Finite Group Databasebeta

← C11×#24525 #14601718

Subgroups — C11×#24525 #14601718

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3095C211yesmaximal, characteristic, complemented
2C2×C11×#452C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C11×#2896C211yesmaximal, characteristic
5C11×#2064C211yesmaximal, characteristic, complemented
6C11×#2063C211yesmaximal, characteristic, complemented
7C11×#2047C211yesmaximal, characteristic, complemented
8C11×#2046C211yesmaximal, characteristic, complemented
9C11×#1979C211yesmaximal, characteristic, complemented
10C11×#1977C211yesmaximal, characteristic, complemented
11C11×#1931C211yesmaximal, characteristic, complemented
12C11×#1930C211yesmaximal, characteristic, complemented
13C11×#1901C211yesmaximal, characteristic, complemented
14C11×#1855C211yesmaximal, characteristic, complemented
15C11×#1785C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#485—21no—
23C11×#485—21no—
24C11×#484—21no—
25C11×#483—21no—
26C11×#452—21no—
27C11×#452—21no—
28C11×#452—21no—
29C11×#452—21no—
30C11×#433—21no—
31C11×#433—21no—
32C11×#432—21no—
33C11×#431—21no—
34C2×C11×#108C2211yescharacteristic
35C2×C11×#108C2211yescharacteristic
36C11×#428C2211yescharacteristic
37C11×#428C2211yescharacteristic
38C11×#424C2211yescharacteristic
39C11×#424C2211yescharacteristic
40C11×#419C2211yescharacteristic
41C11×#419C2211yescharacteristic
42C11×#419C2211yescharacteristic
43C11×#419C2211yescharacteristic
44C11×#418C2211yescharacteristic
45C11×#418C2211yescharacteristic
46C11×#417—21no—
47C11×#417—21no—
48C11×#416—21no—
49C11×#416—21no—
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#101C2211yescharacteristic
53C2×C11×#101C2211yescharacteristic
54C2×C11×#101C2211yescharacteristic
55C2×C11×#101C2211yescharacteristic
56C2×C11×#100C2211yescharacteristic
57C2×C11×#100C2211yescharacteristic
58C11×#407C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C11×#405C2211yescharacteristic
62C11×#405C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#341C2211yescharacteristic
66C11×#341C2211yescharacteristic
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—21no—
70C2×C11×#41—21no—
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C22×Q8×C11C2311yescharacteristic
76C22×Q8×C11C2311yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C2×C11×Q16—22no—
82C2×C11×Q16—21no—
83C2×C11×Q16—21no—
84C2×C11×Q16—41no—
85C2×C11×SD16—22no—
86C2×C11×SD16—21no—
87C2×C11×SD16—21no—
88C2×C11×SD16—41no—
89C2×C11×M16—21no—
90C2×C11×M16—41no—
91C2×C11×M16—41no—
92C2×C11×M16C2311yescharacteristic
93C2×C11×M16C2311yescharacteristic
94C2×C11×M16C2311yescharacteristic
95C2×C11×M16C2311yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C22×C8×C11—21no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×C22⋊Q8—21no—
102C11×C22⋊Q8—21no—
103C11×C22⋊Q8—21no—
104C11×C22⋊Q8—21no—
105C11×#117—21no—
106C11×#117—21no—
107C11×#117D411yescharacteristic
108C11×#117D411yescharacteristic
109C11×#117C2311yescharacteristic
110C11×#117C2311yescharacteristic
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11—21no—
118C11×#108—41no—
119C11×#108—41no—
120C11×#107—21no—
121C11×#107—21no—
122C11×#106—21no—
123C11×#106—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×#103—21no—
129C11×#103—21no—
130C11×#103—21no—
131C11×#103—21no—
132C11×#103—21no—
133C11×#103—21no—
134C11×#103—21no—
135C11×#103—21no—
136C11×#103—21no—
137C11×#103—21no—
138C11×#102—21no—
139C11×#102—21no—
140C11×#102—21no—
141C11×#102—21no—
142C11×#102—21no—
143C11×#102—21no—
144C11×#101—22no—
145C11×#101—41no—
146C11×#101—41no—
147C11×#101—41no—
148C11×#100—22no—
149C11×#100—41no—
