Subgroups — C₃×#2255 #72970

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₃×#499	C₂	1	1	yes	maximal, characteristic
3	C₃×#367	C₂	1	2	yes	maximal
4	C₃×#366	C₂	1	2	yes	maximal
5	C₃×#346	C₂	1	1	yes	maximal, characteristic
6	#2255	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×C₄⋊Q₈	—	2	1	no	—
8	C₃×#125	—	2	1	no	—
9	C₂×C₃×C₁₆	C₂²	1	2	yes	—
10	C₃×#107	—	2	1	no	—
11	C₃×#107	C₂²	1	1	yes	characteristic
12	C₃×#107	C₂²	1	2	yes	—
13	C₃×#107	C₂²	1	1	yes	characteristic
14	C₃×#106	—	2	1	no	—
15	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
16	#500	C₂×C₃	1	1	yes	characteristic
17	#499	C₂×C₃	1	1	yes	characteristic
18	#367	C₂×C₃	1	2	yes	—
19	#366	C₂×C₃	1	2	yes	—
20	#346	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×Q₈	—	4	1	no	—
22	C₂×C₃×C₈	D₄	1	1	yes	characteristic
23	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
24	C₃×C₄⋊C₄	—	2	1	no	—
25	C₃×C₄⋊C₄	—	2	1	no	—
26	C₃×C₄⋊C₄	—	2	2	no	—
27	C₃×C₄⋊C₄	—	4	1	no	—
28	C₃×C₄⋊C₄	—	4	1	no	—
29	C₃×C₄⋊C₄	—	4	1	no	—
30	C₃×C₄²	D₄	1	1	yes	characteristic
31	C₃×C₁₆	Q₈	1	4	yes	complemented
32	C₄⋊Q₈	—	2	1	no	—
33	#125	—	2	1	no	—
34	C₂×C₁₆	C₂²×C₃	1	2	yes	—
35	#107	—	2	1	no	—
36	#107	C₂²×C₃	1	1	yes	characteristic
37	#107	C₂²×C₃	1	2	yes	—
38	#107	C₂²×C₃	1	1	yes	characteristic
39	#106	—	2	1	no	—
40	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
41	C₃×Q₈	—	8	2	no	—
42	C₂×C₃×C₄	—	4	1	no	—
43	C₂×C₃×C₄	—	4	1	no	—
44	C₂×C₃×C₄	—	4	2	no	—
45	C₂×C₃×C₄	D₈	1	1	yes	characteristic
46	C₂×C₃×C₄	D₈	1	1	yes	characteristic
47	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
48	C₃×C₈	Q₁₆	1	2	yes	—
49	C₃×C₈	C₂×Q₈	1	2	yes	—
50	C₂×Q₈	—	4	1	no	—
51	C₂×C₈	C₃×D₄	1	1	yes	characteristic
52	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
53	C₄⋊C₄	—	2	1	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	2	no	—
56	C₄⋊C₄	—	4	1	no	—
57	C₄⋊C₄	—	4	1	no	—
58	C₄⋊C₄	—	4	1	no	—
59	C₄²	C₃×D₄	1	1	yes	characteristic
60	C₁₆	C₃×Q₈	1	4	yes	complemented
61	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
62	C₃×C₄	—	2	1	no	—
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	8	1	no	—
65	C₃×C₄	—	8	2	no	—
66	C₃×C₄	—	8	1	no	—
67	C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
68	C₃×C₄	C₂×Q₁₆	1	1	yes	characteristic
69	Q₈	—	8	2	no	—
70	C₂×C₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	C₃×D₈	1	1	yes	characteristic
74	C₂×C₄	C₃×D₈	1	1	yes	characteristic
75	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
76	C₈	C₃×Q₁₆	1	2	yes	—
77	C₈	C₂×C₃×Q₈	1	2	yes	—
78	C₂×C₃	#500	1	1	yes	characteristic
79	C₂×C₃	#509	1	1	yes	characteristic
80	C₂×C₃	#510	1	1	yes	characteristic
81	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	8	2	no	—
85	C₄	—	8	1	no	—
86	C₄	—	8	1	no	—
87	C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
88	C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
89	C₃	#2255	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	C₃×#500	1	1	yes	characteristic
91	C₂	C₃×#509	1	1	yes	characteristic
92	C₂	C₃×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
6. #2255	C₃	direct (N × H)
31. C₃×C₁₆	Q₈	semidirect
60. C₁₆	C₃×Q₈	semidirect
89. C₃	#2255	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×#500	2
C₃×#499	2
C₃×#367	2
C₃×#366	2
C₃×#346	2
#2255	3

Subgroups — C3×#2255 #72970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2255 #72970