Subgroups — C₃×#1322 #67882

Order 384.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊C₁₆	C₂	1	2	yes	maximal
3	#1322	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄²	C₄	1	1	yes	characteristic
7	C₂×C₃×C₁₆	—	2	2	no	—
8	C₃×C₄⋊C₈	—	2	2	no	—
9	C₂×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
10	C₂²⋊C₁₆	C₂×C₃	1	2	yes	—
11	C₂²×C₃×C₄	C₈	1	1	yes	characteristic
12	C₂²×C₃×C₄	C₈	1	1	yes	characteristic
13	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₈	—	2	1	no	—
15	C₂×C₃×C₈	—	4	1	no	—
16	C₂×C₃×C₈	—	4	1	no	—
17	C₂×C₃×C₈	D₄	1	2	yes	—
18	C₃×C₄²	—	2	1	no	—
19	C₃×C₄²	—	2	1	no	—
20	C₃×C₁₆	—	4	2	no	—
21	C₂²×C₈	C₃×C₄	1	1	yes	characteristic
22	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₄²	C₃×C₄	1	1	yes	characteristic
24	C₂×C₁₆	—	2	2	no	—
25	C₄⋊C₈	—	2	2	no	—
26	C₂³×C₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	4	1	no	—
33	C₂×C₃×C₄	C₁₆	1	2	yes	complemented
34	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₃×C₄	M₁₆	1	1	yes	characteristic
36	C₃×C₈	—	2	2	no	—
37	C₃×C₈	—	4	1	no	—
38	C₂²×C₄	C₃×C₈	1	1	yes	characteristic
39	C₂²×C₄	C₃×C₈	1	1	yes	characteristic
40	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	4	1	no	—
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	C₃×D₄	1	2	yes	—
45	C₄²	—	2	1	no	—
46	C₄²	—	2	1	no	—
47	C₁₆	—	4	2	no	—
48	C₂²×C₃	—	2	1	no	—
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	C₂²⋊C₈	1	1	yes	characteristic
51	C₂²×C₃	C₂×C₁₆	1	1	yes	characteristic
52	C₂²×C₃	M₃₂	1	1	yes	characteristic
53	C₃×C₄	—	2	1	no	—
54	C₃×C₄	—	2	2	no	—
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	#99	1	1	yes	characteristic
57	C₃×C₄	#101	1	1	yes	characteristic
58	C₂³	C₂×C₃×C₈	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	4	1	no	—
65	C₂×C₄	C₃×C₁₆	1	2	yes	complemented
66	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄	C₃×M₁₆	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₈	—	4	1	no	—
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	—	2	1	no	—
72	C₂×C₃	#324	1	1	yes	characteristic
73	C₂×C₃	C₂²⋊C₁₆	1	1	yes	characteristic
74	C₂×C₃	#349	1	1	yes	characteristic
75	C₂²	—	2	1	no	—
76	C₂²	—	2	1	no	—
77	C₂²	C₃×C₂²⋊C₈	1	1	yes	characteristic
78	C₂²	C₂×C₃×C₁₆	1	1	yes	characteristic
79	C₂²	C₃×M₃₂	1	1	yes	characteristic
80	C₄	—	2	1	no	—
81	C₄	—	2	2	no	—
82	C₄	—	4	1	no	—
83	C₄	C₃×#99	1	1	yes	characteristic
84	C₄	C₃×#101	1	1	yes	characteristic
85	C₃	#1322	1	1	yes	characteristic, direct product factor, Sylow
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	C₃×#324	1	1	yes	characteristic
89	C₂	C₃×C₂²⋊C₁₆	1	1	yes	characteristic
90	C₂	C₃×#349	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²⋊C₄
commutator	C₂²	C₂×C₃×C₁₆
Frattini, cosocle	C₂²×C₈	C₂²×C₃
socle	C₂²×C₃	C₂²⋊C₈
prime radical	C₂³×C₃	C₂×C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1322	C₃	direct (N × H)
33. C₂×C₃×C₄	C₁₆	semidirect
65. C₂×C₄	C₃×C₁₆	semidirect
85. C₃	#1322	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×C₄⋊C₈	2
C₃×C₂²⋊C₁₆	2
#1322	3

Subgroups — C3×#1322 #67882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1322 #67882