Finite Group Databasebeta

← C11×#8461 #14585654

Subgroups — C11×#8461 #14585654

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#1985C211yesmaximal, characteristic, complemented
3C11×#1552C211yesmaximal, characteristic, complemented
4C11×#1551C211yesmaximal, characteristic
5C11×#1531C211yesmaximal, characteristic, complemented
6C11×#1530C211yesmaximal, characteristic
7C11×#1467C211yesmaximal, characteristic, complemented
8C11×#559—21no—
9C11×#557—21no—
10C11×#556—21no—
11C11×#556—22no—
12C11×#554—21no—
13C11×#552—22no—
14C11×#539—22no—
15C11×#536C412yes—
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C11×#529—22no—
19C11×#520C412yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C11×#432C2211yescharacteristic
22C11×#432C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C11×#336—22no—
26C11×#333—21no—
27C11×#332—21no—
28C11×#332—21no—
29C11×#331—21no—
30C11×#330—22no—
31C11×#329—22no—
32C11×#324—22no—
33C2×C11×#41C2×C412yes—
34C22×Q8×C11C2×C411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#126—24no—
43C11×#126—24no—
44C11×#125—22no—
45C11×#125—24no—
46C11×#125D412yes—
47C11×#124—22no—
48C11×#124—22no—
49C11×#124D412yes—
50C11×#123—24no—
51C11×#123—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×#121—21no—
58C11×#121—21no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11—21no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C11×#117—24no—
73C11×#117—22no—
74C11×#117C2×C412yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4D412yes—
78C2×C42×C11D412yes—
79C2×C42×C11C2311yescharacteristic
80C11×C4⋊C8—21no—
81C11×C4⋊C8—21no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8—21no—
84C11×C22⋊C8—21no—
85C11×C22⋊C8—21no—
86C11×#97—21no—
87C11×#97—21no—
88C11×#97—21no—
89C11×#97—21no—
90#8461C1111yesmaximal, characteristic, direct product factor, Sylow
91C11×#41—44no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—42no—
97C2×Q8×C11C22⋊C412yes—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11C22⋊C412yes—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11C22⋊C412yes—
105C22×C4×C11C22⋊C412yes—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—42no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4C22⋊C412yes—
130C11×C4⋊C4C22⋊C412yes—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C42×C11—24no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145#3507C2×C1111yescharacteristic
146#1985C2×C1111yescharacteristic, complemented
147#1552C2×C1111yescharacteristic, complemented
148#1551C2×C1111yescharacteristic
149#1531C2×C1111yescharacteristic, complemented
150#1530C2×C1111yescharacteristic
151#1467C2×C1111yescharacteristic, complemented
152C23×C11—22no—
153C23×C11C2×C22⋊C411yescharacteristic
154Q8×C11—42no—
155Q8×C11—42no—
156Q8×C11—42no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—81no—
160D4×C11—42no—
161D4×C11—44no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—81no—
165C2×C4×C11—22no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—41no—
175C2×C4×C11—44no—
176C2×C4×C11—42no—
177C2×C4×C11—84no—
178C2×C4×C11C2×C22⋊C411yescharacteristic
179C2×C4×C11C2×C22⋊C411yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C8×C11—42no—
185C8×C11—81no—
186C8×C11—81no—
187C8×C11—81no—
188#559—21no—
189#557—21no—
190#556—21no—
191#556—22no—
192#554—21no—
193#552—22no—
194#539—22no—
195#536C4×C1112yes—
196#533C22×C1111yescharacteristic
197#532C22×C1111yescharacteristic
198#529—22no—
199#520C4×C1112yes—
200C2×C4×Q8C22×C1111yescharacteristic
201#432C22×C1111yescharacteristic
202#432C22×C1111yescharacteristic
203C2×C4⋊C8C22×C1111yescharacteristic
204C2×#97C22×C1111yescharacteristic
205#336—22no—
206#333—21no—
207#332—21no—
208#332—21no—
209#331—21no—
210#330—22no—
