Finite Group Databasebeta

← C11×#25193 #14602386

Subgroups — C11×#25193 #14602386

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3062C211yesmaximal, characteristic, complemented
2C11×#3045C211yesmaximal, characteristic, complemented
3C2×C11×#454C211yesmaximal, characteristic, complemented
4C11×#3013C211yesmaximal, characteristic, complemented
5C2×C11×#444C211yesmaximal, characteristic, complemented
6C11×#2898C211yesmaximal, characteristic, complemented
7C11×#2064C211yesmaximal, characteristic, complemented
8C11×#2051C211yesmaximal, characteristic, complemented
9C11×#2039C211yesmaximal, characteristic, complemented
10C11×#2004C211yesmaximal, characteristic, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C11×#1938C211yesmaximal, characteristic, complemented
13C11×#1908C211yesmaximal, characteristic, complemented
14C11×#1907C211yesmaximal, characteristic, complemented
15C11×#1859C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×#137C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C11×#135C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22C2×C11×#131C2211yescharacteristic
23C11×#537C2211yescharacteristic
24C11×#535C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C11×#520C2211yescharacteristic
27C11×#469—21no—
28C11×#468—21no—
29C11×#466—21no—
30C11×#465—21no—
31C11×#464—21no—
32C11×#463—21no—
33C11×#460—21no—
34C11×#459—21no—
35C11×#454—24no—
36C11×#452—21no—
37C11×#451—21no—
38C11×#449—21no—
39C11×#448—21no—
40C11×#444—24no—
41C2×C11×#108C2211yescharacteristic
42C11×#428C2211yescharacteristic
43C11×#424C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic
47C11×#419—21no—
48C11×#419C2211yescharacteristic
49C11×#417—21no—
50C11×#417C2211yescharacteristic
51C11×#417C2211yescharacteristic
52C11×#417C2211yescharacteristic
53C11×#416—21no—
54C11×#416C2211yescharacteristic
55C2×C11×#103—21no—
56C2×C11×#103C2211yescharacteristic
57C2×C11×#103C2211yescharacteristic
58C2×C11×#102C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic
60C2×C11×#101C2211yescharacteristic
61C2×C11×#100C2211yescharacteristic
62C11×#408C2211yescharacteristic
63C2×C11×#97C2211yescharacteristic
64C11×#384C2211yescharacteristic
65C11×#343C2211yescharacteristic
66C11×#343C2211yescharacteristic
67C11×#341C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×2−1+4—22no—
70C11×2−1+4—22no—
71C11×2−1+4—22no—
72C11×2−1+4—41no—
73C2×C11×#41—21no—
74C2×C11×#41—21no—
75C2×C11×#41—41no—
76C2×C11×#41C2311yescharacteristic
77C2×C11×#41C2311yescharacteristic
78C2×C11×#41C2311yescharacteristic
79C22×Q8×C11—21no—
80C22×Q8×C11—21no—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C11×#137—22no—
84C11×#137—41no—
85C11×AGL(1,ℤ/8)—22no—
86C11×AGL(1,ℤ/8)—22no—
87C11×AGL(1,ℤ/8)—22no—
88C11×AGL(1,ℤ/8)—41no—
89C11×#135—22no—
90C11×#135—22no—
91C2×C11×Q16—21no—
92C2×C11×Q16D411yescharacteristic
93C2×C11×SD16—21no—
94C2×C11×SD16—21no—
95C2×C11×SD16—21no—
96C2×C11×SD16D411yescharacteristic
97C2×C11×SD16D411yescharacteristic
98C2×C11×D8—21no—
99C2×C11×D8—21no—
100C2×C11×D8D411yescharacteristic
101C11×#131—22no—
102C11×#131—22no—
103C11×#131—41no—
104C11×#131—41no—
105C2×C11×M16—21no—
106C2×C11×M16—21no—
107C2×C11×M16C2311yescharacteristic
108C2×C11×M16C2311yescharacteristic
109C2×C11×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C22×C8×C11—21no—
112C22×C8×C11—21no—
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2311yescharacteristic
