Finite Group Databasebeta

← C11×#36727 #14613920

Subgroups — C11×#36727 #14613920

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2847C212yesmaximal, complemented
2C11×#2748C214yesmaximal, complemented
3C11×#2741C214yesmaximal, complemented
4C11×#2703C214yesmaximal, complemented
5C11×#2671C214yesmaximal, complemented
6C11×#2656C211yesmaximal, characteristic, complemented
7C11×#2646C211yesmaximal, characteristic, complemented
8C11×#2443C214yesmaximal, complemented
9C11×#2424C214yesmaximal, complemented
10C11×#2325C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C2×C11×#123C2214yescomplemented
14C2×C11×#121C2212yes—
15C2×C11×#121C2214yes—
16C2×C11×#121C2214yes—
17C2×C11×#121C2212yes—
18C2×C11×#121C2212yes—
19C2×C11×#120C2214yes—
20C2×C4×D4×C11C2214yes—
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C11×#400C2214yescomplemented
24C11×#399C2214yescomplemented
25C11×#399C2214yescomplemented
26C11×#398C2214yescomplemented
27C11×#398C2214yescomplemented
28C11×#397C2214yescomplemented
29C11×#396C2214yes—
30C11×#394C2214yes—
31C11×#394C2214yes—
32C11×#394C2214yescomplemented
33C11×#392C2214yes—
34C11×#392C2214yescomplemented
35C11×#390C2214yes—
36C11×#388C2214yes—
37C11×#388C2214yescomplemented
38C11×#388C2214yescomplemented
39C11×#387C2214yescomplemented
40C11×#387C2214yescomplemented
41C11×#386C2214yes—
42C11×#386C2214yes—
43C11×#386C2214yes—
44C11×#386C2214yes—
45C11×#386C2214yes—
46C11×#386C2214yescomplemented
47C11×#385C2214yes—
48C11×#385C2214yescomplemented
49C11×#385C2214yescomplemented
50C11×#380C2212yes—
51C11×#380C2214yes—
52C11×#380C2214yes—
53C11×#380C2212yes—
54C11×#380C2212yes—
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C25×C11C2311yescharacteristic
58C22×D4×C11C2314yes—
59C22×D4×C11C2314yes—
60C22×D4×C11C2314yes—
61C22×D4×C11C2312yes—
62C22×D4×C11C2314yes—
63C23×C4×C11—24no—
64C23×C4×C11—44no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2312yes—
67C23×C4×C11C2312yes—
68C23×C4×C11C2312yes—
69C23×C4×C11C2312yes—
70C23×C4×C11C2314yes—
71C23×C4×C11C2311yescharacteristic
72C11×#123—48no—
73C11×#121—28no—
74C11×#121—44no—
75C11×#121—44no—
76C11×#121—48no—
77C11×#121—48no—
78C11×#120—48no—
79C4×D4×C11—48no—
80C2×C11×C4⋊C4—44no—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C42×C11C2314yes—
105C11×#95C2314yes—
106C11×#95C2314yes—
107C11×#95C2314yes—
108C11×#95C2314yes—
109C11×#95C2314yes—
110C11×#95C2314yes—
111C11×#95C2314yes—
112C11×#95C2314yes—
113C11×#95C2314yes—
114#36727C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—42no—
120C24×C11C2414yes—
121C24×C11C2411yescharacteristic
122C24×C11C2411yescharacteristic
123C24×C11C2411yescharacteristic
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11—28no—
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11—24no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—44no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11—416no—
158C22×C4×C11#4114yes—
159C22×C4×C11C2414yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—44no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—44no—
173C11×C4⋊C4—44no—
174C11×C4⋊C4—44no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—44no—
183C11×C22⋊C4—44no—
184C11×C22⋊C4—44no—
185C11×C22⋊C4—44no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—44no—
188C42×C11—44no—
189#2847C2×C1112yescomplemented
190#2748C2×C1114yescomplemented
191#2741C2×C1114yescomplemented
192#2703C2×C1114yescomplemented
193#2671C2×C1114yescomplemented
194#2656C2×C1111yescharacteristic, complemented
195#2646C2×C1111yescharacteristic, complemented
196#2443C2×C1114yescomplemented
197#2424C2×C1114yescomplemented
198#2325C2×C1112yescomplemented
199C2×#380C2×C1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—28no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—21no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)14yes—
