Finite Group Databasebeta

← C11×#24142 #14601335

Subgroups — C11×#24142 #14601335

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3505C211yesmaximal, characteristic, complemented
2C11×#2626C211yesmaximal, characteristic, complemented
3C11×#2617C211yesmaximal, characteristic, complemented
4C11×#2321C211yesmaximal, characteristic, complemented
5C11×#2044C212yesmaximal, complemented
6C11×#2021C212yesmaximal, complemented
7C11×#1996C211yesmaximal, characteristic, complemented
8C11×#1964C211yesmaximal, characteristic, complemented
9C11×#1889C212yesmaximal, complemented
10C11×#1867C212yesmaximal, complemented
11C11×#1799C211yesmaximal, characteristic, complemented
12C11×#553—22no—
13C11×#553—21no—
14C11×#552—21no—
15C11×#551—22no—
16C11×#548—21no—
17C11×#546—21no—
18C11×#539—21no—
19C11×#538—21no—
20C11×#534C2212yes—
21C11×#529—21no—
22C11×#525—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120C2211yescharacteristic
26C2×C11×#120C2212yes—
27C11×#518C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C2×C11×#99C2212yes—
31C2×C11×#99C2212yes—
32C2×C11×#99C2212yes—
33C11×#399—21no—
34C11×#397—21no—
35C11×#396—22no—
36C11×#394—22no—
37C11×#393—21no—
38C11×#392—21no—
39C11×#390—21no—
40C11×#388—21no—
41C11×#388—21no—
42C11×#386—21no—
43C11×#386C2212yes—
44C11×#386C2211yescharacteristic
45C11×#385C2211yescharacteristic
46C11×#385C2212yes—
47C11×#380C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C11×#379C2211yescharacteristic
50C11×#379C2212yes—
51C4×C11×C22⋊C4C2211yescharacteristic
52C11×#342C2212yes—
53C11×#342C2212yes—
54C11×#342C2212yes—
55C25×C11C2311yescharacteristic
56C2×C11×#41—21no—
57C22×Q8×C11D411yescharacteristic, complemented
58C22×D4×C11—21no—
59C22×D4×C11—22no—
60C22×D4×C11D411yescharacteristic, complemented
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2312yes—
63C23×C4×C11D411yescharacteristic, complemented
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—22no—
69C11×#125—21no—
70C11×#125—22no—
71C11×#124—21no—
72C11×#124—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×#121—21no—
85C11×#121—22no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#120—22no—
93C11×#120—22no—
94C11×#120—22no—
95C11×#120—22no—
96C11×#120—24no—
97C11×#120—42no—
98C4×Q8×C11—21no—
99C4×D4×C11—22no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—22no—
109C11×#117—21no—
110C11×#117—22no—
111C11×#117—22no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4D411yescharacteristic, complemented
117C2×C11×C4⋊C4D411yescharacteristic, complemented
118C2×C11×C4⋊C4D412yescomplemented
119C2×C11×C4⋊C4D411yescharacteristic, complemented
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—22no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—22no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—22no—
135C2×C11×C22⋊C4D411yescharacteristic, complemented
136C2×C11×C22⋊C4D412yescomplemented
137C2×C11×C22⋊C4C2312yes—
138C2×C11×C22⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2311yescharacteristic
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C42×C11—21no—
144C2×C42×C11D411yescharacteristic, complemented
145C11×#99—24no—
146C11×#99—42no—
147C11×#99—42no—
148C11×#95—21no—
149C11×#95—21no—
150C11×#95—21no—
151C11×#95—21no—
152C11×#95—22no—
153C11×#95—21no—
154C11×#95—22no—
155#24142C1111yesmaximal, characteristic, direct product factor, Sylow
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—81no—
163C24×C11—81no—
164C24×C11C2×D412yes—
165C24×C11C2×D411yescharacteristic
166C24×C11#4112yescomplemented
167C24×C11C2411yescharacteristic
