Subgroups — C₃×#89455 #13055116

Order 1344.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6433	C₂	1	2	yes	maximal
2	C₃×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#6392	C₂	1	2	yes	maximal
4	C₃×#6391	C₂	1	2	yes	maximal
5	#89455	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
8	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊Dic₇	C₂²	1	4	yes	—
10	C₃×Dic₇⋊C₄	—	2	4	no	—
11	#6433	C₂×C₃	1	2	yes	—
12	C₄×C₇×C₈	C₂×C₃	1	1	yes	characteristic
13	#6392	C₂×C₃	1	2	yes	—
14	#6391	C₂×C₃	1	2	yes	—
15	C₃×#499	—	7	1	no	maximal, Hall
16	C₂×C₃×C₄×C₇	D₄	1	2	yes	—
17	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
18	C₂×C₃×Dic₇	—	2	4	no	—
19	C₃×C₇×C₈	Q₈	1	2	yes	—
20	C₃×C₇×C₈	Q₈	1	2	yes	—
21	C₂×C₇×C₈	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₇×C₈	C₂²×C₃	1	1	yes	characteristic
23	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
24	C₄⋊Dic₇	C₂²×C₃	1	4	yes	—
25	Dic₇⋊C₄	—	2	4	no	—
26	C₃×#125	—	7	2	no	—
27	C₃×#107	—	7	2	no	—
28	C₃×#106	—	7	2	no	—
29	C₃×C₄×C₈	D₇	1	1	yes	characteristic
30	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
31	C₃×C₄×C₇	—	2	2	no	—
32	C₃×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
33	C₃×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
34	C₃×Dic₇	—	4	4	no	—
35	#499	—	7	1	no	Sylow
36	C₂×C₄×C₇	C₃×D₄	1	2	yes	—
37	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
38	C₂×Dic₇	—	2	4	no	—
39	C₇×C₈	C₃×Q₈	1	2	yes	—
40	C₇×C₈	C₃×Q₈	1	2	yes	—
41	C₂×C₃×C₈	C₂×D₇	1	1	yes	characteristic
42	C₂×C₃×C₈	C₂×D₇	1	1	yes	characteristic
43	C₃×C₄⋊C₄	—	7	4	no	—
44	C₃×C₄⋊C₄	—	14	4	no	—
45	C₃×C₄²	C₂×D₇	1	1	yes	characteristic
46	C₂×C₃×C₇	C₄⋊Q₈	1	1	yes	characteristic
47	C₂×C₃×C₇	#135	1	2	yes	—
48	#125	—	7	2	no	—
49	#107	—	7	2	no	—
50	#106	—	7	2	no	—
51	C₄×C₈	C₃×D₇	1	1	yes	characteristic
52	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
53	C₄×C₇	—	2	2	no	—
54	C₄×C₇	C₂×C₃×Q₈	1	1	yes	characteristic
55	C₄×C₇	C₂×C₃×Q₈	1	1	yes	characteristic
56	Dic₇	—	4	4	no	—
57	C₂×C₃×C₄	—	14	4	no	—
58	C₂×C₃×C₄	D₂₈	1	2	yes	—
59	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
60	C₃×C₈	Dic₁₄	1	2	yes	—
61	C₃×C₈	Dic₁₄	1	2	yes	—
62	C₃×C₇	#499	1	1	yes	characteristic, complemented, Hall
63	C₂×C₈	C₂×C₃×D₇	1	1	yes	characteristic
64	C₂×C₈	C₂×C₃×D₇	1	1	yes	characteristic
65	C₄⋊C₄	—	7	4	no	—
66	C₄⋊C₄	—	14	4	no	—
67	C₄²	C₂×C₃×D₇	1	1	yes	characteristic
68	C₂×C₇	C₃×C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₇	C₃×#135	1	2	yes	—
70	C₂²×C₃	C₂×D₂₈	1	1	yes	characteristic
71	C₃×C₄	—	2	2	no	—
72	C₃×C₄	—	28	4	no	—
73	C₃×C₄	C₂×Dic₁₄	1	1	yes	characteristic
74	C₃×C₄	C₂×Dic₁₄	1	1	yes	characteristic
75	C₂×C₄	—	14	4	no	—
76	C₂×C₄	C₃×D₂₈	1	2	yes	—
77	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
78	C₈	C₃×Dic₁₄	1	2	yes	—
79	C₈	C₃×Dic₁₄	1	2	yes	—
80	C₇	C₃×#499	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	#6432	1	1	yes	characteristic
82	C₂×C₃	#6467	1	2	yes	—
83	C₂²	C₂×C₃×D₂₈	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	28	4	no	—
86	C₄	C₂×C₃×Dic₁₄	1	1	yes	characteristic
87	C₄	C₂×C₃×Dic₁₄	1	1	yes	characteristic
88	C₃	#89455	1	1	yes	characteristic, direct product factor, Sylow
89	C₂	C₃×#6432	1	1	yes	characteristic
90	C₂	C₃×#6467	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×#499
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
5. #89455	C₃	direct (N × H)
62. C₃×C₇	#499	semidirect
80. C₇	C₃×#499	semidirect
88. C₃	#89455	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×#6433	2
C₃×C₄×C₇×C₈	2
C₃×#6392	2
C₃×#6391	2
#89455	3
C₃×#499	7

Subgroups — C3×#89455 #13055116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89455 #13055116