Finite Group Databasebeta

← C11×#22771 #14599964

Subgroups — C11×#22771 #14599964

Order 2816.

810 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×C4×C11×Q16C211yesmaximal, characteristic
2C11×#2355C211yesmaximal, characteristic
3Q8×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1933C212yesmaximal
5C11×#1921C212yesmaximal
6C11×#1878C212yesmaximal
7C11×#1834C211yesmaximal, characteristic
8C11×#1803C211yesmaximal, characteristic
9C11×#1803C211yesmaximal, characteristic
10C8×C11×C4⋊C4C211yesmaximal, characteristic
11C4×C11×#103C212yesmaximal
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C4×C11×Q16C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C11×#103C2212yes—
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C4×C8×C11C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#391C2212yes—
26C11×#389—22no—
27C11×#389C2212yes—
28C11×#387—22no—
29C11×#384—21no—
30C11×#384C2211yescharacteristic
31C11×#384C2211yescharacteristic
32C11×#382—21no—
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×Q8×C11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—24no—
53C4×Q8×C11—42no—
54C4×Q8×C11C2×C414yes—
55C4×Q8×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C11×#107C2×C414yes—
77C11×C4⋊C8—22no—
78C11×#103—24no—
79C11×#103—42no—
80C11×#103C2×C414yes—
81C11×#103C2×C414yes—
82C4×C8×C11—42no—
83C4×C8×C11C2×C414yes—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95D412yes—
89#22771C1111yesmaximal, characteristic, direct product factor, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C22×C412yes—
99C2×Q8×C11C22×C412yes—
100C2×Q8×C11#4112yes—
101C2×Q8×C11#4112yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C11×Q16—28no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C412yes—
122C2×C8×C11C22×C412yes—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—81no—
136C11×C4⋊C4—81no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4Q1614yescomplemented
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4C22×C412yes—
141C42×C11—24no—
142C42×C11—24no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—44no—
146C42×C11—82no—
147C42×C11C22×C412yes—
148C42×C11#4112yes—
149C2×C4×Q16C2×C1111yescharacteristic
150#2355C2×C1111yescharacteristic
151Q8×C4⋊C4C2×C1111yescharacteristic
152#1933C2×C1112yes—
153#1921C2×C1112yes—
154#1878C2×C1112yes—
155#1834C2×C1111yescharacteristic
156#1803C2×C1111yescharacteristic
157#1803C2×C1111yescharacteristic
158C8×C4⋊C4C2×C1111yescharacteristic
159C4×#103C2×C1112yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—22no—
162Q8×C11—22no—
163Q8×C11—22no—
164Q8×C11—22no—
165Q8×C11—22no—
166Q8×C11—41no—
167Q8×C11—41no—
168Q8×C11#11714yes—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
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—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C4×D412yes—
195C2×C4×C11C4×D412yes—
196C2×C4×C11C2×Q1614yes—
197C2×C4×C11C2×Q1612yes—
198C2×C4×C11#13512yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C8×C11—22no—
206C8×C11—22no—
207C8×C11—42no—
208C22×Q16C22×C1111yescharacteristic
209C2×C4×Q8C22×C1112yes—
210C2×C4×Q8C22×C1111yescharacteristic
211C2×C4×Q8C22×C1111yescharacteristic
212C4×Q16C4×C1118yescomplemented
213C2×#107C22×C1111yescharacteristic
214C2×C4⋊C8C22×C1111yescharacteristic
215C2×#103C22×C1112yes—
216C2×#103C22×C1112yes—
217C2×#103C22×C1111yescharacteristic
218C2×#103C22×C1111yescharacteristic
219C2×C4×C8C22×C1112yes—
220C2×C4×C8C22×C1111yescharacteristic
221#391C22×C1112yes—
222#389—22no—
223#389C22×C1112yes—
224#387—22no—
225#384—21no—
226#384C22×C1111yescharacteristic
227#384C22×C1111yescharacteristic
228#382—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4C22×C1112yes—
232C4×C4⋊C4C22×C1111yescharacteristic
233#340C22×C1112yes—
234#340C22×C1112yes—
235#340C22×C1112yes—
236#340C22×C1112yes—
237#336C22×C1112yes—
238C22×C11C2×C4×D411yescharacteristic
239C22×C11#54611yescharacteristic
240C22×C11#54811yescharacteristic
241C22×C11C22×Q1611yescharacteristic
242C22×C11C2×#13511yescharacteristic
243C22×C11#57711yescharacteristic
