Finite Group Databasebeta

← C11×#18220 #14595413

Subgroups — C11×#18220 #14595413

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic, complemented
2C11×#3101C212yesmaximal
3C11×#2536C211yesmaximal, characteristic
4C11×#1611C214yesmaximal, complemented
5C11×#1599C214yesmaximal
6C11×#1518C212yesmaximal, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C2×C11×C22⋊Q8—21no—
16C11×#519—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#483C2214yes—
20C11×#476—22no—
21C11×#461—22no—
22C11×#450C2214yes—
23C4×C11×SD16—24no—
24C11×#431C2212yes—
25C11×#398C2212yes—
26C11×#394C2212yes—
27C11×#388—22no—
28C11×#382C2211yescharacteristic
29C11×#380—21no—
30C11×#328C2218yes—
31C11×#324C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11—21no—
35C2×C11×SD16—24no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—24no—
39C11×C4⋊Q8—28no—
40C11×C4⋊Q8D412yes—
41C11×C4⋊Q8D412yes—
42C11×#125—24no—
43C11×#125—24no—
44C11×#125—28no—
45C11×#125—22no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—44no—
49C11×C22⋊Q8C2314yes—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C11×#117—24no—
61C11×#117—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11D412yes—
71C2×C42×C11C2311yescharacteristic
72C11×#106—24no—
73C11×C4⋊C8—22no—
74C11×#103—24no—
75C11×#102—24no—
76C11×C22⋊C8C2314yes—
77C4×C8×C11—22no—
78C11×#95—22no—
79C11×#95—21no—
80C11×#95C2312yes—
81#18220C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11SD1614yescomplemented
88C2×Q8×C11C2×D414yes—
89C2×D4×C11—22no—
90C2×D4×C11—42no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C11×SD16—48no—
102C2×C8×C11—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—44no—
117C11×C4⋊C4C2×D414yes—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—44no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—44no—
123C42×C11—28no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—24no—
127C42×C11C2×D412yes—
128C42×C11C2×D412yes—
129#3502C2×C1111yescharacteristic, complemented
130#3101C2×C1112yes—
131#2536C2×C1111yescharacteristic
132#1611C2×C1114yescomplemented
133#1599C2×C1114yes—
134#1518C2×C1112yescomplemented
135#1461C2×C1111yescharacteristic, complemented
136C23×C11—22no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11C22×D411yescharacteristic
144Q8×C11—28no—
145Q8×C11—44no—
146Q8×C11—44no—
147Q8×C11—84no—
148D4×C11—24no—
149D4×C11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—84no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12012yes—
168C2×C4×C11C2×SD1614yes—
169C2×C4×C11C2×SD1612yes—
170C2×C4×C11#13712yes—
171C2×C4×C11C22×D412yes—
172C8×C11—44no—
173Q82—22no—
174#557—22no—
175#557—24no—
176#544—21no—
177#544C22×C1114yes—
178#533—22no—
179#533C22×C1112yes—
180C2×C22⋊Q8—21no—
181#519—21no—
182C2×C4×Q8C22×C1111yescharacteristic
183C2×C4×D4C22×C1111yescharacteristic
184#483C22×C1114yes—
185#476—22no—
186#461—22no—
187#450C22×C1114yes—
188C4×SD16—24no—
189#431C22×C1112yes—
190#398C22×C1112yes—
191#394C22×C1112yes—
192#388—22no—
193#382C22×C1111yescharacteristic
194#380—21no—
195#328C22×C1118yes—
196#324C22×C1114yes—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11C2×#12011yescharacteristic
207C22×C11C22×SD1611yescharacteristic
208C22×C11C2×#13711yescharacteristic
209C4×C11—24no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—44no—
214C4×C11—42no—
215C4×C11—44no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11#44814yes—
219C22×Q8D4×C1111yescharacteristic
220C22×D4C23×C1111yescharacteristic
221C23×C4—21no—
222C2×SD16—24no—
223C4⋊Q8—22no—
224C4⋊Q8—22no—
225C4⋊Q8—24no—
226C4⋊Q8—28no—
227C4⋊Q8D4×C1112yes—
228C4⋊Q8D4×C1112yes—
229#125—24no—
230#125—24no—
231#125—28no—
232#125—22no—
233C22⋊Q8—22no—
234C22⋊Q8—24no—
235C22⋊Q8—44no—
236C22⋊Q8C23×C1114yes—
237C4×Q8—24no—
238C4×Q8—24no—
239C4×Q8—24no—
240C4×Q8—24no—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8D4×C1114yes—
245C4×D4—22no—
246C4×D4—22no—
247#117—24no—
248#117—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4D4×C1111yescharacteristic
252C2×C4⋊C4C23×C1111yescharacteristic
253C2×C4⋊C4C23×C1112yes—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C42D4×C1112yes—
258C2×C42C23×C1111yescharacteristic
259#106—24no—
260C4⋊C8—22no—
261#103—24no—
262#102—24no—
263C22⋊C8C23×C1114yes—
264C4×C8—22no—
265#95—22no—
266#95—21no—
267#95C23×C1112yes—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—82no—
271C2×C11C2×#44811yescharacteristic
272C2×C11#302011yescharacteristic
273C2×C11#302511yescharacteristic
274C24—21no—
275C2×Q8—24no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8C11×SD1614yescomplemented
280C2×Q8C2×D4×C1114yes—
281C2×D4—22no—
282C2×D4—42no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4C2×D4×C1112yes—
289C22×C4C2×D4×C1112yes—
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C24×C1111yescharacteristic
293SD16—48no—
294C2×C8—24no—
295C4⋊C4—24no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—28no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—44no—
309C4⋊C4C2×D4×C1114yes—
310C22⋊C4—24no—
311C22⋊C4—44no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—44no—
315C42—28no—
316C42—22no—
317C42—22no—
318C42—24no—
319C42C2×D4×C1112yes—
320C42C2×D4×C1112yes—
321C11#1822011yescharacteristic, direct product factor, Sylow
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23C22×D4×C1111yescharacteristic
330Q8—28no—
331Q8—44no—
332Q8—44no—
333Q8—84no—
334D4—24no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—84no—
351C2×C4C11×#12011yescharacteristic
352C2×C4C11×#12011yescharacteristic
353C2×C4C11×#12012yes—
354C2×C4C2×C11×SD1614yes—
355C2×C4C2×C11×SD1612yes—
356C2×C4C11×#13712yes—
357C2×C4C22×D4×C1112yes—
358C8—44no—
359C22—21no—
360C22—21no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C2×C11×#12011yescharacteristic
369C22C22×C11×SD1611yescharacteristic
370C22C2×C11×#13711yescharacteristic
371C4—24no—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—44no—
376C4—42no—
377C4—44no—
378C4—82no—
379C4—81no—
380C4C11×#44814yes—
381C2—21no—
382C2—21no—
383C2—82no—
384C2C2×C11×#44811yescharacteristic
385C2C11×#302011yescharacteristic
386C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3502C2semidirect
4. C11×#1611C2semidirect
6. C11×#1518C2semidirect
7. C11×#1461C2semidirect
81. #18220C11direct (N × H)
87. C2×Q8×C11SD16semidirect
129. #3502C2×C11semidirect
132. #1611C2×C11semidirect
134. #1518C2×C11semidirect
135. #1461C2×C11semidirect
279. C2×Q8C11×SD16semidirect
321. C11#18220direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#31012
C11×#25362
C11×#16112
C11×#15992
C11×#15182
C11×#14612
#1822011