Group #13506387 — subgroups

Subgroups — #13506387

Order 1792.

806 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 331 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	C₂×#89455	C₂	1	4	yes	maximal
2	#11730752	C₂	1	2	yes	maximal
3	C₄×C₇×#97	C₂	1	1	yes	maximal, characteristic
4	#11727570	C₂	1	8	yes	maximal
5	C₂×#6433	C₂²	1	4	yes	—
6	C₂×C₇×#97	C₂²	1	4	yes	—
7	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
8	C₄³×C₇	C₂²	1	1	yes	characteristic
9	C₂×#6392	C₂²	1	8	yes	—
10	C₂×#6391	C₂²	1	8	yes	—
11	#89708	C₂²	1	4	yes	—
12	#89707	C₂²	1	4	yes	—
13	#89700	—	2	8	no	—
14	#89455	—	2	16	no	—
15	#33315	—	7	1	no	maximal, Sylow
16	C₂²×C₇×C₈	C₂³	1	4	yes	—
17	C₂×C₄²×C₇	D₄	1	4	yes	—
18	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₇	C₂³	1	2	yes	—
20	C₂×C₄⋊Dic₇	—	2	8	no	—
21	C₂×C₄⋊Dic₇	C₂³	1	8	yes	—
22	C₂×Dic₇⋊C₄	—	2	8	no	—
23	#6433	—	2	16	no	—
24	C₇×#97	Q₈	1	16	yes	—
25	C₄×C₇×C₈	D₄	1	8	yes	—
26	C₇⋊#95	—	2	8	no	—
27	#6392	—	2	16	no	—
28	#6391	—	2	16	no	—
29	C₂×#499	—	7	4	no	—
30	#2859	—	7	2	no	—
31	#1847	—	7	8	no	—
32	C₄×#97	D₇	1	1	yes	characteristic
33	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
34	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
35	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
36	C₂²×Dic₇	—	2	8	no	—
37	C₂×C₇×C₈	C₂×D₄	1	8	yes	—
38	C₂×C₇×C₈	C₂×Q₈	1	16	yes	—
39	C₄²×C₇	—	4	4	no	—
40	C₄²×C₇	C₂×D₄	1	4	yes	—
41	C₄²×C₇	C₂×Q₈	1	8	yes	—
42	C₄⋊Dic₇	—	2	16	no	—
43	C₄⋊Dic₇	—	4	16	no	—
44	Dic₇⋊C₄	—	4	16	no	—
45	C₂×#125	—	7	4	no	—
46	#499	—	14	16	no	—
47	C₂×#107	—	7	8	no	—
48	C₂×#106	—	7	8	no	—
49	C₂×#97	C₂×D₇	1	4	yes	—
50	C₂×C₄×C₈	C₂×D₇	1	2	yes	—
51	#389	—	14	8	no	—
52	#384	—	7	4	no	—
53	#382	—	7	4	no	—
54	C₄³	C₂×D₇	1	1	yes	characteristic
55	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
56	C₂×C₄×C₇	—	2	8	no	—
57	C₂×C₄×C₇	—	2	4	no	—
