Finite Group Databasebeta

← #46781107

Subgroups — #46781107

Order 33664.

322 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30681902C211yesmaximal, characteristic, complemented
2C2×C22⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
3#30681662C214yesmaximal, complemented
4C2×#121×C263C211yesmaximal, characteristic
5C2×#16862360—21no—
6C22×C263⋊C8—21no—
7C22⋊(C263⋊C8)—21no—
8C22⋊(C263⋊C8)—21no—
9C22⋊(C263⋊C8)C2212yes—
10C22⋊(C263⋊C8)C2212yes—
11C22×D4×C263C411yescharacteristic
12C22×D4×C263C412yes—
13C23×C4×C263C2211yescharacteristic
14#121×C263—21no—
15#121×C263—21no—
16#121×C263—21no—
17#121×C263—21no—
18C2×C4⋊C4×C263C411yescharacteristic
19C2×C22⋊C4×C263C2212yes—
20#16862360—42no—
21C2×C263⋊C8—22no—
22C2×C263⋊C8—22no—
23C2×C263⋊C8—42no—
24C24×C263C2×C411yescharacteristic
25C24×C263C2×C412yes—
26C2×D4×C263—22no—
27C2×D4×C263—22no—
28C2×D4×C263—21no—
29C2×D4×C263—21no—
30C2×D4×C263—42no—
31C2×D4×C263—44no—
32C22×C4×C263—42no—
33C22×C4×C263C2×C411yescharacteristic
34C22×C4×C263C2×C412yes—
35C22×C4×C263D411yescharacteristic
36C22×C4×C263D411yescharacteristic
37C22×C4×C263D411yescharacteristic
38C22×C4×C263D411yescharacteristic
39C22×C4×C263C2311yescharacteristic
40C4⋊C4×C263—21no—
41C4⋊C4×C263—21no—
42C22⋊C4×C263—22no—
43C22⋊C4×C263—22no—
44C263⋊C8—42no—
45C263⋊C8—42no—
46C23×C263—22no—
47C23×C263—22no—
48C23×C263—22no—
49C23×C263—24no—
50C23×C263—41no—
51C23×C263—42no—
52C23×C263—42no—
53C23×C263C22⋊C411yescharacteristic
54C23×C263C22⋊C411yescharacteristic
55C23×C263C22×C411yescharacteristic
56D4×C263—42no—
57D4×C263—44no—
58D4×C263—44no—
59D4×C263—42no—
60C2×C4×C263—22no—
61C2×C4×C263—22no—
62C2×C4×C263—22no—
63C2×C4×C263—22no—
64C2×C4×C263—41no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263—42no—
68C2×C4×C263C22⋊C411yescharacteristic
69C2×C4×C263C22⋊C411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C22×C263—21no—
73C22×C263—21no—
74C22×C263—21no—
75C22×C263—21no—
76C22×C263—21no—
77C22×C263—21no—
78C22×C263—21no—
79C22×C263—44no—
80C22×C263—42no—
81C22×C263—42no—
82C22×C263—42no—
83C22×C263—84no—
84C22×C263#10012yes—
85C22×C263C2×C22⋊C411yescharacteristic
86C22×C263#13112yes—
87C4×C263—21no—
88C4×C263—21no—
89C4×C263—21no—
90C4×C263—42no—
91C4×C263#9912yes—
92C2×C263—22no—
93C2×C263—22no—
94C2×C263—41no—
95C2×C263—82no—
96C2×C263#40811yescharacteristic
97C2×C263C2×#9911yescharacteristic
98C2×C263C2×#10011yescharacteristic
99C263#147111yescharacteristic, complemented, Sylow
100#1471—2631nomaximal, Sylow
101C2×#121D26311yescharacteristic
102#407—2631no—
103C2×C22⋊C8—2631no—
104#323—2634no—
105C22×D4Dic26311yescharacteristic
106C22×D4Dic26312yes—
107C23×C4C2×D26311yescharacteristic
108C2×M16—5261no—
109C22×C8—5261no—
110#121—21no—
111#121—21no—
112#121—21no—
113#121—21no—
114C2×C4⋊C4Dic26311yescharacteristic
115C2×C22⋊C4C2×D26312yes—
116C22⋊C8—2632no—
117C22⋊C8—2632no—
118C22⋊C8—5261no—
119C22⋊C8—5261no—
120C24C2×Dic26311yescharacteristic
121C24C2×Dic26312yes—
122C2×D4—22no—
123C2×D4—22no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—42no—
127C2×D4—44no—
128C22×C4—42no—
129C22×C4C2×Dic26311yescharacteristic
130C22×C4C2×Dic26312yes—
131C22×C4C22⋊D26311yescharacteristic
132C22×C4C22⋊D26311yescharacteristic
133C22×C4C22⋊D26311yescharacteristic
134C22×C4C22⋊D26311yescharacteristic
135C22×C4C22×D26311yescharacteristic
136M16—10522no—
137C2×C8—5262no—
138C2×C8—5262no—
139C2×C8—10522no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C23—22no—
145C23—22no—
146C23—22no—
147C23—24no—
148C23—41no—
149C23—42no—
150C23—42no—
151C23C22⋊Dic26311yescharacteristic
152C23C22⋊Dic26311yescharacteristic
153C23C22×Dic26311yescharacteristic
154D4—42no—
155D4—44no—
156D4—44no—
157D4—42no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4C22⋊Dic26311yescharacteristic
167C2×C4C22⋊Dic26311yescharacteristic
168C2×C4C2×C22⋊D26311yescharacteristic
169C2×C4C2×C22⋊D26311yescharacteristic
170C8—10522no—
171C8—10522no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—44no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—84no—
184C22#2255438712yes—
185C22C2×C22⋊Dic26311yescharacteristic
186C22#2255447712yes—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—42no—
191C4#2255438512yes—
192C2—22no—
193C2—22no—
194C2—41no—
195C2—82no—
196C2#3068190511yescharacteristic
197C2C2×#2255438511yescharacteristic
198C2C2×#2255438711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic263
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting, prime radicalC2×#121×C263C2
socleC22×C263C2×C22⋊C4
cosocleC22×C4×C263C23
hypercenterC2×#121D263
hypocenterC263#1471
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #30681902C2semidirect
2. C2×C22⋊(C263⋊C8)C2semidirect
3. #30681662C2semidirect
99. C263#1471semidirect

Maximal subgroups

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

subgroupindex
#306819022
C2×C22⋊(C263⋊C8)2
#306816622
C2×#121×C2632
#1471263