Finite Group Databasebeta

← C11×#22224 #14599417

Subgroups — C11×#22224 #14599417

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#489C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C4×C11×#124C211yesmaximal, characteristic
4C11×#1993C211yesmaximal, characteristic, complemented
5C11×#1959C211yesmaximal, characteristic
6C11×#1927C212yesmaximal, complemented
7C11×#1925C212yesmaximal
8C11×#1864C212yesmaximal
9C11×#1863C212yesmaximal, complemented
10C11×#1847C211yesmaximal, characteristic, complemented
11C11×#1745C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#124C2211yescharacteristic
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#489C418yescomplemented
18C2×C11×#107C2212yes—
19C2×C11×#106C2212yes—
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#97C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C11×#391—21no—
27C11×#391C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#389—21no—
30C11×#389C2212yes—
31C11×#388—21no—
32C11×#388—21no—
33C11×#384C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4—21no—
39C43×C11C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yescomplemented
52C11×#124—22no—
53C11×#124C2×C414yes—
54C4×Q8×C11—42no—
55C4×Q8×C11—44no—
56C4×D4×C11—42no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C11×#107—42no—
81C11×#106—42no—
82C11×#103—42no—
83C11×#103C2×C418yescomplemented
84C11×#102—42no—
85C11×#102C2×C418yes—
86C11×#97—22no—
87C11×#97C2×C414yescomplemented
88C11×#95—21no—
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94#22224C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C2×Q8×C11—24no—
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11C22×C412yes—
103C2×D4×C11—21no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11C22×C414yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4C22×C414yes—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—42no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—41no—
149C42×C11—41no—
150C42×C11—42no—
151C42×C11—44no—
152C42×C11C22×C412yes—
153C42×C11#4112yes—
154C2×#489C2×C1111yescharacteristic
155C4×C4⋊Q8C2×C1111yescharacteristic, complemented
156C4×#124C2×C1111yescharacteristic
157#1993C2×C1111yescharacteristic, complemented
158#1959C2×C1111yescharacteristic
159#1927C2×C1112yescomplemented
160#1925C2×C1112yes—
161#1864C2×C1112yes—
162#1863C2×C1112yescomplemented
163#1847C2×C1111yescharacteristic, complemented
164#1745C2×C1111yescharacteristic, complemented
165C23×C11—22no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11C22×D411yescharacteristic
173Q8×C11—24no—
174Q8×C11—48no—
175Q8×C11—42no—
176D4×C11—24no—
177D4×C11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—84no—
208C2×C4×C11C4×D412yes—
209C2×C4×C11C4×D412yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)12yes—
215C2×C4×C112−1+412yes—
216C8×C11—24no—
217C8×C11—42no—
218C2×C4⋊Q8C22×C1111yescharacteristic
219C2×#124C22×C1111yescharacteristic
220C2×C4×Q8—21no—
221C2×C4×Q8C22×C1111yescharacteristic
222C2×C4×D4C22×C1111yescharacteristic
223#489C4×C1118yescomplemented
224C2×#107C22×C1112yes—
225C2×#106C22×C1112yes—
226C2×#103C22×C1112yes—
227C2×#103C22×C1112yes—
228C2×#102C22×C1112yes—
229C2×#102C22×C1112yes—
230C2×#97C22×C1111yescharacteristic
231C2×#97C22×C1111yescharacteristic
232#391—21no—
233#391C22×C1111yescharacteristic
234#390C22×C1111yescharacteristic
235#389—21no—
236#389C22×C1112yes—
237#388—21no—
238#388—21no—
239#384C22×C1111yescharacteristic
240#382C22×C1111yescharacteristic
241C4×C4⋊C4—21no—
242C4×C4⋊C4C22×C1112yes—
243C4×C22⋊C4—21no—
244C4×C22⋊C4—21no—
245C43C22×C1111yescharacteristic
246#340C22×C1112yes—
247#340C22×C1112yes—
248#336C22×C1112yes—
249#336C22×C1112yes—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11C2×C4×D411yescharacteristic
258C22×C11#53511yescharacteristic
259C22×C11#53611yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C22×C11#57511yescharacteristic
263C22×C11#57511yescharacteristic
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—22no—
267C4×C11—22no—
268C4×C11—42no—
269C4×C11—44no—
270C4×C11—41no—
271C4×C11—41no—
272C4×C11—81no—
273C4×C11—82no—
274C4×C11—81no—
275C4×C11#52012yes—
276C4×C11#54212yes—
277C22×Q8—21no—