168C11×#41—82no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—81no—
172C2×D4×C11—21no—
173C2×D4×C11—22no—
174C2×D4×C11—21no—
175C2×D4×C11—22no—
176C2×D4×C11—22no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—22no—
180C2×D4×C11—21no—
181C2×D4×C11—22no—
182C2×D4×C11—21no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—24no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—44no—
190C2×D4×C11—81no—
191C2×D4×C11—81no—
192C2×D4×C11—81no—
193C2×D4×C11—82no—
194C2×D4×C11—82no—
195C22×C4×C11—21no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—81no—
207C22×C4×C11—81no—
208C22×C4×C11—81no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C11×C4⋊C4—22no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—81no—
234C11×C4⋊C4—81no—
235C11×C4⋊C4—81no—
236C11×C4⋊C4—82no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—21no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—22no—
253C11×C22⋊C4—22no—
254C11×C22⋊C4—22no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—44no—
260C11×C22⋊C4—41no—
261C11×C22⋊C4—41no—
262C11×C22⋊C4—41no—
263C11×C22⋊C4—41no—
264C11×C22⋊C4—81no—
265C11×C22⋊C4—82no—
266C11×C22⋊C4—81no—
267C11×C22⋊C4—82no—
268C11×C22⋊C4—81no—
269C11×C22⋊C4—82no—
270C11×C22⋊C4#4112yescomplemented
271C42×C11—22no—
272C42×C11—22no—
273C42×C11—21no—
274C42×C11—21no—
275C42×C11—81no—
276#3505C2×C1111yescharacteristic, complemented
277#2626C2×C1111yescharacteristic, complemented
278#2617C2×C1111yescharacteristic, complemented
279#2321C2×C1111yescharacteristic, complemented
280#2044C2×C1112yescomplemented
281#2021C2×C1112yescomplemented
282#1996C2×C1111yescharacteristic, complemented
283#1964C2×C1111yescharacteristic, complemented
284#1889C2×C1112yescomplemented
285#1867C2×C1112yescomplemented
286#1799C2×C1111yescharacteristic, complemented
287C23×C11—21no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—21no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—42no—
301C23×C11—41no—
302C23×C11—42no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—42no—
306C23×C11—41no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—82no—
315C23×C11—82no—
316C23×C11—82no—
317C23×C11—82no—
318C23×C11C22×D411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C22×D411yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C112−1+411yescharacteristic
325Q8×C11—42no—
326Q8×C11—81no—
327D4×C11—42no—
328D4×C11—42no—
329D4×C11—42no—
330D4×C11—41no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—42no—
334D4×C11—42no—
335D4×C11—41no—
336D4×C11—81no—
337D4×C11—82no—
338D4×C11—84no—
339D4×C11—82no—
340D4×C11—88no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—42no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—42no—
363C2×C4×C11—41no—
364C2×C4×C11—42no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—41no—
370C2×C4×C11—42no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—41no—
374C2×C4×C11—42no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—81no—
380C2×C4×C11—82no—
381C2×C4×C11—82no—
382C2×C4×C11#12011yescharacteristic
383C2×C4×C11#12011yescharacteristic
384C2×C4×C11#12011yescharacteristic
385C2×C4×C11#12011yescharacteristic
386#553—22no—
387#553—21no—
388#552—21no—
389#551—22no—
390#548—21no—
391#546—21no—
392#539—21no—
393#538—21no—
394#534C22×C1112yes—
395#529—21no—
396#525—21no—
397C2×C22⋊Q8C22×C1111yescharacteristic
398C2×#121C22×C1111yescharacteristic
399C2×#120C22×C1111yescharacteristic
400C2×#120C22×C1112yes—
401#518C22×C1112yes—
402C2×C4×D4C22×C1111yescharacteristic
403C22×C22⋊C4C22×C1111yescharacteristic