226C23×C112−1+412yes—
227C23×C11C2511yescharacteristic
228D4×C11—416no—
229D4×C11—84no—
230D4×C11—88no—
231D4×C11—88no—
232D4×C11—88no—
233C2×C4×C11—28no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—44no—
254C2×C4×C11—48no—
255C2×C4×C11—48no—
256C2×C4×C11—84no—
257C2×C4×C11—84no—
258C2×C4×C11—88no—
259C2×C4×C11C2×#4114yes—
260C2×C4×C11H(5,𝔽2)14yes—
261C24×C4C22×C1111yescharacteristic
262C2×#123C22×C1114yescomplemented
263C2×#121C22×C1112yes—
264C2×#121C22×C1112yes—
265C2×#121C22×C1112yes—
266C2×#121C22×C1114yes—
267C2×#121C22×C1114yes—
268C2×#120C22×C1114yes—
269C2×C4×D4C22×C1114yes—
270C22×C4⋊C4C22×C1112yes—
271C22×C22⋊C4C22×C1112yes—
272#400C22×C1114yescomplemented
273#399C22×C1114yescomplemented
274#399C22×C1114yescomplemented
275#398C22×C1114yescomplemented
276#398C22×C1114yescomplemented
277#397C22×C1114yescomplemented
278#396C22×C1114yes—
279#394C22×C1114yes—
280#394C22×C1114yes—
281#394C22×C1114yescomplemented
282#392C22×C1114yes—
283#392C22×C1114yescomplemented
284#390C22×C1114yes—
285#388C22×C1114yes—
286#388C22×C1114yescomplemented
287#388C22×C1114yescomplemented
288#387C22×C1114yescomplemented
289#387C22×C1114yescomplemented
290#386C22×C1114yes—
291#386C22×C1114yes—
292#386C22×C1114yes—
293#386C22×C1114yes—
294#386C22×C1114yes—
295#386C22×C1114yescomplemented
296#385C22×C1114yes—
297#385C22×C1114yescomplemented
298#385C22×C1114yescomplemented
299#380C22×C1112yes—
300#380C22×C1112yes—
301#380C22×C1112yes—
302#380C22×C1114yes—
303#380C22×C1114yes—
304C2×#95C22×C1111yescharacteristic
305C2×#95C22×C1111yescharacteristic
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—416no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11#54014yes—
329C22×C11C22×#4111yescharacteristic
330C22×C11C2×H(5,𝔽2)12yes—
331C22×C11C2×H(5,𝔽2)12yes—
332C22×C11C2×H(5,𝔽2)11yescharacteristic
333C22×C11C2×2−1+411yescharacteristic
334C4×C11—24no—
335C4×C11—24no—
336C4×C11—44no—
337C4×C11—44no—
338C4×C11—44no—
339C4×C11—44no—
340C4×C11—44no—
341C25C23×C1111yescharacteristic
342C22×D4C23×C1114yes—
343C22×D4C23×C1114yes—
344C22×D4C23×C1114yes—
345C22×D4C23×C1112yes—
346C22×D4C23×C1114yes—
347C23×C4—24no—
348C23×C4—44no—
349C23×C4C23×C1111yescharacteristic
350C23×C4C23×C1112yes—
351C23×C4C23×C1112yes—
352C23×C4C23×C1112yes—
353C23×C4C23×C1112yes—
354C23×C4C23×C1114yes—
355C23×C4C23×C1111yescharacteristic
356#123—48no—
357#121—28no—
358#121—44no—
359#121—44no—
360#121—48no—
361#121—48no—
362#120—48no—
363C4×D4—48no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C23×C1114yes—
366C2×C4⋊C4C23×C1112yes—
367C2×C4⋊C4C23×C1114yes—
368C2×C4⋊C4C23×C1114yes—
369C2×C4⋊C4C23×C1112yes—
370C2×C4⋊C4C23×C1112yes—
371C2×C4⋊C4C23×C1114yes—
372C2×C4⋊C4C23×C1114yes—
373C2×C4⋊C4C23×C1114yes—
374C2×C22⋊C4—44no—
375C2×C22⋊C4C23×C1114yes—
376C2×C22⋊C4C23×C1114yes—
377C2×C22⋊C4C23×C1114yes—
378C2×C22⋊C4C23×C1114yes—
379C2×C22⋊C4C23×C1114yes—
380C2×C22⋊C4C23×C1114yes—
381C2×C22⋊C4C23×C1114yes—
382C2×C22⋊C4C23×C1114yes—
383C2×C22⋊C4C23×C1114yes—
384C2×C22⋊C4C23×C1114yes—
385C2×C22⋊C4C23×C1114yes—
386C2×C22⋊C4C23×C1114yes—
387C2×C22⋊C4C23×C1114yes—
388C2×C42C23×C1114yes—
389#95C23×C1114yes—
390#95C23×C1114yes—
391#95C23×C1114yes—
392#95C23×C1114yes—
393#95C23×C1114yes—
394#95C23×C1114yes—
395#95C23×C1114yes—
396#95C23×C1114yes—
397#95C23×C1114yes—
398C2×C11—24no—
399C2×C11—42no—
400C2×C11—42no—
401C2×C11—84no—
402C2×C11C2×#54011yescharacteristic
403C2×C11#349011yescharacteristic
404C2×C11#349211yescharacteristic
405C2×C11#353612yes—
406C2×C11#353712yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—24no—
411C24—42no—
412C24C24×C1114yes—
413C24C24×C1111yescharacteristic
414C24C24×C1111yescharacteristic
