Subgroups — C₃×#89284 #13051149

Order 1344.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#107	C₂	1	1	yes	maximal, characteristic
2	C₃×#6392	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#89284	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₇×C₄⋊C₄	—	2	1	no	—
7	C₃×C₄⋊Dic₇	—	2	1	no	—
8	C₃×C₇⋊C₁₆	C₄	1	2	yes	complemented
9	C₇×#107	C₂×C₃	1	1	yes	characteristic
10	#6392	C₂×C₃	1	1	yes	characteristic
11	C₂×C₇⋊C₁₆	C₂×C₃	1	1	yes	characteristic
12	C₃×#366	—	7	1	no	maximal, Hall
13	C₂×C₃×C₄×C₇	—	4	1	no	—
14	C₂×C₃×C₄×C₇	D₄	1	1	yes	characteristic
15	C₂×C₃×Dic₇	—	4	1	no	—
16	C₃×C₇×C₈	C₂×C₄	1	1	yes	characteristic
17	C₃×C₇×C₈	Q₈	1	1	yes	characteristic
18	C₂×C₇×C₈	C₂²×C₃	1	1	yes	characteristic
19	C₇×C₄⋊C₄	—	2	1	no	—
20	C₄⋊Dic₇	—	2	1	no	—
21	C₇⋊C₁₆	C₃×C₄	1	2	yes	complemented
22	C₂×C₃×C₁₆	—	7	1	no	—
23	C₃×#107	—	7	1	no	—
24	C₃×#107	D₇	1	1	yes	characteristic
25	C₂²×C₃×C₇	D₈	1	1	yes	characteristic
26	C₃×C₄×C₇	—	8	1	no	—
27	C₃×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
28	C₃×C₄×C₇	Q₁₆	1	1	yes	characteristic
29	C₃×Dic₇	—	8	1	no	—
30	#366	—	7	1	no	Sylow
31	C₂×C₄×C₇	—	4	1	no	—
32	C₂×C₄×C₇	C₃×D₄	1	1	yes	characteristic
33	C₂×Dic₇	—	4	1	no	—
34	C₇×C₈	C₂×C₃×C₄	1	1	yes	characteristic
35	C₇×C₈	C₃×Q₈	1	1	yes	characteristic
36	C₂×C₃×C₈	C₂×D₇	1	1	yes	characteristic
37	C₃×C₄⋊C₄	—	2	1	no	—
38	C₃×C₄⋊C₄	—	14	1	no	—
39	C₃×C₁₆	—	7	2	no	—
40	C₂×C₃×C₇	#107	1	1	yes	characteristic
41	C₂×C₃×C₇	D₁₆	1	1	yes	characteristic
42	C₂×C₃×C₇	Q₃₂	1	1	yes	characteristic
43	C₂×C₁₆	—	7	1	no	—
44	#107	—	7	1	no	—
45	#107	C₃×D₇	1	1	yes	characteristic
46	C₂²×C₇	C₃×D₈	1	1	yes	characteristic
47	C₄×C₇	—	8	1	no	—
48	C₄×C₇	C₃×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇	C₃×Q₁₆	1	1	yes	characteristic
50	Dic₇	—	8	1	no	—
51	C₂×C₃×C₄	—	4	1	no	—
52	C₂×C₃×C₄	—	28	1	no	—
53	C₂×C₃×C₄	C₂²⋊D₇	1	1	yes	characteristic
54	C₃×C₈	Dic₁₄	1	1	yes	characteristic
55	C₃×C₈	C₄×D₇	1	1	yes	characteristic
56	C₃×C₇	#366	1	1	yes	characteristic, complemented, Hall
57	C₂×C₈	C₂×C₃×D₇	1	1	yes	characteristic
58	C₄⋊C₄	—	2	1	no	—
59	C₄⋊C₄	—	14	1	no	—
60	C₁₆	—	7	2	no	—
61	C₂×C₇	C₃×#107	1	1	yes	characteristic
62	C₂×C₇	C₃×D₁₆	1	1	yes	characteristic
63	C₂×C₇	C₃×Q₃₂	1	1	yes	characteristic
64	C₂²×C₃	#1141	1	1	yes	characteristic
65	C₃×C₄	—	8	1	no	—
66	C₃×C₄	—	56	1	no	—
67	C₃×C₄	Dic₇⋊C₄	1	1	yes	characteristic
68	C₃×C₄	#1144	1	1	yes	characteristic
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	28	1	no	—
71	C₂×C₄	C₃×C₂²⋊D₇	1	1	yes	characteristic
72	C₈	C₃×Dic₁₄	1	1	yes	characteristic
73	C₈	C₃×C₄×D₇	1	1	yes	characteristic
74	C₇	C₃×#366	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₃	#6381	1	1	yes	characteristic
76	C₂×C₃	#6400	1	1	yes	characteristic
77	C₂×C₃	#6403	1	1	yes	characteristic
78	C₂²	C₃×#1141	1	1	yes	characteristic
79	C₄	—	8	1	no	—
80	C₄	—	56	1	no	—
81	C₄	C₃×Dic₇⋊C₄	1	1	yes	characteristic
82	C₄	C₃×#1144	1	1	yes	characteristic
83	C₃	#89284	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	C₃×#6381	1	1	yes	characteristic
85	C₂	C₃×#6400	1	1	yes	characteristic
86	C₂	C₃×#6403	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#1141
commutator	C₇×C₈	C₂×C₃×C₄
Frattini	C₂×C₈	C₂×C₃×D₇
Fitting	C₃×C₇×#107	C₂
socle, prime radical	C₂²×C₃×C₇	D₈
cosocle	C₂×C₇×C₈	C₂²×C₃
hypercenter	C₃×#107	D₇
hypocenter	C₇	C₃×#366
LCS	G ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#107

Complements

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

N	H ≅ G/N	type
4. #89284	C₃	direct (N × H)
8. C₃×C₇⋊C₁₆	C₄	semidirect
21. C₇⋊C₁₆	C₃×C₄	semidirect
56. C₃×C₇	#366	semidirect
74. C₇	C₃×#366	semidirect
83. C₃	#89284	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×#107	2
C₃×#6392	2
C₂×C₃×C₇⋊C₁₆	2
#89284	3
C₃×#366	7

Subgroups — C3×#89284 #13051149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89284 #13051149