	2
C₃×C₄⋊C₈	2
C₃×#102	2
#478	3

Subgroups — C3×#478 #5352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#478 #5352