Finite Group Databasebeta

← C11×#22579 #14599772

Subgroups — C11×#22579 #14599772

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#417C211yesmaximal, characteristic
2C11×#2345C211yesmaximal, characteristic, complemented
3C11×#2341C211yesmaximal, characteristic
4C11×#1936C211yesmaximal, characteristic, complemented
5C11×#1934C211yesmaximal, characteristic, complemented
6C11×#1926C211yesmaximal, characteristic, complemented
7C11×#1925C211yesmaximal, characteristic, complemented
8C11×#1865C211yesmaximal, characteristic, complemented
9C11×#1863C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1809C211yesmaximal, characteristic, complemented
12C11×#1788C211yesmaximal, characteristic
13C11×#1763C211yesmaximal, characteristic, complemented
14C4×C11×#103C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C11×#417C418yescomplemented
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#390—21no—
36C11×#390—21no—
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#387—21no—
42C11×#387—21no—
43C11×#380—21no—
44C11×#380—21no—
45C11×#380C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4—21no—
50C4×C11×C22⋊C4—21no—
51C4×C11×C22⋊C4C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yes—
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C2×C11×M16—41no—
73C2×C11×M16—41no—
74C2×C11×M16C2×C414yes—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—41no—
82C4×Q8×C11—41no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4C2×C414yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
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×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C11×#107—41no—
111C11×#106—41no—
112C11×#103—22no—
113C11×#103—22no—
114C11×#103C2×C414yes—
115C11×#103C2×C414yes—
116C11×#102—41no—
117C11×#102—41no—
118C11×#102C2×C414yes—
119C11×#102C2×C414yes—
120C11×C22⋊C8—22no—
121C11×#97—41no—
122C4×C8×C11—41no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95D411yescharacteristic
130C11×#95D411yescharacteristic
131#22579C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C11×#41—28no—
135C11×#41—44no—
136C11×#41—44no—
137C11×#41—44no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11C22×C412yes—
142C2×Q8×C11#4112yes—
143C2×Q8×C11#4112yes—
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11C22×C412yes—
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—24no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11#4112yes—
177C22×C4×C11C2411yescharacteristic
178C11×M16—44no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
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×C11C22×C412yes—
190C2×C8×C11C22×C412yes—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
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—42no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—81no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4C22×C412yes—
207C11×C4⋊C4C22×C412yes—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—81no—
214C11×C22⋊C4—81no—
215C11×C22⋊C4—81no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—42no—
221C42×C11—42no—
222C42×C11—81no—
223C42×C11—81no—
224C2×#417C2×C1111yescharacteristic
225#2345C2×C1111yescharacteristic, complemented
226#2341C2×C1111yescharacteristic
227#1936C2×C1111yescharacteristic, complemented
228#1934C2×C1111yescharacteristic, complemented
229#1926C2×C1111yescharacteristic, complemented
230#1925C2×C1111yescharacteristic, complemented
231#1865C2×C1111yescharacteristic, complemented
232#1863C2×C1111yescharacteristic, complemented
233#1823C2×C1111yescharacteristic, complemented
234#1809C2×C1111yescharacteristic, complemented
235#1788C2×C1111yescharacteristic
236#1763C2×C1111yescharacteristic, complemented
237C4×#103C2×C1111yescharacteristic, complemented
238#1753C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—22no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11C4×D412yes—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11#11714yes—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—48no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
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—21no—
285C2×C4×C11—48no—
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—84no—
303C2×C4×C11C4×D412yes—
304C2×C4×C11#13712yes—
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C8×C11—22no—
312C8×C11—22no—
313C8×C11—41no—
314C8×C11—41no—
315C22×#41C22×C1111yescharacteristic
316C22×M16C22×C1111yescharacteristic
317C2×C4×Q8C22×C1111yescharacteristic
318C2×C4×Q8C22×C1111yescharacteristic
319C22×C4⋊C4C22×C1111yescharacteristic
320C2×#107C22×C1111yescharacteristic
321C2×#106C22×C1111yescharacteristic
322#417C4×C1118yescomplemented
323C2×#103C22×C1111yescharacteristic
324C2×#103C22×C1111yescharacteristic
325C2×#103C22×C1111yescharacteristic
326C2×#103C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328C2×#102C22×C1111yescharacteristic
329C2×#102C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×C22⋊C8C22×C1111yescharacteristic
332C2×#97C22×C1111yescharacteristic
333C2×C4×C8C22×C1111yescharacteristic
334#390—21no—
335#390—21no—
336#390C22×C1111yescharacteristic
337#390C22×C1111yescharacteristic
338#389C22×C1111yescharacteristic
339#389C22×C1111yescharacteristic
340#387—21no—
341#387—21no—
342#380—21no—
343#380—21no—
344#380C22×C1111yescharacteristic
345#380C22×C1111yescharacteristic
346C4×C4⋊C4C22×C1111yescharacteristic
