Subgroups — C₃×#89307 #13051172

Order 1344.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#6389	C₂	1	1	yes	maximal, characteristic
3	C₃×#6386	C₂	1	1	yes	maximal, characteristic
4	#89307	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₄×Dic₇	C₄	1	1	yes	characteristic
7	C₂×C₃×C₇⋊C₈	C₄	1	1	yes	characteristic
8	C₃×C₇×C₁₆	C₄	1	2	yes	complemented
9	C₃×C₇⋊C₁₆	C₄	1	2	yes	complemented
10	C₇×M₃₂	C₂×C₃	1	1	yes	characteristic
11	#6389	C₂×C₃	1	1	yes	characteristic
12	#6386	C₂×C₃	1	1	yes	characteristic
13	C₃×#347	—	7	1	no	maximal, Hall
14	C₂×C₃×C₄×C₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×Dic₇	—	2	1	no	—
16	C₃×C₇×C₈	C₂×C₄	1	1	yes	characteristic
17	C₃×C₇×C₈	C₂×C₄	1	1	yes	characteristic
18	C₃×C₇⋊C₈	—	2	1	no	—
19	C₂×C₇×C₈	C₂²×C₃	1	1	yes	characteristic
20	C₄×Dic₇	C₃×C₄	1	1	yes	characteristic
21	C₂×C₇⋊C₈	C₃×C₄	1	1	yes	characteristic
22	C₇×C₁₆	C₃×C₄	1	2	yes	complemented
23	C₇⋊C₁₆	C₃×C₄	1	2	yes	complemented
24	C₃×M₃₂	—	7	1	no	—
25	C₃×M₃₂	D₇	1	1	yes	characteristic
26	C₃×#97	—	7	1	no	—
27	C₂²×C₃×C₇	M₁₆	1	1	yes	characteristic
28	C₃×C₄×C₇	C₄²	1	1	yes	characteristic
29	C₃×C₄×C₇	M₁₆	1	1	yes	characteristic
30	C₃×Dic₇	—	4	1	no	—
31	#347	—	7	1	no	Sylow
32	C₂×C₄×C₇	C₂×C₃×C₄	1	1	yes	characteristic
33	C₂×Dic₇	—	2	1	no	—
34	C₇×C₈	C₂×C₃×C₄	1	1	yes	characteristic
35	C₇×C₈	C₂×C₃×C₄	1	1	yes	characteristic
36	C₇⋊C₈	—	2	1	no	—
37	C₂×C₃×C₈	—	7	1	no	—
38	C₂×C₃×C₈	C₂×D₇	1	1	yes	characteristic
39	C₃×C₄²	—	7	1	no	—
40	C₃×C₁₆	—	7	2	no	—
41	C₃×C₁₆	Dic₇	1	2	yes	complemented
42	C₂×C₃×C₇	—	2	1	no	—
43	C₂×C₃×C₇	#97	1	1	yes	characteristic
44	M₃₂	—	7	1	no	—
45	M₃₂	C₃×D₇	1	1	yes	characteristic
46	#97	—	7	1	no	—
47	C₂²×C₇	C₃×M₁₆	1	1	yes	characteristic
48	C₄×C₇	C₃×C₄²	1	1	yes	characteristic
49	C₄×C₇	C₃×M₁₆	1	1	yes	characteristic
50	Dic₇	—	4	1	no	—
51	C₂×C₃×C₄	—	14	1	no	—
52	C₂×C₃×C₄	C₄×D₇	1	1	yes	characteristic
53	C₃×C₈	—	14	1	no	—
54	C₃×C₈	C₄×D₇	1	1	yes	characteristic
55	C₃×C₈	C₂×Dic₇	1	1	yes	characteristic
56	C₃×C₇	#347	1	1	yes	characteristic, complemented, Hall
57	C₂×C₈	—	7	1	no	—
58	C₂×C₈	C₂×C₃×D₇	1	1	yes	characteristic
59	C₄²	—	7	1	no	—
60	C₁₆	—	7	2	no	—
61	C₁₆	C₃×Dic₇	1	2	yes	complemented
62	C₂×C₇	—	2	1	no	—
63	C₂×C₇	C₃×#97	1	1	yes	characteristic
64	C₂²×C₃	#1131	1	1	yes	characteristic
65	C₃×C₄	—	28	1	no	—
66	C₃×C₄	#1131	1	1	yes	characteristic
67	C₃×C₄	C₄×Dic₇	1	1	yes	characteristic
68	C₂×C₄	—	14	1	no	—
69	C₂×C₄	C₃×C₄×D₇	1	1	yes	characteristic
70	C₈	—	14	1	no	—
71	C₈	C₃×C₄×D₇	1	1	yes	characteristic
72	C₈	C₂×C₃×Dic₇	1	1	yes	characteristic
73	C₇	C₃×#347	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	#6389	1	1	yes	characteristic
76	C₂²	C₃×#1131	1	1	yes	characteristic
77	C₄	—	28	1	no	—
78	C₄	C₃×#1131	1	1	yes	characteristic
79	C₄	C₃×C₄×Dic₇	1	1	yes	characteristic
80	C₃	#89307	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	—	2	1	no	—
82	C₂	C₃×#6389	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₄×Dic₇
commutator	C₄×C₇	C₃×C₄²
Frattini	C₂×C₈	C₂×C₃×D₇
Fitting	C₃×C₇×M₃₂	C₂
socle	C₂×C₃×C₇	#97
prime radical	C₂²×C₃×C₇	M₁₆
cosocle	C₂×C₇×C₈	C₂²×C₃
hypercenter	C₃×M₃₂	D₇
hypocenter	C₇	C₃×#347
LCS	G ▷ C₄×C₇ ▷ C₇
UCS	C₁ ◁ C₃×C₄ ◁ C₃×M₃₂

Complements

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

N	H ≅ G/N	type
4. #89307	C₃	direct (N × H)
8. C₃×C₇×C₁₆	C₄	semidirect
9. C₃×C₇⋊C₁₆	C₄	semidirect
22. C₇×C₁₆	C₃×C₄	semidirect
23. C₇⋊C₁₆	C₃×C₄	semidirect
41. C₃×C₁₆	Dic₇	semidirect
56. C₃×C₇	#347	semidirect
61. C₁₆	C₃×Dic₇	semidirect
73. C₇	C₃×#347	semidirect
80. C₃	#89307	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×C₇×M₃₂	2
C₃×#6389	2
C₃×#6386	2
#89307	3
C₃×#347	7

Subgroups — C3×#89307 #13051172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89307 #13051172