Finite Group Databasebeta

← C11×#36705 #14613898

Subgroups — C11×#36705 #14613898

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#538C211yesmaximal, characteristic
2C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C11×#2849C212yesmaximal, complemented
4C11×#2689C214yesmaximal, complemented
5C11×#2687C214yesmaximal, complemented
6C11×#2674C214yesmaximal, complemented
7C11×#2672C214yesmaximal, complemented
8C11×#2622C212yesmaximal, complemented
9C11×#2591C211yesmaximal, characteristic, complemented
10C11×#2583C211yesmaximal, characteristic, complemented
11C11×#2579C212yesmaximal, complemented
12C11×#2487C212yesmaximal, complemented
13C11×#2436C211yesmaximal, characteristic, complemented
14C11×#2434C211yesmaximal, characteristic, complemented
15C11×#2312C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C11×#538—28no—
19C2×C11×C4⋊Q8C2212yescomplemented
20C2×C11×#126C2212yes—
21C2×C11×#124C2212yes—
22C2×C11×#124C2212yescomplemented
23C2×C11×#123C2212yes—
24C2×C11×#123C2214yes—
25C2×C11×C22⋊Q8—28no—
26C2×C11×C22⋊Q8C2214yes—
27C2×C11×C22⋊Q8C2214yes—
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×#121C2212yes—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#120C2212yes—
32C2×C4×D4×C11C2212yes—
33C22×C11×C4⋊C4C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C11×#400C2214yescomplemented
39C11×#400C2212yescomplemented
40C11×#399C2214yescomplemented
41C11×#398C2212yescomplemented
42C11×#398C2214yescomplemented
43C11×#397C2214yes—
44C11×#397C2214yes—
45C11×#396C2214yescomplemented
46C11×#395C2214yescomplemented
47C11×#395C2212yescomplemented
48C11×#394C2214yes—
49C11×#394C2214yes—
50C11×#394C2212yescomplemented
51C11×#393C2214yescomplemented
52C11×#391C2212yescomplemented
53C11×#391C2212yescomplemented
54C11×#389C2214yescomplemented
55C11×#389C2214yescomplemented
56C11×#388C2214yes—
57C11×#388C2214yes—
58C11×#388C2214yescomplemented
59C11×#387C2214yescomplemented
60C11×#386C2214yes—
61C11×#386C2212yes—
62C11×#386C2212yes—
63C11×#386C2212yes—
64C11×#386C2212yes—
65C11×#385C2214yes—
66C11×#385C2212yes—
67C11×#385C2212yes—
68C11×#385C2212yes—
69C11×#385C2212yes—
70C11×#385C2214yescomplemented
71C11×#381C2214yes—
72C11×#380C2212yes—
73C11×#380C2214yescomplemented
74C11×#379C2212yes—
75C4×C11×C22⋊C4C2211yescharacteristic
76C4×C11×C22⋊C4C2211yescharacteristic
77C25×C11C2311yescharacteristic
78C22×Q8×C11—24no—
79C22×Q8×C11—44no—
80C22×Q8×C11C2312yes—
81C22×Q8×C11C2312yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11C2312yes—
84C22×D4×C11C2312yes—
85C22×D4×C11C2312yes—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—24no—
88C23×C4×C11—44no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2314yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2312yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C11×C4⋊Q8—44no—
98C11×#126—28no—
99C11×#124—28no—
100C11×#124—44no—
101C11×#123—28no—
102C11×#123—48no—
103C11×C22⋊Q8—24no—
104C11×C22⋊Q8—216no—
105C11×C22⋊Q8—216no—
106C11×#121—24no—
107C11×#121—28no—
108C11×#120—28no—
