Finite Group Databasebeta

← C11×#22478 #14599671

Subgroups — C11×#22478 #14599671

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C11×#2344C212yesmaximal, complemented
3C11×#1996C212yesmaximal, complemented
4C11×#1899C214yesmaximal
5C11×#1820C212yesmaximal, complemented
6C11×#1799C211yesmaximal, characteristic
7C4×C11×#99C211yesmaximal, characteristic
8C11×#1740C212yesmaximal, complemented
9C11×#552—22no—
10C11×#552—24no—
11C11×#552—22no—
12C2×C11×#126C412yescomplemented
13C2×C11×#125C412yescomplemented
14C2×C11×#125C411yescharacteristic, complemented
15C2×C11×#123C2212yes—
16C2×C11×C22⋊Q8C411yescharacteristic, complemented
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C411yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C411yescharacteristic, complemented
21C2×C11×#117C2214yes—
22C2×C11×#117C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C2×C11×#99C2212yes—
25C2×C11×#99C2212yes—
26C11×#389—22no—
27C11×#387—24no—
28C11×#381C2214yes—
29C11×#380C2212yes—
30C4×C11×C4⋊C4—22no—
31C4×C11×C22⋊C4C2212yes—
32C11×#342C2214yes—
33C11×#342C2214yes—
34C11×#342C2211yescharacteristic
35C11×#342C2212yes—
36C11×#342C2211yescharacteristic
37C22×Q8×C11C2×C411yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C11×#126—24no—
43C11×#126—24no—
44C11×#125—24no—
45C11×#125—24no—
46C11×#125—22no—
47C11×#125—22no—
48C11×#123—24no—
49C11×#123—24no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C11×#117—24no—
60C11×#117—24no—
61C11×#117—22no—
62C11×#117—21no—
63C11×#117—21no—
64C11×#117—28no—
65C11×#117—44no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C412yes—
70C2×C11×C4⋊C4C2×C412yes—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C412yes—
73C2×C11×C4⋊C4C2×C412yes—
74C2×C11×C4⋊C4C2×C412yes—
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C412yes—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D414yes—
80C2×C11×C4⋊C4D412yes—
81C2×C11×C22⋊C4C2×C412yes—
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C412yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C11×C22⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C42×C11—24no—
90C2×C42×C11—22no—
91C2×C42×C11C2×C412yes—
92C2×C42×C11C2×C412yes—
93C2×C42×C11C2×C411yescharacteristic
94C11×#99—24no—
95C11×#99—42no—
96C11×#95—22no—
97C11×#95—24no—
98C11×#95—22no—
99C11×#95—24no—
100#22478C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11C22×C411yescharacteristic
102C24×C11C2411yescharacteristic
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—42no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—48no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4C22⋊C412yes—
145C11×C4⋊C4C22⋊C411yescharacteristic
146C11×C4⋊C4C22⋊C411yescharacteristic
147C11×C4⋊C4C22⋊C412yes—
148C11×C4⋊C4C22⋊C412yes—
149C11×C4⋊C4C22⋊C414yes—
150C11×C4⋊C4C22⋊C414yes—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4#4114yes—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—48no—
170C42×C11—44no—
171C2×#552C2×C1111yescharacteristic
172#2344C2×C1112yescomplemented
173#1996C2×C1112yescomplemented
174#1899C2×C1114yes—
175#1820C2×C1112yescomplemented
176#1799C2×C1111yescharacteristic
177C4×#99C2×C1111yescharacteristic
178#1740C2×C1112yescomplemented
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C23×C411yescharacteristic