278C22×Q8C23×C1111yescharacteristic
279C22×D4C23×C1111yescharacteristic
280C23×C4—21no—
281C22×C8C23×C1112yes—
282C22×C8C23×C1112yes—
283C4⋊Q8—22no—
284C4⋊Q8C2×C4×C1114yescomplemented
285#124—22no—
286#124C2×C4×C1114yes—
287C4×Q8—42no—
288C4×Q8—44no—
289C4×D4—42no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4C23×C1111yescharacteristic
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C4⋊C4C23×C1112yes—
298C2×C4⋊C4C23×C1112yes—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C42—22no—
305C2×C42—21no—
306C2×C42D4×C1111yescharacteristic
307C2×C42D4×C1111yescharacteristic
308C2×C42D4×C1111yescharacteristic
309C2×C42D4×C1111yescharacteristic
310C2×C42C23×C1111yescharacteristic
311C2×C42C23×C1111yescharacteristic
312C2×C42C23×C1111yescharacteristic
313#107—42no—
314#106—42no—
315#103—42no—
316#103C2×C4×C1118yescomplemented
317#102—42no—
318#102C2×C4×C1118yes—
319#97—22no—
320#97C2×C4×C1114yescomplemented
321#95—21no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—22no—
326#95—22no—
327C2×C11—82no—
328C2×C11#232611yescharacteristic
329C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
330C2×C11C4×#13711yescharacteristic
331C2×C11#321411yescharacteristic
332C2×C11#321511yescharacteristic
333C2×C11#323811yescharacteristic
334C2×C11#324011yescharacteristic
335C24—21no—
336C2×Q8—24no—
337C2×Q8—21no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—42no—
341C2×Q8—42no—
342C2×Q8C22×C4×C1112yes—
343C2×D4—21no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4C22×C4×C1112yes—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1111yescharacteristic
358C22×C4C2×D4×C1111yescharacteristic
359C22×C4C2×D4×C1111yescharacteristic
360C22×C4C2×D4×C1111yescharacteristic
361C22×C4C24×C1111yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8C22×C4×C1114yes—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—44no—
377C4⋊C4—42no—
378C4⋊C4C22×C4×C1114yes—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C42—22no—
385C42—22no—
386C42—22no—
387C42—22no—
388C42—41no—
389C42—41no—
390C42—42no—
391C42—44no—
392C42C22×C4×C1112yes—
393C42C11×#4112yes—
394C11#2222411yescharacteristic, direct product factor, Sylow
395C23—22no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C22×D4×C1111yescharacteristic
403Q8—24no—
404Q8—48no—
405Q8—42no—
406D4—24no—
407D4—42no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—84no—
438C2×C4C4×D4×C1112yes—
439C2×C4C4×D4×C1112yes—
440C2×C4C11×AGL(1,ℤ/8)12yes—
441C2×C4C11×#13712yes—
442C2×C4C23×C4×C1111yescharacteristic
443C2×C4C2×C11×#4111yescharacteristic
444C2×C4C11×H(5,𝔽2)12yes—
445C2×C4C11×2−1+412yes—
446C8—24no—
447C8—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C2×C4×D4×C1111yescharacteristic
456C22C11×#53511yescharacteristic
457C22C11×#53611yescharacteristic
458C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
459C22C2×C11×#13711yescharacteristic
460C22C11×#57511yescharacteristic
461C22C11×#57511yescharacteristic
462C4—22no—
463C4—22no—
464C4—22no—
465C4—22no—
466C4—44no—
467C4—41no—
468C4—41no—
469C4—42no—
470C4—81no—
471C4—82no—
472C4—81no—
473C4C11×#52012yes—
474C4C11×#54212yes—
475C2—82no—
476C2C11×#232611yescharacteristic
477C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
478C2C4×C11×#13711yescharacteristic
479C2C11×#321411yescharacteristic
480C2C11×#321511yescharacteristic
481C2C11×#323811yescharacteristic
482C2C11×#324011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4×C11×C4⋊Q8C2semidirect
4. C11×#1993C2semidirect
6. C11×#1927C2semidirect
9. C11×#1863C2semidirect
10. C11×#1847C2semidirect
11. C11×#1745C2semidirect
17. C11×#489C4semidirect
51. C11×C4⋊Q8C2×C4semidirect
83. C11×#103C2×C4semidirect
87. C11×#97C2×C4semidirect
94. #22224C11direct (N × H)
155. C4×C4⋊Q8C2×C11semidirect
157. #1993C2×C11semidirect
159. #1927C2×C11semidirect
162. #1863C2×C11semidirect
163. #1847C2×C11semidirect
164. #1745C2×C11semidirect
223. #489C4×C11semidirect
284. C4⋊Q8C2×C4×C11semidirect
316. #103C2×C4×C11semidirect
320. #97C2×C4×C11semidirect
394. C11#22224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4892
C4×C11×C4⋊Q82
C4×C11×#1242
C11×#19932
C11×#19592
C11×#19272
C11×#19252
C11×#18642
C11×#18632
C11×#18472
C11×#17452
#2222411