Finite Group Databasebeta

← C11×#24149 #14601342

Subgroups — C11×#24149 #14601342

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3510C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic, complemented
4C11×#2545C211yesmaximal, characteristic, complemented
5C11×#2038C211yesmaximal, characteristic, complemented
6C11×#2037C211yesmaximal, characteristic
7C11×#2005C211yesmaximal, characteristic, complemented
8C11×#2004C211yesmaximal, characteristic
9C11×#1986C211yesmaximal, characteristic, complemented
10C11×#1967C211yesmaximal, characteristic, complemented
11C11×#1886C211yesmaximal, characteristic, complemented
12C11×#1885C211yesmaximal, characteristic, complemented
13C11×#1857C211yesmaximal, characteristic, complemented
14C11×#1856C211yesmaximal, characteristic, complemented
15C11×#1806C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C11×#559—21no—
18C11×#559—21no—
19C11×#556—21no—
20C11×#556—21no—
21C11×#551—22no—
22C11×#551—22no—
23C11×#542—21no—
24C11×#542—21no—
25C11×#536C2211yescharacteristic
26C11×#535C2211yescharacteristic
27C11×#533C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C11×#529—21no—
30C11×#529—21no—
31C2×C11×#124C2211yescharacteristic
32C2×C11×#124C2211yescharacteristic
33C11×#519C2211yescharacteristic
34C11×#518C2211yescharacteristic
35C4×C11×#41C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C11×#479—21no—
38C11×#479—21no—
39C11×#477—21no—
40C11×#475—21no—
41C11×#441—21no—
42C11×#440—21no—
43C4×C11×Q16—21no—
44C4×C11×SD16—21no—
45C11×#428C2211yescharacteristic
46C11×#428C2211yescharacteristic
47C11×#428C2211yescharacteristic
48C11×#423C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C11×#419C2211yescharacteristic
52C11×#419C2211yescharacteristic
53C11×#419C2211yescharacteristic
54C11×#417C2211yescharacteristic
55C2×C11×#101C2211yescharacteristic
56C2×C11×#101C2211yescharacteristic
57C2×C11×#100C2211yescharacteristic
58C2×C11×#100C2211yescharacteristic
59C4×C11×M16C2211yescharacteristic
60C11×#396—22no—
61C11×#391C2211yescharacteristic
62C11×#390C2211yescharacteristic
63C11×#388—22no—
64C4×C11×C4⋊C4C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C11×#137—22no—
76C11×#137—22no—
77C2×C11×Q16—21no—
78C2×C11×SD16—21no—
79C2×C11×M16C2311yescharacteristic
80C2×C11×M16C2311yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—22no—
85C11×C4⋊Q8—41no—
86C11×C4⋊Q8D411yescharacteristic
87C11×C4⋊Q8D411yescharacteristic
88C11×#127—21no—
89C11×#126—22no—
90C11×#126—22no—
91C11×#126—22no—
92C11×#126—22no—
93C11×#125D411yescharacteristic
94C11×#125D411yescharacteristic
95C11×#124—22no—
96C11×#124—22no—
97C11×#124—21no—
98C11×#124—21no—
99C11×#124—22no—
100C11×#124—21no—
101C11×#124—21no—
102C11×#124—21no—
103C11×#124—21no—
104C11×#124—41no—
105C11×#123—22no—
106C11×#123—22no—
107C11×#123—22no—
108C11×#123—22no—
109C11×#123—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×#121—21no—
117C11×#121—21no—
118C11×#120—22no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11D411yescharacteristic
130C4×Q8×C11D411yescharacteristic
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11D411yescharacteristic
140C4×D4×C11D411yescharacteristic
141C11×#117—22no—
142C11×#117—22no—
143C11×#117—22no—
144C11×#117—21no—
145C11×#117C2311yescharacteristic
146C11×#117C2311yescharacteristic
147C11×#117C2311yescharacteristic
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—22no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4—22no—
153C2×C11×C22⋊C4—22no—
154C2×C11×C22⋊C4—22no—
155C2×C11×C22⋊C4D412yes—
156C2×C11×C22⋊C4D412yes—
157C2×C42×C11—21no—
158C2×C42×C11—21no—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C11×#107—21no—
163C11×#107—21no—
164C11×#107—21no—
165C11×#106—21no—
166C11×#106—21no—
167C11×#106—21no—
168C11×C4⋊C8—21no—
169C11×C4⋊C8—21no—
170C11×#104—41no—
171C11×#104—41no—