58	C₂×C₄×C₇	#127	1	4	yes	—
59	C₂×C₄×C₇	C₄⋊Q₈	1	8	yes	—
60	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
61	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
62	C₂×Dic₇	—	4	8	no	—
63	C₂×Dic₇	—	4	16	no	—
64	C₇×C₈	C₄⋊Q₈	1	16	yes	—
65	C₂²×C₈	C₂²×D₇	1	4	yes	—
66	#125	—	14	16	no	—
67	C₂×C₄⋊C₄	—	7	8	no	—
68	C₂×C₄⋊C₄	—	14	8	no	—
69	C₂×C₄⋊C₄	—	14	8	no	—
70	C₂×C₄²	D₂₈	1	4	yes	—
71	C₂×C₄²	C₂²×D₇	1	2	yes	—
72	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
73	#107	—	14	16	no	—
74	#106	—	14	16	no	—
75	#97	Dic₁₄	1	16	yes	—
76	C₄×C₈	D₂₈	1	8	yes	—
77	#95	—	14	8	no	—
78	C₂²×C₇	C₂×#127	1	1	yes	characteristic
79	C₂²×C₇	C₂×C₄⋊Q₈	1	2	yes	—
80	C₂²×C₇	#575	1	4	yes	—
81	C₄×C₇	—	2	4	no	—
82	C₄×C₇	—	2	8	no	—
83	C₄×C₇	C₂×C₄⋊Q₈	1	4	yes	—
84	Dic₇	—	8	8	no	—
85	C₂²×C₄	—	14	8	no	—
86	C₂²×C₄	C₂×D₂₈	1	4	yes	—
87	C₂²×C₄	C₂×D₂₈	1	2	yes	—
88	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
89	C₂×C₈	C₂×Dic₁₄	1	16	yes	—
90	C₂×C₈	C₂×D₂₈	1	8	yes	—
91	C₄⋊C₄	—	14	16	no	—
92	C₄⋊C₄	—	28	16	no	—
93	C₄⋊C₄	—	28	16	no	—
94	C₄²	—	4	4	no	—
95	C₄²	C₂×Dic₁₄	1	8	yes	—
96	C₄²	C₂×D₂₈	1	4	yes	—
97	C₂×C₇	#2868	1	1	yes	characteristic
98	C₂×C₇	#3150	1	2	yes	—
99	C₂×C₇	#3166	1	4	yes	—
100	C₂³	C₂²×D₂₈	1	1	yes	characteristic
101	C₂×C₄	—	2	8	no	—
102	C₂×C₄	—	2	4	no	—
103	C₂×C₄	—	28	8	no	—
104	C₂×C₄	—	28	16	no	—
105	C₂×C₄	#6432	1	8	yes	—
106	C₂×C₄	#6437	1	4	yes	—
107	C₂×C₄	C₂²×Dic₁₄	1	4	yes	—
108	C₂×C₄	C₂²×D₂₈	1	2	yes	—
109	C₈	#6432	1	16	yes	—
110	C₇	#33315	1	1	yes	characteristic, complemented, Sylow
111	C₂²	C₂×#6432	1	2	yes	—
112	C₂²	C₂×#6437	1	1	yes	characteristic
113	C₂²	#90439	1	4	yes	—
114	C₄	—	2	4	no	—
115	C₄	—	2	8	no	—
116	C₄	—	56	8	no	—
117	C₄	C₂×#6432	1	4	yes	—
118	C₂	#11730756	1	1	yes	characteristic
119	C₂	#11735944	1	2	yes	—
120	C₂	#11735952	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#89455

