Finite Group Databasebeta

← C11×#14041 #14591234

Subgroups — C11×#14041 #14591234

Order 2816.

1386 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#389C211yesmaximal, characteristic
2C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1445C212yesmaximal
5C11×#1442C212yesmaximal
6C11×#1436C212yesmaximal
7C11×#1436C212yesmaximal
8C11×C4⋊#95C211yesmaximal, characteristic
9C11×C4⋊#95C211yesmaximal, characteristic
10C11×C4⋊#95C211yesmaximal, characteristic
11C11×C4⋊#95C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2212yes—
23C11×#389C418yescomplemented
24C4×C11×C4⋊C4—24no—
25C4×C11×C4⋊C4—24no—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—42no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×C11×C4⋊C4C2×C414yes—
67C2×C11×C4⋊C4C2×C418yes—
68C2×C11×C4⋊C4Q814yes—
69C2×C11×C4⋊C4Q814yes—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11—24no—
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11—42no—
79C2×C42×C11—42no—
80C2×C42×C11C2×C414yes—
81C2×C42×C11D414yes—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—24no—
85C11×#95—24no—
86C11×#95—24no—
87C11×#95—24no—
88C11×#95—42no—
89C11×#95—42no—
90C11×#95—42no—
91C11×#95—42no—
92C11×#95—42no—
93C11×#95C2×C418yes—
94#14041C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11C2411yescharacteristic
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C22×C414yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×Q814yes—
162C22×C4×C11C2×Q812yes—
163C22×C4×C11C2×Q812yes—
164C22×C4×C11C2×Q812yes—
165C22×C4×C11C2×Q812yes—
166C22×C4×C11#4112yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11#4112yes—
170C22×C4×C11#4112yes—
171C22×C4×C11#4112yes—
172C22×C4×C11#4112yes—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—48no—
179C11×C4⋊C4—44no—
180C42×C11—28no—
181C42×C11—28no—
182C42×C11—48no—
183C42×C11—44no—
184C2×#389C2×C1111yescharacteristic
185C2×C4×C4⋊C4C2×C1111yescharacteristic
186C2×C4×C4⋊C4C2×C1111yescharacteristic
187#1445C2×C1112yes—
188#1442C2×C1112yes—
189#1436C2×C1112yes—
190#1436C2×C1112yes—
191C4⋊#95C2×C1111yescharacteristic
192C4⋊#95C2×C1111yescharacteristic
193C4⋊#95C2×C1111yescharacteristic
194C4⋊#95C2×C1111yescharacteristic
195C23×C11C23×C411yescharacteristic
196C23×C11C22×D411yescharacteristic
197C23×C11C22×Q811yescharacteristic
198C23×C11C22×Q811yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C11C2×#4111yescharacteristic
202C23×C11C2×#4111yescharacteristic
203C23×C11C2×#4111yescharacteristic
204C23×C11C2×#4111yescharacteristic
205C23×C11C2×#4111yescharacteristic
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C11H(5,𝔽2)11yescharacteristic
208C23×C11H(5,𝔽2)11yescharacteristic
209C23×C112−1+411yescharacteristic
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11#11714yes—
279C2×C4×C11C4×D414yes—
280C2×C4×C11C4×Q814yes—
281C2×C4×C11C4×Q814yes—
282C2×C4×C11C22⋊Q814yes—
283C2×C4×C11C22⋊Q814yes—
284C2×C4×C11#12314yes—
285C2×C4×C11#12514yes—
286C2×C4×C11#12614yes—
287C22×C4⋊C4C22×C1111yescharacteristic
288C22×C4⋊C4C22×C1111yescharacteristic
289C22×C4⋊C4C22×C1111yescharacteristic
290C22×C4⋊C4C22×C1111yescharacteristic
291C22×C4⋊C4C22×C1111yescharacteristic
292C22×C4⋊C4C22×C1111yescharacteristic
293C22×C4⋊C4C22×C1112yes—
294C22×C42C22×C1111yescharacteristic
295C22×C42C22×C1111yescharacteristic
296C22×C42C22×C1111yescharacteristic
297C22×C42C22×C1112yes—
