Finite Group Databasebeta

← #46783763

Subgroups — #46783763

Order 33664.

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

normal subgroups only

This group has 478 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
1C2×#22554496C211yesmaximal, characteristic, complemented
2#30682507C211yesmaximal, characteristic, complemented
3C2×#22554466C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5C2×#22554386C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7#418×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10C22×C22⋊D263—22no—
11#22554496—22no—
12#22554496—22no—
13C2×#16862364—21no—
14C2×#16862361—21no—
15C2×#16862360C2211yescharacteristic
16#22554467—21no—
17#22554466—22no—
18#22554466—22no—
19#22554458—21no—
20#22554445—22no—
21#22554440—22no—
22C2×C4×Dic263C2211yescharacteristic
23#22554396—22no—
24#22554386—22no—
25C22×D4×C263C2211yescharacteristic
26C2×M16×C263C2211yescharacteristic
27#117×C263C2211yescharacteristic
28#102×C263—22no—
29C23×D263D412yes—
30#16862376—21no—
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34C2×Dic526D411yescharacteristic, complemented
35C2×D1052—24no—
36C2×D1052—21no—
37C2×D1052—21no—
38C2×D1052—21no—
39C2×D1052—21no—
40C2×D1052—21no—
41C2×D1052—21no—
42C2×D1052D411yescharacteristic, complemented
43C2×C22⋊D263—28no—
44C2×C22⋊D263—21no—
45C2×C22⋊D263—48no—
46C22×Dic263—21no—
47C2×C4×D263—21no—
48#16862364—24no—
49#16862361—24no—
50#16862360—21no—
51#16862360D412yescomplemented
52C2×C263⋊C8—21no—
53(C2×D263)⋊C4—24no—
54C4×Dic263—21no—
55C4×Dic263D412yescomplemented
56C24×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263—21no—
59C2×D4×C263—21no—
60C2×D4×C263—21no—
61C2×D4×C263—21no—
62C2×D4×C263D412yescomplemented
63C22×C4×C263C2311yescharacteristic
64M16×C263—21no—
65M16×C263—21no—
66C2×C8×C263—21no—
67C4⋊C4×C263D412yescomplemented
68C22⋊C4×C263—21no—
69C42×C263—21no—
70C22×D263—22no—
71C22×D263—21no—
72C22×D263—22no—
73C22×D263—22no—
74C22×D263—44no—
75Dic526—21no—
76Dic526—21no—
77D1052—21no—
78D1052—21no—
79D1052—41no—
80D1052—41no—
81D1052—41no—
82D1052—41no—
83D1052—84no—
84C22⋊D263—416no—
85C22⋊D263—41no—
86C22⋊D263—41no—
87C2×Dic263—24no—
88C2×Dic263—22no—
89C2×Dic263—21no—
90C4×D263—41no—
91C4×D263—41no—
92C263⋊C8—22no—
93C23×C263—22no—
94C23×C263—44no—
95C23×C263—41no—
96C23×C263—41no—
97C23×C263C2×D411yescharacteristic
98D4×C263—22no—
99D4×C263—22no—
100D4×C263—41no—
101D4×C263—41no—
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—41no—
110C22×C263—22no—
111C22×C263—44no—
112C22×C263—42no—
113C22×C263—82no—
114C22×C263—82no—
115C22×C263#12011yescharacteristic
116C22×C263#12011yescharacteristic
117C22×C263#12111yescharacteristic
118C2×D263—44no—
119C2×D263—41no—
120C2×D263—42no—
121C2×D263—42no—
122C2×D263—44no—
123C2×D263—82no—
124C4×C263—42no—
125C4×C263#12011yescharacteristic
126C4×C263#12111yescharacteristic
127C4×C263#12111yescharacteristic
128C4×C263#12711yescharacteristic
129Dic263—24no—
130Dic263—41no—
131C2×C263—21no—
132C2×C263—21no—
133C2×C263—82no—
134C2×C263#39211yescharacteristic
135C2×C263#45312yes—
136D263—81no—
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#418D26311yescharacteristic, complemented
