Finite Group Databasebeta

← #46781105

Subgroups — #46781105

Order 33664.

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

normal subgroups only

This group has 322 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
1C2×#22554443C211yesmaximal, characteristic
2#30681900C211yesmaximal, characteristic, complemented
3C22⋊C8×D263C211yesmaximal, characteristic, complemented
4#30681662C211yesmaximal, characteristic, complemented
5#30681661C211yesmaximal, characteristic, complemented
6#30681661C211yesmaximal, characteristic, complemented
7#323×C263C211yesmaximal, characteristic, complemented
8C22×D1052C411yescharacteristic
9C22×C22⋊D263C411yescharacteristic
10C22×C22⋊D263C411yescharacteristic
11C22×C4×D263C2211yescharacteristic
12C2×#16862359—21no—
13C2×C8×D263—21no—
14#22554443—21no—
15#22554443—21no—
16#22554443—21no—
17#22554443—21no—
18C2×Dic263⋊C4C411yescharacteristic
19C2×(C2×D263)⋊C4C2211yescharacteristic
20C22⋊(C263⋊C8)C2211yescharacteristic
21C22⋊(C263⋊C8)C2211yescharacteristic
22(C2×D263)⋊C8—21no—
23(C2×D263)⋊C8—21no—
24C2×C22⋊C4×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26C22⋊C8×C263C2211yescharacteristic
27C23×D263C2×C411yescharacteristic
28C23×D263C2×C411yescharacteristic
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—42no—
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34C2×C22⋊D263—21no—
35C2×C22⋊D263—21no—
36C2×C22⋊D263—42no—
37C2×C22⋊D263—42no—
38C22×Dic263C2×C411yescharacteristic
39C22×Dic263C2×C411yescharacteristic
40C2×C4×D263—42no—
41C2×C4×D263D411yescharacteristic
42C2×C4×D263D411yescharacteristic
43C2×C4×D263D411yescharacteristic
44C2×C4×D263D411yescharacteristic
45#16862359—42no—
46C2×C263⋊C8—21no—
47C2×C263⋊C8—21no—
48C8×D263—42no—
49Dic263⋊C4—21no—
50Dic263⋊C4—21no—
51(C2×D263)⋊C4—21no—
52(C2×D263)⋊C4—21no—
53C24×C263C2×C411yescharacteristic
54C22×C4×C263C2×C411yescharacteristic
55C22×C4×C263C2311yescharacteristic
56C2×C8×C263—21no—
57C2×C8×C263—21no—
58C22⋊C4×C263—21no—
59C22⋊C4×C263—21no—
60C22×D263—21no—
61C22×D263—21no—
62C22×D263—22no—
63C22×D263—21no—
64C22×D263—21no—
65C22×D263—21no—
66C22×D263—41no—
67C22×D263—41no—
68C22×D263—41no—
69C22×D263C22⋊C411yescharacteristic
70C22×D263C22⋊C411yescharacteristic
71D1052—42no—
72D1052—42no—
73C22⋊D263—42no—
74C22⋊D263—42no—
75C22⋊D263—42no—
76C22⋊D263—42no—
77C2×Dic263—22no—
78C2×Dic263—21no—
79C2×Dic263—41no—
80C2×Dic263C22⋊C411yescharacteristic
81C2×Dic263C22⋊C411yescharacteristic
82C4×D263—22no—
83C4×D263—22no—
84C4×D263—41no—
85C4×D263—41no—
86C263⋊C8—41no—
87C263⋊C8—41no—
88C23×C263—21no—
89C23×C263—21no—
90C23×C263—21no—
91C23×C263—41no—
92C23×C263—41no—
93C23×C263C22×C411yescharacteristic
94C2×C4×C263—21no—
95C2×C4×C263—41no—
96C2×C4×C263—41no—
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263C2×D411yescharacteristic
99C8×C263—41no—
100C8×C263—41no—
101C22×C263—21no—
102C22×C263—21no—
103C22×C263—41no—
104C22×C263—41no—
105C22×C263—41no—
106C22×C263—81no—
107C22×C263—81no—
108C22×C263C2×C22⋊C411yescharacteristic
109C22×C263#13111yescharacteristic
110C22×C263#13111yescharacteristic
111C2×D263—21no—
112C2×D263—21no—
113C2×D263—21no—
114C2×D263—21no—
115C2×D263—21no—
116C2×D263—42no—
117C2×D263—42no—
118C2×D263—41no—
119C2×D263—41no—
120C2×D263—41no—
121C2×D263—81no—
122C2×D263—81no—
123C2×D263#10012yes—
124C4×C263—21no—
125C4×C263—21no—
126C4×C263—41no—
127Dic263—21no—
128Dic263—41no—
