Finite Group Databasebeta

← C11×#23026 #14600219

Subgroups — C11×#23026 #14600219

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
3C2×C11×#427C211yesmaximal, characteristic
4C11×#2362C212yesmaximal
5C11×#1969C211yesmaximal, characteristic, complemented
6C11×#1942C211yesmaximal, characteristic, complemented
7C11×#1927C212yesmaximal, complemented
8C11×#1873C212yesmaximal
9C11×#1865C212yesmaximal, complemented
10C4×C11×#107C211yesmaximal, characteristic, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11C2212yes—
16C2×C11×#117C2212yes—
17C11×#467C418yescomplemented
18C4×C11×Q16—24no—
19C11×#427—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C11×#391C2212yes—
31C11×#389C2212yes—
32C11×#388—22no—
33C11×#388—22no—
34C11×#387—22no—
35C4×C11×C4⋊C4—22no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C22×Q8×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2×C414yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8C2×C418yes—
56C4×Q8×C11—24no—
57C4×Q8×C11—42no—
58C11×#117—24no—
59C11×#117—42no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C11×#107—22no—
76C11×#107C2×C414yes—
77C11×#107D414yes—
78C11×#106—24no—
79C11×#103—24no—
80C11×#103—42no—
81C11×#103C2×C418yes—
82C11×C22⋊C8—22no—
83C4×C8×C11—22no—
84C4×C8×C11—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#23026C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C22×C414yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C11×Q16—28no—
116C2×C8×C11—28no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11C22×C412yes—
126C2×C8×C11C22×C412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11#4112yes—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—44no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4C22×C414yes—
137C11×C4⋊C4C2×D414yes—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—44no—
142C42×C11—21no—
143C42×C11—21no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11—44no—
147C42×C11—44no—
148C42×C11—44no—
149C2×#467C2×C1111yescharacteristic
150C2×C4×Q16C2×C1111yescharacteristic, complemented
151C2×#427C2×C1111yescharacteristic
152#2362C2×C1112yes—
153#1969C2×C1111yescharacteristic, complemented
154#1942C2×C1111yescharacteristic, complemented
155#1927C2×C1112yescomplemented
156#1873C2×C1112yes—
157#1865C2×C1112yescomplemented
158C4×#107C2×C1111yescharacteristic, complemented
159C8×C22⋊C4C2×C1111yescharacteristic
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11C4×D412yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—24no—
169Q8×C11—24no—
170Q8×C11—42no—
171Q8×C11—42no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—21no—
185C2×C4×C11—24no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
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×C11C4×D412yes—
201C2×C4×C11#13512yes—
202C2×C4×C11#13512yes—
203C2×C4×C11C23×C411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
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—41no—
212C8×C11C4×D414yes—
213C22×Q16C22×C1111yescharacteristic
214C23×C8C22×C1111yescharacteristic
215C2×C22⋊Q8C22×C1112yes—
216C2×C4×Q8C22×C1112yes—
217C2×#117C22×C1112yes—
218#467C4×C1118yescomplemented
219C4×Q16—24no—
220#427—24no—
221C2×#107C22×C1111yescharacteristic
222C2×#107C22×C1111yescharacteristic
223C2×#107C22×C1111yescharacteristic
224C2×#106C22×C1112yes—
225C2×#103C22×C1112yes—
226C2×#103C22×C1112yes—
227C2×#103C22×C1112yes—
228C2×C22⋊C8C22×C1111yescharacteristic
229C2×C4×C8C22×C1111yescharacteristic
230C2×C4×C8C22×C1111yescharacteristic
231#391C22×C1112yes—
232#389C22×C1112yes—
233#388—22no—
234#388—22no—
235#387—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4C22×C1112yes—
238C4×C22⋊C4C22×C1111yescharacteristic
239#340C22×C1112yes—
240#340C22×C1112yes—
241#336C22×C1111yescharacteristic
242#336C22×C1111yescharacteristic
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11C2×C4×D411yescharacteristic
251C22×C11D4211yescharacteristic
252C22×C11#54711yescharacteristic
253C22×C11C2×#13511yescharacteristic
254C22×C11C2×#13511yescharacteristic
255C22×C11#57811yescharacteristic
256C22×C11#57811yescharacteristic
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—41no—
261C4×C11—44no—
262C4×C11—44no—
263C4×C11—41no—
264C4×C11—44no—
265C4×C11—82no—
266C4×C11C2×C4×D411yescharacteristic
267C4×C11#52011yescharacteristic
268C4×C11#54811yescharacteristic