187C23×C11C22×D412yes—
188C23×C11C2×#4112yes—
189C23×C11H(5,𝔽2)11yescharacteristic
190C23×C112−1+411yescharacteristic
191Q8×C11—42no—
192Q8×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11C2×C22⋊C412yes—
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11C2×C22⋊C414yes—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C2×C22⋊C411yescharacteristic
235#552—22no—
236#552—24no—
237#552—22no—
238C2×#126C4×C1112yescomplemented
239C2×#125C4×C1112yescomplemented
240C2×#125C4×C1111yescharacteristic, complemented
241C2×#123C22×C1112yes—
242C2×C22⋊Q8C4×C1111yescharacteristic, complemented
243C2×C22⋊Q8C22×C1111yescharacteristic
244C2×C4×Q8C4×C1111yescharacteristic, complemented
245C2×C4×D4C22×C1111yescharacteristic
246C2×#117C4×C1111yescharacteristic, complemented
247C2×#117C22×C1114yes—
248C2×#117C22×C1112yes—
249C22×C4⋊C4C22×C1111yescharacteristic
250C2×#99C22×C1112yes—
251C2×#99C22×C1112yes—
252#389—22no—
253#387—24no—
254#381C22×C1114yes—
255#380C22×C1112yes—
256C4×C4⋊C4—22no—
257C4×C22⋊C4C22×C1112yes—
258#342C22×C1112yes—
259#342C22×C1111yescharacteristic
260#342C22×C1114yes—
261#342C22×C1114yes—
262#342C22×C1111yescharacteristic
263C22×C11—22no—
264C22×C11—21no—
265C22×C11—22no—
266C22×C11—21no—
267C22×C11—42no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C22×C22⋊C411yescharacteristic
276C22×C11C4×#4111yescharacteristic
277C22×C11#52011yescharacteristic
278C22×C11#54612yes—
279C22×C11#54712yes—
280C4×C11—22no—
281C4×C11—24no—
282C4×C11—22no—
283C4×C11—21no—
284C4×C11—22no—
285C4×C11—44no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—42no—
289C4×C11—41no—
290C4×C11—42no—
291C4×C11—84no—
292C4×C11—82no—
293C4×C11#41012yes—
294C22×Q8C2×C4×C1111yescharacteristic
295C22×D4C23×C1111yescharacteristic
296C23×C4C2×C4×C1111yescharacteristic
297C23×C4C23×C1112yes—
298C23×C4C23×C1111yescharacteristic
299#126—24no—
300#126—24no—
301#125—24no—
302#125—24no—
303#125—22no—
304#125—22no—
305#123—24no—
306#123—24no—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C4×Q8—22no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×D4—22no—
315C4×D4—22no—
316#117—24no—
317#117—24no—
318#117—22no—
319#117—21no—
320#117—21no—
321#117—28no—
322#117—44no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4C2×C4×C1111yescharacteristic
326C2×C4⋊C4C2×C4×C1112yes—
327C2×C4⋊C4C2×C4×C1112yes—
328C2×C4⋊C4C2×C4×C1111yescharacteristic
329C2×C4⋊C4C2×C4×C1112yes—
330C2×C4⋊C4C2×C4×C1112yes—
331C2×C4⋊C4C2×C4×C1112yes—
332C2×C4⋊C4C2×C4×C1111yescharacteristic
333C2×C4⋊C4C2×C4×C1111yescharacteristic
334C2×C4⋊C4C2×C4×C1112yes—
335C2×C4⋊C4D4×C1112yes—
336C2×C4⋊C4D4×C1114yes—
337C2×C4⋊C4D4×C1112yes—
338C2×C22⋊C4C2×C4×C1112yes—
339C2×C22⋊C4C2×C4×C1111yescharacteristic
340C2×C22⋊C4C2×C4×C1112yes—
341C2×C22⋊C4C23×C1114yes—
342C2×C22⋊C4C23×C1112yes—
343C2×C22⋊C4C23×C1111yescharacteristic
344C2×C22⋊C4C23×C1112yes—
345C2×C22⋊C4C23×C1112yes—
346C2×C42—24no—
347C2×C42—22no—
348C2×C42C2×C4×C1112yes—
349C2×C42C2×C4×C1112yes—
350C2×C42C2×C4×C1111yescharacteristic
351#99—24no—
352#99—42no—
353#95—22no—
354#95—24no—
355#95—22no—
356#95—24no—
357C2×C11—22no—
358C2×C11—22no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—81no—
362C2×C11#233911yescharacteristic