415C24C24×C1111yescharacteristic
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—416no—
450C22×C4C11×#4114yes—
451C22×C4C24×C1114yes—
452C22×C4C24×C1114yes—
453C22×C4C24×C1114yes—
454C22×C4C24×C1114yes—
455C22×C4C24×C1114yes—
456C22×C4C24×C1112yes—
457C22×C4C24×C1112yes—
458C4⋊C4—24no—
459C4⋊C4—28no—
460C4⋊C4—44no—
461C4⋊C4—44no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—44no—
465C4⋊C4—44no—
466C4⋊C4—44no—
467C22⋊C4—28no—
468C22⋊C4—28no—
469C22⋊C4—28no—
470C22⋊C4—28no—
471C22⋊C4—28no—
472C22⋊C4—44no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—44no—
478C22⋊C4—44no—
479C22⋊C4—44no—
480C42—44no—
481C11#3672711yescharacteristic, direct product factor, Sylow
482C23—22no—
483C23—21no—
484C23—21no—
485C23—28no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—21no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—48no—
502C23—48no—
503C23—44no—
504C23—44no—
505C23C2×C11×#4112yes—
506C23C11×H(5,𝔽2)12yes—
507C23C11×H(5,𝔽2)14yes—
508C23C11×2−1+412yes—
509C23C25×C1111yescharacteristic
510D4—416no—
511D4—84no—
512D4—88no—
513D4—88no—
514D4—88no—
515C2×C4—28no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—44no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—84no—
539C2×C4—84no—
540C2×C4—88no—
541C2×C4C2×C11×#4114yes—
542C2×C4C11×H(5,𝔽2)14yes—
543C22—22no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—22no—
548C22—22no—
549C22—24no—
550C22—24no—
551C22—416no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—42no—
557C22—42no—
558C22—44no—
559C22—44no—
560C22—44no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22C11×#54014yes—
566C22C22×C11×#4111yescharacteristic
567C22C2×C11×H(5,𝔽2)12yes—
568C22C2×C11×H(5,𝔽2)12yes—
569C22C2×C11×H(5,𝔽2)11yescharacteristic
570C22C2×C11×2−1+411yescharacteristic
571C4—24no—
572C4—24no—
573C4—44no—
574C4—44no—
575C4—44no—
576C4—44no—
577C4—44no—
578C2—24no—
579C2—42no—
580C2—42no—
581C2—84no—
582C2C2×C11×#54011yescharacteristic
583C2C11×#349011yescharacteristic
584C2C11×#349211yescharacteristic
585C2C11×#353612yes—
586C2C11×#353712yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2847C2semidirect
2. C11×#2748C2semidirect
3. C11×#2741C2semidirect
4. C11×#2703C2semidirect
5. C11×#2671C2semidirect
6. C11×#2656C2semidirect
7. C11×#2646C2semidirect
8. C11×#2443C2semidirect
9. C11×#2424C2semidirect
10. C11×#2325C2semidirect
11. C2×C11×#380C2semidirect
13. C2×C11×#123C22semidirect
23. C11×#400C22semidirect
24. C11×#399C22semidirect
25. C11×#399C22semidirect
26. C11×#398C22semidirect
27. C11×#398C22semidirect
28. C11×#397C22semidirect
32. C11×#394C22semidirect
34. C11×#392C22semidirect
37. C11×#388C22semidirect
38. C11×#388C22semidirect
39. C11×#387C22semidirect
40. C11×#387C22semidirect
46. C11×#386C22semidirect
48. C11×#385C22semidirect
49. C11×#385C22semidirect
114. #36727C11direct (N × H)
189. #2847C2×C11semidirect
190. #2748C2×C11semidirect
191. #2741C2×C11semidirect
192. #2703C2×C11semidirect
193. #2671C2×C11semidirect
194. #2656C2×C11semidirect
195. #2646C2×C11semidirect
196. #2443C2×C11semidirect
197. #2424C2×C11semidirect
198. #2325C2×C11semidirect
199. C2×#380C2×C11semidirect
262. C2×#123C22×C11semidirect
272. #400C22×C11semidirect
273. #399C22×C11semidirect
274. #399C22×C11semidirect
275. #398C22×C11semidirect
276. #398C22×C11semidirect
277. #397C22×C11semidirect
281. #394C22×C11semidirect
283. #392C22×C11semidirect
286. #388C22×C11semidirect
287. #388C22×C11semidirect
288. #387C22×C11semidirect
289. #387C22×C11semidirect
295. #386C22×C11semidirect
297. #385C22×C11semidirect
298. #385C22×C11semidirect
481. C11#36727direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28472
C11×#27482
C11×#27412
C11×#27032
C11×#26712
C11×#26562
C11×#26462
C11×#24432
C11×#24242
C11×#23252
C2×C11×#3802
#3672711