Finite Group Databasebeta

← C11×#22085 #14599278

Subgroups — C11×#22085 #14599278

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#484C211yesmaximal, characteristic
2C4×C11×C22⋊Q8C211yesmaximal, characteristic
3C2×C11×#389C211yesmaximal, characteristic
4C11×#1943C212yesmaximal, complemented
5C11×#1935C212yesmaximal, complemented
6C11×#1918C212yesmaximal, complemented
7C11×#1872C211yesmaximal, characteristic
8C11×#1865C212yesmaximal, complemented
9C11×#1853C211yesmaximal, characteristic
10C11×#1824C211yesmaximal, characteristic
11C11×#1749C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#484C418yescomplemented
19C2×C11×#107C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2212yes—
26C11×#391C2211yescharacteristic
27C11×#389—21no—
28C11×#389—21no—
29C11×#389C2212yes—
30C11×#389C2212yes—
31C11×#389C2211yescharacteristic
32C11×#387—21no—
33C11×#385—21no—
34C11×#380C2211yescharacteristic
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C2×C11×#95—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8C2×C414yes—
54C4×Q8×C11—42no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—42no—
64C2×C11×C4⋊C4—44no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11—42no—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C11×#107C2×C418yescomplemented
81C11×#106—42no—
82C11×#103—42no—
83C11×#103C2×C418yescomplemented
84C11×C22⋊C8—22no—
85C11×C22⋊C8C2×C414yes—
86C11×#97—42no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94#22085C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C412yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4112yes—
127C22×C4×C11C2411yescharacteristic
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11C22×C414yes—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4C22×C414yes—
148C11×C4⋊C4C22×C412yes—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—42no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—41no—
154C42×C11—41no—
155C42×C11—42no—
156C42×C11—42no—
157C2×#484C2×C1111yescharacteristic
158C4×C22⋊Q8C2×C1111yescharacteristic
159C2×#389C2×C1111yescharacteristic
160#1943C2×C1112yescomplemented
161#1935C2×C1112yescomplemented
162#1918C2×C1112yescomplemented
163#1872C2×C1111yescharacteristic
164#1865C2×C1112yescomplemented
165#1853C2×C1111yescharacteristic
166#1824C2×C1111yescharacteristic
167#1749C2×C1111yescharacteristic
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11C4×D412yes—
173C23×C11#13712yes—
174C23×C11#13712yes—
175C23×C11C22×D411yescharacteristic
176Q8×C11—24no—
177Q8×C11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—21no—
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—21no—
195C2×C4×C11—21no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11—48no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—84no—
215C2×C4×C11C4×D412yes—
216C2×C4×C11AGL(1,ℤ/8)12yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)12yes—
220C2×C4×C112−1+412yes—
221C8×C11—24no—
222C8×C11—42no—
223C2×C22⋊Q8C22×C1111yescharacteristic
224C2×C4×Q8C22×C1111yescharacteristic
225C22×C4⋊C4—21no—
226C22×C4⋊C4C22×C1111yescharacteristic
227C22×C4⋊C4C22×C1111yescharacteristic
228C22×C42C22×C1111yescharacteristic
229#484C4×C1118yescomplemented
230C2×#107C22×C1112yes—
231C2×#106C22×C1112yes—
232C2×#103C22×C1112yes—
233C2×#103C22×C1112yes—
234C2×C22⋊C8C22×C1111yescharacteristic
235C2×C22⋊C8C22×C1111yescharacteristic
236C2×#97C22×C1112yes—
237#391C22×C1111yescharacteristic
238#389—21no—
239#389—21no—
240#389C22×C1112yes—
241#389C22×C1112yes—
242#389C22×C1111yescharacteristic
243#387—21no—
244#385—21no—
245#380C22×C1111yescharacteristic
246C4×C4⋊C4—21no—
247C4×C4⋊C4C22×C1111yescharacteristic
248C4×C22⋊C4—21no—
249C2×#95—21no—
250#340C22×C1112yes—
251#340C22×C1112yes—
252#340C22×C1112yes—
253#340C22×C1112yes—
254#336C22×C1112yes—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11#44114yes—
262C22×C11C2×C4×D411yescharacteristic
263C22×C11#53411yescharacteristic
264C22×C11#53611yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C22×C11#57511yescharacteristic
