Finite Group Databasebeta

← #14648274

Subgroups — #14648274

Order 2816.

412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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#13077682C211yesmaximal, characteristic
2#13069443C211yesmaximal, characteristic
3#13067407C211yesmaximal, characteristic, complemented
4#13067276C211yesmaximal, characteristic
5#13066448C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#1574C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66889—22no—
13C42×Dic11C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622538C2211yescharacteristic
16#10622451—21no—
17#10622447—21no—
18#10622340—22no—
19#10622301—21no—
20C8×D44—21no—
21C11×#335—21no—
22C11×#334—21no—
23#10622123C411yescharacteristic, complemented
24#10622123C411yescharacteristic, complemented
25#10622119C411yescharacteristic, complemented
26#10622119C411yescharacteristic, complemented
27#10622118—21no—
28#10622117—21no—
29C2×#4339D412yes—
30C2×C11×M16—21no—
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4×Dic11—21no—
35C2×C4×Dic11—21no—
36C2×C4×Dic11—21no—
37C2×#4313—22no—
38C2×C8×D11—22no—
39#66928Q812yes—
40#66927C2×C411yescharacteristic
41C4×D44—21no—
42C4×D44—21no—
43#66922C2×C411yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8C2×C411yescharacteristic
47C11×C4⋊C8C2×C411yescharacteristic
48C11×C4⋊C8D411yescharacteristic
49C11×C4⋊C8D411yescharacteristic
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56#66889—44no—
57(C2×D11)⋊C8—22no—
58(C2×D11)⋊C8—22no—
59C4⋊(C11⋊C8)C2×C411yescharacteristic
60C4⋊(C11⋊C8)C2×C411yescharacteristic
61C4⋊(C11⋊C8)D411yescharacteristic
62C4⋊(C11⋊C8)D411yescharacteristic
63C4×C11⋊C8—21no—
64C4×C11⋊C8—21no—
65#8934—111nomaximal, Sylow
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C2×C22⋊D11—22no—
70C22×Dic11—41no—
71#4339—42no—
72#4339—42no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44C4⋊C412yes—
76C2×C4×D11—22no—
77C2×Dic22C4⋊C412yes—
78C11×M16—42no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—41no—
84C42×C11C22×C411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×Q811yescharacteristic
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4×Dic11—22no—
93C4×Dic11—22no—
94C4×Dic11—22no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97C4×Dic11—41no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102#4313—82no—
103C8×D11—82no—
104#2979—111no—
105#1962—111no—
106#1574—111no—
107#1574D1111yescharacteristic, complemented
108#1543—111no—
109#1276—111no—
110#1276—111no—
111C23×C11#12311yescharacteristic
112C22×D11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×C4⋊C411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11C4×D411yescharacteristic
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C22⋊D11—82no—
126C2×Dic11—22no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130D44—42no—
131D44—41no—
132D44—41no—
133D44—41no—
134D44—41no—
135C4×D11—42no—
136C4×D11—42no—
137Dic22—42no—
138C8×C11—41no—
139C8×C11—41no—
140C8×C11—41no—
141C8×C11—41no—
142C8×C11—81no—
143C11⋊C8—41no—
144C11⋊C8—41no—
145C11⋊C8—41no—
146C11⋊C8—41no—
147#532—111no—
148#436—221no—
149#436—221no—
150C8×D4—221no—
151C8×D4—221no—
152#431—111no—
153#431—111no—
154#431C2×D1111yescharacteristic
155#431C2×D1111yescharacteristic
156#423C2×D1111yescharacteristic
157C2×#104—222no—
158#408—222no—
159C43—111no—
160#335—21no—
161#335—221no—
162#334—21no—
163#334—221no—
164#333—111no—
165#333—111no—
166#331—111no—
167#331—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#38511yescharacteristic
172C2×D11—42no—
173C2×D11—42no—
174C2×D11—42no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11#44311yescharacteristic
179C4×C11#44311yescharacteristic
180C4×C11#44411yescharacteristic
181C4×C11#44411yescharacteristic
182C4×C11#45311yescharacteristic
183C4×C11#45511yescharacteristic
184Dic11—44no—
185Dic11—42no—
186C2×#41—112no—
187C2×M16—21no—
188C2×M16—222no—
189C22×C8—222no—
190C4⋊Q8—111no—
191#127—111no—
192#124—112no—
193#121—221no—
194#121—221no—
195C4×D4—221no—
196C4×D4—221no—
197C2×C42—221no—
198C2×C42—221no—
199C2×C42—221no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206C4⋊C8—111no—
207C4⋊C8C4×D1111yescharacteristic
208C4⋊C8C4×D1111yescharacteristic
209C4⋊C8C22⋊D1111yescharacteristic
210C4⋊C8C22⋊D1111yescharacteristic
211#104—444no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C22⋊C8—222no—
215C22⋊C8—222no—
216C22⋊C8—221no—
217C22⋊C8—221no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—221no—
221C4×C8—221no—
222C2×C11—41no—
223C2×C11#185611yescharacteristic
224C2×C11#186611yescharacteristic
225C2×C11#186611yescharacteristic
226D11—82no—
227#41—442no—
228#41—442no—
229C2×Q8—112no—
230C2×D4—112no—
231C2×D4—222no—
232C2×D4—221no—
233C2×D4—221no—
234C22×C4—222no—
235C22×C4—441no—
236C22×C4#433911yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4#434311yescharacteristic
239M16—42no—
240M16—882no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—882no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C22⋊C4—222no—
254C22⋊C4—222no—
255C42—222no—
256C42—222no—
257C42—222no—
258C42—441no—
259C42—441no—
260C42—441no—
261C42C2×C4×D1111yescharacteristic
262C42D4×D1111yescharacteristic
263C42Q8×D1111yescharacteristic
264C42C2×C22⋊D1111yescharacteristic
265C11#893411yescharacteristic, complemented, Sylow
266C23—222no—
267C23#6694711yescharacteristic
268Q8—442no—
269D4—442no—
270D4—441no—
271D4—441no—
272D4—441no—
273D4—441no—
274D4—882no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—222no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4C4⋊C4×D1111yescharacteristic
288C2×C4#6694611yescharacteristic
289C2×C4#6694911yescharacteristic
290C2×C4C4×C22⋊D1111yescharacteristic
291C2×C4#6699011yescharacteristic
292C2×C4#6699911yescharacteristic
293C8—41no—
294C8—41no—
295C8—41no—
296C8—41no—
297C8—81no—
298C8—441no—
299C8—441no—
300C8—441no—
301C8—441no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—442no—
306C22—442no—
307C22—442no—
308C22#1062260211yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—444no—
313C4—442no—
314C4#1062250711yescharacteristic
315C4#1062250811yescharacteristic
316C4#1062275711yescharacteristic
317C4#1062275811yescharacteristic
318C4#1062281111yescharacteristic
319C4#1062281511yescharacteristic
320C2—41no—
321C2—882no—
322C2#1306882411yescharacteristic
323C2#1306888811yescharacteristic
324C2#1306889011yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1574C2
socleC22×C11#385
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1574D11
hypocenterC11#8934
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #13067407C2semidirect
5. #13066448C2semidirect
6. #13066448C2semidirect
7. C11×#1574C2semidirect
23. #10622123C4semidirect
24. #10622123C4semidirect
25. #10622119C4semidirect
26. #10622119C4semidirect
107. #1574D11semidirect
265. C11#8934semidirect

Maximal subgroups

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

subgroupindex
#130776822
#130694432
#130674072
#130672762
#130664482
C11×#15742
#893411