109C4×D4×C11—28no—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2314yes—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2314yes—
123C2×C11×C4⋊C4C2314yes—
124C2×C11×C4⋊C4C2314yes—
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4D418yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2312yes—
130C2×C11×C22⋊C4C2312yes—
131C2×C11×C22⋊C4C2312yes—
132C2×C11×C22⋊C4C2312yes—
133C2×C11×C22⋊C4C2312yes—
134C2×C11×C22⋊C4C2312yes—
135C2×C11×C22⋊C4C2312yes—
136C2×C11×C22⋊C4C2314yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C42×C11C2312yes—
145C2×C42×C11C2312yes—
146C2×C42×C11C2312yes—
147C11×#95C2312yes—
148C11×#95C2312yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11×#95C2314yes—
157C11×#95C2314yes—
158#36705C1111yesmaximal, characteristic, direct product factor, Sylow
159C24×C11—24no—
160C24×C11—42no—
161C24×C11—42no—
162C24×C11C2×D414yes—
163C24×C11C2412yes—
164C24×C11C2412yes—
165C24×C11C2411yescharacteristic
166C2×Q8×C11—24no—
167C2×Q8×C11—24no—
168C2×Q8×C11—22no—
169C2×Q8×C11—24no—
170C2×Q8×C11—24no—
171C2×Q8×C11—42no—
172C2×Q8×C11—42no—
173C2×Q8×C11—42no—
174C2×Q8×C11—416no—
175C2×D4×C11—24no—
176C2×D4×C11—28no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—22no—
180C2×D4×C11—44no—
181C2×D4×C11—42no—
182C2×D4×C11—44no—
183C22×C4×C11—22no—
184C22×C4×C11—24no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—28no—
189C22×C4×C11—28no—
190C22×C4×C11—24no—
191C22×C4×C11—44no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—44no—
198C22×C4×C11—416no—
199C22×C4×C11C2×D414yes—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2414yes—
203C22×C4×C11C2414yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C11×C4⋊C4—28no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—28no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—28no—
222C11×C4⋊C4—44no—
223C11×C4⋊C4—44no—
224C11×C4⋊C4—44no—
225C11×C4⋊C4—44no—
226C11×C22⋊C4—28no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—28no—
235C11×C22⋊C4—44no—
236C11×C22⋊C4—44no—
237C11×C22⋊C4—44no—
238C11×C22⋊C4—44no—
239C11×C22⋊C4—44no—
240C11×C22⋊C4C2×D418yes—
241C11×C22⋊C4C2×D418yes—
242C42×C11—24no—
243C42×C11—42no—
244C42×C11—42no—
245C2×#538C2×C1111yescharacteristic
246C22×C22⋊Q8C2×C1111yescharacteristic, complemented
247#2849C2×C1112yescomplemented
248#2689C2×C1114yescomplemented
249#2687C2×C1114yescomplemented
250#2674C2×C1114yescomplemented
251#2672C2×C1114yescomplemented
252#2622C2×C1112yescomplemented
253#2591C2×C1111yescharacteristic, complemented
254#2583C2×C1111yescharacteristic, complemented
255#2579C2×C1112yescomplemented
256#2487C2×C1112yescomplemented
257#2436C2×C1111yescharacteristic, complemented
258#2434C2×C1111yescharacteristic, complemented
259#2312C2×C1111yescharacteristic, complemented
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—28no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—22no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—44no—
271C23×C11—44no—
272C23×C11—416no—
273C23×C11C22×D414yes—
274C23×C11C22×D412yes—
275C23×C112−1+414yes—
276C23×C11C2511yescharacteristic
277Q8×C11—48no—
278Q8×C11—48no—
279Q8×C11—82no—
280D4×C11—48no—
