Finite Group Databasebeta

← C11×#23483 #14600676

Subgroups — C11×#23483 #14600676

Order 2816.

1610 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, 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×#1735C211yesmaximal, 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×#121C2212yes—
19C2×C11×#121C2212yes—
20C2×C11×#120—22no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#428—24no—
25C2×C11×#107C2212yescomplemented
26C2×C11×#106C2212yescomplemented
27C11×#418—24no—
28C2×C11×#102—24no—
29C2×C11×#102C2214yes—
30C2×C11×#102C2214yes—
31C11×#408—24no—
32C2×C11×C22⋊C8C2214yescomplemented
33C11×#391—21no—
34C11×#390—21no—
35C11×#386—22no—
36C11×#380C2214yescomplemented
37C11×#340C2212yescomplemented
38C11×#340C2212yescomplemented
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—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11D412yes—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11D414yes—
58C22×D4×C11C2312yes—
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16D414yescomplemented
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×#127—28no—
71C11×#124—28no—
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—24no—
75C11×#121—24no—
76C11×#120—216no—
77C11×#117—22no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117D414yes—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—24no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C11×#107—24no—
96C11×#106—24no—
97C11×#102—28no—
98C11×#102—28no—
99C11×C22⋊C8—28no—
100C11×#95—24no—
101#23483C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—22no—
103C24×C11—24no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—82no—
107C24×C11—82no—
108C24×C11C2×D412yes—
109C24×C11C2×D411yescharacteristic
110C11×#41—44no—
111C11×#41—44no—
112C11×#41—44no—
113C11×#41—44no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—28no—
125C2×D4×C11—22no—
126C2×D4×C11—28no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—44no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—44no—
137C2×D4×C11—84no—
138C2×D4×C11—84no—
139C2×D4×C11C2×D414yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—42no—
151C22×C4×C11—82no—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C11×M16—28no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—44no—
168C2×C8×C11C2×D414yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4C2×D412yes—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—84no—
183C42×C11—24no—
184C42×C11—42no—
185C2×#535C2×C1111yescharacteristic
186C2×#428C2×C1111yescharacteristic, complemented
187C2×#418C2×C1111yescharacteristic, complemented
188C22×#102C2×C1111yescharacteristic, complemented
189C2×#408C2×C1111yescharacteristic, complemented
190#2311C2×C1111yescharacteristic, complemented
191#2034C2×C1114yescomplemented
192#2033C2×C1114yescomplemented
193#1735C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—48no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—88no—
210C23×C11—88no—
211C23×C11#12012yes—
212C23×C11#12112yes—
213C23×C11#12312yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—44no—
216D4×C11—24no—
217D4×C11—24no—
218D4×C11—48no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—48no—
222D4×C11—44no—
223D4×C11—88no—
224D4×C11—88no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—84no—
242C2×C4×C11#12012yes—
243C2×C4×C11#12114yes—
244C2×C4×C11#12114yes—
245C2×C4×C11#12112yes—
246C2×C4×C11#12314yes—
247C2×C4×C11#12312yes—
248C2×C4×C11#12414yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C8×C11—24no—
256C8×C11—42no—
257C22×#41C22×C1111yescharacteristic
258C23×D4C22×C1111yescharacteristic
259C22×M16C22×C1111yescharacteristic
260C23×C8C22×C1111yescharacteristic
261#535—24no—
262#535—24no—
263C2×#127—21no—
264C2×#124—21no—
265C2×#121C22×C1112yes—
266C2×#121C22×C1112yes—
267C2×#120—22no—
268C2×#117C22×C1111yescharacteristic
269C2×#117C22×C1111yescharacteristic
270C22×C4⋊C4C22×C1111yescharacteristic
271#428—24no—
272C2×#107C22×C1112yescomplemented
273C2×#106C22×C1112yescomplemented
274#418—24no—
275C2×#102—24no—
276C2×#102C22×C1114yes—
277C2×#102C22×C1114yes—
278#408—24no—
279C2×C22⋊C8C22×C1114yescomplemented
280#391—21no—
281#390—21no—
282#386—22no—
283#380C22×C1114yescomplemented
284#340C22×C1112yescomplemented
285#340C22×C1112yescomplemented
286C22×C11—24no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—24no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—42no—
294C22×C11—44no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—816no—
299C22×C11—84no—
300C22×C11—84no—
301C22×C11#39414yes—
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×#12111yescharacteristic
304C22×C11C2×#12311yescharacteristic
305C22×C11#57612yes—
306C22×C11#57712yes—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—82no—
311C4×C11—82no—
312C4×C11#39414yes—
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12111yescharacteristic
315C4×C11C2×#12311yescharacteristic
316C4×C11C2×#12411yescharacteristic
317C25—21no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C22×Q8D4×C1111yescharacteristic
