Finite Group Databasebeta

← C11×#24253 #14601446

Subgroups — C11×#24253 #14601446

Order 2816.

1424 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×#547C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#452C212yesmaximal, complemented
4C2×C11×#440C211yesmaximal, characteristic, complemented
5C11×#2536C211yesmaximal, characteristic, complemented
6C11×#2036C212yesmaximal, complemented
7C11×#2001C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1955C211yesmaximal, characteristic, complemented
10C11×#1804C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2211yescharacteristic
15C11×#547—24no—
16C11×#547—24no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4—21no—
26C11×#462—24no—
27C11×#452—28no—
28C11×#440—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C11×#97C2211yescharacteristic
40C11×#398—21no—
41C11×#394—21no—
42C11×#388—22no—
43C11×#382C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2312yes—
54C22×D4×C11—22no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C2×C11×Q16—24no—
61C2×C11×Q16—24no—
62C2×C11×Q16—42no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16D414yescomplemented
66C22×C8×C11C2312yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8D414yes—
71C11×#123—216no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—42no—
76C11×#121—28no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11D414yes—
83C2×C11×C4⋊C4—28no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#107—22no—
101C11×C4⋊C8—22no—
102C11×#103—24no—
103C11×#103—24no—
104C11×#103—22no—
105C11×#103—42no—
106C11×#102—22no—
107C11×#102—24no—
108C11×C22⋊C8—24no—
109C11×C22⋊C8—42no—
110C11×#97—22no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114#24253C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C24×C11C2×D412yes—
117C11×#41—48no—
118C11×#41—48no—
119C11×#41—48no—
120C11×#41—48no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D414yes—
132C2×Q8×C11C2×D412yes—
133C2×D4×C11—28no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×D412yes—
143C2×D4×C11#4112yes—
144C22×C4×C11—28no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—44no—
158C22×C4×C11—44no—
159C22×C4×C11—44no—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C11×Q16—48no—
165C11×SD16—28no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—22no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—44no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4C2×D412yes—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—44no—
191C11×C22⋊C4—44no—
192C42×C11—42no—
193C42×C11C2×D412yes—
194C42×C11C2×D412yes—
195C2×#547C2×C1111yescharacteristic
196C2×#462C2×C1111yescharacteristic, complemented
197C2×#452C2×C1112yescomplemented
198C2×#440C2×C1111yescharacteristic, complemented
199#2536C2×C1111yescharacteristic, complemented
200#2036C2×C1112yescomplemented
201#2001C2×C1112yescomplemented
202#1960C2×C1111yescharacteristic, complemented
203#1955C2×C1111yescharacteristic, complemented
204#1804C2×C1111yescharacteristic, complemented
205#1788C2×C1112yescomplemented
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—24no—
222Q8×C11—24no—
223Q8×C11—42no—
224Q8×C11—41no—
225Q8×C11—42no—
226Q8×C11—41no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—44no—
231D4×C11—416no—
232D4×C11#12114yes—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—48no—
242C2×C4×C11—416no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11#12012yes—
258C2×C4×C11#12012yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C8×C11—22no—
266C8×C11—41no—
267C8×C11—42no—
268C22×#41C22×C1112yes—
269C22×Q16C22×C1112yes—
270C22×SD16C22×C1111yescharacteristic
271#547—24no—
272#547—24no—
273C2×C4⋊Q8C22×C1111yescharacteristic
274C2×#123—22no—
275C2×C22⋊Q8C22×C1112yes—
276C2×C22⋊Q8C22×C1112yes—
277C2×#121—21no—
278C2×C4×Q8C22×C1111yescharacteristic
279C2×C4×D4C22×C1111yescharacteristic
280C2×C4×D4C22×C1111yescharacteristic
281C22×C4⋊C4—21no—
282#462—24no—
283#452—28no—
284#440—24no—
285C2×#107C22×C1111yescharacteristic
286C2×C4⋊C8C22×C1111yescharacteristic
287C2×#103C22×C1111yescharacteristic
288C2×#103C22×C1112yes—
289C2×#103C22×C1112yes—
290C2×#103C22×C1112yes—
291C2×#102C22×C1112yes—
292C2×#102C22×C1111yescharacteristic
293C2×C22⋊C8C22×C1112yes—
294C2×C22⋊C8C22×C1112yes—
295C2×#97C22×C1111yescharacteristic
296#398—21no—
297#394—21no—
298#388—22no—
299#382C22×C1111yescharacteristic
300#380C22×C1112yes—
301#340C22×C1112yes—
302C22×C11—24no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11C2×#12011yescharacteristic
315C22×C11D4211yescharacteristic
316C22×C11#54611yescharacteristic
317C22×C11#57512yes—
318C22×C11#57812yes—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—42no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—81no—
326C4×C11—82no—