404C2×#99C22×C1112yes—
405C2×#99C22×C1112yes—
406C2×#99C22×C1112yes—
407#399—21no—
408#397—21no—
409#396—22no—
410#394—22no—
411#393—21no—
412#392—21no—
413#390—21no—
414#388—21no—
415#388—21no—
416#386—21no—
417#386C22×C1111yescharacteristic
418#386C22×C1112yes—
419#385C22×C1111yescharacteristic
420#385C22×C1112yes—
421#380C22×C1111yescharacteristic
422#380C22×C1111yescharacteristic
423#379C22×C1111yescharacteristic
424#379C22×C1112yes—
425C4×C22⋊C4C22×C1111yescharacteristic
426#342C22×C1112yes—
427#342C22×C1112yes—
428#342C22×C1112yes—
429C22×C11—21no—
430C22×C11—21no—
431C22×C11—21no—
432C22×C11—21no—
433C22×C11—21no—
434C22×C11—21no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—44no—
442C22×C11—42no—
443C22×C11—44no—
444C22×C11—41no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—41no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—82no—
452C22×C11—81no—
453C22×C11—82no—
454C22×C11—82no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—82no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11C2×#12011yescharacteristic
461C22×C11#52511yescharacteristic
462C22×C11#53711yescharacteristic
463C22×C11#54611yescharacteristic
464C22×C11#54711yescharacteristic
465C22×C11#54811yescharacteristic
466C22×C11#55011yescharacteristic
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11—21no—
471C4×C11—42no—
472C4×C11—41no—
473C4×C11—42no—
474C4×C11—41no—
475C4×C11—42no—
476C4×C11—41no—
477C4×C11—42no—
478C4×C11—82no—
479C4×C11—81no—
480C4×C11—82no—
481C4×C11—81no—
482C25C23×C1111yescharacteristic
483C2×#41—21no—
484C22×Q8D4×C1111yescharacteristic, complemented
485C22×D4—21no—
486C22×D4—22no—
487C22×D4D4×C1111yescharacteristic, complemented
488C22×D4C23×C1111yescharacteristic
489C22×D4C23×C1112yes—
490C23×C4D4×C1111yescharacteristic, complemented
491C23×C4C23×C1111yescharacteristic
492C23×C4C23×C1111yescharacteristic
493#126—22no—
494#126—22no—
495#126—22no—
496#125—21no—
497#125—22no—
498#124—21no—
499#124—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8—21no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511#121—21no—
512#121—22no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—22no—
518#121—22no—
519#120—22no—
520#120—22no—
521#120—22no—
522#120—22no—
523#120—24no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4D4×C1111yescharacteristic, complemented
544C2×C4⋊C4D4×C1111yescharacteristic, complemented
545C2×C4⋊C4D4×C1112yescomplemented
546C2×C4⋊C4D4×C1111yescharacteristic, complemented
547C2×C22⋊C4—22no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4D4×C1111yescharacteristic, complemented
563C2×C22⋊C4D4×C1112yescomplemented
564C2×C22⋊C4C23×C1112yes—
565C2×C22⋊C4C23×C1111yescharacteristic
566C2×C22⋊C4C23×C1112yes—
567C2×C22⋊C4C23×C1111yescharacteristic
568C2×C22⋊C4C23×C1112yes—
569C2×C22⋊C4C23×C1111yescharacteristic
570C2×C42—21no—
571C2×C42D4×C1111yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C2×C11—21no—
583C2×C11—21no—
584C2×C11—21no—
585C2×C11—21no—
586C2×C11—21no—
587C2×C11—21no—
588C2×C11—82no—
589C2×C11—81no—
590C2×C11—82no—
591C2×C11#240711yescharacteristic
592C2×C11#302611yescharacteristic
593C2×C11#302711yescharacteristic
594C24—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—81no—
601C24—81no—
602C24C2×D4×C1112yes—
603C24C2×D4×C1111yescharacteristic
604C24C11×#4112yescomplemented
605C24C24×C1111yescharacteristic
606#41—82no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—81no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—44no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—82no—