244C22×C11#57711yescharacteristic
245C4×C11—24no—
246C4×C11—22no—
247C4×C11—24no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—82no—
253C4×C11—82no—
254C4×C11C4×Q1614yes—
255C4×C11C2×#11711yescharacteristic
256C4×C11#52011yescharacteristic
257C4×C11#55211yescharacteristic
258C4×C11#55311yescharacteristic
259C22×Q8C23×C1111yescharacteristic
260C22×Q8C23×C1111yescharacteristic
261C2×Q16—22no—
262C2×Q16—22no—
263C2×Q16C2×C4×C1114yes—
264C22×C8C23×C1112yes—
265C22×C8C23×C1111yescharacteristic
266C22×C8C23×C1111yescharacteristic
267C4×Q8—22no—
268C4×Q8—22no—
269C4×Q8—24no—
270C4×Q8—42no—
271C4×Q8C2×C4×C1114yes—
272C4×Q8C2×C4×C1114yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4D4×C1111yescharacteristic
282C2×C4⋊C4D4×C1111yescharacteristic
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1111yescharacteristic
286C2×C4⋊C4C23×C1111yescharacteristic
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42C23×C1112yes—
292C2×C42C23×C1111yescharacteristic
293#107C2×C4×C1114yes—
294C4⋊C8—22no—
295#103—24no—
296#103—42no—
297#103C2×C4×C1114yes—
298#103C2×C4×C1114yes—
299C4×C8—42no—
300C4×C8C2×C4×C1114yes—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—22no—
305#95D4×C1112yes—
306C2×C11#235211yescharacteristic
307C2×C11C2×C4×Q1611yescharacteristic
308C2×C11#295211yescharacteristic
309C2×C11#329911yescharacteristic
310C2×C11#330411yescharacteristic
311C2×C11#336311yescharacteristic
312C2×C11#336511yescharacteristic
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8C22×C4×C1112yes—
322C2×Q8C22×C4×C1112yes—
323C2×Q8C11×#4112yes—
324C2×Q8C11×#4112yes—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4C2×D4×C1112yes—
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C24×C1111yescharacteristic
336Q16—28no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8C22×C4×C1112yes—
345C2×C8C22×C4×C1112yes—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—44no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—81no—
359C4⋊C4—81no—
360C4⋊C4—82no—
361C4⋊C4C11×Q1614yescomplemented
362C4⋊C4C22×C4×C1112yes—
363C4⋊C4C22×C4×C1112yes—
364C42—24no—
365C42—24no—
366C42—22no—
367C42—22no—
368C42—44no—
369C42—82no—
370C42C22×C4×C1112yes—
371C42C11×#4112yes—
372C11#2277111yescharacteristic, direct product factor, Sylow
373C23C22×D4×C1111yescharacteristic
374Q8—22no—
375Q8—22no—
376Q8—22no—
377Q8—22no—
378Q8—22no—
379Q8—41no—
380Q8—41no—
381Q8C11×#11714yes—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4C4×D4×C1112yes—
408C2×C4C4×D4×C1112yes—
409C2×C4C2×C11×Q1614yes—
410C2×C4C2×C11×Q1612yes—
411C2×C4C11×#13512yes—
412C2×C4C23×C4×C1111yescharacteristic
413C2×C4C2×C11×#4111yescharacteristic
414C2×C4C2×C11×#4111yescharacteristic
415C2×C4C2×C11×#4111yescharacteristic
416C2×C4C11×H(5,𝔽2)11yescharacteristic
417C2×C4C11×2−1+411yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C22C2×C4×D4×C1111yescharacteristic
422C22C11×#54611yescharacteristic
423C22C11×#54811yescharacteristic
424C22C22×C11×Q1611yescharacteristic
425C22C2×C11×#13511yescharacteristic
426C22C11×#57711yescharacteristic
427C22C11×#57711yescharacteristic
428C4—22no—
429C4—24no—
430C4—24no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—82no—
436C4—82no—
437C4C4×C11×Q1614yes—
438C4C2×C11×#11711yescharacteristic
439C4C11×#52011yescharacteristic
440C4C11×#55211yescharacteristic
441C4C11×#55311yescharacteristic
442C2C11×#235211yescharacteristic
443C2C2×C4×C11×Q1611yescharacteristic
444C2C11×#295211yescharacteristic
445C2C11×#329911yescharacteristic
446C2C11×#330411yescharacteristic
447C2C11×#336311yescharacteristic
448C2C11×#336511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×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
16. C4×C11×Q16C4semidirect
89. #22771C11direct (N × H)
138. C11×C4⋊C4Q16semidirect
212. C4×Q16C4×C11semidirect
361. C4⋊C4C11×Q16semidirect
372. C11#22771direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×Q162
C11×#23552
Q8×C11×C4⋊C42
C11×#19332
C11×#19212
C11×#18782
C11×#18342
C11×#18032
C8×C11×C4⋊C42
C4×C11×#1032
#2277111