Finite Group Databasebeta

← C11×#24834 #14602027

Subgroups — C11×#24834 #14602027

Order 2816.

852 conjugacy classes of subgroups.

The subgroup lattice has 460 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×#2349C211yesmaximal, characteristic
5C11×#2085C212yesmaximal, complemented
6C11×#2066C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1940C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal
10C11×#1805C211yesmaximal, characteristic, complemented
11C11×#1804C212yesmaximal
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C11×#476—24no—
18C11×#440—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C11×#400—21no—
29C11×#400—21no—
30C11×#391—22no—
31C11×#391C2212yes—
32C11×#389C2212yes—
33C11×#385—22no—
34C11×#382C2211yescharacteristic
35C11×#382C2212yes—
36C11×#380—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C2×C11×#95—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16Q814yescomplemented
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—42no—
61C4×D4×C11D414yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C11×#107—22no—
76C11×#106—24no—
77C11×C4⋊C8—22no—
78C11×C4⋊C8—42no—
79C11×#103—22no—
80C11×#103—42no—
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×#95—22no—
90C11×#95—22no—
91C11×#95D411yescharacteristic
92C11×#95D411yescharacteristic
93#24834C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×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—44no—
101C2×Q8×C11—42no—
102C2×Q8×C11C2×Q812yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C2×D412yes—
107C2×D4×C11C2×Q812yes—
108C2×D4×C11#4112yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—82no—
118C22×C4×C11—82no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C11×SD16—28no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11C2×Q812yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—82no—
145C11×C4⋊C4C2×D412yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—44no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—42no—
151C42×C11C2×D412yes—
152C42×C11#4112yes—
153C2×#476C2×C1111yescharacteristic
154C2×#440C2×C1111yescharacteristic
155#2568C2×C1111yescharacteristic, complemented
156#2349C2×C1111yescharacteristic
157#2085C2×C1112yescomplemented
158#2066C2×C1112yescomplemented
159#1993C2×C1111yescharacteristic, complemented
160#1940C2×C1111yescharacteristic, complemented
161#1877C2×C1112yes—
162#1805C2×C1111yescharacteristic, complemented
163#1804C2×C1112yes—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11C22×D411yescharacteristic
170Q8×C11—22no—
171Q8×C11—22no—
172Q8×C11—41no—
173Q8×C11—41no—
174Q8×C11—84no—
175D4×C11—22no—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11C22⋊Q814yes—
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—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—84no—
200C2×C4×C11—88no—
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C8×C11—22no—
210C8×C11—41no—
211C8×C11—42no—
212C22×SD16C22×C1111yescharacteristic
213C2×C4⋊Q8C22×C1111yescharacteristic
214C2×C4×Q8C22×C1111yescharacteristic
215C2×C4×D4C22×C1112yes—
216C2×C4×D4C22×C1111yescharacteristic
217#476—24no—
218#440—24no—
219C2×#107C22×C1111yescharacteristic
220C2×#106C22×C1112yes—
221C2×C4⋊C8C22×C1111yescharacteristic
222C2×C4⋊C8C22×C1112yes—
223C2×#103C22×C1111yescharacteristic
224C2×#103C22×C1112yes—
225C2×#102C22×C1111yescharacteristic
226C2×#102C22×C1112yes—
227C2×#97C22×C1111yescharacteristic
228#400—21no—
229#400—21no—
230#391—22no—
231#391C22×C1112yes—
232#389C22×C1112yes—
233#385—22no—
234#382C22×C1112yes—
235#382C22×C1111yescharacteristic
236#380—21no—
237C4×C4⋊C4C22×C1111yescharacteristic
238C2×#95—21no—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#340C22×C1112yes—
242#336C22×C1112yes—
243C22×C11—24no—
244C22×C11—44no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—44no—
248C22×C11C2×#12111yescharacteristic
249C22×C11#54611yescharacteristic
250C22×C11D4×Q811yescharacteristic
251C22×C11#57512yes—
