Finite Group Databasebeta

← #46783809

Subgroups — #46783809

Order 33664.

348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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#30682738C211yesmaximal, characteristic
2C2×#22554501C211yesmaximal, characteristic, complemented
3#30682512C211yesmaximal, characteristic, complemented
4#30681956C211yesmaximal, characteristic, complemented
5#30681911C211yesmaximal, characteristic, complemented
6#30681709C211yesmaximal, characteristic, complemented
7#419×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C2×#16862376C2211yescharacteristic
10#22554503—21no—
11#22554503—21no—
12#22554501—22no—
13#22554501—22no—
14#22554498—21no—
15#22554498—21no—
16#22554492—22no—
17C2×#16862366—21no—
18C2×#16862363—21no—
19C2×#16862360C2211yescharacteristic
20#22554468—21no—
21#22554459—21no—
22#22554453—22no—
23#22554446—22no—
24#22554429C2211yescharacteristic
25#22554398—22no—
26#22554384—22no—
27C22×Q8×C263C2211yescharacteristic
28C2×M16×C263C2211yescharacteristic
29#117×C263C2211yescharacteristic
30#103×C263—22no—
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35#16862376—21no—
36#16862376—21no—
37#16862376—21no—
38#16862376—21no—
39C2×Dic526D411yescharacteristic
40C2×Dic526D411yescharacteristic
41C2×D1052D411yescharacteristic
42C2×D1052D411yescharacteristic
43C2×C22⋊D263—21no—
44C2×C22⋊D263—21no—
45C2×C4×D263—21no—
46C2×C4×D263—21no—
47Dic1052—22no—
48#16862366—24no—
49#16862365—22no—
50#16862365—22no—
51#16862363—24no—
52D2104—22no—
53#16862360—21no—
54#16862360D412yes—
55C2×C263⋊C8—21no—
56C4⋊Dic263—21no—
57Dic263⋊C4—24no—
58C22⋊Dic263D412yes—
59(C2×D263)⋊C4—24no—
60C4×Dic263—21no—
61C2×Q8×C263—21no—
62C2×Q8×C263—21no—
63C2×Q8×C263—21no—
64C2×Q8×C263—21no—
65C2×Q8×C263—21no—
66C2×Q8×C263D412yes—
67C22×C4×C263—21no—
68C22×C4×C263C2311yescharacteristic
69M16×C263—21no—
70M16×C263—21no—
71C2×C8×C263D412yes—
72C4⋊C4×C263—21no—
73C22⋊C4×C263—21no—
74C42×C263—21no—
75C22×D263—21no—
76C22×D263—21no—
77Dic526—21no—
78Dic526—21no—
79Dic526—21no—
80Dic526—21no—
81D1052—21no—
82D1052—21no—
83D1052—21no—
84D1052—21no—
85C22⋊D263—41no—
86C22⋊D263—41no—
87C22⋊D263—41no—
88C22⋊D263—41no—
89C2×Dic263—22no—
90C2×Dic263—21no—
91C2×Dic263—21no—
92C4×D263—41no—
93C4×D263—41no—
94C4×D263—41no—
95C4×D263—41no—
96C263⋊C8—22no—
97C23×C263C2×D411yescharacteristic
98Q8×C263—22no—
99Q8×C263—22no—
100Q8×C263—41no—
101Q8×C263—41no—
102C2×C4×C263—22no—
103C2×C4×C263—41no—
104C2×C4×C263—41no—
105C2×C4×C263—41no—
106C2×C4×C263C2×D411yescharacteristic
107C2×C4×C263C2×D411yescharacteristic
108C2×C4×C263C2×D411yescharacteristic
109C2×C4×C263C2×D411yescharacteristic
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263#4111yescharacteristic
112C8×C263—22no—
113C22×C263—41no—
114C22×C263#12011yescharacteristic
115C22×C263#12111yescharacteristic
116C22×C263#12711yescharacteristic
117C2×D263—42no—
118C2×D263—41no—
119C2×D263—41no—
120C2×D263—81no—
121C4×C263—42no—
122C4×C263—81no—
123C4×C263#12011yescharacteristic
124C4×C263#12011yescharacteristic
125C4×C263#12111yescharacteristic
126C4×C263#12111yescharacteristic
127Dic263—42no—
128Dic263—41no—
129Dic263—41no—
130C2×C263—21no—
131C2×C263—21no—
132C2×C263—21no—
