Finite Group Databasebeta

← C11×#23935 #14601128

Subgroups — C11×#23935 #14601128

Order 2816.

1276 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#452C212yesmaximal
3C11×#2297C211yesmaximal, characteristic
4C11×#2024C211yesmaximal, characteristic, complemented
5C11×#2023C211yesmaximal, characteristic, complemented
6C11×#2016C211yesmaximal, characteristic, complemented
7C11×#2013C211yesmaximal, characteristic, complemented
8C11×#1880C212yesmaximal, complemented
9C11×#1878C212yesmaximal, complemented
10C11×#1873C212yesmaximal, complemented
11C11×#1817C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C11×#533—28no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2212yes—
23C2×C11×#117—21no—
24C2×C11×#117C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C11×#452—28no—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2212yes—
32C11×#391C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#390C2211yescharacteristic
35C11×#390C2211yescharacteristic
36C11×#386—21no—
37C11×#386—21no—
38C4×C11×C22⋊C4—21no—
39C4×C11×C22⋊C4—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C22×Q8×C11—21no—
50C22×Q8×C11C2312yes—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×Q16—24no—
59C2×C11×Q16—24no—
60C2×C11×Q16—42no—
61C2×C11×SD16—24no—
62C2×C11×SD16—24no—
63C2×C11×SD16—42no—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8—24no—
68C11×#125—28no—
69C11×C22⋊Q8—28no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8D418yes—
72C4×Q8×C11—28no—
73C4×Q8×C11—24no—
74C4×Q8×C11—24no—
75C11×#117—28no—
76C11×#117—42no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—24no—
92C2×C42×C11—22no—
93C2×C42×C11—21no—
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×#103—24no—
99C11×#103—42no—
100C11×#103—42no—
101C11×#102—24no—
102C11×C22⋊C8—24no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107#23935C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11C2×D411yescharacteristic
110C11×#41—48no—
111C11×#41—48no—
112C2×Q8×C11—24no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11C2×D414yes—
124C2×Q8×C11#4112yes—
125C2×D4×C11—24no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11#4112yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—41no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C11×Q16—48no—
157C11×SD16—48no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2×D414yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C42×C11—28no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—42no—
185C2×#533C2×C1111yescharacteristic, complemented
186C2×#452C2×C1112yes—
187#2297C2×C1111yescharacteristic
188#2024C2×C1111yescharacteristic, complemented
189#2023C2×C1111yescharacteristic, complemented
190#2016C2×C1111yescharacteristic, complemented
191#2013C2×C1111yescharacteristic, complemented
192#1880C2×C1112yescomplemented
193#1878C2×C1112yescomplemented
194#1873C2×C1112yescomplemented
195#1817C2×C1111yescharacteristic, complemented
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—22no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11#12012yes—
210C23×C11C22×D411yescharacteristic
211Q8×C11—24no—
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—48no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218D4×C11—24no—
219D4×C11—48no—
220D4×C11—42no—
221C2×C4×C11—28no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—21no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—44no—
239C2×C4×C11—48no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11#12012yes—
253C2×C4×C11#13512yes—
254C2×C4×C11#13712yes—
255C2×C4×C11#13712yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)12yes—
260C8×C11—42no—
261C8×C11—42no—
262C22×#41C22×C1111yescharacteristic
263C22×Q16C22×C1112yes—
264C22×SD16C22×C1112yes—
265#533—28no—
266C2×C4⋊Q8C22×C1111yescharacteristic
267C2×C4⋊Q8C22×C1111yescharacteristic
268C2×#125—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8C22×C1112yes—
271C2×C4×Q8—21no—
272C2×C4×Q8C22×C1112yes—
273C2×#117—21no—
274C2×#117C22×C1111yescharacteristic
275C22×C42C22×C1111yescharacteristic
276#452—28no—
277C2×#103C22×C1112yes—
278C2×#103C22×C1112yes—
279C2×#103C22×C1112yes—
280C2×#102C22×C1112yes—
281C2×C22⋊C8C22×C1112yes—
282#391C22×C1111yescharacteristic
283#391C22×C1111yescharacteristic
284#390C22×C1111yescharacteristic
285#390C22×C1111yescharacteristic
286#386—21no—
287#386—21no—
288C4×C22⋊C4—21no—
289C4×C22⋊C4—21no—
290#340C22×C1112yes—
291#340C22×C1112yes—
292#336C22×C1112yes—
293#336C22×C1111yescharacteristic
294#336C22×C1111yescharacteristic
