Finite Group Databasebeta

← C11×#24696 #14601889

Subgroups — C11×#24696 #14601889

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2567C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic
5C11×#2071C212yesmaximal
6C11×#2055C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1947C212yesmaximal, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1928C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#474—24no—
17C11×#440—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2212yes—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#97C2211yescharacteristic
27C11×#395—21no—
28C11×#395—21no—
29C11×#391C2212yes—
30C11×#390C2212yes—
31C11×#389—22no—
32C11×#388—22no—
33C11×#384C2212yes—
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⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C42×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C11×#107—22no—
76C11×#107—24no—
77C11×C4⋊C8—24no—
78C11×C4⋊C8—22no—
79C11×#103—24no—
80C11×#103—22no—
81C11×#102—22no—
82C11×#102—24no—
83C11×#97—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#24696C1111yesmaximal, 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—42no—
99C2×Q8×C11—82no—
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—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—82no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
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—24no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—82no—
140C11×C4⋊C4—82no—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—44no—
144C11×C22⋊C4—82no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—42no—
148C42×C11—82no—
149C42×C11C2×D412yes—
150C42×C11#4112yes—
151C2×#474C2×C1111yescharacteristic
152C2×#440C2×C1111yescharacteristic
153#2567C2×C1111yescharacteristic, complemented
154#2357C2×C1111yescharacteristic
155#2071C2×C1112yes—
156#2055C2×C1112yes—
157#1993C2×C1111yescharacteristic, complemented
158#1947C2×C1112yescomplemented
159#1940C2×C1111yescharacteristic, complemented
160#1928C2×C1112yescomplemented
161#1805C2×C1111yescharacteristic, complemented
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11C22×D411yescharacteristic
168Q8×C11—22no—
169Q8×C11—22no—
170Q8×C11—41no—
171Q8×C11—41no—
172Q8×C11—84no—
173D4×C11—22no—
174D4×C11—22no—
175D4×C11—41no—
176D4×C11—41no—
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—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—84no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#13714yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C8×C11—22no—
208C8×C11—42no—
209C8×C11—41no—
210C22×SD16C22×C1111yescharacteristic
211C2×C4⋊Q8C22×C1111yescharacteristic
212C2×C4×Q8C22×C1111yescharacteristic
213C2×C4×D4C22×C1111yescharacteristic
214#474—24no—
215#440—24no—
216C2×#107C22×C1111yescharacteristic
217C2×#107C22×C1112yes—
218C2×C4⋊C8C22×C1112yes—
219C2×C4⋊C8C22×C1111yescharacteristic
220C2×#103C22×C1112yes—
221C2×#103C22×C1111yescharacteristic
222C2×#102C22×C1112yes—
223C2×#102C22×C1111yescharacteristic
224C2×#97C22×C1111yescharacteristic
225#395—21no—
226#395—21no—
227#391C22×C1112yes—
228#390C22×C1112yes—
229#389—22no—
230#388—22no—
231#384C22×C1112yes—
232#382C22×C1111yescharacteristic
233#381—21no—
234C4×C4⋊C4C22×C1112yes—
235C4×C4⋊C4C22×C1111yescharacteristic
236C4×C22⋊C4—21no—
237#340C22×C1112yes—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#336C22×C1112yes—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11C2×#12111yescharacteristic
247C22×C11#54711yescharacteristic
248C22×C11#54811yescharacteristic
249C22×C11C2×#13712yes—
250C22×C11#57612yes—
251C4×C11—24no—
252C4×C11—22no—
253C4×C11—22no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—82no—
258C4×C11—81no—
259C4×C11—82no—
260C4×C11#52511yescharacteristic
261C4×C11#53611yescharacteristic