115C11×#127—21no—
116C11×#124—21no—
117C11×#124—22no—
118C11×#124—22no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—41no—
126C11×#120—41no—
127C4×Q8×C11—21no—
128C4×D4×C11—21no—
129C4×D4×C11—41no—
130C11×#117—21no—
131C11×#117C2311yescharacteristic
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—41no—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4—41no—
137C2×C42×C11C2311yescharacteristic
138C11×#108—22no—
139C11×#107—21no—
140C11×#106—21no—
141C11×C4⋊C8—21no—
142C11×C4⋊C8—21no—
143C11×#104—22no—
144C11×#104—22no—
145C11×#104D414yescomplemented
146C11×#103—21no—
147C11×#103—21no—
148C11×#103—21no—
149C11×#103—21no—
150C11×#103—21no—
151C11×#103—21no—
152C11×#103—21no—
153C11×#103—21no—
154C11×#103—21no—
155C11×#103D411yescharacteristic
156C11×#103D411yescharacteristic
157C11×#102—21no—
158C11×#102—21no—
159C11×#102—21no—
160C11×#102—21no—
161C11×#102—21no—
162C11×#102—21no—
163C11×#102—21no—
164C11×#102D411yescharacteristic
165C11×#102D411yescharacteristic
166C11×#101—22no—
167C11×#100—41no—
168C11×C22⋊C8—21no—
169C11×C22⋊C8—21no—
170C11×#97—22no—
171#25193C1111yesmaximal, characteristic, direct product factor, Sylow
172C24×C11—21no—
173C11×#41—21no—
174C11×#41—21no—
175C11×#41—24no—
176C11×#41—21no—
177C11×#41—21no—
178C11×#41—21no—
179C11×#41—21no—
180C11×#41—21no—
181C11×#41—21no—
182C11×#41—21no—
183C11×#41—21no—
184C11×#41—42no—
185C11×#41—44no—
186C11×#41—42no—
187C11×#41—44no—
188C11×#41—42no—
189C11×#41C2×D412yes—
190C11×#41#4112yes—
191C2×Q8×C11—21no—
192C2×Q8×C11—24no—
193C2×Q8×C11—21no—
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—21no—
197C2×Q8×C11—41no—
198C2×Q8×C11—42no—
199C2×Q8×C11—42no—
200C2×Q8×C11—42no—
201C2×Q8×C11C2×D411yescharacteristic
202C2×Q8×C11C2×D411yescharacteristic
203C2×Q8×C11C2×D411yescharacteristic
204C2×Q8×C11#4112yes—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—41no—
215C2×D4×C11—41no—
216C2×D4×C11—41no—
217C2×D4×C11—41no—
218C2×D4×C11C2×D411yescharacteristic
219C2×D4×C11C2×D411yescharacteristic
220C2×D4×C11C2×D411yescharacteristic
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—41no—
229C22×C4×C11—41no—
230C22×C4×C11—41no—
231C22×C4×C11C2411yescharacteristic
232C11×Q16—22no—
233C11×Q16—42no—
234C11×SD16—22no—
235C11×SD16—22no—
236C11×SD16—42no—
237C11×SD16—42no—
238C11×SD16—42no—
239C11×D8—22no—
240C11×D8—42no—
241C11×D8—42no—
242C11×M16—21no—
243C11×M16—21no—
244C11×M16—21no—
245C11×M16—21no—
246C11×M16—21no—
247C11×M16—21no—
248C11×M16—21no—
249C11×M16—42no—
250C11×M16—42no—
251C11×M16C2×D412yes—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—42no—
261C2×C8×C11—42no—
262C2×C8×C11C2×D411yescharacteristic
263C2×C8×C11C2×D411yescharacteristic
264C2×C8×C11C2×D411yescharacteristic
265C2×C8×C11C2×D411yescharacteristic
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—41no—
271C11×C4⋊C4—41no—
272C11×C4⋊C4—82no—
273C11×C4⋊C4C2×D411yescharacteristic
274C11×C4⋊C4C2×D411yescharacteristic
275C11×C22⋊C4—21no—
276C11×C22⋊C4—44no—
277C11×C22⋊C4—41no—
278C11×C22⋊C4—41no—
279C11×C22⋊C4—41no—
280C11×C22⋊C4—41no—
281C11×C22⋊C4—41no—
282C42×C11—21no—
283C42×C11—21no—
284C42×C11—41no—
285C42×C11C2×D412yes—
286#3062C2×C1111yescharacteristic, complemented
287#3045C2×C1111yescharacteristic, complemented
288C2×#454C2×C1111yescharacteristic, complemented
289#3013C2×C1111yescharacteristic, complemented