172C11×#103—21no—
173C11×#103—21no—
174C11×#103—21no—
175C11×#103—21no—
176C11×#103—21no—
177C11×#103—21no—
178C11×#103—21no—
179C11×#102—21no—
180C11×#101—22no—
181C11×#101—41no—
182C11×#100—22no—
183C11×#100—41no—
184C11×#97—21no—
185C4×C8×C11—21no—
186C11×#95—21no—
187C11×#95—22no—
188#24149C1111yesmaximal, characteristic, direct product factor, Sylow
189C24×C11C2×D412yes—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41—21no—
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—21no—
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—21no—
204C2×Q8×C11—21no—
205C2×Q8×C11—21no—
206C2×Q8×C11—21no—
207C2×Q8×C11C2×D411yescharacteristic
208C2×Q8×C11#4112yes—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11—21no—
218C2×D4×C11C2×D411yescharacteristic
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C11×Q16—24no—
233C11×SD16—24no—
234C11×M16—21no—
235C11×M16—21no—
236C11×M16—21no—
237C11×M16—21no—
238C11×M16—21no—
239C11×M16—21no—
240C11×M16—21no—
241C11×M16#4112yes—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—44no—
261C11×C4⋊C4—42no—
262C11×C4⋊C4—41no—
263C11×C4⋊C4—41no—
264C11×C4⋊C4C2×D411yescharacteristic
265C11×C4⋊C4C2×D411yescharacteristic
266C11×C4⋊C4C2×D411yescharacteristic
267C11×C4⋊C4C2×D411yescharacteristic
268C11×C4⋊C4C2×D411yescharacteristic
269C11×C4⋊C4C2×D411yescharacteristic
270C11×C22⋊C4—22no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—21no—
277C11×C22⋊C4—21no—
278C11×C22⋊C4—21no—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—21no—
284C11×C22⋊C4—21no—
285C11×C22⋊C4—44no—
286C11×C22⋊C4—44no—
287C42×C11—22no—
288C42×C11—22no—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—21no—
292C42×C11—21no—
293C42×C11—21no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—41no—
299C42×C11—41no—
300C42×C11C2×D411yescharacteristic
301C42×C11C2×D411yescharacteristic
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D411yescharacteristic
304#3510C2×C1111yescharacteristic
305#3078C2×C1111yescharacteristic, complemented
306C4×#137C2×C1111yescharacteristic, complemented
307#2545C2×C1111yescharacteristic, complemented
308#2038C2×C1111yescharacteristic, complemented
309#2037C2×C1111yescharacteristic
310#2005C2×C1111yescharacteristic, complemented
311#2004C2×C1111yescharacteristic
312#1986C2×C1111yescharacteristic, complemented
313#1967C2×C1111yescharacteristic, complemented
314#1886C2×C1111yescharacteristic, complemented
315#1885C2×C1111yescharacteristic, complemented
316#1857C2×C1111yescharacteristic, complemented
317#1856C2×C1111yescharacteristic, complemented
318#1806C2×C1111yescharacteristic, complemented
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11C22×D411yescharacteristic
326Q8×C11—22no—
327Q8×C11—21no—
328Q8×C11—21no—
329Q8×C11—22no—
330Q8×C11—41no—
331Q8×C11—41no—
332Q8×C11—41no—
333Q8×C11—41no—
334Q8×C11—41no—
335Q8×C11—41no—
336Q8×C11—81no—
337Q8×C11—81no—
338D4×C11—21no—
339D4×C11—21no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11—41no—
343D4×C11—41no—
344D4×C11—41no—
345D4×C11—41no—
346D4×C11—82no—
347D4×C11—82no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—22no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—42no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—81no—
374C2×C4×C11—81no—
375C2×C4×C11—82no—
376C2×C4×C11—82no—
377C2×C4×C11#12011yescharacteristic
378C2×C4×C11#12011yescharacteristic
379C2×C4×C11#12011yescharacteristic
380C2×C4×C11#12011yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C2×#4111yescharacteristic
384C2×C4×C11C2×#4111yescharacteristic
385C2×C4×C11H(5,𝔽2)11yescharacteristic
386C2×C4×C112−1+411yescharacteristic
387C8×C11—22no—
388C8×C11—41no—
389C8×C11—41no—
390C8×C11—41no—
391C2×#137C22×C1111yescharacteristic
392#559—21no—
393#559—21no—
394#556—21no—
395#556—21no—
396#551—22no—
397#551—22no—
398#542—21no—
399#542—21no—
