Finite Group Databasebeta

← C11×#8983 #14586176

Subgroups — C11×#8983 #14586176

Order 2816.

560 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
1C2×C11×#475C211yesmaximal, characteristic
2Q8×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#1990C211yesmaximal, characteristic
4C11×#1981C211yesmaximal, characteristic
5C2×C11×Q8⋊C8C211yesmaximal, characteristic
6C11×#1296C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#475—22no—
12C11×#475C414yescomplemented
13C2×C11×#106—21no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17C2×C11×#103—21no—
18C2×C11×#103—21no—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#389—21no—
21C11×#389—22no—
22C11×#384—21no—
23C11×#384C2211yescharacteristic
24C4×C11×C4⋊C4—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×Q8⋊C8—22no—
28C22×Q8×C11—21no—
29C22×Q8×C11D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8C2×C412yes—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—42no—
40C4×Q8×C11—42no—
41C4×Q8×C11C2×C412yes—
42C4×Q8×C11D412yes—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11—21no—
55C2×C42×C11—22no—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#106—24no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8C2×C412yes—
63C11×#103—24no—
64C11×#103—42no—
65C11×#103—42no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C11×#95—22no—
69C11×#95—21no—
70#8983C1111yesmaximal, characteristic, direct product factor, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11C22⋊C412yes—
81C2×Q8×C11SD1612yes—
82C2×Q8×C11Q1612yes—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—44no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—82no—
118C11×C4⋊C4C22⋊C412yes—
119C11×C4⋊C4SD1612yes—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11—44no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11C22×C411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128C42×C11#4111yescharacteristic
129C2×#475C2×C1111yescharacteristic
130Q8×C4⋊C4C2×C1111yescharacteristic
131#1990C2×C1111yescharacteristic
132#1981C2×C1111yescharacteristic
133C2×Q8⋊C8C2×C1111yescharacteristic
134#1296C2×C1111yescharacteristic
135#1279C2×C1111yescharacteristic
136C23×C11#12011yescharacteristic
137Q8×C11—22no—
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—81no—
143Q8×C11—81no—
144Q8×C11#10314yescomplemented
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11C4×D411yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C2×C4×C11C2×SD1611yescharacteristic
172C2×C4×C11C2×SD1611yescharacteristic
173C2×C4×C11C2×Q1611yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C8×C11—42no—
180C8×C11—42no—
181C8×C11—81no—
182C2×C4⋊Q8C22×C1111yescharacteristic
183C2×C4×Q8—21no—
184C2×C4×Q8C22×C1111yescharacteristic
185#475—22no—
186#475C4×C1114yescomplemented
187C2×#106—21no—
188C2×C4⋊C8C22×C1111yescharacteristic
189C2×C4⋊C8C22×C1111yescharacteristic
190C2×#103—21no—
191C2×#103—21no—
192C2×#103—21no—
193C2×C4×C8C22×C1111yescharacteristic
194#389—21no—
195#389—22no—
196#384—21no—
197#384C22×C1111yescharacteristic
198C4×C4⋊C4—21no—
199C4×C4⋊C4C22×C1111yescharacteristic
200#340—22no—
201Q8⋊C8—22no—
202C22×C11#38611yescharacteristic
203C22×C11#44811yescharacteristic
204C22×C11#44911yescharacteristic
205C22×C11#45011yescharacteristic
206C22×C11#45111yescharacteristic
207C22×C11#45511yescharacteristic
208C22×C11#45611yescharacteristic
209C4×C11—24no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—42no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11C2×#10311yescharacteristic
218C4×C11#41711yescharacteristic
219C4×C11C4×SD1611yescharacteristic
220C4×C11#44011yescharacteristic
221C4×C11#46011yescharacteristic
