Finite Group Databasebeta

← C11×#23959 #14601152

Subgroups — C11×#23959 #14601152

Order 2816.

1192 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3495C211yesmaximal, characteristic, complemented
2C11×#3005C211yesmaximal, characteristic
3C11×#2896C211yesmaximal, characteristic, complemented
4C11×#2432C211yesmaximal, characteristic, complemented
5C11×#2028C211yesmaximal, characteristic, complemented
6C11×#2027C211yesmaximal, characteristic, complemented
7C11×#2005C211yesmaximal, characteristic, complemented
8C11×#2003C211yesmaximal, characteristic, complemented
9C11×#1901C211yesmaximal, characteristic, complemented
10C11×#1888C211yesmaximal, characteristic, complemented
11C11×#1886C211yesmaximal, characteristic, complemented
12C11×#1883C211yesmaximal, characteristic, complemented
13C11×#1882C211yesmaximal, characteristic, complemented
14C11×#1871C211yesmaximal, characteristic, complemented
15C11×#1826C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×#137C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C11×#556—21no—
21C11×#554—21no—
22C11×#552—21no—
23C11×#552—22no—
24C11×#552—21no—
25C11×#551—22no—
26C11×#544C2211yescharacteristic
27C11×#542—21no—
28C11×#541—21no—
29C11×#536C2211yescharacteristic
30C11×#533—21no—
31C2×C11×C4⋊Q8C2211yescharacteristic
32C11×#529—21no—
33C2×C11×#124C2211yescharacteristic
34C11×#525C2211yescharacteristic
35C2×C11×C22⋊Q8C2211yescharacteristic
36C11×#520C2211yescharacteristic
37C11×#519C2211yescharacteristic
38C2×C11×#117C2211yescharacteristic
39C11×#452—21no—
40C11×#452—21no—
41C11×#449—21no—
42C11×#449—21no—
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C11×#419C2211yescharacteristic
46C11×#419C2211yescharacteristic
47C11×#419C2211yescharacteristic
48C11×#418C2211yescharacteristic
49C11×#418C2211yescharacteristic
50C11×#418C2211yescharacteristic
51C11×#417—21no—
52C11×#417—21no—
53C11×#416—21no—
54C11×#416—21no—
55C2×C11×#101C2211yescharacteristic
56C2×C11×#101C2211yescharacteristic
57C11×#407C2211yescharacteristic
58C11×#394—22no—
59C11×#391C2211yescharacteristic
60C11×#390C2211yescharacteristic
61C11×#385—22no—
62C4×C11×C22⋊C4C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—21no—
74C2×C11×#41—21no—
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41—41no—
78C2×C11×#41—41no—
79C2×C11×#41C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C11×#137—22no—
87C11×#137—41no—
88C11×AGL(1,ℤ/8)—22no—
89C11×AGL(1,ℤ/8)—41no—
90C2×C11×Q16—21no—
91C2×C11×SD16—21no—
92C2×C11×SD16—21no—
93C2×C11×D8—21no—
94C2×C11×M16—21no—
95C2×C11×M16—41no—
96C2×C11×M16—41no—
97C2×C11×M16C2311yescharacteristic
98C2×C11×M16C2311yescharacteristic
99C2×C11×M16C2311yescharacteristic
100C2×C11×M16C2311yescharacteristic
101C22×C8×C11—21no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8—41no—
107C11×#126—22no—
108C11×#126—22no—
109C11×#126—22no—
110C11×#126—22no—
111C11×#125—22no—
112C11×#125—22no—
113C11×#125—22no—
114C11×#125—21no—
115C11×#125—21no—
116C11×#124—22no—
117C11×#124—21no—
118C11×#124—22no—
119C11×#124—41no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—21no—
123C11×#123—22no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—21no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8—22no—
131C11×C22⋊Q8—21no—
132C11×C22⋊Q8—21no—
133C11×C22⋊Q8D411yescharacteristic
134C11×C22⋊Q8D411yescharacteristic
135C11×#121D411yescharacteristic
136C11×#121D411yescharacteristic