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11C2×#12011yescharacteristic
310C22×C11#52511yescharacteristic
311C22×C11#53511yescharacteristic
312C22×C11C2×#13511yescharacteristic
313C22×C11C2×#13711yescharacteristic
314C22×C11C2×#13711yescharacteristic
315C22×C11#57511yescharacteristic
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11—42no—
321C4×C11—44no—
322C4×C11—41no—
323C4×C11—44no—
324C4×C11—81no—
325C4×C11—81no—
326C4×C11#54612yes—
327C4×C11#54612yes—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—24no—
331C2×#41—42no—
332C22×Q8—21no—
333C22×Q8C23×C1112yes—
334C22×Q8C23×C1111yescharacteristic
335C22×D4—21no—
336C22×D4C23×C1111yescharacteristic
337C23×C4—21no—
338C23×C4D4×C1111yescharacteristic
339C23×C4D4×C1111yescharacteristic
340C23×C4C23×C1111yescharacteristic
341C2×Q16—24no—
342C2×Q16—24no—
343C2×Q16—42no—
344C2×SD16—24no—
345C2×SD16—24no—
346C2×SD16—42no—
347C22×C8C23×C1112yes—
348C22×C8C23×C1112yes—
349C4⋊Q8—24no—
350C4⋊Q8—24no—
351#125—28no—
352C22⋊Q8—28no—
353C22⋊Q8—24no—
354C22⋊Q8D4×C1118yes—
355C4×Q8—28no—
356C4×Q8—24no—
357C4×Q8—24no—
358#117—28no—
359#117—42no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C4⋊C4C23×C1112yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—21no—
377C2×C42D4×C1111yescharacteristic
378C2×C42D4×C1111yescharacteristic
379C2×C42C23×C1111yescharacteristic
380C2×C42C23×C1111yescharacteristic
381#103—24no—
382#103—42no—
383#103—42no—
384#102—24no—
385C22⋊C8—24no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390C2×C11—42no—
391C2×C11—82no—
392C2×C11#240411yescharacteristic
393C2×C11#300211yescharacteristic
394C2×C11#300411yescharacteristic
395C2×C11#310711yescharacteristic
396C2×C11#311611yescharacteristic
397C2×C11#321011yescharacteristic
398C2×C11#321611yescharacteristic
399C24—21no—
400C24C2×D4×C1111yescharacteristic
401#41—48no—
402#41—48no—
403C2×Q8—24no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—42no—
413C2×Q8—42no—
414C2×Q8C2×D4×C1114yes—
415C2×Q8C11×#4112yes—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4C11×#4112yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1114yes—
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
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—28no—
458C4⋊C4—24no—
459C4⋊C4—28no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4C2×D4×C1114yes—
464C22⋊C4—28no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C42—28no—
471C42—22no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—42no—
476C11#2393511yescharacteristic, direct product factor, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C11×#12012yes—
491C23C22×D4×C1111yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—24no—
495Q8—48no—
496Q8—42no—
497Q8—42no—
498Q8—42no—
499D4—24no—
500D4—48no—
501D4—42no—
502C2×C4—28no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4C11×#12012yes—
534C2×C4C11×#13512yes—
535C2×C4C11×#13712yes—
536C2×C4C11×#13712yes—
537C2×C4C22×D4×C1112yes—
538C2×C4C2×C11×#4111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C2×C4C11×H(5,𝔽2)12yes—
541C8—42no—
542C8—42no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C11×#12011yescharacteristic
558C22C11×#52511yescharacteristic
559C22C11×#53511yescharacteristic
560C22C2×C11×#13511yescharacteristic
561C22C2×C11×#13711yescharacteristic
562C22C2×C11×#13711yescharacteristic
563C22C11×#57511yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—42no—
569C4—44no—
570C4—41no—
571C4—44no—
572C4—81no—
573C4—81no—
574C4C11×#54612yes—
575C4C11×#54612yes—
576C2—42no—
577C2—82no—
578C2C11×#240411yescharacteristic
579C2C11×#300211yescharacteristic
580C2C11×#300411yescharacteristic
581C2C11×#310711yescharacteristic
582C2C11×#311611yescharacteristic
583C2C11×#321011yescharacteristic
584C2C11×#321611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#533C2semidirect
4. C11×#2024C2semidirect
5. C11×#2023C2semidirect
6. C11×#2016C2semidirect
7. C11×#2013C2semidirect
8. C11×#1880C2semidirect
9. C11×#1878C2semidirect
10. C11×#1873C2semidirect
11. C11×#1817C2semidirect
107. #23935C11direct (N × H)
185. C2×#533C2×C11semidirect
188. #2024C2×C11semidirect
189. #2023C2×C11semidirect
190. #2016C2×C11semidirect
191. #2013C2×C11semidirect
192. #1880C2×C11semidirect
193. #1878C2×C11semidirect
194. #1873C2×C11semidirect
195. #1817C2×C11semidirect
476. C11#23935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4522
C11×#22972
C11×#20242
C11×#20232
C11×#20162
C11×#20132
C11×#18802
C11×#18782
C11×#18732
C11×#18172
#2393511