Finite Group Databasebeta

← C11×#14456 #14591649

Subgroups — C11×#14456 #14591649

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#385C211yesmaximal, characteristic
2C11×#1445C211yesmaximal, characteristic, complemented
3C11×#1443C211yesmaximal, characteristic, complemented
4C11×#1441C211yesmaximal, characteristic, complemented
5C11×#1441C211yesmaximal, characteristic, complemented
6C11×#1439C211yesmaximal, characteristic
7C11×#1439C211yesmaximal, characteristic
8C11×#1437C211yesmaximal, characteristic
9C11×#1437C211yesmaximal, characteristic
10C11×#1436C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C11×#1434C211yesmaximal, 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×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×#385C418yescomplemented
30C2×C11×#95C2211yescharacteristic
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
52C25×C11C2311yescharacteristic
53C23×C4×C11—41no—
54C23×C4×C11—41no—
55C23×C4×C11—41no—
56C23×C4×C11—41no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11C2×C414yes—
60C23×C4×C11C2311yescharacteristic
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
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4C2×C414yes—
85C2×C11×C4⋊C4C2×C414yes—
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—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
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⋊C4C2×C414yes—
102C2×C11×C22⋊C4C2×C414yes—
103C2×C11×C22⋊C4Q814yes—
104C2×C42×C11—22no—
105C2×C42×C11—22no—
106C2×C42×C11—22no—
107C2×C42×C11—41no—
108C2×C42×C11—41no—
109C2×C42×C11—41no—
110C11×#95—22no—
111C11×#95—22no—
112C11×#95—22no—
113C11×#95—41no—
114C11×#95—41no—
115C11×#95—41no—
116C11×#95—41no—
117C11×#95—41no—
118C11×#95—41no—
119C11×#95—41no—
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×#95C2×C414yes—
131C11×#95C2×C414yes—
132#14456C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
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×C11C22×C412yes—
146C24×C11C2×Q812yes—
147C24×C11#4112yes—
148C24×C11C2411yescharacteristic
149C22×C4×C11—21no—
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—44no—
236C22×C4×C11—44no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11C22×C412yes—
243C22×C4×C11C22×C412yes—
244C22×C4×C11C22×C412yes—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C22×C412yes—
247C22×C4×C11C22×C412yes—
248C22×C4×C11C2×Q812yes—
249C22×C4×C11C2×Q812yes—
250C22×C4×C11#4112yes—
251C22×C4×C11#4112yes—
252C22×C4×C11#4112yes—
253C22×C4×C11#4112yes—
254C11×C4⋊C4—44no—
255C11×C4⋊C4—44no—
256C11×C4⋊C4—44no—
257C11×C4⋊C4—44no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—44no—
260C11×C22⋊C4—44no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C11×C22⋊C4—44no—
264C42×C11—44no—
265C42×C11—44no—
266C2×#385C2×C1111yescharacteristic
267#1445C2×C1111yescharacteristic, complemented
268#1443C2×C1111yescharacteristic, complemented
269#1441C2×C1111yescharacteristic, complemented
270#1441C2×C1111yescharacteristic, complemented
271#1439C2×C1111yescharacteristic
272#1439C2×C1111yescharacteristic
273#1437C2×C1111yescharacteristic
274#1437C2×C1111yescharacteristic
275#1436C2×C1111yescharacteristic, complemented
276C4⋊#95C2×C1111yescharacteristic, complemented
277#1434C2×C1111yescharacteristic, complemented
278#1434C2×C1111yescharacteristic, complemented
279C22⋊#95C2×C1111yescharacteristic
280C22⋊#95C2×C1111yescharacteristic
281C23×C11—22no—
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—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×C11C4×Q814yes—
316C23×C11C23×C411yescharacteristic
317C23×C11C22×Q811yescharacteristic
318C23×C11C2×#4111yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
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
331C2×C4×C11—22no—
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—22no—
363C2×C4×C11—22no—
