Finite Group Databasebeta

← #46783765

Subgroups — #46783765

Order 33664.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22554498C211yesmaximal, characteristic, complemented
2#30682507C211yesmaximal, characteristic, complemented
3C2×#22554467C211yesmaximal, characteristic, complemented
4C2×#22554398C211yesmaximal, characteristic, complemented
5#30681942C211yesmaximal, characteristic, complemented
6C2×#22554386C211yesmaximal, characteristic, complemented
7#339×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×D1052—22no—
10C22×D1052C2211yescharacteristic
11C22×D1052C2211yescharacteristic
12#22554498—22no—
13#22554498—22no—
14C2×#16862365—21no—
15C2×D2104—21no—
16C2×#16862360C2211yescharacteristic
17#22554467—22no—
18#22554467—21no—
19#22554467—22no—
20#22554458—21no—
21#22554445—22no—
22#22554440—22no—
23#22554398—22no—
24#22554390—22no—
25#22554386—22no—
26C2×M16×C263C2211yescharacteristic
27#117×C263C2211yescharacteristic
28C2×C42×C263C2211yescharacteristic
29C23×D263—21no—
30C23×D263D412yes—
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35C2×Dic526D411yescharacteristic, complemented
36C2×D1052—28no—
37C2×D1052—24no—
38C2×D1052—21no—
39C2×D1052—21no—
40C2×D1052—21no—
41C2×D1052—21no—
42C2×D1052—21no—
43C2×D1052—21no—
44C2×D1052—21no—
45C2×D1052—21no—
46C2×D1052—21no—
47C2×D1052—21no—
48C2×D1052—21no—
49C2×D1052—48no—
50C2×D1052D411yescharacteristic, complemented
51C2×D1052D412yescomplemented
52C2×C22⋊D263—21no—
53C2×C4×D263—21no—
54#16862365—24no—
55D2104—24no—
56#16862360—21no—
57#16862360—21no—
58C2×C263⋊C8—21no—
59(C2×D263)⋊C4—24no—
60C22×C4×C263—21no—
61C22×C4×C263C2311yescharacteristic
62M16×C263—21no—
63M16×C263D412yescomplemented
64C2×C8×C263—21no—
65C4⋊C4×C263D412yescomplemented
66C22⋊C4×C263—21no—
67C42×C263—21no—
68C42×C263—21no—
69C42×C263D412yescomplemented
70C22×D263—22no—
71C22×D263—21no—
72C22×D263—22no—
73C22×D263—22no—
74C22×D263—22no—
75C22×D263—44no—
76C22×D263—44no—
77C22×D263—41no—
78C22×D263—41no—
79Dic526—21no—
80Dic526—21no—
81D1052—21no—
82D1052—22no—
83D1052—22no—
84D1052—21no—
85D1052—416no—
86D1052—41no—
87D1052—41no—
88D1052—41no—
89D1052—41no—
90D1052—41no—
91D1052—41no—
92D1052—84no—
93C22⋊D263—41no—
94C22⋊D263—41no—
95C2×Dic263—21no—
96C4×D263—41no—
97C4×D263—41no—
98C263⋊C8—41no—
99C23×C263C2×D411yescharacteristic
100C2×C4×C263—24no—
101C2×C4×C263—22no—
102C2×C4×C263—22no—
103C2×C4×C263C2×D411yescharacteristic
104C2×C4×C263C2×D411yescharacteristic
105C2×C4×C263C2×D411yescharacteristic
106C2×C4×C263C2×D411yescharacteristic
107C2×C4×C263C2×D411yescharacteristic
108C2×C4×C263#4111yescharacteristic
109C8×C263—22no—
110C22×C263—22no—
111C22×C263#12011yescharacteristic
112C22×C263#12011yescharacteristic
113C22×C263#12111yescharacteristic
114C2×D263—44no—
115C2×D263—44no—
116C2×D263—41no—
117C2×D263—42no—
118C2×D263—42no—
119C2×D263—42no—
120C2×D263—44no—
121C2×D263—82no—
122C2×D263—82no—
123C2×D263—82no—
124C4×C263—24no—
125C4×C263—42no—
126C4×C263#12011yescharacteristic
127C4×C263#12111yescharacteristic
128C4×C263#12111yescharacteristic
129C4×C263#12711yescharacteristic
130Dic263—41no—
131C2×C263—21no—
132C2×C263—21no—
133C2×C263#39211yescharacteristic
134C2×C263#45312yes—
135D263—81no—
136D263—82no—
137D263—82no—
138C263#200211yescharacteristic, complemented, Sylow
139#2002—2631nomaximal, Sylow
140C2×AGL(1,ℤ/8)—2631no—
141#535—2631no—
142C2×#127—2631no—