327C4×C11C2×#12111yescharacteristic
328C4×C11#53511yescharacteristic
329C4×C11D4211yescharacteristic
330C4×C11#54611yescharacteristic
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—42no—
336C2×#41—42no—
337C22×Q8C23×C1111yescharacteristic
338C22×Q8C23×C1112yes—
339C22×D4—22no—
340C22×D4D4×C1111yescharacteristic
341C22×D4C23×C1111yescharacteristic
342C23×C4—21no—
343C23×C4—22no—
344C23×C4C23×C1112yes—
345C2×Q16—24no—
346C2×Q16—24no—
347C2×Q16—42no—
348C2×SD16—22no—
349C2×SD16—22no—
350C2×SD16D4×C1114yescomplemented
351C22×C8C23×C1112yes—
352C22×C8C23×C1111yescharacteristic
353C22×C8C23×C1111yescharacteristic
354C4⋊Q8—22no—
355C4⋊Q8D4×C1114yes—
356#123—216no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360C22⋊Q8—42no—
361#121—28no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4D4×C1114yes—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4D4×C1111yescharacteristic
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C4⋊C4C23×C1112yes—
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4D4×C1112yes—
383C2×C42—21no—
384C2×C42C23×C1111yescharacteristic
385#107—22no—
386C4⋊C8—22no—
387#103—24no—
388#103—24no—
389#103—22no—
390#103—42no—
391#102—22no—
392#102—24no—
393C22⋊C8—24no—
394C22⋊C8—42no—
395#97—22no—
396#95—22no—
397#95—21no—
398#95—21no—
399C2×C11—44no—
400C2×C11—82no—
401C2×C11#240811yescharacteristic
402C2×C11#300511yescharacteristic
403C2×C11#301111yescharacteristic
404C2×C11#326912yes—
405C2×C11#331512yes—
406C24—21no—
407C24C2×D4×C1112yes—
408#41—48no—
409#41—48no—
410#41—48no—
411#41—48no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—21no—
421C2×Q8—22no—
422C2×Q8C2×D4×C1114yes—
423C2×Q8C2×D4×C1112yes—
424C2×D4—28no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—42no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4C2×D4×C1112yes—
433C2×D4C2×D4×C1112yes—
434C2×D4C11×#4112yes—
435C22×C4—28no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4C2×D4×C1112yes—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C24×C1111yescharacteristic
455Q16—48no—
456SD16—28no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—21no—
463C2×C8—22no—
464C2×C8—21no—
465C2×C8C2×D4×C1112yes—
466C4⋊C4—28no—
467C4⋊C4—22no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—44no—
476C4⋊C4—42no—
477C4⋊C4C2×D4×C1112yes—
478C22⋊C4—28no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—44no—
482C22⋊C4—44no—
483C42—42no—
484C42C2×D4×C1112yes—
485C42C2×D4×C1112yes—
486C11#2425311yescharacteristic, direct product factor, Sylow
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23C22×D4×C1111yescharacteristic
500Q8—22no—
501Q8—22no—
502Q8—24no—
503Q8—24no—
504Q8—42no—
505Q8—41no—
506Q8—42no—
507Q8—41no—
508D4—22no—
509D4—22no—
510D4—22no—
511D4—44no—
512D4—416no—
513D4C11×#12114yes—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—48no—
523C2×C4—416no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4C11×#12012yes—
539C2×C4C11×#12012yes—
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C22×D4×C1111yescharacteristic
542C2×C4C22×D4×C1111yescharacteristic
543C2×C4C2×C11×#4111yescharacteristic
544C2×C4C11×H(5,𝔽2)11yescharacteristic
545C2×C4C11×H(5,𝔽2)11yescharacteristic
546C8—22no—
547C8—41no—
548C8—42no—
549C22—24no—
550C22—42no—
551C22—42no—
552C22—44no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22C2×C11×#12011yescharacteristic
562C22D42×C1111yescharacteristic
563C22C11×#54611yescharacteristic
564C22C11×#57512yes—
565C22C11×#57812yes—
566C4—22no—
567C4—22no—
568C4—42no—
569C4—44no—
570C4—42no—
571C4—42no—
572C4—81no—
573C4—82no—
574C4C2×C11×#12111yescharacteristic
575C4C11×#53511yescharacteristic
576C4D42×C1111yescharacteristic
577C4C11×#54611yescharacteristic
578C2—44no—
579C2—82no—
580C2C11×#240811yescharacteristic
581C2C11×#300511yescharacteristic
582C2C11×#301111yescharacteristic
583C2C11×#326912yes—
584C2C11×#331512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
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×#462C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#440C2semidirect
5. C11×#2536C2semidirect
6. C11×#2036C2semidirect
7. C11×#2001C2semidirect
8. C11×#1960C2semidirect
9. C11×#1955C2semidirect
10. C11×#1804C2semidirect
11. C11×#1788C2semidirect
65. C2×C11×SD16D4semidirect
114. #24253C11direct (N × H)
196. C2×#462C2×C11semidirect
197. C2×#452C2×C11semidirect
198. C2×#440C2×C11semidirect
199. #2536C2×C11semidirect
200. #2036C2×C11semidirect
201. #2001C2×C11semidirect
202. #1960C2×C11semidirect
203. #1955C2×C11semidirect
204. #1804C2×C11semidirect
205. #1788C2×C11semidirect
350. C2×SD16D4×C11semidirect
486. C11#24253direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4622
C2×C11×#4522
C2×C11×#4402
C11×#25362
C11×#20362
C11×#20012
C11×#19602
C11×#19552
C11×#18042
C11×#17882
#2425311