Finite Group Databasebeta

← C11×#15515 #14592708

Subgroups — C11×#15515 #14592708

Order 2816.

1522 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#400C211yesmaximal, characteristic, complemented
2C2×C11×#398C211yesmaximal, characteristic, complemented
3C2×C11×#385C211yesmaximal, characteristic
4C2×C11×#385C211yesmaximal, characteristic
5C11×#1444C211yesmaximal, characteristic, complemented
6C11×#1443C211yesmaximal, characteristic, complemented
7C11×#1442C211yesmaximal, characteristic, complemented
8C11×#1441C211yesmaximal, characteristic, complemented
9C11×#1439C211yesmaximal, characteristic
10C11×#1439C211yesmaximal, characteristic
11C11×#1439C211yesmaximal, characteristic
12C11×#1437C211yesmaximal, characteristic
13C11×C4⋊#95C211yesmaximal, characteristic, complemented
14C11×#1434C211yesmaximal, characteristic, complemented
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×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C11×#400—24no—
32C11×#398—24no—
33C11×#385—24no—
34C11×#385—24no—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C25×C11C2311yescharacteristic
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11—41no—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C4⋊C4—41no—
89C2×C11×C4⋊C4—41no—
90C2×C11×C4⋊C4—41no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4D414yes—
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—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4—41no—
113C2×C11×C22⋊C4—41no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4Q814yes—
116C2×C42×C11—22no—
117C2×C42×C11—22no—
118C2×C42×C11—41no—
119C11×#95—22no—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—22no—
126C11×#95—22no—
127C11×#95—22no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—41no—
134C11×#95—41no—
135C11×#95—41no—
136C11×#95—41no—
137C11×#95—41no—
138C11×#95D414yes—
139#15515C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11C2×Q812yes—
153C24×C11#4112yes—
154C24×C11#4112yes—
155C24×C11C2411yescharacteristic
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—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×C11C2×D412yes—
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×Q812yes—
256C22×C4×C11C2×Q812yes—
257C22×C4×C11#4112yes—
258C22×C4×C11#4112yes—
259C22×C4×C11#4112yes—
260C22×C4×C11#4112yes—
261C11×C4⋊C4—44no—
262C11×C4⋊C4—44no—
263C11×C4⋊C4—44no—
264C11×C4⋊C4—44no—
265C11×C4⋊C4—44no—
266C11×C4⋊C4—44no—
267C11×C4⋊C4—44no—
268C11×C22⋊C4—28no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—44no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C11×C22⋊C4—44no—
274C42×C11—44no—
275C2×#400C2×C1111yescharacteristic, complemented
276C2×#398C2×C1111yescharacteristic, complemented
277C2×#385C2×C1111yescharacteristic
278C2×#385C2×C1111yescharacteristic
279#1444C2×C1111yescharacteristic, complemented
280#1443C2×C1111yescharacteristic, complemented
281#1442C2×C1111yescharacteristic, complemented
282#1441C2×C1111yescharacteristic, complemented
283#1439C2×C1111yescharacteristic
284#1439C2×C1111yescharacteristic
285#1439C2×C1111yescharacteristic
286#1437C2×C1111yescharacteristic
287C4⋊#95C2×C1111yescharacteristic, complemented
288#1434C2×C1111yescharacteristic, complemented
289C22⋊#95C2×C1111yescharacteristic
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—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11#12514yes—
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C22×Q811yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
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
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—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—416no—
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—
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×C11C22⋊Q814yes—
439C24×C4C22×C1111yescharacteristic
440C22×C4⋊C4C22×C1111yescharacteristic
