Finite Group Databasebeta

← C11×#24699 #14601892

Subgroups — C11×#24699 #14601892

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#477C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic
5C11×#2074C212yesmaximal
6C11×#2056C212yesmaximal
7C11×#1993C211yesmaximal, characteristic
8C11×#1949C212yesmaximal
9C11×#1940C211yesmaximal, characteristic
10C11×#1928C212yesmaximal
11C11×#1805C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#477—24no—
17C11×#441—24no—
18C2×C11×#107C2212yes—
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#97C2211yescharacteristic
27C11×#400—21no—
28C11×#400—21no—
29C11×#391—22no—
30C11×#391C2212yes—
31C11×#391C2212yes—
32C11×#387—22no—
33C11×#383—21no—
34C11×#382C2212yes—
35C11×#382C2211yescharacteristic
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#376—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16—22no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11—22no—
68C2×C42×C11—21no—
69C2×C42×C11C2312yes—
70C2×C42×C11C2311yescharacteristic
71C11×#107—24no—
72C11×#106—22no—
73C11×C4⋊C8—24no—
74C11×C4⋊C8—22no—
75C11×#103—22no—
76C11×#103—24no—
77C11×#103—24no—
78C11×#103—22no—
79C11×#97—22no—
80C11×#95—21no—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#24699C1111yesmaximal, characteristic, direct product factor, Sylow
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—44no—
103C2×Q8×C11—42no—
104C2×Q8×C11C2×D412yes—
105C2×Q8×C11#4112yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C11×Q16—28no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—22no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11#4112yes—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4C2×D412yes—
139C42×C11—24no—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11—44no—
143C42×C11—42no—
144C42×C11C2×D412yes—
145C42×C11#4112yes—
146C2×#477C2×C1111yescharacteristic
147C2×#441C2×C1111yescharacteristic
148#2568C2×C1111yescharacteristic
149#2356C2×C1111yescharacteristic
150#2074C2×C1112yes—
151#2056C2×C1112yes—
152#1993C2×C1111yescharacteristic
153#1949C2×C1112yes—
154#1940C2×C1111yescharacteristic
155#1928C2×C1112yes—
156#1805C2×C1111yescharacteristic
157C23×C11C22×D411yescharacteristic
158Q8×C11—22no—
159Q8×C11—22no—
160Q8×C11—22no—
161Q8×C11—22no—
162Q8×C11—41no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—41no—
166Q8×C11—84no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—44no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11#12112yes—
191C2×C4×C11#12112yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C112−1+411yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C8×C11—22no—
199C8×C11—42no—
200C8×C11—41no—
201C22×Q16C22×C1111yescharacteristic
202C2×C4⋊Q8C22×C1111yescharacteristic
203C2×C4×Q8C22×C1111yescharacteristic
204C2×C4×Q8C22×C1111yescharacteristic
205#477—24no—
206#441—24no—
207C2×#107C22×C1112yes—
208C2×#106C22×C1111yescharacteristic
209C2×C4⋊C8C22×C1111yescharacteristic
210C2×C4⋊C8C22×C1112yes—
211C2×#103C22×C1112yes—
212C2×#103C22×C1112yes—
213C2×#103C22×C1111yescharacteristic
214C2×#103C22×C1111yescharacteristic
215C2×#97C22×C1111yescharacteristic
216#400—21no—
217#400—21no—
218#391—22no—
219#391C22×C1112yes—
220#391C22×C1112yes—
221#387—22no—
222#383—21no—
223#382C22×C1112yes—
224#382C22×C1111yescharacteristic
225C4×C4⋊C4C22×C1112yes—
226C4×C4⋊C4C22×C1111yescharacteristic
227#376—21no—
228#340C22×C1112yes—
229#340C22×C1112yes—
230#340C22×C1112yes—
231#336C22×C1112yes—
