Finite Group Databasebeta

← C11×#23946 #14601139

Subgroups — C11×#23946 #14601139

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#542C211yesmaximal, characteristic
2C2×C11×#451C211yesmaximal, characteristic, complemented
3C2×C11×#448C211yesmaximal, characteristic
4C11×#2310C211yesmaximal, characteristic, complemented
5C11×#2024C212yesmaximal, complemented
6C11×#2015C212yesmaximal, complemented
7C11×#1878C212yesmaximal, complemented
8C11×#1877C212yesmaximal, complemented
9C11×#1875C211yesmaximal, characteristic
10C11×#1873C211yesmaximal, characteristic, complemented
11C11×#1818C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C11×#542—24no—
16C11×#542—24no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#126—21no—
19C2×C11×#124—21no—
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C11×#451—24no—
30C11×#448—24no—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#391—21no—
38C11×#391—21no—
39C11×#391C2212yes—
40C11×#391C2212yes—
41C11×#381—21no—
42C11×#381—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#336C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—24no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2311yescharacteristic
54C22×Q8×C11C2312yes—
55C22×D4×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C2×C11×Q16—24no—
61C2×C11×Q16—24no—
62C2×C11×Q16—42no—
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16—42no—
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×#126—28no—
71C11×#124—28no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#123—28no—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8D414yes—
78C11×#121—22no—
79C11×#121D414yes—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C11×#117—22no—
85C11×#117—22no—
86C11×#117—42no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C11×#103—24no—
108C11×#103—24no—
109C11×#103—42no—
110C11×#102—42no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—22no—
113C11×#95—22no—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117#23946C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—24no—
121C2×Q8×C11—24no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—48no—
131C2×Q8×C11—48no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11—82no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11#4114yes—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—82no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—24no—
151C22×C4×C11—22no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—82no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2411yescharacteristic
163C11×Q16—48no—
164C11×SD16—48no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4C2×D412yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—42no—
190C42×C11—24no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—42no—
196C2×#542C2×C1111yescharacteristic
197C2×#451C2×C1111yescharacteristic, complemented
198C2×#448C2×C1111yescharacteristic
199#2310C2×C1111yescharacteristic, complemented
200#2024C2×C1112yescomplemented
201#2015C2×C1112yescomplemented
202#1878C2×C1112yescomplemented
203#1877C2×C1112yescomplemented
204#1875C2×C1111yescharacteristic
205#1873C2×C1111yescharacteristic, complemented
206#1818C2×C1111yescharacteristic, complemented
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11#12012yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—48no—
222Q8×C11—42no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—84no—
226D4×C11—24no—
227D4×C11—42no—
228D4×C11—84no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—84no—
256C2×C4×C11#12012yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4112yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C8×C11—42no—
262C8×C11—42no—
263C23×Q8C22×C1111yescharacteristic
264C22×Q16C22×C1112yes—
265C22×SD16C22×C1112yes—
266#542—24no—
267#542—24no—
268C2×C4⋊Q8C22×C1111yescharacteristic
269C2×#126—21no—
270C2×#124—21no—
271C2×#124C22×C1111yescharacteristic
272C2×#123—21no—
273C2×C22⋊Q8—21no—
274C2×C22⋊Q8C22×C1111yescharacteristic
275C2×#121C22×C1111yescharacteristic
276C2×C4×Q8C22×C1111yescharacteristic
277C2×C4×D4C22×C1111yescharacteristic
278C2×#117C22×C1111yescharacteristic
279C2×#117C22×C1111yescharacteristic
280#451—24no—
281#448—24no—
282C2×#103C22×C1112yes—
283C2×#103C22×C1112yes—
284C2×#103C22×C1112yes—
285C2×#102C22×C1112yes—
286C2×C22⋊C8C22×C1111yescharacteristic
287C2×C22⋊C8C22×C1111yescharacteristic
288#391—21no—
289#391—21no—
290#391C22×C1112yes—
291#391C22×C1112yes—
292#381—21no—
293#381—21no—
294#340C22×C1112yes—
295#340C22×C1112yes—
296#336C22×C1112yes—
