Finite Group Databasebeta

← C11×#24179 #14601372

Subgroups — C11×#24179 #14601372

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C11×#3037C211yesmaximal, characteristic
4C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
5C11×#2038C212yesmaximal, complemented
6C11×#2005C212yesmaximal, complemented
7C11×#1994C211yesmaximal, characteristic, complemented
8C11×#1962C211yesmaximal, characteristic
9C11×#1882C212yesmaximal, complemented
10C11×#1859C212yesmaximal, complemented
11C11×#1801C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C11×#559—21no—
14C11×#557—21no—
15C11×#556—21no—
16C11×#556—22no—
17C11×#554—21no—
18C11×#552—22no—
19C11×#539—22no—
20C11×#536C2212yes—
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#529—22no—
25C11×#520C2212yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C11×#479—22no—
29C11×#477—21no—
30C11×#475—21no—
31C11×#464—22no—
32C11×#462—21no—
33C11×#460—21no—
34C11×#428C2212yes—
35C11×#423C2211yescharacteristic
36C11×#423C2211yescharacteristic
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yes—
39C11×#419C2212yes—
40C11×#417C2212yes—
41C2×C11×#101C2212yes—
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#389—22no—
45C11×#384C2211yescharacteristic
46C4×C11×C4⋊C4—22no—
47C43×C11C2211yescharacteristic
48C11×#343C2212yes—
49C11×#339C2212yes—
50C11×#339C2212yes—
51C2×C11×#41C2312yes—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2311yescharacteristic
54C11×#137—24no—
55C11×#137—42no—
56C2×C11×Q16—22no—
57C2×C11×SD16—22no—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8D411yescharacteristic
66C11×#127D411yescharacteristic
67C11×#126—24no—
68C11×#126—24no—
69C11×#125—22no—
70C11×#125—24no—
71C11×#125D412yes—
72C11×#124—22no—
73C11×#124—22no—
74C11×#124D412yes—
75C11×#123—24no—
76C11×#123—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×#121—21no—
83C11×#121—21no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—24no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C11×#117—24no—
102C11×#117—22no—
103C11×#117C2312yes—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D412yes—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11D412yes—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×#107—22no—
119C11×#106—22no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—21no—
124C11×#104—24no—
125C11×#104—42no—
126C11×#103—22no—
127C11×#103—22no—
128C11×#103—22no—
129C11×#102—22no—
130C11×#101—42no—
131C11×#95—22no—
132C11×#95—22no—
133#24179C1111yesmaximal, characteristic, direct product factor, Sylow
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D412yes—
152C2×Q8×C11#4112yes—
153C2×D4×C11—22no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11C2×D412yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C11×Q16—44no—
169C11×SD16—44no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—44no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4C2×D412yes—
196C11×C4⋊C4C2×D412yes—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C42×C11—24no—
204C42×C11—24no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11—22no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—42no—
212C42×C11—41no—
213C42×C11—41no—
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11#4112yes—
219#3507C2×C1111yescharacteristic
220#3078C2×C1111yescharacteristic, complemented
221#3037C2×C1111yescharacteristic
222C4×C4⋊Q8C2×C1111yescharacteristic, complemented
223#2038C2×C1112yescomplemented
224#2005C2×C1112yescomplemented
225#1994C2×C1111yescharacteristic, complemented
226#1962C2×C1111yescharacteristic
227#1882C2×C1112yescomplemented
228#1859C2×C1112yescomplemented
229#1801C2×C1111yescharacteristic, complemented
230C23×C11—22no—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—42no—
243Q8×C11—81no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—81no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—84no—
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12011yescharacteristic
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C8×C11—42no—
285C8×C11—42no—
286C2×#137C22×C1112yes—
287#559—21no—
288#557—21no—
289#556—21no—
290#556—22no—
291#554—21no—
292#552—22no—
293#539—22no—
294#536C22×C1112yes—
295#533C22×C1111yescharacteristic
296#532C22×C1111yescharacteristic
297C2×C4⋊Q8C22×C1111yescharacteristic
298#529—22no—
299#520C22×C1112yes—
300C2×C4×Q8C22×C1111yescharacteristic
301C2×C4×Q8C22×C1111yescharacteristic
302#479—22no—
303#477—21no—
304#475—21no—
305#464—22no—
306#462—21no—
307#460—21no—
308#428C22×C1112yes—
309#423C22×C1111yescharacteristic
310#423C22×C1111yescharacteristic
311C2×#104C22×C1112yes—
312C2×#104C22×C1112yes—
313#419C22×C1112yes—
314#417C22×C1112yes—
315C2×#101C22×C1112yes—
316#391C22×C1111yescharacteristic
317#391C22×C1111yescharacteristic
318#389—22no—
319#384C22×C1111yescharacteristic
320C4×C4⋊C4—22no—
321C43C22×C1111yescharacteristic
