Group #33261 — subgroups

Subgroups — #33261

Order 256.

303 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 303 conjugacy classes of subgroups — too many to draw. Only its 143 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	#2647	C₂	1	2	yes	maximal
2	#1944	C₂	1	2	yes	maximal
3	#1943	C₂	1	2	yes	maximal
4	#1942	C₂	1	2	yes	maximal
5	#1942	C₂	1	2	yes	maximal
6	#1846	C₂	1	1	yes	maximal, characteristic
7	#1845	C₂	1	1	yes	maximal, characteristic
8	#1836	C₂	1	2	yes	maximal
9	#1726	C₂	1	1	yes	maximal, characteristic
10	C₂×#107	C₂²	1	2	yes	—
11	C₂×#107	C₂²	1	2	yes	—
12	C₂×#107	C₂²	1	2	yes	—
13	C₂×#106	C₂²	1	2	yes	—
14	C₂×#97	C₂²	1	1	yes	characteristic
15	C₂×#97	C₂²	1	1	yes	characteristic
16	C₂×#97	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
20	#400	—	2	4	no	—
21	#398	—	2	4	no	—
22	#389	C₂²	1	4	yes	—
23	#389	C₂²	1	4	yes	—
24	#384	C₂²	1	2	yes	—
25	#382	C₂²	1	2	yes	—
26	#376	C₂²	1	1	yes	characteristic
27	#340	C₂²	1	4	yes	—
28	#340	C₂²	1	4	yes	—
29	C₂²×C₈	C₂³	1	1	yes	characteristic
30	C₂²×C₈	C₂³	1	1	yes	characteristic
31	C₂²×C₈	C₂³	1	1	yes	characteristic
32	C₂²×C₈	C₂³	1	1	yes	characteristic
33	C₂×C₄⋊C₄	—	2	4	no	—
34	C₂×C₄⋊C₄	—	2	4	no	—
35	C₂×C₄⋊C₄	—	2	4	no	—
36	C₂×C₄⋊C₄	C₂³	1	4	yes	—
37	C₂×C₄⋊C₄	C₂³	1	4	yes	—
38	C₂×C₄²	C₂³	1	1	yes	characteristic
39	C₂×C₄²	C₂³	1	1	yes	characteristic
40	C₂×C₄²	C₂³	1	1	yes	characteristic
41	#107	—	2	4	no	—
42	#107	—	2	4	no	—
43	#107	—	2	4	no	—
44	#106	—	2	4	no	—
45	#97	—	2	2	no	—
46	#97	—	2	2	no	—
47	#97	Q₈	1	4	yes	—
48	C₄×C₈	—	2	2	no	—
49	C₄×C₈	—	2	2	no	—
50	C₄×C₈	Q₈	1	4	yes	—
51	#95	—	2	4	no	—
52	#95	—	2	4	no	—
53	#95	—	2	4	no	—
54	#95	D₄	1	2	yes	—
55	#95	D₄	1	2	yes	—
56	C₂²×C₄	—	2	4	no	—
57	C₂²×C₄	—	2	4	no	—
58	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄	C₂×D₄	1	2	yes	—
60	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄	C₂×D₄	1	2	yes	—
62	C₂²×C₄	C₂⁴	1	1	yes	characteristic
63	C₂×C₈	—	2	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	—	2	1	no	—
67	C₂×C₈	C₂×Q₈	1	2	yes	—
68	C₂×C₈	C₂×Q₈	1	2	yes	—
69	C₂×C₈	C₂×Q₈	1	2	yes	—
70	C₂×C₈	C₂×Q₈	1	2	yes	—
71	C₂×C₈	#41	1	2	yes	—
72	C₂×C₈	#41	1	2	yes	—
73	C₂×C₈	#41	1	2	yes	—
74	C₂×C₈	#41	1	2	yes	—
75	C₄⋊C₄	—	2	4	no	—
76	C₄⋊C₄	—	2	4	no	—
77	C₄⋊C₄	—	2	4	no	—
78	C₄⋊C₄	—	2	4	no	—
79	C₄⋊C₄	—	8	4	no	—
80	C₄⋊C₄	—	8	4	no	—
81	C₄⋊C₄	—	8	4	no	—
82	C₄²	—	2	1	no	—
83	C₄²	—	2	1	no	—
84	C₄²	—	2	1	no	—
85	C₄²	—	2	1	no	—
86	C₄²	C₂×Q₈	1	2	yes	—
87	C₄²	C₂×Q₈	1	2	yes	—
88	C₂³	C₂²×D₄	1	1	yes	characteristic
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	4	4	no	—
99	C₂×C₄	—	4	4	no	—
100	C₂×C₄	—	4	4	no	—
101	C₂×C₄	—	4	4	no	—
102	C₂×C₄	—	4	4	no	—
103	C₂×C₄	—	4	4	no	—
104	C₂×C₄	C₄⋊Q₈	1	4	yes	—
105	C₂×C₄	C₂²×Q₈	1	1	yes	characteristic
106	C₂×C₄	C₂²×Q₈	1	1	yes	characteristic
107	C₂×C₄	C₂×#41	1	1	yes	characteristic
108	C₂×C₄	C₂×#41	1	1	yes	characteristic
109	C₂×C₄	C₂×#41	1	1	yes	characteristic
110	C₂×C₄	C₂×#41	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	2	2	no	—
113	C₈	#125	1	4	yes	—
114	C₈	#125	1	4	yes	—
115	C₂²	C₂×C₄⋊Q₈	1	1	yes	characteristic
116	C₂²	#532	1	1	yes	characteristic
117	C₂²	#532	1	1	yes	characteristic
118	C₂²	#576	1	2	yes	—
119	C₂²	#578	1	2	yes	—
120	C₄	—	2	4	no	—
121	C₄	—	4	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	4	1	no	—
124	C₄	—	8	4	no	—
125	C₄	—	8	4	no	—
126	C₄	C₂×#125	1	1	yes	characteristic
127	C₄	C₂×#125	1	1	yes	characteristic
128	C₄	#533	1	1	yes	characteristic
129	C₄	#533	1	1	yes	characteristic
130	C₂	#2859	1	1	yes	characteristic
131	C₂	#3164	1	2	yes	—
132	C₂	#3175	1	2	yes	—
133	C₂	#3176	1	1	yes	characteristic
134	C₂	#3177	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#2647