347C4×C4⋊C4C22×C1111yescharacteristic
348C4×C22⋊C4—21no—
349C4×C22⋊C4—21no—
350C4×C22⋊C4C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#336C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11C2×C4×D411yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11C2×#13711yescharacteristic
377C22×C11#57511yescharacteristic
378C22×C11#57611yescharacteristic
379C22×C11#57711yescharacteristic
380C4×C11—22no—
381C4×C11—24no—
382C4×C11—22no—
383C4×C11—41no—
384C4×C11—42no—
385C4×C11—42no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11—81no—
392C4×C11C2×#11711yescharacteristic
393C4×C11#51811yescharacteristic
394C4×C11#55111yescharacteristic
395C4×C11#55111yescharacteristic
396C2×#41—22no—
397C2×#41—22no—
398C2×#41—22no—
399C2×#41—41no—
400C2×#41—41no—
401C2×#41C2×C4×C1114yes—
402C22×Q8C23×C1111yescharacteristic
403C22×D4—21no—
404C22×D4C23×C1111yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4C23×C1111yescharacteristic
408C2×M16—41no—
409C2×M16—41no—
410C2×M16C2×C4×C1114yes—
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—41no—
418C4×Q8—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4C2×C4×C1114yes—
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C4⋊C4C23×C1111yescharacteristic
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C1111yescharacteristic
439C2×C22⋊C4D4×C1111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C1111yescharacteristic
445C2×C42C23×C1111yescharacteristic
446#107—41no—
447#106—41no—
448#103—22no—
449#103—22no—
450#103C2×C4×C1114yes—
451#103C2×C4×C1114yes—
452#102—41no—
453#102—41no—
454#102C2×C4×C1114yes—
455#102C2×C4×C1114yes—
456C22⋊C8—22no—
457#97—41no—
458C4×C8—41no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95D4×C1111yescharacteristic
466#95D4×C1111yescharacteristic
467C2×C11—42no—
468C2×C11—82no—
469C2×C11#234211yescharacteristic
470C2×C11C4×#13711yescharacteristic
471C2×C11#294611yescharacteristic
472C2×C11#330911yescharacteristic
473C2×C11#331611yescharacteristic
474C2×C11#332611yescharacteristic
475C2×C11#333311yescharacteristic
476C24—21no—
477C24C2×D4×C1111yescharacteristic
478#41—28no—
479#41—44no—
480#41—44no—
481#41—44no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C22×C4×C1112yes—
486C2×Q8C11×#4112yes—
487C2×Q8C11×#4112yes—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4C22×C4×C1112yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4C22×C4×C1112yes—
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C2×D4×C1111yescharacteristic
520C22×C4C11×#4112yes—
521C22×C4C24×C1111yescharacteristic
522M16—44no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8C22×C4×C1112yes—
534C2×C8C22×C4×C1112yes—
535C4⋊C4—24no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4C22×C4×C1112yes—
551C4⋊C4C22×C4×C1112yes—
552C22⋊C4—22no—
553C22⋊C4—41no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—42no—
565C42—42no—
566C42—81no—
567C42—81no—
568C11#2257911yescharacteristic, direct product factor, Sylow
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C4×D4×C1112yes—
583C23C22×D4×C1111yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8C11×#11714yes—
588D4—22no—
589D4—22no—
590D4—48no—
591D4—41no—
592D4—41no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
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—84no—
633C2×C4C4×D4×C1112yes—
634C2×C4C11×#13712yes—
635C2×C4C23×C4×C1111yescharacteristic
636C2×C4C2×C11×#4111yescharacteristic
637C2×C4C2×C11×#4111yescharacteristic
638C2×C4C2×C11×#4111yescharacteristic
639C2×C4C11×H(5,𝔽2)11yescharacteristic
640C2×C4C11×H(5,𝔽2)11yescharacteristic
641C8—22no—
642C8—22no—
643C8—41no—
644C8—41no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22C2×C4×D4×C1111yescharacteristic
660C22C11×#54611yescharacteristic
661C22C11×#54611yescharacteristic
662C22C2×C11×#13711yescharacteristic
663C22C11×#57511yescharacteristic
664C22C11×#57611yescharacteristic
665C22C11×#57711yescharacteristic
666C4—22no—
667C4—22no—
668C4—24no—
669C4—42no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4C2×C11×#11711yescharacteristic
679C4C11×#51811yescharacteristic
680C4C11×#55111yescharacteristic
681C4C11×#55111yescharacteristic
682C2—42no—
683C2—82no—
684C2C11×#234211yescharacteristic
685C2C4×C11×#13711yescharacteristic
686C2C11×#294611yescharacteristic
687C2C11×#330911yescharacteristic
688C2C11×#331611yescharacteristic
689C2C11×#332611yescharacteristic
690C2C11×#333311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2345C2semidirect
4. C11×#1936C2semidirect
5. C11×#1934C2semidirect
6. C11×#1926C2semidirect
7. C11×#1925C2semidirect
8. C11×#1865C2semidirect
9. C11×#1863C2semidirect
10. C11×#1823C2semidirect
11. C11×#1809C2semidirect
13. C11×#1763C2semidirect
14. C4×C11×#103C2semidirect
15. C11×#1753C2semidirect
23. C11×#417C4semidirect
131. #22579C11direct (N × H)
225. #2345C2×C11semidirect
227. #1936C2×C11semidirect
228. #1934C2×C11semidirect
229. #1926C2×C11semidirect
230. #1925C2×C11semidirect
231. #1865C2×C11semidirect
232. #1863C2×C11semidirect
233. #1823C2×C11semidirect
234. #1809C2×C11semidirect
236. #1763C2×C11semidirect
237. C4×#103C2×C11semidirect
238. #1753C2×C11semidirect
322. #417C4×C11semidirect
568. C11#22579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4172
C11×#23452
C11×#23412
C11×#19362
C11×#19342
C11×#19262
C11×#19252
C11×#18652
C11×#18632
C11×#18232
C11×#18092
C11×#17882
C11×#17632
C4×C11×#1032
C11×#17532
#2257911