Finite Group Databasebeta

← #46781237

Subgroups — #46781237

Order 33664.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#30682451C211yesmaximal, characteristic
2C22⋊C8×D263C211yesmaximal, characteristic, complemented
3#30681785C211yesmaximal, characteristic, complemented
4#30681675C211yesmaximal, characteristic, complemented
5#30681673C211yesmaximal, characteristic, complemented
6#30681671C211yesmaximal, characteristic, complemented
7#328×C263C211yesmaximal, characteristic, complemented
8C2×#16862377C411yescharacteristic, complemented
9C22×C4×D263C2211yescharacteristic
10C2×C8×D263—21no—
11#22554455—21no—
12#22554446C411yescharacteristic, complemented
13#22554445C411yescharacteristic, complemented
14#22554444C2211yescharacteristic
15#22554440—21no—
16#22554432—21no—
17(C22⋊D263)⋊C4—21no—
18#22554428C411yescharacteristic, complemented
19C2×(C2×D263)⋊C4—21no—
20C2×C4×Dic263—21no—
21C22⋊(C263⋊C8)C2211yescharacteristic
22(C2×D263)⋊C8—21no—
23C263⋊#95C2211yescharacteristic
24C22⋊Q8×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C23×D263D411yescharacteristic
28#16862377—42no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052C2×C411yescharacteristic
32C2×C22⋊D263—21no—
33C22×Dic263—21no—
34C22×Dic263D411yescharacteristic
35C2×C4×D263—21no—
36C2×C4×D263—42no—
37C2×C4×D263C2×C411yescharacteristic
38C2×C4×D263C2×C411yescharacteristic
39C2×C4×D263D411yescharacteristic
40C2×C4×D263D411yescharacteristic
41C2×C263⋊C8—21no—
42C8×D263—42no—
43C4⋊Dic263C2×C411yescharacteristic
44Dic263⋊C4—21no—
45(C2×D263)⋊C4—24no—
46(C2×D263)⋊C4—21no—
47(C2×D263)⋊C4—21no—
48(C2×D263)⋊C4—21no—
49(C2×D263)⋊C4—21no—
50C4×Dic263—21no—
51C4×Dic263—42no—
52C2×Q8×C263C2×C411yescharacteristic
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55C2×C8×C263—21no—
56C4⋊C4×C263—21no—
57C4⋊C4×C263C2×C411yescharacteristic
58C22⋊C4×C263—21no—
59C22×D263—21no—
60C22×D263—21no—
61C22×D263—22no—
62C22×D263—21no—
63C22×D263—41no—
64C22×D263C22⋊C411yescharacteristic
65C22×D263C22⋊C411yescharacteristic
66D1052—41no—
67D1052—42no—
68D1052—42no—
69C22⋊D263—41no—
70C22⋊D263—41no—
71C2×Dic263—22no—
72C2×Dic263—22no—
73C2×Dic263—21no—
74C2×Dic263—41no—
75C2×Dic263—41no—
76C2×Dic263C22⋊C411yescharacteristic
77C2×Dic263C22⋊C411yescharacteristic
78C4×D263—22no—
79C4×D263—22no—
80C4×D263—41no—
81C4×D263—41no—
82C4×D263—42no—
83C263⋊C8—41no—
84C23×C263C2×D411yescharacteristic
85Q8×C263—41no—
86C2×C4×C263—22no—
87C2×C4×C263—21no—
88C2×C4×C263—21no—
89C2×C4×C263—41no—
90C2×C4×C263—41no—
91C2×C4×C263—41no—
92C2×C4×C263C22×C411yescharacteristic
93C2×C4×C263C2×D411yescharacteristic
94C8×C263—41no—
95C22×C263—21no—
96C22×C263—21no—
97C22×C263C2×C22⋊C411yescharacteristic
98C22×C263#13511yescharacteristic
99C22×C263#13511yescharacteristic
100C2×D263—21no—
101C2×D263—21no—
102C2×D263—21no—
103C2×D263—21no—
104C2×D263—21no—
105C2×D263—42no—
106C2×D263—42no—
107C2×D263—41no—
108C2×D263—41no—
109C2×D263—41no—
110C2×D263#10412yes—
111C4×C263—21no—
112C4×C263—21no—
113C4×C263—42no—
114C4×C263—41no—
115C4×C263—41no—
116Dic263—21no—
117Dic263—42no—
118Dic263—41no—
119Dic263#9912yes—
120C2×C263—21no—
121C2×C263—21no—
122C2×C263C2×#9911yescharacteristic
