Finite Group Databasebeta

← #14656971

Subgroups — #14656971

Order 2816.

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

normal subgroups only

This group has 352 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
1#13074268C211yesmaximal, characteristic
2#13069559C211yesmaximal, characteristic
3#13067168C211yesmaximal, characteristic
4#13067129C211yesmaximal, characteristic
5#13066508C211yesmaximal, characteristic
6#13066482C211yesmaximal, characteristic
7C11×#1285C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622597—21no—
13#10622597—21no—
14#10622550C2211yescharacteristic
15#10622546—21no—
16#10622545C2211yescharacteristic
17#10622541—21no—
18C4×#4318C2211yescharacteristic
19#10622268—21no—
20#10622260—21no—
21#10622161—21no—
22#10622161—21no—
23#10622105—21no—
24#10622105—21no—
25#10622105—21no—
26#10622105—21no—
27C2×C11×C4⋊C4—21no—
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34#66977—21no—
35#66977—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C2×#4318—21no—
42#66923—21no—
43#66922Q811yescharacteristic
44#66922Q811yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C11×#97—21no—
53C11×#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C11⋊#95D411yescharacteristic
61C11⋊#95D411yescharacteristic
62C11⋊#95D411yescharacteristic
63#66867—21no—
64C4×C11⋊C8—21no—
65#10381—111nomaximal, Sylow
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—42no—
80C42×C11—41no—
81C42×C11—41no—
82C42×C11C2×Q811yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C22⋊Dic11—41no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—42no—
92C4⋊Dic11—81no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99C4×Dic11—42no—
100C4×Dic11—41no—
101#4318—22no—
102#4318—41no—
103C2×C11⋊C8—41no—
104#2606—111no—
105#1986—111no—
106#1515—111no—
107#1506—111no—
108#1300—111no—
109#1288—111no—
110#1285D1111yescharacteristic
111C23×C11#12011yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11#12411yescharacteristic
126C2×C4×C11#12411yescharacteristic
127C2×C4×C11#12411yescharacteristic
128C2×Dic11—22no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142Dic22—81no—
143Dic22—81no—
144C8×C11—81no—
145C8×C11—81no—
146C11⋊C8—42no—
147#533—111no—
148#432C2×D1111yescharacteristic
149#432C2×D1111yescharacteristic
150C4×M16—111no—
151#398—221no—
152#398—221no—
153#389—221no—
154#389—221no—
155#387—221no—
156#387—221no—
157#383—111no—
158C4×C4⋊C4C2×D1111yescharacteristic
159#376—111no—
160#339—221no—
161#339—221no—
162#328—221no—
163#328—221no—
164#328—221no—
165#328—221no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39311yescharacteristic
169C22×C11#45511yescharacteristic
170C22×C11#45611yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—42no—
178C4×C11—81no—
179Dic11—42no—
180Dic11—81no—
181Dic11—81no—
182Dic11—81no—
183Dic11—81no—
184Dic11—81no—
185C2×M16—221no—
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188#125—221no—
189C22⋊Q8—221no—
190C22⋊Q8—221no—
191C4×Q8—221no—
192C4×Q8—221no—
193#117—221no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C42—221no—
202C2×C42D4411yescharacteristic
203C2×C42D4411yescharacteristic
204C2×C42C22×D1111yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C22⋊C8—21no—
208C22⋊C8—21no—
209#97—21no—
210#97—21no—
211#97—221no—
212C4×C8—221no—
213#95—21no—
214#95—111no—
215#95—111no—
216#95—111no—
217#95—111no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11#202811yescharacteristic
226C2×C11#203111yescharacteristic
227C2×C11#203111yescharacteristic
228C2×Q8—221no—
229C2×Q8—221no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4C2×D4411yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4D4×D1111yescharacteristic
239M16—222no—
240M16—441no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—441no—
244C4⋊C4—42no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—442no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—881no—
256C4⋊C4—881no—
257C22⋊C4—441no—
258C42—41no—
259C42—41no—
260C42—442no—
261C42—441no—
262C42#433911yescharacteristic
263C42#433911yescharacteristic
264C42#434111yescharacteristic
265C42Q8×D1111yescharacteristic
266C11#1038111yescharacteristic, complemented, Sylow
267C23#6693511yescharacteristic
268Q8—881no—
269Q8—881no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—222no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4#6692811yescharacteristic
295C2×C4#6693811yescharacteristic
296C2×C4#6693811yescharacteristic
297C2×C4#6694911yescharacteristic
298C2×C4#6694911yescharacteristic
299C2×C4#6695011yescharacteristic
300C8—81no—
301C8—81no—
302C8—442no—
303C22—21no—
304C22—21no—
305C22#1062228611yescharacteristic
306C22#1062235911yescharacteristic
307C22#1062236511yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—81no—
316C4—442no—
317C4—881no—
318C4—881no—
319C4—881no—
320C4—881no—
321C4—881no—
322C2—21no—
323C2—21no—
324C2#1306977811yescharacteristic
325C2#1306978711yescharacteristic
326C2#1306978911yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1285D11
hypocenterC11#10381
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
266. C11#10381semidirect

Maximal subgroups

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

subgroupindex
#130742682
#130695592
#130671682
#130671292
#130665082
#130664822
C11×#12852
#1038111