C₂

yes

maximal

#1944

C₂

yes

maximal

#1943

C₂

yes

maximal

#1942

C₂

yes

maximal

#1942

C₂

yes

maximal

#1846

C₂

yes

maximal, characteristic

#1845

C₂

yes

maximal, characteristic

#1836

C₂

yes

maximal

#1726

C₂

yes

maximal, characteristic

C₂×#107

C₂²

yes

—

C₂×#107

C₂²

yes

—

C₂×#107

C₂²

yes

—

C₂×#106

C₂²

yes

—

C₂×#97

C₂²

yes

characteristic

C₂×#97

C₂²

yes

characteristic

C₂×#97

C₂²

yes

characteristic

C₂×C₄×C₈

C₂²

yes

characteristic

C₂×C₄×C₈

C₂²

yes

characteristic

C₂×C₄×C₈

C₂²

yes

—

—

C₂²

yes

—

#389

C₂²

yes

—

#384

C₂²

yes

—

#382

C₂²

yes

—

#376

C₂²

yes

characteristic

#340

C₂²

yes

—

#340

C₂²

yes

—

C₂²×C₈

C₂³

yes

characteristic

C₂²×C₈

C₂³

yes

characteristic

C₂²×C₈

C₂³

yes

characteristic

C₂²×C₈

C₂³

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂³

yes

—

C₂×C₄⋊C₄

C₂³

yes

—

C₂×C₄²

C₂³

yes

characteristic

C₂×C₄²

C₂³

yes

characteristic

C₂×C₄²

C₂³

yes

—

—

—

—

—

—

Q₈

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Q₈

yes

—

—

—

—

D₄

yes

—

#95

D₄

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄

yes

characteristic

C₂²×C₄

C₂×D₄

yes

—

C₂²×C₄

C₂×D₄

yes

characteristic

C₂²×C₄

C₂×D₄

yes

—

C₂²×C₄

C₂⁴

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Q₈

yes

—

C₂×C₈

C₂×Q₈

yes

—

C₂×C₈

C₂×Q₈

yes

—

C₂×C₈

C₂×Q₈

yes

—

C₂×C₈

#41

yes

—

C₂×C₈

#41

yes

—

C₂×C₈

#41

yes

—

C₂×C₈

#41

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×Q₈

yes

—

C₄²

C₂×Q₈

yes

—

C₂³

C₂²×D₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₄⋊Q₈

yes

—

105

C₂×C₄

C₂²×Q₈

yes

characteristic

106

C₂×C₄

C₂²×Q₈

yes

characteristic

107

C₂×C₄

C₂×#41

yes

characteristic

108

C₂×C₄

C₂×#41

yes

characteristic

109

C₂×C₄

C₂×#41

yes

characteristic

110

C₂×C₄

C₂×#41

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

#125

yes

—

114

C₈

#125

yes

—

115

C₂²

C₂×C₄⋊Q₈

yes

characteristic

116

C₂²

#532

yes

characteristic

117

C₂²

#532

yes

characteristic

118

C₂²

#576

yes

—

119

C₂²

#578

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

C₂×#125

yes

characteristic

127

C₄

C₂×#125

yes

characteristic

128

C₄

#533

yes

characteristic

129

C₄

#533

yes

characteristic

130

C₂

#2859

yes

characteristic

131

C₂

#3164

yes

—

132

C₂

#3175

yes

—

133

C₂

#3176

yes

characteristic

134

C₂

#3177

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #376 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

subgroup

G/H

center, socle, prime radical

C₂³

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³ ◁ #376 ◁ G

LECS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

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

subgroup	index
#2647	2
#1944	2
#1943	2
#1942	2
#1846	2
#1845	2
#1836	2
#1726	2

subgroup

index

Subgroups — #33261

Conjugacy classes of subgroups

Maximal subgroups