Finite Group Databasebeta

← #46783946

Subgroups — #46783946

Order 33664.

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

normal subgroups only

This group has 316 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
1C2×#22554450C211yesmaximal, characteristic
2C2×#22554401C211yesmaximal, characteristic, complemented
3C2×#22554395C211yesmaximal, characteristic, complemented
4C2×#22554393C211yesmaximal, characteristic, complemented
5C2×(C2×D263)⋊C8C211yesmaximal, characteristic
6#30681795C211yesmaximal, characteristic
7#340×C263C211yesmaximal, characteristic, complemented
8C22×Dic526C2211yescharacteristic
9C22×C4×D263C2211yescharacteristic
10C22×C263⋊C8C2211yescharacteristic
11#22554450—22no—
12#22554450—22no—
13C2×C4⋊Dic263—21no—
14C2×C4⋊Dic263C2211yescharacteristic
15C2×(C2×D263)⋊C4—21no—
16C2×(C2×D263)⋊C4—21no—
17#22554401—22no—
18#22554395—22no—
19#22554393—22no—
20(C2×D263)⋊C8—22no—
21C263⋊#95—21no—
22C22×C8×C263C2211yescharacteristic
23C2×C4⋊C4×C263C2211yescharacteristic
24C2×C4⋊C4×C263C2211yescharacteristic
25C23×D263D411yescharacteristic
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526D412yes—
32C22×Dic263—21no—
33C22×Dic263—21no—
34C22×Dic263D411yescharacteristic
35C2×C4×D263—21no—
36C2×C4×D263—21no—
37C2×C4×D263—21no—
38C2×C4×D263—21no—
39C2×C4×D263—21no—
40C2×C4×D263—21no—
41C2×C263⋊C8—21no—
42C2×C263⋊C8—21no—
43C2×C263⋊C8D412yes—
44C4⋊Dic263—24no—
45C4⋊Dic263—21no—
46C4⋊Dic263—21no—
47(C2×D263)⋊C4—24no—
48(C2×D263)⋊C4—42no—
49C22×C4×C263—21no—
50C22×C4×C263—21no—
51C22×C4×C263C2311yescharacteristic
52C2×C8×C263—21no—
53C2×C8×C263—21no—
54C2×C8×C263—21no—
55C4⋊C4×C263—21no—
56C4⋊C4×C263—21no—
57C4⋊C4×C263—21no—
58C4⋊C4×C263D412yes—
59C22×D263—21no—
60C22×D263—21no—
61C22×D263—21no—
62C22×D263—21no—
63C22×D263—21no—
64C22×D263—21no—
65C22×D263SD1612yes—
66Dic526—22no—
67Dic526—22no—
68Dic526—41no—
69Dic526—41no—
70C2×Dic263—22no—
71C2×Dic263—21no—
72C2×Dic263—21no—
73C2×Dic263—21no—
74C2×Dic263—41no—
75C2×Dic263—41no—
76C2×Dic263—41no—
77C2×Dic263—41no—
78C2×Dic263—41no—
79C4×D263—41no—
80C4×D263—41no—
81C4×D263—41no—
82C4×D263—41no—
83C263⋊C8—22no—
84C23×C263C2×D411yescharacteristic
85C2×C4×C263—22no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263—41no—
90C2×C4×C263—41no—
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263C2×D411yescharacteristic
94C2×C4×C263#4111yescharacteristic
95C2×C4×C263#4111yescharacteristic
96C2×C4×C263#4111yescharacteristic
97C8×C263—41no—
98C22×C263#12011yescharacteristic
99C22×C263#12111yescharacteristic
100C22×C263#12311yescharacteristic
101C22×C263C2×SD1611yescharacteristic
102C22×C263#13511yescharacteristic
103C22×C263#13711yescharacteristic
104C22×C263#13711yescharacteristic
105C2×D263—22no—
106C2×D263—22no—
107C2×D263—22no—
108C2×D263—41no—
109C2×D263—41no—
110C2×D263—41no—
111C2×D263—41no—
112C4×C263—42no—
113C4×C263—81no—
114C4×C263#12111yescharacteristic
115C4×C263#12111yescharacteristic
116C4×C263#12311yescharacteristic
117C4×C263#12411yescharacteristic
118Dic263—41no—
119Dic263—42no—
120Dic263—81no—
121C2×C263#39411yescharacteristic
122C2×C263#44811yescharacteristic
123C2×C263#45211yescharacteristic
124C2×C263#46511yescharacteristic
125C2×C263#47011yescharacteristic
126C2×C263#48311yescharacteristic
127C2×C263#48511yescharacteristic
