Finite Group Databasebeta

← #14853558

Subgroups — #14853558

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#13070183C212yesmaximal
3#13069859C212yesmaximal
4#13069309C212yesmaximal
5#13069295C212yesmaximal
6#13068631C212yesmaximal
7#13068621C212yesmaximal
8#13068473C211yesmaximal, characteristic
9C11×#2327C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2212yes—
12C11×#391C2212yes—
13C11×#387—22no—
14C11×#387—22no—
15C11×#382C2211yescharacteristic
16C11×#376C2211yescharacteristic
17C2×#66899C2212yes—
18C2×#66899C2212yes—
19C2×#66899C2212yes—
20C2×#66899C2212yes—
21#10622549C2211yescharacteristic
22#10622548C2211yescharacteristic
23#10622541C2212yes—
24#10622541C2212yes—
25C2×C4⋊(C11⋊C8)C2212yes—
26C2×#66867C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622273—22no—
29#10622270—22no—
30#10622167C2212yes—
31#10622167C2212yes—
32#10622167C2212yes—
33#10622167C2212yes—
34#10622162C2212yes—
35C22×Q8×C11C2312yes—
36C11×C4⋊Q8—24no—
37C4×Q8×C11—24no—
38C4×Q8×C11—24no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4C2312yes—
43C2×C42×C11—22no—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11C2312yes—
49C2×C4⋊Dic11C2312yes—
50C2×Dic11⋊C4—22no—
51C2×Dic11⋊C4—22no—
52C22×C11⋊C8C2312yes—
53C22×C11⋊C8C2312yes—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—24no—
57C11×#95D412yes—
58C11×#95D412yes—
59#66899—24no—
60#66899—24no—
61#66899—42no—
62#66899—42no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C4⋊(C11⋊C8)—24no—
67#66867—41no—
68C4×C11⋊C8—41no—
69#29135—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11#4114yes—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—44no—
90C42×C11—22no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—44no—
94C42×C11#4114yes—
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—82no—
100Dic11⋊C4—82no—
101Dic11⋊C4—82no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108#2647—111no—
109#2327D1111yescharacteristic
110#2101—112no—
111#2043—112no—
112#1935—112no—
113#1933—112no—
114#1805—112no—
115#1803—112no—
116#1768—111no—
117C23×C11C22×D411yescharacteristic
118Q8×C11—24no—
119Q8×C11—24no—
120Q8×C11—42no—
121Q8×C11—42no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—24no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11#12414yes—
138C2×C4×C11C2×#4112yes—
139C2×C4×C11C2×#4112yes—
140C2×C4×C11H(5,𝔽2)11yescharacteristic
141C2×C4×C112−1+411yescharacteristic
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C11⋊C8—42no—
149C11⋊C8—42no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151C2×C4×Q8C2×D1112yes—
152C2×C4⋊C8—112no—
153C2×#103—112no—
154C2×#103—112no—
155C2×#103—112no—
156C2×#103—112no—
157C2×#97—111no—
158C2×C4×C8—111no—
159#400—222no—
160#398—222no—
161#391C2×D1112yes—
162#389—112no—
163#389—112no—
164#387—22no—
165#387—22no—
166#384—111no—
167#382—111no—
168#382C2×D1111yescharacteristic
169#376C2×D1111yescharacteristic
170#340—112no—
171#340—112no—
172#340—112no—
173#340—112no—
174#336—112no—
175C22×C11#52511yescharacteristic
176C22×C11C2×#12411yescharacteristic
177C22×C11#53711yescharacteristic
178C22×C11#57712yes—
179C22×C11#57812yes—
180C4×C11—24no—
181C4×C11—44no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—42no—
185C4×C11—82no—
186C4×C11#55212yes—
187C4×C11#55312yes—
188Dic11—82no—
189Dic11—82no—
190C22×Q8C22×D1112yes—
191C22×C8—112no—
192C22×C8—112no—
193C4⋊Q8—24no—
194C4×Q8—24no—
195C4×Q8—24no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—112no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4—222no—
204C2×C4⋊C4C22×D1112yes—
205C2×C42—22no—
206C2×C42C22×D1111yescharacteristic
207C2×C42C22×D1111yescharacteristic
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—224no—
210#103—224no—
211#103—224no—
212#103—442no—
213#103—442no—
214#97—441no—
215C4×C8—441no—
216#95—21no—
217#95—21no—
218#95—24no—
219#95—222no—
220#95—222no—
221#95—222no—
222#95C22⋊D1112yes—
223#95C22⋊D1112yes—
224C2×C11#256211yescharacteristic
225C2×C11#312611yescharacteristic
226C2×C11#312711yescharacteristic
227C2×C11#313712yes—
228C2×C11#325812yes—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8#433914yes—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4C2×C22⋊D1112yes—
240C22×C4C2×C22⋊D1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242C22×C4C2×C22⋊D1112yes—
243C22×C4C23×D1111yescharacteristic
244C2×C8—222no—
245C2×C8—222no—
246C2×C8—222no—
247C2×C8—222no—
248C2×C8—222no—
249C2×C8—222no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—44no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—882no—
260C4⋊C4—882no—
261C4⋊C4—882no—
262C42—22no—
263C42—21no—
264C42—21no—
265C42—44no—
266C42#434114yes—
267C11#2913511yescharacteristic, complemented, Sylow
268C23C22×C22⋊D1111yescharacteristic
269Q8—24no—
270Q8—24no—
271Q8—42no—
272Q8—42no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4#6698914yes—
295C2×C4C2×#433912yes—
296C2×C4C2×#434112yes—
297C2×C4#6704211yescharacteristic
298C2×C4#6704311yescharacteristic
299C8—442no—
300C8—442no—
301C22#1062332211yescharacteristic
302C22C2×#6698911yescharacteristic
303C22#1062336411yescharacteristic
304C22#1062336812yes—
305C22#1062336912yes—
306C4—24no—
307C4—44no—
308C4—41no—
309C4—41no—
310C4—42no—
311C4—82no—
312C4—882no—
313C4—882no—
314C4#1062307212yes—
315C4#1062309612yes—
316C2#1307378211yescharacteristic
317C2#1307890711yescharacteristic
318C2#1307891611yescharacteristic
319C2#1307898112yes—
320C2#1308003612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2327C2
socle, prime radicalC23×C11C22×D4
hypercenter#2327D11
hypocenterC11#29135
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2327

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
#130701832
#130698592
#130693092
#130692952
#130686312
#130686212
#130684732
C11×#23272
#2913511