Subgroups — C₃×#485 #5359

Order 192.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#117	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×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
8	#485	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
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	C₂²	1	1	yes	characteristic
15	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₂²⋊C₄	—	2	1	no	—
18	C₃×C₂²⋊C₄	—	2	1	no	—
19	C₃×C₄²	—	2	1	no	—
20	C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
21	#117	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	#103	C₂×C₃	1	1	yes	characteristic, complemented
25	#103	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
27	C₂³×C₃	D₄	1	1	yes	characteristic
28	C₃×Q₈	—	2	1	no	—
29	C₃×Q₈	—	2	1	no	—
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	—	2	1	no	—
34	C₂×C₃×C₄	—	2	1	no	—
35	C₂×C₃×C₄	—	2	1	no	—
36	C₂×C₃×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
38	C₃×C₈	—	2	1	no	—
39	C₃×C₈	—	2	1	no	—
40	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
42	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
43	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
50	C₄²	—	2	1	no	—
51	C₂²×C₃	—	2	1	no	—
52	C₂²×C₃	—	2	1	no	—
53	C₂²×C₃	—	2	1	no	—
54	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
60	C₃×C₄	#41	1	1	yes	characteristic
61	C₃×C₄	#41	1	1	yes	characteristic
62	C₂³	C₃×D₄	1	1	yes	characteristic
63	Q₈	—	2	1	no	—
64	Q₈	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	C₃×D₄	1	1	yes	characteristic
72	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	2	1	no	—
75	C₂×C₃	—	4	1	no	—
76	C₂×C₃	#123	1	1	yes	characteristic
77	C₂×C₃	#135	1	1	yes	characteristic
78	C₂×C₃	#137	1	1	yes	characteristic
79	C₂²	—	2	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	C₃×#41	1	1	yes	characteristic
89	C₄	C₃×#41	1	1	yes	characteristic
90	C₃	#485	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	—	4	1	no	—
92	C₂	C₃×#123	1	1	yes	characteristic
93	C₂	C₃×#135	1	1	yes	characteristic
94	C₂	C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂³×C₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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	semidirect
4. C₃×#106	C₂	semidirect
5. C₃×#103	C₂	semidirect
6. C₃×#103	C₂	semidirect
8. #485	C₃	direct (N × H)
22. #107	C₂×C₃	semidirect
23. #106	C₂×C₃	semidirect
24. #103	C₂×C₃	semidirect
25. #103	C₂×C₃	semidirect
90. C₃	#485	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×C₂²⋊Q₈	2
C₃×#117	2
C₃×#107	2
C₃×#106	2
C₃×#103	2
C₃×C₂²⋊C₈	2
#485	3

Subgroups — C3×#485 #5359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#485 #5359