Finite Group Databasebeta

← C11×#23131 #14600324

Subgroups — C11×#23131 #14600324

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#465C211yesmaximal, characteristic
2C11×#2363C211yesmaximal, characteristic
3C11×#2362C211yesmaximal, characteristic, complemented
4C11×#1934C211yesmaximal, characteristic, complemented
5C11×#1933C211yesmaximal, characteristic, complemented
6C11×#1920C211yesmaximal, characteristic, complemented
7C11×#1919C211yesmaximal, characteristic, complemented
8C11×#1880C211yesmaximal, characteristic, complemented
9C11×#1877C211yesmaximal, characteristic, complemented
10C11×#1875C211yesmaximal, characteristic
11C11×#1873C211yesmaximal, characteristic, complemented
12C4×C11×#103C211yesmaximal, characteristic, complemented
13C4×C11×#102C211yesmaximal, characteristic, complemented
14C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
15C11×#1735C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#465C418yescomplemented
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#391C2211yescharacteristic
36C11×#390—21no—
37C11×#390C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#388—21no—
41C11×#388—21no—
42C11×#388—21no—
43C11×#387—21no—
44C11×#386—21no—
45C4×C11×C4⋊C4—21no—
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4—21no—
49C4×C11×C22⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C2×C11×SD16C2×C414yes—
68C22×C8×C11—41no—
69C22×C8×C11—41no—
70C22×C8×C11C2×C414yescomplemented
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8C2×C414yescomplemented
77C11×#121—22no—
78C11×#121C2×C414yes—
79C4×Q8×C11—22no—
80C4×Q8×C11—41no—
81C4×D4×C11—22no—
82C4×D4×C11—41no—
83C11×#117—22no—
84C11×#117—22no—
85C11×#117—41no—
86C11×#117—41no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4D411yescharacteristic
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×#106C2×C414yescomplemented
114C11×#103—22no—
115C11×#103—41no—
116C11×#103C2×C414yescomplemented
117C11×#102—22no—
118C11×#102—41no—
119C11×#102C2×C414yes—
120C11×C22⋊C8—22no—
121C4×C8×C11—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#23131C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—81no—
147C2×D4×C11—81no—
148C2×D4×C11C22×C412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
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—42no—
161C22×C4×C11—42no—
162C22×C4×C11—81no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C11×SD16—44no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—44no—
183C2×C8×C11C22×C412yes—
184C2×C8×C11C22×C412yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—81no—
197C11×C4⋊C4C22×C412yes—
198C11×C4⋊C4C22×C412yes—
199C11×C4⋊C4#4112yes—
200C11×C4⋊C4#4112yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—42no—
215C42×C11—42no—
216C42×C11—42no—
217C42×C11—42no—
218C42×C11—81no—
219C2×#465C2×C1111yescharacteristic
220#2363C2×C1111yescharacteristic
221#2362C2×C1111yescharacteristic, complemented
222#1934C2×C1111yescharacteristic, complemented
223#1933C2×C1111yescharacteristic, complemented
224#1920C2×C1111yescharacteristic, complemented
225#1919C2×C1111yescharacteristic, complemented
226#1880C2×C1111yescharacteristic, complemented
227#1877C2×C1111yescharacteristic, complemented
228#1875C2×C1111yescharacteristic
229#1873C2×C1111yescharacteristic, complemented
230C4×#103C2×C1111yescharacteristic, complemented
231C4×#102C2×C1111yescharacteristic, complemented
232C8×C22⋊C4C2×C1111yescharacteristic, complemented
233#1735C2×C1111yescharacteristic, complemented
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—22no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C4×D412yes—