262C4×C11#55211yescharacteristic
263C4×C11#55611yescharacteristic
264C22×Q8—21no—
265C22×Q8C23×C1111yescharacteristic
266C22×D4C23×C1111yescharacteristic
267C23×C4—21no—
268C2×SD16—22no—
269C2×SD16—22no—
270C2×SD16—22no—
271C22×C8C23×C1111yescharacteristic
272C22×C8C23×C1112yes—
273C22×C8C23×C1111yescharacteristic
274C4⋊Q8—22no—
275C4⋊Q8—22no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×D4—22no—
279C4×D4D4×C1114yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4D4×C1112yes—
285C2×C4⋊C4C23×C1111yescharacteristic
286C2×C4⋊C4C23×C1112yes—
287C2×C4⋊C4C23×C1112yes—
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C22⋊C4—21no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C42—21no—
293C2×C42—22no—
294C2×C42C23×C1112yes—
295C2×C42C23×C1111yescharacteristic
296#107—22no—
297#107—24no—
298C4⋊C8—24no—
299C4⋊C8—22no—
300#103—24no—
301#103—22no—
302#102—22no—
303#102—24no—
304#97—22no—
305#95—21no—
306#95—22no—
307#95—21no—
308#95—22no—
309#95—22no—
310#95D4×C1111yescharacteristic
311#95D4×C1111yescharacteristic
312C2×C11—82no—
313C2×C11#241511yescharacteristic
314C2×C11#303911yescharacteristic
315C2×C11#304111yescharacteristic
316C2×C11#334612yes—
317C2×C11#337512yes—
318C24—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—42no—
325C2×Q8—82no—
326C2×Q8C11×#4112yes—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4C2×D4×C1112yes—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—82no—
340C22×C4C2×D4×C1112yes—
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C2×D4×C1112yes—
344C22×C4C24×C1111yescharacteristic
345SD16—28no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C11×#4112yes—
355C4⋊C4—24no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—82no—
366C4⋊C4—82no—
367C4⋊C4C2×D4×C1112yes—
368C22⋊C4—24no—
369C22⋊C4—44no—
370C22⋊C4—82no—
371C42—22no—
372C42—22no—
373C42—42no—
374C42—82no—
375C42C2×D4×C1112yes—
376C42C11×#4112yes—
377C11#2469611yescharacteristic, direct product factor, Sylow
378C23—22no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23C22×D4×C1111yescharacteristic
384Q8—22no—
385Q8—22no—
386Q8—41no—
387Q8—41no—
388Q8—84no—
389D4—22no—
390D4—22no—
391D4—41no—
392D4—41no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—84no—
414C2×C4C11×#12112yes—
415C2×C4C11×#12112yes—
416C2×C4C11×#13714yes—
417C2×C4C22×D4×C1111yescharacteristic
418C2×C4C2×C11×#4111yescharacteristic
419C2×C4C2×C11×#4111yescharacteristic
420C2×C4C2×C11×#4111yescharacteristic
421C2×C4C11×2−1+411yescharacteristic
422C2×C4C11×2−1+411yescharacteristic
423C8—22no—
424C8—42no—
425C8—41no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—82no—
430C22—82no—
431C22C2×C11×#12111yescharacteristic
432C22C11×#54711yescharacteristic
433C22C11×#54811yescharacteristic
434C22C2×C11×#13712yes—
435C22C11×#57612yes—
436C4—22no—
437C4—22no—
438C4—24no—
439C4—42no—
440C4—42no—
441C4—42no—
442C4—82no—
443C4—81no—
444C4—82no—
445C4C11×#52511yescharacteristic
446C4C11×#53611yescharacteristic
447C4C11×#55211yescharacteristic
448C4C11×#55611yescharacteristic
449C2—82no—
450C2C11×#241511yescharacteristic
451C2C11×#303911yescharacteristic
452C2C11×#304111yescharacteristic
453C2C11×#334612yes—
454C2C11×#337512yes—
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×#2567C2semidirect
7. C11×#1993C2semidirect
8. C11×#1947C2semidirect
9. C11×#1940C2semidirect
10. C11×#1928C2semidirect
11. C11×#1805C2semidirect
91. #24696C11direct (N × H)
153. #2567C2×C11semidirect
157. #1993C2×C11semidirect
158. #1947C2×C11semidirect
159. #1940C2×C11semidirect
160. #1928C2×C11semidirect
161. #1805C2×C11semidirect
377. C11#24696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C2×C11×#4402
C11×#25672
C11×#23572
C11×#20712
C11×#20552
C11×#19932
C11×#19472
C11×#19402
C11×#19282
C11×#18052
#2469611