128D263—42no—
129C263#203511yescharacteristic, complemented, Sylow
130#2035—2631nomaximal, Sylow
131C2×C22⋊Q8—2631no—
132C2×#106—2631no—
133C2×#103—2631no—
134C2×#103—2631no—
135C2×C22⋊C8—2631no—
136#380—2631no—
137#340D26311yescharacteristic, complemented
138C22×Q8—2631no—
139C23×C4—2631no—
140C22×C8—2631no—
141C22×C8C2×D26311yescharacteristic
142C22⋊Q8—5262no—
143C22⋊Q8—5262no—
144C2×C4⋊C4—2631no—
145C2×C4⋊C4—5261no—
146C2×C4⋊C4C2×D26311yescharacteristic
147C2×C4⋊C4C2×D26311yescharacteristic
148C2×C22⋊C4—5261no—
149C2×C22⋊C4—5261no—
150#106—5262no—
151#103—5262no—
152#103—5262no—
153C22⋊C8—5262no—
154#95—5261no—
155C24—2631no—
156C2×Q8—2632no—
157C2×Q8—5261no—
158C2×Q8—5261no—
159C2×Q8—5261no—
160C2×Q8—5261no—
161C2×Q8—5261no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—2631no—
165C22×C4—5261no—
166C22×C4—5261no—
167C22×C4—5261no—
168C22×C4—5261no—
169C22×C4—5261no—
170C22×C4—5261no—
171C22×C4—5261no—
172C22×C4—5261no—
173C22×C4C22×D26311yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—2632no—
178C2×C8—5261no—
179C2×C8—5261no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—5264no—
184C4⋊C4—5261no—
185C4⋊C4—5261no—
186C4⋊C4D105212yes—
187C22⋊C4—5264no—
188C22⋊C4—10522no—
189C23—2632no—
190C23—5261no—
191C23—5261no—
192C23—5261no—
193C23—5261no—
194C23—5261no—
195C23—5261no—
196C23D4×D26311yescharacteristic
197Q8—5262no—
198Q8—5262no—
199Q8—10521no—
200Q8—10521no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—5262no—
208C2×C4—5261no—
209C2×C4—5261no—
210C2×C4—5261no—
211C2×C4—10521no—
212C2×C4—10521no—
213C2×C4—10521no—
214C2×C4—10521no—
215C2×C4—10521no—
216C2×C4—10521no—
217C2×C4—10521no—
218C2×C4—10521no—
219C2×C4—10521no—
220C2×C4D4×D26311yescharacteristic
221C2×C4D4×D26311yescharacteristic
222C2×C4C2×D105211yescharacteristic
223C2×C4#1686237611yescharacteristic
224C2×C4#1686237611yescharacteristic
225C2×C4#1686237711yescharacteristic
226C8—41no—
227C8—5262no—
228C22—5262no—
229C22—5262no—
230C22—5262no—
231C22—10521no—
232C22—10521no—
233C22—10521no—
234C22—10521no—
235C22#2255444011yescharacteristic
236C22#2255444311yescharacteristic
237C22#2255445511yescharacteristic
238C22SD16×D26311yescharacteristic
239C22#2255448911yescharacteristic
240C22#2255449911yescharacteristic
241C22#2255450211yescharacteristic
242C4—42no—
243C4—81no—
244C4—10521no—
245C4—10522no—
246C4—21041no—
247C4#2255444311yescharacteristic
248C4#2255444511yescharacteristic
249C4#2255445511yescharacteristic
250C4#2255445811yescharacteristic
251C2—10522no—
252C2#3068185611yescharacteristic
253C2#3068207811yescharacteristic
254C2#3068210111yescharacteristic
255C2#3068216611yescharacteristic
256C2#3068219511yescharacteristic
257C2#3068227011yescharacteristic
258C2#3068228111yescharacteristic
subgroupG/H
centerC23D4×D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#340×C263C2
socleC23×C263C2×D4
prime radicalC23×D263D4
hypercenter#340D263
hypocenterC263#2035
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#22554401C2semidirect
3. C2×#22554395C2semidirect
4. C2×#22554393C2semidirect
7. #340×C263C2semidirect
129. C263#2035semidirect
137. #340D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544502
C2×#225544012
C2×#225543952
C2×#225543932
C2×(C2×D263)⋊C82
#306817952
#340×C2632
#2035263