Group #13187799 — subgroups

Subgroups — C₇×#10583 #13187799

Order 1792.

406 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2844	C₂	1	1	yes	maximal, characteristic
2	C₇×#1847	C₂	1	3	yes	maximal
3	C₇×#1295	C₂	1	3	yes	maximal
4	C₂×C₇×#107	—	2	3	no	—
5	C₂×C₇×#106	—	2	3	no	—
6	C₂×C₇×#97	C₂²	1	3	yes	—
7	C₇×#400	—	2	3	no	—
8	C₇×#395	—	2	3	no	—
9	C₇×#384	C₂²	1	1	yes	characteristic
10	C₇×#382	C₂²	1	3	yes	—
11	#10583	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₇×Q₈	—	2	1	no	—
13	C₂²×C₇×C₈	—	2	3	no	—
14	C₂×C₇×C₄⋊C₄	—	2	3	no	—
15	C₂×C₇×C₄⋊C₄	—	2	3	no	—
16	C₂×C₇×C₄⋊C₄	D₄	1	3	yes	—
17	C₂×C₇×C₄⋊C₄	D₄	1	3	yes	—
18	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
19	C₇×#107	—	4	6	no	—
20	C₇×#106	—	4	6	no	—
21	C₇×#97	—	2	3	no	—
22	C₇×#97	Q₈	1	6	yes	complemented
23	C₇×#95	—	2	3	no	—
24	C₇×#95	—	2	1	no	—
25	C₇×#95	—	2	6	no	—
26	#2844	C₂×C₇	1	1	yes	characteristic
27	#1847	C₂×C₇	1	3	yes	—
28	#1295	C₂×C₇	1	3	yes	—
29	C₂×C₇×Q₈	—	8	3	no	—
30	C₂²×C₄×C₇	—	2	3	no	—
31	C₂²×C₄×C₇	—	2	3	no	—
32	C₂²×C₄×C₇	—	4	1	no	—
33	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
34	C₂×C₇×C₈	—	2	6	no	—
35	C₂×C₇×C₈	—	2	6	no	—
36	C₂×C₇×C₈	—	2	6	no	—
37	C₇×C₄⋊C₄	—	4	3	no	—
38	C₇×C₄⋊C₄	—	4	3	no	—
39	C₇×C₄⋊C₄	—	4	3	no	—
40	C₇×C₄⋊C₄	—	4	3	no	—
41	C₇×C₄⋊C₄	—	8	3	no	—
42	C₄²×C₇	C₂×Q₈	1	3	yes	—
43	C₄²×C₇	#41	1	1	yes	characteristic
44	C₂×#107	—	2	3	no	—
45	C₂×#106	—	2	3	no	—
46	C₂×#97	C₂²×C₇	1	3	yes	—
47	#400	—	2	3	no	—
48	#395	—	2	3	no	—
49	#384	C₂²×C₇	1	1	yes	characteristic
50	#382	C₂²×C₇	1	3	yes	—
51	C₂³×C₇	#120	1	1	yes	characteristic
52	C₇×Q₈	—	8	4	no	—
53	C₂×C₄×C₇	—	2	3	no	—
54	C₂×C₄×C₇	—	2	3	no	—
55	C₂×C₄×C₇	—	4	3	no	—
56	C₂×C₄×C₇	—	4	3	no	—
57	C₂×C₄×C₇	—	4	6	no	—
58	C₂×C₄×C₇	—	4	6	no	—
59	C₂×C₄×C₇	—	8	3	no	—
60	C₂×C₄×C₇	C₂²⋊Q₈	1	3	yes	—
61	C₂×C₄×C₇	C₄⋊Q₈	1	3	yes	—
62	C₇×C₈	—	2	12	no	—
63	C₂²×Q₈	—	2	1	no	—
64	C₂²×C₈	—	2	3	no	—
65	C₂×C₄⋊C₄	—	2	3	no	—
66	C₂×C₄⋊C₄	—	2	3	no	—
67	C₂×C₄⋊C₄	C₇×D₄	1	3	yes	—
68	C₂×C₄⋊C₄	C₇×D₄	1	3	yes	—
69	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
70	#107	—	4	6	no	—
71	#106	—	4	6	no	—
72	#97	—	2	3	no	—
73	#97	C₇×Q₈	1	6	yes	complemented
74	#95	—	2	3	no	—
75	#95	—	2	1	no	—
76	#95	—	2	6	no	—
77	C₂²×C₇	#395	1	1	yes	characteristic
78	C₂²×C₇	#453	1	3	yes	—
79	C₂²×C₇	#456	1	3	yes	—
80	C₄×C₇	—	2	3	no	—
81	C₄×C₇	—	2	3	no	—
82	C₄×C₇	—	8	3	no	—
83	C₄×C₇	—	8	3	no	—
84	C₄×C₇	—	16	1	no	—
85	C₂×Q₈	—	8	3	no	—
86	C₂²×C₄	—	2	3	no	—
87	C₂²×C₄	—	2	3	no	—
88	C₂²×C₄	—	4	1	no	—
89	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
90	C₂×C₈	—	2	6	no	—
91	C₂×C₈	—	2	6	no	—
92	C₂×C₈	—	2	6	no	—
93	C₄⋊C₄	—	4	3	no	—
94	C₄⋊C₄	—	4	3	no	—
95	C₄⋊C₄	—	4	3	no	—
96	C₄⋊C₄	—	4	3	no	—
97	C₄⋊C₄	—	8	3	no	—
98	C₄²	C₂×C₇×Q₈	1	3	yes	—
99	C₄²	C₇×#41	1	1	yes	characteristic
100	C₂×C₇	#1655	1	1	yes	characteristic
101	C₂×C₇	#1660	1	3	yes	—
102	C₂×C₇	#2060	1	3	yes	—
103	C₂³	C₇×#120	1	1	yes	characteristic
104	Q₈	—	8	4	no	—
105	C₂×C₄	—	2	3	no	—
106	C₂×C₄	—	2	3	no	—
107	C₂×C₄	—	4	3	no	—
108	C₂×C₄	—	4	3	no	—
109	C₂×C₄	—	4	6	no	—
110	C₂×C₄	—	4	6	no	—
111	C₂×C₄	—	8	3	no	—
112	C₂×C₄	C₇×C₂²⋊Q₈	1	3	yes	—
113	C₂×C₄	C₇×C₄⋊Q₈	1	3	yes	—
114	C₈	—	2	12	no	—
115	C₇	#10583	1	1	yes	characteristic, direct product factor, Sylow
116	C₂²	C₇×#395	1	1	yes	characteristic
117	C₂²	C₇×#453	1	3	yes	—
118	C₂²	C₇×#456	1	3	yes	—
119	C₄	—	2	3	no	—
120	C₄	—	2	3	no	—
121	C₄	—	8	3	no	—
122	C₄	—	8	3	no	—
123	C₄	—	16	1	no	—
124	C₂	C₇×#1655	1	1	yes	characteristic
125	C₂	C₇×#1660	1	3	yes	—
126	C₂	C₇×#2060	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇×#2844