632C2×D4—82no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4C2×D4×C1111yescharacteristic
648C22×C4C2×D4×C1112yes—
649C22×C4C2×D4×C1111yescharacteristic
650C22×C4C2×D4×C1112yes—
651C22×C4C2×D4×C1111yescharacteristic
652C22×C4C2×D4×C1112yes—
653C22×C4C2×D4×C1111yescharacteristic
654C22×C4C2×D4×C1111yescharacteristic
655C22×C4C2×D4×C1111yescharacteristic
656C22×C4C2×D4×C1111yescharacteristic
657C22×C4C2×D4×C1111yescharacteristic
658C22×C4C2×D4×C1111yescharacteristic
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—82no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—21no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—22no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—21no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—21no—
697C22⋊C4—44no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—81no—
703C22⋊C4—82no—
704C22⋊C4—81no—
705C22⋊C4—82no—
706C22⋊C4—81no—
707C22⋊C4—82no—
708C22⋊C4C11×#4112yescomplemented
709C42—22no—
710C42—22no—
711C42—21no—
712C42—21no—
713C42—81no—
714C11#2414211yescharacteristic, direct product factor, Sylow
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C1111yescharacteristic
747C23C22×D4×C1111yescharacteristic
748C23C22×D4×C1111yescharacteristic
749C23C2×C11×#4111yescharacteristic
750C23C2×C11×#4111yescharacteristic
751C23C11×H(5,𝔽2)11yescharacteristic
752C23C11×2−1+411yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—82no—
766D4—84no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4C11×#12011yescharacteristic
811C2×C4C11×#12011yescharacteristic
812C2×C4C11×#12011yescharacteristic
813C2×C4C11×#12011yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×C11×#12011yescharacteristic
846C22C11×#52511yescharacteristic
847C22C11×#53711yescharacteristic
848C22C11×#54611yescharacteristic
849C22C11×#54711yescharacteristic
850C22C11×#54811yescharacteristic
851C22C11×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C11×#240711yescharacteristic
877C2C11×#302611yescharacteristic
878C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3505C2semidirect
2. C11×#2626C2semidirect
3. C11×#2617C2semidirect
4. C11×#2321C2semidirect
5. C11×#2044C2semidirect
6. C11×#2021C2semidirect
7. C11×#1996C2semidirect
8. C11×#1964C2semidirect
9. C11×#1889C2semidirect
10. C11×#1867C2semidirect
11. C11×#1799C2semidirect
57. C22×Q8×C11D4semidirect
60. C22×D4×C11D4semidirect
63. C23×C4×C11D4semidirect
116. C2×C11×C4⋊C4D4semidirect
117. C2×C11×C4⋊C4D4semidirect
118. C2×C11×C4⋊C4D4semidirect
119. C2×C11×C4⋊C4D4semidirect
135. C2×C11×C22⋊C4D4semidirect
136. C2×C11×C22⋊C4D4semidirect
144. C2×C42×C11D4semidirect
155. #24142C11direct (N × H)
166. C24×C11#41semidirect
270. C11×C22⋊C4#41semidirect
276. #3505C2×C11semidirect
277. #2626C2×C11semidirect
278. #2617C2×C11semidirect
279. #2321C2×C11semidirect
280. #2044C2×C11semidirect
281. #2021C2×C11semidirect
282. #1996C2×C11semidirect
283. #1964C2×C11semidirect
284. #1889C2×C11semidirect
285. #1867C2×C11semidirect
286. #1799C2×C11semidirect
484. C22×Q8D4×C11semidirect
487. C22×D4D4×C11semidirect
490. C23×C4D4×C11semidirect
543. C2×C4⋊C4D4×C11semidirect
544. C2×C4⋊C4D4×C11semidirect
545. C2×C4⋊C4D4×C11semidirect
546. C2×C4⋊C4D4×C11semidirect
562. C2×C22⋊C4D4×C11semidirect
563. C2×C22⋊C4D4×C11semidirect
571. C2×C42D4×C11semidirect
604. C24C11×#41semidirect
708. C22⋊C4C11×#41semidirect
714. C11#24142direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35052
C11×#26262
C11×#26172
C11×#23212
C11×#20442
C11×#20212
C11×#19962
C11×#19642
C11×#18892
C11×#18672
C11×#17992
#2414211