Subgroups — #13056300

Order 1344.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#95	C₂	1	1	yes	maximal, characteristic
2	#10620670	C₂	1	3	yes	maximal
3	#10620670	C₂	1	3	yes	maximal
4	C₇⋊#401	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₄×C₇	C₂²	1	3	yes	—
6	C₂²×Dic₂₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₁	C₂²	1	3	yes	—
8	C₇×#95	D₃	1	1	yes	characteristic
9	C₇⋊#95	—	3	3	no	—
10	C₇⋊#95	—	3	3	no	—
11	C₃⋊#401	—	7	1	no	maximal, Hall
12	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
13	C₂×C₃×C₄×C₇	—	2	3	no	—
14	C₂×C₃×C₄×C₇	—	2	6	no	—
15	C₂×Dic₂₁	—	2	3	no	—
16	C₂×Dic₂₁	—	2	3	no	—
17	C₂×Dic₂₁	—	2	3	no	—
18	C₂×Dic₂₁	—	2	3	no	—
19	C₂²×C₄×C₇	C₂×D₃	1	3	yes	—
20	C₂²×Dic₇	—	3	1	no	—
21	C₂²×Dic₇	—	3	3	no	—
22	C₃×#95	D₇	1	1	yes	characteristic
23	C₃⋊#95	—	7	3	no	—
24	C₃⋊#95	—	7	3	no	—
25	C₂²×C₃×C₇	#41	1	3	yes	—
26	C₂²×C₃×C₇	#41	1	3	yes	—
27	C₂²×C₃×C₇	#41	1	1	yes	characteristic
28	C₃×C₄×C₇	—	4	3	no	—
29	Dic₂₁	—	4	1	no	—
30	Dic₂₁	—	4	3	no	—
31	#401	—	21	1	no	Sylow
32	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
33	C₂×C₄×C₇	—	2	3	no	—
34	C₂×C₄×C₇	—	2	6	no	—
35	C₂×Dic₇	—	6	3	no	—
36	C₂×Dic₇	—	6	3	no	—
37	C₂×Dic₇	—	6	3	no	—
38	C₂×Dic₇	—	6	3	no	—
39	C₂²×C₃×C₄	C₂×D₇	1	3	yes	—
40	C₂²×Dic₃	—	7	1	no	—
41	C₂²×Dic₃	—	7	3	no	—
42	C₂×C₃×C₇	#126	1	1	yes	characteristic
43	C₂×C₃×C₇	#126	1	3	yes	—
44	C₂×C₃×C₇	#126	1	3	yes	—
45	#95	—	21	3	no	—
46	#95	—	21	3	no	—
47	#95	D₂₁	1	1	yes	characteristic
48	C₂²×C₇	#235	1	3	yes	—
49	C₂²×C₇	#237	1	3	yes	—
50	C₂²×C₇	#239	1	1	yes	characteristic
51	C₄×C₇	—	4	3	no	—
52	Dic₇	—	12	1	no	—
53	Dic₇	—	12	3	no	—
54	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
55	C₂×C₃×C₄	—	2	3	no	—
56	C₂×C₃×C₄	—	2	6	no	—
57	C₂×Dic₃	—	14	3	no	—
58	C₂×Dic₃	—	14	3	no	—
59	C₂×Dic₃	—	14	3	no	—
60	C₂×Dic₃	—	14	3	no	—
61	C₃×C₇	#401	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₄	—	21	1	no	—
63	C₂²×C₄	—	21	3	no	—
64	C₂²×C₄	C₂×D₂₁	1	3	yes	—
65	C₂×C₇	#876	1	1	yes	characteristic
66	C₂×C₇	#879	1	3	yes	—
67	C₂×C₇	#898	1	3	yes	—
68	C₂²×C₃	#1157	1	3	yes	—
69	C₂²×C₃	#1159	1	3	yes	—
70	C₂²×C₃	#1161	1	1	yes	characteristic
71	C₃×C₄	—	4	3	no	—
72	Dic₃	—	28	1	no	—
73	Dic₃	—	28	3	no	—
74	C₂³	C₂²×D₂₁	1	1	yes	characteristic
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	6	no	—
77	C₂×C₄	—	42	3	no	—
78	C₂×C₄	—	42	3	no	—
79	C₂×C₄	—	42	3	no	—
80	C₂×C₄	—	42	3	no	—
81	C₇	C₃⋊#401	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₃	#6439	1	1	yes	characteristic
83	C₂×C₃	#6442	1	3	yes	—
84	C₂×C₃	#6461	1	3	yes	—
85	C₂²	#66728	1	3	yes	—
86	C₂²	#66730	1	3	yes	—
87	C₂²	#66732	1	1	yes	characteristic
88	C₄	—	4	3	no	—
89	C₄	—	84	1	no	—
90	C₄	—	84	3	no	—
91	C₃	C₇⋊#401	1	1	yes	characteristic, complemented, Sylow
92	C₂	#10621359	1	1	yes	characteristic
93	C₂	#10621362	1	3	yes	—
94	C₂	#10621381	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₁
commutator, socle, prime radical, cosocle	C₂³×C₃×C₇	C₂³
Fitting	C₃×C₇×#95	C₂
hypercenter	#95	D₂₁
hypocenter	C₃×C₇	#401
LCS	G ▷ C₂³×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
61. C₃×C₇	#401	semidirect
81. C₇	C₃⋊#401	semidirect
91. C₃	C₇⋊#401	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×#95	2
#10620670	2
C₇⋊#401	3
C₃⋊#401	7