Finite Group Databasebeta

← #46783749

Subgroups — #46783749

Order 33664.

444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#16862363C211yesmaximal, characteristic, complemented
2C2×#22554446C211yesmaximal, characteristic, complemented
3C2×#22554445C211yesmaximal, characteristic
4C2×#22554392C211yesmaximal, characteristic, complemented
5C2×(C2×D263)⋊C8C211yesmaximal, characteristic, complemented
6#30681700C211yesmaximal, characteristic, complemented
7C2×#103×C263C211yesmaximal, characteristic, complemented
8C22×D1052—21no—
9C22×D1052C2211yescharacteristic
10C22×C4×D263C2211yescharacteristic
11C2×#16862363—22no—
12C2×#16862363—22no—
13C2×#16862363—22no—
14C22×C263⋊C8C2211yescharacteristic
15#22554446—22no—
16#22554446—22no—
17#22554445—22no—
18#22554445—22no—
19C2×C4⋊Dic263C2211yescharacteristic
20C2×Dic263⋊C4—21no—
21C2×(C2×D263)⋊C4—21no—
22C2×(C2×D263)⋊C4—21no—
23#22554392—22no—
24(C2×D263)⋊C8—22no—
25C22×Q8×C263C2211yescharacteristic
26C22×C8×C263C2211yescharacteristic
27C2×C4⋊C4×C263C2211yescharacteristic
28#103×C263—22no—
29C23×D263—21no—
30C23×D263D411yescharacteristic
31C2×D1052—24no—
32C2×D1052—21no—
33C2×D1052—21no—
34C2×D1052—21no—
35C2×D1052—21no—
36C2×D1052—21no—
37C2×D1052—42no—
38C2×D1052—42no—
39C2×D1052D412yes—
40C22×Dic263—21no—
41C22×Dic263D411yescharacteristic
42C2×C4×D263—21no—
43C2×C4×D263—21no—
44C2×C4×D263—21no—
45C2×C4×D263—21no—
46C2×C4×D263—21no—
47C2×C4×D263—21no—
48#16862363—28no—
49C2×C263⋊C8—21no—
50C2×C263⋊C8—21no—
51C2×C263⋊C8D412yescomplemented
52C4⋊Dic263—21no—
53C4⋊Dic263D412yescomplemented
54Dic263⋊C4—24no—
55(C2×D263)⋊C4—24no—
56(C2×D263)⋊C4—24no—
57C2×Q8×C263—21no—
58C2×Q8×C263—21no—
59C2×Q8×C263—21no—
60C2×Q8×C263—21no—
61C2×Q8×C263—21no—
62C2×Q8×C263D412yescomplemented
63C22×C4×C263—21no—
64C22×C4×C263—21no—
65C22×C4×C263C2311yescharacteristic
66C2×C8×C263—21no—
67C2×C8×C263—21no—
68C2×C8×C263—21no—
69C4⋊C4×C263—21no—
70C4⋊C4×C263D412yes—
71C22×D263—21no—
72C22×D263—21no—
73C22×D263—21no—
74C22×D263—21no—
75C22×D263—21no—
76C22×D263—21no—
77C22×D263—22no—
78C22×D263—41no—
79C22×D263—41no—
80C22×D263—41no—
81C22×D263—41no—
82C22×D263—41no—
83C22×D263—41no—
84C22×D263SD1612yescomplemented
85D1052—22no—
86D1052—22no—
87D1052—48no—
88D1052—41no—
89D1052—41no—
90C2×Dic263—21no—
91C2×Dic263—22no—
92C2×Dic263—21no—
93C2×Dic263—21no—
94C2×Dic263—41no—
95C2×Dic263—41no—
96C4×D263—41no—
97C4×D263—41no—
98C4×D263—41no—
99C4×D263—41no—
100C263⋊C8—22no—
101C23×C263C2×D411yescharacteristic
102Q8×C263—22no—
103Q8×C263—22no—
104Q8×C263—41no—
105Q8×C263—41no—
106C2×C4×C263—22no—
107C2×C4×C263—22no—
108C2×C4×C263—41no—
109C2×C4×C263—41no—
110C2×C4×C263—41no—
111C2×C4×C263—41no—
112C2×C4×C263C2×D411yescharacteristic
113C2×C4×C263C2×D411yescharacteristic
114C2×C4×C263C2×D411yescharacteristic
115C2×C4×C263C2×D411yescharacteristic
116C2×C4×C263C2×D411yescharacteristic
117C2×C4×C263#4111yescharacteristic
118C8×C263—41no—
119C22×C263#12011yescharacteristic
120C22×C263#12011yescharacteristic
121C22×C263#12111yescharacteristic
122C22×C263C2×SD1611yescharacteristic
123C22×C263#13511yescharacteristic
124C22×C263AGL(1,ℤ/8)11yescharacteristic
125C22×C263#13711yescharacteristic
126C2×D263—22no—
127C2×D263—22no—
128C2×D263—22no—
129C2×D263—41no—
130C2×D263—41no—
131C2×D263—41no—
132C2×D263—41no—
133C2×D263—42no—
134C2×D263—42no—
135C2×D263—42no—
136C2×D263—81no—
137C2×D263—81no—
138C2×D263—81no—
139C2×D263—81no—
140C4×C263—42no—
141C4×C263—42no—
142C4×C263#12011yescharacteristic
143C4×C263#12111yescharacteristic
144C4×C263#12111yescharacteristic
145C4×C263#12711yescharacteristic
146Dic263—41no—
147Dic263—42no—
148C2×C263#39211yescharacteristic
149C2×C263#44811yescharacteristic
150C2×C263#44911yescharacteristic
151C2×C263#45011yescharacteristic
152C2×C263#45211yescharacteristic
153C2×C263#46511yescharacteristic
154C2×C263#46811yescharacteristic
155D263—42no—
156D263—82no—
157C263#200011yescharacteristic, complemented, Sylow
