Subgroups — C₃×#1304 #67864

Order 384.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#379	C₂	1	3	yes	maximal
2	#1304	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
3	C₂⁵×C₃	C₂²	1	1	yes	characteristic
4	C₂×C₃×C₂²⋊C₄	—	2	6	no	—
5	C₂×C₃×C₂²⋊C₄	C₄	1	6	yes	complemented
6	#379	C₂×C₃	1	3	yes	—
7	C₂⁴×C₃	—	4	6	no	—
8	C₂⁴×C₃	C₂×C₄	1	3	yes	—
9	C₂⁴×C₃	D₄	1	3	yes	—
10	C₂⁴×C₃	Q₈	1	1	yes	characteristic
11	C₂²×C₃×C₄	—	2	6	no	—
12	C₃×C₂²⋊C₄	—	4	12	no	—
13	C₃×C₂²⋊C₄	—	4	6	no	—
14	C₂⁵	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₂²⋊C₄	—	2	6	no	—
16	C₂×C₂²⋊C₄	C₃×C₄	1	6	yes	complemented
17	C₂³×C₃	—	2	6	no	—
18	C₂³×C₃	—	2	12	no	—
19	C₂³×C₃	—	4	6	no	—
20	C₂³×C₃	—	4	3	no	—
21	C₂³×C₃	—	4	3	no	—
22	C₂³×C₃	—	4	16	no	—
23	C₂³×C₃	C₄²	1	1	yes	characteristic
24	C₂³×C₃	C₂²⋊C₄	1	3	yes	—
25	C₂³×C₃	C₄⋊C₄	1	3	yes	—
26	C₂×C₃×C₄	—	4	12	no	—
27	C₂×C₃×C₄	—	4	6	no	—
28	C₂⁴	—	4	6	no	—
29	C₂⁴	C₂×C₃×C₄	1	3	yes	—
30	C₂⁴	C₃×D₄	1	3	yes	—
31	C₂⁴	C₃×Q₈	1	1	yes	characteristic
32	C₂²×C₄	—	2	6	no	—
33	C₂²⋊C₄	—	4	12	no	—
34	C₂²⋊C₄	—	4	6	no	—
35	C₂²×C₃	—	2	6	no	—
36	C₂²×C₃	—	2	3	no	—
37	C₂²×C₃	—	2	3	no	—
38	C₂²×C₃	—	2	6	no	—
39	C₂²×C₃	—	4	12	no	—
40	C₂²×C₃	—	4	12	no	—
41	C₂²×C₃	—	4	4	no	—
42	C₂²×C₃	#95	1	1	yes	characteristic
43	C₂²×C₃	#99	1	6	yes	—
44	C₃×C₄	—	8	6	no	—
45	C₂³	—	2	6	no	—
46	C₂³	—	2	12	no	—
47	C₂³	—	4	6	no	—
48	C₂³	—	4	3	no	—
49	C₂³	—	4	3	no	—
50	C₂³	—	4	16	no	—
51	C₂³	C₃×C₄²	1	1	yes	characteristic
52	C₂³	C₃×C₂²⋊C₄	1	3	yes	—
53	C₂³	C₃×C₄⋊C₄	1	3	yes	—
54	C₂×C₄	—	4	12	no	—
55	C₂×C₄	—	4	6	no	—
56	C₂×C₃	—	2	6	no	—
57	C₂×C₃	—	4	1	no	—
58	C₂×C₃	—	4	3	no	—
59	C₂×C₃	#342	1	3	yes	—
60	C₂²	—	2	6	no	—
61	C₂²	—	2	3	no	—
62	C₂²	—	2	3	no	—
63	C₂²	—	2	6	no	—
64	C₂²	—	4	12	no	—
65	C₂²	—	4	12	no	—
66	C₂²	—	4	4	no	—
67	C₂²	C₃×#95	1	1	yes	characteristic
68	C₂²	C₃×#99	1	6	yes	—
69	C₄	—	8	6	no	—
70	C₃	#1304	1	1	yes	characteristic, direct product factor, Sylow
71	C₂	—	2	6	no	—
72	C₂	—	4	1	no	—
73	C₂	—	4	3	no	—
74	C₂	C₃×#342	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	#95
commutator	C₂³	C₃×C₄²
Frattini, cosocle	C₂⁵	C₂²×C₃
prime radical	C₂⁵×C₃	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂⁵×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. #1304	C₃	direct (N × H)
5. C₂×C₃×C₂²⋊C₄	C₄	semidirect
16. C₂×C₂²⋊C₄	C₃×C₄	semidirect
70. C₃	#1304	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×#379	2
#1304	3

Subgroups — C3×#1304 #67864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1304 #67864