Finite Group Databasebeta

← C11×#14576 #14591769

Subgroups — C11×#14576 #14591769

Order 2816.

1498 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#397C211yesmaximal, characteristic
2C2×C11×#388C211yesmaximal, characteristic
3C2×C11×#388C211yesmaximal, characteristic
4C11×#1444C211yesmaximal, characteristic, complemented
5C11×#1443C211yesmaximal, characteristic, complemented
6C11×#1443C211yesmaximal, characteristic, complemented
7C11×#1441C211yesmaximal, characteristic, complemented
8C11×#1439C211yesmaximal, characteristic
9C11×#1436C211yesmaximal, characteristic, complemented
10C11×#1436C211yesmaximal, characteristic, complemented
11C11×#1436C211yesmaximal, characteristic, complemented
12C11×#1434C211yesmaximal, characteristic, complemented
13C11×C22⋊#95C211yesmaximal, characteristic
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×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×#397C418yescomplemented
30C11×#388—24no—
31C11×#388—24no—
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
53C2×C11×#95C2211yescharacteristic
54C25×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
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
75C23×C4×C11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4C2×C414yescomplemented
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—41no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4—41no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4—41no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4C2×C414yes—
103C2×C11×C22⋊C4C2×C414yes—
104C2×C11×C22⋊C4C2×C414yes—
105C2×C11×C22⋊C4D414yes—
106C2×C42×C11—22no—
107C2×C42×C11—22no—
108C2×C42×C11—22no—
109C2×C42×C11—41no—
110C2×C42×C11—41no—
111C2×C42×C11—41no—
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—22no—
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×#95C2×C414yescomplemented
132C11×#95C2×C414yescomplemented
133C11×#95C2×C414yescomplemented
134#14576C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11—21no—
147C24×C11C22×C412yes—
148C24×C11C2×D412yes—
149C24×C11#4112yes—
150C24×C11C2411yescharacteristic
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—44no—
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×C11C22×C412yes—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C22×C412yes—
247C22×C4×C11C22×C412yes—
248C22×C4×C11C22×C412yes—
249C22×C4×C11C22×C412yes—
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2×D412yes—
252C22×C4×C11#4112yes—
253C22×C4×C11#4112yes—
254C22×C4×C11#4112yes—
255C22×C4×C11#4112yes—
256C11×C4⋊C4—44no—
257C11×C4⋊C4—44no—
258C11×C4⋊C4—44no—
259C11×C4⋊C4—44no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4—28no—
262C11×C22⋊C4—44no—
263C11×C22⋊C4—44no—
264C11×C22⋊C4—44no—
265C11×C22⋊C4—44no—
266C42×C11—44no—
267C42×C11—44no—
268C2×#397C2×C1111yescharacteristic
269C2×#388C2×C1111yescharacteristic
270C2×#388C2×C1111yescharacteristic
271#1444C2×C1111yescharacteristic, complemented
272#1443C2×C1111yescharacteristic, complemented
273#1443C2×C1111yescharacteristic, complemented
274#1441C2×C1111yescharacteristic, complemented
275#1439C2×C1111yescharacteristic
276#1436C2×C1111yescharacteristic, complemented
277#1436C2×C1111yescharacteristic, complemented
278#1436C2×C1111yescharacteristic, complemented
279#1434C2×C1111yescharacteristic, complemented
280C22⋊#95C2×C1111yescharacteristic
281C22⋊#95C2×C1111yescharacteristic
282C22⋊#95C2×C1111yescharacteristic
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—22no—
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×C11C4×D414yes—
318C23×C11C23×C411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C11H(5,𝔽2)11yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C112−1+411yescharacteristic
331C23×C112−1+411yescharacteristic
332C23×C112−1+411yescharacteristic
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—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—416no—
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—41no—
432C24×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
444C22×C42C22×C1111yescharacteristic
445#397C4×C1118yescomplemented
446#388—24no—
447#388—24no—
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
468C2×#95C22×C1111yescharacteristic
469C2×#95C22×C1111yescharacteristic
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
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—42no—
484C22×C11—42no—
485C22×C11C2×C4×D411yescharacteristic
486C22×C11C4×#4111yescharacteristic
487C22×C11C4×#4111yescharacteristic
488C22×C11#51811yescharacteristic
489C22×C11#52011yescharacteristic
490C22×C11#52011yescharacteristic
491C22×C11#52011yescharacteristic
492C22×C11#53411yescharacteristic
493C22×C11#53711yescharacteristic
494C22×C11#53811yescharacteristic
495C22×C11#53811yescharacteristic
496C22×C11#53811yescharacteristic
497C22×C11#53811yescharacteristic
498C22×C11#53911yescharacteristic
499C22×C11#53911yescharacteristic
500C22×C11#54011yescharacteristic
501C22×C11#54211yescharacteristic
502C22×C11#54211yescharacteristic
503C22×C11#54211yescharacteristic
504C22×C11#54611yescharacteristic
505C22×C11#54611yescharacteristic
506C22×C11#54711yescharacteristic
507C22×C11#54711yescharacteristic
508C22×C11#55111yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55211yescharacteristic
512C22×C11#55211yescharacteristic
513C22×C11#55211yescharacteristic
514C22×C11#55311yescharacteristic
515C22×C11#55611yescharacteristic
516C22×C11#56011yescharacteristic
517C22×C11#56311yescharacteristic
