Finite Group Databasebeta

← C11×#33799 #14610992

Subgroups — C11×#33799 #14610992

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic
2C11×#3160C211yesmaximal, characteristic, complemented
3C11×#2253C212yesmaximal, complemented
4C11×#2242C212yesmaximal, complemented
5C11×#2237C212yesmaximal, complemented
6C11×#2234C212yesmaximal
7C11×#2227C211yesmaximal, characteristic, complemented
8C11×#2226C211yesmaximal, characteristic, complemented
9C11×#2225C211yesmaximal, characteristic, complemented
10C11×#2224C211yesmaximal, characteristic, complemented
11C11×#2162C211yesmaximal, characteristic, complemented
12C11×#533—21no—
13C11×#529—21no—
14C11×#500C2211yescharacteristic
15C11×#500C2211yescharacteristic
16C11×#499—21no—
17C11×#499C2212yes—
18C11×#499C2211yescharacteristic
19C11×#498—21no—
20C11×#495C2211yescharacteristic
21C11×#488—21no—
22C11×#467C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C11×#465—21no—
25C4×C11×Q16C2211yescharacteristic
26C4×C11×SD16—21no—
27C4×C11×D8C2211yescharacteristic
28C11×#427—21no—
29C11×#427C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C11×#367C2212yes—
32C11×#367C2212yes—
33C11×#366C2212yes—
34C11×#366C2212yes—
35C11×C4⋊C16C2211yescharacteristic
36C11×C4⋊C16C2211yescharacteristic
37C11×#358C2212yes—
38C11×#358C2212yes—
39C11×#357C2212yes—
40C11×#357C2212yes—
41C11×C22⋊C16C2212yes—
42C4×C11×C16C2212yes—
43C2×C11×Q16C2311yescharacteristic
44C2×C11×SD16—21no—
45C2×C11×D8C2311yescharacteristic
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×#126—41no—
51C11×#125—22no—
52C11×#125—21no—
53C11×#124—21no—
54C11×#123—41no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—41no—
57C11×C22⋊Q8—41no—
58C11×#121—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—41no—
61C4×Q8×C11—41no—
62C4×D4×C11—21no—
63C4×D4×C11—41no—
64C11×#117—22no—
65C11×#117—41no—
66C2×C42×C11D411yescharacteristic
67C2×C11×C16C2312yes—
68C2×C11×C16C2312yes—
69C11×#107—21no—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2312yes—
73C11×#107C2311yescharacteristic
74C11×#107C2311yescharacteristic
75C11×#106—22no—
76C11×#106—22no—
77C11×#106—21no—
78C11×#103—21no—
79C11×#103—21no—
80C11×#102—21no—
81C11×#102—21no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2311yescharacteristic
85C4×C8×C11C2311yescharacteristic
86#33799C1111yesmaximal, characteristic, direct product factor, Sylow
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11D811yescharacteristic
94C22×C4×C11D811yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C11×Q16—21no—
97C11×Q16—21no—
98C11×SD16—42no—
99C11×D8—21no—
100C11×D8—21no—
101C2×C8×C11—22no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—42no—
127C42×C11—41no—
128C42×C11D811yescharacteristic
129C42×C11D811yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C11×C16—22no—
133C11×C16—22no—
134#3168C2×C1111yescharacteristic
135#3160C2×C1111yescharacteristic, complemented
136#2253C2×C1112yescomplemented
137#2242C2×C1112yescomplemented
138#2237C2×C1112yescomplemented
139#2234C2×C1112yes—
140#2227C2×C1111yescharacteristic, complemented
141#2226C2×C1111yescharacteristic, complemented
142#2225C2×C1111yescharacteristic, complemented
143#2224C2×C1111yescharacteristic, complemented
144#2162C2×C1111yescharacteristic, complemented
145C23×C11—41no—
146C23×C11C2×D811yescharacteristic
147Q8×C11—41no—
148Q8×C11—41no—
149Q8×C11—82no—
150Q8×C11—82no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—82no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—82no—
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C8×C11—21no—
171C8×C11—21no—
172C8×C11#13712yes—
173C8×C112−1+411yescharacteristic
174C8×C112−1+411yescharacteristic
175#533—21no—
176#529—21no—
177#500C22×C1111yescharacteristic
178#500C22×C1111yescharacteristic
179#499—21no—
180#499C22×C1112yes—
181#499C22×C1111yescharacteristic
182#498—21no—
183#495C22×C1111yescharacteristic
184#488—21no—
185#467C22×C1111yescharacteristic
186#466C22×C1111yescharacteristic
187#465—21no—
188C4×Q16C22×C1111yescharacteristic
189C4×SD16—21no—
190C4×D8C22×C1111yescharacteristic
191#427—21no—
