Finite Group Databasebeta

← C11×#14475 #14591668

Subgroups — C11×#14475 #14591668

Order 2816.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#126C211yesmaximal, characteristic
2C2×C11×#388C211yesmaximal, characteristic
3C2×C11×#385C211yesmaximal, characteristic
4C11×#1445C211yesmaximal, characteristic, complemented
5C11×#1441C211yesmaximal, characteristic, complemented
6C11×#1441C211yesmaximal, characteristic, complemented
7C11×#1441C211yesmaximal, characteristic, complemented
8C11×#1440C211yesmaximal, characteristic
9C11×#1440C211yesmaximal, characteristic
10C11×#1436C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C11×C4⋊#95C211yesmaximal, characteristic, complemented
13C11×#1434C211yesmaximal, characteristic, complemented
14C11×C22⋊#95C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C2×C11×#126—24no—
18C2×C11×#126—24no—
19C2×C11×#126C418yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C22×C42×C11C2211yescharacteristic
34C11×#388—24no—
35C11×#385—24no—
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
55C2×C11×#95C2211yescharacteristic
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11—41no—
63C23×C4×C11—41no—
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
77C23×C4×C11C2311yescharacteristic
78C11×#126—232no—
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—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4C2×C414yescomplemented
95C2×C11×C4⋊C4C2×C414yescomplemented
96C2×C11×C4⋊C4C2×C414yescomplemented
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4—41no—
108C2×C11×C22⋊C4—41no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4C2×C414yes—
111C2×C11×C22⋊C4C2×C414yes—
112C2×C11×C22⋊C4C2×C414yes—
113C2×C11×C22⋊C4D414yes—
114C2×C11×C22⋊C4D414yes—
115C2×C42×C11—22no—
116C2×C42×C11—22no—
117C2×C42×C11—22no—
118C2×C42×C11—22no—
119C2×C42×C11—41no—
120C2×C42×C11C2×C414yescomplemented
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—41no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95—41no—
133C11×#95—41no—
134C11×#95—41no—
135C11×#95—41no—
136C11×#95—41no—
137C11×#95—41no—
138C11×#95—41no—
139C11×#95—41no—
140C11×#95—41no—
141#14475C1111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11C22×C412yes—
155C24×C11C2×D412yes—
156C24×C11C2×D412yes—
157C24×C11C2411yescharacteristic
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—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11—44no—
245C22×C4×C11—44no—
246C22×C4×C11—44no—
247C22×C4×C11—44no—
248C22×C4×C11—44no—
249C22×C4×C11C22×C412yes—
250C22×C4×C11C22×C412yes—
251C22×C4×C11C22×C412yes—
252C22×C4×C11C22×C412yes—
253C22×C4×C11C22×C412yes—
254C22×C4×C11C22×C412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11#4112yes—
260C22×C4×C11#4112yes—
261C22×C4×C11#4112yes—
262C22×C4×C11#4112yes—
263C11×C4⋊C4—28no—
264C11×C4⋊C4—28no—
265C11×C4⋊C4—28no—
266C11×C4⋊C4—44no—
267C11×C4⋊C4—44no—
268C11×C4⋊C4—44no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C11×C22⋊C4—44no—
274C11×C22⋊C4C22⋊C4116yes—
275C42×C11—28no—
276C42×C11—44no—
277C22×#126C2×C1111yescharacteristic
278C2×#388C2×C1111yescharacteristic
279C2×#385C2×C1111yescharacteristic
280#1445C2×C1111yescharacteristic, complemented
281#1441C2×C1111yescharacteristic, complemented
282#1441C2×C1111yescharacteristic, complemented
283#1441C2×C1111yescharacteristic, complemented
284#1440C2×C1111yescharacteristic
285#1440C2×C1111yescharacteristic
286#1436C2×C1111yescharacteristic, complemented
287C4⋊#95C2×C1111yescharacteristic, complemented
288C4⋊#95C2×C1111yescharacteristic, complemented
289#1434C2×C1111yescharacteristic, complemented
290C22⋊#95C2×C1111yescharacteristic
291C22⋊#95C2×C1111yescharacteristic
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—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
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×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11C2×C22⋊C414yes—
327C23×C11C23×C411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C112−1+411yescharacteristic
339C23×C112−1+411yescharacteristic
340C23×C112−1+411yescharacteristic
341C23×C112−1+411yescharacteristic
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—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—416no—
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—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11C2×C22⋊C414yes—
