Finite Group Databasebeta

← C11×#23486 #14600679

Subgroups — C11×#23486 #14600679

Order 2816.

1610 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#427C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C22×C11×#102C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic, complemented
6C11×#2311C211yesmaximal, characteristic, complemented
7C11×#2034C214yesmaximal, complemented
8C11×#2033C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#535—24no—
15C11×#535—24no—
16C2×C11×#127—21no—
17C2×C11×#124—21no—
18C2×C11×#121C2214yes—
19C2×C11×#120—22no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#427—24no—
24C2×C11×#107C2212yescomplemented
25C2×C11×#106C2212yescomplemented
26C11×#418—24no—
27C2×C11×#102—24no—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2214yes—
31C11×#408—24no—
32C2×C11×C22⋊C8C2212yescomplemented
33C2×C11×C22⋊C8C2212yescomplemented
34C11×#391—21no—
35C11×#390—21no—
36C11×#386—22no—
37C11×#380C2214yescomplemented
38C11×#340C2214yescomplemented
39C25×C11—21no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—24no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D412yes—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11D414yes—
57C22×D4×C11C2312yes—
58C23×C4×C11—21no—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11D414yescomplemented
67C22×C8×C11C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#127—28no—
71C11×#124—28no—
72C11×#121—28no—
73C11×#121—28no—
74C11×#120—216no—
75C11×#117—22no—
76C11×#117—22no—
77C11×#117—22no—
78C11×#117D414yes—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—24no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C11×#107—24no—
92C11×#106—24no—
93C11×#102—28no—
94C11×#102—24no—
95C11×#102—24no—
96C11×C22⋊C8—24no—
97C11×C22⋊C8—24no—
98C11×#95—24no—
99#23486C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—82no—
105C24×C11—82no—
106C24×C11C2×D412yes—
107C24×C11C2×D411yescharacteristic
108C11×#41—44no—
109C11×#41—44no—
110C11×#41—44no—
111C11×#41—44no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—216no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—28no—
122C2×D4×C11—22no—
123C2×D4×C11—28no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—44no—
134C2×D4×C11—84no—
135C2×D4×C11—84no—
136C2×D4×C11C2×D414yes—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—42no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C11×M16—44no—
158C2×C8×C11—28no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—22no—
166C2×C8×C11C2×D412yes—
167C2×C8×C11C2×D412yes—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C2×D414yes—
175C11×C22⋊C4—216no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—84no—
179C42×C11—24no—
180C42×C11—42no—
181C2×#535C2×C1111yescharacteristic
182C2×#427C2×C1111yescharacteristic, complemented
183C2×#418C2×C1111yescharacteristic, complemented
184C22×#102C2×C1111yescharacteristic, complemented
185C2×#408C2×C1111yescharacteristic, complemented
186#2311C2×C1111yescharacteristic, complemented
187#2034C2×C1114yescomplemented
188#2033C2×C1114yescomplemented
189#1736C2×C1111yescharacteristic, complemented
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—48no—
203C23×C11—88no—
204C23×C11—88no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11#12012yes—
208C23×C11#12112yes—
209C23×C11#12312yes—
210C23×C11C22×D411yescharacteristic
211Q8×C11—44no—
212D4×C11—24no—
213D4×C11—24no—
214D4×C11—48no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—48no—
218D4×C11—44no—
219D4×C11—816no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—84no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12114yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12314yes—
241C2×C4×C11#12312yes—
242C2×C4×C11#12414yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C8×C11—22no—
250C8×C11—22no—
251C8×C11—42no—
252C22×#41C22×C1111yescharacteristic
253C23×D4C22×C1111yescharacteristic
254C22×M16C22×C1111yescharacteristic
255C23×C8C22×C1111yescharacteristic
256#535—24no—
257#535—24no—
258C2×#127—21no—
259C2×#124—21no—
260C2×#121C22×C1114yes—
261C2×#120—22no—
262C2×#117C22×C1111yescharacteristic
263C2×#117C22×C1111yescharacteristic
264C22×C4⋊C4C22×C1111yescharacteristic
265#427—24no—
266C2×#107C22×C1112yescomplemented
267C2×#106C22×C1112yescomplemented
268#418—24no—
269C2×#102—24no—
270C2×#102C22×C1112yes—
271C2×#102C22×C1112yes—
272C2×#102C22×C1114yes—
273#408—24no—
274C2×C22⋊C8C22×C1112yescomplemented
275C2×C22⋊C8C22×C1112yescomplemented
276#391—21no—
277#390—21no—
278#386—22no—
279#380C22×C1114yescomplemented
280#340C22×C1114yescomplemented
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—44no—
286C22×C11—42no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—48no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—816no—
293C22×C11—84no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11#39414yes—
297C22×C11C2×#12011yescharacteristic
298C22×C11C2×#12111yescharacteristic
299C22×C11C2×#12311yescharacteristic
300C22×C11#57612yes—
301C22×C11#57712yes—
302C4×C11—42no—
303C4×C11—44no—
304C4×C11—82no—
305C4×C11—82no—
306C4×C11#39414yes—
307C4×C11C2×#12111yescharacteristic
308C4×C11C2×#12111yescharacteristic
