Finite Group Databasebeta

← C11×#25018 #14602211

Subgroups — C11×#25018 #14602211

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#481C211yesmaximal, characteristic, complemented
2C2×C11×#482C211yesmaximal, characteristic, complemented
3C11×#2535C211yesmaximal, characteristic
4C11×#2352C211yesmaximal, characteristic, complemented
5C11×#2077C211yesmaximal, characteristic, complemented
6C11×#2077C211yesmaximal, characteristic, complemented
7C11×#2033C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1954C211yesmaximal, characteristic, complemented
10C11×#1949C211yesmaximal, characteristic, complemented
11C11×#1854C211yesmaximal, characteristic, complemented
12C11×#1852C211yesmaximal, characteristic, complemented
13C11×#1846C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C11×#482—24no—
23C11×#481—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C11×#397—21no—
41C11×#392—21no—
42C11×#388—21no—
43C11×#387—21no—
44C11×#386—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#382C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11D411yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—41no—
76C11×#121—41no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C11×#117—22no—
82C11×#117—41no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11—21no—
106C2×C42×C11C2311yescharacteristic
107C11×#107—22no—
108C11×#107—41no—
109C11×#107—41no—
110C11×#106—22no—
111C11×#106—22no—
112C11×#106—22no—
113C11×C4⋊C8—22no—
114C11×#102—22no—
115C11×#102—22no—
116C11×#102—22no—
117C11×#102D414yescomplemented
118C11×C22⋊C8—22no—
119C11×C22⋊C8—22no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
122C4×C8×C11—22no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132#25018C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C24×C11C2×D411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—41no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—81no—
149C2×D4×C11—81no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—81no—
174C22×C4×C11—81no—
175C22×C4×C11—81no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
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×C11C2×D412yes—
192C2×C8×C11#4112yes—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
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—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4C2×D412yes—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C11×C22⋊C4—81no—
219C42×C11—42no—
220C42×C11—81no—
221C42×C11#4112yes—
222C42×C11#4112yes—
223C2×#481C2×C1111yescharacteristic, complemented
224C2×#482C2×C1111yescharacteristic, complemented
225#2535C2×C1111yescharacteristic
226#2352C2×C1111yescharacteristic, complemented
227#2077C2×C1111yescharacteristic, complemented
228#2077C2×C1111yescharacteristic, complemented
229#2033C2×C1111yescharacteristic, complemented
230#2033C2×C1111yescharacteristic, complemented
231#1954C2×C1111yescharacteristic, complemented
232#1949C2×C1111yescharacteristic, complemented
233#1854C2×C1111yescharacteristic, complemented
234#1852C2×C1111yescharacteristic, complemented
235#1846C2×C1111yescharacteristic, complemented
236#1804C2×C1111yescharacteristic, complemented
237C4×#102C2×C1111yescharacteristic, complemented
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—22no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11#13512yes—
259C23×C11C22×D411yescharacteristic
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—44no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—84no—
266D4×C11—84no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
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—84no—
307C2×C4×C11—84no—
308C2×C4×C11#12312yes—
309C2×C4×C11#12312yes—
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C112−1+411yescharacteristic
316C8×C11—22no—
317C8×C11—22no—
318C8×C11—41no—
319C8×C11—41no—
320C2×#121C22×C1111yescharacteristic
321C2×#121C22×C1111yescharacteristic
322C2×C4×D4C22×C1111yescharacteristic
323C2×C4×D4C22×C1111yescharacteristic
324C2×#117C22×C1111yescharacteristic
325C22×C4⋊C4C22×C1111yescharacteristic
326#482—24no—
327#481—24no—
328C2×#107C22×C1111yescharacteristic
329C2×#107C22×C1111yescharacteristic
330C2×#107C22×C1111yescharacteristic
331C2×#106C22×C1111yescharacteristic
332C2×#106C22×C1111yescharacteristic
333C2×#106C22×C1111yescharacteristic
334C2×C4⋊C8C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×C22⋊C8C22×C1111yescharacteristic
340C2×C22⋊C8C22×C1111yescharacteristic
341C2×C22⋊C8C22×C1111yescharacteristic
342C2×C22⋊C8C22×C1111yescharacteristic
343C2×C4×C8C22×C1111yescharacteristic
344#397—21no—
345#392—21no—
346#388—21no—
347#387—21no—
348#386—21no—
349#386—21no—
350#386—21no—
351#382C22×C1111yescharacteristic
352#382C22×C1111yescharacteristic
353#380C22×C1111yescharacteristic
354#380C22×C1111yescharacteristic
355#380C22×C1111yescharacteristic
356#380C22×C1111yescharacteristic
357C4×C4⋊C4C22×C1111yescharacteristic
358C4×C22⋊C4—21no—
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—42no—
