Subgroups — C₃×#1276 #67836

Order 384.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#431	C₂	1	2	yes	maximal
2	C₃×C₄³	C₂	1	1	yes	maximal, characteristic
3	#1276	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₄²	—	2	2	no	—
5	C₂×C₃×C₄²	C₄	1	2	yes	—
6	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₃×C₄⋊C₈	C₄	1	4	yes	complemented
8	C₃×C₂²⋊C₈	—	2	2	no	—
9	C₃×C₄×C₈	—	2	2	no	—
10	#431	C₂×C₃	1	2	yes	—
11	C₄³	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₃×C₄	—	2	2	no	—
13	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄	D₄	1	2	yes	—
15	C₂×C₃×C₈	—	2	4	no	—
16	C₃×C₄²	—	2	8	no	—
17	C₃×C₄²	—	2	2	no	—
18	C₃×C₄²	C₈	1	4	yes	complemented
19	C₃×C₄²	C₂×C₄	1	2	yes	—
20	C₃×C₄²	D₄	1	1	yes	characteristic
21	C₃×C₄²	Q₈	1	1	yes	characteristic
22	C₂×C₄²	—	2	2	no	—
23	C₂×C₄²	C₃×C₄	1	2	yes	—
24	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
25	C₄⋊C₈	C₃×C₄	1	4	yes	complemented
26	C₂²⋊C₈	—	2	2	no	—
27	C₄×C₈	—	2	2	no	—
28	C₂³×C₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₃×C₄	—	2	8	no	—
30	C₂×C₃×C₄	—	2	4	no	—
31	C₂×C₃×C₄	—	2	4	no	—
32	C₂×C₃×C₄	C₄²	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
34	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
35	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₃×C₄	C₂×C₈	1	2	yes	—
37	C₂×C₃×C₄	M₁₆	1	2	yes	—
38	C₃×C₈	—	4	4	no	—
39	C₂²×C₄	—	2	2	no	—
40	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂²×C₄	C₃×D₄	1	2	yes	—
42	C₂×C₈	—	2	4	no	—
43	C₄²	—	2	8	no	—
44	C₄²	—	2	2	no	—
45	C₄²	C₃×C₈	1	4	yes	complemented
46	C₄²	C₂×C₃×C₄	1	2	yes	—
47	C₄²	C₃×D₄	1	1	yes	characteristic
48	C₄²	C₃×Q₈	1	1	yes	characteristic
49	C₂²×C₃	—	2	2	no	—
50	C₂²×C₃	#95	1	1	yes	characteristic
51	C₂²×C₃	C₂²⋊C₈	1	2	yes	—
52	C₃×C₄	—	2	8	no	—
53	C₃×C₄	—	2	2	no	—
54	C₃×C₄	C₄×C₈	1	1	yes	characteristic
55	C₃×C₄	#97	1	1	yes	characteristic
56	C₃×C₄	#104	1	4	yes	—
57	C₃×C₄	C₄⋊C₈	1	2	yes	—
58	C₂³	C₃×C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄	—	2	8	no	—
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	C₃×C₄²	1	1	yes	characteristic
63	C₂×C₄	C₃×C₂²⋊C₄	1	2	yes	—
64	C₂×C₄	C₃×C₄⋊C₄	1	2	yes	—
65	C₂×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄	C₂×C₃×C₈	1	2	yes	—
67	C₂×C₄	C₃×M₁₆	1	2	yes	—
68	C₈	—	4	4	no	—
69	C₂×C₃	—	2	2	no	—
70	C₂×C₃	#336	1	1	yes	characteristic
71	C₂×C₃	#339	1	2	yes	—
72	C₂²	—	2	2	no	—
73	C₂²	C₃×#95	1	1	yes	characteristic
74	C₂²	C₃×C₂²⋊C₈	1	2	yes	—
75	C₄	—	2	8	no	—
76	C₄	—	2	2	no	—
77	C₄	C₃×C₄×C₈	1	1	yes	characteristic
78	C₄	C₃×#97	1	1	yes	characteristic
79	C₄	C₃×#104	1	4	yes	—
80	C₄	C₃×C₄⋊C₈	1	2	yes	—
81	C₃	#1276	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	—	2	2	no	—
83	C₂	C₃×#336	1	1	yes	characteristic
84	C₂	C₃×#339	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	D₄
commutator	C₄	C₃×C₄×C₈
Frattini, cosocle	C₂×C₄²	C₂²×C₃
socle	C₂²×C₃	#95
prime radical	C₂³×C₃	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
3. #1276	C₃	direct (N × H)
7. C₃×C₄⋊C₈	C₄	semidirect
18. C₃×C₄²	C₈	semidirect
25. C₄⋊C₈	C₃×C₄	semidirect
45. C₄²	C₃×C₈	semidirect
81. C₃	#1276	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×#431	2
C₃×C₄³	2
#1276	3

Subgroups — C3×#1276 #67836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1276 #67836