Finite Group Databasebeta

← #46781343

Subgroups — #46781343

Order 33664.

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

normal subgroups only

This group has 264 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#124×D263C211yesmaximal, characteristic
2#30681993C211yesmaximal, characteristic, complemented
3#30681890C211yesmaximal, characteristic, complemented
4#30681678C211yesmaximal, characteristic, complemented
5#30681677C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic, complemented
7#329×C263C211yesmaximal, characteristic, complemented
8C2×Q8×D263C411yescharacteristic
9C2×D4×D263C411yescharacteristic
10C2×#16862359—21no—
11#22554459C411yescharacteristic
12#22554458C2211yescharacteristic
13#22554457C411yescharacteristic
14#22554456—21no—
15#22554456—21no—
16C22⋊C4×D263—21no—
17C22⋊C4×D263—21no—
18C42×D263C2211yescharacteristic
19Dic263⋊C8—21no—
20(C2×D263)⋊C8—21no—
21#22554381C2211yescharacteristic, complemented
22#22554381C2211yescharacteristic, complemented
23C8×Dic263—21no—
24#124×C263C2211yescharacteristic
25#97×C263C2211yescharacteristic, complemented
26#97×C263C2211yescharacteristic, complemented
27C23×D263—21no—
28C2×Dic526—21no—
29C2×Dic526C2×C411yescharacteristic
30Q8×D263—42no—
31C2×D1052C2×C411yescharacteristic
32C2×C22⋊D263—21no—
33D4×D263—42no—
34C2×C4×D263—21no—
35C2×C4×D263C2×C411yescharacteristic
36C2×C4×D263D411yescharacteristic
37C2×C4×D263D411yescharacteristic
38#16862359—24no—
39C2×C263⋊C8—21no—
40C2×C263⋊C8—21no—
41C22⋊Dic263—21no—
42C22⋊Dic263—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46(C2×D263)⋊C4—21no—
47C4×Dic263C2×C411yescharacteristic
48C4×Dic263D411yescharacteristic
49C4×Dic263D411yescharacteristic
50C2×Q8×C263C2×C411yescharacteristic
51C2×D4×C263C2×C411yescharacteristic
52C2×C8×C263—21no—
53C2×C8×C263—21no—
54C22⋊C4×C263—21no—
55C22⋊C4×C263—21no—
56C42×C263C2311yescharacteristic
57C22×D263—21no—
58C22×D263—42no—
59C22×D263—42no—
60C22×D263—42no—
61C22×D263C22⋊C411yescharacteristic
62Dic526—42no—
63Dic526—41no—
64D1052—41no—
65C22⋊D263—42no—
66C2×Dic263—21no—
67C2×Dic263C22⋊C411yescharacteristic
68C2×Dic263C22⋊C411yescharacteristic
69C2×Dic263C22⋊C411yescharacteristic
70C4×D263—22no—
71C4×D263—22no—
72C4×D263—41no—
73C4×D263—42no—
74C263⋊C8—22no—
75C263⋊C8—41no—
76C23×C263—21no—
77Q8×C263—41no—
78D4×C263—41no—
79C2×C4×C263—21no—
80C2×C4×C263C22×C411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C8×C263—22no—
84C8×C263—41no—
85C22×C263—41no—
86C22×C263—41no—
87C22×C263—41no—
88C22×C263C2×C22⋊C411yescharacteristic
89C2×D263—21no—
90C2×D263—21no—
91C2×D263—41no—
92C2×D263—41no—
93C2×D263—41no—
94C2×D263—84no—
95C2×D263#10412yes—
96C4×C263—21no—
97C4×C263—21no—
98C4×C263—21no—
99C4×C263—41no—
100Dic263—21no—
101Dic263—21no—
102Dic263—41no—
103Dic263#10012yes—
104C2×C263—81no—
105C2×C263C2×#10011yescharacteristic
106C2×C263C2×#10411yescharacteristic
107C2×C263#42111yescharacteristic
108D263—22no—
109D263—81no—
110C263#152711yescharacteristic, complemented, Sylow
111#1527—2631nomaximal, Sylow
112C2×#124—2631no—
113#432—2631no—
114C4×M16—2631no—
115#329—2631no—
116#329—2631no—
117#329—2631no—
118#329D26311yescharacteristic, complemented
119C22×Q8—2631no—
120C22×D4—2631no—
121C2×M16—5261no—
122#124—2631no—
123#124—2631no—
124#124—2631no—
125#124—5261no—
126#124—5261no—
127#124C2×D26311yescharacteristic
128C2×C22⋊C4—5261no—
129C2×C22⋊C4—5261no—
130C2×C42—2631no—
131C4⋊C8—5261no—
132C22⋊C8—5261no—
133#97—2631no—
134#97—2631no—
135#97C2×D26311yescharacteristic, complemented
136#97C2×D26311yescharacteristic, complemented
137C4×C8—5261no—
138C24—5261no—
139C2×Q8—2631no—
140C2×Q8—5261no—
141C2×Q8—10522no—
142C2×Q8C4×D26311yescharacteristic
143C2×D4—2631no—
144C2×D4—5261no—
145C2×D4—10522no—
146C2×D4C4×D26311yescharacteristic
147C22×C4—2631no—
148C22×C4—2631no—
149C22×C4—2631no—
150C22×C4—5261no—
151M16—5264no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—5261no—
155C2×C8—5261no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—5261no—
159C22⋊C4—5261no—
160C22⋊C4—5261no—
161C22⋊C4—5261no—
162C22⋊C4—5261no—
163C22⋊C4—5261no—
164C42—2631no—
165C42—2631no—
166C42—2631no—
167C42C22×D26311yescharacteristic
168C23—21no—
169C23—2631no—
170C23—5261no—
171C23—10522no—
172C23—10522no—
173C23—10522no—
174Q8—41no—
175Q8—10521no—
176Q8—10522no—
177D4—41no—
178D4—10521no—
179D4—10522no—
180C2×C4—21no—
181C2×C4—2631no—
182C2×C4—2631no—
183C2×C4—2631no—
184C2×C4—5262no—
185C2×C4—5262no—
186C2×C4—5261no—
187C2×C4—10521no—
188C2×C4—10522no—
189C2×C4C2×C4×D26311yescharacteristic
190C2×C4D4×D26311yescharacteristic
191C2×C4D4×D26311yescharacteristic
192C8—22no—
193C8—41no—
194C8—5262no—
195C8—10521no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—2632no—
200C22—5261no—
201C22—5261no—
202C22—10521no—
203C22—10521no—
204C22—10521no—
205C22—21044no—
206C22C22⋊C4×D26311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—2632no—
212C4—5261no—
213C4—5261no—
214C4—10521no—
215C2—81no—
216C2—5262no—
217C2—21041no—
218C2#100×D26311yescharacteristic
219C2#104×D26311yescharacteristic
220C2#3068195311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC2×D4×D263C4
cosocleC42×C263C23
hypercenter#329D263
hypocenterC263#1527
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. #30681993C2semidirect
3. #30681890C2semidirect
4. #30681678C2semidirect
5. #30681677C2semidirect
6. #30681677C2semidirect
7. #329×C263C2semidirect
21. #22554381C22semidirect
22. #22554381C22semidirect
25. #97×C263C22semidirect
26. #97×C263C22semidirect
110. C263#1527semidirect
118. #329D263semidirect
135. #97C2×D263semidirect
136. #97C2×D263semidirect

Maximal subgroups

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

subgroupindex
#124×D2632
#306819932
#306818902
#306816782
#306816772
#329×C2632
#1527263