Finite Group Databasebeta

← C11×#15504 #14592697

Subgroups — C11×#15504 #14592697

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#397C211yesmaximal, characteristic
2C2×C11×#393C211yesmaximal, characteristic
3C2×C11×#391C211yesmaximal, characteristic, complemented
4C2×C11×#391C211yesmaximal, characteristic, complemented
5C11×#1445C211yesmaximal, characteristic, complemented
6C11×#1443C211yesmaximal, characteristic, complemented
7C11×#1443C211yesmaximal, characteristic, complemented
8C11×#1441C211yesmaximal, characteristic, complemented
9C11×#1440C211yesmaximal, characteristic
10C11×#1439C211yesmaximal, characteristic
11C11×#1439C211yesmaximal, characteristic
12C11×#1437C211yesmaximal, characteristic
13C11×#1437C211yesmaximal, characteristic
14C11×#1436C211yesmaximal, characteristic, complemented
15C11×#1434C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C11×#397—24no—
30C11×#393—24no—
31C11×#391—24no—
32C11×#391—24no—
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
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C25×C11C2311yescharacteristic
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—41no—
61C22×Q8×C11—41no—
62C22×Q8×C11D414yes—
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
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
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—41no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
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×C42×C11—22no—
108C2×C42×C11—22no—
109C2×C42×C11—22no—
110C2×C42×C11—41no—
111C2×C42×C11—41no—
112C2×C42×C11—41no—
113C11×#95—22no—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95—22no—
119C11×#95—22no—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—22no—
126C11×#95—22no—
127C11×#95—22no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95—41no—
133C11×#95—41no—
134C11×#95D414yes—
135#15504C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11#4112yes—
151C24×C11C2411yescharacteristic
152C2×Q8×C11—28no—
153C2×Q8×C11—28no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C2×Q8×C11—44no—
157C2×Q8×C11—44no—
158C2×Q8×C11—44no—
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—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D412yes—
251C22×C4×C11#4112yes—
252C22×C4×C11#4112yes—
253C22×C4×C11#4112yes—
254C22×C4×C11#4112yes—
255C22×C4×C11#4112yes—
256C22×C4×C11#4112yes—
257C11×C4⋊C4—44no—
258C11×C4⋊C4—44no—
259C11×C4⋊C4—44no—
260C11×C22⋊C4—44no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C11×C22⋊C4—44no—
264C11×C22⋊C4—44no—
265C11×C22⋊C4—44no—
266C11×C22⋊C4—44no—
267C42×C11—44no—
268C42×C11—44no—
269C2×#397C2×C1111yescharacteristic
270C2×#393C2×C1111yescharacteristic
271C2×#391C2×C1111yescharacteristic, complemented
272C2×#391C2×C1111yescharacteristic, complemented
273#1445C2×C1111yescharacteristic, complemented
274#1443C2×C1111yescharacteristic, complemented
275#1443C2×C1111yescharacteristic, complemented
276#1441C2×C1111yescharacteristic, complemented
277#1440C2×C1111yescharacteristic
278#1439C2×C1111yescharacteristic
279#1439C2×C1111yescharacteristic
280#1437C2×C1111yescharacteristic
281#1437C2×C1111yescharacteristic
282#1436C2×C1111yescharacteristic, complemented
283#1434C2×C1111yescharacteristic, complemented
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
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—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11C22×D411yescharacteristic
320C23×C11C22×D411yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11H(5,𝔽2)11yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C112−1+411yescharacteristic
332C23×C112−1+411yescharacteristic
333C23×C112−1+411yescharacteristic
334Q8×C11—416no—
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—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