150C11×C22⋊C8—21no—
151C11×C22⋊C8—21no—
152C11×C22⋊C8—21no—
153C11×C22⋊C8—21no—
154C11×C22⋊C8D411yescharacteristic
155C11×C22⋊C8D411yescharacteristic
156C11×C22⋊C8D411yescharacteristic
157C11×C22⋊C8D411yescharacteristic
158C11×#97—21no—
159C11×#97—21no—
160C4×C8×C11—21no—
161C4×C8×C11—21no—
162#24525C1111yesmaximal, characteristic, direct product factor, Sylow
163C24×C11—21no—
164C24×C11#4111yescharacteristic
165C11×#41—24no—
166C11×#41—24no—
167C11×#41—42no—
168C11×#41—42no—
169C11×#41—42no—
170C11×#41—42no—
171C11×#41—42no—
172C11×#41—42no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11#4112yes—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—42no—
191C2×D4×C11—42no—
192C2×D4×C11—41no—
193C2×D4×C11—41no—
194C2×D4×C11#4112yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—41no—
207C22×C4×C11—41no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11#4111yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C11×Q16—42no—
215C11×Q16—42no—
216C11×SD16—42no—
217C11×SD16—42no—
218C11×M16—21no—
219C11×M16—21no—
220C11×M16—21no—
221C11×M16—21no—
222C11×M16—21no—
223C11×M16—21no—
224C11×M16—21no—
225C11×M16—21no—
226C11×M16—21no—
227C11×M16—21no—
228C11×M16—21no—
229C11×M16—21no—
230C11×M16—42no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—42no—
242C2×C8×C11C2×D411yescharacteristic
243C2×C8×C11C2×D411yescharacteristic
244C2×C8×C11C2×D411yescharacteristic
245C2×C8×C11C2×D411yescharacteristic
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—41no—
251C11×C4⋊C4—41no—
252C11×C4⋊C4C2×D411yescharacteristic
253C11×C4⋊C4C2×D411yescharacteristic
254C11×C4⋊C4C2×D411yescharacteristic
255C11×C4⋊C4C2×D411yescharacteristic
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C11×C22⋊C4—41no—
261C11×C22⋊C4—41no—
262C42×C11—21no—
263C42×C11—21no—
264C42×C11—21no—
265C42×C11—21no—
266#3095C2×C1111yescharacteristic, complemented
267C2×#452C2×C1111yescharacteristic
268#2924C2×C1111yescharacteristic, complemented
269#2896C2×C1111yescharacteristic
270#2064C2×C1111yescharacteristic, complemented
271#2063C2×C1111yescharacteristic, complemented
272#2047C2×C1111yescharacteristic, complemented
273#2046C2×C1111yescharacteristic, complemented
274#1979C2×C1111yescharacteristic, complemented
275#1977C2×C1111yescharacteristic, complemented
276#1931C2×C1111yescharacteristic, complemented
277#1930C2×C1111yescharacteristic, complemented
278#1901C2×C1111yescharacteristic, complemented
279#1855C2×C1111yescharacteristic, complemented
280#1785C2×C1111yescharacteristic
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—81no—
289C23×C11—81no—
290C23×C11#12111yescharacteristic
291C23×C11#12111yescharacteristic
292C23×C11C2×#4111yescharacteristic
293Q8×C11—22no—
294Q8×C11—22no—
295Q8×C11—41no—
296Q8×C11—41no—
297Q8×C11—41no—
298Q8×C11—41no—
299Q8×C11—41no—
300Q8×C11—41no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—44no—
304D4×C11—44no—
305D4×C11—41no—
306D4×C11—41no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—22no—
322C2×C4×C11—44no—
323C2×C4×C11—44no—
324C2×C4×C11—42no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—81no—
332C2×C4×C11—81no—
333C2×C4×C11#12111yescharacteristic
334C2×C4×C11#12111yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C8×C11—21no—
342C8×C11—21no—
343C8×C11—21no—
344C8×C11—21no—
345C8×C11—41no—
346C8×C11—41no—
347C8×C11—41no—
348C8×C11—41no—
349C8×C11—41no—
350C8×C11—41no—
351C22×#41C22×C1111yescharacteristic
352C22×Q16C22×C1111yescharacteristic
353C22×SD16C22×C1111yescharacteristic
354C22×M16C22×C1111yescharacteristic
355C2×C22⋊Q8C22×C1111yescharacteristic
356C2×#117C22×C1111yescharacteristic
357#485—21no—
