Finite Group Databasebeta

← C11×#23967 #14601160

Subgroups — C11×#23967 #14601160

Order 2816.

1240 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C2×C11×#451C211yesmaximal, characteristic, complemented
3C22×C11×#103C211yesmaximal, characteristic, complemented
4C11×#2409C211yesmaximal, characteristic
5C11×#2026C212yesmaximal, complemented
6C11×#2001C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1878C212yesmaximal, complemented
9C11×#1873C212yesmaximal, complemented
10C11×#1869C211yesmaximal, characteristic
11C11×#1823C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C23×C8×C11C2211yescharacteristic
15C11×#552—24no—
16C11×#552—24no—
17C2×C11×#126—21no—
18C2×C11×#125—21no—
19C2×C11×#125C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117—21no—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#451—24no—
30C2×C11×#103—24no—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2212yes—
37C11×#395—21no—
38C11×#393—21no—
39C11×#391C2212yes—
40C11×#386—21no—
41C11×#385—21no—
42C11×#380C2211yescharacteristic
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11—24no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2312yes—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C2×C11×Q16—24no—
60C2×C11×Q16—24no—
61C2×C11×Q16—42no—
62C22×C8×C11—22no—
63C22×C8×C11—42no—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C11×#126—28no—
67C11×#125—28no—
68C11×#125—22no—
69C11×#125—22no—
70C11×#123—28no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—42no—
76C11×C22⋊Q8D414yes—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C11×#117—28no—
82C11×#117—22no—
83C11×#117—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D414yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#103—24no—
109C11×#103—24no—
110C11×#103—24no—
111C11×#103—42no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—42no—
114C11×#95—21no—
115C11×#95—22no—
116C11×#95—22no—
117#23967C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—21no—
121C2×Q8×C11—22no—
122C2×Q8×C11—28no—
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—44no—
130C2×Q8×C11—48no—
131C2×Q8×C11—44no—
132C2×Q8×C11—42no—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11#4114yes—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—44no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2411yescharacteristic
162C11×Q16—48no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—44no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—44no—
183C11×C4⋊C4C2×D412yes—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—44no—
192C11×C22⋊C4—42no—
193C42×C11—24no—
194C42×C11—24no—
195C42×C11—21no—
196C42×C11—21no—
197C2×#552C2×C1111yescharacteristic
198C2×#451C2×C1111yescharacteristic, complemented
199C22×#103C2×C1111yescharacteristic, complemented
200#2409C2×C1111yescharacteristic
201#2026C2×C1112yescomplemented
202#2001C2×C1112yescomplemented
203#1892C2×C1111yescharacteristic, complemented
204#1878C2×C1112yescomplemented
205#1873C2×C1112yescomplemented
206#1869C2×C1111yescharacteristic
207#1823C2×C1111yescharacteristic, complemented
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—22no—
215C23×C11#12012yes—
216C23×C11#13512yes—
217C23×C11#13712yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—48no—
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—42no—
226Q8×C11—42no—
227D4×C11—44no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—48no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—48no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11#12012yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4112yes—
264C2×C4×C11H(5,𝔽2)12yes—
265C8×C11—42no—
266C8×C11—42no—
267C23×Q8C22×C1111yescharacteristic
268C22×Q16C22×C1112yes—
269C23×C8C22×C1111yescharacteristic
270#552—24no—
271#552—24no—
272C2×#126—21no—
273C2×#125—21no—
274C2×#125C22×C1111yescharacteristic
275C2×#123—21no—
276C2×C22⋊Q8C22×C1111yescharacteristic
277C2×C22⋊Q8C22×C1112yes—
278C2×C22⋊Q8C22×C1111yescharacteristic
279C2×C4×Q8C22×C1111yescharacteristic
280C2×C4×D4C22×C1111yescharacteristic
281C2×#117—21no—
282C2×#117C22×C1111yescharacteristic
283C22×C4⋊C4C22×C1111yescharacteristic
284#451—24no—
285C2×#103—24no—
286C2×#103C22×C1112yes—
287C2×#103C22×C1112yes—
288C2×#103C22×C1112yes—
289C2×#103C22×C1112yes—
290C2×C22⋊C8C22×C1111yescharacteristic
291C2×C22⋊C8C22×C1112yes—
292#395—21no—
293#393—21no—
294#391C22×C1112yes—
295#386—21no—
296#385—21no—
297#380C22×C1111yescharacteristic
298#340C22×C1112yes—
299#340C22×C1112yes—
300#340C22×C1112yes—