248C23×C11C22×D411yescharacteristic
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—84no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
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—84no—
296C2×C4×C11C4×D412yes—
297C2×C4×C11#13512yes—
298C2×C4×C11#13512yes—
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C8×C11—22no—
306C8×C11—22no—
307C8×C11—41no—
308C8×C11—41no—
309C22×SD16C22×C1111yescharacteristic
310C23×C8C22×C1111yescharacteristic
311C2×C22⋊Q8C22×C1111yescharacteristic
312C2×#121C22×C1111yescharacteristic
313C2×C4×Q8C22×C1111yescharacteristic
314C2×C4×D4C22×C1111yescharacteristic
315C2×#117C22×C1111yescharacteristic
316C2×#117C22×C1111yescharacteristic
317#465C4×C1118yescomplemented
318C2×#106C22×C1111yescharacteristic
319C2×#103C22×C1111yescharacteristic
320C2×#103C22×C1111yescharacteristic
321C2×#103C22×C1111yescharacteristic
322C2×#102C22×C1111yescharacteristic
323C2×#102C22×C1111yescharacteristic
324C2×#102C22×C1111yescharacteristic
325C2×C22⋊C8C22×C1111yescharacteristic
326C2×C4×C8C22×C1111yescharacteristic
327C2×C4×C8C22×C1111yescharacteristic
328#391C22×C1111yescharacteristic
329#390—21no—
330#390C22×C1111yescharacteristic
331#389C22×C1111yescharacteristic
332#389C22×C1111yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#387—21no—
337#386—21no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4C22×C1111yescharacteristic
340C4×C4⋊C4C22×C1111yescharacteristic
341C4×C22⋊C4—21no—
342C4×C22⋊C4C22×C1111yescharacteristic
343#340C22×C1111yescharacteristic
344#340C22×C1111yescharacteristic
345#340C22×C1111yescharacteristic
346#340C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#336C22×C1111yescharacteristic
352#336C22×C1111yescharacteristic
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11C2×C4×D411yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11C2×#13511yescharacteristic
371C22×C11C2×#13511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57711yescharacteristic
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C4×#4111yescharacteristic
387C4×C11#51811yescharacteristic
388C4×C11#55311yescharacteristic
389C4×C11#55311yescharacteristic
390C22×Q8C23×C1111yescharacteristic
391C22×D4—21no—
392C22×D4C23×C1111yescharacteristic
393C23×C4—21no—
394C23×C4C23×C1111yescharacteristic
395C2×SD16—41no—
396C2×SD16—41no—
397C2×SD16C2×C4×C1114yes—
398C22×C8—41no—
399C22×C8—41no—
400C22×C8C2×C4×C1114yescomplemented
401C22×C8C23×C1111yescharacteristic
402C22×C8C23×C1111yescharacteristic
403C22×C8C23×C1111yescharacteristic
404C22×C8C23×C1111yescharacteristic
405C22⋊Q8—22no—
406C22⋊Q8C2×C4×C1114yescomplemented
407#121—22no—
408#121C2×C4×C1114yes—
409C4×Q8—22no—
410C4×Q8—41no—
411C4×D4—22no—
412C4×D4—41no—
413#117—22no—
414#117—22no—
415#117—41no—
416#117—41no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4C23×C1111yescharacteristic
422C2×C4⋊C4C23×C1111yescharacteristic
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C4⋊C4C23×C1111yescharacteristic
425C2×C4⋊C4C23×C1111yescharacteristic
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4D4×C1111yescharacteristic
435C2×C22⋊C4D4×C1111yescharacteristic
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42C23×C1111yescharacteristic
442C2×C42C23×C1111yescharacteristic
443#106C2×C4×C1114yescomplemented
444#103—22no—
445#103—41no—
446#103C2×C4×C1114yescomplemented
447#102—22no—
448#102—41no—
449#102C2×C4×C1114yes—
450C22⋊C8—22no—
451C4×C8—41no—
452C4×C8—41no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95D4×C1111yescharacteristic
460#95D4×C1111yescharacteristic
461C2×C11—42no—
462C2×C11—82no—
