Subgroups — C₃×#1334 #67894

Order 384.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₃×#334	C₂	1	1	yes	maximal, characteristic
4	#1334	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₁₆	C₄	1	1	yes	characteristic
6	C₃×C₄×Q₈	—	2	1	no	—
7	C₂×C₃×C₁₆	—	2	1	no	—
8	C₃×#107	C₄	1	1	yes	characteristic
9	C₃×C₄⋊C₈	—	2	1	no	—
10	C₃×#103	—	2	1	no	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic
13	#346	C₂×C₃	1	1	yes	characteristic
14	#334	C₂×C₃	1	1	yes	characteristic
15	C₂×C₃×Q₈	—	2	1	no	—
16	C₃×Q₁₆	—	2	1	no	—
17	C₃×Q₁₆	C₈	1	2	yes	complemented
18	C₂×C₃×C₈	—	4	1	no	—
19	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×C₈	D₄	1	1	yes	characteristic
21	C₃×C₄⋊C₄	—	2	1	no	—
22	C₃×C₄⋊C₄	—	4	1	no	—
23	C₃×C₄²	—	4	1	no	—
24	C₃×C₄²	D₄	1	1	yes	characteristic
25	C₃×C₁₆	—	2	2	no	—
26	C₂×Q₁₆	C₃×C₄	1	1	yes	characteristic
27	C₄×Q₈	—	2	1	no	—
28	C₂×C₁₆	—	2	1	no	—
29	#107	C₃×C₄	1	1	yes	characteristic
30	C₄⋊C₈	—	2	1	no	—
31	#103	—	2	1	no	—
32	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
33	C₃×Q₈	—	2	2	no	—
34	C₃×Q₈	—	4	1	no	—
35	C₂×C₃×C₄	—	4	1	no	—
36	C₂×C₃×C₄	—	4	1	no	—
37	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₃×C₄	D₈	1	1	yes	characteristic
39	C₂×C₃×C₄	SD₁₆	1	1	yes	characteristic
40	C₃×C₈	—	2	1	no	—
41	C₃×C₈	—	8	1	no	—
42	C₃×C₈	C₂×C₈	1	1	yes	characteristic
43	C₃×C₈	M₁₆	1	1	yes	characteristic
44	C₂×Q₈	—	2	1	no	—
45	Q₁₆	—	2	1	no	—
46	Q₁₆	C₃×C₈	1	2	yes	complemented
47	C₂×C₈	—	4	1	no	—
48	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂×C₈	C₃×D₄	1	1	yes	characteristic
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	4	1	no	—
52	C₄²	—	4	1	no	—
53	C₄²	C₃×D₄	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂²×C₃	#102	1	1	yes	characteristic
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	—	2	1	no	—
58	C₃×C₄	—	4	2	no	—
59	C₃×C₄	—	8	1	no	—
60	C₃×C₄	C₂²⋊C₈	1	1	yes	characteristic
61	C₃×C₄	#104	1	1	yes	characteristic
62	Q₈	—	2	2	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	4	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄	C₃×D₈	1	1	yes	characteristic
68	C₂×C₄	C₃×SD₁₆	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	8	1	no	—
71	C₈	C₂×C₃×C₈	1	1	yes	characteristic
72	C₈	C₃×M₁₆	1	1	yes	characteristic
73	C₂×C₃	D₄⋊C₈	1	1	yes	characteristic
74	C₂×C₃	#360	1	1	yes	characteristic
75	C₂×C₃	#362	1	1	yes	characteristic
76	C₂²	C₃×#102	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	2	no	—
80	C₄	—	8	1	no	—
81	C₄	C₃×C₂²⋊C₈	1	1	yes	characteristic
82	C₄	C₃×#104	1	1	yes	characteristic
83	C₃	#1334	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	C₃×D₄⋊C₈	1	1	yes	characteristic
85	C₂	C₃×#360	1	1	yes	characteristic
86	C₂	C₃×#362	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	#102
commutator	C₈	C₂×C₃×C₈
Frattini, cosocle	C₄×C₈	C₂²×C₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1334	C₃	direct (N × H)
17. C₃×Q₁₆	C₈	semidirect
46. Q₁₆	C₃×C₈	semidirect
83. C₃	#1334	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×C₄×Q₁₆	2
C₃×#346	2
C₃×#334	2
#1334	3

Subgroups — C3×#1334 #67894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1334 #67894