Finite Group Databasebeta

← C11×#24828 #14602021

Subgroups — C11×#24828 #14602021

Order 2816.

824 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×#475C211yesmaximal, characteristic, complemented
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic
4C11×#2351C211yesmaximal, characteristic, complemented
5C11×#2085C212yesmaximal, complemented
6C11×#2065C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1940C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1805C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#475—24no—
18C11×#440—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#97C2211yescharacteristic
28C11×#393—21no—
29C11×#393—21no—
30C11×#390C2212yes—
31C11×#389—22no—
32C11×#389C2212yes—
33C11×#382—21no—
34C11×#382C2211yescharacteristic
35C11×#382C2212yes—
36C11×#380—22no—
37C4×C11×C4⋊C4—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
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×SD16Q814yescomplemented
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—24no—
57C4×Q8×C11—42no—
58C4×Q8×C11D414yes—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
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×C11×C22⋊C4—22no—
73C2×C42×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C11×#107—22no—
78C11×#106—24no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—42no—
81C11×#103—22no—
82C11×#103—24no—
83C11×#102—22no—
84C11×#102—42no—
85C11×#97—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95D411yescharacteristic
92C11×#95D411yescharacteristic
93#24828C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—42no—
99C2×Q8×C11—82no—
100C2×Q8×C11C2×D412yes—
101C2×Q8×C11C2×Q812yes—
102C2×Q8×C11#4112yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11C2×Q812yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—44no—
115C22×C4×C11—42no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C11×SD16—28no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11C2×Q812yes—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—44no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—82no—
146C11×C22⋊C4—82no—
147C42×C11—24no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—44no—
151C42×C11C2×D412yes—
152C42×C11#4112yes—
153C2×#475C2×C1111yescharacteristic, complemented
154C2×#440C2×C1111yescharacteristic
155#2563C2×C1111yescharacteristic
156#2351C2×C1111yescharacteristic, complemented
157#2085C2×C1112yescomplemented
158#2065C2×C1112yes—
159#1993C2×C1111yescharacteristic, complemented
160#1940C2×C1111yescharacteristic, complemented
161#1880C2×C1112yes—
162#1805C2×C1112yescomplemented
163#1804C2×C1111yescharacteristic
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11C22×D411yescharacteristic
170Q8×C11—22no—
171Q8×C11—22no—
172Q8×C11—22no—
173Q8×C11—84no—
174Q8×C11C22⋊Q814yes—
175D4×C11—22no—
176D4×C11—22no—
177D4×C11—41no—
178D4×C11—41no—
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—22no—
190C2×C4×C11—22no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—84no—
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×C1112yes—
215C2×C4×Q8C22×C1111yescharacteristic
216C2×C4×D4C22×C1111yescharacteristic
217#475—24no—
218#440—24no—
219C2×#107C22×C1111yescharacteristic
220C2×#106C22×C1112yes—
221C2×C4⋊C8C22×C1111yescharacteristic
222C2×C4⋊C8C22×C1112yes—
223C2×#103C22×C1112yes—
224C2×#103C22×C1111yescharacteristic
225C2×#102C22×C1111yescharacteristic
226C2×#102C22×C1112yes—
227C2×#97C22×C1111yescharacteristic
228#393—21no—
229#393—21no—
230#390C22×C1112yes—
231#389—22no—
232#389C22×C1112yes—
233#382—21no—
234#382C22×C1112yes—
235#382C22×C1111yescharacteristic
236#380—22no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4C22×C1111yescharacteristic
239#340C22×C1112yes—
240#340C22×C1112yes—
241#340C22×C1112yes—
242#336C22×C1112yes—
243C22×C11—44no—