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—41no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—42no—
276C4×C11—44no—
277C4×C11—82no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11#52012yes—
281C4×C11#53912yes—
282C22×Q8C23×C1111yescharacteristic
283C23×C4—21no—
284C23×C4—21no—
285C23×C4D4×C1111yescharacteristic
286C23×C4D4×C1111yescharacteristic
287C23×C4C23×C1111yescharacteristic
288C22×C8C23×C1112yes—
289C22×C8C23×C1112yes—
290C22⋊Q8—22no—
291C22⋊Q8C2×C4×C1114yes—
292C4×Q8—42no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4C2×C4×C1114yes—
304C2×C4⋊C4C23×C1112yes—
305C2×C4⋊C4C23×C1111yescharacteristic
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C4⋊C4C23×C1112yes—
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—42no—
314C2×C42D4×C1111yescharacteristic
315C2×C42D4×C1111yescharacteristic
316C2×C42C23×C1111yescharacteristic
317C2×C42C23×C1111yescharacteristic
318#107C2×C4×C1118yescomplemented
319#106—42no—
320#103—42no—
321#103C2×C4×C1118yescomplemented
322C22⋊C8—22no—
323C22⋊C8C2×C4×C1114yes—
324#97—42no—
325#95—22no—
326#95—22no—
327#95—21no—
328#95—21no—
329#95—21no—
330#95—21no—
331#95—21no—
332C2×C11—24no—
333C2×C11#232211yescharacteristic
334C2×C11C2×#44111yescharacteristic
335C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
336C2×C11#319311yescharacteristic
337C2×C11#319611yescharacteristic
338C2×C11#323611yescharacteristic
339C2×C11#323911yescharacteristic
340C24C2×D4×C1111yescharacteristic
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8C22×C4×C1112yes—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C22×C4×C1112yes—
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C11×#4112yes—
372C22×C4C24×C1111yescharacteristic
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8C22×C4×C1114yes—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—42no—
388C4⋊C4—44no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—44no—
392C4⋊C4C22×C4×C1114yes—
393C4⋊C4C22×C4×C1112yes—
394C22⋊C4—24no—
395C22⋊C4—42no—
396C42—22no—
397C42—22no—
398C42—41no—
399C42—41no—
400C42—42no—
401C42—42no—
402C11#2208511yescharacteristic, direct product factor, Sylow
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23C4×D4×C1112yes—
408C23C11×#13712yes—
409C23C11×#13712yes—
410C23C22×D4×C1111yescharacteristic
411Q8—24no—
412Q8—42no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—48no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—84no—
450C2×C4C4×D4×C1112yes—
451C2×C4C11×AGL(1,ℤ/8)12yes—
452C2×C4C23×C4×C1111yescharacteristic
453C2×C4C2×C11×#4111yescharacteristic
454C2×C4C11×H(5,𝔽2)12yes—
455C2×C4C11×2−1+412yes—
456C8—24no—
457C8—42no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22C11×#44114yes—
465C22C2×C4×D4×C1111yescharacteristic
466C22C11×#53411yescharacteristic
467C22C11×#53611yescharacteristic
468C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
469C22C2×C11×#13711yescharacteristic
470C22C2×C11×#13711yescharacteristic
471C22C11×#57511yescharacteristic
472C4—22no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—44no—
478C4—42no—
479C4—42no—
480C4—82no—
481C4—81no—
482C4—81no—
483C4C11×#52012yes—
484C4C11×#53912yes—
485C2—24no—
486C2C11×#232211yescharacteristic
487C2C2×C11×#44111yescharacteristic
488C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
489C2C11×#319311yescharacteristic
490C2C11×#319611yescharacteristic
491C2C11×#323611yescharacteristic
492C2C11×#323911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1943C2semidirect
5. C11×#1935C2semidirect
6. C11×#1918C2semidirect
8. C11×#1865C2semidirect
18. C11×#484C4semidirect
80. C11×#107C2×C4semidirect
83. C11×#103C2×C4semidirect
94. #22085C11direct (N × H)
160. #1943C2×C11semidirect
161. #1935C2×C11semidirect
162. #1918C2×C11semidirect
164. #1865C2×C11semidirect
229. #484C4×C11semidirect
318. #107C2×C4×C11semidirect
321. #103C2×C4×C11semidirect
402. C11#22085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4842
C4×C11×C22⋊Q82
C2×C11×#3892
C11×#19432
C11×#19352
C11×#19182
C11×#18722
C11×#18652
C11×#18532
C11×#18242
C11×#17492
#2208511