143C2×#104—2631no—
144#418—2631no—
145C2×#100—2631no—
146#339D26311yescharacteristic, complemented
147C2×#41—2631no—
148C22×D4—2631no—
149C22×D4—2631no—
150C22×D4—5262no—
151AGL(1,ℤ/8)—5262no—
152AGL(1,ℤ/8)—5262no—
153C2×SD16—5261no—
154C2×D8—5261no—
155C2×M16—2631no—
156C2×M16C2×D26311yescharacteristic
157#127—5262no—
158#127—5261no—
159#127—5262no—
160#124—5261no—
161#121—5262no—
162#120—5262no—
163#117C2×D26311yescharacteristic
164C2×C42C2×D26311yescharacteristic
165#104—5262no—
166#102—5262no—
167#100—5262no—
168C24—2632no—
169C24—5261no—
170#41—5261no—
171#41—5261no—
172#41—5261no—
173#41—5261no—
174C2×Q8—2631no—
175C2×D4—2631no—
176C2×D4—2632no—
177C2×D4—5268no—
178C2×D4—5264no—
179C2×D4—5261no—
180C2×D4—5261no—
181C2×D4—5261no—
182C2×D4—5261no—
183C2×D4—5261no—
184C2×D4—5261no—
185C2×D4—5261no—
186C2×D4—5261no—
187C2×D4—5261no—
188C2×D4—5261no—
189C2×D4—5261no—
190C2×D4—5261no—
191C2×D4—10528no—
192C22×C4—21no—
193C22×C4—5261no—
194C22×C4C22×D26311yescharacteristic
195SD16—5264no—
196D8—5264no—
197M16—21no—
198M16—5261no—
199M16—5261no—
200M16D105212yescomplemented
201C2×C8—21no—
202C2×C8—5261no—
203C4⋊C4D105212yescomplemented
204C22⋊C4—21no—
205C22⋊C4—5264no—
206C42—21no—
207C42—21no—
208C42D105212yescomplemented
209C23—5262no—
210C23—5262no—
211C23—5262no—
212C23—5261no—
213C23—5262no—
214C23—10524no—
215C23—10524no—
216C23—10521no—
217C23—10521no—
218C23D4×D26311yescharacteristic
219Q8—5261no—
220Q8—5261no—
221D4—5261no—
222D4—5262no—
223D4—5262no—
224D4—5261no—
225D4—105216no—
226D4—10521no—
227D4—10521no—
228D4—10521no—
229D4—10521no—
230D4—10521no—
231D4—10521no—
232D4—10521no—
233D4—10521no—
234D4—21044no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—5261no—
239C2×C4—10521no—
240C2×C4—10521no—
241C2×C4D4×D26311yescharacteristic
242C2×C4D4×D26311yescharacteristic
243C2×C4C2×D105211yescharacteristic
244C2×C4C2×D105211yescharacteristic
245C2×C4C2×D105211yescharacteristic
246C2×C4#1686237711yescharacteristic
247C8—22no—
248C8—10521no—
249C22—22no—
250C22—10524no—
251C22—10524no—
252C22—10521no—
253C22—10522no—
254C22—10522no—
255C22—10522no—
256C22—10524no—
257C22—21042no—
258C22—21042no—
259C22—21042no—
260C22#2255444011yescharacteristic
261C22#2255444011yescharacteristic
262C22#2255444511yescharacteristic
263C4—24no—
264C4—42no—
265C4—10521no—
266C4#2255444011yescharacteristic
267C4#2255444511yescharacteristic
268C4#2255444511yescharacteristic
269C4#2255446711yescharacteristic
270C2—21no—
271C2—21no—
272C2—21042no—
273C2—21042no—
274C2—21041no—
275C2#3068184811yescharacteristic
276C2#3068210712yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263#120
hypercenter#339D263
hypocenterC263#2002
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#22554498C2semidirect
2. #30682507C2semidirect
3. C2×#22554467C2semidirect
4. C2×#22554398C2semidirect
5. #30681942C2semidirect
6. C2×#22554386C2semidirect
7. #339×C263C2semidirect
35. C2×Dic526D4semidirect
50. C2×D1052D4semidirect
51. C2×D1052D4semidirect
63. M16×C263D4semidirect
65. C4⋊C4×C263D4semidirect
69. C42×C263D4semidirect
138. C263#2002semidirect
146. #339D263semidirect
200. M16D1052semidirect
203. C4⋊C4D1052semidirect
208. C42D1052semidirect

Maximal subgroups

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

subgroupindex
C2×#225544982
#306825072
C2×#225544672
C2×#225543982
#306819422
C2×#225543862
#339×C2632
#2002263