Finite Group Databasebeta

← C11×#15514 #14592707

Subgroups — C11×#15514 #14592707

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#400C211yesmaximal, characteristic, complemented
2C2×C11×#385C211yesmaximal, characteristic
3C11×#1445C211yesmaximal, characteristic, complemented
4C11×#1445C211yesmaximal, characteristic, complemented
5C11×#1442C211yesmaximal, characteristic, complemented
6C11×#1441C211yesmaximal, characteristic, complemented
7C11×#1441C211yesmaximal, characteristic, complemented
8C11×#1439C211yesmaximal, characteristic
9C11×#1439C211yesmaximal, characteristic
10C11×#1439C211yesmaximal, characteristic
11C11×#1437C211yesmaximal, characteristic
12C11×#1436C211yesmaximal, characteristic, complemented
13C11×#1434C211yesmaximal, characteristic, complemented
14C11×C22⋊#95C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C11×#400—24no—
30C11×#385—24no—
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C25×C11C2311yescharacteristic
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C4⋊C4—41no—
89C2×C11×C4⋊C4—41no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4—41no—
103C2×C11×C22⋊C4—41no—
104C2×C11×C22⋊C4—41no—
105C2×C11×C22⋊C4—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4Q814yes—
108C2×C42×C11—22no—
109C2×C42×C11—41no—
110C2×C42×C11—41no—
111C11×#95—22no—
112C11×#95—22no—
113C11×#95—22no—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95—22no—
119C11×#95—22no—
120C11×#95—41no—
121C11×#95—41no—
122C11×#95—41no—
123C11×#95—41no—
124C11×#95—41no—
125C11×#95—41no—
126C11×#95—41no—
127C11×#95—41no—
128C11×#95—41no—
129C11×#95—41no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95D414yes—
133#15514C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11C2×Q812yes—
147C24×C11#4112yes—
148C24×C11#4112yes—
149C24×C11C2411yescharacteristic
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—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—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11—44no—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×Q812yes—
249C22×C4×C11C2×Q812yes—
250C22×C4×C11#4112yes—
251C22×C4×C11#4112yes—
252C22×C4×C11#4112yes—
253C22×C4×C11#4112yes—
254C22×C4×C11#4112yes—
255C11×C4⋊C4—44no—
256C11×C4⋊C4—44no—
257C11×C4⋊C4—44no—
258C11×C4⋊C4—44no—
259C11×C4⋊C4—44no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C11×C22⋊C4—44no—
264C11×C22⋊C4—44no—
265C11×C22⋊C4—44no—
266C42×C11—44no—
267C2×#400C2×C1111yescharacteristic, complemented
268C2×#385C2×C1111yescharacteristic
269#1445C2×C1111yescharacteristic, complemented
270#1445C2×C1111yescharacteristic, complemented
271#1442C2×C1111yescharacteristic, complemented
272#1441C2×C1111yescharacteristic, complemented
273#1441C2×C1111yescharacteristic, complemented
274#1439C2×C1111yescharacteristic
275#1439C2×C1111yescharacteristic
276#1439C2×C1111yescharacteristic
277#1437C2×C1111yescharacteristic
278#1436C2×C1111yescharacteristic, complemented
279#1434C2×C1111yescharacteristic, complemented
280C22⋊#95C2×C1111yescharacteristic
281C22⋊#95C2×C1111yescharacteristic
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11#12514yes—
317C23×C11C22×D411yescharacteristic
318C23×C11C22×Q811yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C11H(5,𝔽2)11yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C112−1+411yescharacteristic
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—416no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C24×C4C22×C1111yescharacteristic
432C22×C4⋊C4C22×C1111yescharacteristic
433C22×C4⋊C4C22×C1111yescharacteristic
434C22×C4⋊C4C22×C1111yescharacteristic
435C22×C4⋊C4C22×C1111yescharacteristic
436C22×C4⋊C4C22×C1111yescharacteristic
437C22×C22⋊C4C22×C1111yescharacteristic
438C22×C22⋊C4C22×C1111yescharacteristic
439C22×C22⋊C4C22×C1111yescharacteristic
