Subgroups — C₃×#416 #5290

Order 192.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#103	C₂	1	2	yes	maximal, complemented
5	C₃×#102	C₂	1	2	yes	maximal, complemented
6	#416	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	—	2	2	no	—
8	C₃×#41	C₄	1	4	yes	complemented
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₄	—	2	1	no	—
11	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄	—	2	1	no	—
13	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈	—	2	2	no	—
15	C₂×C₃×C₈	C₂²	1	2	yes	—
16	C₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃×C₂²⋊C₄	—	2	1	no	—
18	C₃×C₄²	—	2	1	no	—
19	C₂×#41	C₂×C₃	1	1	yes	characteristic
20	C₂²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	#117	C₂×C₃	1	1	yes	characteristic, complemented
22	#103	C₂×C₃	1	2	yes	complemented
23	#102	C₂×C₃	1	2	yes	complemented
24	C₂³×C₃	—	2	1	no	—
25	C₂³×C₃	D₄	1	1	yes	characteristic
26	C₃×Q₈	—	2	1	no	—
27	C₃×Q₈	C₂×C₄	1	2	yes	—
28	C₃×D₄	—	2	4	no	—
29	C₃×D₄	—	2	1	no	—
30	C₃×D₄	C₂×C₄	1	2	yes	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	4	no	—
33	C₂×C₃×C₄	—	2	2	no	—
34	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
35	C₂×C₃×C₄	D₄	1	2	yes	—
36	C₂×C₃×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
38	C₃×C₈	—	2	2	no	—
39	#41	—	2	2	no	—
40	#41	C₃×C₄	1	4	yes	complemented
41	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
42	C₂×D₄	—	2	1	no	—
43	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
44	C₂²×C₄	—	2	1	no	—
45	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₈	—	2	2	no	—
47	C₂×C₈	C₂²×C₃	1	2	yes	—
48	C₄⋊C₄	C₂²×C₃	1	2	yes	—
49	C₂²⋊C₄	—	2	1	no	—
50	C₄²	—	2	1	no	—
51	C₂²×C₃	—	2	2	no	—
52	C₂²×C₃	—	2	2	no	—
53	C₂²×C₃	—	4	2	no	—
54	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	—	4	2	no	—
58	C₃×C₄	C₂²⋊C₄	1	2	yes	—
59	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₃×C₄	C₂×D₄	1	1	yes	characteristic
61	C₂³	—	2	1	no	—
62	C₂³	C₃×D₄	1	1	yes	characteristic
63	Q₈	—	2	1	no	—
64	Q₈	C₂×C₃×C₄	1	2	yes	—
65	D₄	—	2	4	no	—
66	D₄	—	2	1	no	—
67	D₄	C₂×C₃×C₄	1	2	yes	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	2	2	no	—
71	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
72	C₂×C₄	C₃×D₄	1	1	yes	characteristic
73	C₂×C₄	C₃×D₄	1	2	yes	—
74	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	—	4	2	no	—
78	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₃	#135	1	2	yes	—
80	C₂²	—	2	2	no	—
81	C₂²	—	2	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	C₃×C₂²⋊C₄	1	2	yes	—
84	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	4	2	no	—
87	C₄	C₃×C₂²⋊C₄	1	2	yes	—
88	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
89	C₄	C₂×C₃×D₄	1	1	yes	characteristic
90	C₃	#416	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	—	2	2	no	—
92	C₂	—	4	2	no	—
93	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
94	C₂	C₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×D₄
prime radical	C₂×C₃×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ 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. C₃×#117	C₂	semidirect
4. C₃×#103	C₂	semidirect
5. C₃×#102	C₂	semidirect
6. #416	C₃	direct (N × H)
8. C₃×#41	C₄	semidirect
20. C₂²×C₈	C₂×C₃	semidirect
21. #117	C₂×C₃	semidirect
22. #103	C₂×C₃	semidirect
23. #102	C₂×C₃	semidirect
40. #41	C₃×C₄	semidirect
90. C₃	#416	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#41	2
C₂²×C₃×C₈	2
C₃×#117	2
C₃×#103	2
C₃×#102	2
#416	3

Subgroups — C3×#416 #5290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#416 #5290