Finite Group Databasebeta

← C11×#24031 #14601224

Subgroups — C11×#24031 #14601224

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3488C211yesmaximal, characteristic
2C11×#3093C211yesmaximal, characteristic, complemented
3C11×#2896C211yesmaximal, characteristic, complemented
4C11×#2500C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#2039C211yesmaximal, characteristic, complemented
7C11×#2037C211yesmaximal, characteristic, complemented
8C11×#2037C211yesmaximal, characteristic, complemented
9C11×#1900C211yesmaximal, characteristic, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1860C211yesmaximal, characteristic, complemented
12C11×#1859C211yesmaximal, characteristic, complemented
13C11×#1792C211yesmaximal, characteristic, complemented
14C11×#1792C211yesmaximal, characteristic, complemented
15C11×#1789C211yesmaximal, characteristic, complemented
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C11×#550—21no—
20C11×#548—21no—
21C11×#546—21no—
22C11×#546—22no—
23D42×C11—22no—
24D42×C11—21no—
25C11×#537—21no—
26C11×#537C2211yescharacteristic
27C11×#535—21no—
28C11×#535C2211yescharacteristic
29C11×#525—21no—
30C11×#525C2211yescharacteristic
31C2×C11×#121—21no—
32C2×C11×#121C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic, complemented
35C11×#485—21no—
36C11×#485—21no—
37C11×#482—21no—
38C11×#482—21no—
39C11×#428C2211yescharacteristic, complemented
40C11×#428C2211yescharacteristic, complemented
41C2×C11×#104C2211yescharacteristic
42C2×C11×#104C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic, complemented
44C2×C11×#104C2211yescharacteristic, complemented
45C2×C11×#104C2211yescharacteristic, complemented
46C2×C11×#104C2211yescharacteristic, complemented
47C11×#419—21no—
48C11×#418—21no—
49C11×#417C2211yescharacteristic
50C11×#417C2211yescharacteristic
51C11×#417C2211yescharacteristic, complemented
52C11×#417C2211yescharacteristic, complemented
53C11×#417C2211yescharacteristic, complemented
54C11×#417C2211yescharacteristic, complemented
55C11×#416—21no—
56C11×#416—21no—
57C2×C11×#100C2211yescharacteristic, complemented
58C2×C11×#100C2211yescharacteristic, complemented
59C11×#407C2211yescharacteristic, complemented
60C11×#394—22no—
61C11×#390C2211yescharacteristic, complemented
62C11×#390C2211yescharacteristic, complemented
63C11×#388—22no—
64C11×#384C2211yescharacteristic, complemented
65C11×#382C2211yescharacteristic, complemented
66C4×C11×C22⋊C4C2211yescharacteristic, complemented
67C11×#343C2211yescharacteristic, complemented
68C11×#343C2211yescharacteristic, complemented
69C11×#339C2211yescharacteristic, complemented
70C11×#339C2211yescharacteristic, complemented
71C11×H(5,𝔽2)—22no—
72C11×H(5,𝔽2)—22no—
73C11×H(5,𝔽2)—41no—
74C11×H(5,𝔽2)—41no—
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—22no—
80C2×C11×#41—22no—
81C2×C11×#41—41no—
82C2×C11×#41—41no—
83C2×C11×#41D411yescharacteristic
84C2×C11×#41D411yescharacteristic
85C2×C11×#41C2311yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C22×Q8×C11D411yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—22no—
91C22×D4×C11—22no—
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11D411yescharacteristic
95C22×D4×C11D412yes—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C2×C11×M16—21no—
100C2×C11×M16—41no—
