Finite Group Databasebeta

← C11×#14512 #14591705

Subgroups — C11×#14512 #14591705

Order 2816.

1298 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#388C211yesmaximal, characteristic
2C11×#1442C211yesmaximal, characteristic, complemented
3C11×#1441C211yesmaximal, characteristic, complemented
4C11×#1440C211yesmaximal, characteristic
5C11×#1440C211yesmaximal, characteristic
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×#1434C211yesmaximal, characteristic, complemented
15C11×#1434C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊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×C42×C11C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C11×#388C418yescomplemented
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×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—41no—
70C2×C11×C4⋊C4—41no—
71C2×C11×C4⋊C4—41no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4C2×C414yes—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4—41no—
88C2×C11×C22⋊C4—41no—
89C2×C11×C22⋊C4—41no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4C2×C414yes—
95C2×C11×C22⋊C4C2×C414yes—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C42×C11—22no—
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×C42×C11—41no—
101C2×C42×C11—41no—
102C2×C42×C11—41no—
103C2×C42×C11—41no—
104C2×C42×C11—41no—
105C2×C42×C11C2×C414yes—
106C11×#95—22no—
107C11×#95—22no—
108C11×#95—22no—
109C11×#95—22no—
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×#95C2×C414yes—
127C11×#95C2×C414yes—
128#14512C1111yesmaximal, characteristic, direct product factor, Sylow
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
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×C11C22×C412yes—
144C24×C11C2411yescharacteristic
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
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×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C22×C412yes—
236C22×C4×C11C22×C412yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×C4×C11#4112yes—
240C22×C4×C11#4112yes—
241C22×C4×C11#4112yes—
242C22×C4×C11#4112yes—
243C11×C4⋊C4—44no—
244C11×C4⋊C4—44no—
245C11×C4⋊C4—44no—
246C11×C22⋊C4—28no—
247C11×C22⋊C4—44no—
248C11×C22⋊C4—44no—
249C11×C22⋊C4—44no—
250C11×C22⋊C4—44no—
251C11×C22⋊C4—44no—
252C11×C22⋊C4—44no—
253C42×C11—44no—
254C42×C11—44no—
255C42×C11—44no—
256C2×#388C2×C1111yescharacteristic
257#1442C2×C1111yescharacteristic, complemented
258#1441C2×C1111yescharacteristic, complemented
259#1440C2×C1111yescharacteristic
260#1440C2×C1111yescharacteristic
261#1439C2×C1111yescharacteristic
262#1439C2×C1111yescharacteristic
263#1437C2×C1111yescharacteristic
264#1437C2×C1111yescharacteristic
265#1436C2×C1111yescharacteristic, complemented
266C4⋊#95C2×C1111yescharacteristic, complemented
267#1434C2×C1111yescharacteristic, complemented
268#1434C2×C1111yescharacteristic, complemented
269#1434C2×C1111yescharacteristic, complemented
270#1434C2×C1111yescharacteristic, complemented
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
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×C11C23×C411yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C11H(5,𝔽2)11yescharacteristic
315C23×C11H(5,𝔽2)11yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C112−1+411yescharacteristic
320C23×C112−1+411yescharacteristic
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
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—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11#11714yes—
419C22×C4⋊C4C22×C1111yescharacteristic
420C22×C4⋊C4C22×C1111yescharacteristic
421C22×C4⋊C4C22×C1111yescharacteristic
422C22×C22⋊C4C22×C1111yescharacteristic
423C22×C22⋊C4C22×C1111yescharacteristic
424C22×C22⋊C4C22×C1111yescharacteristic
425C22×C22⋊C4C22×C1111yescharacteristic
426C22×C22⋊C4C22×C1111yescharacteristic
427C22×C22⋊C4C22×C1111yescharacteristic
428C22×C22⋊C4C22×C1111yescharacteristic