358#485—21no—
359#484—21no—
360#483—21no—
361#452—21no—
362#452—21no—
363#452—21no—
364#452—21no—
365#433—21no—
366#433—21no—
367#432—21no—
368#431—21no—
369C2×#108C22×C1111yescharacteristic
370C2×#108C22×C1111yescharacteristic
371#428C22×C1111yescharacteristic
372#428C22×C1111yescharacteristic
373#424C22×C1111yescharacteristic
374#424C22×C1111yescharacteristic
375#419C22×C1111yescharacteristic
376#419C22×C1111yescharacteristic
377#419C22×C1111yescharacteristic
378#419C22×C1111yescharacteristic
379#418C22×C1111yescharacteristic
380#418C22×C1111yescharacteristic
381#417—21no—
382#417—21no—
383#416—21no—
384#416—21no—
385C2×#103C22×C1111yescharacteristic
386C2×#102C22×C1111yescharacteristic
387C2×#101C22×C1111yescharacteristic
388C2×#101C22×C1111yescharacteristic
389C2×#101C22×C1111yescharacteristic
390C2×#101C22×C1111yescharacteristic
391C2×#100C22×C1111yescharacteristic
392C2×#100C22×C1111yescharacteristic
393#407C22×C1111yescharacteristic
394#407C22×C1111yescharacteristic
395C2×C22⋊C8C22×C1111yescharacteristic
396#405C22×C1111yescharacteristic
397#405C22×C1111yescharacteristic
398#343C22×C1111yescharacteristic
399#343C22×C1111yescharacteristic
400#341C22×C1111yescharacteristic
401#341C22×C1111yescharacteristic
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—42no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—82no—
414C22×C11—82no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11C2×#12111yescharacteristic
418C22×C11#55111yescharacteristic
419C22×C11#55111yescharacteristic
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—42no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11#52511yescharacteristic
430C4×C11#53511yescharacteristic
431C4×C11#54611yescharacteristic
432C4×C11#54611yescharacteristic
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—41no—
440C2×#41—41no—
441C22×Q8C23×C1111yescharacteristic
442C22×Q8C23×C1111yescharacteristic
443C22×D4—21no—
444C22×D4C23×C1111yescharacteristic
445C23×C4—21no—
446C23×C4C23×C1111yescharacteristic
447C2×Q16—22no—
448C2×Q16—21no—
449C2×Q16—21no—
450C2×Q16—41no—
451C2×SD16—22no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×SD16—41no—
455C2×M16—21no—
456C2×M16—41no—
457C2×M16—41no—
458C2×M16C23×C1111yescharacteristic
459C2×M16C23×C1111yescharacteristic
460C2×M16C23×C1111yescharacteristic
461C2×M16C23×C1111yescharacteristic
462C2×M16C23×C1111yescharacteristic
463C2×M16C23×C1111yescharacteristic
464C22×C8—21no—
465C22×C8C23×C1111yescharacteristic
466C22×C8C23×C1111yescharacteristic
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471#117—21no—
472#117—21no—
473#117D4×C1111yescharacteristic
474#117D4×C1111yescharacteristic
475#117C23×C1111yescharacteristic
476#117C23×C1111yescharacteristic
477C2×C4⋊C4—21no—
478C2×C4⋊C4D4×C1111yescharacteristic
479C2×C4⋊C4D4×C1111yescharacteristic
480C2×C4⋊C4C23×C1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C42—21no—
484#108—41no—
485#108—41no—
486#107—21no—
487#107—21no—
488#106—21no—
489#106—21no—
490C4⋊C8—21no—
491C4⋊C8—21no—
492C4⋊C8—21no—
493C4⋊C8—21no—
494#103—21no—
495#103—21no—
496#103—21no—
497#103—21no—
498#103—21no—
499#103—21no—
500#103—21no—
501#103—21no—
502#103—21no—
503#103—21no—
504#102—21no—
505#102—21no—
506#102—21no—
507#102—21no—
508#102—21no—
509#102—21no—
510#101—22no—
511#101—41no—
512#101—41no—
513#101—41no—
514#100—22no—
515#100—41no—
516C22⋊C8—21no—
517C22⋊C8—21no—
518C22⋊C8—21no—
519C22⋊C8—21no—
520C22⋊C8D4×C1111yescharacteristic
521C22⋊C8D4×C1111yescharacteristic
522C22⋊C8D4×C1111yescharacteristic
523C22⋊C8D4×C1111yescharacteristic
524#97—21no—
525#97—21no—
526C4×C8—21no—
527C4×C8—21no—
