Subgroups — C₃×#1830 #72545

Order 384.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#101	C₂	1	2	yes	maximal
3	C₃×#344	C₂	1	4	yes	maximal
4	#1830	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic
6	C₂×C₃×M₁₆	C₂²	1	4	yes	—
7	C₃×C₄×Q₈	—	2	4	no	—
8	C₃×#117	C₄	1	4	yes	—
9	C₃×#117	C₂²	1	2	yes	—
10	C₃×#101	—	2	4	no	—
11	#519	C₂×C₃	1	1	yes	characteristic
12	C₂×#101	C₂×C₃	1	2	yes	—
13	#344	C₂×C₃	1	4	yes	—
14	C₂×C₃×Q₈	—	2	4	no	—
15	C₂×C₃×Q₈	D₄	1	4	yes	—
16	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
17	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
18	C₃×M₁₆	—	2	4	no	—
19	C₃×M₁₆	—	2	4	no	—
20	C₂×C₃×C₈	—	2	4	no	—
21	C₃×C₄⋊C₄	—	2	4	no	—
22	C₃×C₄⋊C₄	—	2	2	no	—
23	C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
24	C₃×C₄²	—	2	4	no	—
25	C₃×C₄²	—	2	2	no	—
26	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic
27	C₂×M₁₆	C₂²×C₃	1	4	yes	—
28	C₄×Q₈	—	2	4	no	—
29	#117	C₃×C₄	1	4	yes	—
30	#117	C₂²×C₃	1	2	yes	—
31	#101	—	2	4	no	—
32	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
33	C₃×Q₈	—	2	8	no	—
34	C₂×C₃×C₄	—	2	4	no	—
35	C₂×C₃×C₄	—	2	4	no	—
36	C₂×C₃×C₄	C₂²⋊C₄	1	4	yes	—
37	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
38	C₂×C₃×C₄	#41	1	4	yes	—
39	C₃×C₈	—	4	4	no	—
40	C₂×Q₈	—	2	4	no	—
41	C₂×Q₈	C₃×D₄	1	4	yes	—
42	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
43	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
44	M₁₆	—	2	4	no	—
45	M₁₆	—	2	4	no	—
46	C₂×C₈	—	2	4	no	—
47	C₄⋊C₄	—	2	4	no	—
48	C₄⋊C₄	—	2	2	no	—
49	C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
50	C₄²	—	2	4	no	—
51	C₄²	—	2	2	no	—
52	C₂²×C₃	—	4	1	no	—
53	C₂²×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₃	#117	1	2	yes	—
55	C₃×C₄	—	2	4	no	—
56	C₃×C₄	—	4	4	no	—
57	C₃×C₄	#123	1	4	yes	—
58	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
59	Q₈	—	2	8	no	—
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	C₃×C₂²⋊C₄	1	4	yes	—
63	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
64	C₂×C₄	C₃×#41	1	4	yes	—
65	C₈	—	4	4	no	—
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	—	2	2	no	—
68	C₂×C₃	#381	1	1	yes	characteristic
69	C₂²	—	4	1	no	—
70	C₂²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
71	C₂²	C₃×#117	1	2	yes	—
72	C₄	—	2	4	no	—
73	C₄	—	4	4	no	—
74	C₄	C₃×#123	1	4	yes	—
75	C₃	#1830	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	2	1	no	—
77	C₂	—	2	2	no	—
78	C₂	C₃×#381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#381
commutator	C₂³	C₂²×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃
prime radical	C₂³×C₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1830	C₃	direct (N × H)
75. C₃	#1830	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×#519	2
C₂×C₃×#101	2
C₃×#344	2
#1830	3

Subgroups — C3×#1830 #72545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1830 #72545