C₂

yes

maximal

#11730752

C₂

yes

maximal

C₄×C₇×#97

C₂

yes

maximal, characteristic

#11727570

C₂

yes

maximal

C₂×#6433

C₂²

yes

—

C₂×C₇×#97

C₂²

yes

—

C₂×C₄×C₇×C₈

C₂²

yes

—

C₄³×C₇

C₂²

yes

characteristic

C₂×#6392

C₂²

yes

—

C₂×#6391

C₂²

yes

—

#89708

C₂²

yes

—

#89707

C₂²

yes

—

—

—

—

C₂²×C₇×C₈

C₂³

yes

—

C₂×C₄²×C₇

D₄

yes

—

C₂×C₄²×C₇

C₂³

yes

characteristic

C₂×C₄²×C₇

C₂³

yes

—

C₂×C₄⋊Dic₇

—

C₂×C₄⋊Dic₇

C₂³

yes

—

C₂×Dic₇⋊C₄

—

#6433

—

C₇×#97

Q₈

yes

—

C₄×C₇×C₈

D₄

yes

—

—

—

—

—

—

—

C₄×#97

D₇

yes

characteristic

C₂²×C₄×C₇

C₂×D₄

yes

—

C₂²×C₄×C₇

C₂×D₄

yes

—

C₂²×C₄×C₇

C₂⁴

yes

characteristic

C₂²×Dic₇

—

C₂×C₇×C₈

C₂×D₄

yes

—

C₂×C₇×C₈

C₂×Q₈

yes

—

C₄²×C₇

—

C₄²×C₇

C₂×D₄

yes

—

C₄²×C₇

C₂×Q₈

yes

—

C₄⋊Dic₇

—

C₄⋊Dic₇

—

Dic₇⋊C₄

—

—

—

—

—

C₂×#97

C₂×D₇

yes

—

C₂×C₄×C₈

C₂×D₇

yes

—

#389

—

#384

—

#382

—

C₄³

C₂×D₇

yes

characteristic

C₂³×C₇

C₂²×D₄

yes

characteristic

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

#127

yes

—

C₂×C₄×C₇

C₄⋊Q₈

yes

—

C₂×C₄×C₇

C₂²×D₄

yes

—

C₂×C₄×C₇

C₂²×Q₈

yes

—

C₂×Dic₇

—

C₂×Dic₇

—

C₇×C₈

C₄⋊Q₈

yes

—

C₂²×C₈

C₂²×D₇

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

D₂₈

yes

—

C₂×C₄²

C₂²×D₇

yes

—

C₂×C₄²

C₂²×D₇

yes

—

—

Dic₁₄

yes

—

C₄×C₈

D₂₈

yes

—

#95

—

C₂²×C₇

C₂×#127

yes

characteristic

C₂²×C₇

C₂×C₄⋊Q₈

yes

—

C₂²×C₇

#575

yes

—

C₄×C₇

—

C₄×C₇

—

C₄×C₇

C₂×C₄⋊Q₈

yes

—

Dic₇

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₈

yes

—

C₂²×C₄

C₂×D₂₈

yes

—

C₂²×C₄

C₂³×D₇

yes

characteristic

C₂×C₈

C₂×Dic₁₄

yes

—

C₂×C₈

C₂×D₂₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×Dic₁₄

yes

—

C₄²

C₂×D₂₈

yes

—

C₂×C₇

#2868

yes

characteristic

C₂×C₇

#3150

yes

—

C₂×C₇

#3166

yes

—

100

C₂³

C₂²×D₂₈

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

#6432

yes

—

106

C₂×C₄

#6437

yes

—

107

C₂×C₄

C₂²×Dic₁₄

yes

—

108

C₂×C₄

C₂²×D₂₈

yes

—

109

C₈

#6432

yes

—

110

C₇

#33315

yes

characteristic, complemented, Sylow

111

C₂²

C₂×#6432

yes

—

112

C₂²

C₂×#6437

yes

characteristic

113

C₂²

#90439

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×#6432

yes

—

118

C₂

#11730756

yes

characteristic

119

C₂

#11735944

yes

—

120

C₂

#11735952

yes

—

	subgroup	G/H
center	C₂³	C₂²×D₂₈
commutator, cosocle	C₂²×C₄×C₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇
Fitting	C₄×C₇×#97	C₂
socle, prime radical	C₂³×C₇	C₂²×D₄
hypercenter	C₄×#97	D₇
hypocenter	C₇	#33315
LCS	G ▷ C₂²×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

subgroup

G/H

center

C₂³

C₂²×D₂₈

commutator, cosocle

C₂²×C₄×C₇

C₂⁴

Frattini

C₂²×C₄

C₂³×D₇

Fitting

C₄×C₇×#97

C₂

socle, prime radical

C₂³×C₇

C₂²×D₄

hypercenter

C₄×#97

D₇

hypocenter

C₇

#33315

LCS

G ▷ C₂²×C₄×C₇ ▷ C₂×C₇ ▷ C₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

N	H ≅ G/N	type
110. C₇	#33315	semidirect

H ≅ G/N

type

110. C₇

#33315

semidirect

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

subgroup	index
C₂×#89455	2
#11730752	2
C₄×C₇×#97	2
#11727570	2
#33315	7

subgroup

index

C₄×C₇×#97

Subgroups — #13506387

Conjugacy classes of subgroups

Complements

Maximal subgroups