101C2×C11×M16—41no—
102C2×C11×M16C2311yescharacteristic
103C2×C11×M16C2311yescharacteristic
104C2×C11×M16C2311yescharacteristic
105C2×C11×M16C2311yescharacteristic
106C22×C8×C11—21no—
107C11×#127—22no—
108C11×#127—21no—
109C11×#124—22no—
110C11×#124—21no—
111C11×#123—22no—
112C11×#123—21no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8D411yescharacteristic
117C11×C22⋊Q8D411yescharacteristic
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121—21no—
132C11×#121D411yescharacteristic
133C11×#121D411yescharacteristic
134C11×#120—22no—
135C11×#120—22no—
136C11×#120—22no—
137C11×#120—21no—
138C11×#120—22no—
139C4×Q8×C11—21no—
140C4×D4×C11—22no—
141C4×D4×C11—22no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117—21no—
149C11×#117—21no—
150C11×#117—21no—
151C11×#117C2311yescharacteristic
152C2×C11×C4⋊C4—21no—
153C2×C11×C4⋊C4—22no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—22no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—22no—
161C2×C11×C22⋊C4—22no—
162C2×C11×C22⋊C4D412yes—
163C2×C42×C11—21no—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C11×#107—21no—
167C11×#107—21no—
168C11×#106—21no—
169C11×#106—21no—
170C11×#104—22no—
171C11×#104—22no—
172C11×#104—41no—
173C11×#104—41no—
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×#100—41no—
189C11×#100—41no—
190C11×C22⋊C8—21no—
191C11×C22⋊C8—21no—
192C11×#95—21no—
193C11×#95—22no—
194#24031C1111yesmaximal, characteristic, direct product factor, Sylow
195C24×C11—22no—
196C24×C11—21no—
197C24×C11C2×D412yes—
198C24×C11C2×D411yescharacteristic
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—22no—
202C11×#41—22no—
203C11×#41—21no—
204C11×#41—21no—
205C11×#41—21no—
206C11×#41—21no—
207C11×#41—21no—
208C11×#41—21no—
209C11×#41—21no—
210C11×#41—21no—
211C11×#41—42no—
212C11×#41—42no—
213C11×#41—41no—
214C11×#41—41no—
215C11×#41—42no—
216C11×#41—42no—
217C11×#41—42no—
218C11×#41—42no—
219C11×#41—42no—
220C11×#41—42no—
221C11×#41#4112yes—
222C11×#41#4112yes—
223C2×Q8×C11—21no—
224C2×Q8×C11—22no—
225C2×Q8×C11—41no—
226C2×Q8×C11C2×D411yescharacteristic
227C2×Q8×C11C2×D411yescharacteristic
228C2×Q8×C11C2×D411yescharacteristic
229C2×D4×C11—21no—
230C2×D4×C11—22no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11—21no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—41no—
252C2×D4×C11—42no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11—42no—
256C2×D4×C11—44no—
257C2×D4×C11—44no—
258C2×D4×C11—42no—
259C2×D4×C11—42no—
260C2×D4×C11—82no—
261C2×D4×C11—84no—
262C2×D4×C11C2×D411yescharacteristic
263C2×D4×C11C2×D411yescharacteristic
264C2×D4×C11C2×D411yescharacteristic
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—22no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—22no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D412yes—
289C22×C4×C11C2411yescharacteristic
290C11×M16—21no—
291C11×M16—21no—
292C11×M16—21no—
293C11×M16—21no—
294C11×M16—21no—
295C11×M16—21no—
296C11×M16—21no—
297C11×M16—21no—
298C11×M16—42no—
299C2×C8×C11—21no—
300C2×C8×C11—21no—
301C2×C8×C11—21no—
302C2×C8×C11—21no—
303C2×C8×C11—42no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4—21no—
310C11×C4⋊C4—21no—
311C11×C4⋊C4—21no—
312C11×C4⋊C4—21no—
313C11×C4⋊C4—21no—
314C11×C4⋊C4—82no—
315C11×C4⋊C4C2×D411yescharacteristic
316C11×C4⋊C4C2×D411yescharacteristic