440C22×C22⋊C4C22×C1111yescharacteristic
441C22×C22⋊C4C22×C1111yescharacteristic
442C22×C22⋊C4C22×C1111yescharacteristic
443C22×C42C22×C1111yescharacteristic
444#400—24no—
445#385—24no—
446C2×#95C22×C1111yescharacteristic
447C2×#95C22×C1111yescharacteristic
448C2×#95C22×C1111yescharacteristic
449C2×#95C22×C1111yescharacteristic
450C2×#95C22×C1111yescharacteristic
451C2×#95C22×C1111yescharacteristic
452C2×#95C22×C1111yescharacteristic
453C2×#95C22×C1111yescharacteristic
454C2×#95C22×C1111yescharacteristic
455C2×#95C22×C1111yescharacteristic
456C2×#95C22×C1111yescharacteristic
457C2×#95C22×C1111yescharacteristic
458C2×#95C22×C1111yescharacteristic
459C2×#95C22×C1111yescharacteristic
460C2×#95C22×C1111yescharacteristic
461C2×#95C22×C1111yescharacteristic
462C2×#95C22×C1111yescharacteristic
463C2×#95C22×C1111yescharacteristic
464C2×#95C22×C1111yescharacteristic
465C2×#95C22×C1111yescharacteristic
466C2×#95C22×C1111yescharacteristic
467C2×#95C22×C1111yescharacteristic
468C22×C11—24no—
469C22×C11—24no—
470C22×C11—24no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11#52511yescharacteristic
484C22×C11C2×#12511yescharacteristic
485C22×C11#52911yescharacteristic
486C22×C11#52911yescharacteristic
487C22×C11#53211yescharacteristic
488C22×C11#53311yescharacteristic
489C22×C11#53511yescharacteristic
490C22×C11#53811yescharacteristic
491C22×C11#53811yescharacteristic
492C22×C11#53811yescharacteristic
493C22×C11#53911yescharacteristic
494C22×C11#53911yescharacteristic
495C22×C11#54011yescharacteristic
496C22×C11#54211yescharacteristic
497C22×C11#54311yescharacteristic
498C22×C11#54611yescharacteristic
499C22×C11#54611yescharacteristic
500C22×C11#54611yescharacteristic
501C22×C11D4×Q811yescharacteristic
502C22×C11#55111yescharacteristic
503C22×C11#55111yescharacteristic
504C22×C11#55111yescharacteristic
505C22×C11#55111yescharacteristic
506C22×C11#55111yescharacteristic
507C22×C11#55211yescharacteristic
508C22×C11#55211yescharacteristic
509C22×C11#55311yescharacteristic
510C22×C11#55311yescharacteristic
511C22×C11#55311yescharacteristic
512C22×C11#55411yescharacteristic
513C22×C11#55411yescharacteristic
514C22×C11#55411yescharacteristic
515C22×C11#55911yescharacteristic
516C22×C11#56011yescharacteristic
517C22×C11#56211yescharacteristic
518C4×C11—42no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—81no—
529C4×C11—81no—
530C4×C11—81no—
531C4×C11—81no—
532C25C23×C1111yescharacteristic
533C23×C4—22no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4C23×C1111yescharacteristic
541C23×C4C23×C1111yescharacteristic
542C23×C4C23×C1111yescharacteristic
543C23×C4C23×C1111yescharacteristic
544C23×C4C23×C1111yescharacteristic
545C23×C4C23×C1111yescharacteristic
546C23×C4C23×C1111yescharacteristic
547C23×C4C23×C1111yescharacteristic
548C23×C4C23×C1111yescharacteristic
549C23×C4C23×C1111yescharacteristic
550C23×C4C23×C1111yescharacteristic
551C23×C4C23×C1111yescharacteristic
552C23×C4C23×C1111yescharacteristic
553C23×C4C23×C1111yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4Q8×C1114yes—
587C2×C42—22no—
588C2×C42—41no—
589C2×C42—41no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95D4×C1114yes—
612C2×C11—44no—
613C2×C11#245711yescharacteristic
614C2×C11#247311yescharacteristic
615C2×C11#250511yescharacteristic
616C2×C11#251511yescharacteristic
617C2×C11#255611yescharacteristic
618C2×C11#255711yescharacteristic
619C2×C11#256911yescharacteristic
620C2×C11#258911yescharacteristic
621C2×C11#260311yescharacteristic
622C2×C11#268511yescharacteristic
623C2×C11#269211yescharacteristic
624C2×C11#274311yescharacteristic
625C2×C11#275011yescharacteristic
626C2×C11#278011yescharacteristic
627C2×C11#279611yescharacteristic
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C2×Q8×C1112yes—
