Finite Group Databasebeta

← C11×#24697 #14601890

Subgroups — C11×#24697 #14601890

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic
5C11×#2073C212yesmaximal
6C11×#2055C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1949C212yesmaximal, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1927C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#476—24no—
17C11×#440—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#97C2211yescharacteristic
27C11×#400—21no—
28C11×#400—21no—
29C11×#391—22no—
30C11×#391C2212yes—
31C11×#390C2212yes—
32C11×#388—22no—
33C11×#382C2212yes—
34C11×#382C2211yescharacteristic
35C11×#381—21no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
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×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—21no—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C2×C42×C11C2311yescharacteristic
73C11×#107—22no—
74C11×#106—24no—
75C11×C4⋊C8—24no—
76C11×C4⋊C8—22no—
77C11×#103—24no—
78C11×#103—22no—
79C11×#102—22no—
80C11×#102—24no—
81C11×#97—22no—
82C11×#95—21no—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#24697C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×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—44no—
99C2×Q8×C11—42no—
100C2×Q8×C11#4112yes—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C2×D412yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—82no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C11×SD16—28no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11#4112yes—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—82no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—42no—
146C42×C11—82no—
147C42×C11C2×D412yes—
148C42×C11#4112yes—
149C2×#476C2×C1111yescharacteristic
150C2×#440C2×C1111yescharacteristic
151#2568C2×C1111yescharacteristic, complemented
152#2357C2×C1111yescharacteristic
153#2073C2×C1112yes—
154#2055C2×C1112yes—
155#1993C2×C1111yescharacteristic, complemented
156#1949C2×C1112yescomplemented
157#1940C2×C1111yescharacteristic, complemented
158#1927C2×C1112yescomplemented
159#1805C2×C1111yescharacteristic, complemented
160C23×C11—22no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11C22×D411yescharacteristic
166Q8×C11—22no—
167Q8×C11—22no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11—84no—
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—41no—
174D4×C11—41no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—84no—
196C2×C4×C11#12112yes—
197C2×C4×C11#12112yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C2×C4×C112−1+411yescharacteristic
204C8×C11—22no—
205C8×C11—42no—
206C8×C11—41no—
207C22×SD16C22×C1111yescharacteristic
208C2×C4⋊Q8C22×C1111yescharacteristic
209C2×C4×Q8C22×C1111yescharacteristic
210C2×C4×D4C22×C1111yescharacteristic
211#476—24no—
212#440—24no—
213C2×#107C22×C1111yescharacteristic
214C2×#106C22×C1112yes—
215C2×C4⋊C8C22×C1112yes—
216C2×C4⋊C8C22×C1111yescharacteristic
217C2×#103C22×C1112yes—
218C2×#103C22×C1111yescharacteristic
219C2×#102C22×C1112yes—
220C2×#102C22×C1111yescharacteristic
221C2×#97C22×C1111yescharacteristic
222#400—21no—
223#400—21no—
224#391—22no—
225#391C22×C1112yes—
226#390C22×C1112yes—
227#388—22no—
228#382C22×C1112yes—
229#382C22×C1111yescharacteristic
230#381—21no—
231C4×C4⋊C4C22×C1112yes—
232C4×C4⋊C4C22×C1111yescharacteristic
233C4×C22⋊C4—21no—
234#340C22×C1112yes—
235#340C22×C1112yes—
236#340C22×C1112yes—
237#336C22×C1112yes—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11C2×#12111yescharacteristic
244C22×C11#54711yescharacteristic
245C22×C11#54811yescharacteristic
246C22×C11#57512yes—
247C22×C11#57712yes—
248C4×C11—22no—
249C4×C11—22no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11—82no—
256C4×C11—81no—
257C4×C11#52511yescharacteristic
258C4×C11#53611yescharacteristic
259C4×C11#55211yescharacteristic