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—21no—
323C11×C22⋊C4—21no—
324C11×C22⋊C4—21no—
325C11×C22⋊C4—21no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—22no—
328C11×C22⋊C4—21no—
329C11×C22⋊C4—42no—
330C11×C22⋊C4—44no—
331C11×C22⋊C4—41no—
332C11×C22⋊C4—41no—
333C11×C22⋊C4—82no—
334C42×C11—22no—
335C42×C11—21no—
336C42×C11—21no—
337C42×C11—21no—
338C42×C11—21no—
339C42×C11—21no—
340C42×C11—41no—
341C42×C11—41no—
342#3488C2×C1111yescharacteristic
343#3093C2×C1111yescharacteristic, complemented
344#2896C2×C1111yescharacteristic, complemented
345#2500C2×C1111yescharacteristic, complemented
346#2040C2×C1111yescharacteristic, complemented
347#2039C2×C1111yescharacteristic, complemented
348#2037C2×C1111yescharacteristic, complemented
349#2037C2×C1111yescharacteristic, complemented
350#1900C2×C1111yescharacteristic, complemented
351#1871C2×C1111yescharacteristic, complemented
352#1860C2×C1111yescharacteristic, complemented
353#1859C2×C1111yescharacteristic, complemented
354#1792C2×C1111yescharacteristic, complemented
355#1792C2×C1111yescharacteristic, complemented
356#1789C2×C1111yescharacteristic, complemented
357C23×C11—21no—
358C23×C11—21no—
359C23×C11—21no—
360C23×C11—22no—
361C23×C11—21no—
362C23×C11—21no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—42no—
368C23×C11—42no—
369C23×C11—44no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—81no—
373C23×C11—82no—
374C23×C11—82no—
375C23×C11#12011yescharacteristic
376C23×C11#12011yescharacteristic
377C23×C11C22×D411yescharacteristic
378Q8×C11—21no—
379Q8×C11—21no—
380Q8×C11—21no—
381Q8×C11—21no—
382Q8×C11—21no—
383Q8×C11—42no—
384Q8×C11#12312yes—
385D4×C11—22no—
386D4×C11—22no—
387D4×C11—21no—
388D4×C11—21no—
389D4×C11—21no—
390D4×C11—21no—
391D4×C11—21no—
392D4×C11—42no—
393D4×C11—42no—
394D4×C11—44no—
395D4×C11—42no—
396D4×C11—44no—
397D4×C11—44no—
398D4×C11—42no—
399D4×C11—41no—
400D4×C11—41no—
401D4×C11—41no—
402D4×C11—41no—
403D4×C11—41no—
404D4×C11—41no—
405D4×C11—41no—
406D4×C11—41no—
407D4×C11—81no—
408D4×C11—82no—
409D4×C11—82no—
410D4×C11—82no—
411D4×C11—82no—
412D4×C11#12312yes—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—22no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—42no—
433C2×C4×C11—42no—
434C2×C4×C11—42no—
435C2×C4×C11—44no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—42no—
443C2×C4×C11—41no—
444C2×C4×C11—42no—
445C2×C4×C11—41no—
446C2×C4×C11—42no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—82no—
451C2×C4×C11#12011yescharacteristic
452C2×C4×C11#12011yescharacteristic
453C2×C4×C11C22×D411yescharacteristic
454C2×C4×C11C22×D411yescharacteristic
455C2×C4×C11C2×#4111yescharacteristic
456C2×C4×C11C2×#4111yescharacteristic
457C2×C4×C11H(5,𝔽2)11yescharacteristic
458C2×C4×C11H(5,𝔽2)11yescharacteristic
459C8×C11—41no—
460C8×C11—41no—
461C8×C11—41no—
462C8×C11—41no—
463C2×H(5,𝔽2)C22×C1111yescharacteristic
464C22×#41C22×C1111yescharacteristic
465C22×M16C22×C1111yescharacteristic, complemented
466#550—21no—
467#548—21no—
468#546—21no—
469#546—22no—
470D42—22no—
471D42—21no—
472#537—21no—
473#537C22×C1111yescharacteristic
474#535—21no—
475#535C22×C1111yescharacteristic
476#525—21no—
477#525C22×C1111yescharacteristic
478C2×#121—21no—
479C2×#121C22×C1111yescharacteristic
480#520C22×C1111yescharacteristic