298#389C4×C1118yescomplemented
299C4×C4⋊C4—24no—
300C4×C4⋊C4—24no—
301C2×#95C22×C1112yes—
302C2×#95C22×C1112yes—
303C2×#95C22×C1112yes—
304C2×#95C22×C1111yescharacteristic
305C2×#95C22×C1112yes—
306C2×#95C22×C1111yescharacteristic
307C2×#95C22×C1112yes—
308C2×#95C22×C1112yes—
309C2×#95C22×C1112yes—
310C2×#95C22×C1112yes—
311C2×#95C22×C1112yes—
312C2×#95C22×C1112yes—
313C22×C11C2×#11711yescharacteristic
314C22×C11C2×C4×D411yescharacteristic
315C22×C11C2×C4×Q811yescharacteristic
316C22×C11C2×C4×Q811yescharacteristic
317C22×C11C4×#4111yescharacteristic
318C22×C11#51811yescharacteristic
319C22×C11#52011yescharacteristic
320C22×C11C2×C22⋊Q811yescharacteristic
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11C2×#12311yescharacteristic
323C22×C11#52511yescharacteristic
324C22×C11C2×#12511yescharacteristic
325C22×C11C2×#12611yescharacteristic
326C22×C11#52911yescharacteristic
327C22×C11#53311yescharacteristic
328C22×C11#53511yescharacteristic
329C22×C11#53711yescharacteristic
330C22×C11#54011yescharacteristic
331C22×C11#54211yescharacteristic
332C22×C11#55211yescharacteristic
333C22×C11#55311yescharacteristic
334C22×C11#55311yescharacteristic
335C22×C11#55311yescharacteristic
336C22×C11#55411yescharacteristic
337C22×C11#55411yescharacteristic
338C22×C11#55411yescharacteristic
339C22×C11#55411yescharacteristic
340C22×C11#55511yescharacteristic
341C22×C11#55611yescharacteristic
342C22×C11#55711yescharacteristic
343C22×C11#55711yescharacteristic
344C22×C11Q8211yescharacteristic
345C22×C11#55911yescharacteristic
346C22×C11#55911yescharacteristic
347C22×C11#55911yescharacteristic
348C4×C11—24no—
349C4×C11—24no—
350C4×C11—42no—
351C4×C11—44no—
352C4×C11—44no—
353C4×C11—44no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—82no—
358C4×C11#38718yes—
359C23×C4C23×C1112yes—
360C23×C4C23×C1112yes—
361C23×C4C23×C1111yescharacteristic
362C23×C4C23×C1112yes—
363C23×C4C23×C1111yescharacteristic
364C23×C4C23×C1112yes—
365C23×C4C23×C1111yescharacteristic
366C23×C4C23×C1111yescharacteristic
367C23×C4C23×C1111yescharacteristic
368C23×C4C23×C1111yescharacteristic
369C23×C4C23×C1111yescharacteristic
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4C2×C4×C1114yes—
387C2×C4⋊C4C2×C4×C1114yes—
388C2×C4⋊C4C2×C4×C1118yes—
389C2×C4⋊C4Q8×C1114yes—
390C2×C4⋊C4Q8×C1114yes—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C2×C4×C1114yes—
402C2×C42D4×C1114yes—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95C2×C4×C1118yes—
415C2×C11C2×#38711yescharacteristic
416C2×C11C4×C22⋊Q811yescharacteristic
417C2×C11#232411yescharacteristic
418C2×C11#235511yescharacteristic
419C2×C11#235711yescharacteristic
420C2×C11#236911yescharacteristic
421C2×C11#237011yescharacteristic
422C2×C11#248511yescharacteristic
423C2×C11#248711yescharacteristic
424C2×C11#250711yescharacteristic
425C2×C11#250911yescharacteristic
426C2×C11#251111yescharacteristic
427C2×C11#251311yescharacteristic
428C2×C11#258011yescharacteristic
429C2×C11#258211yescharacteristic
430C24C24×C1111yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4C22×C4×C1114yes—
489C22×C4C22×C4×C1114yes—
490C22×C4C22×C4×C1112yes—
491C22×C4C22×C4×C1112yes—
492C22×C4C22×C4×C1112yes—
493C22×C4C2×D4×C1112yes—
494C22×C4C2×D4×C1112yes—
495C22×C4C2×D4×C1112yes—
496C22×C4C2×Q8×C1114yes—
497C22×C4C2×Q8×C1112yes—
498C22×C4C2×Q8×C1112yes—
499C22×C4C2×Q8×C1112yes—