463C2×C11#236411yescharacteristic
464C2×C11C4×#13511yescharacteristic
465C2×C11#294911yescharacteristic
466C2×C11#329611yescharacteristic
467C2×C11#330111yescharacteristic
468C2×C11#330311yescharacteristic
469C2×C11#330411yescharacteristic
470C24—21no—
471C24C2×D4×C1111yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C22×C4×C1112yes—
478C2×D4—24no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4C22×C4×C1112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4C22×C4×C1112yes—
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C11×#4112yes—
508C22×C4C24×C1111yescharacteristic
509SD16—44no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—44no—
521C2×C8C22×C4×C1112yes—
522C2×C8C22×C4×C1112yes—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4C22×C4×C1112yes—
536C4⋊C4C22×C4×C1112yes—
537C4⋊C4C11×#4112yes—
538C4⋊C4C11×#4112yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42—42no—
554C42—42no—
555C42—42no—
556C42—81no—
557C11#2313111yescharacteristic, direct product factor, Sylow
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C4×D4×C1112yes—
572C23C22×D4×C1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—84no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—84no—
620C2×C4C4×D4×C1112yes—
621C2×C4C11×#13512yes—
622C2×C4C11×#13512yes—
623C2×C4C23×C4×C1111yescharacteristic
624C2×C4C2×C11×#4111yescharacteristic
625C2×C4C2×C11×#4111yescharacteristic
626C2×C4C2×C11×#4111yescharacteristic
627C2×C4C11×H(5,𝔽2)11yescharacteristic
628C2×C4C11×H(5,𝔽2)11yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22C2×C4×D4×C1111yescharacteristic
648C22C11×#54611yescharacteristic
649C22C11×#54611yescharacteristic
650C22C2×C11×#13511yescharacteristic
651C22C2×C11×#13511yescharacteristic
652C22C11×#57711yescharacteristic
653C22C11×#57711yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—42no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4C4×C11×#4111yescharacteristic
667C4C11×#51811yescharacteristic
668C4C11×#55311yescharacteristic
669C4C11×#55311yescharacteristic
670C2—42no—
671C2—82no—
672C2C11×#236411yescharacteristic
673C2C4×C11×#13511yescharacteristic
674C2C11×#294911yescharacteristic
675C2C11×#329611yescharacteristic
676C2C11×#330111yescharacteristic
677C2C11×#330311yescharacteristic
678C2C11×#330411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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
3. C11×#2362C2semidirect
4. C11×#1934C2semidirect
5. C11×#1933C2semidirect
6. C11×#1920C2semidirect
7. C11×#1919C2semidirect
8. C11×#1880C2semidirect
9. C11×#1877C2semidirect
11. C11×#1873C2semidirect
12. C4×C11×#103C2semidirect
13. C4×C11×#102C2semidirect
14. C8×C11×C22⋊C4C2semidirect
15. C11×#1735C2semidirect
24. C11×#465C4semidirect
70. C22×C8×C11C2×C4semidirect
76. C11×C22⋊Q8C2×C4semidirect
113. C11×#106C2×C4semidirect
116. C11×#103C2×C4semidirect
131. #23131C11direct (N × H)
221. #2362C2×C11semidirect
222. #1934C2×C11semidirect
223. #1933C2×C11semidirect
224. #1920C2×C11semidirect
225. #1919C2×C11semidirect
226. #1880C2×C11semidirect
227. #1877C2×C11semidirect
229. #1873C2×C11semidirect
230. C4×#103C2×C11semidirect
231. C4×#102C2×C11semidirect
232. C8×C22⋊C4C2×C11semidirect
233. #1735C2×C11semidirect
317. #465C4×C11semidirect
400. C22×C8C2×C4×C11semidirect
406. C22⋊Q8C2×C4×C11semidirect
443. #106C2×C4×C11semidirect
446. #103C2×C4×C11semidirect
557. C11#23131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4652
C11×#23632
C11×#23622
C11×#19342
C11×#19332
C11×#19202
C11×#19192
C11×#18802
C11×#18772
C11×#18752
C11×#18732
C4×C11×#1032
C4×C11×#1022
C8×C11×C22⋊C42
C11×#17352
#2313111