309C4×C11C2×#12311yescharacteristic
310C4×C11C2×#12411yescharacteristic
311C25—21no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41—22no—
318C22×Q8D4×C1111yescharacteristic
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—21no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4D4×C1112yes—
327C22×D4D4×C1111yescharacteristic
328C22×D4D4×C1114yes—
329C22×D4C23×C1112yes—
330C23×C4—21no—
331C23×C4C23×C1112yes—
332C23×C4C23×C1111yescharacteristic
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8D4×C1114yescomplemented
339C22×C8C23×C1112yes—
340C22×C8C23×C1111yescharacteristic
341C22×C8C23×C1111yescharacteristic
342#127—28no—
343#124—28no—
344#121—28no—
345#121—28no—
346#120—216no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117D4×C1114yes—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4C23×C1112yes—
355C2×C4⋊C4C23×C1112yes—
356C2×C4⋊C4C23×C1112yes—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—24no—
361C2×C42—21no—
362C2×C42—21no—
363#107—24no—
364#106—24no—
365#102—28no—
366#102—24no—
367#102—24no—
368C22⋊C8—24no—
369C22⋊C8—24no—
370#95—24no—
371C2×C11—24no—
372C2×C11—82no—
373C2×C11—84no—
374C2×C11C2×#39411yescharacteristic
375C2×C11#301212yes—
376C2×C11#305711yescharacteristic
377C2×C11#305811yescharacteristic
378C2×C11#309612yes—
379C24—22no—
380C24—24no—
381C24—42no—
382C24—42no—
383C24—82no—
384C24—82no—
385C24C2×D4×C1112yes—
386C24C2×D4×C1111yescharacteristic
387#41—44no—
388#41—44no—
389#41—44no—
390#41—44no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—216no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—28no—
401C2×D4—22no—
402C2×D4—28no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—44no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—44no—
413C2×D4—84no—
414C2×D4—84no—
415C2×D4C2×D4×C1114yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—42no—
426C22×C4—82no—
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1112yes—
430C22×C4C2×D4×C1112yes—
431C22×C4C2×D4×C1112yes—
432C22×C4C11×#4112yes—
433C22×C4C11×#4112yes—
434C22×C4C11×#4112yes—
435C22×C4C24×C1111yescharacteristic
436M16—44no—
437C2×C8—28no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8C2×D4×C1112yes—
446C2×C8C2×D4×C1112yes—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—42no—
453C4⋊C4C2×D4×C1114yes—
454C22⋊C4—216no—
455C22⋊C4—24no—
456C22⋊C4—42no—
457C22⋊C4—84no—
458C42—24no—
459C42—42no—
460C11#2348611yescharacteristic, direct product factor, Sylow
461C23—22no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—24no—
469C23—42no—
470C23—42no—
471C23—48no—
472C23—44no—
473C23—44no—
474C23—88no—
475C23—84no—
476C23—84no—
477C23—88no—
478C23C11×#12012yes—
479C23C11×#12112yes—
480C23C11×#12312yes—
481C23C22×D4×C1111yescharacteristic
482Q8—44no—
483D4—24no—
484D4—24no—
485D4—48no—
486D4—42no—
487D4—42no—
488D4—48no—
489D4—44no—
490D4—816no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4C11×#12012yes—
508C2×C4C11×#12114yes—
509C2×C4C11×#12114yes—
510C2×C4C11×#12112yes—
511C2×C4C11×#12314yes—
512C2×C4C11×#12312yes—
513C2×C4C11×#12414yes—
514C2×C4C22×D4×C1111yescharacteristic
515C2×C4C22×D4×C1111yescharacteristic
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C2×C11×#4111yescharacteristic
518C2×C4C2×C11×#4111yescharacteristic
519C2×C4C2×C11×#4111yescharacteristic
520C8—22no—
521C8—22no—
522C8—42no—
523C22—24no—
524C22—22no—
525C22—22no—
526C22—24no—
527C22—42no—
528C22—44no—
529C22—44no—
530C22—48no—
531C22—42no—
532C22—42no—
533C22—44no—
534C22—816no—
535C22—82no—
536C22—82no—
537C22—84no—
538C22C11×#39414yes—
539C22C2×C11×#12011yescharacteristic
540C22C2×C11×#12111yescharacteristic
541C22C2×C11×#12311yescharacteristic
542C22C11×#57612yes—
543C22C11×#57712yes—
544C4—42no—
545C4—44no—
546C4—82no—
547C4—82no—
548C4C11×#39414yes—
549C4C2×C11×#12111yescharacteristic
550C4C2×C11×#12111yescharacteristic
551C4C2×C11×#12311yescharacteristic
552C4C2×C11×#12411yescharacteristic
553C2—24no—
554C2—82no—
555C2—84no—
556C2C2×C11×#39411yescharacteristic
557C2C11×#301212yes—
558C2C11×#305711yescharacteristic
559C2C11×#305811yescharacteristic
560C2C11×#309612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#427C2semidirect
3. C2×C11×#418C2semidirect
4. C22×C11×#102C2semidirect
5. C2×C11×#408C2semidirect
6. C11×#2311C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1736C2semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#106C22semidirect
32. C2×C11×C22⋊C8C22semidirect
33. C2×C11×C22⋊C8C22semidirect
37. C11×#380C22semidirect
38. C11×#340C22semidirect
66. C22×C8×C11D4semidirect
99. #23486C11direct (N × H)
182. C2×#427C2×C11semidirect
183. C2×#418C2×C11semidirect
184. C22×#102C2×C11semidirect
185. C2×#408C2×C11semidirect
186. #2311C2×C11semidirect
187. #2034C2×C11semidirect
188. #2033C2×C11semidirect
189. #1736C2×C11semidirect
266. C2×#107C22×C11semidirect
267. C2×#106C22×C11semidirect
274. C2×C22⋊C8C22×C11semidirect
275. C2×C22⋊C8C22×C11semidirect
279. #380C22×C11semidirect
280. #340C22×C11semidirect
338. C22×C8D4×C11semidirect
460. C11#23486direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4272
C2×C11×#4182
C22×C11×#1022
C2×C11×#4082
C11×#23112
C11×#20342
C11×#20332
C11×#17362
#2348611