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—21no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4D4×C1112yes—
334C22×D4D4×C1111yescharacteristic
335C22×D4D4×C1114yes—
336C22×D4C23×C1112yes—
337C23×C4—21no—
338C23×C4C23×C1112yes—
339C23×C4C23×C1111yescharacteristic
340C2×M16—22no—
341C2×M16—22no—
342C2×M16D4×C1114yescomplemented
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8C23×C1112yes—
347C22×C8C23×C1112yes—
348#127—28no—
349#124—28no—
350#121—24no—
351#121—24no—
352#121—24no—
353#121—24no—
354#120—216no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117D4×C1114yes—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C23×C1112yes—
363C2×C4⋊C4C23×C1112yes—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—24no—
371C2×C42—21no—
372C2×C42—21no—
373#107—24no—
374#106—24no—
375#102—28no—
376#102—28no—
377C22⋊C8—28no—
378#95—24no—
379C2×C11—24no—
380C2×C11—82no—
381C2×C11—84no—
382C2×C11C2×#39411yescharacteristic
383C2×C11#300811yescharacteristic
384C2×C11#300911yescharacteristic
385C2×C11#306212yes—
386C2×C11#309612yes—
387C24—22no—
388C24—24no—
389C24—42no—
390C24—42no—
391C24—82no—
392C24—82no—
393C24C2×D4×C1112yes—
394C24C2×D4×C1111yescharacteristic
395#41—44no—
396#41—44no—
397#41—44no—
398#41—44no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—24no—
408C2×D4—22no—
409C2×D4—28no—
410C2×D4—22no—
411C2×D4—28no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—44no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—44no—
422C2×D4—84no—
423C2×D4—84no—
424C2×D4C2×D4×C1114yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—82no—
437C22×C4C2×D4×C1112yes—
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1112yes—
440C22×C4C2×D4×C1112yes—
441C22×C4C2×D4×C1112yes—
442C22×C4C11×#4112yes—
443C22×C4C11×#4112yes—
444C22×C4C11×#4112yes—
445C22×C4C24×C1111yescharacteristic
446M16—28no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—44no—
453C2×C8C2×D4×C1114yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—42no—
461C4⋊C4C2×D4×C1112yes—
462C4⋊C4C2×D4×C1112yes—
463C22⋊C4—28no—
464C22⋊C4—28no—
465C22⋊C4—24no—
466C22⋊C4—42no—
467C22⋊C4—84no—
468C42—24no—
469C42—42no—
470C11#2348311yescharacteristic, direct product factor, Sylow
471C23—22no—
472C23—22no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—24no—
478C23—24no—
479C23—42no—
480C23—42no—
481C23—48no—
482C23—44no—
483C23—44no—
484C23—84no—
485C23—84no—
486C23—88no—
487C23—88no—
488C23C11×#12012yes—
489C23C11×#12112yes—
490C23C11×#12312yes—
491C23C22×D4×C1111yescharacteristic
492Q8—44no—
493D4—24no—
494D4—24no—
495D4—48no—
496D4—42no—
497D4—42no—
498D4—48no—
499D4—44no—
500D4—88no—
501D4—88no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4C11×#12012yes—
520C2×C4C11×#12114yes—
521C2×C4C11×#12114yes—
522C2×C4C11×#12112yes—
523C2×C4C11×#12314yes—
524C2×C4C11×#12312yes—
525C2×C4C11×#12414yes—
526C2×C4C22×D4×C1111yescharacteristic
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C22×D4×C1111yescharacteristic
529C2×C4C2×C11×#4111yescharacteristic
530C2×C4C2×C11×#4111yescharacteristic
531C2×C4C2×C11×#4111yescharacteristic
532C8—24no—
533C8—42no—
534C22—22no—
535C22—22no—
536C22—24no—
537C22—24no—
538C22—42no—
539C22—44no—
540C22—42no—
541C22—44no—
542C22—42no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—816no—
547C22—84no—
548C22—84no—
549C22C11×#39414yes—
550C22C2×C11×#12011yescharacteristic
551C22C2×C11×#12111yescharacteristic
552C22C2×C11×#12311yescharacteristic
553C22C11×#57612yes—
554C22C11×#57712yes—
555C4—42no—
556C4—42no—
557C4—42no—
558C4—82no—
559C4—82no—
560C4C11×#39414yes—
561C4C2×C11×#12111yescharacteristic
562C4C2×C11×#12111yescharacteristic
563C4C2×C11×#12311yescharacteristic
564C4C2×C11×#12411yescharacteristic
565C2—24no—
566C2—82no—
567C2—84no—
568C2C2×C11×#39411yescharacteristic
569C2C11×#300811yescharacteristic
570C2C11×#300911yescharacteristic
571C2C11×#306212yes—
572C2C11×#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×#428C2semidirect
3. C2×C11×#418C2semidirect
4. C22×C11×#102C2semidirect
5. C2×C11×#408C2semidirect
6. C11×#2311C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1735C2semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×#106C22semidirect
32. C2×C11×C22⋊C8C22semidirect
36. C11×#380C22semidirect
37. C11×#340C22semidirect
38. C11×#340C22semidirect
64. C2×C11×M16D4semidirect
101. #23483C11direct (N × H)
186. C2×#428C2×C11semidirect
187. C2×#418C2×C11semidirect
188. C22×#102C2×C11semidirect
189. C2×#408C2×C11semidirect
190. #2311C2×C11semidirect
191. #2034C2×C11semidirect
192. #2033C2×C11semidirect
193. #1735C2×C11semidirect
272. C2×#107C22×C11semidirect
273. C2×#106C22×C11semidirect
279. C2×C22⋊C8C22×C11semidirect
283. #380C22×C11semidirect
284. #340C22×C11semidirect
285. #340C22×C11semidirect
342. C2×M16D4×C11semidirect
470. C11#23483direct (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×#4282
C2×C11×#4182
C22×C11×#1022
C2×C11×#4082
C11×#23112
C11×#20342
C11×#20332
C11×#17352
#2348311