Finite Group Databasebeta

← C11×#24505 #14601698

Subgroups — C11×#24505 #14601698

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#452C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2855C211yesmaximal, characteristic, complemented
4C11×#2297C211yesmaximal, characteristic
5C11×#2067C211yesmaximal, characteristic, complemented
6C11×#2066C211yesmaximal, characteristic, complemented
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#1969C211yesmaximal, characteristic, complemented
10C11×#1968C211yesmaximal, characteristic, complemented
11C11×#1934C211yesmaximal, characteristic, complemented
12C11×#1933C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#452—24no—
23C11×#431—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#390C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#389C2211yescharacteristic
48C11×#387—21no—
49C11×#387—21no—
50C11×#386—21no—
51C11×#386—21no—
52C11×#385—21no—
53C11×#381—21no—
54C11×#380C2211yescharacteristic
55C4×C11×C22⋊C4—21no—
56C4×C11×C22⋊C4—21no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11D411yescharacteristic
73C23×C4×C11D411yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C2×C11×Q16—22no—
76C2×C11×Q16—22no—
77C2×C11×Q16—41no—
78C2×C11×SD16—22no—
79C2×C11×SD16—22no—
80C2×C11×SD16—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×#117—41no—
88C11×#117—41no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—22no—
105C2×C42×C11—22no—
106C2×C42×C11—21no—
107C2×C42×C11D411yescharacteristic
108C2×C42×C11D411yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#107—41no—
112C11×#106—41no—
113C11×C4⋊C8—22no—
114C11×C4⋊C8—22no—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—41no—
118C11×#103—41no—
119C11×#103—41no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—41no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8D414yes—
125C4×C8×C11—22no—
126C4×C8×C11—22no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24505C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
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—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11#4112yes—
157C2×D4×C11—24no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11#4112yes—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—24no—
174C22×C4×C11—22no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—41no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C11×Q16—44no—
195C11×SD16—44no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C2×D412yes—
207C2×C8×C11C2×D412yes—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C42×C11—22no—
229C42×C11—22no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—42no—
235C2×#452C2×C1111yescharacteristic
236C2×#431C2×C1111yescharacteristic, complemented
237#2855C2×C1111yescharacteristic, complemented
238#2297C2×C1111yescharacteristic
239#2067C2×C1111yescharacteristic, complemented
240#2066C2×C1111yescharacteristic, complemented
241#2056C2×C1111yescharacteristic, complemented
242#2055C2×C1111yescharacteristic, complemented
243#1969C2×C1111yescharacteristic, complemented
244#1968C2×C1111yescharacteristic, complemented
245#1934C2×C1111yescharacteristic, complemented
246#1933C2×C1111yescharacteristic, complemented
247#1873C2×C1111yescharacteristic, complemented
248#1854C2×C1111yescharacteristic, complemented
249#1788C2×C1111yescharacteristic
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—22no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11#12112yes—
264C23×C11C22×D411yescharacteristic
265Q8×C11—22no—
266Q8×C11—22no—
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273D4×C11—22no—
274D4×C11—22no—
275D4×C11—48no—
276D4×C11—41no—
277D4×C11—41no—
278C2×C4×C11—28no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—44no—
296C2×C4×C11—48no—
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—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11#12112yes—
318C2×C4×C11#13512yes—
319C2×C4×C11#13512yes—
320C2×C4×C11#13712yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C8×C11—22no—
328C8×C11—22no—
329C8×C11—41no—
330C8×C11—41no—
331C22×#41C22×C1111yescharacteristic
332C22×Q16C22×C1111yescharacteristic
333C22×SD16C22×C1111yescharacteristic
334C2×C22⋊Q8C22×C1111yescharacteristic
335C2×#117C22×C1111yescharacteristic
336C22×C42C22×C1111yescharacteristic
337#452—24no—
338#431—24no—
339C2×#107C22×C1111yescharacteristic
340C2×#106C22×C1111yescharacteristic
341C2×C4⋊C8C22×C1111yescharacteristic
342C2×C4⋊C8C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#103C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×#102C22×C1111yescharacteristic
351C2×C22⋊C8C22×C1111yescharacteristic
352C2×C22⋊C8C22×C1111yescharacteristic
353C2×C4×C8C22×C1111yescharacteristic
354C2×C4×C8C22×C1111yescharacteristic
355#391C22×C1111yescharacteristic
356#391C22×C1111yescharacteristic
357#391C22×C1111yescharacteristic
358#391C22×C1111yescharacteristic
359#390C22×C1111yescharacteristic
360#390C22×C1111yescharacteristic
361#389C22×C1111yescharacteristic
362#389C22×C1111yescharacteristic
363#387—21no—
364#387—21no—
365#386—21no—
366#386—21no—
367#385—21no—
368#381—21no—
369#380C22×C1111yescharacteristic
370C4×C22⋊C4—21no—
371C4×C22⋊C4—21no—
372#340C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11C2×#12111yescharacteristic