322#343C22×C1112yes—
323#339C22×C1112yes—
324#339C22×C1112yes—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11C2×#12011yescharacteristic
331C22×C11#52511yescharacteristic
332C22×C11#53711yescharacteristic
333C4×C11—24no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11#45612yes—
346C4×C11#54611yescharacteristic
347C4×C11#54711yescharacteristic
348C4×C11#54811yescharacteristic
349C4×C11#55011yescharacteristic
350C2×#41C23×C1112yes—
351C22×Q8C23×C1111yescharacteristic
352C22×Q8C23×C1111yescharacteristic
353#137—24no—
354#137—42no—
355C2×Q16—22no—
356C2×SD16—22no—
357C2×M16C23×C1112yes—
358C2×M16C23×C1112yes—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8D4×C1111yescharacteristic
363C4⋊Q8D4×C1111yescharacteristic
364C4⋊Q8D4×C1111yescharacteristic
365#127D4×C1111yescharacteristic
366#126—24no—
367#126—24no—
368#125—22no—
369#125—24no—
370#125D4×C1112yes—
371#124—22no—
372#124—22no—
373#124D4×C1112yes—
374#123—24no—
375#123—24no—
376C22⋊Q8—24no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381#121—21no—
382#121—21no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—24no—
398C4×D4—21no—
399C4×D4—21no—
400#117—24no—
401#117—22no—
402#117C23×C1112yes—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4D4×C1112yes—
408C2×C4⋊C4C23×C1111yescharacteristic
409C2×C4⋊C4C23×C1111yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42D4×C1112yes—
414C2×C42C23×C1111yescharacteristic
415C2×C42C23×C1111yescharacteristic
416C2×C42C23×C1111yescharacteristic
417#107—22no—
418#106—22no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423#104—24no—
424#104—42no—
425#103—22no—
426#103—22no—
427#103—22no—
428#102—22no—
429#101—42no—
430#95—22no—
431#95—22no—
432C2×C11—21no—
433C2×C11—21no—
434C2×C11—82no—
435C2×C11#240711yescharacteristic
436C2×C11C2×#45611yescharacteristic
437C2×C11#301811yescharacteristic
438#41—22no—
439#41—22no—
440#41—22no—
441#41—22no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8C2×D4×C1112yes—
456C2×Q8C11×#4112yes—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4C2×D4×C1112yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4C2×D4×C1112yes—
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1112yes—
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C24×C1111yescharacteristic
472Q16—44no—
473SD16—44no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—24no—
481C4⋊C4—28no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—44no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C1112yes—
500C4⋊C4C2×D4×C1112yes—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C42—24no—
508C42—24no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—41no—
517C42—41no—
518C42C2×D4×C1111yescharacteristic
519C42C2×D4×C1111yescharacteristic
520C42C2×D4×C1111yescharacteristic
521C42C2×D4×C1111yescharacteristic
522C42C11×#4112yes—
523C11#2417911yescharacteristic, direct product factor, Sylow
524C23—22no—
525C23C22×D4×C1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—22no—
529Q8—22no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—42no—
537Q8—81no—
538D4—22no—
539D4—22no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—81no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4C11×#12011yescharacteristic
569C2×C4C11×#12011yescharacteristic
570C2×C4C11×#12011yescharacteristic
571C2×C4C11×#12011yescharacteristic
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C22×D4×C1111yescharacteristic
574C2×C4C2×C11×#4111yescharacteristic
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C11×H(5,𝔽2)11yescharacteristic
577C2×C4C11×2−1+411yescharacteristic
578C8—42no—
579C8—42no—
580C22—21no—
581C22—21no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22C2×C11×#12011yescharacteristic
586C22C11×#52511yescharacteristic
587C22C11×#53711yescharacteristic
588C4—24no—
589C4—21no—
590C4—21no—
591C4—21no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4C11×#45612yes—
601C4C11×#54611yescharacteristic
602C4C11×#54711yescharacteristic
603C4C11×#54811yescharacteristic
604C4C11×#55011yescharacteristic
605C2—21no—
606C2—21no—
607C2—82no—
608C2C11×#240711yescharacteristic
609C2C2×C11×#45611yescharacteristic
610C2C11×#301811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3078C2semidirect
4. C4×C11×C4⋊Q8C2semidirect
5. C11×#2038C2semidirect
6. C11×#2005C2semidirect
7. C11×#1994C2semidirect
9. C11×#1882C2semidirect
10. C11×#1859C2semidirect
11. C11×#1801C2semidirect
133. #24179C11direct (N × H)
220. #3078C2×C11semidirect
222. C4×C4⋊Q8C2×C11semidirect
223. #2038C2×C11semidirect
224. #2005C2×C11semidirect
225. #1994C2×C11semidirect
227. #1882C2×C11semidirect
228. #1859C2×C11semidirect
229. #1801C2×C11semidirect
523. C11#24179direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#30782
C11×#30372
C4×C11×C4⋊Q82
C11×#20382
C11×#20052
C11×#19942
C11×#19622
C11×#18822
C11×#18592
C11×#18012
#2417911