Subgroups — C₃×#1342 #67902

Order 384.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#470	C₂	1	1	yes	maximal, characteristic
2	C₃×#349	C₂	1	1	yes	maximal, characteristic
3	C₃×#338	C₂	1	1	yes	maximal, characteristic
4	#1342	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₁₆	C₄	1	1	yes	characteristic
6	C₂×C₃×M₁₆	—	2	1	no	—
7	C₂×C₃×M₁₆	C₂²	1	1	yes	characteristic
8	C₃×C₂²⋊Q₈	—	2	1	no	—
9	C₃×M₃₂	—	2	1	no	—
10	C₃×#106	C₄	1	1	yes	characteristic
11	C₃×#103	—	2	1	no	—
12	#470	C₂×C₃	1	1	yes	characteristic
13	#349	C₂×C₃	1	1	yes	characteristic
14	#338	C₂×C₃	1	1	yes	characteristic
15	C₂×C₃×Q₈	—	2	1	no	—
16	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
17	C₃×Q₁₆	—	4	1	no	—
18	C₃×M₁₆	—	4	1	no	—
19	C₃×M₁₆	—	4	1	no	—
20	C₃×M₁₆	—	4	1	no	—
21	C₂×C₃×C₈	—	2	2	no	—
22	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₈	D₄	1	1	yes	characteristic
24	C₃×C₄⋊C₄	—	2	1	no	—
25	C₃×C₄⋊C₄	—	4	1	no	—
26	C₃×C₂²⋊C₄	—	4	1	no	—
27	C₃×C₁₆	—	4	1	no	—
28	C₂×Q₁₆	C₃×C₄	1	1	yes	characteristic
29	C₂×M₁₆	—	2	1	no	—
30	C₂×M₁₆	C₂²×C₃	1	1	yes	characteristic
31	C₂²⋊Q₈	—	2	1	no	—
32	M₃₂	—	2	1	no	—
33	#106	C₃×C₄	1	1	yes	characteristic
34	#103	—	2	1	no	—
35	C₂³×C₃	SD₁₆	1	1	yes	characteristic
36	C₃×Q₈	—	4	1	no	—
37	C₃×Q₈	—	4	1	no	—
38	C₂×C₃×C₄	—	2	1	no	—
39	C₂×C₃×C₄	—	2	1	no	—
40	C₂×C₃×C₄	—	4	1	no	—
41	C₂×C₃×C₄	—	4	1	no	—
42	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₃×C₄	D₈	1	1	yes	characteristic
44	C₃×C₈	—	2	1	no	—
45	C₃×C₈	—	2	1	no	—
46	C₃×C₈	—	4	2	no	—
47	C₂×Q₈	—	2	1	no	—
48	C₂²×C₄	C₃×D₄	1	1	yes	characteristic
49	Q₁₆	—	4	1	no	—
50	M₁₆	—	4	1	no	—
51	M₁₆	—	4	1	no	—
52	M₁₆	—	4	1	no	—
53	C₂×C₈	—	2	2	no	—
54	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂×C₈	C₃×D₄	1	1	yes	characteristic
56	C₄⋊C₄	—	2	1	no	—
57	C₄⋊C₄	—	4	1	no	—
58	C₂²⋊C₄	—	4	1	no	—
59	C₁₆	—	4	1	no	—
60	C₂²×C₃	—	2	1	no	—
61	C₂²×C₃	—	4	1	no	—
62	C₂²×C₃	#102	1	1	yes	characteristic
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	8	1	no	—
65	C₃×C₄	—	8	1	no	—
66	C₃×C₄	#99	1	1	yes	characteristic
67	C₃×C₄	#104	1	1	yes	characteristic
68	C₂³	C₃×SD₁₆	1	1	yes	characteristic
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄	C₃×D₈	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	4	2	no	—
80	C₂×C₃	—	2	1	no	—
81	C₂×C₃	—	4	1	no	—
82	C₂×C₃	#327	1	1	yes	characteristic
83	C₂²	—	2	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	C₃×#102	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	8	1	no	—
88	C₄	—	8	1	no	—
89	C₄	C₃×#99	1	1	yes	characteristic
90	C₄	C₃×#104	1	1	yes	characteristic
91	C₃	#1342	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	C₃×#327	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#327
commutator	C₂×C₈	C₂×C₃×C₄
Frattini, cosocle	C₂×M₁₆	C₂²×C₃
prime radical	C₂³×C₃	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1342	C₃	direct (N × H)
91. C₃	#1342	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×#470	2
C₃×#349	2
C₃×#338	2
#1342	3

Subgroups — C3×#1342 #67902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1342 #67902