518C22×C11#56311yescharacteristic
519C22×C11#56311yescharacteristic
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—42no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—42no—
532C4×C11—81no—
533C4×C11—81no—
534C25C23×C1111yescharacteristic
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—41no—
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
554C23×C4C23×C1111yescharacteristic
555C23×C4C23×C1111yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4C2×C4×C1114yescomplemented
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—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4C2×C4×C1114yes—
583C2×C22⋊C4C2×C4×C1114yes—
584C2×C22⋊C4C2×C4×C1114yes—
585C2×C22⋊C4D4×C1114yes—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—41no—
590C2×C42—41no—
591C2×C42—41no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
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#95C2×C4×C1114yescomplemented
612#95C2×C4×C1114yescomplemented
613#95C2×C4×C1114yescomplemented
614C2×C11—44no—
615C2×C11#232511yescharacteristic
616C2×C11#233511yescharacteristic
617C2×C11#233711yescharacteristic
618C2×C11#235911yescharacteristic
619C2×C11#235911yescharacteristic
620C2×C11#237311yescharacteristic
621C2×C11#238311yescharacteristic
622C2×C11#268811yescharacteristic
623C2×C11#269511yescharacteristic
624C2×C11#271511yescharacteristic
625C2×C11#271711yescharacteristic
626C2×C11#273511yescharacteristic
627C2×C11#273811yescharacteristic
628C2×C11#274511yescharacteristic
629C2×C11#276511yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C22×C4×C1112yes—
643C24C2×D4×C1112yes—
644C24C11×#4112yes—
645C24C24×C1111yescharacteristic
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×C4C22×C4×C1112yes—
740C22×C4C22×C4×C1112yes—
741C22×C4C22×C4×C1112yes—
742C22×C4C22×C4×C1112yes—
743C22×C4C22×C4×C1112yes—
744C22×C4C22×C4×C1112yes—
745C22×C4C2×D4×C1112yes—
746C22×C4C2×D4×C1112yes—
747C22×C4C11×#4112yes—
748C22×C4C11×#4112yes—
749C22×C4C11×#4112yes—
750C22×C4C11×#4112yes—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C42—44no—
762C42—44no—
763C11#1457611yescharacteristic, direct product factor, Sylow
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—22no—
781C23—22no—
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—
798C23C4×D4×C1114yes—
799C23C23×C4×C1111yescharacteristic
800C23C22×D4×C1111yescharacteristic
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
812C23C11×2−1+411yescharacteristic
813C23C11×2−1+411yescharacteristic
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—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—416no—
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—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×C4×D4×C1111yescharacteristic
929C22C4×C11×#4111yescharacteristic
930C22C4×C11×#4111yescharacteristic
931C22C11×#51811yescharacteristic
932C22C11×#52011yescharacteristic
933C22C11×#52011yescharacteristic
934C22C11×#52011yescharacteristic
935C22C11×#53411yescharacteristic
936C22C11×#53711yescharacteristic
937C22C11×#53811yescharacteristic
938C22C11×#53811yescharacteristic
939C22C11×#53811yescharacteristic
940C22C11×#53811yescharacteristic
941C22C11×#53911yescharacteristic
942C22C11×#53911yescharacteristic
943C22C11×#54011yescharacteristic
944C22C11×#54211yescharacteristic
945C22C11×#54211yescharacteristic
946C22C11×#54211yescharacteristic
947C22C11×#54611yescharacteristic
948C22C11×#54611yescharacteristic
949C22C11×#54711yescharacteristic
950C22C11×#54711yescharacteristic
951C22C11×#55111yescharacteristic
952C22C11×#55111yescharacteristic
953C22C11×#55111yescharacteristic
954C22C11×#55211yescharacteristic
955C22C11×#55211yescharacteristic
956C22C11×#55211yescharacteristic
957C22C11×#55311yescharacteristic
958C22C11×#55611yescharacteristic
959C22C11×#56011yescharacteristic
960C22C11×#56311yescharacteristic
961C22C11×#56311yescharacteristic
962C22C11×#56311yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—81no—
977C2—44no—
978C2C11×#232511yescharacteristic
979C2C11×#233511yescharacteristic
980C2C11×#233711yescharacteristic
981C2C11×#235911yescharacteristic
982C2C11×#235911yescharacteristic
983C2C11×#237311yescharacteristic
984C2C11×#238311yescharacteristic
985C2C11×#268811yescharacteristic
986C2C11×#269511yescharacteristic
987C2C11×#271511yescharacteristic
988C2C11×#271711yescharacteristic
989C2C11×#273511yescharacteristic
990C2C11×#273811yescharacteristic
991C2C11×#274511yescharacteristic
992C2C11×#276511yescharacteristic
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×#1444C2semidirect
5. C11×#1443C2semidirect
6. C11×#1443C2semidirect
7. C11×#1441C2semidirect
9. C11×#1436C2semidirect
10. C11×#1436C2semidirect
11. C11×#1436C2semidirect
12. C11×#1434C2semidirect
29. C11×#397C4semidirect
87. C2×C11×C4⋊C4C2×C4semidirect
131. C11×#95C2×C4semidirect
132. C11×#95C2×C4semidirect
133. C11×#95C2×C4semidirect
134. #14576C11direct (N × H)
271. #1444C2×C11semidirect
272. #1443C2×C11semidirect
273. #1443C2×C11semidirect
274. #1441C2×C11semidirect
276. #1436C2×C11semidirect
277. #1436C2×C11semidirect
278. #1436C2×C11semidirect
279. #1434C2×C11semidirect
445. #397C4×C11semidirect
567. C2×C4⋊C4C2×C4×C11semidirect
611. #95C2×C4×C11semidirect
612. #95C2×C4×C11semidirect
613. #95C2×C4×C11semidirect
763. C11#14576direct (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×#3882
C11×#14442
C11×#14432
C11×#14412
C11×#14392
C11×#14362
C11×#14342
C11×C22⋊#952
#1457611