281D4×C11—82no—
282D4×C11—84no—
283D4×C11—84no—
284C2×C4×C11—28no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—44no—
311C2×C4×C11—44no—
312C2×C4×C11—416no—
313C2×C4×C11—44no—
314C2×C4×C11—44no—
315C2×C4×C11—44no—
316C2×C4×C11—84no—
317C2×C4×C11C22×D414yes—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11H(5,𝔽2)14yes—
321C23×Q8C22×C1111yescharacteristic
322C24×C4C22×C1111yescharacteristic
323#538—28no—
324C2×C4⋊Q8C22×C1112yescomplemented
325C2×#126C22×C1112yes—
326C2×#124C22×C1112yes—
327C2×#124C22×C1112yescomplemented
328C2×#123C22×C1112yes—
329C2×#123C22×C1114yes—
330C2×C22⋊Q8—28no—
331C2×C22⋊Q8C22×C1111yescharacteristic
332C2×C22⋊Q8C22×C1114yes—
333C2×C22⋊Q8C22×C1114yes—
334C2×#121C22×C1111yescharacteristic
335C2×#121C22×C1112yes—
336C2×#120C22×C1112yes—
337C2×C4×D4C22×C1112yes—
338C22×C4⋊C4C22×C1111yescharacteristic
339C22×C4⋊C4C22×C1111yescharacteristic
340C22×C4⋊C4C22×C1111yescharacteristic
341C22×C22⋊C4C22×C1111yescharacteristic
342C22×C22⋊C4C22×C1111yescharacteristic
343#400C22×C1112yescomplemented
344#400C22×C1114yescomplemented
345#399C22×C1114yescomplemented
346#398C22×C1114yescomplemented
347#398C22×C1112yescomplemented
348#397C22×C1114yes—
349#397C22×C1114yes—
350#396C22×C1114yescomplemented
351#395C22×C1112yescomplemented
352#395C22×C1114yescomplemented
353#394C22×C1114yes—
354#394C22×C1114yes—
355#394C22×C1112yescomplemented
356#393C22×C1114yescomplemented
357#391C22×C1112yescomplemented
358#391C22×C1112yescomplemented
359#389C22×C1114yescomplemented
360#389C22×C1114yescomplemented
361#388C22×C1114yes—
362#388C22×C1114yes—
363#388C22×C1114yescomplemented
364#387C22×C1114yescomplemented
365#386C22×C1112yes—
366#386C22×C1112yes—
367#386C22×C1112yes—
368#386C22×C1114yes—
369#386C22×C1112yes—
370#385C22×C1112yes—
371#385C22×C1112yes—
372#385C22×C1112yes—
373#385C22×C1114yes—
374#385C22×C1112yes—
375#385C22×C1114yescomplemented
376#381C22×C1114yes—
377#380C22×C1112yes—
378#380C22×C1114yescomplemented
379#379C22×C1112yes—
380C4×C22⋊C4C22×C1111yescharacteristic
381C4×C22⋊C4C22×C1111yescharacteristic
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—28no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—24no—
388C22×C11—416no—
389C22×C11—48no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—48no—
394C22×C11#53614yes—
395C22×C11C23×D411yescharacteristic
396C22×C11C2×H(5,𝔽2)12yes—
397C22×C11C2×2−1+412yes—
398C22×C11#58512yes—
399C4×C11—24no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—24no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—44no—
410C4×C11—44no—
411C25C23×C1111yescharacteristic
412C22×Q8—24no—
413C22×Q8—44no—
414C22×Q8C23×C1112yes—
415C22×Q8C23×C1112yes—
416C22×Q8C23×C1111yescharacteristic
417C22×D4C23×C1112yes—
418C22×D4C23×C1112yes—
419C22×D4C23×C1112yes—
420C22×D4C23×C1111yescharacteristic
421C23×C4—24no—
422C23×C4—44no—
423C23×C4C23×C1111yescharacteristic
424C23×C4C23×C1114yes—
425C23×C4C23×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C23×C4C23×C1111yescharacteristic
428C23×C4C23×C1112yes—
429C23×C4C23×C1111yescharacteristic
