Subgroups — C₃×#1446 #72161

Order 384.

736 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#95	C₂	1	6	yes	maximal
3	#1446	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×Q₈	—	2	12	no	—
5	C₂²×C₃×Q₈	C₄	1	4	yes	complemented
6	C₂³×C₃×C₄	C₂²	1	4	yes	—
7	C₂³×C₃×C₄	C₂²	1	3	yes	—
8	C₃×#95	—	2	12	no	—
9	C₂³×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₂×#95	C₂×C₃	1	6	yes	—
11	C₂⁴×C₃	C₂³	1	1	yes	characteristic
12	C₂×C₃×Q₈	—	2	32	no	—
13	C₂×C₃×Q₈	—	2	24	no	—
14	C₂²×C₃×C₄	—	2	12	no	—
15	C₂²×C₃×C₄	—	2	12	no	—
16	C₂²×C₃×C₄	—	2	12	no	—
17	C₂²×C₃×C₄	C₂×C₄	1	6	yes	—
18	C₂²×C₃×C₄	D₄	1	12	yes	—
19	C₂²×C₃×C₄	Q₈	1	8	yes	complemented
20	C₂²×Q₈	—	2	12	no	—
21	C₂²×Q₈	C₃×C₄	1	4	yes	complemented
22	C₂³×C₄	C₂²×C₃	1	4	yes	—
23	C₂³×C₄	C₂²×C₃	1	3	yes	—
24	#95	—	2	12	no	—
25	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
26	C₂³×C₃	C₂×D₄	1	6	yes	—
27	C₂³×C₃	C₂×Q₈	1	4	yes	—
28	C₂³×C₃	#41	1	4	yes	—
29	C₃×Q₈	—	2	32	no	—
30	C₂×C₃×C₄	—	2	12	no	—
31	C₂×C₃×C₄	—	2	24	no	—
32	C₂×C₃×C₄	—	2	24	no	—
33	C₂×C₃×C₄	—	4	4	no	—
34	C₂×C₃×C₄	—	4	12	no	—
35	C₂×C₃×C₄	C₂²⋊C₄	1	12	yes	—
36	C₂⁴	C₂³×C₃	1	1	yes	characteristic
37	C₂×Q₈	—	2	32	no	—
38	C₂×Q₈	—	2	24	no	—
39	C₂²×C₄	—	2	12	no	—
40	C₂²×C₄	—	2	12	no	—
41	C₂²×C₄	—	2	12	no	—
42	C₂²×C₄	C₂×C₃×C₄	1	6	yes	—
43	C₂²×C₄	C₃×D₄	1	12	yes	—
44	C₂²×C₄	C₃×Q₈	1	8	yes	complemented
45	C₂²×C₃	C₂×C₂²⋊C₄	1	3	yes	—
46	C₂²×C₃	C₄×Q₈	1	4	yes	—
47	C₂²×C₃	#120	1	4	yes	—
48	C₂²×C₃	C₂²⋊Q₈	1	12	yes	—
49	C₂²×C₃	#124	1	6	yes	—
50	C₂²×C₃	C₄⋊Q₈	1	6	yes	—
51	C₃×C₄	—	2	12	no	—
52	C₃×C₄	—	4	8	no	—
53	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
54	C₂³	C₂×C₃×D₄	1	6	yes	—
55	C₂³	C₂×C₃×Q₈	1	4	yes	—
56	C₂³	C₃×#41	1	4	yes	—
57	Q₈	—	2	32	no	—
58	C₂×C₄	—	2	12	no	—
59	C₂×C₄	—	2	24	no	—
60	C₂×C₄	—	2	24	no	—
61	C₂×C₄	—	4	4	no	—
62	C₂×C₄	—	4	12	no	—
63	C₂×C₄	C₃×C₂²⋊C₄	1	12	yes	—
64	C₂×C₃	#379	1	1	yes	characteristic
65	C₂×C₃	#391	1	6	yes	—
66	C₂×C₃	#393	1	4	yes	—
67	C₂×C₃	#395	1	4	yes	—
68	C₂²	C₂×C₃×C₂²⋊C₄	1	3	yes	—
69	C₂²	C₃×C₄×Q₈	1	4	yes	—
70	C₂²	C₃×#120	1	4	yes	—
71	C₂²	C₃×C₂²⋊Q₈	1	12	yes	—
72	C₂²	C₃×#124	1	6	yes	—
73	C₂²	C₃×C₄⋊Q₈	1	6	yes	—
74	C₄	—	2	12	no	—
75	C₄	—	4	8	no	—
76	C₃	#1446	1	1	yes	characteristic, direct product factor, Sylow
77	C₂	C₃×#379	1	1	yes	characteristic
78	C₂	C₃×#391	1	6	yes	—
79	C₂	C₃×#393	1	4	yes	—
80	C₂	C₃×#395	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #1446	C₃	direct (N × H)
5. C₂²×C₃×Q₈	C₄	semidirect
19. C₂²×C₃×C₄	Q₈	semidirect
21. C₂²×Q₈	C₃×C₄	semidirect
44. C₂²×C₄	C₃×Q₈	semidirect
76. C₃	#1446	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×Q₈	2
C₂×C₃×#95	2
#1446	3

Subgroups — C3×#1446 #72161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1446 #72161