440C2×C4×C11C2×C22⋊C414yes—
441C24×C4C22×C1111yescharacteristic
442C2×#126—24no—
443C2×#126—24no—
444C2×#126C4×C1118yescomplemented
445C22×C4⋊C4C22×C1111yescharacteristic
446C22×C4⋊C4C22×C1111yescharacteristic
447C22×C4⋊C4C22×C1111yescharacteristic
448C22×C4⋊C4C22×C1111yescharacteristic
449C22×C4⋊C4C22×C1111yescharacteristic
450C22×C4⋊C4C22×C1111yescharacteristic
451C22×C22⋊C4C22×C1111yescharacteristic
452C22×C22⋊C4C22×C1111yescharacteristic
453C22×C22⋊C4C22×C1111yescharacteristic
454C22×C22⋊C4C22×C1111yescharacteristic
455C22×C22⋊C4C22×C1111yescharacteristic
456C22×C22⋊C4C22×C1111yescharacteristic
457C22×C42C22×C1111yescharacteristic
458C22×C42C22×C1111yescharacteristic
459#388—24no—
460#385—24no—
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
472C2×#95C22×C1111yescharacteristic
473C2×#95C22×C1111yescharacteristic
474C2×#95C22×C1111yescharacteristic
475C2×#95C22×C1111yescharacteristic
476C2×#95C22×C1111yescharacteristic
477C2×#95C22×C1111yescharacteristic
478C2×#95C22×C1111yescharacteristic
479C2×#95C22×C1111yescharacteristic
480C2×#95C22×C1111yescharacteristic
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11C22×C22⋊C411yescharacteristic
497C22×C11C4×#4111yescharacteristic
498C22×C11C4×#4111yescharacteristic
499C22×C11#52011yescharacteristic
500C22×C11#52011yescharacteristic
501C22×C11#52011yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#53511yescharacteristic
504C22×C11#53611yescharacteristic
505C22×C11#53711yescharacteristic
506C22×C11#53711yescharacteristic
507C22×C11#53811yescharacteristic
508C22×C11#53811yescharacteristic
509C22×C11#53911yescharacteristic
510C22×C11#53911yescharacteristic
511C22×C11#54111yescharacteristic
512C22×C11#54111yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11#54211yescharacteristic
515C22×C11#54611yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54711yescharacteristic
520C22×C11#54711yescharacteristic
521C22×C11#54711yescharacteristic
522C22×C11#54711yescharacteristic
523C22×C11#55111yescharacteristic
524C22×C11#55211yescharacteristic
525C22×C11#55311yescharacteristic
526C22×C11#55611yescharacteristic
527C22×C11#56011yescharacteristic
528C22×C11#56311yescharacteristic
529C22×C11#56311yescharacteristic
530C22×C11#56311yescharacteristic
531C4×C11—24no—
532C4×C11—24no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—81no—
542C4×C11—81no—
543C4×C11—81no—
544C4×C11—81no—
545C25C23×C1111yescharacteristic
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4—41no—
552C23×C4—41no—
553C23×C4C23×C1111yescharacteristic
554C23×C4C23×C1111yescharacteristic
555C23×C4C23×C1111yescharacteristic
556C23×C4C23×C1111yescharacteristic
557C23×C4C23×C1111yescharacteristic
558C23×C4C23×C1111yescharacteristic
559C23×C4C23×C1111yescharacteristic
560C23×C4C23×C1111yescharacteristic
561C23×C4C23×C1111yescharacteristic
562C23×C4C23×C1111yescharacteristic
563C23×C4C23×C1111yescharacteristic
564C23×C4C23×C1111yescharacteristic
565C23×C4C23×C1111yescharacteristic
566C23×C4C23×C1111yescharacteristic
567#126—232no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4C2×C4×C1114yescomplemented
584C2×C4⋊C4C2×C4×C1114yescomplemented
585C2×C4⋊C4C2×C4×C1114yescomplemented
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4C2×C4×C1114yes—
600C2×C22⋊C4C2×C4×C1114yes—
601C2×C22⋊C4C2×C4×C1114yes—
602C2×C22⋊C4D4×C1114yes—
603C2×C22⋊C4D4×C1114yes—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—41no—
609C2×C42C2×C4×C1114yescomplemented
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630C2×C11—44no—
631C2×C11#231111yescharacteristic
632C2×C11#233411yescharacteristic
633C2×C11#233411yescharacteristic
634C2×C11#233911yescharacteristic
635C2×C11#233911yescharacteristic
636C2×C11#237311yescharacteristic
637C2×C11#238311yescharacteristic
638C2×C11#268511yescharacteristic
639C2×C11#268911yescharacteristic
640C2×C11#269111yescharacteristic
641C2×C11#269511yescharacteristic
642C2×C11#269811yescharacteristic
643C2×C11#271511yescharacteristic
644C2×C11#271811yescharacteristic
645C2×C11#272211yescharacteristic
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C22×C4×C1112yes—
659C24C2×D4×C1112yes—
660C24C2×D4×C1112yes—
661C24C24×C1111yescharacteristic