133C2×C263#39211yescharacteristic
134D263—81no—
135D263—81no—
136C263#200911yescharacteristic, complemented, Sylow
137#2009—2631nomaximal, Sylow
138#575—2631no—
139C2×#137—2631no—
140#536—2631no—
141#421—2631no—
142#419D26311yescharacteristic, complemented
143#410—2631no—
144#344—2631no—
145C2×#41—2631no—
146C2×#41—2631no—
147C22×Q8C2×D26311yescharacteristic
148#137—5261no—
149#137—5261no—
150#137—5262no—
151#137—5262no—
152AGL(1,ℤ/8)—5261no—
153AGL(1,ℤ/8)—5261no—
154#135—5262no—
155C2×Q16—5261no—
156C2×SD16—5261no—
157C2×M16—2631no—
158C2×M16C2×D26311yescharacteristic
159C4⋊Q8—5261no—
160#124—5261no—
161#123—5262no—
162C22⋊Q8—5262no—
163#117—2631no—
164#117C2×D26311yescharacteristic
165#104—5262no—
166#103—22no—
167#99—5262no—
168#41—5261no—
169#41—5261no—
170#41—5261no—
171#41—5261no—
172#41—5261no—
173#41—5261no—
174#41—5261no—
175#41—5261no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—2631no—
182C2×Q8—2631no—
183C2×Q8D105212yes—
184C2×D4—2631no—
185C2×D4—2631no—
186C2×D4—5261no—
187C2×D4—5261no—
188C22×C4—21no—
189C22×C4—5261no—
190C22×C4—5261no—
191C22×C4C22×D26311yescharacteristic
192Q16—5262no—
193Q16—5264no—
194SD16—5262no—
195SD16—5262no—
196SD16—5264no—
197D8—5262no—
198M16—21no—
199M16—21no—
200M16—2632no—
201M16—5261no—
202C2×C8—5261no—
203C2×C8C22⋊D26312yes—
204C4⋊C4—21no—
205C4⋊C4—5264no—
206C4⋊C4—5261no—
207C22⋊C4—21no—
208C22⋊C4—2632no—
209C22⋊C4—5264no—
210C42—21no—
211C42—5261no—
212C23—5261no—
213C23—5261no—
214C23D4×D26311yescharacteristic
215Q8—22no—
216Q8—22no—
217Q8—41no—
218Q8—41no—
219Q8—5261no—
220Q8—5261no—
221Q8—5261no—
222Q8—5261no—
223D4—5261no—
224D4—5261no—
225D4—5261no—
226D4—5261no—
227D4—10521no—
228D4—10521no—
229D4—10521no—
230D4—10521no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—5262no—
236C2×C4—5261no—
237C2×C4—5261no—
238C2×C4—10521no—
239C2×C4—10521no—
240C2×C4—10521no—
241C2×C4—10521no—
242C2×C4D4×D26311yescharacteristic
243C2×C4D4×D26311yescharacteristic
244C2×C4D4×D26311yescharacteristic
245C2×C4C2×C22⋊D26311yescharacteristic
246C2×C4C2×D105211yescharacteristic
247C2×C4#1686237611yescharacteristic
248C8—22no—
249C8—5262no—
250C22—41no—
251C22—10522no—
252C22—10521no—
253C22—10521no—
254C22—21041no—
255C22#2255444011yescharacteristic
256C22#2255444311yescharacteristic
257C22#2255446611yescharacteristic
258C4—42no—
259C4—81no—
260C4—10522no—
261C4—10521no—
262C4—10521no—
263C4#2255443811yescharacteristic
264C4#2255444011yescharacteristic
265C4#2255444311yescharacteristic
266C4#2255444411yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—21041no—
271C2—21041no—
272C2#3068184711yescharacteristic
subgroupG/H
centerC2#30681847
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#419×C263C2
socleC2×C263#392
prime radical#30682738C2
hypercenter#419D263
hypocenterC263#2009
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C2×#22554501C2semidirect
3. #30682512C2semidirect
4. #30681956C2semidirect
5. #30681911C2semidirect
6. #30681709C2semidirect
7. #419×C263C2semidirect
136. C263#2009semidirect
142. #419D263semidirect

Maximal subgroups

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

subgroupindex
#306827382
C2×#225545012
#306825122
#306819562
#306819112
#306817092
#419×C2632
#2009263