Finite Group Databasebeta

← #46781332

Subgroups — #46781332

Order 33664.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#30682467C211yesmaximal, characteristic
2#30681890C211yesmaximal, characteristic, complemented
3#97×D263C211yesmaximal, characteristic, complemented
4#30681679C211yesmaximal, characteristic, complemented
5#30681679C211yesmaximal, characteristic, complemented
6#30681678C211yesmaximal, characteristic, complemented
7#329×C263C211yesmaximal, characteristic, complemented
8C2×#16862359—21no—
9C2×C8×D263—21no—
10#22554463—21no—
11#22554462C2211yescharacteristic
12#22554452—21no—
13#22554446C411yescharacteristic
14#22554441C411yescharacteristic
15Q8×Dic263C411yescharacteristic
16D4×Dic263C411yescharacteristic
17(C22⋊D263)⋊C4—21no—
18#22554426—21no—
19C42×D263C2211yescharacteristic
20#22554381C2211yescharacteristic
21#22554381C2211yescharacteristic
22#22554380—21no—
23C8×Dic263—21no—
24#124×C263C2211yescharacteristic
25#97×C263C2211yescharacteristic
26#97×C263C2211yescharacteristic
27C2×C22⋊D263—21no—
28C22×Dic263—21no—
29C2×C4×D263C2×C411yescharacteristic
30C2×C4×D263D411yescharacteristic
31C2×C4×D263D411yescharacteristic
32#16862359—24no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C8×D263—24no—
36C4⋊Dic263—21no—
37C4⋊Dic263C2×C411yescharacteristic
38C4⋊Dic263C2×C411yescharacteristic
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42C22⋊Dic263—21no—
43C22⋊Dic263—21no—
44(C2×D263)⋊C4—21no—
45C4×Dic263—21no—
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263D411yescharacteristic
48C4×Dic263D411yescharacteristic
49C2×Q8×C263C2×C411yescharacteristic
50C2×D4×C263C2×C411yescharacteristic
51C2×C8×C263—21no—
52C2×C8×C263—21no—
53C22⋊C4×C263—21no—
54C22⋊C4×C263—21no—
55C42×C263C2311yescharacteristic
56C22×D263C22⋊C411yescharacteristic
57C22⋊D263—42no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—42no—
61C2×Dic263C22⋊C411yescharacteristic
62C2×Dic263C22⋊C411yescharacteristic
63C2×Dic263C22⋊C411yescharacteristic
64C4×D263—22no—
65C4×D263—22no—
66C4×D263—41no—
67C263⋊C8—22no—
68C263⋊C8—22no—
69C23×C263—21no—
70Q8×C263—41no—
71D4×C263—41no—
72C2×C4×C263—21no—
73C2×C4×C263C22×C411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C8×C263—22no—
77C8×C263—22no—
78C22×C263—41no—
79C22×C263—41no—
80C22×C263—41no—
81C22×C263C2×C22⋊C411yescharacteristic
82C2×D263—21no—
83C2×D263—21no—
84C2×D263#10412yes—
85C4×C263—21no—
86C4×C263—21no—
87C4×C263—21no—
88C4×C263—41no—
89Dic263—21no—
90Dic263—21no—
91Dic263—41no—
92Dic263—41no—
93Dic263#10412yes—
94C2×C263—81no—
95C2×C263#41311yescharacteristic
96C2×C263C2×#10411yescharacteristic
97C2×C263C2×#10411yescharacteristic
98D263—22no—
99C263#152411yescharacteristic, complemented, Sylow
100#1524—2631nomaximal, Sylow
101#529—2631no—
102C4×M16—2631no—
103C2×#97—2631no—
104#330—2631no—
105#330—2631no—
106#329—2631no—
107#329D26311yescharacteristic, complemented
108C2×M16—5261no—
109C22×C8—5261no—
110#126—5261no—
111#125—2631no—
112#124C2×D26311yescharacteristic
113#123—5261no—
114C22⋊Q8—2631no—
115#121—2631no—
116C4×Q8—2631no—
117C4×D4—2631no—
118C4×D4—5261no—
119#117—5261no—
120C2×C42—2631no—
121#97—2631no—
122#97—2631no—
123#97—5261no—
124#97C2×D26311yescharacteristic
125#97C2×D26311yescharacteristic
126C4×C8—5261no—
127C2×Q8C4×D26311yescharacteristic
128C2×D4—5261no—
129C2×D4C4×D26311yescharacteristic
130C22×C4—2631no—
131C22×C4—2631no—
132C22×C4—2631no—
133C22×C4—5261no—
134M16—5264no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—5264no—
138C2×C8—5261no—
139C2×C8—5261no—
140C4⋊C4—2631no—
141C4⋊C4—2631no—
142C4⋊C4—5261no—
143C4⋊C4—5261no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C22⋊C4—21no—
147C22⋊C4—21no—
148C22⋊C4—5261no—
149C22⋊C4—5261no—
150C22⋊C4—5261no—
151C42—2631no—
152C42—2631no—
153C42—2631no—
154C42—5261no—
155C42C22×D26311yescharacteristic
156C23—21no—
157C23—2631no—
158Q8—41no—
159D4—41no—
160D4—10522no—
161C2×C4—21no—
162C2×C4—2631no—
163C2×C4—2631no—
164C2×C4—2631no—
165C2×C4—5262no—
166C2×C4—5262no—
167C2×C4—5261no—
168C2×C4—5261no—
169C2×C4—10521no—
170C2×C4—10522no—
171C2×C4C2×C4×D26311yescharacteristic
172C2×C4D4×D26311yescharacteristic
173C2×C4D4×D26311yescharacteristic
174C8—22no—
175C8—22no—
176C8—5262no—
177C8—5262no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2632no—
182C22—5261no—
183C22—5261no—
184C22C22⋊C4×D26311yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—2632no—
190C4—5261no—
191C4—5261no—
192C4—10521no—
193C4—10521no—
194C2—81no—
195C2—5262no—
196C2#3068191911yescharacteristic
197C2#104×D26311yescharacteristic
198C2#104×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554441C4
cosocleC42×C263C23
hypercenter#329D263
hypocenterC263#1524
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #30681890C2semidirect
3. #97×D263C2semidirect
4. #30681679C2semidirect
5. #30681679C2semidirect
6. #30681678C2semidirect
7. #329×C263C2semidirect
99. C263#1524semidirect
107. #329D263semidirect

Maximal subgroups

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

subgroupindex
#306824672
#306818902
#97×D2632
#306816792
#306816782
#329×C2632
#1524263