481C2×#117C22×C1111yescharacteristic, complemented
482#485—21no—
483#485—21no—
484#482—21no—
485#482—21no—
486#428C22×C1111yescharacteristic, complemented
487#428C22×C1111yescharacteristic, complemented
488C2×#104C22×C1111yescharacteristic
489C2×#104C22×C1111yescharacteristic
490C2×#104C22×C1111yescharacteristic, complemented
491C2×#104C22×C1111yescharacteristic, complemented
492C2×#104C22×C1111yescharacteristic, complemented
493C2×#104C22×C1111yescharacteristic, complemented
494#419—21no—
495#418—21no—
496#417C22×C1111yescharacteristic
497#417C22×C1111yescharacteristic
498#417C22×C1111yescharacteristic, complemented
499#417C22×C1111yescharacteristic, complemented
500#417C22×C1111yescharacteristic, complemented
501#417C22×C1111yescharacteristic, complemented
502#416—21no—
503#416—21no—
504C2×#100C22×C1111yescharacteristic, complemented
505C2×#100C22×C1111yescharacteristic, complemented
506#407C22×C1111yescharacteristic, complemented
507#394—22no—
508#390C22×C1111yescharacteristic, complemented
509#390C22×C1111yescharacteristic, complemented
510#388—22no—
511#384C22×C1111yescharacteristic, complemented
512#382C22×C1111yescharacteristic, complemented
513C4×C22⋊C4C22×C1111yescharacteristic, complemented
514#343C22×C1111yescharacteristic, complemented
515#343C22×C1111yescharacteristic, complemented
516#339C22×C1111yescharacteristic, complemented
517#339C22×C1111yescharacteristic, complemented
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—22no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—21no—
527C22×C11—41no—
528C22×C11—41no—
529C22×C11—41no—
530C22×C11—41no—
531C22×C11—42no—
532C22×C11—41no—
533C22×C11—42no—
534C22×C11—41no—
535C22×C11—42no—
536C22×C11—41no—
537C22×C11—41no—
538C22×C11—81no—
539C22×C11—81no—
540C22×C11—82no—
541C22×C11—82no—
542C22×C11—84no—
543C22×C11—164no—
544C22×C11C2×#12011yescharacteristic
545C22×C11#54611yescharacteristic
546C22×C11#54611yescharacteristic
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—22no—
550C4×C11—42no—
551C4×C11—41no—
552C4×C11—41no—
553C4×C11—41no—
554C4×C11—42no—
555C4×C11—41no—
556C4×C11—81no—
557C4×C11—81no—
558C4×C11—81no—
559C4×C11C2×#12311yescharacteristic
560C4×C11#53411yescharacteristic
561C4×C11#54611yescharacteristic
562C4×C11#54611yescharacteristic
563H(5,𝔽2)—22no—
564H(5,𝔽2)—22no—
565H(5,𝔽2)—41no—
566H(5,𝔽2)—41no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—22no—
572C2×#41—22no—
573C2×#41—41no—
574C2×#41—41no—
575C2×#41D4×C1111yescharacteristic
576C2×#41D4×C1111yescharacteristic
577C2×#41C23×C1111yescharacteristic
578C2×#41C23×C1111yescharacteristic
579C2×#41C23×C1111yescharacteristic
580C22×Q8D4×C1111yescharacteristic
581C22×D4—21no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4D4×C1111yescharacteristic
587C22×D4D4×C1112yes—
588C22×D4C23×C1111yescharacteristic
589C23×C4—21no—
590C23×C4C23×C1111yescharacteristic
591C2×M16—21no—
592C2×M16—41no—
593C2×M16—41no—
594C2×M16C23×C1111yescharacteristic
595C2×M16C23×C1111yescharacteristic
596C2×M16C23×C1111yescharacteristic
597C2×M16C23×C1111yescharacteristic
598C22×C8—21no—
599#127—22no—
600#127—21no—
601#124—22no—
602#124—21no—
603#123—22no—
604#123—21no—
605C22⋊Q8—22no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C1111yescharacteristic
