Finite Group Databasebeta

← C11×#23025 #14600218

Subgroups — C11×#23025 #14600218

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C22×C11×#107C211yesmaximal, characteristic, complemented
4C11×#2361C212yesmaximal, complemented
5C11×#1970C211yesmaximal, characteristic, complemented
6C11×#1942C211yesmaximal, characteristic, complemented
7C11×#1925C212yesmaximal, complemented
8C11×#1874C212yesmaximal, complemented
9C11×#1862C212yesmaximal, complemented
10C4×C11×#107C211yesmaximal, characteristic, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×C4×D4×C11—22no—
16C2×C4×D4×C11C2212yes—
17C22×C11×C4⋊C4C2212yes—
18C11×#466C418yescomplemented
19C4×C11×D8—24no—
20C2×C11×#107—24no—
21C2×C11×#107C2212yes—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#390C2212yes—
32C11×#389C2212yes—
33C11×#388—22no—
34C11×#386—22no—
35C11×#385—22no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11C2312yes—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11C2311yescharacteristic
47C2×C11×D8—22no—
48C2×C11×D8—22no—
49C2×C11×D8C2×C414yescomplemented
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11C2×C414yescomplemented
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#121—24no—
58C11×#121C2×C418yescomplemented
59C4×D4×C11—24no—
60C4×D4×C11—42no—
61C4×D4×C11—48no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C42×C11—22no—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C11×#107—22no—
79C11×#107—24no—
80C11×#107C2×C414yescomplemented
81C11×#107D414yescomplemented
82C11×#102—24no—
83C11×#102—42no—
84C11×#102C2×C418yescomplemented
85C11×C22⋊C8—22no—
86C4×C8×C11—22no—
87C4×C8×C11—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95D411yescharacteristic
91C11×#95D411yescharacteristic
92#23025C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—22no—
94C24×C11C2×D411yescharacteristic
95C2×D4×C11—28no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—44no—
102C2×D4×C11—44no—
103C2×D4×C11C22×C414yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—44no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11—44no—
115C22×C4×C11—82no—
116C22×C4×C11—82no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4112yes—
124C22×C4×C11C2411yescharacteristic
125C11×D8—28no—
126C2×C8×C11—28no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C22×C412yes—
136C2×C8×C11C22×C412yes—
137C2×C8×C11C2×D412yes—
138C2×C8×C11#4112yes—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4C22×C414yes—
146C11×C4⋊C4C2×D414yes—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—82no—
152C11×C22⋊C4D814yescomplemented
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—44no—
158C2×#466C2×C1111yescharacteristic
159C2×C4×D8C2×C1111yescharacteristic, complemented
160C22×#107C2×C1111yescharacteristic, complemented
161#2361C2×C1112yescomplemented
162#1970C2×C1111yescharacteristic, complemented
163#1942C2×C1111yescharacteristic, complemented
164#1925C2×C1112yescomplemented
165#1874C2×C1112yescomplemented
166#1862C2×C1112yescomplemented
167C4×#107C2×C1111yescharacteristic, complemented
168C8×C22⋊C4C2×C1111yescharacteristic, complemented
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—24no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11C4×D412yes—
181C23×C11C2×D812yes—
182C23×C11#13512yes—
183C23×C11C22×D411yescharacteristic
184D4×C11—24no—
185D4×C11—24no—
186D4×C11—416no—
187D4×C11—42no—
188D4×C11—42no—
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—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—88no—