290C2×#444C2×C1111yescharacteristic, complemented
291#2898C2×C1111yescharacteristic, complemented
292#2064C2×C1111yescharacteristic, complemented
293#2051C2×C1111yescharacteristic, complemented
294#2039C2×C1111yescharacteristic, complemented
295#2004C2×C1111yescharacteristic, complemented
296#1959C2×C1111yescharacteristic, complemented
297#1938C2×C1111yescharacteristic, complemented
298#1908C2×C1111yescharacteristic, complemented
299#1907C2×C1111yescharacteristic, complemented
300#1859C2×C1111yescharacteristic, complemented
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—81no—
308C23×C11—81no—
309C23×C11H(5,𝔽2)11yescharacteristic
310Q8×C11—21no—
311Q8×C11—21no—
312Q8×C11—21no—
313Q8×C11—22no—
314Q8×C11—21no—
315Q8×C11—22no—
316Q8×C11—21no—
317Q8×C11—44no—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11#12112yes—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—21no—
324D4×C11—21no—
325D4×C11—21no—
326D4×C11—21no—
327D4×C11—21no—
328D4×C11—44no—
329D4×C11—41no—
330D4×C11—41no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—41no—
334D4×C11—41no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—161no—
338D4×C11—161no—
339D4×C11—161no—
340D4×C11#12112yes—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—44no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—44no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—81no—
363C2×C4×C11—81no—
364C2×C4×C11—161no—
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4111yescharacteristic
369C2×C4×C11C2×#4111yescharacteristic
370C2×C4×C11H(5,𝔽2)11yescharacteristic
371C8×C11—21no—
372C8×C11—21no—
373C8×C11—21no—
374C8×C11—21no—
375C8×C11—22no—
376C8×C11—41no—
377C8×C11—41no—
378C8×C11—41no—
379C2×2−1+4C22×C1111yescharacteristic
380C2×#137C22×C1111yescharacteristic
381C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
382C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
383C2×#135C22×C1111yescharacteristic
384C2×#131C22×C1111yescharacteristic
385C2×#131C22×C1111yescharacteristic
386#537C22×C1111yescharacteristic
387#535C22×C1111yescharacteristic
388C2×#124C22×C1111yescharacteristic
389#520C22×C1111yescharacteristic
390#469—21no—
391#468—21no—
392#466—21no—
393#465—21no—
394#464—21no—
395#463—21no—
396#460—21no—
397#459—21no—
398#454—24no—
399#452—21no—
400#451—21no—
401#449—21no—
402#448—21no—
403#444—24no—
404C2×#108C22×C1111yescharacteristic
405#428C22×C1111yescharacteristic
406#424C22×C1111yescharacteristic
407C2×#104C22×C1111yescharacteristic
408C2×#104C22×C1111yescharacteristic
409C2×#104C22×C1111yescharacteristic
410#419—21no—
411#419C22×C1111yescharacteristic
412#417—21no—
413#417C22×C1111yescharacteristic
414#417C22×C1111yescharacteristic
415#417C22×C1111yescharacteristic
416#416—21no—
417#416C22×C1111yescharacteristic
418C2×#103—21no—
419C2×#103C22×C1111yescharacteristic
420C2×#103C22×C1111yescharacteristic
421C2×#102C22×C1111yescharacteristic
422C2×#102C22×C1111yescharacteristic
423C2×#101C22×C1111yescharacteristic
424C2×#100C22×C1111yescharacteristic
425#408C22×C1111yescharacteristic
426C2×#97C22×C1111yescharacteristic
427#384C22×C1111yescharacteristic
428#343C22×C1111yescharacteristic
429#343C22×C1111yescharacteristic
430#341C22×C1111yescharacteristic
431#339C22×C1111yescharacteristic
432C22×C11—21no—
433C22×C11—21no—
434C22×C11—22no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—82no—
444C22×C11—81no—
