Subgroups — C₂×C₃×#384 #84148

Order 384.

888 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄⋊C₄	C₂	1	6	yes	maximal
2	C₂²×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₃×#384	C₂	1	8	yes	maximal, direct product factor
4	C₂×#384	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃×C₄	C₂²	1	4	yes	—
6	C₂³×C₃×C₄	C₂²	1	3	yes	—
7	C₂×C₃×C₄⋊C₄	—	2	24	no	—
8	C₂×C₃×C₄⋊C₄	C₂²	1	24	yes	—
9	C₂×C₃×C₄²	C₄	1	8	yes	complemented
10	C₂×C₃×C₄²	C₂²	1	4	yes	—
11	C₂²×C₄⋊C₄	C₂×C₃	1	6	yes	—
12	C₂²×C₄²	C₂×C₃	1	1	yes	characteristic
13	#384	C₂×C₃	1	8	yes	direct product factor
14	C₂⁴×C₃	C₂³	1	1	yes	characteristic
15	C₂²×C₃×C₄	—	2	24	no	—
16	C₂²×C₃×C₄	C₂×C₄	1	12	yes	—
17	C₂²×C₃×C₄	D₄	1	12	yes	—
18	C₂²×C₃×C₄	Q₈	1	12	yes	—
19	C₂²×C₃×C₄	C₂³	1	8	yes	—
20	C₂²×C₃×C₄	C₂³	1	6	yes	—
21	C₃×C₄⋊C₄	—	2	48	no	—
22	C₃×C₄²	C₂×C₄	1	16	yes	complemented
23	C₂³×C₄	C₂²×C₃	1	4	yes	—
24	C₂³×C₄	C₂²×C₃	1	3	yes	—
25	C₂×C₄⋊C₄	—	2	24	no	—
26	C₂×C₄⋊C₄	C₂²×C₃	1	24	yes	—
27	C₂×C₄²	C₃×C₄	1	8	yes	complemented
28	C₂×C₄²	C₂²×C₃	1	4	yes	—
29	C₂³×C₃	C₂²×C₄	1	2	yes	—
30	C₂³×C₃	C₂×D₄	1	6	yes	—
31	C₂³×C₃	C₂×Q₈	1	6	yes	—
32	C₂³×C₃	C₂⁴	1	1	yes	characteristic
33	C₂×C₃×C₄	—	2	24	no	—
34	C₂×C₃×C₄	—	4	16	no	—
35	C₂×C₃×C₄	C₄⋊C₄	1	48	yes	complemented
36	C₂×C₃×C₄	C₂²×C₄	1	12	yes	—
37	C₂×C₃×C₄	C₂×D₄	1	12	yes	—
38	C₂×C₃×C₄	C₂×Q₈	1	12	yes	—
39	C₂⁴	C₂³×C₃	1	1	yes	characteristic
40	C₂²×C₄	—	2	24	no	—
41	C₂²×C₄	C₂×C₃×C₄	1	12	yes	—
42	C₂²×C₄	C₃×D₄	1	12	yes	—
43	C₂²×C₄	C₃×Q₈	1	12	yes	—
44	C₂²×C₄	C₂³×C₃	1	8	yes	—
45	C₂²×C₄	C₂³×C₃	1	6	yes	—
46	C₄⋊C₄	—	2	48	no	—
47	C₄²	C₂×C₃×C₄	1	16	yes	complemented
48	C₂²×C₃	C₂×C₄⋊C₄	1	12	yes	—
49	C₂²×C₃	#127	1	4	yes	—
50	C₂²×C₃	C₄⋊Q₈	1	12	yes	—
51	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
52	C₂²×C₃	C₂²×D₄	1	3	yes	—
53	C₂²×C₃	C₂²×Q₈	1	3	yes	—
54	C₃×C₄	—	4	8	no	—
55	C₃×C₄	C₂×C₄⋊C₄	1	24	yes	complemented
56	C₂³	C₂²×C₃×C₄	1	2	yes	—
57	C₂³	C₂×C₃×D₄	1	6	yes	—
58	C₂³	C₂×C₃×Q₈	1	6	yes	—
59	C₂³	C₂⁴×C₃	1	1	yes	characteristic
60	C₂×C₄	—	2	24	no	—
61	C₂×C₄	—	4	16	no	—
62	C₂×C₄	C₃×C₄⋊C₄	1	48	yes	complemented
63	C₂×C₄	C₂²×C₃×C₄	1	12	yes	—
64	C₂×C₄	C₂×C₃×D₄	1	12	yes	—
65	C₂×C₄	C₂×C₃×Q₈	1	12	yes	—
66	C₂×C₃	#384	1	8	yes	direct product factor
67	C₂×C₃	C₂²×C₄⋊C₄	1	3	yes	—
68	C₂×C₃	C₂×#127	1	1	yes	characteristic
69	C₂×C₃	C₂×C₄⋊Q₈	1	3	yes	—
70	C₂²	C₂×C₃×C₄⋊C₄	1	12	yes	—
71	C₂²	C₃×#127	1	4	yes	—
72	C₂²	C₃×C₄⋊Q₈	1	12	yes	—
73	C₂²	C₂³×C₃×C₄	1	1	yes	characteristic
74	C₂²	C₂²×C₃×D₄	1	3	yes	—
75	C₂²	C₂²×C₃×Q₈	1	3	yes	—
76	C₄	—	4	8	no	—
77	C₄	C₂×C₃×C₄⋊C₄	1	24	yes	complemented
78	C₃	C₂×#384	1	1	yes	characteristic, direct product factor, Sylow
79	C₂	C₃×#384	1	8	yes	direct product factor
80	C₂	C₂²×C₃×C₄⋊C₄	1	3	yes	—
81	C₂	C₂×C₃×#127	1	1	yes	characteristic
82	C₂	C₂×C₃×C₄⋊Q₈	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×#384	C₂	direct (N × H)
4. C₂×#384	C₃	direct (N × H)
9. C₂×C₃×C₄²	C₄	semidirect
13. #384	C₂×C₃	direct (N × H)
22. C₃×C₄²	C₂×C₄	semidirect
27. C₂×C₄²	C₃×C₄	semidirect
35. C₂×C₃×C₄	C₄⋊C₄	semidirect
47. C₄²	C₂×C₃×C₄	semidirect
55. C₃×C₄	C₂×C₄⋊C₄	semidirect
62. C₂×C₄	C₃×C₄⋊C₄	semidirect
66. C₂×C₃	#384	direct (N × H)
77. C₄	C₂×C₃×C₄⋊C₄	semidirect
78. C₃	C₂×#384	direct (N × H)
79. C₂	C₃×#384	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₄⋊C₄	2
C₂²×C₃×C₄²	2
C₃×#384	2
C₂×#384	3

Subgroups — C2×C3×#384 #84148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#384 #84148