C₂

yes

maximal, characteristic

C₇×#1847

C₂

yes

maximal

C₇×#1295

C₂

yes

maximal

C₂×C₇×#107

—

C₂×C₇×#106

—

C₂×C₇×#97

C₂²

yes

—

C₇×#400

—

C₇×#395

—

C₇×#384

C₂²

yes

characteristic

C₇×#382

C₂²

yes

—

#10583

C₇

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₇×Q₈

—

C₂²×C₇×C₈

—

C₂×C₇×C₄⋊C₄

—

C₂×C₇×C₄⋊C₄

—

C₂×C₇×C₄⋊C₄

D₄

yes

—

C₂×C₇×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₇

C₂³

yes

characteristic

C₇×#107

—

C₇×#106

—

C₇×#97

—

C₇×#97

Q₈

yes

complemented

C₇×#95

—

C₇×#95

—

C₇×#95

—

#2844

C₂×C₇

yes

characteristic

#1847

C₂×C₇

yes

—

#1295

C₂×C₇

yes

—

C₂×C₇×Q₈

—

C₂²×C₄×C₇

—

C₂²×C₄×C₇

—

C₂²×C₄×C₇

—

C₂²×C₄×C₇

C₂×D₄

yes

—

C₂×C₇×C₈

—

C₂×C₇×C₈

—

C₂×C₇×C₈

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₇×C₄⋊C₄

—

C₄²×C₇

C₂×Q₈

yes

—

C₄²×C₇

yes

—

—

C₂×#97

C₂²×C₇

yes

—

#400

—

#395

—

#384

C₂²×C₇

yes

characteristic

#382

C₂²×C₇

yes

—

C₂³×C₇

#120

yes

characteristic

C₇×Q₈

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₇

C₄⋊Q₈

yes

—

C₇×C₈

—

C₂²×Q₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₇×D₄

yes

—

C₂×C₄⋊C₄

C₇×D₄

yes

—

C₂×C₄²

C₂³×C₇

yes

—

—

—

C₇×Q₈

yes

—

—

—

C₂²×C₇

#395

yes

characteristic

C₂²×C₇

#453

yes

—

C₂²×C₇

#456

yes

—

C₄×C₇

—

C₄×C₇

—

C₄×C₇

—

C₄×C₇

—

C₄×C₇

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₇×D₄

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×C₇×Q₈

yes

—

C₄²

C₇×#41

yes

characteristic

100

C₂×C₇

#1655

yes

characteristic

101

C₂×C₇

#1660

yes

—

102

C₂×C₇

#2060

yes

—

103

C₂³

C₇×#120

yes

characteristic

104

Q₈

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₇×C₂²⋊Q₈

yes

—

113

C₂×C₄

C₇×C₄⋊Q₈

yes

—

114

C₈

—

115

C₇

#10583

yes

characteristic, direct product factor, Sylow

116

C₂²

C₇×#395

yes

characteristic

117

C₂²

C₇×#453

yes

—

118

C₂²

C₇×#456

yes

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₂

C₇×#1655

yes

characteristic

125

C₂

C₇×#1660

yes

—

126

C₂

C₇×#2060

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₇

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₇

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇ ◁ G

N	H ≅ G/N	type
11. #10583	C₇	direct (N × H)
22. C₇×#97	Q₈	semidirect
73. #97	C₇×Q₈	semidirect
115. C₇	#10583	direct (N × H)

H ≅ G/N

type

11. #10583

C₇

direct (N × H)

22. C₇×#97

Q₈

semidirect

73. #97

C₇×Q₈

semidirect

115. C₇

#10583

direct (N × H)

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

subgroup	index
C₇×#2844	2
C₇×#1847	2
C₇×#1295	2
#10583	7

subgroup

index

Subgroups — C₇×#10583 #13187799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C7×#10583 #13187799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#10583 #13187799