Subgroups — C₃×#1829 #72544

Order 384.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#100	C₂	1	2	yes	maximal
3	C₃×#344	C₂	1	4	yes	maximal, complemented
4	#1829	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
6	C₂×C₃×M₁₆	C₂²	1	4	yes	—
7	C₃×C₄×D₄	—	2	4	no	—
8	C₃×#117	C₂²	1	2	yes	—
9	C₂×C₃×C₂²⋊C₄	C₄	1	4	yes	—
10	C₃×#100	—	2	4	no	—
11	#518	C₂×C₃	1	1	yes	characteristic
12	C₂×#100	C₂×C₃	1	2	yes	—
13	#344	C₂×C₃	1	4	yes	complemented
14	C₂⁴×C₃	C₂×C₄	1	2	yes	—
15	C₂×C₃×D₄	—	2	4	no	—
16	C₂×C₃×D₄	D₄	1	4	yes	—
17	C₂²×C₃×C₄	—	2	4	no	—
18	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
19	C₃×M₁₆	—	2	4	no	—
20	C₃×M₁₆	—	2	4	no	—
21	C₂×C₃×C₈	—	2	4	no	—
22	C₃×C₄⋊C₄	—	2	2	no	—
23	C₃×C₂²⋊C₄	—	2	4	no	—
24	C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
25	C₃×C₄²	—	2	2	no	—
26	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
27	C₂×M₁₆	C₂²×C₃	1	4	yes	—
28	C₄×D₄	—	2	4	no	—
29	#117	C₂²×C₃	1	2	yes	—
30	C₂×C₂²⋊C₄	C₃×C₄	1	4	yes	—
31	#100	—	2	4	no	—
32	C₂³×C₃	—	2	4	no	—
33	C₂³×C₃	—	8	2	no	—
34	C₂³×C₃	C₂²⋊C₄	1	4	yes	—
35	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
36	C₃×D₄	—	2	8	no	—
37	C₂×C₃×C₄	—	2	4	no	—
38	C₂×C₃×C₄	—	8	4	no	—
39	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
40	C₂×C₃×C₄	#41	1	4	yes	—
41	C₃×C₈	—	4	4	no	—
42	C₂⁴	C₂×C₃×C₄	1	2	yes	—
43	C₂×D₄	—	2	4	no	—
44	C₂×D₄	C₃×D₄	1	4	yes	—
45	C₂²×C₄	—	2	4	no	—
46	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
47	M₁₆	—	2	4	no	—
48	M₁₆	—	2	4	no	—
49	C₂×C₈	—	2	4	no	—
50	C₄⋊C₄	—	2	2	no	—
51	C₂²⋊C₄	—	2	4	no	—
52	C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
53	C₄²	—	2	2	no	—
54	C₂²×C₃	—	2	4	no	—
55	C₂²×C₃	—	4	1	no	—
56	C₂²×C₃	—	4	4	no	—
57	C₂²×C₃	—	8	4	no	—
58	C₂²×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₃	#117	1	2	yes	—
60	C₃×C₄	—	4	4	no	—
61	C₃×C₄	#123	1	4	yes	—
62	C₂³	—	2	4	no	—
63	C₂³	—	8	2	no	—
64	C₂³	C₃×C₂²⋊C₄	1	4	yes	—
65	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
66	D₄	—	2	8	no	—
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	—	8	4	no	—
69	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
70	C₂×C₄	C₃×#41	1	4	yes	—
71	C₈	—	4	4	no	—
72	C₂×C₃	—	2	1	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂×C₃	—	4	4	no	—
75	C₂×C₃	#381	1	1	yes	characteristic
76	C₂²	—	2	4	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	4	no	—
79	C₂²	—	8	4	no	—
80	C₂²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
81	C₂²	C₃×#117	1	2	yes	—
82	C₄	—	4	4	no	—
83	C₄	C₃×#123	1	4	yes	—
84	C₃	#1829	1	1	yes	characteristic, direct product factor, Sylow
85	C₂	—	2	1	no	—
86	C₂	—	2	2	no	—
87	C₂	—	4	4	no	—
88	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	C₂²×C₃×D₄	C₂²
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
3. C₃×#344	C₂	semidirect
4. #1829	C₃	direct (N × H)
13. #344	C₂×C₃	semidirect
84. C₃	#1829	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×#518	2
C₂×C₃×#100	2
C₃×#344	2
#1829	3

Subgroups — C3×#1829 #72544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1829 #72544