Subgroups — C₃×#2982 #84846

Order 384.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×Q₈	C₂	1	8	yes	maximal, complemented
3	C₃×#431	C₂	1	6	yes	maximal
4	#2982	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×Q₈	C₄	1	1	yes	characteristic
6	C₃×C₄×Q₈	C₄	1	4	yes	—
7	C₃×C₄×Q₈	C₂²	1	4	yes	—
8	C₂×C₃×C₄⋊C₄	C₄	1	3	yes	—
9	C₂×C₃×C₄²	C₂²	1	3	yes	—
10	C₃×C₄⋊C₈	C₂²	1	12	yes	—
11	C₃×C₂²⋊C₈	C₂²	1	4	yes	—
12	C₃×C₄×C₈	C₂²	1	12	yes	—
13	C₂×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
14	C₈×Q₈	C₂×C₃	1	8	yes	complemented
15	#431	C₂×C₃	1	6	yes	—
16	C₂×C₃×Q₈	C₈	1	8	yes	complemented
17	C₂×C₃×Q₈	C₂×C₄	1	4	yes	—
18	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
19	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
20	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₂×C₃×C₈	C₂³	1	8	yes	—
22	C₃×C₄⋊C₄	C₂×C₄	1	12	yes	—
23	C₃×C₄²	C₂×C₄	1	6	yes	—
24	C₃×C₄²	C₂³	1	6	yes	—
25	C₂²×Q₈	C₃×C₄	1	1	yes	characteristic
26	C₄×Q₈	C₃×C₄	1	4	yes	—
27	C₄×Q₈	C₂²×C₃	1	4	yes	—
28	C₂×C₄⋊C₄	C₃×C₄	1	3	yes	—
29	C₂×C₄²	C₂²×C₃	1	3	yes	—
30	C₄⋊C₈	C₂²×C₃	1	12	yes	—
31	C₂²⋊C₈	C₂²×C₃	1	4	yes	—
32	C₄×C₈	C₂²×C₃	1	12	yes	—
33	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
34	C₃×Q₈	C₂×C₈	1	16	yes	—
35	C₂×C₃×C₄	—	2	2	no	—
36	C₂×C₃×C₄	—	4	3	no	—
37	C₂×C₃×C₄	C₂×C₈	1	12	yes	—
38	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₃×C₄	C₂²×C₄	1	6	yes	—
40	C₂×C₃×C₄	C₂²×C₄	1	6	yes	—
41	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
42	C₃×C₈	—	2	8	no	—
43	C₂×Q₈	C₃×C₈	1	8	yes	complemented
44	C₂×Q₈	C₂×C₃×C₄	1	4	yes	—
45	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
46	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
47	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
48	C₂×C₈	C₂³×C₃	1	8	yes	—
49	C₄⋊C₄	C₂×C₃×C₄	1	12	yes	—
50	C₄²	C₂×C₃×C₄	1	6	yes	—
51	C₄²	C₂³×C₃	1	6	yes	—
52	C₂²×C₃	—	2	1	no	—
53	C₂²×C₃	—	2	1	no	—
54	C₂²×C₃	C₂²×C₈	1	2	yes	—
55	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	—	2	6	no	—
58	C₃×C₄	C₂²×C₈	1	12	yes	—
59	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
60	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
61	Q₈	C₂×C₃×C₈	1	16	yes	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	4	3	no	—
64	C₂×C₄	C₂×C₃×C₈	1	12	yes	—
65	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
66	C₂×C₄	C₂²×C₃×C₄	1	6	yes	—
67	C₂×C₄	C₂²×C₃×C₄	1	6	yes	—
68	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
69	C₈	—	2	8	no	—
70	C₂×C₃	—	2	2	no	—
71	C₂×C₃	#519	1	1	yes	characteristic
72	C₂×C₃	C₂³×C₈	1	1	yes	characteristic
73	C₂×C₃	#568	1	1	yes	characteristic
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	C₂²×C₃×C₈	1	2	yes	—
77	C₂²	C₂³×C₃×C₄	1	1	yes	characteristic
78	C₄	—	2	6	no	—
79	C₄	—	2	1	no	—
80	C₄	C₂²×C₃×C₈	1	12	yes	—
81	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
82	C₃	#2982	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	2	2	no	—
84	C₂	C₃×#519	1	1	yes	characteristic
85	C₂	C₂³×C₃×C₈	1	1	yes	characteristic
86	C₂	C₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂⁴
commutator	C₂	C₂³×C₃×C₈
Frattini, cosocle	C₂×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₄
prime radical	C₂³×C₃	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₈×Q₈	C₂	semidirect
4. #2982	C₃	direct (N × H)
14. C₈×Q₈	C₂×C₃	semidirect
16. C₂×C₃×Q₈	C₈	semidirect
43. C₂×Q₈	C₃×C₈	semidirect
82. C₃	#2982	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×Q₈	2
C₃×C₈×Q₈	2
C₃×#431	2
#2982	3

Subgroups — C3×#2982 #84846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2982 #84846