297#336C22×C1112yes—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11C2×#12011yescharacteristic
309C22×C11#52511yescharacteristic
310C22×C11#53511yescharacteristic
311C22×C11#57712yes—
312C22×C11#57812yes—
313C4×C11—22no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—41no—
317C4×C11—41no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—82no—
323C4×C11#54612yes—
324C4×C11#54612yes—
325C22×Q8—24no—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—42no—
331C22×Q8C23×C1111yescharacteristic
332C22×Q8C23×C1112yes—
333C22×D4—21no—
334C22×D4C23×C1111yescharacteristic
335C23×C4—21no—
336C23×C4—21no—
337C23×C4C23×C1111yescharacteristic
338C2×Q16—24no—
339C2×Q16—24no—
340C2×Q16—42no—
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—42no—
344C22×C8C23×C1112yes—
345C22×C8C23×C1112yes—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348#126—28no—
349#124—28no—
350#124—22no—
351#124—22no—
352#123—28no—
353C22⋊Q8—28no—
354C22⋊Q8—22no—
355C22⋊Q8D4×C1114yes—
356#121—22no—
357#121D4×C1114yes—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×D4—22no—
361C4×D4—22no—
362#117—22no—
363#117—22no—
364#117—42no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4D4×C1111yescharacteristic
369C2×C4⋊C4D4×C1111yescharacteristic
370C2×C4⋊C4C23×C1112yes—
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C4⋊C4C23×C1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4D4×C1111yescharacteristic
380C2×C22⋊C4D4×C1111yescharacteristic
381C2×C42—21no—
382C2×C42—21no—
383C2×C42C23×C1111yescharacteristic
384C2×C42C23×C1111yescharacteristic
385#103—24no—
386#103—24no—
387#103—42no—
388#102—42no—
389C22⋊C8—22no—
390C22⋊C8—22no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395C2×C11—42no—
396C2×C11—82no—
397C2×C11#240411yescharacteristic
398C2×C11#300911yescharacteristic
399C2×C11#301111yescharacteristic
400C2×C11#312112yes—
401C2×C11#322512yes—
402C24—21no—
403C24C2×D4×C1111yescharacteristic
404C2×Q8—24no—
405C2×Q8—24no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—48no—
415C2×Q8—48no—
416C2×Q8—42no—
417C2×Q8—42no—
418C2×Q8—82no—
419C2×Q8C2×D4×C1112yes—
420C2×Q8C11×#4114yes—
421C2×D4—24no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—82no—
426C2×D4C2×D4×C1112yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—82no—
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1112yes—
445C22×C4C2×D4×C1112yes—
446C22×C4C24×C1111yescharacteristic
447Q16—48no—
448SD16—48no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4C2×D4×C1112yes—
465C4⋊C4C2×D4×C1112yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—24no—
473C22⋊C4—42no—
474C42—24no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—42no—
480C11#2394611yescharacteristic, direct product factor, Sylow
481C23—21no—
482C23—21no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—42no—
489C23—42no—
490C23C11×#12012yes—
491C23C22×D4×C1111yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—24no—
495Q8—48no—
496Q8—42no—
497Q8—42no—
498Q8—42no—
499Q8—84no—
500D4—24no—
501D4—42no—
502D4—84no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—48no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—84no—
530C2×C4C11×#12012yes—
531C2×C4C22×D4×C1111yescharacteristic
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C2×C11×#4112yes—
534C2×C4C11×H(5,𝔽2)12yes—
535C8—42no—
536C8—42no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—82no—
546C22—82no—
547C22C2×C11×#12011yescharacteristic
548C22C11×#52511yescharacteristic
549C22C11×#53511yescharacteristic
550C22C11×#57712yes—
551C22C11×#57812yes—
552C4—22no—
553C4—44no—
554C4—42no—
555C4—41no—
556C4—41no—
557C4—42no—
558C4—42no—
559C4—41no—
560C4—41no—
561C4—82no—
562C4C11×#54612yes—
563C4C11×#54612yes—
564C2—42no—
565C2—82no—
566C2C11×#240411yescharacteristic
567C2C11×#300911yescharacteristic
568C2C11×#301111yescharacteristic
569C2C11×#312112yes—
570C2C11×#322512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
4. C11×#2310C2semidirect
5. C11×#2024C2semidirect
6. C11×#2015C2semidirect
7. C11×#1878C2semidirect
8. C11×#1877C2semidirect
10. C11×#1873C2semidirect
11. C11×#1818C2semidirect
117. #23946C11direct (N × H)
197. C2×#451C2×C11semidirect
199. #2310C2×C11semidirect
200. #2024C2×C11semidirect
201. #2015C2×C11semidirect
202. #1878C2×C11semidirect
203. #1877C2×C11semidirect
205. #1873C2×C11semidirect
206. #1818C2×C11semidirect
480. C11#23946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5422
C2×C11×#4512
C2×C11×#4482
C11×#23102
C11×#20242
C11×#20152
C11×#18782
C11×#18772
C11×#18752
C11×#18732
C11×#18182
#2394611