137C11×#120—21no—
138C4×Q8×C11—22no—
139C4×Q8×C11—21no—
140C4×Q8×C11—21no—
141C4×Q8×C11—21no—
142C4×Q8×C11—21no—
143C4×Q8×C11—21no—
144C4×D4×C11—22no—
145C4×D4×C11—21no—
146C4×D4×C11—22no—
147C4×D4×C11—21no—
148C4×D4×C11—21no—
149C11×#117—22no—
150C11×#117—22no—
151C11×#117—21no—
152C11×#117—21no—
153C11×#117—22no—
154C11×#117—21no—
155C11×#117D411yescharacteristic
156C11×#117D411yescharacteristic
157C11×#117C2311yescharacteristic
158C11×#117C2311yescharacteristic
159C11×#117C2311yescharacteristic
160C2×C11×C4⋊C4—21no—
161C2×C11×C4⋊C4—22no—
162C2×C11×C4⋊C4D412yes—
163C2×C11×C4⋊C4D411yescharacteristic
164C2×C11×C4⋊C4D411yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4—21no—
167C2×C11×C22⋊C4—21no—
168C2×C11×C22⋊C4—22no—
169C2×C11×C22⋊C4—22no—
170C2×C11×C22⋊C4D412yes—
171C2×C42×C11—21no—
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C11×#104—41no—
175C11×#104—41no—
176C11×#103—21no—
177C11×#103—21no—
178C11×#103—21no—
179C11×#103—21no—
180C11×#103—21no—
181C11×#103—21no—
182C11×#102—21no—
183C11×#102—21no—
184C11×#102—21no—
185C11×#102—21no—
186C11×#102—21no—
187C11×#102—21no—
188C11×#101—41no—
189C11×#101—41no—
190C11×C22⋊C8—21no—
191C11×C22⋊C8—21no—
192C11×#95—21no—
193C11×#95—22no—
194#23959C1111yesmaximal, characteristic, direct product factor, Sylow
195C24×C11—21no—
196C24×C11C2×D411yescharacteristic
197C11×#41—24no—
198C11×#41—24no—
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—42no—
204C11×#41—42no—
205C11×#41—42no—
206C11×#41—42no—
207C11×#41—42no—
208C11×#41—42no—
209C2×Q8×C11—22no—
210C2×Q8×C11—21no—
211C2×Q8×C11—21no—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—21no—
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—21no—
218C2×Q8×C11—21no—
219C2×Q8×C11—21no—
220C2×Q8×C11—21no—
221C2×Q8×C11C2×D411yescharacteristic
222C2×Q8×C11#4112yes—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—42no—
232C2×D4×C11—42no—
233C2×D4×C11—41no—
234C2×D4×C11—41no—
235C2×D4×C11C2×D411yescharacteristic
236C2×D4×C11#4112yes—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—22no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—42no—
249C22×C4×C11—42no—
250C22×C4×C11—41no—
251C22×C4×C11—41no—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2411yescharacteristic
260C11×Q16—42no—
261C11×SD16—42no—
262C11×SD16—42no—
263C11×D8—42no—
264C11×M16—21no—
265C11×M16—21no—
266C11×M16—21no—
267C11×M16—21no—
268C11×M16—21no—
269C11×M16—21no—
270C11×M16—21no—
271C11×M16—21no—
272C11×M16—42no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—42no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—44no—
295C11×C4⋊C4C2×D411yescharacteristic
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D411yescharacteristic
299C11×C4⋊C4C2×D411yescharacteristic
300C11×C4⋊C4C2×D411yescharacteristic
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—44no—
316C11×C22⋊C4—44no—
317C11×C22⋊C4—42no—
318C42×C11—22no—
319C42×C11—22no—
320C42×C11—22no—
321C42×C11—21no—
322C42×C11—21no—
323C42×C11—21no—
324C42×C11—21no—
325C42×C11—21no—
326C42×C11—21no—
327C42×C11—21no—
328C42×C11—21no—
329C42×C11—21no—
330#3495C2×C1111yescharacteristic, complemented
331#3005C2×C1111yescharacteristic
332#2896C2×C1111yescharacteristic, complemented
333#2432C2×C1111yescharacteristic, complemented
334#2028C2×C1111yescharacteristic, complemented
335#2027C2×C1111yescharacteristic, complemented
336#2005C2×C1111yescharacteristic, complemented