252C22×C11#57712yes—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—82no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11C2×C22⋊Q811yescharacteristic
263C4×C11#53711yescharacteristic
264C4×C11#55211yescharacteristic
265C4×C11#55411yescharacteristic
266C22×Q8—21no—
267C22×Q8C23×C1111yescharacteristic
268C22×D4C23×C1111yescharacteristic
269C23×C4—21no—
270C23×C4—22no—
271C2×SD16—22no—
272C2×SD16—22no—
273C2×SD16Q8×C1114yescomplemented
274C22×C8C23×C1112yes—
275C22×C8C23×C1111yescharacteristic
276C22×C8C23×C1111yescharacteristic
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4×Q8—22no—
280C4×Q8—22no—
281C4×D4—24no—
282C4×D4—22no—
283C4×D4—42no—
284C4×D4D4×C1114yes—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4D4×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C42—21no—
296C2×C42C23×C1112yes—
297C2×C42C23×C1111yescharacteristic
298#107—22no—
299#106—24no—
300C4⋊C8—22no—
301C4⋊C8—42no—
302#103—22no—
303#103—42no—
304#102—22no—
305#102—24no—
306#97—22no—
307#95—21no—
308#95—22no—
309#95—21no—
310#95—22no—
311#95—22no—
312#95—22no—
313#95—22no—
314#95D4×C1111yescharacteristic
315#95D4×C1111yescharacteristic
316C2×C11—44no—
317C2×C11#241711yescharacteristic
318C2×C11#304011yescharacteristic
319C2×C11#304211yescharacteristic
320C2×C11#331112yes—
321C2×C11#338812yes—
322C24—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—44no—
329C2×Q8—42no—
330C2×Q8C2×Q8×C1112yes—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4C2×D4×C1112yes—
335C2×D4C2×Q8×C1112yes—
336C2×D4C11×#4112yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—24no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—82no—
346C22×C4—82no—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C24×C1111yescharacteristic
352SD16—28no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8—22no—
360C2×C8—21no—
361C2×C8C2×Q8×C1112yes—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—82no—
373C4⋊C4C2×D4×C1112yes—
374C22⋊C4—24no—
375C22⋊C4—44no—
376C42—22no—
377C42—22no—
378C42—42no—
379C42C2×D4×C1112yes—
380C42C11×#4112yes—
381C11#2483411yescharacteristic, direct product factor, Sylow
382C23—22no—
383C23—22no—
384C23—22no—
385C23—42no—
386C23—42no—
387C23C22×D4×C1111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—41no—
391Q8—41no—
392Q8—84no—
393D4—22no—
394D4—22no—
395D4—22no—
396D4C11×C22⋊Q814yes—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—84no—
418C2×C4—88no—
419C2×C4C11×#12112yes—
420C2×C4C11×#12112yes—
421C2×C4C22×D4×C1111yescharacteristic
422C2×C4C22×Q8×C1111yescharacteristic
423C2×C4C2×C11×#4111yescharacteristic
424C2×C4C2×C11×#4111yescharacteristic
425C2×C4C11×H(5,𝔽2)11yescharacteristic
426C2×C4C11×2−1+411yescharacteristic
427C8—22no—
428C8—41no—
429C8—42no—
430C22—24no—
431C22—42no—
432C22—42no—
433C22—44no—
434C22—44no—
435C22C2×C11×#12111yescharacteristic
436C22C11×#54611yescharacteristic
437C22D4×Q8×C1111yescharacteristic
438C22C11×#57512yes—
439C22C11×#57712yes—
440C4—22no—
441C4—22no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—82no—
447C4—81no—
448C4—82no—
449C4C2×C11×C22⋊Q811yescharacteristic
450C4C11×#53711yescharacteristic
451C4C11×#55211yescharacteristic
452C4C11×#55411yescharacteristic
453C2—44no—
454C2C11×#241711yescharacteristic
455C2C11×#304011yescharacteristic
456C2C11×#304211yescharacteristic
457C2C11×#331112yes—
458C2C11×#338812yes—
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
5. C11×#2085C2semidirect
6. C11×#2066C2semidirect
7. C11×#1993C2semidirect
8. C11×#1940C2semidirect
10. C11×#1805C2semidirect
50. C2×C11×SD16Q8semidirect
93. #24834C11direct (N × H)
155. #2568C2×C11semidirect
157. #2085C2×C11semidirect
158. #2066C2×C11semidirect
159. #1993C2×C11semidirect
160. #1940C2×C11semidirect
162. #1805C2×C11semidirect
273. C2×SD16Q8×C11semidirect
381. C11#24834direct (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×#23492
C11×#20852
C11×#20662
C11×#19932
C11×#19402
C11×#18772
C11×#18052
C11×#18042
#2483411