Group #2514 — subgroups

Subgroups — #2514

Order 128.

186 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 96 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	#401	C₂	1	2	yes	maximal
2	#400	C₂	1	2	yes	maximal
3	#391	C₂	1	1	yes	maximal, characteristic
4	#391	C₂	1	1	yes	maximal, characteristic
5	#391	C₂	1	1	yes	maximal, characteristic
6	#389	C₂	1	1	yes	maximal, characteristic
7	#387	C₂	1	2	yes	maximal
8	#383	C₂	1	2	yes	maximal
9	#382	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₄²	C₂²	1	1	yes	characteristic
20	C₂×C₄²	C₂²	1	1	yes	characteristic
21	C₂×C₄²	C₂²	1	2	yes	—
22	C₂×C₄²	C₂²	1	1	yes	characteristic
23	#95	C₂²	1	1	yes	characteristic
24	#95	C₂²	1	2	yes	—
25	#95	C₂²	1	1	yes	characteristic
26	#95	C₂²	1	2	yes	—
27	#95	C₂²	1	2	yes	—
28	#95	C₂²	1	2	yes	—
29	#95	C₂²	1	2	yes	—
30	#95	C₂²	1	2	yes	—
31	#95	C₂²	1	2	yes	—
32	#95	C₂²	1	2	yes	—
33	#95	C₂²	1	2	yes	—
34	#95	C₂²	1	2	yes	—
35	C₂×Q₈	—	2	2	no	—
36	C₂×Q₈	—	2	2	no	—
37	C₂×Q₈	—	2	2	no	—
38	C₂²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₄	C₂³	1	2	yes	—
40	C₂²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₄	C₂³	1	1	yes	characteristic
42	C₂²×C₄	C₂³	1	2	yes	—
43	C₂²×C₄	C₂³	1	1	yes	characteristic
44	C₂²×C₄	C₂³	1	2	yes	—
45	C₂²×C₄	C₂³	1	2	yes	—
46	C₂²×C₄	C₂³	1	1	yes	characteristic
47	C₂²×C₄	C₂³	1	1	yes	characteristic
48	C₂²×C₄	C₂³	1	1	yes	characteristic
49	C₄⋊C₄	—	2	2	no	—
50	C₄⋊C₄	—	2	2	no	—
51	C₄⋊C₄	—	2	4	no	—
52	C₄⋊C₄	—	2	2	no	—
53	C₄⋊C₄	—	2	2	no	—
54	C₄⋊C₄	—	2	2	no	—
55	C₄²	—	2	2	no	—
56	C₄²	—	2	2	no	—
57	C₄²	—	2	4	no	—
58	C₄²	—	2	2	no	—
59	C₂³	C₂⁴	1	1	yes	characteristic
60	Q₈	—	4	4	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	2	no	—
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	#41	1	2	yes	—
90	C₂×C₄	#41	1	2	yes	—
91	C₂×C₄	#41	1	2	yes	—
92	C₂×C₄	#41	1	2	yes	—
93	C₂×C₄	#41	1	2	yes	—
94	C₂²	C₂×#41	1	1	yes	characteristic
95	C₂²	C₂×#41	1	1	yes	characteristic
96	C₂²	C₂×#41	1	1	yes	characteristic
97	C₂²	C₂×#41	1	1	yes	characteristic
98	C₂²	C₂×#41	1	1	yes	characteristic
99	C₂²	2₋¹⁺⁴	1	1	yes	characteristic
100	C₂²	2₋¹⁺⁴	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	2	2	no	—
103	C₄	—	4	2	no	—
104	C₄	—	4	2	no	—
105	C₄	—	4	1	no	—
106	C₄	—	4	1	no	—
107	C₄	—	4	1	no	—
108	C₄	—	4	1	no	—
109	C₄	—	4	2	no	—
110	C₄	—	4	2	no	—
111	C₄	#126	1	4	yes	—
112	C₂	C₂×#126	1	1	yes	characteristic
113	C₂	#529	1	1	yes	characteristic
114	C₂	#541	1	1	yes	characteristic
115	C₂	#552	1	1	yes	characteristic
116	C₂	#556	1	1	yes	characteristic
117	C₂	#556	1	1	yes	characteristic
118	C₂	#556	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#401

C₂

yes

maximal

#400

C₂

yes

maximal

#391

C₂

yes

maximal, characteristic

#391

C₂

yes

maximal, characteristic

#391

C₂

yes

maximal, characteristic

#389

C₂

yes

maximal, characteristic

#387

C₂

yes

maximal

#383

C₂

yes

maximal

#382

C₂

yes

maximal, characteristic

C₄×C₄⋊C₄

C₂

yes

maximal, characteristic

C₄×C₄⋊C₄

C₂

yes

maximal, characteristic

C₂²×Q₈

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

—

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

—

C₂×C₄²

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

—

#95

C₂²

yes

characteristic

#95

C₂²

yes

—

#95

C₂²

yes

—

#95

C₂²

yes

—

#95

C₂²

yes

—

#95

C₂²

yes

—

#95

C₂²

yes

—

#95

C₂²

yes

—

#95

C₂²

yes

—

#95

C₂²

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

—

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

—

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

—

C₂²×C₄

C₂³

yes

—

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂⁴

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#41

yes

—

C₂×C₄

#41

yes

—

C₂×C₄

#41

yes

—

C₂×C₄

#41

yes

—

C₂×C₄

#41

yes

—

C₂²

C₂×#41

yes

characteristic

C₂²

C₂×#41

yes

characteristic

C₂²

C₂×#41

yes

characteristic

C₂²

C₂×#41

yes

characteristic

C₂²

C₂×#41

yes

characteristic

C₂²

2₋¹⁺⁴

yes

characteristic

100

C₂²

2₋¹⁺⁴

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#126

yes

—

112

C₂

C₂×#126

yes

characteristic

113

C₂

#529

yes

characteristic

114

C₂

#541

yes

characteristic

115

C₂

#552

yes

characteristic

116

C₂

#556

yes

characteristic

117

C₂

#556

yes

characteristic

118

C₂

#556

yes

characteristic

	subgroup	G/H
center, commutator, Frattini, socle, prime radical, cosocle	C₂³	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

subgroup

G/H

center, commutator, Frattini, socle, prime radical, cosocle

C₂³

C₂⁴

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³ ◁ G

LECS

G ▷ C₂³ ▷ C₁

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

subgroup	index
#401	2
#400	2
#391	2
#389	2
#387	2
#383	2
#382	2
C₄×C₄⋊C₄	2

subgroup

index

C₄×C₄⋊C₄

Subgroups — #2514

Conjugacy classes of subgroups

Maximal subgroups