337#2003C2×C1111yescharacteristic, complemented
338#1901C2×C1111yescharacteristic, complemented
339#1888C2×C1111yescharacteristic, complemented
340#1886C2×C1111yescharacteristic, complemented
341#1883C2×C1111yescharacteristic, complemented
342#1882C2×C1111yescharacteristic, complemented
343#1871C2×C1111yescharacteristic, complemented
344#1826C2×C1111yescharacteristic, complemented
345C23×C11—21no—
346C23×C11—21no—
347C23×C11—21no—
348C23×C11—22no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11#12011yescharacteristic
356C23×C11#12011yescharacteristic
357C23×C11C22×D411yescharacteristic
358Q8×C11—22no—
359Q8×C11—21no—
360Q8×C11—22no—
361Q8×C11—21no—
362Q8×C11—41no—
363Q8×C11—41no—
364Q8×C11—41no—
365Q8×C11—41no—
366Q8×C11—41no—
367Q8×C11—41no—
368Q8×C11—82no—
369D4×C11—22no—
370D4×C11—21no—
371D4×C11—22no—
372D4×C11—21no—
373D4×C11—42no—
374D4×C11—44no—
375D4×C11—44no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—41no—
379D4×C11—41no—
380D4×C11—81no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11—41no—
407C2×C4×C11—42no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—42no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—81no—
418C2×C4×C11—82no—
419C2×C4×C11#12011yescharacteristic
420C2×C4×C11#12011yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C2×#4111yescharacteristic
424C2×C4×C11C2×#4111yescharacteristic
425C2×C4×C11H(5,𝔽2)11yescharacteristic
426C2×C4×C11H(5,𝔽2)11yescharacteristic
427C8×C11—41no—
428C8×C11—41no—
429C8×C11—41no—
430C8×C11—41no—
431C22×#41C22×C1111yescharacteristic
432C2×#137C22×C1111yescharacteristic
433C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
434C22×M16C22×C1111yescharacteristic
435#556—21no—
436#554—21no—
437#552—21no—
438#552—22no—
439#552—21no—
440#551—22no—
441#544C22×C1111yescharacteristic
442#542—21no—
443#541—21no—
444#536C22×C1111yescharacteristic
445#533—21no—
446C2×C4⋊Q8C22×C1111yescharacteristic
447#529—21no—
448C2×#124C22×C1111yescharacteristic
449#525C22×C1111yescharacteristic
450C2×C22⋊Q8C22×C1111yescharacteristic
451#520C22×C1111yescharacteristic
452#519C22×C1111yescharacteristic
453C2×#117C22×C1111yescharacteristic
454#452—21no—
455#452—21no—
456#449—21no—
457#449—21no—
458C2×#104C22×C1111yescharacteristic
459C2×#104C22×C1111yescharacteristic
460#419C22×C1111yescharacteristic
461#419C22×C1111yescharacteristic
462#419C22×C1111yescharacteristic
463#418C22×C1111yescharacteristic
464#418C22×C1111yescharacteristic
465#418C22×C1111yescharacteristic
466#417—21no—
467#417—21no—
468#416—21no—
469#416—21no—
470C2×#101C22×C1111yescharacteristic
471C2×#101C22×C1111yescharacteristic
472#407C22×C1111yescharacteristic
473#394—22no—
474#391C22×C1111yescharacteristic
475#390C22×C1111yescharacteristic
476#385—22no—
477C4×C22⋊C4C22×C1111yescharacteristic
478#343C22×C1111yescharacteristic
479#343C22×C1111yescharacteristic
480#339C22×C1111yescharacteristic
481#339C22×C1111yescharacteristic
482#339C22×C1111yescharacteristic
483#339C22×C1111yescharacteristic
484#339C22×C1111yescharacteristic
485#339C22×C1111yescharacteristic
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—44no—
495C22×C11—42no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—82no—
502C22×C11—81no—
503C22×C11—81no—
504C22×C11C2×#12011yescharacteristic
505C22×C11#54611yescharacteristic
506C22×C11#54611yescharacteristic
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—41no—
513C4×C11—42no—