232C22×C11C2×#12111yescharacteristic
233C22×C11#54711yescharacteristic
234C22×C11#54811yescharacteristic
235C22×C11#57512yes—
236C22×C11#57812yes—
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—42no—
242C4×C11—42no—
243C4×C11—42no—
244C4×C11—82no—
245C4×C11—82no—
246C4×C11—81no—
247C4×C11#52511yescharacteristic
248C4×C11#53611yescharacteristic
249C4×C11#55211yescharacteristic
250C4×C11#55611yescharacteristic
251C22×Q8—21no—
252C22×Q8C23×C1111yescharacteristic
253C22×Q8C23×C1111yescharacteristic
254C2×Q16—22no—
255C2×Q16—22no—
256C2×Q16—22no—
257C22×C8C23×C1111yescharacteristic
258C22×C8C23×C1112yes—
259C22×C8C23×C1111yescharacteristic
260C4⋊Q8—22no—
261C4⋊Q8—22no—
262C4×Q8—22no—
263C4×Q8—22no—
264C4×Q8—22no—
265C4×Q8D4×C1114yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C1112yes—
270C2×C4⋊C4C23×C1111yescharacteristic
271C2×C4⋊C4C23×C1112yes—
272C2×C4⋊C4C23×C1112yes—
273C2×C4⋊C4C23×C1111yescharacteristic
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—22no—
277C2×C42C23×C1112yes—
278C2×C42C23×C1111yescharacteristic
279#107—24no—
280#106—22no—
281C4⋊C8—24no—
282C4⋊C8—22no—
283#103—22no—
284#103—24no—
285#103—24no—
286#103—22no—
287#97—22no—
288#95—21no—
289#95—22no—
290#95—22no—
291#95—21no—
292#95—22no—
293#95—22no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95D4×C1111yescharacteristic
298#95D4×C1111yescharacteristic
299C2×C11#241511yescharacteristic
300C2×C11#304011yescharacteristic
301C2×C11#304411yescharacteristic
302C2×C11#334912yes—
303C2×C11#337712yes—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—44no—
315C2×Q8—42no—
316C2×Q8C2×D4×C1112yes—
317C2×Q8C11×#4112yes—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4C2×D4×C1112yes—
325C22×C4C2×D4×C1112yes—
326C22×C4C2×D4×C1111yescharacteristic
327C22×C4C2×D4×C1111yescharacteristic
328C22×C4C24×C1111yescharacteristic
329Q16—28no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8C11×#4112yes—
339C4⋊C4—24no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4C2×D4×C1112yes—
351C42—24no—
352C42—22no—
353C42—22no—
354C42—44no—
355C42—42no—
356C42C2×D4×C1112yes—
357C42C11×#4112yes—
358C11#2469911yescharacteristic, direct product factor, Sylow
359C23C22×D4×C1111yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366Q8—41no—
367Q8—41no—
368Q8—84no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4C11×#12112yes—
393C2×C4C11×#12112yes—
394C2×C4C22×D4×C1111yescharacteristic
395C2×C4C2×C11×#4111yescharacteristic
396C2×C4C2×C11×#4111yescharacteristic
397C2×C4C2×C11×#4111yescharacteristic
398C2×C4C11×2−1+411yescharacteristic
399C2×C4C11×2−1+411yescharacteristic
400C8—22no—
401C8—42no—
402C8—41no—
403C22C2×C11×#12111yescharacteristic
404C22C11×#54711yescharacteristic
405C22C11×#54811yescharacteristic
406C22C11×#57512yes—
407C22C11×#57812yes—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—42no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4—82no—
418C4C11×#52511yescharacteristic
419C4C11×#53611yescharacteristic
420C4C11×#55211yescharacteristic
421C4C11×#55611yescharacteristic
422C2C11×#241511yescharacteristic
423C2C11×#304011yescharacteristic
424C2C11×#304411yescharacteristic
425C2C11×#334912yes—
426C2C11×#337712yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
91. #24699C11direct (N × H)
358. C11#24699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4772
C2×C11×#4412
C11×#25682
C11×#23562
C11×#20742
C11×#20562
C11×#19932
C11×#19492
C11×#19402
C11×#19282
C11×#18052
#2469911