378C22×C11—41no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—41no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11C2×#12311yescharacteristic
387C22×C11D4211yescharacteristic
388C22×C11#54711yescharacteristic
389C22×C11C2×#13511yescharacteristic
390C22×C11#57511yescharacteristic
391C22×C11#57611yescharacteristic
392C22×C11#57711yescharacteristic
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11—42no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11#53211yescharacteristic
405C4×C11#54211yescharacteristic
406C4×C11#54711yescharacteristic
407C4×C11#55311yescharacteristic
408C22×D4—21no—
409C22×D4—21no—
410C22×D4D4×C1111yescharacteristic
411C22×D4C23×C1111yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4C23×C1111yescharacteristic
415C23×C4C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420#121—22no—
421#121—22no—
422#121—41no—
423#121—41no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428#117—22no—
429#117—41no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4D4×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4D4×C1111yescharacteristic
450C2×C22⋊C4D4×C1111yescharacteristic
451C2×C42—21no—
452C2×C42—21no—
453C2×C42C23×C1111yescharacteristic
454#107—22no—
455#107—41no—
456#107—41no—
457#106—22no—
458#106—22no—
459#106—22no—
460C4⋊C8—22no—
461#102—22no—
462#102—22no—
463#102—22no—
464#102D4×C1114yescomplemented
465C22⋊C8—22no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469C4×C8—22no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479C2×C11—42no—
480C2×C11—81no—
481C2×C11—82no—
482C2×C11#242211yescharacteristic
483C2×C11#309111yescharacteristic
484C2×C11#309611yescharacteristic
485C2×C11#327311yescharacteristic
486C2×C11#328211yescharacteristic
487C2×C11#333911yescharacteristic
488C2×C11#335111yescharacteristic
489C24—21no—
490C24C2×D4×C1111yescharacteristic
491C24C2×D4×C1111yescharacteristic
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—41no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4C2×D4×C1112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C24×C1111yescharacteristic
537C2×C8—21no—
538C2×C8—21no—
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×C8C2×D4×C1112yes—
548C2×C8C11×#4112yes—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4C2×D4×C1112yes—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C42—42no—
576C42—81no—
577C42C11×#4112yes—
578C42C11×#4112yes—
579C11#2501811yescharacteristic, direct product factor, Sylow
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—22no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C11×#13512yes—
601C23C22×D4×C1111yescharacteristic
602D4—22no—
603D4—22no—
604D4—44no—
605D4—41no—
606D4—41no—
607D4—84no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
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—84no—
649C2×C4—84no—
650C2×C4C11×#12312yes—
651C2×C4C11×#12312yes—
652C2×C4C22×D4×C1111yescharacteristic
653C2×C4C2×C11×#4111yescharacteristic
654C2×C4C2×C11×#4111yescharacteristic
655C2×C4C2×C11×#4111yescharacteristic
656C2×C4C11×H(5,𝔽2)11yescharacteristic
657C2×C4C11×2−1+411yescharacteristic
658C8—22no—
659C8—22no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—42no—
673C22—42no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C2×C11×#12311yescharacteristic
684C22D42×C1111yescharacteristic
685C22C11×#54711yescharacteristic
686C22C2×C11×#13511yescharacteristic
687C22C11×#57511yescharacteristic
688C22C11×#57611yescharacteristic
689C22C11×#57711yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4C11×#53211yescharacteristic
702C4C11×#54211yescharacteristic
703C4C11×#54711yescharacteristic
704C4C11×#55311yescharacteristic
705C2—42no—
706C2—81no—
707C2—82no—
708C2C11×#242211yescharacteristic
709C2C11×#309111yescharacteristic
710C2C11×#309611yescharacteristic
711C2C11×#327311yescharacteristic
712C2C11×#328211yescharacteristic
713C2C11×#333911yescharacteristic
714C2C11×#335111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#481C2semidirect
2. C2×C11×#482C2semidirect
4. C11×#2352C2semidirect
5. C11×#2077C2semidirect
6. C11×#2077C2semidirect
7. C11×#2033C2semidirect
8. C11×#2033C2semidirect
9. C11×#1954C2semidirect
10. C11×#1949C2semidirect
11. C11×#1854C2semidirect
12. C11×#1852C2semidirect
13. C11×#1846C2semidirect
14. C11×#1804C2semidirect
15. C4×C11×#102C2semidirect
117. C11×#102D4semidirect
132. #25018C11direct (N × H)
223. C2×#481C2×C11semidirect
224. C2×#482C2×C11semidirect
226. #2352C2×C11semidirect
227. #2077C2×C11semidirect
228. #2077C2×C11semidirect
229. #2033C2×C11semidirect
230. #2033C2×C11semidirect
231. #1954C2×C11semidirect
232. #1949C2×C11semidirect
233. #1854C2×C11semidirect
234. #1852C2×C11semidirect
235. #1846C2×C11semidirect
236. #1804C2×C11semidirect
237. C4×#102C2×C11semidirect
464. #102D4×C11semidirect
579. C11#25018direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4812
C2×C11×#4822
C11×#25352
C11×#23522
C11×#20772
C11×#20332
C11×#19542
C11×#19492
C11×#18542
C11×#18522
C11×#18462
C11×#18042
C4×C11×#1022
#2501811