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—
431C2×C4×C11#12114yes—
432C2×C4×C11#12314yes—
433C23×Q8C22×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×C22⋊C4C22×C1111yescharacteristic
444C22×C42C22×C1111yescharacteristic
445C22×C42C22×C1111yescharacteristic
446#397—24no—
447#393—24no—
448#391—24no—
449#391—24no—
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
468C2×#95C22×C1111yescharacteristic
469C2×#95C22×C1111yescharacteristic
470C2×#95C22×C1111yescharacteristic
471C2×#95C22×C1111yescharacteristic
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—81no—
480C22×C11—81no—
481C22×C11—81no—
482C22×C11—81no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11C2×#12111yescharacteristic
488C22×C11C2×#12311yescharacteristic
489C22×C11#52911yescharacteristic
490C22×C11#52911yescharacteristic
491C22×C11#52911yescharacteristic
492C22×C11#53211yescharacteristic
493C22×C11#53411yescharacteristic
494C22×C11#53611yescharacteristic
495C22×C11#53811yescharacteristic
496C22×C11#53911yescharacteristic
497C22×C11#53911yescharacteristic
498C22×C11#54111yescharacteristic
499C22×C11#54211yescharacteristic
500C22×C11#54211yescharacteristic
501C22×C11#54211yescharacteristic
502C22×C11#54611yescharacteristic
503C22×C11#54611yescharacteristic
504C22×C11#54611yescharacteristic
505C22×C11#54811yescharacteristic
506C22×C11#54811yescharacteristic
507C22×C11#54811yescharacteristic
508C22×C11#54811yescharacteristic
509C22×C11#55011yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55111yescharacteristic
512C22×C11#55111yescharacteristic
513C22×C11#55111yescharacteristic
514C22×C11#55211yescharacteristic
515C22×C11#55611yescharacteristic
516C22×C11#55611yescharacteristic
517C22×C11#55611yescharacteristic
518C22×C11#55611yescharacteristic
519C22×C11#55911yescharacteristic
520C22×C11#56211yescharacteristic
521C22×C11#56311yescharacteristic
522C4×C11—24no—
523C4×C11—24no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—81no—
531C4×C11—81no—
532C4×C11—81no—
533C4×C11—81no—
534C4×C11—81no—
535C4×C11—81no—
536C25C23×C1111yescharacteristic
537C22×Q8—22no—
538C22×Q8—22no—
539C22×Q8—22no—
540C22×Q8—22no—
541C22×Q8—41no—
542C22×Q8—41no—
543C22×Q8D4×C1114yes—
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
554C23×C4C23×C1111yescharacteristic
555C23×C4C23×C1111yescharacteristic
556C23×C4C23×C1111yescharacteristic
557C23×C4C23×C1111yescharacteristic
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
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—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—41no—
592C2×C42—41no—
593C2×C42—41no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95D4×C1114yes—
616C2×C11—82no—
617C2×C11#241211yescharacteristic
618C2×C11#242111yescharacteristic
619C2×C11#242611yescharacteristic
620C2×C11#244811yescharacteristic
621C2×C11#252311yescharacteristic
622C2×C11#252711yescharacteristic
623C2×C11#254511yescharacteristic
624C2×C11#255711yescharacteristic
625C2×C11#256011yescharacteristic
626C2×C11#268711yescharacteristic
627C2×C11#271611yescharacteristic
628C2×C11#272811yescharacteristic
629C2×C11#273011yescharacteristic
630C2×C11#275911yescharacteristic
631C2×C11#279811yescharacteristic
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24C11×#4112yes—
647C24C24×C1111yescharacteristic
648C2×Q8—28no—
649C2×Q8—28no—
650C2×Q8—44no—
651C2×Q8—44no—
652C2×Q8—44no—
653C2×Q8—44no—
654C2×Q8—44no—
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—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4C2×D4×C1112yes—
742C22×C4C2×D4×C1112yes—
743C22×C4C2×D4×C1112yes—
744C22×C4C2×D4×C1112yes—
745C22×C4C2×D4×C1112yes—
746C22×C4C2×D4×C1112yes—
747C22×C4C11×#4112yes—
748C22×C4C11×#4112yes—
749C22×C4C11×#4112yes—
