Subgroups — C₃×#2103 #72818

Order 384.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#430	C₂	1	1	yes	maximal, characteristic
2	C₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₃×#344	C₂	1	2	yes	maximal
4	C₃×#341	C₂	1	2	yes	maximal
5	C₃×#338	C₂	1	1	yes	maximal, characteristic
6	#2103	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×M₁₆	C₂²	1	2	yes	—
8	C₂×C₃×M₁₆	C₂²	1	2	yes	—
9	C₂×C₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₃×#117	C₂²	1	1	yes	characteristic
12	C₃×#108	—	2	2	no	—
13	C₃×C₄⋊C₈	—	2	2	no	—
14	#430	C₂×C₃	1	1	yes	characteristic
15	#424	C₂×C₃	1	1	yes	characteristic
16	#344	C₂×C₃	1	2	yes	—
17	#341	C₂×C₃	1	2	yes	—
18	#338	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
20	C₃×M₁₆	—	2	2	no	—
21	C₃×M₁₆	—	2	2	no	—
22	C₃×M₁₆	—	2	2	no	—
23	C₃×M₁₆	—	2	2	no	—
24	C₃×M₁₆	—	2	2	no	—
25	C₂×C₃×C₈	—	2	1	no	—
26	C₂×C₃×C₈	—	2	2	no	—
27	C₂×C₃×C₈	—	2	2	no	—
28	C₂×C₃×C₈	—	2	2	no	—
29	C₂×C₃×C₈	D₄	1	2	yes	—
30	C₃×C₄⋊C₄	—	2	1	no	—
31	C₃×C₂²⋊C₄	Q₈	1	2	yes	—
32	C₃×C₄²	—	2	1	no	—
33	C₂×M₁₆	C₂²×C₃	1	2	yes	—
34	C₂×M₁₆	C₂²×C₃	1	2	yes	—
35	C₂×M₁₆	C₂²×C₃	1	1	yes	characteristic
36	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
37	#117	C₂²×C₃	1	1	yes	characteristic
38	#108	—	2	2	no	—
39	C₄⋊C₈	—	2	2	no	—
40	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₃×C₄	—	2	2	no	—
42	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
43	C₂×C₃×C₄	#41	1	2	yes	—
44	C₂×C₃×C₄	#41	1	2	yes	—
45	C₂×C₃×C₄	#41	1	1	yes	characteristic
46	C₃×C₈	—	2	2	no	—
47	C₃×C₈	—	4	1	no	—
48	C₃×C₈	—	4	2	no	—
49	C₃×C₈	—	4	2	no	—
50	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
51	M₁₆	—	2	2	no	—
52	M₁₆	—	2	2	no	—
53	M₁₆	—	2	2	no	—
54	M₁₆	—	2	2	no	—
55	M₁₆	—	2	2	no	—
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	—	2	2	no	—
59	C₂×C₈	—	2	2	no	—
60	C₂×C₈	C₃×D₄	1	2	yes	—
61	C₄⋊C₄	—	2	1	no	—
62	C₂²⋊C₄	C₃×Q₈	1	2	yes	—
63	C₄²	—	2	1	no	—
64	C₂²×C₃	—	4	1	no	—
65	C₂²×C₃	C₂²⋊Q₈	1	1	yes	characteristic
66	C₂²×C₃	#125	1	2	yes	—
67	C₃×C₄	—	4	2	no	—
68	C₃×C₄	#123	1	1	yes	characteristic
69	C₃×C₄	#124	1	1	yes	characteristic
70	C₃×C₄	#126	1	2	yes	—
71	C₂³	C₂×C₃×Q₈	1	1	yes	characteristic
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
74	C₂×C₄	C₃×#41	1	2	yes	—
75	C₂×C₄	C₃×#41	1	2	yes	—
76	C₂×C₄	C₃×#41	1	1	yes	characteristic
77	C₈	—	2	2	no	—
78	C₈	—	4	1	no	—
79	C₈	—	4	2	no	—
80	C₈	—	4	2	no	—
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	—	2	2	no	—
83	C₂×C₃	#400	1	1	yes	characteristic
84	C₂²	—	4	1	no	—
85	C₂²	C₃×C₂²⋊Q₈	1	1	yes	characteristic
86	C₂²	C₃×#125	1	2	yes	—
87	C₄	—	4	2	no	—
88	C₄	C₃×#123	1	1	yes	characteristic
89	C₄	C₃×#124	1	1	yes	characteristic
90	C₄	C₃×#126	1	2	yes	—
91	C₃	#2103	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	C₃×#400	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃
socle	C₂×C₃	#400
prime radical	C₂³×C₃	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
6. #2103	C₃	direct (N × H)
91. C₃	#2103	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×#430	2
C₃×#424	2
C₃×#344	2
C₃×#341	2
C₃×#338	2
#2103	3

Subgroups — C3×#2103 #72818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2103 #72818