129Dic263#9912yes—
130C2×C263—21no—
131C2×C263—21no—
132C2×C263—81no—
133C2×C263#40811yescharacteristic
134C2×C263C2×#9911yescharacteristic
135C2×C263C2×#10011yescharacteristic
136D263—22no—
137D263—41no—
138D263—81no—
139C263#147111yescharacteristic, complemented, Sylow
140#1471—2631nomaximal, Sylow
141C2×#121—2631no—
142#407—2631no—
143C2×C22⋊C8—2631no—
144#323—2631no—
145#323—2631no—
146#323—2631no—
147#323D26311yescharacteristic, complemented
148C22×D4—2631no—
149C22×D4—2631no—
150C22×D4—2631no—
151C23×C4—2631no—
152C2×M16—5261no—
153C22×C8—5261no—
154#121—5261no—
155#121—5261no—
156#121—5261no—
157#121—5261no—
158C2×C4⋊C4—2631no—
159C2×C22⋊C4—2631no—
160C2×C22⋊C4C2×D26311yescharacteristic
161C22⋊C8—2631no—
162C22⋊C8—2631no—
163C22⋊C8—5261no—
164C22⋊C8—5261no—
165C22⋊C8C2×D26311yescharacteristic
166C22⋊C8C2×D26311yescharacteristic
167C24—2631no—
168C24—2631no—
169C24C4×D26311yescharacteristic
170C2×D4—5261no—
171C2×D4—5261no—
172C2×D4—5261no—
173C2×D4—5261no—
174C2×D4—5261no—
175C2×D4—5261no—
176C2×D4—10522no—
177C2×D4—10522no—
178C2×D4—10522no—
179C22×C4—2631no—
180C22×C4—2631no—
181C22×C4—2631no—
182C22×C4—2631no—
183C22×C4—2631no—
184C22×C4—2631no—
185C22×C4—10522no—
186C22×C4C4×D26311yescharacteristic
187C22×C4C22×D26311yescharacteristic
188M16—10522no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—5261no—
192C2×C8—5261no—
193C2×C8—10522no—
194C4⋊C4—5261no—
195C4⋊C4—5261no—
196C22⋊C4—21no—
197C22⋊C4—21no—
198C22⋊C4—5261no—
199C22⋊C4—5261no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—41no—
204C23—41no—
205C23—2631no—
206C23—2631no—
207C23—5262no—
208C23—5261no—
209C23—5261no—
210C23—5261no—
211C23—5261no—
212C23—5261no—
213C23—10521no—
214C23—10521no—
215C23—10521no—
216C23C2×C4×D26311yescharacteristic
217D4—10522no—
218D4—10522no—
219D4—10522no—
220D4—10522no—
221D4—10522no—
222D4—10522no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—2631no—
227C2×C4—2631no—
228C2×C4—5262no—
229C2×C4—5262no—
230C2×C4—5262no—
231C2×C4—5261no—
232C2×C4—10521no—
233C2×C4—10521no—
234C2×C4—10521no—
235C2×C4D4×D26311yescharacteristic
236C2×C4D4×D26311yescharacteristic
237C8—41no—
238C8—41no—
239C8—10521no—
240C8—10521no—
241C22—21no—
242C22—21no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—2632no—
247C22—81no—
248C22—81no—
249C22—5261no—
250C22—5261no—
251C22—5261no—
252C22—5261no—
253C22—5261no—
254C22—10522no—
255C22—10522no—
256C22—10521no—
257C22—10521no—
258C22—10521no—
259C22—21041no—
260C22—21041no—
261C22C22⋊C4×D26311yescharacteristic
262C22#2255447611yescharacteristic
263C22#2255447811yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—2632no—
268C4—5261no—
269C4—10521no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—5262no—
274C2—10521no—
275C2—21041no—
276C2#3068190311yescharacteristic
277C2#99×D26311yescharacteristic
278C2#100×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#323×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC2×#22554443C2
cosocleC22×C4×C263C23
hypercenter#323D263
hypocenterC263#1471
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #30681900C2semidirect
3. C22⋊C8×D263C2semidirect
4. #30681662C2semidirect
5. #30681661C2semidirect
6. #30681661C2semidirect
7. #323×C263C2semidirect
139. C263#1471semidirect
147. #323D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544432
#306819002
C22⋊C8×D2632
#306816622
#306816612
#323×C2632
#1471263