Subgroups — C₃×#89471 #13055132

Order 1344.

244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₂₈	C₂	1	4	yes	maximal
2	C₃×#6432	C₂	1	2	yes	maximal
3	C₃×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
4	#89471	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×Dic₁₄	C₂²	1	4	yes	—
6	C₂×C₃×C₇×C₈	C₂²	1	2	yes	—
7	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic
8	C₃×C₄⋊Dic₇	—	2	4	no	—
9	C₃×Dic₂₈	—	2	8	no	—
10	C₂×Dic₂₈	C₂×C₃	1	4	yes	—
11	#6432	C₂×C₃	1	2	yes	—
12	C₄×C₇×C₈	C₂×C₃	1	1	yes	characteristic
13	C₃×#494	—	7	1	no	maximal, Hall
14	C₂×C₃×C₄×C₇	D₄	1	2	yes	—
15	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
16	C₂×C₃×Dic₇	—	2	4	no	—
17	C₃×Dic₁₄	—	2	8	no	—
18	C₃×C₇×C₈	D₄	1	4	yes	—
19	C₂×Dic₁₄	C₂²×C₃	1	4	yes	—
20	C₂×C₇×C₈	C₂²×C₃	1	2	yes	—
21	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
22	C₄⋊Dic₇	—	2	4	no	—
23	Dic₂₈	—	2	8	no	—
24	C₂×C₃×Q₁₆	—	7	4	no	—
25	C₃×C₄⋊Q₈	—	7	2	no	—
26	C₃×C₄×C₈	D₇	1	1	yes	characteristic
27	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
28	C₃×C₄×C₇	Q₁₆	1	4	yes	complemented
29	C₃×C₄×C₇	C₂×D₄	1	2	yes	—
30	C₃×Dic₇	—	4	4	no	—
31	#494	—	7	1	no	Sylow
32	C₂×C₄×C₇	C₃×D₄	1	2	yes	—
33	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
34	C₂×Dic₇	—	2	4	no	—
35	Dic₁₄	—	2	8	no	—
36	C₇×C₈	C₃×D₄	1	4	yes	—
37	C₂×C₃×Q₈	—	7	4	no	—
38	C₃×Q₁₆	—	14	8	no	—
39	C₂×C₃×C₈	C₂×D₇	1	2	yes	—
40	C₃×C₄⋊C₄	—	14	4	no	—
41	C₃×C₄²	C₂×D₇	1	1	yes	characteristic
42	C₂×C₃×C₇	#127	1	1	yes	characteristic
43	C₂×C₃×C₇	C₂×Q₁₆	1	2	yes	—
44	C₂×Q₁₆	—	7	4	no	—
45	C₄⋊Q₈	—	7	2	no	—
46	C₄×C₈	C₃×D₇	1	1	yes	characteristic
47	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
48	C₄×C₇	C₃×Q₁₆	1	4	yes	complemented
49	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
50	Dic₇	—	4	4	no	—
51	C₃×Q₈	—	14	8	no	—
52	C₂×C₃×C₄	—	14	4	no	—
53	C₂×C₃×C₄	D₂₈	1	2	yes	—
54	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
55	C₃×C₈	D₂₈	1	4	yes	—
56	C₃×C₇	#494	1	1	yes	characteristic, complemented, Hall
57	C₂×Q₈	—	7	4	no	—
58	Q₁₆	—	14	8	no	—
59	C₂×C₈	C₂×C₃×D₇	1	2	yes	—
60	C₄⋊C₄	—	14	4	no	—
61	C₄²	C₂×C₃×D₇	1	1	yes	characteristic
62	C₂×C₇	C₃×#127	1	1	yes	characteristic
63	C₂×C₇	C₂×C₃×Q₁₆	1	2	yes	—
64	C₂²×C₃	C₂×D₂₈	1	1	yes	characteristic
65	C₃×C₄	—	28	4	no	—
66	C₃×C₄	Dic₂₈	1	4	yes	complemented
67	C₃×C₄	C₂×D₂₈	1	2	yes	—
68	Q₈	—	14	8	no	—
69	C₂×C₄	—	14	4	no	—
70	C₂×C₄	C₃×D₂₈	1	2	yes	—
71	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
72	C₈	C₃×D₂₈	1	4	yes	—
73	C₇	C₃×#494	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	#6437	1	1	yes	characteristic
75	C₂×C₃	C₂×Dic₂₈	1	2	yes	—
76	C₂²	C₂×C₃×D₂₈	1	1	yes	characteristic
77	C₄	—	28	4	no	—
78	C₄	C₃×Dic₂₈	1	4	yes	complemented
79	C₄	C₂×C₃×D₂₈	1	2	yes	—
80	C₃	#89471	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	C₃×#6437	1	1	yes	characteristic
82	C₂	C₂×C₃×Dic₂₈	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₂₈
commutator, cosocle	C₂×C₄×C₇	C₂³×C₃
Frattini	C₂×C₄	C₂²×C₃×D₇
Fitting	C₃×C₄×C₇×C₈	C₂
socle, prime radical	C₂²×C₃×C₇	C₂×D₄
hypercenter	C₃×C₄×C₈	D₇
hypocenter	C₇	C₃×#494
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #89471	C₃	direct (N × H)
28. C₃×C₄×C₇	Q₁₆	semidirect
48. C₄×C₇	C₃×Q₁₆	semidirect
56. C₃×C₇	#494	semidirect
66. C₃×C₄	Dic₂₈	semidirect
73. C₇	C₃×#494	semidirect
78. C₄	C₃×Dic₂₈	semidirect
80. C₃	#89471	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×Dic₂₈	2
C₃×#6432	2
C₃×C₄×C₇×C₈	2
#89471	3
C₃×#494	7

Subgroups — C3×#89471 #13055132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89471 #13055132