Finite Group Databasebeta

← C11×#24827 #14602020

Subgroups — C11×#24827 #14602020

Order 2816.

880 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#477C211yesmaximal, characteristic, complemented
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic
4C11×#2351C211yesmaximal, characteristic, complemented
5C11×#2083C212yesmaximal, complemented
6C11×#2067C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1940C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1804C211yesmaximal, characteristic
11C11×#1803C212yesmaximal, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—22no—
15C2×C4×Q8×C11C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#477—24no—
19C11×#440—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2212yes—
28C2×C11×#97C2211yescharacteristic
29C11×#399—21no—
30C11×#399—21no—
31C11×#390C2212yes—
32C11×#389—22no—
33C11×#389C2212yes—
34C11×#384C2212yes—
35C11×#382—21no—
36C11×#382C2211yescharacteristic
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—
55C11×C22⋊Q8—48no—
56C4×Q8×C11—22no—
57C4×Q8×C11—24no—
58C4×Q8×C11—42no—
59C4×Q8×C11D414yes—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—21no—
77C2×C42×C11—22no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#107—22no—
81C11×#107—24no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—42no—
84C11×#103—22no—
85C11×#103—24no—
86C11×#102—22no—
87C11×#102—42no—
88C11×#97—22no—
89C11×#95—21no—
90C11×#95—22no—
91C11×#95—21no—
92C11×#95D411yescharacteristic
93C11×#95D411yescharacteristic
94#24827C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—44no—
100C2×Q8×C11—42no—
101C2×Q8×C11C2×D412yes—
102C2×Q8×C11C2×Q812yes—
103C2×Q8×C11#4112yes—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11C2×Q812yes—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—44no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2411yescharacteristic
122C11×SD16—28no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11C2×Q812yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—42no—
149C11×C22⋊C4—44no—
150C42×C11—24no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—44no—
154C42×C11C2×D412yes—
155C42×C11#4112yes—
156C2×#477C2×C1111yescharacteristic, complemented
157C2×#440C2×C1111yescharacteristic
158#2542C2×C1111yescharacteristic
159#2351C2×C1111yescharacteristic, complemented
160#2083C2×C1112yescomplemented
161#2067C2×C1112yes—
162#1993C2×C1111yescharacteristic, complemented
163#1940C2×C1111yescharacteristic, complemented
164#1880C2×C1112yes—
165#1804C2×C1111yescharacteristic
166#1803C2×C1112yescomplemented
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—22no—
175Q8×C11—22no—
176Q8×C11—84no—
177Q8×C11C22⋊Q814yescomplemented
178D4×C11—22no—
179D4×C11—22no—
180D4×C11—41no—
181D4×C11—41no—
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—22no—
192C2×C4×C11—22no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—84no—
203C2×C4×C11#12112yes—
204C2×C4×C11#12112yes—
205C2×C4×C11AGL(1,ℤ/8)14yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C8×C11—22no—
213C8×C11—41no—
214C8×C11—42no—
215C22×SD16C22×C1111yescharacteristic
216C2×C4⋊Q8C22×C1111yescharacteristic
217C2×C22⋊Q8—22no—
218C2×C4×Q8C22×C1112yes—
219C2×C4×Q8C22×C1111yescharacteristic
220C2×C4×D4C22×C1111yescharacteristic
221#477—24no—
222#440—24no—
223C2×#107C22×C1112yes—
224C2×#107C22×C1111yescharacteristic
225C2×C4⋊C8C22×C1111yescharacteristic
226C2×C4⋊C8C22×C1112yes—
227C2×#103C22×C1112yes—
228C2×#103C22×C1111yescharacteristic
229C2×#102C22×C1111yescharacteristic
230C2×#102C22×C1112yes—
231C2×#97C22×C1111yescharacteristic
232#399—21no—
233#399—21no—
234#390C22×C1112yes—
235#389—22no—
236#389C22×C1112yes—
237#384C22×C1112yes—
238#382—21no—
239#382C22×C1111yescharacteristic
240C4×C4⋊C4—21no—
241C4×C4⋊C4C22×C1111yescharacteristic
242#340C22×C1112yes—
243#340C22×C1112yes—
244#340C22×C1112yes—
245#336C22×C1112yes—
246C22×C11—44no—
247C22×C11—42no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—82no—
251C22×C11C2×#12111yescharacteristic
252C22×C11#54611yescharacteristic
253C22×C11D4×Q811yescharacteristic
254C22×C11C2×AGL(1,ℤ/8)12yes—
255C22×C11#57812yes—
256C4×C11—24no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—24no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—81no—