158#2000—2631nomaximal, Sylow
159C22×SD16—2631no—
160C2×C22⋊Q8—2631no—
161C2×#121—2631no—
162C2×#103D26311yescharacteristic, complemented
163C2×#102—2631no—
164C2×C22⋊C8—2631no—
165#340—2631no—
166C22×Q8C2×D26311yescharacteristic
167C22×D4—2631no—
168C22×D4—5261no—
169C23×C4—2631no—
170C2×SD16—5262no—
171C2×SD16—5262no—
172C2×SD16—5262no—
173C22×C8—2631no—
174C22×C8C2×D26311yescharacteristic
175C22⋊Q8—5262no—
176C22⋊Q8—5262no—
177#121—5262no—
178#121—5262no—
179C2×C4⋊C4—2631no—
180C2×C4⋊C4—5261no—
181C2×C4⋊C4C2×D26311yescharacteristic
182C2×C22⋊C4—5261no—
183C2×C22⋊C4—5261no—
184#103—22no—
185#102—5262no—
186C22⋊C8—5262no—
187C24—2631no—
188C24—5261no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8D105212yescomplemented
195C2×D4—2632no—
196C2×D4—5264no—
197C2×D4—5261no—
198C2×D4—5261no—
199C2×D4—5261no—
200C2×D4—5261no—
201C2×D4—5261no—
202C2×D4—10522no—
203C2×D4—10522no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—2631no—
207C22×C4—5261no—
208C22×C4—5261no—
209C22×C4—5261no—
210C22×C4—5261no—
211C22×C4—5261no—
212C22×C4—5261no—
213C22×C4—5261no—
214C22×C4C22×D26311yescharacteristic
215SD16—5268no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—2632no—
220C2×C8—5261no—
221C2×C8—5261no—
222C4⋊C4—21no—
223C4⋊C4—2632no—
224C4⋊C4—5264no—
225C4⋊C4—5261no—
226C4⋊C4C22⋊D26312yes—
227C22⋊C4—5264no—
228C22⋊C4—5264no—
229C23—2632no—
230C23—5261no—
231C23—5261no—
232C23—5261no—
233C23—5261no—
234C23—5261no—
235C23—5261no—
236C23—5262no—
237C23—10521no—
238C23—10521no—
239C23—10521no—
240C23—10521no—
241C23—10521no—
242C23—10521no—
243C23D4×D26311yescharacteristic
244Q8—22no—
245Q8—22no—
246Q8—41no—
247Q8—41no—
248D4—5262no—
249D4—5262no—
250D4—10528no—
251D4—10521no—
252D4—10521no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—5261no—
260C2×C4—5262no—
261C2×C4—5261no—
262C2×C4—5261no—
263C2×C4—10521no—
264C2×C4—10521no—
265C2×C4—10521no—
266C2×C4—10521no—
267C2×C4—10521no—
268C2×C4—10521no—
269C2×C4D4×D26311yescharacteristic
270C2×C4D4×D26311yescharacteristic
271C2×C4D4×D26311yescharacteristic
272C2×C4C2×C22⋊D26311yescharacteristic
273C2×C4C2×D105211yescharacteristic
274C2×C4#1686237611yescharacteristic
275C8—41no—
276C8—5262no—
277C22—5262no—
278C22—5262no—
279C22—5262no—
280C22—10521no—
281C22—10521no—
282C22—10521no—
283C22—10521no—
284C22—10522no—
285C22—10522no—
286C22—10522no—
287C22—21041no—
288C22—21041no—
289C22—21041no—
290C22—21041no—
291C22#2255443811yescharacteristic
292C22#2255444011yescharacteristic
293C22#2255444311yescharacteristic
294C22SD16×D26311yescharacteristic
295C22#2255449311yescharacteristic
296C22#2255449711yescharacteristic
297C22#2255450211yescharacteristic
298C4—42no—
299C4—42no—
300C4—10522no—
301C4—10521no—
302C4#2255444011yescharacteristic
303C4#2255444311yescharacteristic
304C4#2255444411yescharacteristic
305C4#2255446611yescharacteristic
306C2—10522no—
307C2—21042no—
308C2#3068184711yescharacteristic
309C2#3068207811yescharacteristic
310C2#3068208611yescharacteristic
311C2#3068208711yescharacteristic
312C2#3068209911yescharacteristic
313C2#3068217011yescharacteristic
314C2#3068218711yescharacteristic
subgroupG/H
centerC23D4×D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#103×C263C2
socleC23×C263C2×D4
prime radicalC2×#22554445C2
hypercenterC2×#103D263
hypocenterC263#2000
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#16862363C2semidirect
2. C2×#22554446C2semidirect
4. C2×#22554392C2semidirect
5. C2×(C2×D263)⋊C8C2semidirect
6. #30681700C2semidirect
7. C2×#103×C263C2semidirect
51. C2×C263⋊C8D4semidirect
53. C4⋊Dic263D4semidirect
62. C2×Q8×C263D4semidirect
84. C22×D263SD16semidirect
157. C263#2000semidirect
162. C2×#103D263semidirect
194. C2×Q8D1052semidirect

Maximal subgroups

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

subgroupindex
C22×#168623632
C2×#225544462
C2×#225544452
C2×#225543922
C2×(C2×D263)⋊C82
#306817002
C2×#103×C2632
#2000263