429C22×C42C22×C1111yescharacteristic
430C22×C42C22×C1111yescharacteristic
431C22×C42C22×C1111yescharacteristic
432#388C4×C1118yescomplemented
433C2×#95C22×C1111yescharacteristic
434C2×#95C22×C1111yescharacteristic
435C2×#95C22×C1111yescharacteristic
436C2×#95C22×C1111yescharacteristic
437C2×#95C22×C1111yescharacteristic
438C2×#95C22×C1111yescharacteristic
439C2×#95C22×C1111yescharacteristic
440C2×#95C22×C1111yescharacteristic
441C2×#95C22×C1111yescharacteristic
442C2×#95C22×C1111yescharacteristic
443C2×#95C22×C1111yescharacteristic
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
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11C2×#11711yescharacteristic
471C22×C11C4×#4111yescharacteristic
472C22×C11C4×#4111yescharacteristic
473C22×C11#51811yescharacteristic
474C22×C11#51811yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11#52011yescharacteristic
477C22×C11#53811yescharacteristic
478C22×C11#53811yescharacteristic
479C22×C11#53811yescharacteristic
480C22×C11#53911yescharacteristic
481C22×C11#54011yescharacteristic
482C22×C11#54011yescharacteristic
483C22×C11#54111yescharacteristic
484C22×C11#54211yescharacteristic
485C22×C11#54211yescharacteristic
486C22×C11#54211yescharacteristic
487C22×C11#54211yescharacteristic
488C22×C11#54211yescharacteristic
489C22×C11#55111yescharacteristic
490C22×C11#55111yescharacteristic
491C22×C11#55111yescharacteristic
492C22×C11#55211yescharacteristic
493C22×C11#55211yescharacteristic
494C22×C11#55311yescharacteristic
495C22×C11#55311yescharacteristic
496C22×C11#55311yescharacteristic
497C22×C11#55311yescharacteristic
498C22×C11#55511yescharacteristic
499C22×C11#55511yescharacteristic
500C22×C11#55911yescharacteristic
501C22×C11#56011yescharacteristic
502C22×C11#56011yescharacteristic
503C22×C11#56211yescharacteristic
504C22×C11#56211yescharacteristic
505C4×C11—24no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—42no—
515C4×C11—81no—
516C4×C11—81no—
517C4×C11—81no—
518C4×C11—81no—
519C25C23×C1111yescharacteristic
520C23×C4C23×C1111yescharacteristic
521C23×C4C23×C1111yescharacteristic
522C23×C4C23×C1111yescharacteristic
523C23×C4C23×C1111yescharacteristic
524C23×C4C23×C1111yescharacteristic
525C23×C4C23×C1111yescharacteristic
526C23×C4C23×C1111yescharacteristic
527C23×C4C23×C1111yescharacteristic
528C23×C4C23×C1111yescharacteristic
529C23×C4C23×C1111yescharacteristic
530C23×C4C23×C1111yescharacteristic
531C23×C4C23×C1111yescharacteristic
532C23×C4C23×C1111yescharacteristic
533C23×C4C23×C1111yescharacteristic
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4C2×C4×C1114yes—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4C2×C4×C1114yes—
562C2×C22⋊C4C2×C4×C1114yes—
563C2×C22⋊C4C2×C4×C1114yes—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—41no—
568C2×C42—41no—
569C2×C42—41no—
570C2×C42—41no—
571C2×C42—41no—
572C2×C42C2×C4×C1114yes—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—41no—
581#95—41no—
582#95—41no—
583#95—41no—
584#95—41no—
585#95—41no—
586#95—41no—
587#95—41no—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—41no—
593#95C2×C4×C1114yes—
594#95C2×C4×C1114yes—
595C2×C11—82no—
596C2×C11#231911yescharacteristic
597C2×C11#233411yescharacteristic
598C2×C11#233711yescharacteristic
599C2×C11#234611yescharacteristic
600C2×C11#235311yescharacteristic
601C2×C11#237411yescharacteristic
602C2×C11#237711yescharacteristic
603C2×C11#273711yescharacteristic
604C2×C11#274111yescharacteristic
605C2×C11#275411yescharacteristic
606C2×C11#275611yescharacteristic
607C2×C11#276111yescharacteristic
608C2×C11#277211yescharacteristic
609C2×C11#279511yescharacteristic
610C2×C11#280311yescharacteristic
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24C22×C4×C1112yes—
626C24C24×C1111yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
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×C4C22×C4×C1112yes—
