Finite Group Databasebeta

← #46781677

Subgroups — #46781677

Order 33664.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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#30682533C211yesmaximal, characteristic, complemented
2#30682091C211yesmaximal, characteristic, complemented
3#30682071C211yesmaximal, characteristic
4#30681856C211yesmaximal, characteristic, complemented
5#30681674C211yesmaximal, characteristic, complemented
6#30681663C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862365—21no—
10C2×#16862361—21no—
11#22554463—21no—
12#22554460—21no—
13#22554451—21no—
14#22554451—21no—
15#22554449C2211yescharacteristic
16#22554447—21no—
17D4×Dic263—21no—
18C2×Dic263⋊C4C2211yescharacteristic
19C2×(C2×D263)⋊C4—21no—
20C2×(C2×D263)⋊C4—21no—
21#22554392—21no—
22#22554390—21no—
23C22⋊(C263⋊C8)C2211yescharacteristic
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C23×D263—21no—
28C2×Dic526D411yescharacteristic
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—42no—
32C22×Dic263—21no—
33C22×Dic263D411yescharacteristic
34C22×Dic263D411yescharacteristic
35#16862365—42no—
36#16862361—42no—
37C2×C263⋊C8—21no—
38C4⋊Dic263—21no—
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43Dic263⋊C4—21no—
44Dic263⋊C4—21no—
45C22⋊Dic263—21no—
46C22⋊Dic263—21no—
47C22⋊Dic263—21no—
48C22⋊Dic263—21no—
49(C2×D263)⋊C4—42no—
50(C2×D263)⋊C4—42no—
51C4×Dic263—21no—
52C2×D4×C263—21no—
53C2×D4×C263D411yescharacteristic
54C22×C4×C263—21no—
55C22×C4×C263C2311yescharacteristic
56C2×C8×C263—21no—
57C4⋊C4×C263D411yescharacteristic
58C22⋊C4×C263—21no—
59C22×D263—22no—
60C22×D263—41no—
61C22×D263—41no—
62C22×D263—41no—
63C22×D263—41no—
64C22×D263—41no—
65C22×D263—41no—
66Dic526—41no—
67D1052—22no—
68D1052—22no—
69D1052—41no—
70D1052—41no—
71C2×Dic263—21no—
72C2×Dic263—21no—
73C2×Dic263—21no—
74C2×Dic263—21no—
75C2×Dic263—21no—
76C2×Dic263—21no—
77C2×Dic263—41no—
78C2×Dic263—81no—
79C263⋊C8—41no—
80C23×C263—21no—
81C23×C263C2×D411yescharacteristic
82D4×C263—41no—
83D4×C263—41no—
84D4×C263—41no—
85C2×C4×C263—21no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263—41no—
90C2×C4×C263C2×D411yescharacteristic
91C2×C4×C263C2×D411yescharacteristic
92C8×C263—41no—
93C22×C263—21no—
94C22×C263—21no—
95C22×C263—41no—
96C22×C263—41no—
97C22×C263—41no—
98C22×C263#12011yescharacteristic
99C22×C263#13511yescharacteristic
100C22×C263AGL(1,ℤ/8)11yescharacteristic
101C2×D263—42no—
102C2×D263—42no—
103C2×D263—42no—
104C2×D263—81no—
105C2×D263—81no—
106C2×D263—81no—
107C2×D263—81no—
108C4×C263—21no—
109C4×C263—21no—
110C4×C263—41no—
111C4×C263—81no—
112Dic263—41no—
113Dic263—41no—
114Dic263—41no—
115Dic263—41no—
116C2×C263—21no—
117C2×C263—21no—
118C2×C263—81no—
119C2×C263#44911yescharacteristic
120C2×C263#45411yescharacteristic
121C2×C263B(4,𝔽2)11yescharacteristic
122D263—82no—
123C263#159711yescharacteristic, complemented, Sylow
124#1597—2631nomaximal, Sylow
125#539—2631no—
126#450—2631no—
127#447—2631no—
128#394—2631no—
129#328—2631no—
130#327D26311yescharacteristic, complemented
131#324—2631no—
132C22×D4—2631no—
133C2×SD16—5261no—
134C2×D8—5261no—
135#126—5261no—
136#125—5261no—
137#123—5261no—
138#123—5261no—
139C22⋊Q8—2631no—
140C22⋊Q8—5261no—
141#121C2×D26311yescharacteristic
142C4×D4—5261no—
143C2×C4⋊C4—2631no—
144C2×C22⋊C4—5261no—
145C2×C22⋊C4—5261no—
146#102—5261no—
147#102—5261no—
148C22⋊C8—2631no—
149C22⋊C8C2×D26311yescharacteristic
150#95C2×D26311yescharacteristic
151C24—5261no—
152C2×Q8—2631no—
153C2×D4—21no—
154C2×D4—5261no—
155C2×D4—5261no—
156C2×D4—10522no—
157C2×D4D105211yescharacteristic
158C22×C4—21no—
159C22×C4—2631no—
160C22×C4—2631no—
161C22×C4—5261no—
162C22×C4C22×D26311yescharacteristic
163SD16—10522no—
164D8—10522no—
165C2×C8—21no—
166C2×C8—5261no—
167C4⋊C4—2631no—
168C4⋊C4—5261no—
169C4⋊C4—5261no—
170C4⋊C4—5261no—
171C4⋊C4—5261no—
172C4⋊C4—5261no—
173C4⋊C4—5261no—
174C4⋊C4D105211yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—5261no—
177C22⋊C4—5261no—
178C22⋊C4—5261no—
179C22⋊C4—5261no—
180C22⋊C4—10522no—
181C22⋊C4—10522no—
182C42—5261no—
183C23—21no—
184C23—5262no—
185C23—10521no—
186C23—10521no—
187C23—10521no—
188C23—10521no—
189C23—10521no—
190C23—10521no—
191C23D4×D26311yescharacteristic
192Q8—10521no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—5262no—
197D4—5262no—
198D4—10521no—
199D4—10521no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—5261no—
206C2×C4—5261no—
207C2×C4—5261no—
208C2×C4—5261no—
209C2×C4—5261no—
210C2×C4—5261no—
211C2×C4—10521no—
212C2×C4—21041no—
213C2×C4D4×D26311yescharacteristic
214C2×C4C2×D105211yescharacteristic
215C8—41no—
216C8—10521no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—10522no—
223C22—10522no—
224C22—10522no—
225C22—21041no—
226C22—21041no—
227C22—21041no—
228C22—21041no—
229C22#2255444011yescharacteristic
230C22#2255449111yescharacteristic
231C22#2255449411yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—81no—
236C4—10521no—
237C4—10521no—
238C4—10521no—
239C4—10521no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—21042no—
244C2#3068208411yescharacteristic
245C2#3068211211yescharacteristic
246C2#3068212611yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263#120
prime radical#30682071C2
hypercenter#327D263
hypocenterC263#1597
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #30682533C2semidirect
2. #30682091C2semidirect
4. #30681856C2semidirect
5. #30681674C2semidirect
6. #30681663C2semidirect
7. #327×C263C2semidirect
123. C263#1597semidirect
130. #327D263semidirect

Maximal subgroups

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

subgroupindex
#306825332
#306820912
#306820712
#306818562
#306816742
#306816632
#327×C2632
#1597263