364C2×C4×C11—416no—
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#11714yes—
430C24×C4C22×C1111yescharacteristic
431C22×C4⋊C4C22×C1111yescharacteristic
432C22×C4⋊C4C22×C1111yescharacteristic
433C22×C4⋊C4C22×C1111yescharacteristic
434C22×C4⋊C4C22×C1111yescharacteristic
435C22×C22⋊C4C22×C1111yescharacteristic
436C22×C22⋊C4C22×C1111yescharacteristic
437C22×C22⋊C4C22×C1111yescharacteristic
438C22×C22⋊C4C22×C1111yescharacteristic
439C22×C22⋊C4C22×C1111yescharacteristic
440C22×C22⋊C4C22×C1111yescharacteristic
441C22×C42C22×C1111yescharacteristic
442C22×C42C22×C1111yescharacteristic
443#385C4×C1118yescomplemented
444C2×#95C22×C1111yescharacteristic
445C2×#95C22×C1111yescharacteristic
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
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—42no—
470C22×C11—42no—
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×C11C2×#11711yescharacteristic
482C22×C11C2×C4×Q811yescharacteristic
483C22×C11C4×#4111yescharacteristic
484C22×C11#51811yescharacteristic
485C22×C11#51811yescharacteristic
486C22×C11#51811yescharacteristic
487C22×C11#52011yescharacteristic
488C22×C11#53811yescharacteristic
489C22×C11#53811yescharacteristic
490C22×C11#53911yescharacteristic
491C22×C11#53911yescharacteristic
492C22×C11#54011yescharacteristic
493C22×C11#54011yescharacteristic
494C22×C11#54011yescharacteristic
495C22×C11#54211yescharacteristic
496C22×C11#54211yescharacteristic
497C22×C11#54211yescharacteristic
498C22×C11#54311yescharacteristic
499C22×C11#54411yescharacteristic
500C22×C11#55111yescharacteristic
501C22×C11#55111yescharacteristic
502C22×C11#55111yescharacteristic
503C22×C11#55111yescharacteristic
504C22×C11#55311yescharacteristic
505C22×C11#55311yescharacteristic
506C22×C11#55311yescharacteristic
507C22×C11#55311yescharacteristic
508C22×C11#55411yescharacteristic
509C22×C11#55411yescharacteristic
510C22×C11#55411yescharacteristic
511C22×C11#55411yescharacteristic
512C22×C11#56011yescharacteristic
513C22×C11#56011yescharacteristic
514C22×C11#56011yescharacteristic
515C22×C11H(3,𝔽4)11yescharacteristic
516C4×C11—24no—
517C4×C11—42no—
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—81no—
527C4×C11—81no—
528C4×C11—81no—
529C4×C11—81no—
530C25C23×C1111yescharacteristic
531C23×C4—41no—
532C23×C4—41no—
533C23×C4—41no—
534C23×C4—41no—
535C23×C4—41no—
536C23×C4—41no—
537C23×C4C2×C4×C1114yes—
538C23×C4C23×C1111yescharacteristic
539C23×C4C23×C1111yescharacteristic
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
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4C2×C4×C1114yes—
563C2×C4⋊C4C2×C4×C1114yes—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4C2×C4×C1114yes—
580C2×C22⋊C4C2×C4×C1114yes—
581C2×C22⋊C4Q8×C1114yes—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
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#95C2×C4×C1114yes—
609#95C2×C4×C1114yes—
610C2×C11—44no—
611C2×C11#231911yescharacteristic
612C2×C11#232911yescharacteristic
613C2×C11#233511yescharacteristic
614C2×C11#234511yescharacteristic
615C2×C11#235311yescharacteristic
616C2×C11#236811yescharacteristic
617C2×C11#237511yescharacteristic
618C2×C11#274611yescharacteristic
619C2×C11#274811yescharacteristic
620C2×C11#274911yescharacteristic
621C2×C11#275311yescharacteristic
622C2×C11#275711yescharacteristic
623C2×C11#276311yescharacteristic
624C2×C11#278011yescharacteristic
625C2×C11#279011yescharacteristic
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24C22×C4×C1112yes—
639C24C2×Q8×C1112yes—
640C24C11×#4112yes—
641C24C24×C1111yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
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—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4C22×C4×C1112yes—
736C22×C4C22×C4×C1112yes—
737C22×C4C22×C4×C1112yes—
738C22×C4C22×C4×C1112yes—
739C22×C4C22×C4×C1112yes—
740C22×C4C22×C4×C1112yes—
