Subgroups — C₃×#1295 #67855

Order 384.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#97	C₂	1	2	yes	maximal
2	C₃×#382	C₂	1	1	yes	maximal, characteristic
3	#1295	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	—	2	2	no	—
5	C₂×C₃×C₄⋊C₄	C₄	1	2	yes	—
6	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₃×#97	—	2	2	no	—
8	C₃×#97	C₄	1	4	yes	complemented
9	C₃×#95	—	2	2	no	—
10	C₂×#97	C₂×C₃	1	2	yes	—
11	#382	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	8	no	—
16	C₂×C₃×C₈	—	2	4	no	—
17	C₃×C₄⋊C₄	—	4	2	no	—
18	C₃×C₄²	C₂×C₄	1	2	yes	—
19	C₃×C₄²	D₄	1	1	yes	characteristic
20	C₃×C₄²	Q₈	1	1	yes	characteristic
21	C₂²×C₈	—	2	2	no	—
22	C₂×C₄⋊C₄	C₃×C₄	1	2	yes	—
23	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
24	#97	—	2	2	no	—
25	#97	C₃×C₄	1	4	yes	complemented
26	#95	—	2	2	no	—
27	C₂³×C₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	4	no	—
31	C₂×C₃×C₄	—	4	2	no	—
32	C₂×C₃×C₄	—	4	4	no	—
33	C₂×C₃×C₄	C₄²	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
35	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
36	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
37	C₃×C₈	—	2	8	no	—
38	C₂²×C₄	—	2	2	no	—
39	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂²×C₄	C₃×D₄	1	2	yes	—
41	C₂×C₈	—	2	8	no	—
42	C₂×C₈	—	2	4	no	—
43	C₄⋊C₄	—	4	2	no	—
44	C₄²	C₂×C₃×C₄	1	2	yes	—
45	C₄²	C₃×D₄	1	1	yes	characteristic
46	C₄²	C₃×Q₈	1	1	yes	characteristic
47	C₂²×C₃	#95	1	1	yes	characteristic
48	C₂²×C₃	#100	1	1	yes	characteristic
49	C₂²×C₃	#101	1	1	yes	characteristic
50	C₂²×C₃	#104	1	4	yes	—
51	C₃×C₄	—	2	2	no	—
52	C₃×C₄	—	2	2	no	—
53	C₃×C₄	—	2	1	no	—
54	C₃×C₄	—	2	1	no	—
55	C₃×C₄	—	8	2	no	—
56	C₂³	C₃×C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	4	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	C₈	—	2	8	no	—
67	C₂×C₃	#329	1	2	yes	—
68	C₂×C₃	#330	1	2	yes	—
69	C₂×C₃	#339	1	2	yes	—
70	C₂×C₃	#343	1	1	yes	characteristic
71	C₂²	C₃×#95	1	1	yes	characteristic
72	C₂²	C₃×#100	1	1	yes	characteristic
73	C₂²	C₃×#101	1	1	yes	characteristic
74	C₂²	C₃×#104	1	4	yes	—
75	C₄	—	2	2	no	—
76	C₄	—	2	2	no	—
77	C₄	—	2	1	no	—
78	C₄	—	2	1	no	—
79	C₄	—	8	2	no	—
80	C₃	#1295	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	C₃×#329	1	2	yes	—
82	C₂	C₃×#330	1	2	yes	—
83	C₂	C₃×#339	1	2	yes	—
84	C₂	C₃×#343	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #1295	C₃	direct (N × H)
8. C₃×#97	C₄	semidirect
25. #97	C₃×C₄	semidirect
80. C₃	#1295	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×#97	2
C₃×#382	2
#1295	3

Subgroups — C3×#1295 #67855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1295 #67855