Subgroups — C₃×#1333 #67893

Order 384.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
4	#1333	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×D₈	C₄	1	1	yes	characteristic
6	C₃×C₄×D₄	—	2	1	no	—
7	C₂×C₃×C₁₆	—	2	1	no	—
8	C₃×#107	C₄	1	1	yes	characteristic
9	C₃×C₄⋊C₈	—	2	1	no	—
10	C₃×#102	—	2	1	no	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	C₄×D₈	C₂×C₃	1	1	yes	characteristic
13	#346	C₂×C₃	1	1	yes	characteristic, complemented
14	#334	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₄	—	2	1	no	—
16	C₂²×C₃×C₄	—	4	1	no	—
17	C₃×D₈	—	2	1	no	—
18	C₃×D₈	C₈	1	2	yes	complemented
19	C₂×C₃×C₈	—	4	1	no	—
20	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃×C₈	D₄	1	1	yes	characteristic
22	C₃×C₄⋊C₄	—	2	1	no	—
23	C₃×C₂²⋊C₄	—	4	1	no	—
24	C₃×C₄²	D₄	1	1	yes	characteristic
25	C₃×C₁₆	—	2	2	no	—
26	C₂×D₈	C₃×C₄	1	1	yes	characteristic
27	C₄×D₄	—	2	1	no	—
28	C₂×C₁₆	—	2	1	no	—
29	#107	C₃×C₄	1	1	yes	characteristic
30	C₄⋊C₈	—	2	1	no	—
31	#102	—	2	1	no	—
32	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
33	C₂³×C₃	—	4	1	no	—
34	C₃×D₄	—	2	2	no	—
35	C₃×D₄	—	4	1	no	—
36	C₂×C₃×C₄	—	4	1	no	—
37	C₂×C₃×C₄	—	8	2	no	—
38	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₃×C₄	D₈	1	1	yes	characteristic
40	C₂×C₃×C₄	SD₁₆	1	1	yes	characteristic
41	C₃×C₈	—	2	1	no	—
42	C₃×C₈	—	8	1	no	—
43	C₃×C₈	C₂×C₈	1	1	yes	characteristic
44	C₃×C₈	M₁₆	1	1	yes	characteristic
45	C₂×D₄	—	2	1	no	—
46	C₂²×C₄	—	4	1	no	—
47	D₈	—	2	1	no	—
48	D₈	C₃×C₈	1	2	yes	complemented
49	C₂×C₈	—	4	1	no	—
50	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
51	C₂×C₈	C₃×D₄	1	1	yes	characteristic
52	C₄⋊C₄	—	2	1	no	—
53	C₂²⋊C₄	—	4	1	no	—
54	C₄²	C₃×D₄	1	1	yes	characteristic
55	C₁₆	—	2	2	no	—
56	C₂²×C₃	—	4	2	no	—
57	C₂²×C₃	—	8	1	no	—
58	C₂²×C₃	—	8	1	no	—
59	C₂²×C₃	#102	1	1	yes	characteristic
60	C₃×C₄	—	2	1	no	—
61	C₃×C₄	—	2	1	no	—
62	C₃×C₄	—	8	1	no	—
63	C₃×C₄	C₂²⋊C₈	1	1	yes	characteristic
64	C₃×C₄	#104	1	1	yes	characteristic
65	C₂³	—	4	1	no	—
66	D₄	—	2	2	no	—
67	D₄	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	8	2	no	—
70	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄	C₃×D₈	1	1	yes	characteristic
72	C₂×C₄	C₃×SD₁₆	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	8	1	no	—
75	C₈	C₂×C₃×C₈	1	1	yes	characteristic
76	C₈	C₃×M₁₆	1	1	yes	characteristic
77	C₂×C₃	—	8	2	no	—
78	C₂×C₃	D₄⋊C₈	1	1	yes	characteristic
79	C₂×C₃	#360	1	1	yes	characteristic
80	C₂×C₃	#361	1	1	yes	characteristic
81	C₂²	—	4	2	no	—
82	C₂²	—	8	1	no	—
83	C₂²	—	8	1	no	—
84	C₂²	C₃×#102	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	1	no	—
87	C₄	—	8	1	no	—
88	C₄	C₃×C₂²⋊C₈	1	1	yes	characteristic
89	C₄	C₃×#104	1	1	yes	characteristic
90	C₃	#1333	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	—	8	2	no	—
92	C₂	C₃×D₄⋊C₈	1	1	yes	characteristic
93	C₂	C₃×#360	1	1	yes	characteristic
94	C₂	C₃×#361	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	#102
commutator	C₈	C₂×C₃×C₈
Frattini, cosocle	C₄×C₈	C₂²×C₃
prime radical	C₂×C₃×D₈	C₄
LCS	G ▷ 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
2. C₃×#346	C₂	semidirect
3. C₃×#334	C₂	semidirect
4. #1333	C₃	direct (N × H)
13. #346	C₂×C₃	semidirect
14. #334	C₂×C₃	semidirect
18. C₃×D₈	C₈	semidirect
48. D₈	C₃×C₈	semidirect
90. C₃	#1333	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×C₄×D₈	2
C₃×#346	2
C₃×#334	2
#1333	3

Subgroups — C3×#1333 #67893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1333 #67893