430C23×C4C23×C1111yescharacteristic
431C4⋊Q8—44no—
432#126—28no—
433#124—28no—
434#124—44no—
435#123—28no—
436#123—48no—
437C22⋊Q8—24no—
438C22⋊Q8—216no—
439C22⋊Q8—216no—
440#121—24no—
441#121—28no—
442#120—28no—
443C4×D4—28no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4C23×C1114yes—
448C2×C4⋊C4C23×C1114yes—
449C2×C4⋊C4C23×C1112yes—
450C2×C4⋊C4C23×C1112yes—
451C2×C4⋊C4C23×C1112yes—
452C2×C4⋊C4C23×C1112yes—
453C2×C4⋊C4C23×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1114yes—
456C2×C4⋊C4C23×C1114yes—
457C2×C4⋊C4C23×C1114yes—
458C2×C4⋊C4C23×C1114yes—
459C2×C4⋊C4C23×C1114yes—
460C2×C22⋊C4—24no—
461C2×C22⋊C4D4×C1118yes—
462C2×C22⋊C4C23×C1114yes—
463C2×C22⋊C4C23×C1112yes—
464C2×C22⋊C4C23×C1112yes—
465C2×C22⋊C4C23×C1112yes—
466C2×C22⋊C4C23×C1112yes—
467C2×C22⋊C4C23×C1112yes—
468C2×C22⋊C4C23×C1114yes—
469C2×C22⋊C4C23×C1112yes—
470C2×C22⋊C4C23×C1112yes—
471C2×C22⋊C4C23×C1114yes—
472C2×C22⋊C4C23×C1114yes—
473C2×C22⋊C4C23×C1114yes—
474C2×C22⋊C4C23×C1114yes—
475C2×C22⋊C4C23×C1114yes—
476C2×C22⋊C4C23×C1112yes—
477C2×C22⋊C4C23×C1112yes—
478C2×C42C23×C1112yes—
479C2×C42C23×C1112yes—
480C2×C42C23×C1112yes—
481#95C23×C1112yes—
482#95C23×C1112yes—
483#95C23×C1114yes—
484#95C23×C1114yes—
485#95C23×C1114yes—
486#95C23×C1114yes—
487#95C23×C1114yes—
488#95C23×C1114yes—
489#95C23×C1114yes—
490#95C23×C1114yes—
491#95C23×C1114yes—
492C2×C11—24no—
493C2×C11—44no—
494C2×C11—82no—
495C2×C11C2×#53611yescharacteristic
496C2×C11#348411yescharacteristic
497C2×C11#348511yescharacteristic
498C2×C11#354114yes—
499C24—24no—
500C24—42no—
501C24—42no—
502C24C2×D4×C1114yes—
503C24C24×C1112yes—
504C24C24×C1112yes—
505C24C24×C1111yescharacteristic
506C2×Q8—24no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—416no—
515C2×D4—24no—
516C2×D4—28no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—22no—
520C2×D4—44no—
521C2×D4—42no—
522C2×D4—44no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—24no—
531C22×C4—44no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—44no—
538C22×C4—416no—
539C22×C4C2×D4×C1114yes—
540C22×C4C2×D4×C1114yes—
541C22×C4C24×C1112yes—
542C22×C4C24×C1114yes—
543C22×C4C24×C1114yes—
544C22×C4C24×C1112yes—
545C22×C4C24×C1112yes—
546C22×C4C24×C1112yes—
547C22×C4C24×C1112yes—
548C22×C4C24×C1112yes—
549C22×C4C24×C1111yescharacteristic
550C22×C4C24×C1111yescharacteristic
551C22×C4C24×C1112yes—
552C22×C4C24×C1112yes—
553C4⋊C4—28no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—28no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—28no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C22⋊C4—28no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—28no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—44no—
580C22⋊C4C2×D4×C1118yes—
581C22⋊C4C2×D4×C1118yes—
582C42—24no—
583C42—42no—
584C42—42no—
585C11#3670511yescharacteristic, direct product factor, Sylow
586C23—22no—
587C23—22no—
588C23—28no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—44no—
597C23—44no—
598C23—416no—
599C23C22×D4×C1114yes—
600C23C22×D4×C1112yes—
601C23C11×2−1+414yes—
602C23C25×C1111yescharacteristic
603Q8—48no—
604Q8—48no—