514C4×C11—41no—
515C4×C11—41no—
516C4×C11—41no—
517C4×C11—41no—
518C4×C11—41no—
519C4×C11—41no—
520C4×C11—81no—
521C4×C11#52511yescharacteristic
522C4×C11#53511yescharacteristic
523C4×C11#54611yescharacteristic
524C4×C11#54611yescharacteristic
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41C23×C1111yescharacteristic
534C22×Q8C23×C1111yescharacteristic
535C22×Q8C23×C1111yescharacteristic
536C22×D4—21no—
537C22×D4C23×C1111yescharacteristic
538C23×C4—21no—
539C23×C4C23×C1111yescharacteristic
540#137—22no—
541#137—41no—
542AGL(1,ℤ/8)—22no—
543AGL(1,ℤ/8)—41no—
544C2×Q16—21no—
545C2×SD16—21no—
546C2×SD16—21no—
547C2×D8—21no—
548C2×M16—21no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16C23×C1111yescharacteristic
552C2×M16C23×C1111yescharacteristic
553C2×M16C23×C1111yescharacteristic
554C2×M16C23×C1111yescharacteristic
555C22×C8—21no—
556C4⋊Q8—21no—
557C4⋊Q8—21no—
558C4⋊Q8—21no—
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561#126—22no—
562#126—22no—
563#126—22no—
564#126—22no—
565#125—22no—
566#125—22no—
567#125—22no—
568#125—21no—
569#125—21no—
570#124—22no—
571#124—21no—
572#124—22no—
573#124—41no—
574#123—22no—
575#123—22no—
576#123—21no—
577#123—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—22no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8D4×C1111yescharacteristic
588C22⋊Q8D4×C1111yescharacteristic
589#121D4×C1111yescharacteristic
590#121D4×C1111yescharacteristic
591#120—21no—
592C4×Q8—22no—
593C4×Q8—21no—
594C4×Q8—21no—
595C4×Q8—21no—
596C4×Q8—21no—
597C4×Q8—21no—
598C4×D4—22no—
599C4×D4—21no—
600C4×D4—22no—
601C4×D4—21no—
602C4×D4—21no—
603#117—22no—
604#117—22no—
605#117—21no—
606#117—21no—
607#117—22no—
608#117—21no—
609#117D4×C1111yescharacteristic
610#117D4×C1111yescharacteristic
611#117C23×C1111yescharacteristic
612#117C23×C1111yescharacteristic
613#117C23×C1111yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4D4×C1112yes—
617C2×C4⋊C4D4×C1111yescharacteristic
618C2×C4⋊C4D4×C1111yescharacteristic
619C2×C4⋊C4C23×C1111yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4D4×C1112yes—
625C2×C42—21no—
626C2×C42C23×C1111yescharacteristic
627C2×C42C23×C1111yescharacteristic
628#104—41no—
629#104—41no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#101—41no—
643#101—41no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646#95—21no—
647#95—22no—
648C2×C11—21no—
649C2×C11—21no—
650C2×C11—41no—
651C2×C11—41no—
652C2×C11—81no—
653C2×C11—82no—
654C2×C11#240411yescharacteristic
655C2×C11#301811yescharacteristic
656C2×C11#302011yescharacteristic
657C24—21no—
658C24C2×D4×C1111yescharacteristic
659#41—24no—
660#41—24no—
661#41—21no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—42no—
666#41—42no—
667#41—42no—
668#41—42no—
669#41—42no—
670#41—42no—
671C2×Q8—22no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8C2×D4×C1111yescharacteristic
684C2×Q8C11×#4112yes—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4C2×D4×C1111yescharacteristic
698C2×D4C11×#4112yes—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4C2×D4×C1112yes—
715C22×C4C2×D4×C1111yescharacteristic
716C22×C4C2×D4×C1111yescharacteristic
717C22×C4C2×D4×C1111yescharacteristic
718C22×C4C2×D4×C1111yescharacteristic
719C22×C4C2×D4×C1111yescharacteristic
720C22×C4C2×D4×C1112yes—
721C22×C4C24×C1111yescharacteristic
722Q16—42no—
723SD16—42no—
724SD16—42no—
