Finite Group Databasebeta

← #46783873

Subgroups — #46783873

Order 33664.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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#30682500C211yesmaximal, characteristic, complemented
2C2×#22554439C212yesmaximal, complemented
3C2×#22554384C212yesmaximal, complemented
4#30681705C211yesmaximal, characteristic, complemented
5#379×C263C211yesmaximal, characteristic, complemented
6C22×C22⋊D263—22no—
7C22×C22⋊D263C2212yes—
8#22554454—22no—
9#22554444—22no—
10#22554440—22no—
11#22554439—24no—
12#22554439—24no—
13C2×C22⋊Dic263—22no—
14C2×C22⋊Dic263C2212yes—
15#22554384—24no—
16C25×C263C2211yescharacteristic
17C2×C22⋊C4×C263—22no—
18C2×C22⋊C4×C263C2211yescharacteristic
19C2×C22⋊C4×C263C2211yescharacteristic
20C23×D263D412yescomplemented
21C2×D1052—22no—
22C2×C22⋊D263—28no—
23C2×C22⋊D263—22no—
24C2×C22⋊D263—22no—
25C2×C22⋊D263—22no—
26C2×C22⋊D263—22no—
27C2×C22⋊D263—22no—
28C2×C22⋊D263—22no—
29C2×C22⋊D263—48no—
30C22×Dic263—22no—
31C22×Dic263D412yescomplemented
32C4⋊Dic263—22no—
33C22⋊Dic263—28no—
34C22⋊Dic263—22no—
35C22⋊Dic263D414yescomplemented
36(C2×D263)⋊C4—24no—
37C24×C263—22no—
38C24×C263—21no—
39C24×C263—22no—
40C24×C263—21no—
41C24×C263—44no—
42C24×C263D412yescomplemented
43C24×C263C2311yescharacteristic
44C22×C4×C263—21no—
45C22×C4×C263D412yescomplemented
46C22⋊C4×C263—22no—
47C22⋊C4×C263—22no—
48C22⋊C4×C263—44no—
49C22×D263—22no—
50C22×D263—22no—
51C22×D263—22no—
52C22×D263—44no—
53D1052—82no—
54C22⋊D263—416no—
55C22⋊D263—42no—
56C22⋊D263—42no—
57C22⋊D263—42no—
58C22⋊D263—42no—
59C2×Dic263—22no—
60C2×Dic263—22no—
61C2×Dic263—24no—
62C2×Dic263—22no—
63C2×Dic263—44no—
64C23×C263—24no—
65C23×C263—28no—
66C23×C263—24no—
67C23×C263—22no—
68C23×C263—44no—
69C23×C263—42no—
70C23×C263—42no—
71C23×C263—44no—
72C23×C263—44no—
73C23×C263—48no—
74C23×C263—41no—
75C23×C263—42no—
76C23×C263—41no—
77C23×C263C2×D412yes—
78C23×C263C2×D412yes—
79C23×C263C2×D411yescharacteristic
80C23×C263C2×D411yescharacteristic
81C23×C263#4111yescharacteristic
82C2×C4×C263—22no—
83C2×C4×C263—42no—
84C2×C4×C263—42no—
85C2×C4×C263—41no—
86C22×C263—22no—
87C22×C263—24no—
88C22×C263—24no—
89C22×C263—28no—
90C22×C263—42no—
91C22×C263—41no—
92C22×C263—41no—
93C22×C263—44no—
94C22×C263—44no—
95C22×C263—48no—
96C22×C263—42no—
97C22×C263—42no—
98C22×C263—44no—
99C22×C263#12011yescharacteristic
100C22×C263#12012yes—
101C22×C263#12112yes—
102C22×C263#12111yescharacteristic
103C22×C263#12711yescharacteristic
104C2×D263—44no—
105C2×D263—42no—
106C2×D263—44no—
107C2×D263—82no—
108C4×C263—42no—
109C4×C263—81no—
110Dic263—44no—
111Dic263—42no—
112C2×C263—22no—
113C2×C263—21no—
114C2×C263—22no—
115C2×C263—21no—
116C2×C263—44no—
117C2×C263#39211yescharacteristic
118C2×C263B(4,𝔽2)12yes—
119D263—82no—