301#336C22×C1112yes—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11#45214yes—
312C22×C11C2×#12011yescharacteristic
313C22×C11#54612yes—
314C22×C11C2×#13511yescharacteristic
315C22×C11C2×#13711yescharacteristic
316C22×C11#57812yes—
317C4×C11—22no—
318C4×C11—41no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11—41no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—41no—
325C4×C11—42no—
326C4×C11—82no—
327C4×C11#52511yescharacteristic
328C4×C11#53511yescharacteristic
329C4×C11#54612yes—
330C22×Q8—21no—
331C22×Q8—24no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—42no—
335C22×Q8C23×C1111yescharacteristic
336C22×Q8C23×C1112yes—
337C22×D4D4×C1111yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4C23×C1111yescharacteristic
341C23×C4C23×C1111yescharacteristic
342C2×Q16—24no—
343C2×Q16—24no—
344C2×Q16—42no—
345C22×C8—22no—
346C22×C8—42no—
347C22×C8C23×C1112yes—
348C22×C8C23×C1112yes—
349#126—28no—
350#125—28no—
351#125—22no—
352#125—22no—
353#123—28no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—24no—
358C22⋊Q8—42no—
359C22⋊Q8D4×C1114yes—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×D4—22no—
363C4×D4—22no—
364#117—28no—
365#117—22no—
366#117—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4D4×C1111yescharacteristic
376C2×C4⋊C4D4×C1114yes—
377C2×C4⋊C4C23×C1112yes—
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4D4×C1111yescharacteristic
387C2×C22⋊C4D4×C1111yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C23×C1111yescharacteristic
391#103—24no—
392#103—24no—
393#103—24no—
394#103—42no—
395C22⋊C8—22no—
396C22⋊C8—42no—
397#95—21no—
398#95—22no—
399#95—22no—
400C2×C11—24no—
401C2×C11—81no—
402C2×C11#240411yescharacteristic
403C2×C11C2×#45211yescharacteristic
404C2×C11#301111yescharacteristic
405C2×C11#330012yes—
406C2×C11#331212yes—
407C24C2×D4×C1111yescharacteristic
408C24C2×D4×C1111yescharacteristic
409C2×Q8—21no—
410C2×Q8—22no—
411C2×Q8—28no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—44no—
419C2×Q8—48no—
420C2×Q8—44no—
421C2×Q8—42no—
422C2×Q8C2×D4×C1112yes—
423C2×Q8C11×#4114yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—44no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1112yes—
449C22×C4C2×D4×C1112yes—
450C22×C4C24×C1111yescharacteristic
451Q16—48no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—44no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—44no—
472C4⋊C4C2×D4×C1112yes—
473C4⋊C4C2×D4×C1112yes—
474C4⋊C4C2×D4×C1112yes—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—44no—
481C22⋊C4—42no—
482C42—24no—
483C42—24no—
484C42—21no—
485C42—21no—
486C11#2396711yescharacteristic, direct product factor, Sylow
487C23—22no—
488C23—22no—
489C23—21no—
490C23—22no—
491C23—21no—
492C23—21no—
493C23—22no—
494C23C11×#12012yes—
495C23C11×#13512yes—
496C23C11×#13712yes—
497C23C22×D4×C1111yescharacteristic
498Q8—24no—
499Q8—24no—
500Q8—24no—
501Q8—48no—
502Q8—41no—
503Q8—41no—
504Q8—42no—
505Q8—42no—
506D4—44no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—48no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4C11×#12012yes—
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C22×D4×C1111yescharacteristic
542C2×C4C2×C11×#4112yes—
543C2×C4C11×H(5,𝔽2)12yes—
544C8—42no—
545C8—42no—
546C22—22no—
547C22—22no—
548C22—24no—
549C22—24no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22C11×#45214yes—
556C22C2×C11×#12011yescharacteristic
557C22C11×#54612yes—
558C22C2×C11×#13511yescharacteristic
559C22C2×C11×#13711yescharacteristic
560C22C11×#57812yes—
561C4—22no—
562C4—41no—
563C4—44no—
564C4—42no—
565C4—41no—
566C4—42no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—82no—
571C4C11×#52511yescharacteristic
572C4C11×#53511yescharacteristic
573C4C11×#54612yes—
574C2—24no—
575C2—81no—
576C2C11×#240411yescharacteristic
577C2C2×C11×#45211yescharacteristic
578C2C11×#301111yescharacteristic
579C2C11×#330012yes—
580C2C11×#331212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
3. C22×C11×#103C2semidirect
5. C11×#2026C2semidirect
6. C11×#2001C2semidirect
7. C11×#1892C2semidirect
8. C11×#1878C2semidirect
9. C11×#1873C2semidirect
11. C11×#1823C2semidirect
117. #23967C11direct (N × H)
198. C2×#451C2×C11semidirect
199. C22×#103C2×C11semidirect
201. #2026C2×C11semidirect
202. #2001C2×C11semidirect
203. #1892C2×C11semidirect
204. #1878C2×C11semidirect
205. #1873C2×C11semidirect
207. #1823C2×C11semidirect
486. C11#23967direct (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
C2×C11×#4512
C22×C11×#1032
C11×#24092
C11×#20262
C11×#20012
C11×#18922
C11×#18782
C11×#18732
C11×#18692
C11×#18232
#2396711