363C2×C11C2×#41011yescharacteristic
364C2×C11#288411yescharacteristic
365C24C22×C4×C1111yescharacteristic
366C24C24×C1111yescharacteristic
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—42no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—21no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4C22×C4×C1111yescharacteristic
385C22×C4C22×C4×C1112yes—
386C22×C4C22×C4×C1111yescharacteristic
387C22×C4C22×C4×C1112yes—
388C22×C4C22×C4×C1111yescharacteristic
389C22×C4C22×C4×C1111yescharacteristic
390C22×C4C22×C4×C1112yes—
391C22×C4C22×C4×C1112yes—
392C22×C4C22×C4×C1111yescharacteristic
393C22×C4C2×D4×C1114yes—
394C22×C4C2×D4×C1114yes—
395C22×C4C2×D4×C1112yes—
396C22×C4C2×D4×C1112yes—
397C4⋊C4—24no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—24no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—48no—
407C4⋊C4—44no—
408C4⋊C4C11×C22⋊C412yes—
409C4⋊C4C11×C22⋊C411yescharacteristic
410C4⋊C4C11×C22⋊C411yescharacteristic
411C4⋊C4C11×C22⋊C412yes—
412C4⋊C4C11×C22⋊C412yes—
413C4⋊C4C11×C22⋊C414yes—
414C4⋊C4C11×C22⋊C414yes—
415C22⋊C4—22no—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—24no—
422C22⋊C4—22no—
423C22⋊C4—24no—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4C11×#4114yes—
427C42—22no—
428C42—22no—
429C42—22no—
430C42—22no—
431C42—21no—
432C42—21no—
433C42—48no—
434C42—44no—
435C11#2247811yescharacteristic, direct product factor, Sylow
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23C23×C4×C1111yescharacteristic
444C23C22×D4×C1112yes—
445C23C2×C11×#4112yes—
446C23C11×H(5,𝔽2)11yescharacteristic
447C23C11×2−1+411yescharacteristic
448Q8—42no—
449Q8—42no—
450D4—42no—
451D4—42no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4C2×C11×C22⋊C412yes—
487C2×C4C2×C11×C22⋊C412yes—
488C2×C4C2×C11×C22⋊C411yescharacteristic
489C2×C4C2×C11×C22⋊C414yes—
490C2×C4C2×C11×C22⋊C412yes—
491C2×C4C2×C11×C22⋊C411yescharacteristic
492C22—22no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—81no—
503C22—81no—
504C22C22×C11×C22⋊C411yescharacteristic
505C22C4×C11×#4111yescharacteristic
506C22C11×#52011yescharacteristic
507C22C11×#54612yes—
508C22C11×#54712yes—
509C4—22no—
510C4—24no—
511C4—22no—
512C4—21no—
513C4—22no—
514C4—44no—
515C4—41no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—84no—
521C4—82no—
522C4C11×#41012yes—
523C2—22no—
524C2—22no—
525C2—21no—
526C2—21no—
527C2—81no—
528C2C11×#233911yescharacteristic
529C2C2×C11×#41011yescharacteristic
530C2C11×#288411yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2344C2semidirect
3. C11×#1996C2semidirect
5. C11×#1820C2semidirect
8. C11×#1740C2semidirect
12. C2×C11×#126C4semidirect
13. C2×C11×#125C4semidirect
14. C2×C11×#125C4semidirect
16. C2×C11×C22⋊Q8C4semidirect
18. C2×C4×Q8×C11C4semidirect
20. C2×C11×#117C4semidirect
100. #22478C11direct (N × H)
172. #2344C2×C11semidirect
173. #1996C2×C11semidirect
175. #1820C2×C11semidirect
178. #1740C2×C11semidirect
238. C2×#126C4×C11semidirect
239. C2×#125C4×C11semidirect
240. C2×#125C4×C11semidirect
242. C2×C22⋊Q8C4×C11semidirect
244. C2×C4×Q8C4×C11semidirect
246. C2×#117C4×C11semidirect
435. C11#22478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C11×#23442
C11×#19962
C11×#18992
C11×#18202
C11×#17992
C4×C11×#992
C11×#17402
#2247811