500C22×C4C2×Q8×C1112yes—
501C22×C4C11×#4112yes—
502C22×C4C11×#4112yes—
503C22×C4C11×#4112yes—
504C22×C4C11×#4112yes—
505C22×C4C11×#4112yes—
506C22×C4C11×#4112yes—
507C22×C4C11×#4112yes—
508C4⋊C4—28no—
509C4⋊C4—28no—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—28no—
513C4⋊C4—48no—
514C4⋊C4—44no—
515C42—28no—
516C42—28no—
517C42—48no—
518C42—44no—
519C11#1404111yescharacteristic, direct product factor, Sylow
520C23C23×C4×C1111yescharacteristic
521C23C22×D4×C1111yescharacteristic
522C23C22×Q8×C1111yescharacteristic
523C23C22×Q8×C1111yescharacteristic
524C23C2×C11×#4111yescharacteristic
525C23C2×C11×#4111yescharacteristic
526C23C2×C11×#4111yescharacteristic
527C23C2×C11×#4111yescharacteristic
528C23C2×C11×#4111yescharacteristic
529C23C2×C11×#4111yescharacteristic
530C23C2×C11×#4111yescharacteristic
531C23C11×H(5,𝔽2)11yescharacteristic
532C23C11×H(5,𝔽2)11yescharacteristic
533C23C11×H(5,𝔽2)11yescharacteristic
534C23C11×2−1+411yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4C11×#11714yes—
604C2×C4C4×D4×C1114yes—
605C2×C4C4×Q8×C1114yes—
606C2×C4C4×Q8×C1114yes—
607C2×C4C11×C22⋊Q814yes—
608C2×C4C11×C22⋊Q814yes—
609C2×C4C11×#12314yes—
610C2×C4C11×#12514yes—
611C2×C4C11×#12614yes—
612C22C2×C11×#11711yescharacteristic
613C22C2×C4×D4×C1111yescharacteristic
614C22C2×C4×Q8×C1111yescharacteristic
615C22C2×C4×Q8×C1111yescharacteristic
616C22C4×C11×#4111yescharacteristic
617C22C11×#51811yescharacteristic
618C22C11×#52011yescharacteristic
619C22C2×C11×C22⋊Q811yescharacteristic
620C22C2×C11×C22⋊Q811yescharacteristic
621C22C2×C11×#12311yescharacteristic
622C22C11×#52511yescharacteristic
623C22C2×C11×#12511yescharacteristic
624C22C2×C11×#12611yescharacteristic
625C22C11×#52911yescharacteristic
626C22C11×#53311yescharacteristic
627C22C11×#53511yescharacteristic
628C22C11×#53711yescharacteristic
629C22C11×#54011yescharacteristic
630C22C11×#54211yescharacteristic
631C22C11×#55211yescharacteristic
632C22C11×#55311yescharacteristic
633C22C11×#55311yescharacteristic
634C22C11×#55311yescharacteristic
635C22C11×#55411yescharacteristic
636C22C11×#55411yescharacteristic
637C22C11×#55411yescharacteristic
638C22C11×#55411yescharacteristic
639C22C11×#55511yescharacteristic
640C22C11×#55611yescharacteristic
641C22C11×#55711yescharacteristic
642C22C11×#55711yescharacteristic
643C22Q82×C1111yescharacteristic
644C22C11×#55911yescharacteristic
645C22C11×#55911yescharacteristic
646C22C11×#55911yescharacteristic
647C4—24no—
648C4—24no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—44no—
654C4—44no—
655C4—44no—
656C4—82no—
657C4C11×#38718yes—
658C2C2×C11×#38711yescharacteristic
659C2C4×C11×C22⋊Q811yescharacteristic
660C2C11×#232411yescharacteristic
661C2C11×#235511yescharacteristic
662C2C11×#235711yescharacteristic
663C2C11×#236911yescharacteristic
664C2C11×#237011yescharacteristic
665C2C11×#248511yescharacteristic
666C2C11×#248711yescharacteristic
667C2C11×#250711yescharacteristic
668C2C11×#250911yescharacteristic
669C2C11×#251111yescharacteristic
670C2C11×#251311yescharacteristic
671C2C11×#258011yescharacteristic
672C2C11×#258211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
23. C11×#389C4semidirect
94. #14041C11direct (N × H)
298. #389C4×C11semidirect
519. C11#14041direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3892
C2×C4×C11×C4⋊C42
C11×#14452
C11×#14422
C11×#14362
C11×C4⋊#952
#1404111