145C2×#100—2631no—
146#339—2631no—
147C2×#41—2631no—
148C22×D4—2631no—
149C22×D4—5262no—
150C22×D4C2×D26311yescharacteristic
151AGL(1,ℤ/8)—5262no—
152AGL(1,ℤ/8)—5262no—
153C2×SD16—5261no—
154C2×D8—5261no—
155C2×M16—2631no—
156C2×M16C2×D26311yescharacteristic
157#127—5261no—
158#127—5262no—
159#127—5262no—
160#124—5261no—
161#121—5262no—
162#120—5262no—
163#117C2×D26311yescharacteristic
164C2×C42—2631no—
165#104—5262no—
166#102—22no—
167#100—5262no—
168C24—21no—
169C24—2632no—
170#41—5261no—
171#41—5261no—
172#41—5261no—
173#41—5261no—
174C2×Q8—2631no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—2631no—
181C2×D4—5264no—
182C2×D4—5268no—
183C2×D4—5261no—
184C2×D4—5261no—
185C2×D4—5261no—
186C2×D4—5261no—
187C2×D4—5261no—
188C2×D4—5261no—
189C2×D4—5261no—
190C2×D4—10528no—
191C2×D4D105212yescomplemented
192C22×C4—5261no—
193C22×C4—5261no—
194C22×C4C22×D26311yescharacteristic
195SD16—5264no—
196D8—5264no—
197M16—21no—
198M16—21no—
199M16—2632no—
200M16—5261no—
201C2×C8—21no—
202C2×C8—5261no—
203C4⋊C4C22⋊D26312yescomplemented
204C22⋊C4—21no—
205C22⋊C4—5264no—
206C42—21no—
207C42—2632no—
208C42—5261no—
209C23—22no—
210C23—44no—
211C23—41no—
212C23—41no—
213C23—5262no—
214C23—5261no—
215C23—5262no—
216C23—5262no—
217C23—10524no—
218C23D4×D26311yescharacteristic
219Q8—5261no—
220Q8—5261no—
221D4—22no—
222D4—22no—
223D4—41no—
224D4—41no—
225D4—5261no—
226D4—5261no—
227D4—105216no—
228D4—10521no—
229D4—10521no—
230D4—10521no—
231D4—10521no—
232D4—10521no—
233D4—10521no—
234D4—21044no—
235C2×C4—22no—
236C2×C4—5264no—
237C2×C4—5262no—
238C2×C4—5261no—
239C2×C4—10521no—
240C2×C4—10521no—
241C2×C4D4×D26311yescharacteristic
242C2×C4D4×D26311yescharacteristic
243C2×C4D4×D26311yescharacteristic
244C2×C4C2×C22⋊D26311yescharacteristic
245C2×C4C2×D105211yescharacteristic
246C2×C4#1686237611yescharacteristic
247C8—41no—
248C8—5262no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—82no—
253C22—82no—
254C22—10524no—
255C22—10521no—
256C22—10522no—
257C22—10522no—
258C22—10524no—
259C22—21042no—
260C22#2255443811yescharacteristic
261C22#2255444011yescharacteristic
262C22#2255444311yescharacteristic
263C4—42no—
264C4—5264no—
265C4—10521no—
266C4#2255444011yescharacteristic
267C4#2255444311yescharacteristic
268C4#2255444411yescharacteristic
269C4#2255446611yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—21042no—
274C2—21041no—
275C2#3068184711yescharacteristic
276C2#3068210412yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#418×C263C2
socleC22×C263#120
hypercenter#418D263
hypocenterC263#2002
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#22554496C2semidirect
2. #30682507C2semidirect
3. C2×#22554466C2semidirect
4. C2×#22554396C2semidirect
5. C2×#22554386C2semidirect
6. #30681697C2semidirect
7. #418×C263C2semidirect
34. C2×Dic526D4semidirect
42. C2×D1052D4semidirect
51. #16862360D4semidirect
55. C4×Dic263D4semidirect
62. C2×D4×C263D4semidirect
67. C4⋊C4×C263D4semidirect
138. C263#2002semidirect
144. #418D263semidirect
191. C2×D4D1052semidirect
203. C4⋊C4C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544962
#306825072
C2×#225544662
C2×#225543962
C2×#225543862
#306816972
#418×C2632
#2002263