Finite Group Databasebeta

← C11×#24640 #14601833

Subgroups — C11×#24640 #14601833

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic, complemented
3C11×#2545C211yesmaximal, characteristic, complemented
4C11×#2354C211yesmaximal, characteristic, complemented
5C11×#2055C211yesmaximal, characteristic, complemented
6C11×#2054C211yesmaximal, characteristic
7C11×#2013C211yesmaximal, characteristic, complemented
8C11×#2012C211yesmaximal, characteristic
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1981C211yesmaximal, characteristic, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C11×#1940C211yesmaximal, characteristic, complemented
13C11×#1928C211yesmaximal, characteristic, complemented
14C11×#1925C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C11×#463—24no—
26C11×#440—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C11×#396—21no—
43C11×#396—21no—
44C11×#391C2211yescharacteristic
45C11×#390C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#388—21no—
49C11×#388—21no—
50C11×#388—21no—
51C11×#388—21no—
52C11×#384C2211yescharacteristic
53C11×#380—21no—
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C2×C11×SD16—41no—
72C2×C11×D8—22no—
73C2×C11×D8—41no—
74C2×C11×D8—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×C4⋊Q8—22no—
80C11×C4⋊Q8—41no—
81C11×#124—22no—
82C11×#124—22no—
83C11×#124—22no—
84C11×#124—41no—
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11D414yes—
89C11×#117—44no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11—21no—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×#107—22no—
119C11×C4⋊C8—22no—
120C11×C4⋊C8—41no—
121C11×C4⋊C8—41no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#103—41no—
126C11×#103—41no—
127C11×#103—41no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#102—22no—
131C11×#102—41no—
132C11×#97—22no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95D411yescharacteristic
138C11×#95D411yescharacteristic
139#24640C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11#4112yes—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11C2×D412yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—24no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C11×SD16—28no—
183C11×SD16—44no—
184C11×D8—44no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11#4112yes—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—81no—
211C11×C4⋊C4C2×D412yes—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—81no—
222C11×C22⋊C4—81no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—42no—
228C42×C11—42no—
229C42×C11—42no—
230C42×C11C2×D412yes—
231C42×C11#4112yes—
232C2×#463C2×C1111yescharacteristic
233C2×#440C2×C1111yescharacteristic, complemented
234#2545C2×C1111yescharacteristic, complemented
235#2354C2×C1111yescharacteristic, complemented
236#2055C2×C1111yescharacteristic, complemented
237#2054C2×C1111yescharacteristic
238#2013C2×C1111yescharacteristic, complemented
239#2012C2×C1111yescharacteristic
240#1983C2×C1111yescharacteristic, complemented
241#1981C2×C1111yescharacteristic, complemented
242#1959C2×C1111yescharacteristic, complemented
243#1940C2×C1111yescharacteristic, complemented
244#1928C2×C1111yescharacteristic, complemented
245#1925C2×C1111yescharacteristic, complemented
246#1803C2×C1111yescharacteristic, complemented
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11C22×D411yescharacteristic
262Q8×C11—22no—
263Q8×C11—22no—
264Q8×C11—41no—
265Q8×C11—41no—
266Q8×C11—41no—
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270D4×C11—22no—
271D4×C11—22no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—41no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—48no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11#12112yes—
313C2×C4×C11#12112yes—
314C2×C4×C11AGL(1,ℤ/8)12yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C8×C11—22no—
322C8×C11—41no—
323C8×C11—41no—
324C8×C11—41no—
325C22×SD16C22×C1111yescharacteristic
326C22×SD16C22×C1111yescharacteristic
327C22×D8C22×C1111yescharacteristic
328C2×C4⋊Q8C22×C1111yescharacteristic
329C2×#124C22×C1111yescharacteristic
330C2×#124C22×C1111yescharacteristic
331C2×C4×Q8C22×C1111yescharacteristic
332C2×C4×D4C22×C1111yescharacteristic
333C2×#117—21no—
334#463—24no—
335#440—24no—
336C2×#107C22×C1111yescharacteristic
337C2×C4⋊C8C22×C1111yescharacteristic
338C2×C4⋊C8C22×C1111yescharacteristic
339C2×C4⋊C8C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×#97C22×C1111yescharacteristic
351#396—21no—
352#396—21no—
353#391C22×C1111yescharacteristic
354#390C22×C1111yescharacteristic
355#390C22×C1111yescharacteristic
356#390C22×C1111yescharacteristic
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#384C22×C1111yescharacteristic
362#380—21no—
363C4×C4⋊C4C22×C1111yescharacteristic
364C4×C4⋊C4C22×C1111yescharacteristic
365C4×C4⋊C4C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369#336C22×C1111yescharacteristic
