Finite Group Databasebeta

← #14656737

Subgroups — #14656737

Order 2816.

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 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#13072894C212yesmaximal
2#13068690C212yesmaximal
3#13068688C211yesmaximal, characteristic
4C11⋊#1304C211yesmaximal, characteristic
5C11×#2483C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2212yes—
7C22×C22⋊Dic11C2211yescharacteristic
8C11×#397—22no—
9C11×#385—22no—
10C11×#381—22no—
11C11×#379C2211yescharacteristic
12#10622860C2211yescharacteristic
13#10622860C2212yes—
14#10622824—22no—
15#10622823—22no—
16#10622565—24no—
17#10622559—22no—
18#10622556—22no—
19#10622165—22no—
20#10622164—24no—
21C25×C11C2311yescharacteristic
22C23×C4×C11D412yes—
23C23×C4×C11D412yes—
24C23×Dic11D412yes—
25C2×C11×C4⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4D412yes—
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11D414yes—
43C2×Dic11⋊C4—24no—
44C11×#95—22no—
45C11×#95—24no—
46C11⋊#95—24no—
47C11⋊#95—24no—
48C11⋊#95—24no—
49#10339—111nomaximal, Sylow
50C24×C11—44no—
51C24×C11—42no—
52C24×C11C2×D411yescharacteristic
53C24×C11C2×D412yes—
54C24×C11C2×D412yes—
55C24×C11C2×D411yescharacteristic
56C24×C11#4111yescharacteristic
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—44no—
65C22×C4×C11—44no—
66C22×Dic11—22no—
67C22×Dic11—24no—
68C22×Dic11—22no—
69C22×Dic11—22no—
70C22×Dic11—44no—
71C22×Dic11—41no—
72C11×C4⋊C4—82no—
73C11×C22⋊C4—44no—
74C11×C22⋊C4—42no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C22⋊Dic11—44no—
80C22⋊Dic11—44no—
81C22⋊Dic11—44no—
82C22⋊Dic11—44no—
83C22⋊Dic11—42no—
84C22⋊Dic11—41no—
85C22⋊Dic11—42no—
86C22⋊Dic11—41no—
87Dic11⋊C4—84no—
88#2483—112no—
89#2483D1111yescharacteristic
90#1819—111no—
91#1819—112no—
92#1304—111no—
93C23×C11—24no—
94C23×C11—24no—
95C23×C11—24no—
96C23×C11—24no—
97C23×C11—22no—
98C23×C11—41no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—41no—
104C23×C11—42no—
105C23×C11—88no—
106C23×C11#12012yes—
107C23×C11#12011yescharacteristic
108C23×C11#12111yescharacteristic
109C23×C11#12112yes—
110C23×C11#12711yescharacteristic
111C2×C4×C11—44no—
112C2×C4×C11—44no—
113C2×C4×C11—44no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—44no—
117C2×C4×C11—42no—
118C2×C4×C11—44no—
119C2×C4×C11—82no—
120C2×C4×C11—82no—
121C2×Dic11—44no—
122C2×Dic11—44no—
123C2×Dic11—44no—
124C2×Dic11—42no—
125C2×Dic11—44no—
126C2×Dic11—44no—
127C2×Dic11—82no—
128C2×Dic11—82no—
129C2×Dic11—81no—
130C22×C22⋊C4—111no—
131C22×C22⋊C4C2×D1112yes—
132#397—22no—
133#397—224no—
134#385—22no—
135#385—222no—
136#385—222no—
137#381—22no—
138#381—222no—
139#381—222no—
140#379—112no—
141#379—111no—
142#379C2×D1111yescharacteristic
143#342—224no—
144#342—222no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—21no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—21no—
155C22×C11—44no—
156C22×C11—48no—
157C22×C11—84no—
158C22×C11—82no—
159C22×C11—82no—
160C22×C11#39211yescharacteristic
161C22×C11#45812yes—
162C22×C11#45814yes—
163C4×C11—82no—
164C4×C11—82no—
165C4×C11—82no—
166Dic11—84no—
167Dic11—82no—
168Dic11—161no—
169C25C22×D1111yescharacteristic
170C23×C4—112no—
171C23×C4C22⋊D1112yes—
172C23×C4C22⋊D1112yes—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—224no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—114no—
183C2×C22⋊C4—222no—
184C2×C22⋊C4—222no—
185C2×C22⋊C4—221no—
186C2×C22⋊C4—221no—
187C2×C22⋊C4—222no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C22⋊C4—221no—
191C2×C22⋊C4C22⋊D1112yes—
192#95—22no—
193#95—24no—
194#95—224no—
195#95—224no—
196#95—224no—
197C2×C11—24no—
198C2×C11—22no—
199C2×C11—41no—
200C2×C11—42no—
201C2×C11—41no—
202C2×C11#202212yes—
203C2×C11#202211yescharacteristic
204C24—42no—
205C24—44no—
206C24D4×D1111yescharacteristic
207C24D4×D1112yes—
208C24#434111yescharacteristic
209C24C2×C22⋊D1112yes—
210C24C2×C22⋊D1111yescharacteristic
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—44no—
219C22×C4—44no—
220C22×C4—222no—
221C22×C4—224no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—444no—
225C22×C4—441no—
226C4⋊C4—82no—
227C4⋊C4—884no—
228C22⋊C4—44no—
229C22⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—444no—
235C22⋊C4—444no—
236C22⋊C4—442no—
237C22⋊C4—441no—
238C22⋊C4—441no—
239C22⋊C4—444no—
240C22⋊C4—442no—
241C22⋊C4—444no—
242C11#1033911yescharacteristic, complemented, Sylow
243C23—24no—
244C23—24no—
245C23—24no—
246C23—22no—
247C23—24no—
248C23—41no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—41no—
254C23—42no—
255C23—88no—
256C23#6699012yes—
257C23#6699111yescharacteristic
258C23#6699212yes—
259C23#6699311yescharacteristic
260C23#6700611yescharacteristic
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—444no—
272C2×C4—444no—
273C2×C4—444no—
274C2×C4—442no—
275C2×C4—444no—
276C2×C4—444no—
277C2×C4—882no—
278C2×C4—882no—
279C2×C4—881no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—21no—
289C22—21no—
290C22—48no—
291C22—44no—
292C22—82no—
293C22—84no—
294C22—82no—
295C22#1062266614yes—
296C22#1062283611yescharacteristic
297C22#1062285612yes—
298C4—82no—
299C4—82no—
300C4—82no—
301C4—884no—
302C4—882no—
303C4—1761no—
304C2—22no—
305C2—24no—
306C2—41no—
307C2—42no—
308C2—41no—
309C2#1306974412yes—
310C2#1306974511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, prime radical, cosocleC25×C11C23
FrattiniC25C22×D11
FittingC11×#2483C2
socleC22×C11#392
hypercenter#2483D11
hypocenterC11#10339
LCSG ▷ C25×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2483

Complements

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

NH ≅ G/Ntype
242. C11#10339semidirect

Maximal subgroups

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

subgroupindex
#130728942
#130686902
#130686882
C11⋊#13042
C11×#24832
#1033911