269C4×C11#55311yescharacteristic
270C22×Q8C23×C1112yes—
271C23×C4C23×C1111yescharacteristic
272C2×Q16—22no—
273C2×Q16—22no—
274C2×Q16C2×C4×C1114yes—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8C2×C4×C1114yes—
278C22×C8C23×C1111yescharacteristic
279C22×C8C23×C1111yescharacteristic
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1111yescharacteristic
282C22⋊Q8—24no—
283C22⋊Q8C2×C4×C1118yes—
284C4×Q8—24no—
285C4×Q8—42no—
286#117—24no—
287#117—42no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1112yes—
293C2×C4⋊C4C23×C1112yes—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4D4×C1111yescharacteristic
297C2×C22⋊C4D4×C1111yescharacteristic
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42C23×C1111yescharacteristic
302C2×C42C23×C1111yescharacteristic
303#107—22no—
304#107C2×C4×C1114yes—
305#107D4×C1114yes—
306#106—24no—
307#103—24no—
308#103—42no—
309#103C2×C4×C1118yes—
310C22⋊C8—22no—
311C4×C8—22no—
312C4×C8—22no—
313#95—22no—
314#95—22no—
315#95—22no—
316#95—22no—
317#95D4×C1111yescharacteristic
318#95D4×C1111yescharacteristic
319C2×C11—42no—
320C2×C11#236111yescharacteristic
321C2×C11C4×#13511yescharacteristic
322C2×C11#295011yescharacteristic
323C2×C11#328311yescharacteristic
324C2×C11#328511yescharacteristic
325C2×C11#333611yescharacteristic
326C2×C11#334211yescharacteristic
327C24C2×D4×C1111yescharacteristic
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C22×C4×C1114yes—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4C22×C4×C1112yes—
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C11×#4112yes—
349C22×C4C24×C1111yescharacteristic
350Q16—28no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—28no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8C22×C4×C1112yes—
361C2×C8C22×C4×C1112yes—
362C2×C8C2×D4×C1112yes—
363C2×C8C11×#4112yes—
364C4⋊C4—28no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—44no—
370C4⋊C4—44no—
371C4⋊C4C22×C4×C1114yes—
372C4⋊C4C2×D4×C1114yes—
373C22⋊C4—28no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—44no—
377C42—21no—
378C42—21no—
379C42—21no—
380C42—21no—
381C42—44no—
382C42—44no—
383C42—44no—
384C11#2302611yescharacteristic, direct product factor, Sylow
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23C4×D4×C1112yes—
392C23C22×D4×C1111yescharacteristic
393Q8—24no—
394Q8—24no—
395Q8—42no—
396Q8—42no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—21no—
410C2×C4—24no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4C4×D4×C1112yes—
426C2×C4C11×#13512yes—
427C2×C4C11×#13512yes—
428C2×C4C23×C4×C1111yescharacteristic
429C2×C4C22×D4×C1111yescharacteristic
430C2×C4C2×C11×#4111yescharacteristic
431C2×C4C2×C11×#4111yescharacteristic
432C2×C4C11×H(5,𝔽2)11yescharacteristic
433C2×C4C11×2−1+411yescharacteristic
434C8—22no—
435C8—41no—
436C8—41no—
437C8C4×D4×C1114yes—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22C2×C4×D4×C1111yescharacteristic
446C22D42×C1111yescharacteristic
447C22C11×#54711yescharacteristic
448C22C2×C11×#13511yescharacteristic
449C22C2×C11×#13511yescharacteristic
450C22C11×#57811yescharacteristic
451C22C11×#57811yescharacteristic
452C4—22no—
453C4—22no—
454C4—22no—
455C4—44no—
456C4—41no—
457C4—44no—
458C4—41no—
459C4—44no—
460C4—82no—
461C4C2×C4×D4×C1111yescharacteristic
462C4C11×#52011yescharacteristic
463C4C11×#54811yescharacteristic
464C4C11×#55311yescharacteristic
465C2—42no—
466C2C11×#236111yescharacteristic
467C2C4×C11×#13511yescharacteristic
468C2C11×#295011yescharacteristic
469C2C11×#328311yescharacteristic
470C2C11×#328511yescharacteristic
471C2C11×#333611yescharacteristic
472C2C11×#334211yescharacteristic
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 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×Q16C2semidirect
5. C11×#1969C2semidirect
6. C11×#1942C2semidirect
7. C11×#1927C2semidirect
9. C11×#1865C2semidirect
10. C4×C11×#107C2semidirect
17. C11×#467C4semidirect
91. #23026C11direct (N × H)
150. C2×C4×Q16C2×C11semidirect
153. #1969C2×C11semidirect
154. #1942C2×C11semidirect
155. #1927C2×C11semidirect
157. #1865C2×C11semidirect
158. C4×#107C2×C11semidirect
218. #467C4×C11semidirect
384. C11#23026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C4×C11×Q162
C2×C11×#4272
C11×#23622
C11×#19692
C11×#19422
C11×#19272
C11×#18732
C11×#18652
C4×C11×#1072
C8×C11×C22⋊C42
#2302611