211#329—22no—
212#324—22no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11#37911yescharacteristic
219C22×C11#41312yes—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—42no—
226C4×C11—42no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11—42no—
230C4×C11#45411yescharacteristic
231C4×C11#45611yescharacteristic
232C2×#41C2×C4×C1112yes—
233C22×Q8C2×C4×C1111yescharacteristic
234C22×C8—21no—
235C22×C8—21no—
236C4⋊Q8—22no—
237C4⋊Q8D4×C1111yescharacteristic
238C4⋊Q8D4×C1111yescharacteristic
239C4⋊Q8D4×C1111yescharacteristic
240#127D4×C1111yescharacteristic
241#126—24no—
242#126—24no—
243#125—22no—
244#125—24no—
245#125D4×C1112yes—
246#124—22no—
247#124—22no—
248#124D4×C1112yes—
249#123—24no—
250#123—24no—
251C22⋊Q8—24no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256#121—21no—
257#121—21no—
258C4×Q8—22no—
259C4×Q8—22no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—24no—
269C4×D4—21no—
270C4×D4—21no—
271#117—24no—
272#117—22no—
273#117C2×C4×C1112yes—
274C2×C4⋊C4—22no—
275C2×C4⋊C4C2×C4×C1111yescharacteristic
276C2×C4⋊C4D4×C1112yes—
277C2×C42D4×C1112yes—
278C2×C42C23×C1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285#97—21no—
286#97—21no—
287#97—21no—
288#97—21no—
289C2×C11—22no—
290C2×C11—82no—
291C2×C11#178511yescharacteristic
292C2×C11#179311yescharacteristic
293C2×C11#179411yescharacteristic
294#41—44no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—42no—
300C2×Q8C11×C22⋊C412yes—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4C11×C22⋊C412yes—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4C11×C22⋊C412yes—
308C22×C4C11×C22⋊C412yes—
309C22×C4C22×C4×C1111yescharacteristic
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C2×D4×C1111yescharacteristic
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—42no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—24no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4C11×C22⋊C412yes—
333C4⋊C4C11×C22⋊C412yes—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C42—24no—
341C42—22no—
342C42—22no—
343C42—22no—
344C42C2×D4×C1111yescharacteristic
345C42C2×D4×C1111yescharacteristic
346C42C2×D4×C1111yescharacteristic
347C42C2×D4×C1111yescharacteristic
348C11#846111yescharacteristic, direct product factor, Sylow
349C23—22no—
350C23C2×C11×C22⋊C411yescharacteristic
351Q8—42no—
352Q8—42no—
353Q8—42no—
354Q8—41no—
355Q8—41no—
356Q8—81no—
357D4—42no—
358D4—44no—
359D4—41no—
360D4—41no—
361D4—81no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—41no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—84no—
375C2×C4C2×C11×C22⋊C411yescharacteristic
376C2×C4C2×C11×C22⋊C411yescharacteristic
377C2×C4C11×#12011yescharacteristic
378C2×C4C11×#12011yescharacteristic
379C2×C4C11×#12011yescharacteristic
380C2×C4C11×#12011yescharacteristic
381C8—42no—
382C8—81no—
383C8—81no—
384C8—81no—
385C22—21no—
386C22—21no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22C11×#37911yescharacteristic
391C22C11×#41312yes—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—42no—
399C4—42no—
400C4—42no—
401C4—42no—
402C4C11×#45411yescharacteristic
403C4C11×#45611yescharacteristic
404C2—22no—
405C2—82no—
406C2C11×#178511yescharacteristic
407C2C11×#179311yescharacteristic
408C2C11×#179411yescharacteristic
subgroupG/H
center, socleC22×C11#379
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
2. C11×#1985C2semidirect
3. C11×#1552C2semidirect
5. C11×#1531C2semidirect
7. C11×#1467C2semidirect
90. #8461C11direct (N × H)
146. #1985C2×C11semidirect
147. #1552C2×C11semidirect
149. #1531C2×C11semidirect
151. #1467C2×C11semidirect
348. C11#8461direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#19852
C11×#15522
C11×#15512
C11×#15312
C11×#15302
C11×#14672
#846111