Finite Group Databasebeta

← C11×#11899 #14589092

Subgroups — C11×#11899 #14589092

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×#2487C211yesmaximal, characteristic
2C11×#1799C211yesmaximal, characteristic
3C11×#1460C211yesmaximal, characteristic
4C11×#1352C214yesmaximal, complemented
5C2×C4×D4×C11C2211yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic, complemented
7C11×#431—21no—
8C2×C11×#99—21no—
9C11×#400C412yescomplemented
10C11×#399C2212yes—
11C11×#389—21no—
12C11×#386—21no—
13C11×#385—21no—
14C11×#380—21no—
15C11×#380—21no—
16C11×#380C411yescharacteristic, complemented
17C11×#342C2212yes—
18C11×#323—21no—
19C11×#323C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C42×C11D411yescharacteristic
40C11×C4⋊C8—41no—
41C11×#99—42no—
42C11×C22⋊C8—22no—
43C4×C8×C11—41no—
44C11×#95—22no—
45C11×#95—22no—
46C11×#95—41no—
47C11×#95C2×C412yes—
48#11899C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C2×D411yescharacteristic
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11SD1612yes—
54C2×D4×C11Q1612yes—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—82no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C8×C11—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—82no—
78C11×C4⋊C4—82no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—82no—
85C42×C11—21no—
86C42×C11—21no—
87#2487C2×C1111yescharacteristic
88#1799C2×C1111yescharacteristic
89#1460C2×C1111yescharacteristic
90#1352C2×C1114yescomplemented
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11#10312yes—
100C23×C11C2×C22⋊C411yescharacteristic
101C23×C11C2×SD1611yescharacteristic
102C23×C11C2×Q1611yescharacteristic
103D4×C11—42no—
104D4×C11—42no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—81no—
124C2×C4×C11—84no—
125C2×C4×C11—82no—
126C2×C4×C11—82no—
127C2×C4×C11—82no—
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#10312yes—
131C8×C11—82no—
132C2×C4×D4C22×C1111yescharacteristic
133C22×C4⋊C4C4×C1111yescharacteristic, complemented
134#431—21no—
135C2×#99—21no—
136#400C4×C1112yescomplemented
137#399C22×C1112yes—
138#389—21no—
139#386—21no—
140#385—21no—
141#380—21no—
142#380—21no—
143#380C4×C1111yescharacteristic, complemented
144#342C22×C1112yes—
145#323—21no—
146#323C22×C1112yes—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—22no—
151C22×C11—21no—
152C22×C11—42no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—81no—
161C22×C11C2×#9911yescharacteristic
162C22×C11C2×#10311yescharacteristic
163C22×C11#42111yescharacteristic
164C4×C11—21no—
165C4×C11—22no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—82no—
170C4×C11—82no—
171C4×C11—162no—
172C4×C11#35212yes—
173C22×D4D4×C1111yescharacteristic
174C23×C4—21no—
175C23×C4C2×C4×C1111yescharacteristic
176C23×C4D4×C1111yescharacteristic
177C4×D4—41no—
178C4×D4—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4C2×C4×C1112yes—
186C2×C4⋊C4C2×C4×C1111yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4D4×C1111yescharacteristic
191C2×C22⋊C4C23×C1111yescharacteristic
192C2×C42D4×C1111yescharacteristic
193C4⋊C8—41no—
194#99—42no—
195C22⋊C8—22no—
196C4×C8—41no—
197#95—22no—
198#95—22no—
199#95—41no—
200#95C2×C4×C1112yes—
201C2×C11—21no—
202C2×C11—21no—
203C2×C11—41no—
204C2×C11—42no—
205C2×C11—41no—
206C2×C11#152011yescharacteristic
207C2×C11C2×#35211yescharacteristic
208C2×C11#212811yescharacteristic
209C24C11×C22⋊C411yescharacteristic
210C24C2×D4×C1111yescharacteristic
211C2×D4—41no—
212C2×D4—41no—
213C2×D4C11×SD1612yes—
214C2×D4C11×Q1612yes—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—82no—
226C22×C4C11×C22⋊C411yescharacteristic
227C22×C4C11×C22⋊C411yescharacteristic
228C22×C4C11×C22⋊C411yescharacteristic
229C22×C4C22×C4×C1111yescharacteristic
230C22×C4C2×D4×C1111yescharacteristic
231C2×C8—42no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—82no—
238C4⋊C4—82no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—82no—
245C42—21no—
246C42—21no—
247C11#1189911yescharacteristic, direct product factor, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23C11×#10312yes—
257C23C2×C11×C22⋊C411yescharacteristic
258C23C2×C11×SD1611yescharacteristic
259C23C2×C11×Q1611yescharacteristic
260D4—42no—
261D4—42no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—84no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4C11×#9911yescharacteristic
286C2×C4C11×#9911yescharacteristic
287C2×C4C11×#10312yes—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×C11×#9911yescharacteristic
304C22C2×C11×#10311yescharacteristic
305C22C11×#42111yescharacteristic
306C4—22no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4—162no—
314C4C11×#35212yes—
315C2—21no—
316C2—21no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2C11×#152011yescharacteristic
321C2C2×C11×#35211yescharacteristic
322C2C11×#212811yescharacteristic
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×#1352C2semidirect
6. C22×C11×C4⋊C4C4semidirect
9. C11×#400C4semidirect
16. C11×#380C4semidirect
48. #11899C11direct (N × H)
90. #1352C2×C11semidirect
133. C22×C4⋊C4C4×C11semidirect
136. #400C4×C11semidirect
143. #380C4×C11semidirect
247. C11#11899direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24872
C11×#17992
C11×#14602
C11×#13522
#1189911