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11C2×#12111yescharacteristic
385C22×C11#54611yescharacteristic
386C22×C11#55011yescharacteristic
387C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C11#57511yescharacteristic
389C22×C11#57711yescharacteristic
390C22×C11#57811yescharacteristic
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—42no—
395C4×C11—42no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11#52511yescharacteristic
404C4×C11#53511yescharacteristic
405C4×C11#55311yescharacteristic
406C4×C11#55511yescharacteristic
407C22×Q8C23×C1111yescharacteristic
408C22×Q8C23×C1111yescharacteristic
409C22×D4C23×C1111yescharacteristic
410C22×D4C23×C1111yescharacteristic
411C23×C4—21no—
412C2×SD16—22no—
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16—22no—
416C2×SD16—41no—
417C2×SD16—41no—
418C2×D8—22no—
419C2×D8—41no—
420C2×D8—41no—
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425C4⋊Q8—22no—
426C4⋊Q8—41no—
427#124—22no—
428#124—22no—
429#124—22no—
430#124—41no—
431C4×Q8—22no—
432C4×Q8—22no—
433C4×D4—22no—
434C4×D4D4×C1114yes—
435#117—44no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C1111yescharacteristic
442C2×C4⋊C4D4×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C4⋊C4C23×C1111yescharacteristic
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C1111yescharacteristic
462C2×C42C23×C1111yescharacteristic
463C2×C42C23×C1111yescharacteristic
464#107—22no—
465C4⋊C8—22no—
466C4⋊C8—41no—
467C4⋊C8—41no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—41no—
472#103—41no—
473#103—41no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—41no—
478#97—22no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95D4×C1111yescharacteristic
484#95D4×C1111yescharacteristic
485C2×C11—82no—
486C2×C11—161no—
487C2×C11#241411yescharacteristic
488C2×C11#303611yescharacteristic
489C2×C11#304611yescharacteristic
490C2×C11#330811yescharacteristic
491C2×C11#332111yescharacteristic
492C2×C11#339711yescharacteristic
493C2×C11#340211yescharacteristic
494C24—21no—
495C24—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8C11×#4112yes—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4C2×D4×C1112yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C24×C1111yescharacteristic
536SD16—28no—
537SD16—44no—
538D8—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8C11×#4112yes—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—41no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4C2×D4×C1112yes—
566C22⋊C4—24no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—42no—
582C42—42no—
583C42—42no—
584C42C2×D4×C1112yes—
585C42C11×#4112yes—
586C11#2464011yescharacteristic, direct product factor, Sylow
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C22×D4×C1111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—48no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4C11×#12112yes—
653C2×C4C11×#12112yes—
654C2×C4C11×AGL(1,ℤ/8)12yes—
655C2×C4C22×D4×C1111yescharacteristic
656C2×C4C2×C11×#4111yescharacteristic
657C2×C4C2×C11×#4111yescharacteristic
658C2×C4C2×C11×#4111yescharacteristic
659C2×C4C11×H(5,𝔽2)11yescharacteristic
660C2×C4C11×H(5,𝔽2)11yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×C11×#12111yescharacteristic
680C22C11×#54611yescharacteristic
681C22C11×#55011yescharacteristic
682C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
683C22C11×#57511yescharacteristic
684C22C11×#57711yescharacteristic
685C22C11×#57811yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C11×#52511yescharacteristic
699C4C11×#53511yescharacteristic
700C4C11×#55311yescharacteristic
701C4C11×#55511yescharacteristic
702C2—82no—
703C2—161no—
704C2C11×#241411yescharacteristic
705C2C11×#303611yescharacteristic
706C2C11×#304611yescharacteristic
707C2C11×#330811yescharacteristic
708C2C11×#332111yescharacteristic
709C2C11×#339711yescharacteristic
710C2C11×#340211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#440C2semidirect
3. C11×#2545C2semidirect
4. C11×#2354C2semidirect
5. C11×#2055C2semidirect
7. C11×#2013C2semidirect
9. C11×#1983C2semidirect
10. C11×#1981C2semidirect
11. C11×#1959C2semidirect
12. C11×#1940C2semidirect
13. C11×#1928C2semidirect
14. C11×#1925C2semidirect
15. C11×#1803C2semidirect
139. #24640C11direct (N × H)
233. C2×#440C2×C11semidirect
234. #2545C2×C11semidirect
235. #2354C2×C11semidirect
236. #2055C2×C11semidirect
238. #2013C2×C11semidirect
240. #1983C2×C11semidirect
241. #1981C2×C11semidirect
242. #1959C2×C11semidirect
243. #1940C2×C11semidirect
244. #1928C2×C11semidirect
245. #1925C2×C11semidirect
246. #1803C2×C11semidirect
586. C11#24640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4402
C11×#25452
C11×#23542
C11×#20552
C11×#20542
C11×#20132
C11×#20122
C11×#19832
C11×#19812
C11×#19592
C11×#19402
C11×#19282
C11×#19252
C11×#18032
#2464011