120C263#202111yescharacteristic, complemented, Sylow
121#2021—2631nomaximal, Sylow
122#534—2631no—
123C2×#120—2632no—
124C2×#99—2632no—
125#379D26311yescharacteristic, complemented
126#342—2631no—
127C25C2×D26311yescharacteristic
128C22×D4—2632no—
129C22×D4—5262no—
130#123—5262no—
131#121—5262no—
132#120—5262no—
133#120—5264no—
134#120—5264no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—2632no—
137C2×C22⋊C4—5262no—
138C2×C22⋊C4C2×D26311yescharacteristic
139C2×C22⋊C4C2×D26311yescharacteristic
140#99—5264no—
141C24—22no—
142C24—21no—
143C24—22no—
144C24—21no—
145C24—44no—
146C24—2632no—
147C24D105212yescomplemented
148C24C22×D26311yescharacteristic
149C2×D4—5262no—
150C2×D4—5268no—
151C2×D4—5262no—
152C2×D4—5262no—
153C2×D4—5262no—
154C2×D4—5262no—
155C2×D4—5262no—
156C2×D4—5262no—
157C2×D4—10528no—
158C22×C4—21no—
159C22×C4—2632no—
160C22×C4—5262no—
161C22×C4C22⋊D26312yescomplemented
162C4⋊C4—5262no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—44no—
166C22⋊C4—2634no—
167C22⋊C4—5264no—
168C22⋊C4—5268no—
169C22⋊C4—5262no—
170C23—24no—
171C23—28no—
172C23—24no—
173C23—22no—
174C23—44no—
175C23—42no—
176C23—42no—
177C23—44no—
178C23—48no—
179C23—44no—
180C23—41no—
181C23—42no—
182C23—41no—
183C23—5262no—
184C23—5262no—
185C23—5262no—
186C23—10524no—
187C23D4×D26312yes—
188C23D4×D26312yes—
189C23C2×C22⋊D26311yescharacteristic
190C23C2×D105211yescharacteristic
191C23#1686237611yescharacteristic
192D4—105216no—
193D4—10522no—
194D4—10522no—
195D4—10522no—
196D4—10522no—
197D4—21042no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—5262no—
203C2×C4—5264no—
204C2×C4—5262no—
205C2×C4—5262no—
206C2×C4—10524no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—44no—
219C22—42no—
220C22—10524no—
221C22—10524no—
222C22—10522no—
223C22—21042no—
224C22#2255443811yescharacteristic
225C22#2255444012yes—
226C22#2255444312yes—
227C22#2255444411yescharacteristic
228C22#2255446611yescharacteristic
229C4—42no—
230C4—81no—
231C4—10524no—
232C4—10522no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—21042no—
239C2#3068184711yescharacteristic
240C2#3068212412yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC24×C263C23
FrattiniC24C22×D263
Fitting#379×C263C2
socleC22×C263#120
hypercenter#379D263
hypocenterC263#2021
LCSG ▷ C24×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #30682500C2semidirect
2. C2×#22554439C2semidirect
3. C2×#22554384C2semidirect
4. #30681705C2semidirect
5. #379×C263C2semidirect
20. C23×D263D4semidirect
31. C22×Dic263D4semidirect
35. C22⋊Dic263D4semidirect
42. C24×C263D4semidirect
45. C22×C4×C263D4semidirect
120. C263#2021semidirect
125. #379D263semidirect
147. C24D1052semidirect
161. C22×C4C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306825002
C2×#225544392
C2×#225543842
#306817052
#379×C2632
#2021263