192#427C22×C1112yes—
193C2×C4×C8C22×C1111yescharacteristic
194#367C22×C1112yes—
195#367C22×C1112yes—
196#366C22×C1112yes—
197#366C22×C1112yes—
198C4⋊C16C22×C1111yescharacteristic
199C4⋊C16C22×C1111yescharacteristic
200#358C22×C1112yes—
201#358C22×C1112yes—
202#357C22×C1112yes—
203#357C22×C1112yes—
204C22⋊C16C22×C1112yes—
205C4×C16C22×C1112yes—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11C22×D811yescharacteristic
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—81no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11—82no—
221C4×C11—81no—
222C4×C11#50812yes—
223C4×C11#53611yescharacteristic
224C4×C11C2×#13711yescharacteristic
225C2×Q16C23×C1111yescharacteristic
226C2×SD16—21no—
227C2×D8C23×C1111yescharacteristic
228C22×C8D4×C1111yescharacteristic
229C22×C8C23×C1111yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232#126—41no—
233#125—21no—
234#125—22no—
235#124—21no—
236#123—41no—
237C22⋊Q8—21no—
238C22⋊Q8—41no—
239C22⋊Q8—41no—
240#121—21no—
241C4×Q8—21no—
242C4×Q8—41no—
243C4×Q8—41no—
244C4×D4—21no—
245C4×D4—41no—
246#117—22no—
247#117—41no—
248C2×C42D4×C1111yescharacteristic
249C2×C16C23×C1112yes—
250C2×C16C23×C1112yes—
251#107—21no—
252#107—21no—
253#107C23×C1112yes—
254#107C23×C1112yes—
255#107C23×C1111yescharacteristic
256#107C23×C1111yescharacteristic
257#106—22no—
258#106—22no—
259#106—21no—
260#103—21no—
261#103—21no—
262#102—21no—
263#102—21no—
264C4×C8D4×C1111yescharacteristic
265C4×C8D4×C1111yescharacteristic
266C4×C8C23×C1111yescharacteristic
267C4×C8C23×C1111yescharacteristic
268C2×C11—41no—
269C2×C11—161no—
270C2×C11#322611yescharacteristic
271C2×C11C2×#50811yescharacteristic
272C2×C11#341411yescharacteristic
273C2×Q8—21no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×D4—21no—
277C2×D4—41no—
278C22×C4—41no—
279C22×C4C11×D811yescharacteristic
280C22×C4C11×D811yescharacteristic
281C22×C4C2×D4×C1111yescharacteristic
282Q16—21no—
283Q16—21no—
284SD16—42no—
285D8—21no—
286D8—21no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8C2×D4×C1111yescharacteristic
291C2×C8C2×D4×C1111yescharacteristic
292C2×C8C2×D4×C1111yescharacteristic
293C2×C8C24×C1111yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C42—42no—
313C42—41no—
314C42C11×D811yescharacteristic
315C42C11×D811yescharacteristic
316C42C2×D4×C1111yescharacteristic
317C42C2×D4×C1111yescharacteristic
318C16—22no—
319C16—22no—
320C11#3379911yescharacteristic, direct product factor, Sylow
321C23—41no—
322C23C2×C11×D811yescharacteristic
323Q8—41no—
324Q8—41no—
325Q8—82no—
326Q8—82no—
327D4—41no—
328D4—41no—
329D4—82no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—82no—
340C2×C4C2×C11×D811yescharacteristic
341C2×C4C2×C11×D811yescharacteristic
342C2×C4C2×C11×D811yescharacteristic
343C2×C4C2×C11×D811yescharacteristic
344C2×C4C2×C11×D811yescharacteristic
345C2×C4C22×D4×C1111yescharacteristic
346C8—21no—
347C8—21no—
348C8C11×#13712yes—
349C8C11×2−1+411yescharacteristic
350C8C11×2−1+411yescharacteristic
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C22×C11×D811yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—82no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4C11×#50812yes—
368C4C11×#53611yescharacteristic
369C4C2×C11×#13711yescharacteristic
370C2—41no—
371C2—161no—
372C2C11×#322611yescharacteristic
373C2C2×C11×#50811yescharacteristic
374C2C11×#341411yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3160C2semidirect
3. C11×#2253C2semidirect
4. C11×#2242C2semidirect
5. C11×#2237C2semidirect
7. C11×#2227C2semidirect
8. C11×#2226C2semidirect
9. C11×#2225C2semidirect
10. C11×#2224C2semidirect
11. C11×#2162C2semidirect
86. #33799C11direct (N × H)
135. #3160C2×C11semidirect
136. #2253C2×C11semidirect
137. #2242C2×C11semidirect
138. #2237C2×C11semidirect
140. #2227C2×C11semidirect
141. #2226C2×C11semidirect
142. #2225C2×C11semidirect
143. #2224C2×C11semidirect
144. #2162C2×C11semidirect
320. C11#33799direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31682
C11×#31602
C11×#22532
C11×#22422
C11×#22372
C11×#22342
C11×#22272
C11×#22262
C11×#22252
C11×#22242
C11×#21622
#3379911