400#536C22×C1111yescharacteristic
401#535C22×C1111yescharacteristic
402#533C22×C1111yescharacteristic
403C2×C4⋊Q8C22×C1111yescharacteristic
404#529—21no—
405#529—21no—
406C2×#124C22×C1111yescharacteristic
407C2×#124C22×C1111yescharacteristic
408#519C22×C1111yescharacteristic
409#518C22×C1111yescharacteristic
410C4×#41C22×C1111yescharacteristic
411C2×C4×Q8C22×C1111yescharacteristic
412#479—21no—
413#479—21no—
414#477—21no—
415#475—21no—
416#441—21no—
417#440—21no—
418C4×Q16—21no—
419C4×SD16—21no—
420#428C22×C1111yescharacteristic
421#428C22×C1111yescharacteristic
422#428C22×C1111yescharacteristic
423#423C22×C1111yescharacteristic
424C2×#104C22×C1111yescharacteristic
425C2×#104C22×C1111yescharacteristic
426#419C22×C1111yescharacteristic
427#419C22×C1111yescharacteristic
428#419C22×C1111yescharacteristic
429#417C22×C1111yescharacteristic
430C2×#101C22×C1111yescharacteristic
431C2×#101C22×C1111yescharacteristic
432C2×#100C22×C1111yescharacteristic
433C2×#100C22×C1111yescharacteristic
434C4×M16C22×C1111yescharacteristic
435#396—22no—
436#391C22×C1111yescharacteristic
437#390C22×C1111yescharacteristic
438#388—22no—
439C4×C4⋊C4C22×C1111yescharacteristic
440#339C22×C1111yescharacteristic
441#339C22×C1111yescharacteristic
442#339C22×C1111yescharacteristic
443#339C22×C1111yescharacteristic
444#339C22×C1111yescharacteristic
445#339C22×C1111yescharacteristic
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—41no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—82no—
455C22×C11—82no—
456C22×C11C2×#12011yescharacteristic
457C22×C11#54611yescharacteristic
458C22×C11#54711yescharacteristic
459C4×C11—21no—
460C4×C11—21no—
461C4×C11—21no—
462C4×C11—21no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—41no—
466C4×C11—42no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11—81no—
474C4×C11—81no—
475C4×C11#52511yescharacteristic
476C4×C11#53711yescharacteristic
477C4×C11#54811yescharacteristic
478C4×C11#55011yescharacteristic
479C2×#41C23×C1111yescharacteristic
480C22×Q8C23×C1111yescharacteristic
481C22×Q8C23×C1111yescharacteristic
482C22×D4C23×C1111yescharacteristic
483#137—22no—
484#137—22no—
485C2×Q16—21no—
486C2×SD16—21no—
487C2×M16C23×C1111yescharacteristic
488C2×M16C23×C1111yescharacteristic
489C2×M16C23×C1111yescharacteristic
490C2×M16C23×C1111yescharacteristic
491C4⋊Q8—21no—
492C4⋊Q8—22no—
493C4⋊Q8—41no—
494C4⋊Q8D4×C1111yescharacteristic
495C4⋊Q8D4×C1111yescharacteristic
496#127—21no—
497#126—22no—
498#126—22no—
499#126—22no—
500#126—22no—
501#125D4×C1111yescharacteristic
502#125D4×C1111yescharacteristic
503#124—22no—
504#124—22no—
505#124—21no—
506#124—21no—
507#124—22no—
508#124—21no—
509#124—21no—
510#124—21no—
511#124—21no—
512#124—41no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—21no—
526#120—22no—
527C4×Q8—21no—
528C4×Q8—21no—
529C4×Q8—21no—
530C4×Q8—21no—
531C4×Q8—21no—
532C4×Q8—21no—
533C4×Q8—21no—
534C4×Q8—21no—
535C4×Q8—21no—
536C4×Q8—21no—
537C4×Q8D4×C1111yescharacteristic
538C4×Q8D4×C1111yescharacteristic
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C1111yescharacteristic
548C4×D4D4×C1111yescharacteristic
549#117—22no—
550#117—22no—
551#117—22no—
552#117—21no—
553#117C23×C1111yescharacteristic
554#117C23×C1111yescharacteristic
555#117C23×C1111yescharacteristic
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4C23×C1111yescharacteristic
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4D4×C1112yes—
564C2×C22⋊C4D4×C1112yes—
565C2×C42—21no—
566C2×C42—21no—
567C2×C42C23×C1111yescharacteristic
568C2×C42C23×C1111yescharacteristic
569C2×C42C23×C1111yescharacteristic
570#107—21no—
571#107—21no—
572#107—21no—
573#106—21no—
574#106—21no—
575#106—21no—
576C4⋊C8—21no—
577C4⋊C8—21no—
578#104—41no—
579#104—41no—
580#103—21no—
581#103—21no—
582#103—21no—
583#103—21no—
584#103—21no—
585#103—21no—
586#103—21no—
