Subgroups — C₃×#1330 #67890

Order 384.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
4	#1330	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×M₁₆	—	2	1	no	—
6	C₃×C₄×D₄	C₄	1	1	yes	characteristic
7	C₂×C₃×C₁₆	—	2	1	no	—
8	C₂×C₃×C₁₆	—	2	1	no	—
9	C₃×C₄⋊C₈	C₄	1	1	yes	characteristic
10	C₃×C₂²⋊C₈	—	2	1	no	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	#436	C₂×C₃	1	1	yes	characteristic
13	C₄⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
14	#346	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₄	C₈	1	1	yes	characteristic
16	C₂²×C₃×C₄	—	2	1	no	—
17	C₃×M₁₆	—	4	1	no	—
18	C₃×M₁₆	—	4	1	no	—
19	C₂×C₃×C₈	—	2	1	no	—
20	C₂×C₃×C₈	D₄	1	1	yes	characteristic
21	C₂×C₃×C₈	D₄	1	1	yes	characteristic
22	C₃×C₄⋊C₄	C₈	1	1	yes	characteristic
23	C₃×C₂²⋊C₄	—	2	1	no	—
24	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
25	C₃×C₁₆	—	2	2	no	—
26	C₃×C₁₆	—	4	1	no	—
27	C₂×M₁₆	—	2	1	no	—
28	C₄×D₄	C₃×C₄	1	1	yes	characteristic
29	C₂×C₁₆	—	2	1	no	—
30	C₂×C₁₆	—	2	1	no	—
31	C₄⋊C₈	C₃×C₄	1	1	yes	characteristic
32	C₂²⋊C₈	—	2	1	no	—
33	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
34	C₂³×C₃	—	2	1	no	—
35	C₃×D₄	—	4	1	no	—
36	C₂×C₃×C₄	—	2	1	no	—
37	C₂×C₃×C₄	—	4	1	no	—
38	C₂×C₃×C₄	—	4	1	no	—
39	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₃×C₄	C₂×C₈	1	1	yes	characteristic
41	C₂×C₃×C₄	M₁₆	1	1	yes	characteristic
42	C₃×C₈	—	2	1	no	—
43	C₃×C₈	—	4	1	no	—
44	C₃×C₈	D₈	1	1	yes	characteristic
45	C₃×C₈	SD₁₆	1	1	yes	characteristic
46	C₂×D₄	C₃×C₈	1	1	yes	characteristic
47	C₂²×C₄	—	2	1	no	—
48	M₁₆	—	4	1	no	—
49	M₁₆	—	4	1	no	—
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	C₃×D₄	1	1	yes	characteristic
52	C₂×C₈	C₃×D₄	1	1	yes	characteristic
53	C₄⋊C₄	C₃×C₈	1	1	yes	characteristic
54	C₂²⋊C₄	—	2	1	no	—
55	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
56	C₁₆	—	2	2	no	—
57	C₁₆	—	4	1	no	—
58	C₂²×C₃	—	4	1	no	—
59	C₂²×C₃	—	4	1	no	—
60	C₂²×C₃	—	4	1	no	—
61	C₂²×C₃	C₂²⋊C₈	1	1	yes	characteristic
62	C₃×C₄	—	2	1	no	—
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	4	1	no	—
65	C₃×C₄	#102	1	1	yes	characteristic
66	C₃×C₄	#104	1	1	yes	characteristic
67	C₂³	—	2	1	no	—
68	D₄	—	4	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄	C₂×C₃×C₈	1	1	yes	characteristic
74	C₂×C₄	C₃×M₁₆	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	4	1	no	—
77	C₈	C₃×D₈	1	1	yes	characteristic
78	C₈	C₃×SD₁₆	1	1	yes	characteristic
79	C₂×C₃	—	8	1	no	—
80	C₂×C₃	D₄⋊C₈	1	1	yes	characteristic
81	C₂×C₃	#349	1	1	yes	characteristic
82	C₂×C₃	#350	1	1	yes	characteristic
83	C₂²	—	4	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₃×C₂²⋊C₈	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	2	1	no	—
89	C₄	—	4	1	no	—
90	C₄	C₃×#102	1	1	yes	characteristic
91	C₄	C₃×#104	1	1	yes	characteristic
92	C₃	#1330	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	—	8	1	no	—
94	C₂	C₃×D₄⋊C₈	1	1	yes	characteristic
95	C₂	C₃×#349	1	1	yes	characteristic
96	C₂	C₃×#350	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₃×C₈
Frattini, cosocle	C₄×C₈	C₂²×C₃
socle	C₂²×C₃	C₂²⋊C₈
prime radical	C₂×C₃×D₄	C₈
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄⋊C₁₆	C₂	semidirect
3. C₃×#346	C₂	semidirect
4. #1330	C₃	direct (N × H)
13. C₄⋊C₁₆	C₂×C₃	semidirect
14. #346	C₂×C₃	semidirect
92. C₃	#1330	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×#436	2
C₃×C₄⋊C₁₆	2
C₃×#346	2
#1330	3

Subgroups — C3×#1330 #67890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1330 #67890