445C22×C11—81no—
446C22×C11—81no—
447C22×C11—161no—
448C22×C11#53811yescharacteristic
449C22×C11D4211yescharacteristic
450C22×C11#54611yescharacteristic
451C4×C11—22no—
452C4×C11—42no—
453C4×C11—41no—
454C4×C11—42no—
455C4×C11—41no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11—81no—
459C4×C11—81no—
460C4×C11C2×#12111yescharacteristic
461C4×C11#52511yescharacteristic
462C4×C11D4211yescharacteristic
463C4×C11#54611yescharacteristic
4642−1+4—22no—
4652−1+4—22no—
4662−1+4—22no—
4672−1+4—41no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—41no—
471C2×#41C23×C1111yescharacteristic
472C2×#41C23×C1111yescharacteristic
473C2×#41C23×C1111yescharacteristic
474C22×Q8—21no—
475C22×Q8—21no—
476C22×Q8C23×C1111yescharacteristic
477C22×D4C23×C1111yescharacteristic
478#137—22no—
479#137—41no—
480AGL(1,ℤ/8)—22no—
481AGL(1,ℤ/8)—22no—
482AGL(1,ℤ/8)—22no—
483AGL(1,ℤ/8)—41no—
484#135—22no—
485#135—22no—
486C2×Q16—21no—
487C2×Q16D4×C1111yescharacteristic
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16D4×C1111yescharacteristic
492C2×SD16D4×C1111yescharacteristic
493C2×D8—21no—
494C2×D8—21no—
495C2×D8D4×C1111yescharacteristic
496#131—22no—
497#131—22no—
498#131—41no—
499#131—41no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16C23×C1111yescharacteristic
503C2×M16C23×C1111yescharacteristic
504C2×M16C23×C1111yescharacteristic
505C2×M16C23×C1111yescharacteristic
506C22×C8—21no—
507C22×C8—21no—
508C22×C8C23×C1111yescharacteristic
509C22×C8C23×C1111yescharacteristic
510#127—21no—
511#124—21no—
512#124—22no—
513#124—22no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—41no—
521#120—41no—
522C4×Q8—21no—
523C4×D4—21no—
524C4×D4—41no—
525#117—21no—
526#117C23×C1111yescharacteristic
527C2×C4⋊C4—21no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4C23×C1111yescharacteristic
530C2×C4⋊C4C23×C1111yescharacteristic
531C2×C22⋊C4—41no—
532C2×C42C23×C1111yescharacteristic
533#108—22no—
534#107—21no—
535#106—21no—
536C4⋊C8—21no—
537C4⋊C8—21no—
538#104—22no—
539#104—22no—
540#104D4×C1114yescomplemented
541#103—21no—
542#103—21no—
543#103—21no—
544#103—21no—
545#103—21no—
546#103—21no—
547#103—21no—
548#103—21no—
549#103—21no—
550#103D4×C1111yescharacteristic
551#103D4×C1111yescharacteristic
552#102—21no—
553#102—21no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102D4×C1111yescharacteristic
560#102D4×C1111yescharacteristic
561#101—22no—
562#100—41no—
563C22⋊C8—21no—
564C22⋊C8—21no—
565#97—22no—
566C2×C11—21no—
567C2×C11—21no—
568C2×C11—42no—
569C2×C11—81no—
570C2×C11—81no—
571C2×C11—161no—
572C2×C11#242411yescharacteristic
573C2×C11#328811yescharacteristic
574C2×C11#328911yescharacteristic
575C24—21no—
576#41—21no—
577#41—21no—
578#41—24no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—21no—
584#41—21no—
585#41—21no—
586#41—21no—
587#41—42no—
588#41—44no—
589#41—42no—
590#41—44no—
591#41—42no—
592#41C2×D4×C1112yes—
593#41C11×#4112yes—
594C2×Q8—21no—
595C2×Q8—24no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—41no—
601C2×Q8—42no—
602C2×Q8—42no—
603C2×Q8—42no—
604C2×Q8C2×D4×C1111yescharacteristic
605C2×Q8C2×D4×C1111yescharacteristic
606C2×Q8C2×D4×C1111yescharacteristic
607C2×Q8C11×#4112yes—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4C2×D4×C1111yescharacteristic
622C2×D4C2×D4×C1111yescharacteristic
623C2×D4C2×D4×C1111yescharacteristic