123C2×C263#41611yescharacteristic
124C2×C263C2×#10411yescharacteristic
125D263—22no—
126D263—41no—
127D263—81no—
128C263#150111yescharacteristic, complemented, Sylow
129#1501—2631nomaximal, Sylow
130#525—2631no—
131C2×C22⋊C8—2631no—
132C4×C22⋊C4—2631no—
133#328—2631no—
134#328D26311yescharacteristic, complemented
135#327—2631no—
136#327—2631no—
137C2×#41—2631no—
138C23×C4—2631no—
139C22×C8—5261no—
140#123—5261no—
141C22⋊Q8—2631no—
142C22⋊Q8C2×D26311yescharacteristic
143#121—2631no—
144#121—2631no—
145#120—5261no—
146C4×D4—5261no—
147C4×D4—5261no—
148#117—2631no—
149C2×C22⋊C4—5261no—
150C2×C42—5261no—
151C22⋊C8—2631no—
152C22⋊C8—5261no—
153C22⋊C8C2×D26311yescharacteristic
154#95—2631no—
155#95C2×D26311yescharacteristic
156C24—2631no—
157#41—10522no—
158C2×Q8C4×D26311yescharacteristic
159C2×D4—2631no—
160C2×D4—5261no—
161C2×D4—5261no—
162C2×D4—5261no—
163C22×C4—21no—
164C22×C4—2631no—
165C22×C4—2631no—
166C22×C4—2631no—
167C22×C4—2631no—
168C22×C4—2631no—
169C22×C4—5261no—
170C22×C4—5261no—
171C22×C4—10522no—
172C22×C4C22×D26311yescharacteristic
173C2×C8—21no—
174C2×C8—5261no—
175C2×C8—10522no—
176C4⋊C4—21no—
177C4⋊C4—2631no—
178C4⋊C4—5261no—
179C4⋊C4C4×D26311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—5261no—
182C22⋊C4—5261no—
183C22⋊C4—5261no—
184C22⋊C4—5264no—
185C22⋊C4—5261no—
186C42—5261no—
187C42—10522no—
188C23—2631no—
189C23—2631no—
190C23—5262no—
191C23—5261no—
192C23—5261no—
193C23—5261no—
194C23—10521no—
195C23D4×D26311yescharacteristic
196Q8—41no—
197D4—10521no—
198D4—10522no—
199D4—10522no—
200D4—10521no—
201D4—10521no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—2631no—
209C2×C4—2631no—
210C2×C4—5262no—
211C2×C4—5262no—
212C2×C4—5262no—
213C2×C4—5262no—
214C2×C4—5261no—
215C2×C4—10521no—
216C2×C4—10521no—
217C2×C4—10522no—
218C2×C4—10521no—
219C2×C4—10521no—
220C2×C4C2×C4×D26311yescharacteristic
221C2×C4D4×D26311yescharacteristic
222C8—41no—
223C8—10521no—
224C22—21no—
225C22—21no—
226C22—2632no—
227C22—5261no—
228C22—5261no—
229C22—5261no—
230C22—5261no—
231C22—5261no—
232C22—10522no—
233C22—10522no—
234C22—10521no—
235C22—10521no—
236C22—10521no—
237C22C22⋊C4×D26311yescharacteristic
238C22#2255449111yescharacteristic
239C22#2255449311yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—2632no—
246C4—5261no—
247C4—10522no—
248C4—10521no—
249C2—21no—
250C2—21no—
251C2—5262no—
252C2—10521no—
253C2—21041no—
254C2#99×D26311yescharacteristic
255C2#3068193311yescharacteristic
256C2#104×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#328×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682451C2
cosocleC22×C4×C263C23
hypercenter#328D263
hypocenterC263#1501
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D263C2semidirect
3. #30681785C2semidirect
4. #30681675C2semidirect
5. #30681673C2semidirect
6. #30681671C2semidirect
7. #328×C263C2semidirect
8. C2×#16862377C4semidirect
12. #22554446C4semidirect
13. #22554445C4semidirect
18. #22554428C4semidirect
128. C263#1501semidirect
134. #328D263semidirect

Maximal subgroups

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

subgroupindex
#306824512
C22⋊C8×D2632
#306817852
#306816752
#306816732
#306816712
#328×C2632
#1501263