605Q8—82no—
606D4—48no—
607D4—82no—
608D4—84no—
609D4—84no—
610C2×C4—28no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—416no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—84no—
643C2×C4C22×D4×C1114yes—
644C2×C4C22×D4×C1112yes—
645C2×C4C22×D4×C1112yes—
646C2×C4C11×H(5,𝔽2)14yes—
647C22—22no—
648C22—22no—
649C22—28no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—416no—
654C22—48no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—48no—
659C22C11×#53614yes—
660C22C23×D4×C1111yescharacteristic
661C22C2×C11×H(5,𝔽2)12yes—
662C22C2×C11×2−1+412yes—
663C22C11×#58512yes—
664C4—24no—
665C4—22no—
666C4—22no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—44no—
675C4—44no—
676C2—24no—
677C2—44no—
678C2—82no—
679C2C2×C11×#53611yescharacteristic
680C2C11×#348411yescharacteristic
681C2C11×#348511yescharacteristic
682C2C11×#354114yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC2×C11×#538C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C22⋊Q8C2semidirect
3. C11×#2849C2semidirect
4. C11×#2689C2semidirect
5. C11×#2687C2semidirect
6. C11×#2674C2semidirect
7. C11×#2672C2semidirect
8. C11×#2622C2semidirect
9. C11×#2591C2semidirect
10. C11×#2583C2semidirect
11. C11×#2579C2semidirect
12. C11×#2487C2semidirect
13. C11×#2436C2semidirect
14. C11×#2434C2semidirect
15. C11×#2312C2semidirect
19. C2×C11×C4⋊Q8C22semidirect
22. C2×C11×#124C22semidirect
38. C11×#400C22semidirect
39. C11×#400C22semidirect
40. C11×#399C22semidirect
41. C11×#398C22semidirect
42. C11×#398C22semidirect
45. C11×#396C22semidirect
46. C11×#395C22semidirect
47. C11×#395C22semidirect
50. C11×#394C22semidirect
51. C11×#393C22semidirect
52. C11×#391C22semidirect
53. C11×#391C22semidirect
54. C11×#389C22semidirect
55. C11×#389C22semidirect
58. C11×#388C22semidirect
59. C11×#387C22semidirect
70. C11×#385C22semidirect
73. C11×#380C22semidirect
158. #36705C11direct (N × H)
246. C22×C22⋊Q8C2×C11semidirect
247. #2849C2×C11semidirect
248. #2689C2×C11semidirect
249. #2687C2×C11semidirect
250. #2674C2×C11semidirect
251. #2672C2×C11semidirect
252. #2622C2×C11semidirect
253. #2591C2×C11semidirect
254. #2583C2×C11semidirect
255. #2579C2×C11semidirect
256. #2487C2×C11semidirect
257. #2436C2×C11semidirect
258. #2434C2×C11semidirect
259. #2312C2×C11semidirect
324. C2×C4⋊Q8C22×C11semidirect
327. C2×#124C22×C11semidirect
343. #400C22×C11semidirect
344. #400C22×C11semidirect
345. #399C22×C11semidirect
346. #398C22×C11semidirect
347. #398C22×C11semidirect
350. #396C22×C11semidirect
351. #395C22×C11semidirect
352. #395C22×C11semidirect
355. #394C22×C11semidirect
356. #393C22×C11semidirect
357. #391C22×C11semidirect
358. #391C22×C11semidirect
359. #389C22×C11semidirect
360. #389C22×C11semidirect
363. #388C22×C11semidirect
364. #387C22×C11semidirect
375. #385C22×C11semidirect
378. #380C22×C11semidirect
585. C11#36705direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5382
C22×C11×C22⋊Q82
C11×#28492
C11×#26892
C11×#26872
C11×#26742
C11×#26722
C11×#26222
C11×#25912
C11×#25832
C11×#25792
C11×#24872
C11×#24362
C11×#24342
C11×#23122
#3670511