750C22×C4C11×#4112yes—
751C22×C4C11×#4112yes—
752C22×C4C11×#4112yes—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C42—44no—
764C42—44no—
765C11#1550411yescharacteristic, direct product factor, Sylow
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
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—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23C22×D4×C1111yescharacteristic
802C23C22×D4×C1111yescharacteristic
803C23C2×C11×#4111yescharacteristic
804C23C2×C11×#4111yescharacteristic
805C23C2×C11×#4111yescharacteristic
806C23C2×C11×#4111yescharacteristic
807C23C2×C11×#4111yescharacteristic
808C23C2×C11×#4111yescharacteristic
809C23C2×C11×#4111yescharacteristic
810C23C11×H(5,𝔽2)11yescharacteristic
811C23C11×H(5,𝔽2)11yescharacteristic
812C23C11×H(5,𝔽2)11yescharacteristic
813C23C11×2−1+411yescharacteristic
814C23C11×2−1+411yescharacteristic
815C23C11×2−1+411yescharacteristic
816Q8—416no—
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—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
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—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4C11×#12114yes—
914C2×C4C11×#12314yes—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22C2×C11×#12111yescharacteristic
931C22C2×C11×#12311yescharacteristic
932C22C11×#52911yescharacteristic
933C22C11×#52911yescharacteristic
934C22C11×#52911yescharacteristic
935C22C11×#53211yescharacteristic
936C22C11×#53411yescharacteristic
937C22C11×#53611yescharacteristic
938C22C11×#53811yescharacteristic
939C22C11×#53911yescharacteristic
940C22C11×#53911yescharacteristic
941C22C11×#54111yescharacteristic
942C22C11×#54211yescharacteristic
943C22C11×#54211yescharacteristic
944C22C11×#54211yescharacteristic
945C22C11×#54611yescharacteristic
946C22C11×#54611yescharacteristic
947C22C11×#54611yescharacteristic
948C22C11×#54811yescharacteristic
949C22C11×#54811yescharacteristic
950C22C11×#54811yescharacteristic
951C22C11×#54811yescharacteristic
952C22C11×#55011yescharacteristic
953C22C11×#55111yescharacteristic
954C22C11×#55111yescharacteristic
955C22C11×#55111yescharacteristic
956C22C11×#55111yescharacteristic
957C22C11×#55211yescharacteristic
958C22C11×#55611yescharacteristic
959C22C11×#55611yescharacteristic
960C22C11×#55611yescharacteristic
961C22C11×#55611yescharacteristic
962C22C11×#55911yescharacteristic
963C22C11×#56211yescharacteristic
964C22C11×#56311yescharacteristic
965C4—24no—
966C4—24no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—81no—
977C4—81no—
978C4—81no—
979C2—82no—
980C2C11×#241211yescharacteristic
981C2C11×#242111yescharacteristic
982C2C11×#242611yescharacteristic
983C2C11×#244811yescharacteristic
984C2C11×#252311yescharacteristic
985C2C11×#252711yescharacteristic
986C2C11×#254511yescharacteristic
987C2C11×#255711yescharacteristic
988C2C11×#256011yescharacteristic
989C2C11×#268711yescharacteristic
990C2C11×#271611yescharacteristic
991C2C11×#272811yescharacteristic
992C2C11×#273011yescharacteristic
993C2C11×#275911yescharacteristic
994C2C11×#279811yescharacteristic
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
3. C2×C11×#391C2semidirect
4. C2×C11×#391C2semidirect
5. C11×#1445C2semidirect
6. C11×#1443C2semidirect
7. C11×#1443C2semidirect
8. C11×#1441C2semidirect
14. C11×#1436C2semidirect
15. C11×#1434C2semidirect
135. #15504C11direct (N × H)
271. C2×#391C2×C11semidirect
272. C2×#391C2×C11semidirect
273. #1445C2×C11semidirect
274. #1443C2×C11semidirect
275. #1443C2×C11semidirect
276. #1441C2×C11semidirect
282. #1436C2×C11semidirect
283. #1434C2×C11semidirect
765. C11#15504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3972
C2×C11×#3932
C2×C11×#3912
C11×#14452
C11×#14432
C11×#14412
C11×#14402
C11×#14392
C11×#14372
C11×#14362
C11×#14342
#1550411