441C22×C4⋊C4C22×C1111yescharacteristic
442C22×C4⋊C4C22×C1111yescharacteristic
443C22×C4⋊C4C22×C1111yescharacteristic
444C22×C4⋊C4C22×C1111yescharacteristic
445C22×C4⋊C4C22×C1111yescharacteristic
446C22×C4⋊C4C22×C1111yescharacteristic
447C22×C22⋊C4C22×C1111yescharacteristic
448C22×C22⋊C4C22×C1111yescharacteristic
449C22×C22⋊C4C22×C1111yescharacteristic
450C22×C22⋊C4C22×C1111yescharacteristic
451C22×C22⋊C4C22×C1111yescharacteristic
452C22×C22⋊C4C22×C1111yescharacteristic
453C22×C42C22×C1111yescharacteristic
454#400—24no—
455#398—24no—
456#385—24no—
457#385—24no—
458C2×#95C22×C1111yescharacteristic
459C2×#95C22×C1111yescharacteristic
460C2×#95C22×C1111yescharacteristic
461C2×#95C22×C1111yescharacteristic
462C2×#95C22×C1111yescharacteristic
463C2×#95C22×C1111yescharacteristic
464C2×#95C22×C1111yescharacteristic
465C2×#95C22×C1111yescharacteristic
466C2×#95C22×C1111yescharacteristic
467C2×#95C22×C1111yescharacteristic
468C2×#95C22×C1111yescharacteristic
469C2×#95C22×C1111yescharacteristic
470C2×#95C22×C1111yescharacteristic
471C2×#95C22×C1111yescharacteristic
472C2×#95C22×C1111yescharacteristic
473C2×#95C22×C1111yescharacteristic
474C2×#95C22×C1111yescharacteristic
475C2×#95C22×C1111yescharacteristic
476C2×#95C22×C1111yescharacteristic
477C2×#95C22×C1111yescharacteristic
478C22×C11—24no—
479C22×C11—24no—
480C22×C11—24no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
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×C11C2×C22⋊Q811yescharacteristic
494C22×C11#52511yescharacteristic
495C22×C11C2×#12511yescharacteristic
496C22×C11#52911yescharacteristic
497C22×C11#53211yescharacteristic
498C22×C11#53211yescharacteristic
499C22×C11#53411yescharacteristic
500C22×C11#53511yescharacteristic
501C22×C11#53811yescharacteristic
502C22×C11#53911yescharacteristic
503C22×C11#53911yescharacteristic
504C22×C11#53911yescharacteristic
505C22×C11#54211yescharacteristic
506C22×C11#54211yescharacteristic
507C22×C11#54411yescharacteristic
508C22×C11D4211yescharacteristic
509C22×C11#54611yescharacteristic
510C22×C11#54611yescharacteristic
511C22×C11#54711yescharacteristic
512C22×C11#54811yescharacteristic
513C22×C11#54811yescharacteristic
514C22×C11D4×Q811yescharacteristic
515C22×C11#55111yescharacteristic
516C22×C11#55111yescharacteristic
517C22×C11#55111yescharacteristic
518C22×C11#55111yescharacteristic
519C22×C11#55211yescharacteristic
520C22×C11#55211yescharacteristic
521C22×C11#55311yescharacteristic
522C22×C11#55311yescharacteristic
523C22×C11#55411yescharacteristic
524C22×C11#55411yescharacteristic
525C22×C11#55411yescharacteristic
526C22×C11#56011yescharacteristic
527C22×C11#56311yescharacteristic
528C4×C11—24no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11—81no—
539C4×C11—81no—
540C4×C11—81no—
541C4×C11—81no—
542C25C23×C1111yescharacteristic
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—41no—
547C23×C4—41no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4C23×C1111yescharacteristic
551C23×C4C23×C1111yescharacteristic
552C23×C4C23×C1111yescharacteristic
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
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
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—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4D4×C1114yes—
585C2×C22⋊C4—22no—
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—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4Q8×C1114yes—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—41no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
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—22no—
619#95—22no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95D4×C1114yes—
626C2×C11—44no—
627C2×C11#244211yescharacteristic
628C2×C11#245211yescharacteristic
629C2×C11#246111yescharacteristic
630C2×C11#247311yescharacteristic
631C2×C11#250511yescharacteristic