714C22×C4C22×C4×C1112yes—
715C22×C4C22×C4×C1112yes—
716C22×C4C22×C4×C1112yes—
717C22×C4C22×C4×C1112yes—
718C22×C4C22×C4×C1112yes—
719C22×C4C11×#4112yes—
720C22×C4C11×#4112yes—
721C22×C4C11×#4112yes—
722C22×C4C11×#4112yes—
723C22×C4C11×#4112yes—
724C22×C4C11×#4112yes—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C22⋊C4—28no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C42—44no—
736C42—44no—
737C42—44no—
738C11#1451211yescharacteristic, direct product factor, Sylow
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23C23×C4×C1111yescharacteristic
775C23C2×C11×#4111yescharacteristic
776C23C2×C11×#4111yescharacteristic
777C23C2×C11×#4111yescharacteristic
778C23C2×C11×#4111yescharacteristic
779C23C2×C11×#4111yescharacteristic
780C23C2×C11×#4111yescharacteristic
781C23C11×H(5,𝔽2)11yescharacteristic
782C23C11×H(5,𝔽2)11yescharacteristic
783C23C11×H(5,𝔽2)11yescharacteristic
784C23C11×H(5,𝔽2)11yescharacteristic
785C23C11×H(5,𝔽2)11yescharacteristic
786C23C11×H(5,𝔽2)11yescharacteristic
787C23C11×2−1+411yescharacteristic
788C23C11×2−1+411yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
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—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4C11×#11714yes—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22C2×C11×#11711yescharacteristic
903C22C4×C11×#4111yescharacteristic
904C22C4×C11×#4111yescharacteristic
905C22C11×#51811yescharacteristic
906C22C11×#51811yescharacteristic
907C22C11×#52011yescharacteristic
908C22C11×#52011yescharacteristic
909C22C11×#53811yescharacteristic
910C22C11×#53811yescharacteristic
911C22C11×#53811yescharacteristic
912C22C11×#53911yescharacteristic
913C22C11×#54011yescharacteristic
914C22C11×#54011yescharacteristic
915C22C11×#54111yescharacteristic
916C22C11×#54211yescharacteristic
917C22C11×#54211yescharacteristic
918C22C11×#54211yescharacteristic
919C22C11×#54211yescharacteristic
920C22C11×#54211yescharacteristic
921C22C11×#55111yescharacteristic
922C22C11×#55111yescharacteristic
923C22C11×#55111yescharacteristic
924C22C11×#55211yescharacteristic
925C22C11×#55211yescharacteristic
926C22C11×#55311yescharacteristic
927C22C11×#55311yescharacteristic
928C22C11×#55311yescharacteristic
929C22C11×#55311yescharacteristic
930C22C11×#55511yescharacteristic
931C22C11×#55511yescharacteristic
932C22C11×#55911yescharacteristic
933C22C11×#56011yescharacteristic
934C22C11×#56011yescharacteristic
935C22C11×#56211yescharacteristic
936C22C11×#56211yescharacteristic
937C4—24no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—81no—
948C4—81no—
949C4—81no—
950C4—81no—
951C2—82no—
952C2C11×#231911yescharacteristic
953C2C11×#233411yescharacteristic
954C2C11×#233711yescharacteristic
955C2C11×#234611yescharacteristic
956C2C11×#235311yescharacteristic
957C2C11×#237411yescharacteristic
958C2C11×#237711yescharacteristic
959C2C11×#273711yescharacteristic
960C2C11×#274111yescharacteristic
961C2C11×#275411yescharacteristic
962C2C11×#275611yescharacteristic
963C2C11×#276111yescharacteristic
964C2C11×#277211yescharacteristic
965C2C11×#279511yescharacteristic
966C2C11×#280311yescharacteristic
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×#1442C2semidirect
3. C11×#1441C2semidirect
10. C11×#1436C2semidirect
11. C11×C4⋊#95C2semidirect
12. C11×#1434C2semidirect
13. C11×#1434C2semidirect
14. C11×#1434C2semidirect
15. C11×#1434C2semidirect
29. C11×#388C4semidirect
128. #14512C11direct (N × H)
257. #1442C2×C11semidirect
258. #1441C2×C11semidirect
265. #1436C2×C11semidirect
266. C4⋊#95C2×C11semidirect
267. #1434C2×C11semidirect
268. #1434C2×C11semidirect
269. #1434C2×C11semidirect
270. #1434C2×C11semidirect
432. #388C4×C11semidirect
738. C11#14512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3882
C11×#14422
C11×#14412
C11×#14402
C11×#14392
C11×#14372
C11×#14362
C11×C4⋊#952
C11×#14342
#1451211