528C2×C11—21no—
529C2×C11—21no—
530C2×C11—41no—
531C2×C11—41no—
532C2×C11—82no—
533C2×C11#241111yescharacteristic
534C2×C11#306711yescharacteristic
535C2×C11#306911yescharacteristic
536C24—21no—
537C24C11×#4111yescharacteristic
538#41—24no—
539#41—24no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41—42no—
545#41—42no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C11×#4112yes—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4C11×#4112yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4C2×D4×C1111yescharacteristic
582C22×C4C2×D4×C1111yescharacteristic
583C22×C4C2×D4×C1111yescharacteristic
584C22×C4C2×D4×C1111yescharacteristic
585C22×C4C11×#4111yescharacteristic
586C22×C4C24×C1111yescharacteristic
587Q16—42no—
588Q16—42no—
589SD16—42no—
590SD16—42no—
591M16—21no—
592M16—21no—
593M16—21no—
594M16—21no—
595M16—21no—
596M16—21no—
597M16—21no—
598M16—21no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—42no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—42no—
615C2×C8C2×D4×C1111yescharacteristic
616C2×C8C2×D4×C1111yescharacteristic
617C2×C8C2×D4×C1111yescharacteristic
618C2×C8C2×D4×C1111yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4C2×D4×C1111yescharacteristic
626C4⋊C4C2×D4×C1111yescharacteristic
627C4⋊C4C2×D4×C1111yescharacteristic
628C4⋊C4C2×D4×C1111yescharacteristic
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C11#2452511yescharacteristic, direct product factor, Sylow
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—81no—
648C23—81no—
649C23C11×#12111yescharacteristic
650C23C11×#12111yescharacteristic
651C23C2×C11×#4111yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660D4—22no—
661D4—22no—
662D4—44no—
663D4—44no—
664D4—41no—
665D4—41no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4C11×#12111yescharacteristic
693C2×C4C11×#12111yescharacteristic
694C2×C4C22×D4×C1111yescharacteristic
695C2×C4C22×D4×C1111yescharacteristic
696C2×C4C2×C11×#4111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C11×H(5,𝔽2)11yescharacteristic
699C2×C4C11×H(5,𝔽2)11yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—82no—
722C22—82no—
723C22—81no—
724C22—81no—
725C22C2×C11×#12111yescharacteristic
726C22C11×#55111yescharacteristic
727C22C11×#55111yescharacteristic
728C4—21no—
729C4—21no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—81no—
736C4—81no—
737C4C11×#52511yescharacteristic
738C4C11×#53511yescharacteristic
739C4C11×#54611yescharacteristic
740C4C11×#54611yescharacteristic
741C2—21no—
742C2—21no—
743C2—41no—
744C2—41no—
745C2—82no—
746C2C11×#241111yescharacteristic
747C2C11×#306711yescharacteristic
748C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
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×#3095C2semidirect
3. C11×#2924C2semidirect
5. C11×#2064C2semidirect
6. C11×#2063C2semidirect
7. C11×#2047C2semidirect
8. C11×#2046C2semidirect
9. C11×#1979C2semidirect
10. C11×#1977C2semidirect
11. C11×#1931C2semidirect
12. C11×#1930C2semidirect
13. C11×#1901C2semidirect
14. C11×#1855C2semidirect
162. #24525C11direct (N × H)
266. #3095C2×C11semidirect
268. #2924C2×C11semidirect
270. #2064C2×C11semidirect
271. #2063C2×C11semidirect
272. #2047C2×C11semidirect
273. #2046C2×C11semidirect
274. #1979C2×C11semidirect
275. #1977C2×C11semidirect
276. #1931C2×C11semidirect
277. #1930C2×C11semidirect
278. #1901C2×C11semidirect
279. #1855C2×C11semidirect
639. C11#24525direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30952
C2×C11×#4522
C11×#29242
C11×#28962
C11×#20642
C11×#20632
C11×#20472
C11×#20462
C11×#19792
C11×#19772
C11×#19312
C11×#19302
C11×#19012
C11×#18552
C11×#17852
#2452511