263C4×C11—82no—
264C4×C11—82no—
265C4×C11C2×C22⋊Q811yescharacteristic
266C4×C11#53711yescharacteristic
267C4×C11#55211yescharacteristic
268C4×C11#55411yescharacteristic
269C22×Q8—21no—
270C22×Q8C23×C1111yescharacteristic
271C22×D4C23×C1111yescharacteristic
272C23×C4—21no—
273C2×SD16—22no—
274C2×SD16—22no—
275C2×SD16Q8×C1114yescomplemented
276C22×C8C23×C1112yes—
277C22×C8C23×C1111yescharacteristic
278C22×C8C23×C1111yescharacteristic
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C22⋊Q8—48no—
282C4×Q8—22no—
283C4×Q8—24no—
284C4×Q8—42no—
285C4×Q8D4×C1114yes—
286C4×D4—22no—
287C4×D4—22no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4D4×C1112yes—
295C2×C4⋊C4C23×C1111yescharacteristic
296C2×C4⋊C4C23×C1112yes—
297C2×C4⋊C4C23×C1112yes—
298C2×C4⋊C4C23×C1111yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C42—21no—
303C2×C42—22no—
304C2×C42C23×C1112yes—
305C2×C42C23×C1111yescharacteristic
306#107—22no—
307#107—24no—
308C4⋊C8—22no—
309C4⋊C8—42no—
310#103—22no—
311#103—24no—
312#102—22no—
313#102—42no—
314#97—22no—
315#95—21no—
316#95—22no—
317#95—21no—
318#95D4×C1111yescharacteristic
319#95D4×C1111yescharacteristic
320C2×C11—82no—
321C2×C11#241711yescharacteristic
322C2×C11#303811yescharacteristic
323C2×C11#304411yescharacteristic
324C2×C11#330812yes—
325C2×C11#338612yes—
326C24—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—44no—
331C2×Q8—42no—
332C2×Q8C2×D4×C1112yes—
333C2×Q8C2×Q8×C1112yes—
334C2×Q8C11×#4112yes—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4C2×Q8×C1112yes—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—44no—
347C22×C4—42no—
348C22×C4C2×D4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1112yes—
352C22×C4C24×C1111yescharacteristic
353SD16—28no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—21no—
362C2×C8C2×Q8×C1112yes—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—44no—
373C4⋊C4—44no—
374C4⋊C4—42no—
375C4⋊C4—44no—
376C4⋊C4—44no—
377C4⋊C4C2×D4×C1112yes—
378C22⋊C4—44no—
379C22⋊C4—42no—
380C22⋊C4—44no—
381C42—24no—
382C42—22no—
383C42—22no—
384C42—44no—
385C42C2×D4×C1112yes—
386C42C11×#4112yes—
387C11#2482711yescharacteristic, direct product factor, Sylow
388C23—22no—
389C23—41no—
390C23—41no—
391C23—42no—
392C23—42no—
393C23C22×D4×C1111yescharacteristic
394Q8—22no—
395Q8—22no—
396Q8—22no—
397Q8—84no—
398Q8C11×C22⋊Q814yescomplemented
399D4—22no—
400D4—22no—
401D4—41no—
402D4—41no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—84no—
424C2×C4C11×#12112yes—
425C2×C4C11×#12112yes—
426C2×C4C11×AGL(1,ℤ/8)14yes—
427C2×C4C22×D4×C1111yescharacteristic
428C2×C4C22×Q8×C1111yescharacteristic
429C2×C4C2×C11×#4111yescharacteristic
430C2×C4C2×C11×#4111yescharacteristic
431C2×C4C11×H(5,𝔽2)11yescharacteristic
432C2×C4C11×2−1+411yescharacteristic
433C8—22no—
434C8—41no—
435C8—42no—
436C22—42no—
437C22—44no—
438C22—81no—
439C22—81no—
440C22—82no—
441C22C2×C11×#12111yescharacteristic
442C22C11×#54611yescharacteristic
443C22D4×Q8×C1111yescharacteristic
444C22C2×C11×AGL(1,ℤ/8)12yes—
445C22C11×#57812yes—
446C4—24no—
447C4—22no—
448C4—22no—
449C4—24no—
450C4—42no—
451C4—42no—
452C4—81no—
453C4—82no—
454C4—82no—
455C4C2×C11×C22⋊Q811yescharacteristic
456C4C11×#53711yescharacteristic
457C4C11×#55211yescharacteristic
458C4C11×#55411yescharacteristic
459C2—82no—
460C2C11×#241711yescharacteristic
461C2C11×#303811yescharacteristic
462C2C11×#304411yescharacteristic
463C2C11×#330812yes—
464C2C11×#338612yes—
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×#477C2semidirect
4. C11×#2351C2semidirect
5. C11×#2083C2semidirect
7. C11×#1993C2semidirect
8. C11×#1940C2semidirect
11. C11×#1803C2semidirect
49. C2×C11×SD16Q8semidirect
94. #24827C11direct (N × H)
156. C2×#477C2×C11semidirect
159. #2351C2×C11semidirect
160. #2083C2×C11semidirect
162. #1993C2×C11semidirect
163. #1940C2×C11semidirect
166. #1803C2×C11semidirect
177. Q8×C11C22⋊Q8semidirect
275. C2×SD16Q8×C11semidirect
387. C11#24827direct (N × H)
398. Q8C11×C22⋊Q8semidirect

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×#4402
C11×#25422
C11×#23512
C11×#20832
C11×#20672
C11×#19932
C11×#19402
C11×#18802
C11×#18042
C11×#18032
#2482711