725D8—42no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—42no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—42no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—44no—
757C4⋊C4C2×D4×C1111yescharacteristic
758C4⋊C4C2×D4×C1111yescharacteristic
759C4⋊C4C2×D4×C1111yescharacteristic
760C4⋊C4C2×D4×C1111yescharacteristic
761C4⋊C4C2×D4×C1111yescharacteristic
762C4⋊C4C2×D4×C1111yescharacteristic
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—42no—
780C42—22no—
781C42—22no—
782C42—22no—
783C42—21no—
784C42—21no—
785C42—21no—
786C42—21no—
787C42—21no—
788C42—21no—
789C42—21no—
790C42—21no—
791C42—21no—
792C11#2395911yescharacteristic, direct product factor, Sylow
793C23—21no—
794C23—21no—
795C23—21no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—42no—
800C23—42no—
801C23—41no—
802C23—41no—
803C23C11×#12011yescharacteristic
804C23C11×#12011yescharacteristic
805C23C22×D4×C1111yescharacteristic
806Q8—22no—
807Q8—21no—
808Q8—22no—
809Q8—21no—
810Q8—41no—
811Q8—41no—
812Q8—41no—
813Q8—41no—
814Q8—41no—
815Q8—41no—
816Q8—82no—
817D4—22no—
818D4—21no—
819D4—22no—
820D4—21no—
821D4—42no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—81no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—81no—
866C2×C4—82no—
867C2×C4C11×#12011yescharacteristic
868C2×C4C11×#12011yescharacteristic
869C2×C4C22×D4×C1111yescharacteristic
870C2×C4C22×D4×C1111yescharacteristic
871C2×C4C2×C11×#4111yescharacteristic
872C2×C4C2×C11×#4111yescharacteristic
873C2×C4C11×H(5,𝔽2)11yescharacteristic
874C2×C4C11×H(5,𝔽2)11yescharacteristic
875C8—41no—
876C8—41no—
877C8—41no—
878C8—41no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—44no—
888C22—42no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—81no—
893C22—81no—
894C22—82no—
895C22—81no—
896C22—81no—
897C22C2×C11×#12011yescharacteristic
898C22C11×#54611yescharacteristic
899C22C11×#54611yescharacteristic
900C4—21no—
901C4—21no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—41no—
906C4—42no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—81no—
914C4C11×#52511yescharacteristic
915C4C11×#53511yescharacteristic
916C4C11×#54611yescharacteristic
917C4C11×#54611yescharacteristic
918C2—21no—
919C2—21no—
920C2—41no—
921C2—41no—
922C2—82no—
923C2—81no—
924C2C11×#240411yescharacteristic
925C2C11×#301811yescharacteristic
926C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3005C2
LCSG ▷ C22×C4 ▷ 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×#3495C2semidirect
3. C11×#2896C2semidirect
4. C11×#2432C2semidirect
5. C11×#2028C2semidirect
6. C11×#2027C2semidirect
7. C11×#2005C2semidirect
8. C11×#2003C2semidirect
9. C11×#1901C2semidirect
10. C11×#1888C2semidirect
11. C11×#1886C2semidirect
12. C11×#1883C2semidirect
13. C11×#1882C2semidirect
14. C11×#1871C2semidirect
15. C11×#1826C2semidirect
194. #23959C11direct (N × H)
330. #3495C2×C11semidirect
332. #2896C2×C11semidirect
333. #2432C2×C11semidirect
334. #2028C2×C11semidirect
335. #2027C2×C11semidirect
336. #2005C2×C11semidirect
337. #2003C2×C11semidirect
338. #1901C2×C11semidirect
339. #1888C2×C11semidirect
340. #1886C2×C11semidirect
341. #1883C2×C11semidirect
342. #1882C2×C11semidirect
343. #1871C2×C11semidirect
344. #1826C2×C11semidirect
792. C11#23959direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34952
C11×#30052
C11×#28962
C11×#24322
C11×#20282
C11×#20272
C11×#20052
C11×#20032
C11×#19012
C11×#18882
C11×#18862
C11×#18832
C11×#18822
C11×#18712
C11×#18262
#2395911