Finite Group Databasebeta

← C11×#10067 #14587260

Subgroups — C11×#10067 #14587260

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#500C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic
3C11×#2546C211yesmaximal, characteristic
4C11×#1988C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic
6C2×C11×Q8⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C22×C11×Q16—21no—
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#500—22no—
14C11×#500—22no—
15C11×#462—22no—
16C11×#462—22no—
17C2×C11×#107—22no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#398—22no—
23C11×#391—21no—
24C11×#389—22no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#332—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic
32C2×C11×Q16—24no—
33C2×C11×Q16—42no—
34C2×C11×Q16—42no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—42no—
46C11×C4⋊Q8—42no—
47C11×C4⋊Q8D412yes—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×#107—28no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71C11×#95—24no—
72C11×#95—21no—
73#10067C1111yesmaximal, characteristic, direct product factor, Sylow
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11D812yes—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C11×Q16—48no—
101C2×C8×C11—24no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—48no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4Q1614yescomplemented
123C42×C11—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C2×#500C2×C1111yescharacteristic
132C2×#462C2×C1111yescharacteristic
133#2546C2×C1111yescharacteristic
134#1988C2×C1111yescharacteristic
135C2×#332C2×C1111yescharacteristic
136C2×Q8⋊C8C2×C1111yescharacteristic
137#1279C2×C1111yescharacteristic
138C23×C11#12011yescharacteristic
139Q8×C11—22no—
140Q8×C11—22no—
141Q8×C11—41no—
142Q8×C11—41no—
143Q8×C11—42no—
144Q8×C11—42no—
145Q8×C11—81no—
146Q8×C11—81no—
147Q8×C11—81no—
148Q8×C11—81no—
149Q8×C11—81no—
150Q8×C11—81no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12711yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×Q1612yes—
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11#13712yes—
178C8×C11—24no—
179C8×C11—42no—
180C8×C11—81no—
181C22×Q16—21no—
182C2×C4⋊Q8—21no—
183C2×C4⋊Q8C22×C1111yescharacteristic
184C2×C4⋊Q8C22×C1111yescharacteristic
185C2×C4×Q8C22×C1111yescharacteristic
186#500—22no—
187#500—22no—
188#462—22no—
189#462—22no—
190C2×#107—22no—
191C2×C4⋊C8C22×C1111yescharacteristic
192C2×C4⋊C8C22×C1111yescharacteristic
193C2×#103—21no—
194C2×C4×C8C22×C1111yescharacteristic
195#398—22no—
196#391—21no—
197#389—22no—
198C4×C4⋊C4C22×C1111yescharacteristic
199#340—22no—
200#332—22no—
201Q8⋊C8—22no—
202C22×C11#39211yescharacteristic
203C22×C11#44711yescharacteristic
204C22×C11#44911yescharacteristic
205C22×C11#45112yes—
206C22×C11#45612yes—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—44no—
210C4×C11—42no—
211C4×C11—82no—
212C4×C11—82no—
213C4×C11—81no—
214C4×C11#44711yescharacteristic
215C4×C11#44911yescharacteristic
216C4×C11#46212yes—
217C4×C11#46611yescharacteristic
218C4×C11#46911yescharacteristic
219C4×C11#49411yescharacteristic
220C4×C11#49711yescharacteristic
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8D4×C1111yescharacteristic
224C2×Q16—24no—
225C2×Q16—42no—
226C2×Q16—42no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—42no—
238C4⋊Q8—42no—
239C4⋊Q8D4×C1112yes—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1111yescharacteristic
250C2×C4⋊C4D4×C1112yes—
251C2×C4⋊C4D4×C1112yes—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42C23×C1111yescharacteristic
255#107—28no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C1112yes—
260#103—24no—
261C4×C8—21no—
262C4×C8D4×C1112yes—
263#95—24no—
264#95—21no—
265C2×C11#164812yes—
266C2×C11#164912yes—
267C2×C11#199911yescharacteristic
268C2×C11#200511yescharacteristic
269C2×C11#201611yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8C11×D812yes—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—41no—
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295C22×C4C2×D4×C1111yescharacteristic
296Q16—48no—
297C2×C8—24no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—42no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—48no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4C11×Q1614yescomplemented
319C42—41no—
320C42—41no—
321C42—41no—
322C42—41no—
323C42C2×D4×C1111yescharacteristic
324C42C2×D4×C1111yescharacteristic
325C42C2×D4×C1111yescharacteristic
326C42C11×#4111yescharacteristic
327C11#1006711yescharacteristic, direct product factor, Sylow
328C23C11×#12011yescharacteristic
329Q8—22no—
330Q8—22no—
331Q8—41no—
332Q8—41no—
333Q8—42no—
334Q8—42no—
335Q8—81no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340Q8—81no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4C11×#12011yescharacteristic
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12111yescharacteristic
359C2×C4C11×#12111yescharacteristic
360C2×C4C11×#12111yescharacteristic
361C2×C4C11×#12711yescharacteristic
362C2×C4C2×C11×D811yescharacteristic
363C2×C4C2×C11×Q1612yes—
364C2×C4C11×#13511yescharacteristic
365C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
366C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
367C2×C4C11×#13712yes—
368C8—24no—
369C8—42no—
370C8—81no—
371C22C11×#39211yescharacteristic
372C22C11×#44711yescharacteristic
373C22C11×#44911yescharacteristic
374C22C11×#45112yes—
375C22C11×#45612yes—
376C4—21no—
377C4—21no—
378C4—44no—
379C4—42no—
380C4—82no—
381C4—82no—
382C4—81no—
383C4C11×#44711yescharacteristic
384C4C11×#44911yescharacteristic
385C4C11×#46212yes—
386C4C11×#46611yescharacteristic
387C4C11×#46911yescharacteristic
388C4C11×#49411yescharacteristic
389C4C11×#49711yescharacteristic
390C2C11×#164812yes—
391C2C11×#164912yes—
392C2C11×#199911yescharacteristic
393C2C11×#200511yescharacteristic
394C2C11×#201611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
73. #10067C11direct (N × H)
122. C11×C4⋊C4Q16semidirect
318. C4⋊C4C11×Q16semidirect
327. C11#10067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5002
C2×C11×#4622
C11×#25462
C11×#19882
C2×C11×#3322
C2×C11×Q8⋊C82
C11×#12792
#1006711