641C24C11×#4112yes—
642C24C11×#4112yes—
643C24C24×C1111yescharacteristic
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4C2×D4×C1112yes—
740C22×C4C2×D4×C1112yes—
741C22×C4C2×D4×C1112yes—
742C22×C4C2×Q8×C1112yes—
743C22×C4C2×Q8×C1112yes—
744C22×C4C11×#4112yes—
745C22×C4C11×#4112yes—
746C22×C4C11×#4112yes—
747C22×C4C11×#4112yes—
748C22×C4C11×#4112yes—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C22⋊C4—28no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C42—44no—
761C11#1551411yescharacteristic, direct product factor, Sylow
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C11×#12514yes—
797C23C22×D4×C1111yescharacteristic
798C23C22×Q8×C1111yescharacteristic
799C23C2×C11×#4111yescharacteristic
800C23C2×C11×#4111yescharacteristic
801C23C2×C11×#4111yescharacteristic
802C23C2×C11×#4111yescharacteristic
803C23C2×C11×#4111yescharacteristic
804C23C2×C11×#4111yescharacteristic
805C23C2×C11×#4111yescharacteristic
806C23C11×H(5,𝔽2)11yescharacteristic
807C23C11×H(5,𝔽2)11yescharacteristic
808C23C11×H(5,𝔽2)11yescharacteristic
809C23C11×H(5,𝔽2)11yescharacteristic
810C23C11×H(5,𝔽2)11yescharacteristic
811C23C11×2−1+411yescharacteristic
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—416no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22C11×#52511yescharacteristic
927C22C2×C11×#12511yescharacteristic
928C22C11×#52911yescharacteristic
929C22C11×#52911yescharacteristic
930C22C11×#53211yescharacteristic
931C22C11×#53311yescharacteristic
932C22C11×#53511yescharacteristic
933C22C11×#53811yescharacteristic
934C22C11×#53811yescharacteristic
935C22C11×#53811yescharacteristic
936C22C11×#53911yescharacteristic
937C22C11×#53911yescharacteristic
938C22C11×#54011yescharacteristic
939C22C11×#54211yescharacteristic
940C22C11×#54311yescharacteristic
941C22C11×#54611yescharacteristic
942C22C11×#54611yescharacteristic
943C22C11×#54611yescharacteristic
944C22D4×Q8×C1111yescharacteristic
945C22C11×#55111yescharacteristic
946C22C11×#55111yescharacteristic
947C22C11×#55111yescharacteristic
948C22C11×#55111yescharacteristic
949C22C11×#55111yescharacteristic
950C22C11×#55211yescharacteristic
951C22C11×#55211yescharacteristic
952C22C11×#55311yescharacteristic
953C22C11×#55311yescharacteristic
954C22C11×#55311yescharacteristic
955C22C11×#55411yescharacteristic
956C22C11×#55411yescharacteristic
957C22C11×#55411yescharacteristic
958C22C11×#55911yescharacteristic
959C22C11×#56011yescharacteristic
960C22C11×#56211yescharacteristic
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—81no—
972C4—81no—
973C4—81no—
974C4—81no—
975C2—44no—
976C2C11×#245711yescharacteristic
977C2C11×#247311yescharacteristic
978C2C11×#250511yescharacteristic
979C2C11×#251511yescharacteristic
980C2C11×#255611yescharacteristic
981C2C11×#255711yescharacteristic
982C2C11×#256911yescharacteristic
983C2C11×#258911yescharacteristic
984C2C11×#260311yescharacteristic
985C2C11×#268511yescharacteristic
986C2C11×#269211yescharacteristic
987C2C11×#274311yescharacteristic
988C2C11×#275011yescharacteristic
989C2C11×#278011yescharacteristic
990C2C11×#279611yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#400C2semidirect
3. C11×#1445C2semidirect
4. C11×#1445C2semidirect
5. C11×#1442C2semidirect
6. C11×#1441C2semidirect
7. C11×#1441C2semidirect
12. C11×#1436C2semidirect
13. C11×#1434C2semidirect
133. #15514C11direct (N × H)
267. C2×#400C2×C11semidirect
269. #1445C2×C11semidirect
270. #1445C2×C11semidirect
271. #1442C2×C11semidirect
272. #1441C2×C11semidirect
273. #1441C2×C11semidirect
278. #1436C2×C11semidirect
279. #1434C2×C11semidirect
761. C11#15514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4002
C2×C11×#3852
C11×#14452
C11×#14422
C11×#14412
C11×#14392
C11×#14372
C11×#14362
C11×#14342
C11×C22⋊#952
#1551411