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4C24×C1111yescharacteristic
635Q16—22no—
636Q16—42no—
637SD16—22no—
638SD16—22no—
639SD16—42no—
640SD16—42no—
641SD16—42no—
642D8—22no—
643D8—42no—
644D8—42no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—42no—
653M16—42no—
654M16C2×D4×C1112yes—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8C2×D4×C1111yescharacteristic
666C2×C8C2×D4×C1111yescharacteristic
667C2×C8C2×D4×C1111yescharacteristic
668C2×C8C2×D4×C1111yescharacteristic
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—82no—
676C4⋊C4C2×D4×C1111yescharacteristic
677C4⋊C4C2×D4×C1111yescharacteristic
678C22⋊C4—21no—
679C22⋊C4—44no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C42—21no—
686C42—21no—
687C42—41no—
688C42C2×D4×C1112yes—
689C11#2519311yescharacteristic, direct product factor, Sylow
690C23—21no—
691C23—21no—
692C23—21no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—81no—
697C23—81no—
698C23C11×H(5,𝔽2)11yescharacteristic
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—22no—
703Q8—21no—
704Q8—22no—
705Q8—21no—
706Q8—44no—
707Q8—41no—
708Q8—41no—
709Q8C11×#12112yes—
710D4—22no—
711D4—22no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—44no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—161no—
727D4—161no—
728D4—161no—
729D4C11×#12112yes—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—161no—
754C2×C4C22×D4×C1111yescharacteristic
755C2×C4C22×D4×C1111yescharacteristic
756C2×C4C22×D4×C1111yescharacteristic
757C2×C4C2×C11×#4111yescharacteristic
758C2×C4C2×C11×#4111yescharacteristic
759C2×C4C11×H(5,𝔽2)11yescharacteristic
760C8—21no—
761C8—21no—
762C8—21no—
763C8—21no—
764C8—22no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—21no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—161no—
784C22C11×#53811yescharacteristic
785C22D42×C1111yescharacteristic
786C22C11×#54611yescharacteristic
787C4—22no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4C2×C11×#12111yescharacteristic
797C4C11×#52511yescharacteristic
798C4D42×C1111yescharacteristic
799C4C11×#54611yescharacteristic
800C2—21no—
801C2—21no—
802C2—42no—
803C2—81no—
804C2—81no—
805C2—161no—
806C2C11×#242411yescharacteristic
807C2C11×#328811yescharacteristic
808C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3062C2semidirect
2. C11×#3045C2semidirect
3. C2×C11×#454C2semidirect
4. C11×#3013C2semidirect
5. C2×C11×#444C2semidirect
6. C11×#2898C2semidirect
7. C11×#2064C2semidirect
8. C11×#2051C2semidirect
9. C11×#2039C2semidirect
10. C11×#2004C2semidirect
11. C11×#1959C2semidirect
12. C11×#1938C2semidirect
13. C11×#1908C2semidirect
14. C11×#1907C2semidirect
15. C11×#1859C2semidirect
145. C11×#104D4semidirect
171. #25193C11direct (N × H)
286. #3062C2×C11semidirect
287. #3045C2×C11semidirect
288. C2×#454C2×C11semidirect
289. #3013C2×C11semidirect
290. C2×#444C2×C11semidirect
291. #2898C2×C11semidirect
292. #2064C2×C11semidirect
293. #2051C2×C11semidirect
294. #2039C2×C11semidirect
295. #2004C2×C11semidirect
296. #1959C2×C11semidirect
297. #1938C2×C11semidirect
298. #1908C2×C11semidirect
299. #1907C2×C11semidirect
300. #1859C2×C11semidirect
540. #104D4×C11semidirect
689. C11#25193direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30622
C11×#30452
C2×C11×#4542
C11×#30132
C2×C11×#4442
C11×#28982
C11×#20642
C11×#20512
C11×#20392
C11×#20042
C11×#19592
C11×#19382
C11×#19082
C11×#19072
C11×#18592
#2519311