260C4×C11#55611yescharacteristic
261C22×Q8—21no—
262C22×Q8C23×C1111yescharacteristic
263C22×D4C23×C1111yescharacteristic
264C23×C4—21no—
265C2×SD16—22no—
266C2×SD16—22no—
267C2×SD16—22no—
268C22×C8C23×C1111yescharacteristic
269C22×C8C23×C1112yes—
270C22×C8C23×C1111yescharacteristic
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4×Q8—22no—
274C4×Q8—22no—
275C4×D4—22no—
276C4×D4D4×C1114yes—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4D4×C1112yes—
280C2×C4⋊C4C23×C1111yescharacteristic
281C2×C4⋊C4C23×C1112yes—
282C2×C4⋊C4C23×C1112yes—
283C2×C4⋊C4C23×C1111yescharacteristic
284C2×C22⋊C4—21no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C42—21no—
288C2×C42—22no—
289C2×C42C23×C1112yes—
290C2×C42C23×C1111yescharacteristic
291#107—22no—
292#106—24no—
293C4⋊C8—24no—
294C4⋊C8—22no—
295#103—24no—
296#103—22no—
297#102—22no—
298#102—24no—
299#97—22no—
300#95—21no—
301#95—22no—
302#95—21no—
303#95—22no—
304#95—22no—
305#95—22no—
306#95—22no—
307#95D4×C1111yescharacteristic
308#95D4×C1111yescharacteristic
309C2×C11—82no—
310C2×C11#241511yescharacteristic
311C2×C11#304011yescharacteristic
312C2×C11#304211yescharacteristic
313C2×C11#335012yes—
314C2×C11#337112yes—
315C24—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—44no—
322C2×Q8—42no—
323C2×Q8C11×#4112yes—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4C2×D4×C1112yes—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—24no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—82no—
337C22×C4C2×D4×C1112yes—
338C22×C4C2×D4×C1112yes—
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C2×D4×C1111yescharacteristic
341C22×C4C24×C1111yescharacteristic
342SD16—28no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8C11×#4112yes—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4C2×D4×C1112yes—
363C22⋊C4—24no—
364C22⋊C4—44no—
365C22⋊C4—82no—
366C42—22no—
367C42—22no—
368C42—42no—
369C42—82no—
370C42C2×D4×C1112yes—
371C42C11×#4112yes—
372C11#2469711yescharacteristic, direct product factor, Sylow
373C23—22no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—42no—
378C23C22×D4×C1111yescharacteristic
379Q8—22no—
380Q8—22no—
381Q8—41no—
382Q8—41no—
383Q8—84no—
384D4—22no—
385D4—22no—
386D4—41no—
387D4—41no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—84no—
409C2×C4C11×#12112yes—
410C2×C4C11×#12112yes—
411C2×C4C22×D4×C1111yescharacteristic
412C2×C4C2×C11×#4111yescharacteristic
413C2×C4C2×C11×#4111yescharacteristic
414C2×C4C2×C11×#4111yescharacteristic
415C2×C4C11×2−1+411yescharacteristic
416C2×C4C11×2−1+411yescharacteristic
417C8—22no—
418C8—42no—
419C8—41no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—82no—
424C22—82no—
425C22C2×C11×#12111yescharacteristic
426C22C11×#54711yescharacteristic
427C22C11×#54811yescharacteristic
428C22C11×#57512yes—
429C22C11×#57712yes—
430C4—22no—
431C4—22no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—82no—
437C4—81no—
438C4—82no—
439C4C11×#52511yescharacteristic
440C4C11×#53611yescharacteristic
441C4C11×#55211yescharacteristic
442C4C11×#55611yescharacteristic
443C2—82no—
444C2C11×#241511yescharacteristic
445C2C11×#304011yescharacteristic
446C2C11×#304211yescharacteristic
447C2C11×#335012yes—
448C2C11×#337112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
3. C11×#2568C2semidirect
7. C11×#1993C2semidirect
8. C11×#1949C2semidirect
9. C11×#1940C2semidirect
10. C11×#1927C2semidirect
11. C11×#1805C2semidirect
91. #24697C11direct (N × H)
151. #2568C2×C11semidirect
155. #1993C2×C11semidirect
156. #1949C2×C11semidirect
157. #1940C2×C11semidirect
158. #1927C2×C11semidirect
159. #1805C2×C11semidirect
372. C11#24697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C2×C11×#4402
C11×#25682
C11×#23572
C11×#20732
C11×#20552
C11×#19932
C11×#19492
C11×#19402
C11×#19272
C11×#18052
#2469711