Finite Group Databasebeta

← C11×#11900 #14589093

Subgroups — C11×#11900 #14589093

Order 2816.

452 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C11×#2563C211yesmaximal, characteristic
2C11×#1799C211yesmaximal, characteristic
3C11×#1459C211yesmaximal, characteristic
4C11×#1351C214yesmaximal, complemented
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×C11×#99—21no—
8C2×C11×C22⋊C8—21no—
9C11×#393C412yescomplemented
10C11×#393C2212yes—
11C11×#390—21no—
12C11×#382—21no—
13C11×#380—21no—
14C11×#380—21no—
15C11×#380—21no—
16C4×C11×C4⋊C4C411yescharacteristic, complemented
17C11×#342C2212yes—
18C11×#324—21no—
19C11×#323C2212yes—
20C22×Q8×C11C2×C412yes—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C22×C8×C11—41no—
25C11×C4⋊Q8—41no—
26C11×C4⋊Q8—41no—
27C4×D4×C11—41no—
28C4×D4×C11—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2×C411yescharacteristic
41C11×#99—42no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—41no—
44C11×#95—22no—
45C11×#95—22no—
46C11×#95—41no—
47C11×#95C2×C412yes—
48#11900C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C2×D411yescharacteristic
51C2×Q8×C11—42no—
52C2×Q8×C11—82no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11SD1612yes—
56C2×D4×C11Q1612yes—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C8×C11—42no—
72C2×C8×C11—82no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—82no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—82no—
84C11×C22⋊C4—82no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—42no—
88#2563C2×C1111yescharacteristic
89#1799C2×C1111yescharacteristic
90#1459C2×C1111yescharacteristic
91#1351C2×C1114yescomplemented
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11#10312yes—
101C23×C11C2×C22⋊C411yescharacteristic
102C23×C11C2×SD1611yescharacteristic
103C23×C11C2×Q1611yescharacteristic
104Q8×C11—84no—
105D4×C11—42no—
106D4×C11—42no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11—82no—
127C2×C4×C11—82no—
128C2×C4×C11—82no—
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#10312yes—
132C8×C11—82no—
133C2×C4⋊Q8C4×C1111yescharacteristic, complemented
134C2×C4×D4C22×C1111yescharacteristic
135C2×#99—21no—
136C2×C22⋊C8—21no—
137#393C4×C1112yescomplemented
138#393C22×C1112yes—
139#390—21no—
140#382—21no—
141#380—21no—
142#380—21no—
143#380—21no—
144C4×C4⋊C4C4×C1111yescharacteristic, complemented
145#342C22×C1112yes—
146#324—21no—
147#323C22×C1112yes—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—22no—
152C22×C11—21no—
153C22×C11—42no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—81no—
161C22×C11—81no—
162C22×C11C2×#9911yescharacteristic
163C22×C11C2×#10311yescharacteristic
164C22×C11#42111yescharacteristic
165C4×C11—21no—
166C4×C11—22no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—82no—
171C4×C11—82no—
172C4×C11—162no—
173C4×C11#35412yes—
174C22×Q8C2×C4×C1112yes—
175C22×D4D4×C1111yescharacteristic
176C23×C4D4×C1111yescharacteristic
177C23×C4D4×C1111yescharacteristic
178C22×C8—41no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181C4×D4—41no—
182C4×D4—41no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4D4×C1111yescharacteristic
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4C2×C4×C1111yescharacteristic
192C2×C22⋊C4C23×C1111yescharacteristic
193C2×C42—21no—
194C2×C42C2×C4×C1111yescharacteristic
195#99—42no—
196C22⋊C8—22no—
197C22⋊C8—41no—
198#95—22no—
199#95—22no—
200#95—41no—
201#95C2×C4×C1112yes—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11—41no—
205C2×C11—42no—
206C2×C11—41no—
207C2×C11#152011yescharacteristic
208C2×C11#212211yescharacteristic
209C2×C11C2×#35411yescharacteristic
210C24C11×C22⋊C411yescharacteristic
211C24C2×D4×C1111yescharacteristic
212C2×Q8—42no—
213C2×Q8—82no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4C11×SD1612yes—
217C2×D4C11×Q1612yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4C11×C22⋊C411yescharacteristic
228C22×C4C11×C22⋊C411yescharacteristic
229C22×C4C11×C22⋊C411yescharacteristic
230C22×C4C22×C4×C1111yescharacteristic
231C22×C4C2×D4×C1111yescharacteristic
232C2×C8—42no—
233C2×C8—82no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—82no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—82no—
245C22⋊C4—82no—
246C42—21no—
247C42—21no—
248C42—42no—
249C11#1190011yescharacteristic, direct product factor, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23C11×#10312yes—
259C23C2×C11×C22⋊C411yescharacteristic
260C23C2×C11×SD1611yescharacteristic
261C23C2×C11×Q1611yescharacteristic
262Q8—84no—
263D4—42no—
264D4—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—82no—
287C2×C4C11×#9911yescharacteristic
288C2×C4C11×#9911yescharacteristic
289C2×C4C11×#10312yes—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—22no—
295C22—21no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22—81no—
305C22C2×C11×#9911yescharacteristic
306C22C2×C11×#10311yescharacteristic
307C22C11×#42111yescharacteristic
308C4—21no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—82no—
314C4—82no—
315C4—162no—
316C4C11×#35412yes—
317C2—21no—
318C2—21no—
319C2—41no—
320C2—42no—
321C2—41no—
322C2C11×#152011yescharacteristic
323C2C11×#212211yescharacteristic
324C2C2×C11×#35411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1351C2semidirect
5. C2×C11×C4⋊Q8C4semidirect
9. C11×#393C4semidirect
16. C4×C11×C4⋊C4C4semidirect
48. #11900C11direct (N × H)
91. #1351C2×C11semidirect
133. C2×C4⋊Q8C4×C11semidirect
137. #393C4×C11semidirect
144. C4×C4⋊C4C4×C11semidirect
249. C11#11900direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25632
C11×#17992
C11×#14592
C11×#13512
#1190011