741C22×C4C2×Q8×C1112yes—
742C22×C4C2×Q8×C1112yes—
743C22×C4C11×#4112yes—
744C22×C4C11×#4112yes—
745C22×C4C11×#4112yes—
746C22×C4C11×#4112yes—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C22⋊C4—28no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C42—44no—
758C42—44no—
759C11#1445611yescharacteristic, direct product factor, Sylow
760C23—22no—
761C23—22no—
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—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—
794C23C4×Q8×C1114yes—
795C23C23×C4×C1111yescharacteristic
796C23C22×Q8×C1111yescharacteristic
797C23C2×C11×#4111yescharacteristic
798C23C2×C11×#4111yescharacteristic
799C23C2×C11×#4111yescharacteristic
800C23C2×C11×#4111yescharacteristic
801C23C2×C11×#4111yescharacteristic
802C23C11×H(5,𝔽2)11yescharacteristic
803C23C11×H(5,𝔽2)11yescharacteristic
804C23C11×H(5,𝔽2)11yescharacteristic
805C23C11×H(5,𝔽2)11yescharacteristic
806C23C11×H(5,𝔽2)11yescharacteristic
807C23C11×H(5,𝔽2)11yescharacteristic
808C23C11×H(5,𝔽2)11yescharacteristic
809C23C11×2−1+411yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
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—22no—
843C2×C4—416no—
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×C4C11×#11714yes—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22C2×C11×#11711yescharacteristic
925C22C2×C4×Q8×C1111yescharacteristic
926C22C4×C11×#4111yescharacteristic
927C22C11×#51811yescharacteristic
928C22C11×#51811yescharacteristic
929C22C11×#51811yescharacteristic
930C22C11×#52011yescharacteristic
931C22C11×#53811yescharacteristic
932C22C11×#53811yescharacteristic
933C22C11×#53911yescharacteristic
934C22C11×#53911yescharacteristic
935C22C11×#54011yescharacteristic
936C22C11×#54011yescharacteristic
937C22C11×#54011yescharacteristic
938C22C11×#54211yescharacteristic
939C22C11×#54211yescharacteristic
940C22C11×#54211yescharacteristic
941C22C11×#54311yescharacteristic
942C22C11×#54411yescharacteristic
943C22C11×#55111yescharacteristic
944C22C11×#55111yescharacteristic
945C22C11×#55111yescharacteristic
946C22C11×#55111yescharacteristic
947C22C11×#55311yescharacteristic
948C22C11×#55311yescharacteristic
949C22C11×#55311yescharacteristic
950C22C11×#55311yescharacteristic
951C22C11×#55411yescharacteristic
952C22C11×#55411yescharacteristic
953C22C11×#55411yescharacteristic
954C22C11×#55411yescharacteristic
955C22C11×#56011yescharacteristic
956C22C11×#56011yescharacteristic
957C22C11×#56011yescharacteristic
958C22C11×H(3,𝔽4)11yescharacteristic
959C4—24no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—81no—
971C4—81no—
972C4—81no—
973C2—44no—
974C2C11×#231911yescharacteristic
975C2C11×#232911yescharacteristic
976C2C11×#233511yescharacteristic
977C2C11×#234511yescharacteristic
978C2C11×#235311yescharacteristic
979C2C11×#236811yescharacteristic
980C2C11×#237511yescharacteristic
981C2C11×#274611yescharacteristic
982C2C11×#274811yescharacteristic
983C2C11×#274911yescharacteristic
984C2C11×#275311yescharacteristic
985C2C11×#275711yescharacteristic
986C2C11×#276311yescharacteristic
987C2C11×#278011yescharacteristic
988C2C11×#279011yescharacteristic
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
2. C11×#1445C2semidirect
3. C11×#1443C2semidirect
4. C11×#1441C2semidirect
5. C11×#1441C2semidirect
10. C11×#1436C2semidirect
11. C11×C4⋊#95C2semidirect
12. C11×#1434C2semidirect
13. C11×#1434C2semidirect
29. C11×#385C4semidirect
132. #14456C11direct (N × H)
267. #1445C2×C11semidirect
268. #1443C2×C11semidirect
269. #1441C2×C11semidirect
270. #1441C2×C11semidirect
275. #1436C2×C11semidirect
276. C4⋊#95C2×C11semidirect
277. #1434C2×C11semidirect
278. #1434C2×C11semidirect
443. #385C4×C11semidirect
759. C11#14456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3852
C11×#14452
C11×#14432
C11×#14412
C11×#14392
C11×#14372
C11×#14362
C11×C4⋊#952
C11×#14342
C11×C22⋊#952
#1445611