587#102—21no—
588#101—22no—
589#101—41no—
590#100—22no—
591#100—41no—
592#97—21no—
593C4×C8—21no—
594#95—21no—
595#95—22no—
596C2×C11—21no—
597C2×C11—21no—
598C2×C11—81no—
599C2×C11—82no—
600C2×C11#240711yescharacteristic
601C2×C11#301811yescharacteristic
602C2×C11#302211yescharacteristic
603C24C2×D4×C1112yes—
604#41—21no—
605#41—21no—
606#41—21no—
607#41—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C2×D4×C1111yescharacteristic
622C2×Q8C11×#4112yes—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4C2×D4×C1111yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4C2×D4×C1112yes—
643C22×C4C2×D4×C1111yescharacteristic
644C22×C4C2×D4×C1111yescharacteristic
645C22×C4C24×C1111yescharacteristic
646Q16—24no—
647SD16—24no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16C11×#4112yes—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4C2×D4×C1111yescharacteristic
679C4⋊C4C2×D4×C1111yescharacteristic
680C4⋊C4C2×D4×C1111yescharacteristic
681C4⋊C4C2×D4×C1111yescharacteristic
682C4⋊C4C2×D4×C1111yescharacteristic
683C4⋊C4C2×D4×C1111yescharacteristic
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C42—22no—
702C42—22no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—41no—
713C42—41no—
714C42C2×D4×C1111yescharacteristic
715C42C2×D4×C1111yescharacteristic
716C42C2×D4×C1111yescharacteristic
717C42C2×D4×C1111yescharacteristic
718C11#2414911yescharacteristic, direct product factor, Sylow
719C23—22no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—42no—
724C23—42no—
725C23C22×D4×C1111yescharacteristic
726Q8—22no—
727Q8—21no—
728Q8—21no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—81no—
737Q8—81no—
738D4—21no—
739D4—21no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—82no—
747D4—82no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4C11×#12011yescharacteristic
778C2×C4C11×#12011yescharacteristic
779C2×C4C11×#12011yescharacteristic
780C2×C4C11×#12011yescharacteristic
781C2×C4C22×D4×C1111yescharacteristic
782C2×C4C22×D4×C1111yescharacteristic
783C2×C4C2×C11×#4111yescharacteristic
784C2×C4C2×C11×#4111yescharacteristic
785C2×C4C11×H(5,𝔽2)11yescharacteristic
786C2×C4C11×2−1+411yescharacteristic
787C8—22no—
788C8—41no—
789C8—41no—
790C8—41no—
791C22—21no—
792C22—21no—
793C22—41no—
794C22—42no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—42no—
799C22—82no—
800C22—82no—
801C22C2×C11×#12011yescharacteristic
802C22C11×#54611yescharacteristic
803C22C11×#54711yescharacteristic
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—42no—
809C4—42no—
810C4—41no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—81no—
819C4—81no—
820C4C11×#52511yescharacteristic
821C4C11×#53711yescharacteristic
822C4C11×#54811yescharacteristic
823C4C11×#55011yescharacteristic
824C2—21no—
825C2—21no—
826C2—82no—
827C2—81no—
828C2C11×#240711yescharacteristic
829C2C11×#301811yescharacteristic
830C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3078C2semidirect
3. C4×C11×#137C2semidirect
4. C11×#2545C2semidirect
5. C11×#2038C2semidirect
7. C11×#2005C2semidirect
9. C11×#1986C2semidirect
10. C11×#1967C2semidirect
11. C11×#1886C2semidirect
12. C11×#1885C2semidirect
13. C11×#1857C2semidirect
14. C11×#1856C2semidirect
15. C11×#1806C2semidirect
188. #24149C11direct (N × H)
305. #3078C2×C11semidirect
306. C4×#137C2×C11semidirect
307. #2545C2×C11semidirect
308. #2038C2×C11semidirect
310. #2005C2×C11semidirect
312. #1986C2×C11semidirect
313. #1967C2×C11semidirect
314. #1886C2×C11semidirect
315. #1885C2×C11semidirect
316. #1857C2×C11semidirect
317. #1856C2×C11semidirect
318. #1806C2×C11semidirect
718. C11#24149direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35102
C11×#30782
C4×C11×#1372
C11×#25452
C11×#20382
C11×#20372
C11×#20052
C11×#20042
C11×#19862
C11×#19672
C11×#18862
C11×#18852
C11×#18572
C11×#18562
C11×#18062
#2414911