222C4×C11#46411yescharacteristic
223C4×C11#48311yescharacteristic
224C4×C11#48411yescharacteristic
225C22×Q8—21no—
226C22×Q8D4×C1111yescharacteristic
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C2×C4×C1112yes—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—42no—
237C4×Q8—42no—
238C4×Q8C2×C4×C1112yes—
239C4×Q8D4×C1112yes—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4D4×C1111yescharacteristic
248C2×C4⋊C4D4×C1111yescharacteristic
249C2×C4⋊C4D4×C1111yescharacteristic
250C2×C4⋊C4D4×C1112yes—
251C2×C42—21no—
252C2×C42—22no—
253C2×C42—21no—
254C2×C42C23×C1111yescharacteristic
255#106—24no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8C2×C4×C1112yes—
260#103—24no—
261#103—42no—
262#103—42no—
263C4×C8—21no—
264C4×C8—21no—
265#95—22no—
266#95—21no—
267C2×C11#164211yescharacteristic
268C2×C11#164511yescharacteristic
269C2×C11#164811yescharacteristic
270C2×C11#165111yescharacteristic
271C2×C11#187211yescharacteristic
272C2×C11#188011yescharacteristic
273C2×C11#188211yescharacteristic
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8C11×C22⋊C412yes—
284C2×Q8C11×SD1612yes—
285C2×Q8C11×Q1612yes—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—41no—
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—42no—
313C4⋊C4—44no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—82no—
321C4⋊C4C11×C22⋊C412yes—
322C4⋊C4C11×SD1612yes—
323C42—22no—
324C42—22no—
325C42—44no—
326C42—41no—
327C42—41no—
328C42C22×C4×C1111yescharacteristic
329C42C2×D4×C1111yescharacteristic
330C42C11×#4111yescharacteristic
331C42C11×#4111yescharacteristic
332C11#898311yescharacteristic, direct product factor, Sylow
333C23C11×#12011yescharacteristic
334Q8—22no—
335Q8—22no—
336Q8—22no—
337Q8—42no—
338Q8—42no—
339Q8—81no—
340Q8—81no—
341Q8C11×#10314yescomplemented
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C2×C11×C22⋊C411yescharacteristic
363C2×C4C4×D4×C1111yescharacteristic
364C2×C4C4×D4×C1111yescharacteristic
365C2×C4C11×#12111yescharacteristic
366C2×C4C11×#12111yescharacteristic
367C2×C4C11×#12311yescharacteristic
368C2×C4C2×C11×SD1611yescharacteristic
369C2×C4C2×C11×SD1611yescharacteristic
370C2×C4C2×C11×Q1611yescharacteristic
371C2×C4C11×#13511yescharacteristic
372C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
373C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
374C2×C4C11×#13711yescharacteristic
375C2×C4C11×#13711yescharacteristic
376C8—42no—
377C8—42no—
378C8—81no—
379C22C11×#38611yescharacteristic
380C22C11×#44811yescharacteristic
381C22C11×#44911yescharacteristic
382C22C11×#45011yescharacteristic
383C22C11×#45111yescharacteristic
384C22C11×#45511yescharacteristic
385C22C11×#45611yescharacteristic
386C4—24no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—42no—
391C4—82no—
392C4—81no—
393C4—82no—
394C4C2×C11×#10311yescharacteristic
395C4C11×#41711yescharacteristic
396C4C4×C11×SD1611yescharacteristic
397C4C11×#44011yescharacteristic
398C4C11×#46011yescharacteristic
399C4C11×#46411yescharacteristic
400C4C11×#48311yescharacteristic
401C4C11×#48411yescharacteristic
402C2C11×#164211yescharacteristic
403C2C11×#164511yescharacteristic
404C2C11×#164811yescharacteristic
405C2C11×#165111yescharacteristic
406C2C11×#187211yescharacteristic
407C2C11×#188011yescharacteristic
408C2C11×#188211yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
12. C11×#475C4semidirect
70. #8983C11direct (N × H)
144. Q8×C11#103semidirect
186. #475C4×C11semidirect
332. C11#8983direct (N × H)
341. Q8C11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4752
Q8×C11×C4⋊C42
C11×#19902
C11×#19812
C2×C11×Q8⋊C82
C11×#12962
C11×#12792
#898311