Subgroups — C₃×#2916 #84780

Order 384.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#568	C₂	1	2	yes	maximal
2	C₂×C₃×#131	C₂	1	1	yes	maximal, characteristic
3	C₃×#430	C₂	1	6	yes	maximal, complemented
4	C₂×C₃×#108	C₂	1	6	yes	maximal, complemented
5	#2916	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×#41	C₂²	1	1	yes	characteristic
7	C₃×#131	—	2	8	no	—
8	C₃×#131	C₄	1	8	yes	—
9	C₂×C₃×M₁₆	C₂²	1	12	yes	—
10	C₂×C₃×M₁₆	C₂²	1	3	yes	—
11	C₂²×C₃×C₈	C₂²	1	3	yes	—
12	C₃×#108	C₂²	1	4	yes	—
13	C₃×#108	C₂²	1	12	yes	—
14	#568	C₂×C₃	1	2	yes	—
15	C₂×#131	C₂×C₃	1	1	yes	characteristic
16	#430	C₂×C₃	1	6	yes	complemented
17	C₂×#108	C₂×C₃	1	6	yes	complemented
18	C₃×#41	C₂×C₄	1	4	yes	—
19	C₃×#41	D₄	1	4	yes	—
20	C₂×C₃×Q₈	Q₈	1	1	yes	characteristic
21	C₂×C₃×D₄	Q₈	1	3	yes	—
22	C₂²×C₃×C₄	C₂³	1	3	yes	—
23	C₃×M₁₆	—	2	12	no	—
24	C₃×M₁₆	C₂×C₄	1	12	yes	—
25	C₃×M₁₆	C₂³	1	8	yes	—
26	C₂×C₃×C₈	—	2	12	no	—
27	C₂×C₃×C₈	C₂×C₄	1	12	yes	—
28	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
29	C₂×C₃×C₈	C₂³	1	3	yes	—
30	C₂×#41	C₂²×C₃	1	1	yes	characteristic
31	#131	—	2	8	no	—
32	#131	C₃×C₄	1	8	yes	—
33	C₂×M₁₆	C₂²×C₃	1	12	yes	—
34	C₂×M₁₆	C₂²×C₃	1	3	yes	—
35	C₂²×C₈	C₂²×C₃	1	3	yes	—
36	#108	C₂²×C₃	1	4	yes	—
37	#108	C₂²×C₃	1	12	yes	—
38	C₂³×C₃	C₂×Q₈	1	3	yes	—
39	C₃×Q₈	C₄⋊C₄	1	4	yes	—
40	C₃×D₄	C₄⋊C₄	1	12	yes	—
41	C₂×C₃×C₄	C₂²×C₄	1	6	yes	—
42	C₂×C₃×C₄	C₂×D₄	1	6	yes	—
43	C₂×C₃×C₄	C₂×Q₈	1	3	yes	—
44	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
45	C₃×C₈	—	2	8	no	—
46	C₃×C₈	C₂²×C₄	1	2	yes	—
47	C₃×C₈	C₂²×C₄	1	6	yes	—
48	#41	C₂×C₃×C₄	1	4	yes	—
49	#41	C₃×D₄	1	4	yes	—
50	C₂×Q₈	C₃×Q₈	1	1	yes	characteristic
51	C₂×D₄	C₃×Q₈	1	3	yes	—
52	C₂²×C₄	C₂³×C₃	1	3	yes	—
53	M₁₆	—	2	12	no	—
54	M₁₆	C₂×C₃×C₄	1	12	yes	—
55	M₁₆	C₂³×C₃	1	8	yes	—
56	C₂×C₈	—	2	12	no	—
57	C₂×C₈	C₂×C₃×C₄	1	12	yes	—
58	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
59	C₂×C₈	C₂³×C₃	1	3	yes	—
60	C₂²×C₃	—	4	3	no	—
61	C₂²×C₃	C₂×C₄⋊C₄	1	6	yes	—
62	C₂²×C₃	C₂²×Q₈	1	1	yes	characteristic
63	C₃×C₄	C₂×C₄⋊C₄	1	6	yes	—
64	C₃×C₄	C₂³×C₄	1	1	yes	characteristic
65	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
66	C₂³	C₂×C₃×Q₈	1	3	yes	—
67	Q₈	C₃×C₄⋊C₄	1	4	yes	—
68	D₄	C₃×C₄⋊C₄	1	12	yes	—
69	C₂×C₄	C₂²×C₃×C₄	1	6	yes	—
70	C₂×C₄	C₂×C₃×D₄	1	6	yes	—
71	C₂×C₄	C₂×C₃×Q₈	1	3	yes	—
72	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
73	C₈	—	2	8	no	—
74	C₈	C₂²×C₃×C₄	1	2	yes	—
75	C₈	C₂²×C₃×C₄	1	6	yes	—
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	2	6	no	—
78	C₂×C₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
79	C₂²	—	4	3	no	—
80	C₂²	C₂×C₃×C₄⋊C₄	1	6	yes	—
81	C₂²	C₂²×C₃×Q₈	1	1	yes	characteristic
82	C₄	C₂×C₃×C₄⋊C₄	1	6	yes	—
83	C₄	C₂³×C₃×C₄	1	1	yes	characteristic
84	C₄	C₂²×C₃×D₄	1	1	yes	characteristic
85	C₃	#2916	1	1	yes	characteristic, direct product factor, Sylow
86	C₂	—	2	1	no	—
87	C₂	—	2	6	no	—
88	C₂	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×D₄
commutator	C₄	C₂³×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁴×C₃
socle	C₂×C₃	C₂²×C₄⋊C₄
prime radical	C₂×C₃×#41	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#430	C₂	semidirect
4. C₂×C₃×#108	C₂	semidirect
5. #2916	C₃	direct (N × H)
16. #430	C₂×C₃	semidirect
17. C₂×#108	C₂×C₃	semidirect
85. C₃	#2916	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×#568	2
C₂×C₃×#131	2
C₃×#430	2
C₂×C₃×#108	2
#2916	3

Subgroups — C3×#2916 #84780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2916 #84780