609C22⋊Q8D4×C1111yescharacteristic
610#121—22no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—22no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—22no—
622#121—21no—
623#121—21no—
624#121D4×C1111yescharacteristic
625#121D4×C1111yescharacteristic
626#120—22no—
627#120—22no—
628#120—22no—
629#120—21no—
630#120—22no—
631C4×Q8—21no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—21no—
635C4×D4—22no—
636C4×D4—21no—
637C4×D4—21no—
638#117—21no—
639#117—21no—
640#117—21no—
641#117—21no—
642#117—21no—
643#117C23×C1111yescharacteristic
644C2×C4⋊C4—21no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4C23×C1111yescharacteristic
647C2×C4⋊C4C23×C1111yescharacteristic
648C2×C4⋊C4C23×C1111yescharacteristic
649C2×C22⋊C4—22no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4D4×C1112yes—
655C2×C42—21no—
656C2×C42C23×C1111yescharacteristic
657C2×C42C23×C1111yescharacteristic
658#107—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#104—22no—
663#104—22no—
664#104—41no—
665#104—41no—
666#104—41no—
667#104—41no—
668#103—21no—
669#103—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679#102—21no—
680#100—41no—
681#100—41no—
682C22⋊C8—21no—
683C22⋊C8—21no—
684#95—21no—
685#95—22no—
686C2×C11—21no—
687C2×C11—21no—
688C2×C11—41no—
689C2×C11—41no—
690C2×C11—42no—
691C2×C11—81no—
692C2×C11—82no—
693C2×C11—81no—
694C2×C11#240511yescharacteristic
695C2×C11#301811yescharacteristic
696C2×C11#301911yescharacteristic
697C24—22no—
698C24—21no—
699C24C2×D4×C1112yes—
700C24C2×D4×C1111yescharacteristic
701#41—21no—
702#41—21no—
703#41—22no—
704#41—22no—
705#41—21no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—42no—
714#41—42no—
715#41—41no—
716#41—41no—
717#41—42no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41C11×#4112yes—
724#41C11×#4112yes—
725C2×Q8—21no—
726C2×Q8—22no—
727C2×Q8—41no—
728C2×Q8C2×D4×C1111yescharacteristic
729C2×Q8C2×D4×C1111yescharacteristic
730C2×Q8C2×D4×C1111yescharacteristic
731C2×D4—21no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—41no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—82no—
763C2×D4—84no—
764C2×D4C2×D4×C1111yescharacteristic
765C2×D4C2×D4×C1111yescharacteristic
766C2×D4C2×D4×C1111yescharacteristic
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4C2×D4×C1111yescharacteristic
786C22×C4C2×D4×C1111yescharacteristic
787C22×C4C2×D4×C1111yescharacteristic
788C22×C4C2×D4×C1111yescharacteristic
789C22×C4C2×D4×C1111yescharacteristic
790C22×C4C2×D4×C1112yes—
791C22×C4C24×C1111yescharacteristic
792M16—21no—
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—42no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—42no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—82no—
817C4⋊C4C2×D4×C1111yescharacteristic
818C4⋊C4C2×D4×C1111yescharacteristic
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—21no—
831C22⋊C4—42no—
832C22⋊C4—44no—
833C22⋊C4—41no—
834C22⋊C4—41no—
835C22⋊C4—82no—
836C42—22no—
837C42—21no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—41no—
843C42—41no—
844C11#2403111yescharacteristic, direct product factor, Sylow
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23C11×#12011yescharacteristic
864C23C11×#12011yescharacteristic