215C2×C4×C11—88no—
216C2×C4×C11C4×D412yes—
217C2×C4×C11C2×D812yes—
218C2×C4×C11C2×D812yes—
219C2×C4×C11C23×C411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C8×C11—22no—
226C8×C11—41no—
227C8×C11—41no—
228C8×C11C4×D414yescomplemented
229C22×D8C22×C1111yescharacteristic
230C23×C8C22×C1111yescharacteristic
231C2×#121C22×C1112yes—
232C2×C4×D4—22no—
233C2×C4×D4C22×C1112yes—
234C22×C4⋊C4C22×C1112yes—
235#466C4×C1118yescomplemented
236C4×D8—24no—
237C2×#107—24no—
238C2×#107C22×C1112yes—
239C2×#107C22×C1111yescharacteristic
240C2×#107C22×C1111yescharacteristic
241C2×#107C22×C1111yescharacteristic
242C2×#102C22×C1112yes—
243C2×#102C22×C1112yes—
244C2×#102C22×C1112yes—
245C2×C22⋊C8C22×C1111yescharacteristic
246C2×C4×C8C22×C1111yescharacteristic
247C2×C4×C8C22×C1111yescharacteristic
248#390C22×C1112yes—
249#389C22×C1112yes—
250#388—22no—
251#386—22no—
252#385—22no—
253C4×C4⋊C4C22×C1112yes—
254C4×C22⋊C4C22×C1111yescharacteristic
255#340C22×C1112yes—
256#340C22×C1112yes—
257#336C22×C1111yescharacteristic
258#336C22×C1111yescharacteristic
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11C4×D814yescomplemented
273C22×C11C2×C4×D411yescharacteristic
274C22×C11D4211yescharacteristic
275C22×C11#54711yescharacteristic
276C22×C11C22×D811yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11#57611yescharacteristic
279C22×C11#57811yescharacteristic
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—41no—
284C4×C11—44no—
285C4×C11—44no—
286C4×C11—41no—
287C4×C11—82no—
288C4×C11C2×C4×D411yescharacteristic
289C4×C11#52011yescharacteristic
290C4×C11#54811yescharacteristic
291C4×C11#55311yescharacteristic
292C22×D4—22no—
293C22×D4C23×C1112yes—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4C23×C1111yescharacteristic
297C2×D8—22no—
298C2×D8—22no—
299C2×D8C2×C4×C1114yescomplemented
300C22×C8—22no—
301C22×C8—22no—
302C22×C8C2×C4×C1114yescomplemented
303C22×C8C23×C1111yescharacteristic
304C22×C8C23×C1111yescharacteristic
305C22×C8C23×C1111yescharacteristic
306C22×C8C23×C1111yescharacteristic
307#121—24no—
308#121C2×C4×C1118yescomplemented
309C4×D4—24no—
310C4×D4—42no—
311C4×D4—48no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1112yes—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4D4×C1111yescharacteristic
324C2×C22⋊C4D4×C1111yescharacteristic
325C2×C42—22no—
326C2×C42C23×C1111yescharacteristic
327C2×C42C23×C1111yescharacteristic
328#107—22no—
329#107—24no—
330#107C2×C4×C1114yescomplemented
331#107D4×C1114yescomplemented
332#102—24no—
333#102—42no—
334#102C2×C4×C1118yescomplemented
335C22⋊C8—22no—
336C4×C8—22no—
337C4×C8—22no—
338#95—22no—
339#95—22no—
340#95D4×C1111yescharacteristic
341#95D4×C1111yescharacteristic
342C2×C11—24no—
343C2×C11—84no—
344C2×C11#236111yescharacteristic
345C2×C11C2×C4×D811yescharacteristic
346C2×C11#295111yescharacteristic
347C2×C11D4×D811yescharacteristic
348C2×C11#328511yescharacteristic
349C2×C11#333411yescharacteristic
350C2×C11#333911yescharacteristic
351C24—22no—
352C24C2×D4×C1111yescharacteristic
353C2×D4—28no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4C22×C4×C1114yes—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—82no—
374C22×C4—82no—
375C22×C4C22×C4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C11×#4112yes—
382C22×C4C24×C1111yescharacteristic
383D8—28no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—28no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8C22×C4×C1112yes—
394C2×C8C22×C4×C1112yes—