244C22×C11—42no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—82no—
248C22×C11C2×#12111yescharacteristic
249C22×C11#54611yescharacteristic
250C22×C11D4×Q811yescharacteristic
251C22×C11#57512yes—
252C22×C11#57712yes—
253C4×C11—24no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—81no—
260C4×C11—82no—
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—
270C2×SD16—22no—
271C2×SD16—22no—
272C2×SD16Q8×C1114yescomplemented
273C22×C8C23×C1112yes—
274C22×C8C23×C1111yescharacteristic
275C22×C8C23×C1111yescharacteristic
276C4⋊Q8—22no—
277C4⋊Q8—22no—
278C4×Q8—22no—
279C4×Q8—24no—
280C4×Q8—42no—
281C4×Q8D4×C1114yes—
282C4×D4—22no—
283C4×D4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4D4×C1112yes—
289C2×C4⋊C4C23×C1111yescharacteristic
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C42—21no—
297C2×C42—22no—
298C2×C42C23×C1112yes—
299C2×C42C23×C1111yescharacteristic
300#107—22no—
301#106—24no—
302C4⋊C8—22no—
303C4⋊C8—42no—
304#103—22no—
305#103—24no—
306#102—22no—
307#102—42no—
308#97—22no—
309#95—21no—
310#95—22no—
311#95—22no—
312#95—22no—
313#95—21no—
314#95D4×C1111yescharacteristic
315#95D4×C1111yescharacteristic
316C2×C11—82no—
317C2×C11#241711yescharacteristic
318C2×C11#304011yescharacteristic
319C2×C11#304311yescharacteristic
320C2×C11#332112yes—
321C2×C11#338812yes—
322C24—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—42no—
327C2×Q8—82no—
328C2×Q8C2×D4×C1112yes—
329C2×Q8C2×Q8×C1112yes—
330C2×Q8C11×#4112yes—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4C2×Q8×C1112yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—44no—
343C22×C4—42no—
344C22×C4C2×D4×C1112yes—
345C22×C4C2×D4×C1112yes—
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C24×C1111yescharacteristic
349SD16—28no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—21no—
356C2×C8—22no—
357C2×C8—21no—
358C2×C8C2×Q8×C1112yes—
359C4⋊C4—24no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4—44no—
369C4⋊C4—44no—
370C4⋊C4—42no—
371C4⋊C4C2×D4×C1112yes—
372C22⋊C4—42no—
373C22⋊C4—82no—
374C22⋊C4—82no—
375C42—24no—
376C42—22no—
377C42—22no—
378C42—44no—
379C42C2×D4×C1112yes—
380C42C11×#4112yes—
381C11#2482811yescharacteristic, direct product factor, Sylow
382C23—22no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23C22×D4×C1111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—22no—
391Q8—84no—
392Q8C11×C22⋊Q814yes—
393D4—22no—
394D4—22no—
395D4—41no—
396D4—41no—
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—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—84no—
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—42no—
431C22—44no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22C2×C11×#12111yescharacteristic
436C22C11×#54611yescharacteristic
437C22D4×Q8×C1111yescharacteristic
438C22C11×#57512yes—
439C22C11×#57712yes—
440C4—24no—
441C4—22no—
442C4—22no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—81no—
447C4—82no—
448C4—82no—
449C4C2×C11×C22⋊Q811yescharacteristic
450C4C11×#53711yescharacteristic
451C4C11×#55211yescharacteristic
452C4C11×#55411yescharacteristic
453C2—82no—
454C2C11×#241711yescharacteristic
455C2C11×#304011yescharacteristic
456C2C11×#304311yescharacteristic
457C2C11×#332112yes—
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
1. C2×C11×#475C2semidirect
4. C11×#2351C2semidirect
5. C11×#2085C2semidirect
7. C11×#1993C2semidirect
8. C11×#1940C2semidirect
10. C11×#1805C2semidirect
49. C2×C11×SD16Q8semidirect
93. #24828C11direct (N × H)
153. C2×#475C2×C11semidirect
156. #2351C2×C11semidirect
157. #2085C2×C11semidirect
159. #1993C2×C11semidirect
160. #1940C2×C11semidirect
162. #1805C2×C11semidirect
272. C2×SD16Q8×C11semidirect
381. C11#24828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4752
C2×C11×#4402
C11×#25632
C11×#23512
C11×#20852
C11×#20652
C11×#19932
C11×#19402
C11×#18802
C11×#18052
C11×#18042
#2482811