391C22×C11#52511yescharacteristic
392C22×C11#53511yescharacteristic
393C22×C11C2×#13511yescharacteristic
394C22×C11C2×#13511yescharacteristic
395C22×C11C2×#13711yescharacteristic
396C22×C11#57511yescharacteristic
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—42no—
402C4×C11—41no—
403C4×C11—81no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11#54611yescharacteristic
410C4×C11#54611yescharacteristic
411C4×C11#55111yescharacteristic
412C4×C11#55111yescharacteristic
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—22no—
417C2×#41—41no—
418C2×#41—41no—
419C22×Q8C23×C1111yescharacteristic
420C22×Q8C23×C1111yescharacteristic
421C22×D4—21no—
422C22×D4C23×C1111yescharacteristic
423C23×C4—21no—
424C23×C4D4×C1111yescharacteristic
425C23×C4D4×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C2×Q16—22no—
428C2×Q16—22no—
429C2×Q16—41no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—41no—
433C22×C8C23×C1111yescharacteristic
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439#117—41no—
440#117—41no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C4⋊C4C23×C1111yescharacteristic
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C4⋊C4C23×C1111yescharacteristic
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×C42—22no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42D4×C1111yescharacteristic
460C2×C42D4×C1111yescharacteristic
461C2×C42C23×C1111yescharacteristic
462C2×C42C23×C1111yescharacteristic
463#107—41no—
464#106—41no—
465C4⋊C8—22no—
466C4⋊C8—22no—
467#103—22no—
468#103—22no—
469#103—41no—
470#103—41no—
471#103—41no—
472#102—22no—
473#102—22no—
474#102—41no—
475C22⋊C8—22no—
476C22⋊C8D4×C1114yes—
477C4×C8—22no—
478C4×C8—22no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490C2×C11—42no—
491C2×C11—82no—
492C2×C11#241111yescharacteristic
493C2×C11#305011yescharacteristic
494C2×C11#305611yescharacteristic
495C2×C11#310211yescharacteristic
496C2×C11#310711yescharacteristic
497C2×C11#321011yescharacteristic
498C2×C11#321211yescharacteristic
499C24—21no—
500C24C2×D4×C1111yescharacteristic
501#41—44no—
502#41—44no—
503#41—44no—
504#41—44no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8C11×#4112yes—
517C2×D4—24no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4C11×#4112yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—41no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1112yes—
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×D4×C1111yescharacteristic
552C22×C4C11×#4112yes—
553C22×C4C24×C1111yescharacteristic
554Q16—44no—
555SD16—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8C2×D4×C1112yes—
567C2×C8C2×D4×C1112yes—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C42—22no—
589C42—22no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—42no—
595C11#2450511yescharacteristic, direct product factor, Sylow
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C11×#12112yes—
610C23C22×D4×C1111yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619D4—22no—
620D4—22no—
621D4—48no—
622D4—41no—
623D4—41no—
624C2×C4—28no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—44no—
642C2×C4—48no—
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×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4C11×#12112yes—
664C2×C4C11×#13512yes—
665C2×C4C11×#13512yes—
666C2×C4C11×#13712yes—
667C2×C4C22×D4×C1111yescharacteristic
668C2×C4C2×C11×#4111yescharacteristic
669C2×C4C2×C11×#4111yescharacteristic
670C2×C4C2×C11×#4111yescharacteristic
671C2×C4C11×H(5,𝔽2)11yescharacteristic
672C2×C4C11×H(5,𝔽2)11yescharacteristic
673C8—22no—
674C8—22no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×C11×#12111yescharacteristic
692C22C11×#52511yescharacteristic
693C22C11×#53511yescharacteristic
694C22C2×C11×#13511yescharacteristic
695C22C2×C11×#13511yescharacteristic
696C22C2×C11×#13711yescharacteristic
697C22C11×#57511yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C11×#54611yescharacteristic
711C4C11×#54611yescharacteristic
712C4C11×#55111yescharacteristic
713C4C11×#55111yescharacteristic
714C2—42no—
715C2—82no—
716C2C11×#241111yescharacteristic
717C2C11×#305011yescharacteristic
718C2C11×#305611yescharacteristic
719C2C11×#310211yescharacteristic
720C2C11×#310711yescharacteristic
721C2C11×#321011yescharacteristic
722C2C11×#321211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#431C2semidirect
3. C11×#2855C2semidirect
5. C11×#2067C2semidirect
6. C11×#2066C2semidirect
7. C11×#2056C2semidirect
8. C11×#2055C2semidirect
9. C11×#1969C2semidirect
10. C11×#1968C2semidirect
11. C11×#1934C2semidirect
12. C11×#1933C2semidirect
13. C11×#1873C2semidirect
14. C11×#1854C2semidirect
138. #24505C11direct (N × H)
236. C2×#431C2×C11semidirect
237. #2855C2×C11semidirect
239. #2067C2×C11semidirect
240. #2066C2×C11semidirect
241. #2056C2×C11semidirect
242. #2055C2×C11semidirect
243. #1969C2×C11semidirect
244. #1968C2×C11semidirect
245. #1934C2×C11semidirect
246. #1933C2×C11semidirect
247. #1873C2×C11semidirect
248. #1854C2×C11semidirect
595. C11#24505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4522
C2×C11×#4312
C11×#28552
C11×#22972
C11×#20672
C11×#20662
C11×#20562
C11×#20552
C11×#19692
C11×#19682
C11×#19342
C11×#19332
C11×#18732
C11×#18542
C11×#17882
#2450511