865C23C22×D4×C1111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8C11×#12312yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—82no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4C11×#12312yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4C11×#12011yescharacteristic
940C2×C4C11×#12011yescharacteristic
941C2×C4C22×D4×C1111yescharacteristic
942C2×C4C22×D4×C1111yescharacteristic
943C2×C4C2×C11×#4111yescharacteristic
944C2×C4C2×C11×#4111yescharacteristic
945C2×C4C11×H(5,𝔽2)11yescharacteristic
946C2×C4C11×H(5,𝔽2)11yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×C11×#12011yescharacteristic
978C22C11×#54611yescharacteristic
979C22C11×#54611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×C11×#12311yescharacteristic
993C4C11×#53411yescharacteristic
994C4C11×#54611yescharacteristic
995C4C11×#54611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C11×#240511yescharacteristic
1005C2C11×#301811yescharacteristic
1006C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3488C2
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
2. C11×#3093C2semidirect
3. C11×#2896C2semidirect
4. C11×#2500C2semidirect
5. C11×#2040C2semidirect
6. C11×#2039C2semidirect
7. C11×#2037C2semidirect
8. C11×#2037C2semidirect
9. C11×#1900C2semidirect
10. C11×#1871C2semidirect
11. C11×#1860C2semidirect
12. C11×#1859C2semidirect
13. C11×#1792C2semidirect
14. C11×#1792C2semidirect
15. C11×#1789C2semidirect
18. C22×C11×M16C22semidirect
34. C2×C11×#117C22semidirect
39. C11×#428C22semidirect
40. C11×#428C22semidirect
43. C2×C11×#104C22semidirect
44. C2×C11×#104C22semidirect
45. C2×C11×#104C22semidirect
46. C2×C11×#104C22semidirect
51. C11×#417C22semidirect
52. C11×#417C22semidirect
53. C11×#417C22semidirect
54. C11×#417C22semidirect
57. C2×C11×#100C22semidirect
58. C2×C11×#100C22semidirect
59. C11×#407C22semidirect
61. C11×#390C22semidirect
62. C11×#390C22semidirect
64. C11×#384C22semidirect
65. C11×#382C22semidirect
66. C4×C11×C22⋊C4C22semidirect
67. C11×#343C22semidirect
68. C11×#343C22semidirect
69. C11×#339C22semidirect
70. C11×#339C22semidirect
194. #24031C11direct (N × H)
343. #3093C2×C11semidirect
344. #2896C2×C11semidirect
345. #2500C2×C11semidirect
346. #2040C2×C11semidirect
347. #2039C2×C11semidirect
348. #2037C2×C11semidirect
349. #2037C2×C11semidirect
350. #1900C2×C11semidirect
351. #1871C2×C11semidirect
352. #1860C2×C11semidirect
353. #1859C2×C11semidirect
354. #1792C2×C11semidirect
355. #1792C2×C11semidirect
356. #1789C2×C11semidirect
465. C22×M16C22×C11semidirect
481. C2×#117C22×C11semidirect
486. #428C22×C11semidirect
487. #428C22×C11semidirect
490. C2×#104C22×C11semidirect
491. C2×#104C22×C11semidirect
492. C2×#104C22×C11semidirect
493. C2×#104C22×C11semidirect
498. #417C22×C11semidirect
499. #417C22×C11semidirect
500. #417C22×C11semidirect
501. #417C22×C11semidirect
504. C2×#100C22×C11semidirect
505. C2×#100C22×C11semidirect
506. #407C22×C11semidirect
508. #390C22×C11semidirect
509. #390C22×C11semidirect
511. #384C22×C11semidirect
512. #382C22×C11semidirect
513. C4×C22⋊C4C22×C11semidirect
514. #343C22×C11semidirect
515. #343C22×C11semidirect
516. #339C22×C11semidirect
517. #339C22×C11semidirect
844. C11#24031direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34882
C11×#30932
C11×#28962
C11×#25002
C11×#20402
C11×#20392
C11×#20372
C11×#19002
C11×#18712
C11×#18602
C11×#18592
C11×#17922
C11×#17892
#2403111