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×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4C22×C4×C1112yes—
754C22×C4C22×C4×C1112yes—
755C22×C4C22×C4×C1112yes—
756C22×C4C22×C4×C1112yes—
757C22×C4C22×C4×C1112yes—
758C22×C4C22×C4×C1112yes—
759C22×C4C2×D4×C1112yes—
760C22×C4C2×D4×C1112yes—
761C22×C4C2×D4×C1112yes—
762C22×C4C2×D4×C1112yes—
763C22×C4C11×#4112yes—
764C22×C4C11×#4112yes—
765C22×C4C11×#4112yes—
766C22×C4C11×#4112yes—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4C11×C22⋊C4116yes—
779C42—28no—
780C42—44no—
781C11#1447511yescharacteristic, direct product factor, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23C2×C11×C22⋊C414yes—
817C23C23×C4×C1111yescharacteristic
818C23C22×D4×C1111yescharacteristic
819C23C22×D4×C1111yescharacteristic
820C23C2×C11×#4111yescharacteristic
821C23C2×C11×#4111yescharacteristic
822C23C2×C11×#4111yescharacteristic
823C23C2×C11×#4111yescharacteristic
824C23C11×H(5,𝔽2)11yescharacteristic
825C23C11×H(5,𝔽2)11yescharacteristic
826C23C11×H(5,𝔽2)11yescharacteristic
827C23C11×H(5,𝔽2)11yescharacteristic
828C23C11×2−1+411yescharacteristic
829C23C11×2−1+411yescharacteristic
830C23C11×2−1+411yescharacteristic
831C23C11×2−1+411yescharacteristic
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—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—416no—
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×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4C2×C11×C22⋊C414yes—
930C2×C4C2×C11×C22⋊C414yes—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22C22×C11×C22⋊C411yescharacteristic
947C22C4×C11×#4111yescharacteristic
948C22C4×C11×#4111yescharacteristic
949C22C11×#52011yescharacteristic
950C22C11×#52011yescharacteristic
951C22C11×#52011yescharacteristic
952C22C11×#52011yescharacteristic
953C22C11×#53511yescharacteristic
954C22C11×#53611yescharacteristic
955C22C11×#53711yescharacteristic
956C22C11×#53711yescharacteristic
957C22C11×#53811yescharacteristic
958C22C11×#53811yescharacteristic
959C22C11×#53911yescharacteristic
960C22C11×#53911yescharacteristic
961C22C11×#54111yescharacteristic
962C22C11×#54111yescharacteristic
963C22C11×#54211yescharacteristic
964C22C11×#54211yescharacteristic
965C22C11×#54611yescharacteristic
966C22C11×#54611yescharacteristic
967C22C11×#54611yescharacteristic
968C22C11×#54611yescharacteristic
969C22C11×#54711yescharacteristic
970C22C11×#54711yescharacteristic
971C22C11×#54711yescharacteristic
972C22C11×#54711yescharacteristic
973C22C11×#55111yescharacteristic
974C22C11×#55211yescharacteristic
975C22C11×#55311yescharacteristic
976C22C11×#55611yescharacteristic
977C22C11×#56011yescharacteristic
978C22C11×#56311yescharacteristic
979C22C11×#56311yescharacteristic
980C22C11×#56311yescharacteristic
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—81no—
995C2—44no—
996C2C11×#231111yescharacteristic
997C2C11×#233411yescharacteristic
998C2C11×#233411yescharacteristic
999C2C11×#233911yescharacteristic
1000C2C11×#233911yescharacteristic
1001C2C11×#237311yescharacteristic
1002C2C11×#238311yescharacteristic
1003C2C11×#268511yescharacteristic
1004C2C11×#268911yescharacteristic
1005C2C11×#269111yescharacteristic
1006C2C11×#269511yescharacteristic
1007C2C11×#269811yescharacteristic
1008C2C11×#271511yescharacteristic
1009C2C11×#271811yescharacteristic
1010C2C11×#272211yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1445C2semidirect
5. C11×#1441C2semidirect
6. C11×#1441C2semidirect
7. C11×#1441C2semidirect
10. C11×#1436C2semidirect
11. C11×C4⋊#95C2semidirect
12. C11×C4⋊#95C2semidirect
13. C11×#1434C2semidirect
19. C2×C11×#126C4semidirect
94. C2×C11×C4⋊C4C2×C4semidirect
95. C2×C11×C4⋊C4C2×C4semidirect
96. C2×C11×C4⋊C4C2×C4semidirect
120. C2×C42×C11C2×C4semidirect
141. #14475C11direct (N × H)
280. #1445C2×C11semidirect
281. #1441C2×C11semidirect
282. #1441C2×C11semidirect
283. #1441C2×C11semidirect
286. #1436C2×C11semidirect
287. C4⋊#95C2×C11semidirect
288. C4⋊#95C2×C11semidirect
289. #1434C2×C11semidirect
444. C2×#126C4×C11semidirect
583. C2×C4⋊C4C2×C4×C11semidirect
584. C2×C4⋊C4C2×C4×C11semidirect
585. C2×C4⋊C4C2×C4×C11semidirect
609. C2×C42C2×C4×C11semidirect
781. C11#14475direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1262
C2×C11×#3882
C2×C11×#3852
C11×#14452
C11×#14412
C11×#14402
C11×#14362
C11×C4⋊#952
C11×#14342
C11×C22⋊#952
#1447511