395C2×C8C2×D4×C1112yes—
396C2×C8C11×#4112yes—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—44no—
402C4⋊C4—44no—
403C4⋊C4C22×C4×C1114yes—
404C4⋊C4C2×D4×C1114yes—
405C22⋊C4—22no—
406C22⋊C4—28no—
407C22⋊C4—44no—
408C22⋊C4—44no—
409C22⋊C4—82no—
410C22⋊C4C11×D814yescomplemented
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—44no—
416C11#2302511yescharacteristic, direct product factor, Sylow
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—24no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23C4×D4×C1112yes—
429C23C2×C11×D812yes—
430C23C11×#13512yes—
431C23C22×D4×C1111yescharacteristic
432D4—24no—
433D4—24no—
434D4—416no—
435D4—42no—
436D4—42no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—88no—
463C2×C4—88no—
464C2×C4C4×D4×C1112yes—
465C2×C4C2×C11×D812yes—
466C2×C4C2×C11×D812yes—
467C2×C4C23×C4×C1111yescharacteristic
468C2×C4C22×D4×C1111yescharacteristic
469C2×C4C2×C11×#4111yescharacteristic
470C2×C4C2×C11×#4111yescharacteristic
471C2×C4C11×H(5,𝔽2)11yescharacteristic
472C2×C4C11×2−1+411yescharacteristic
473C8—22no—
474C8—41no—
475C8—41no—
476C8C4×D4×C1114yescomplemented
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—44no—
484C22—44no—
485C22—44no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22C4×C11×D814yescomplemented
491C22C2×C4×D4×C1111yescharacteristic
492C22D42×C1111yescharacteristic
493C22C11×#54711yescharacteristic
494C22C22×C11×D811yescharacteristic
495C22C2×C11×#13511yescharacteristic
496C22C11×#57611yescharacteristic
497C22C11×#57811yescharacteristic
498C4—22no—
499C4—22no—
500C4—22no—
501C4—44no—
502C4—44no—
503C4—41no—
504C4—41no—
505C4—82no—
506C4C2×C4×D4×C1111yescharacteristic
507C4C11×#52011yescharacteristic
508C4C11×#54811yescharacteristic
509C4C11×#55311yescharacteristic
510C2—24no—
511C2—84no—
512C2C11×#236111yescharacteristic
513C2C2×C4×C11×D811yescharacteristic
514C2C11×#295111yescharacteristic
515C2D4×C11×D811yescharacteristic
516C2C11×#328511yescharacteristic
517C2C11×#333411yescharacteristic
518C2C11×#333911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#466C2
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×D8C2semidirect
3. C22×C11×#107C2semidirect
4. C11×#2361C2semidirect
5. C11×#1970C2semidirect
6. C11×#1942C2semidirect
7. C11×#1925C2semidirect
8. C11×#1874C2semidirect
9. C11×#1862C2semidirect
10. C4×C11×#107C2semidirect
11. C8×C11×C22⋊C4C2semidirect
18. C11×#466C4semidirect
49. C2×C11×D8C2×C4semidirect
52. C22×C8×C11C2×C4semidirect
58. C11×#121C2×C4semidirect
80. C11×#107C2×C4semidirect
81. C11×#107D4semidirect
84. C11×#102C2×C4semidirect
92. #23025C11direct (N × H)
152. C11×C22⋊C4D8semidirect
159. C2×C4×D8C2×C11semidirect
160. C22×#107C2×C11semidirect
161. #2361C2×C11semidirect
162. #1970C2×C11semidirect
163. #1942C2×C11semidirect
164. #1925C2×C11semidirect
165. #1874C2×C11semidirect
166. #1862C2×C11semidirect
167. C4×#107C2×C11semidirect
168. C8×C22⋊C4C2×C11semidirect
228. C8×C11C4×D4semidirect
235. #466C4×C11semidirect
272. C22×C11C4×D8semidirect
299. C2×D8C2×C4×C11semidirect
302. C22×C8C2×C4×C11semidirect
308. #121C2×C4×C11semidirect
330. #107C2×C4×C11semidirect
331. #107D4×C11semidirect
334. #102C2×C4×C11semidirect
410. C22⋊C4C11×D8semidirect
416. C11#23025direct (N × H)
476. C8C4×D4×C11semidirect
490. C22C4×C11×D8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C2×C4×C11×D82
C22×C11×#1072
C11×#23612
C11×#19702
C11×#19422
C11×#19252
C11×#18742
C11×#18622
C4×C11×#1072
C8×C11×C22⋊C42
#2302511