Finite Group Databasebeta

← #14853553

Subgroups — #14853553

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074591C211yesmaximal, characteristic
2#13071335C211yesmaximal, characteristic
3#13070185C212yesmaximal
4#13069863C212yesmaximal
5#13069306C212yesmaximal
6#13069292C212yesmaximal
7#13068632C212yesmaximal
8#13068622C212yesmaximal
9C11×#1768C211yesmaximal, characteristic
10C2×#66922C2211yescharacteristic
11C2×C4×Dic22C2212yes—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×#97C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C11×#376C2211yescharacteristic
16C2×#66880C2212yes—
17C2×#66880C2212yes—
18C2×#66880C2212yes—
19C2×#66880C2212yes—
20#10622549C2211yescharacteristic
21#10622549C2211yescharacteristic
22#10622548C2211yescharacteristic
23#10622542C2212yes—
24#10622541C2212yes—
25#10622541C2212yes—
26#10622273—22no—
27#10622270—22no—
28#10622266—22no—
29#10622266—22no—
30C11×#336C2212yes—
31#10622189C2212yes—
32#10622189C2212yes—
33#10622189C2212yes—
34#10622189C2212yes—
35C22×Dic22C2312yes—
36C22×C8×C11C2312yes—
37C22×C8×C11C2312yes—
38C2×C42×C11C2311yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—22no—
44C2×C4⋊Dic11C2312yes—
45C2×C4⋊Dic11C2312yes—
46C2×C4⋊Dic11C2312yes—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4—22no—
49C2×Dic11⋊C4—22no—
50C2×C4×Dic11—22no—
51#66922—24no—
52C4×Dic22—24no—
53C4×Dic22—24no—
54C11×C4⋊C8—24no—
55C11×#97—41no—
56C4×C8×C11—41no—
57C11×#95D412yes—
58C11×#95D412yes—
59C11⋊#95—24no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65#66880—24no—
66#66880—24no—
67#66880—42no—
68#66880—42no—
69#29135—111nomaximal, Sylow
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2411yescharacteristic
75C22×Dic11—22no—
76C22×Dic11—22no—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C2×Dic22—22no—
80C2×Dic22—22no—
81C2×Dic22—22no—
82C2×Dic22—22no—
83C2×Dic22—22no—
84C2×Dic22#4114yes—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C42×C11—22no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11#4114yes—
95C4⋊Dic11—24no—
96C4⋊Dic11—24no—
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—22no—
103C4⋊Dic11—82no—
104Dic11⋊C4—44no—
105Dic11⋊C4—82no—
106Dic11⋊C4—82no—
107C4×Dic11—44no—
108#2647—111no—
109#2327—111no—
110#2101—112no—
111#2043—112no—
112#1935—112no—
113#1933—112no—
114#1805—112no—
115#1803—112no—
116#1768D1111yescharacteristic
117C23×C11C22×D411yescharacteristic
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11#12414yes—
128C2×C4×C11C2×#4112yes—
129C2×C4×C11C2×#4112yes—
130C2×C4×C11H(5,𝔽2)11yescharacteristic
131C2×C4×C112−1+411yescharacteristic
132C2×Dic11—24no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144Dic22—24no—
145Dic22—24no—
146Dic22—42no—
147Dic22—42no—
148C8×C11—42no—
149C8×C11—42no—
150C2×C4⋊Q8—111no—
151C2×C4×Q8—112no—
152C2×C4⋊C8C2×D1112yes—
153C2×#103—112no—
154C2×#103—112no—
155C2×#103—112no—
156C2×#103—112no—
157C2×#97C2×D1111yescharacteristic
158C2×C4×C8C2×D1111yescharacteristic
159#400—222no—
160#398—222no—
161#391—112no—
162#389—112no—
163#389—112no—
164#387—222no—
165#387—222no—
166#384—111no—
167#382—111no—
168#382—111no—
169#376C2×D1111yescharacteristic
170#340—112no—
171#340—112no—
172#340—112no—
173#340—112no—
174#336C2×D1112yes—
175C22×C11#52511yescharacteristic
176C22×C11C2×#12411yescharacteristic
177C22×C11#53711yescharacteristic
178C22×C11#57712yes—
179C22×C11#57812yes—
180C4×C11—24no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—42no—
184C4×C11#55212yes—
185C4×C11#55312yes—
186Dic11—44no—
187Dic11—82no—
188Dic11—82no—
189Dic11—82no—
190C22×Q8—112no—
191C22×C8C22×D1112yes—
192C22×C8C22×D1112yes—
193C4⋊Q8—224no—
194C4×Q8—224no—
195C4×Q8—224no—
196C2×C4⋊C4—112no—
197C2×C4⋊C4—112no—
198C2×C4⋊C4—112no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4—222no—
204C2×C4⋊C4—222no—
205C2×C42—222no—
206C2×C42C22×D1111yescharacteristic
207C2×C42C22×D1111yescharacteristic
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—24no—
210#103—224no—
211#103—224no—
212#103—442no—
213#103—442no—
214#97—41no—
215C4×C8—41no—
216#95—221no—
217#95—221no—
218#95—222no—
219#95—224no—
220#95—222no—
221#95—222no—
222#95D4412yes—
223#95D4412yes—
224C2×C11#256211yescharacteristic
225C2×C11#312611yescharacteristic
226C2×C11#312711yescharacteristic
227C2×C11#313712yes—
228C2×C11#325812yes—
229C2×Q8—114no—
230C2×Q8—222no—
231C2×Q8—222no—
232C2×Q8—222no—
233C2×Q8—222no—
234C2×Q8—222no—
235C22×C4—222no—
236C22×C4—222no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4C2×D4412yes—
240C22×C4C2×D4411yescharacteristic
241C22×C4C2×D4411yescharacteristic
242C22×C4C2×D4412yes—
243C22×C4C23×D1111yescharacteristic
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C4⋊C4—224no—
251C4⋊C4—224no—
252C4⋊C4—222no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—444no—
259C4⋊C4—882no—
260C4⋊C4—882no—
261C4⋊C4—882no—
262C42—21no—
263C42—21no—
264C42—22no—
265C42—444no—
266C42#433914yes—
267C11#2913511yescharacteristic, complemented, Sylow
268C23C22×D4411yescharacteristic
269Q8—224no—
270Q8—224no—
271Q8—442no—
272Q8—442no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—224no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4#6692814yes—
295C2×C4C2×#433912yes—
296C2×C4#6703711yescharacteristic
297C2×C4#6704011yescharacteristic
298C2×C4#41×D1112yes—
299C8—42no—
300C8—42no—
301C22C2×#6692811yescharacteristic
302C22#1062304111yescharacteristic
303C22#1062305511yescharacteristic
304C22#1062328212yes—
305C22#1062328412yes—
306C4—24no—
307C4—41no—
308C4—41no—
309C4—42no—
310C4—444no—
311C4—882no—
312C4—882no—
313C4—882no—
314C4#1062308912yes—
315C4#1062311212yes—
316C2#1307377711yescharacteristic
317C2#1307890811yescharacteristic
318C2#1307891711yescharacteristic
319C2#1307898312yes—
320C2#1308004412yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1768C2
socle, prime radicalC23×C11C22×D4
hypercenter#1768D11
hypocenterC11#29135
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
267. C11#29135semidirect

Maximal subgroups

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

subgroupindex
#130745912
#130713352
#130701852
#130698632
#130693062
#130692922
#130686322
#130686222
C11×#17682
#2913511