632C2×C11#255311yescharacteristic
633C2×C11#255811yescharacteristic
634C2×C11#256411yescharacteristic
635C2×C11#260311yescharacteristic
636C2×C11#267811yescharacteristic
637C2×C11#272011yescharacteristic
638C2×C11#272811yescharacteristic
639C2×C11#274611yescharacteristic
640C2×C11#276411yescharacteristic
641C2×C11#279011yescharacteristic
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24C2×Q8×C1112yes—
655C24C11×#4112yes—
656C24C11×#4112yes—
657C24C24×C1111yescharacteristic
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4C2×D4×C1112yes—
752C22×C4C2×D4×C1112yes—
753C22×C4C2×D4×C1112yes—
754C22×C4C2×D4×C1112yes—
755C22×C4C2×D4×C1112yes—
756C22×C4C2×D4×C1112yes—
757C22×C4C2×Q8×C1112yes—
758C22×C4C2×Q8×C1112yes—
759C22×C4C11×#4112yes—
760C22×C4C11×#4112yes—
761C22×C4C11×#4112yes—
762C22×C4C11×#4112yes—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C42—44no—
777C11#1551511yescharacteristic, direct product factor, Sylow
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
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—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23C11×#12514yes—
813C23C22×D4×C1111yescharacteristic
814C23C22×D4×C1111yescharacteristic
815C23C22×Q8×C1111yescharacteristic
816C23C2×C11×#4111yescharacteristic
817C23C2×C11×#4111yescharacteristic
818C23C2×C11×#4111yescharacteristic
819C23C2×C11×#4111yescharacteristic
820C23C2×C11×#4111yescharacteristic
821C23C2×C11×#4111yescharacteristic
822C23C11×H(5,𝔽2)11yescharacteristic
823C23C11×H(5,𝔽2)11yescharacteristic
824C23C11×H(5,𝔽2)11yescharacteristic
825C23C11×H(5,𝔽2)11yescharacteristic
826C23C11×2−1+411yescharacteristic
827C23C11×2−1+411yescharacteristic
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—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—416no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×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×C4C11×C22⋊Q814yes—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22C2×C11×C22⋊Q811yescharacteristic
943C22C11×#52511yescharacteristic
944C22C2×C11×#12511yescharacteristic
945C22C11×#52911yescharacteristic
946C22C11×#53211yescharacteristic
947C22C11×#53211yescharacteristic
948C22C11×#53411yescharacteristic
949C22C11×#53511yescharacteristic
950C22C11×#53811yescharacteristic
951C22C11×#53911yescharacteristic
952C22C11×#53911yescharacteristic
953C22C11×#53911yescharacteristic
954C22C11×#54211yescharacteristic
955C22C11×#54211yescharacteristic
956C22C11×#54411yescharacteristic
957C22D42×C1111yescharacteristic
958C22C11×#54611yescharacteristic
959C22C11×#54611yescharacteristic
960C22C11×#54711yescharacteristic
961C22C11×#54811yescharacteristic
962C22C11×#54811yescharacteristic
963C22D4×Q8×C1111yescharacteristic
964C22C11×#55111yescharacteristic
965C22C11×#55111yescharacteristic
966C22C11×#55111yescharacteristic
967C22C11×#55111yescharacteristic
968C22C11×#55211yescharacteristic
969C22C11×#55211yescharacteristic
970C22C11×#55311yescharacteristic
971C22C11×#55311yescharacteristic
972C22C11×#55411yescharacteristic
973C22C11×#55411yescharacteristic
974C22C11×#55411yescharacteristic
975C22C11×#56011yescharacteristic
976C22C11×#56311yescharacteristic
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C4—81no—
990C4—81no—
991C2—44no—
992C2C11×#244211yescharacteristic
993C2C11×#245211yescharacteristic
994C2C11×#246111yescharacteristic
995C2C11×#247311yescharacteristic
996C2C11×#250511yescharacteristic
997C2C11×#255311yescharacteristic
998C2C11×#255811yescharacteristic
999C2C11×#256411yescharacteristic
1000C2C11×#260311yescharacteristic
1001C2C11×#267811yescharacteristic
1002C2C11×#272011yescharacteristic
1003C2C11×#272811yescharacteristic
1004C2C11×#274611yescharacteristic
1005C2C11×#276411yescharacteristic
1006C2C11×#279011yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#400C2semidirect
2. C2×C11×#398C2semidirect
5. C11×#1444C2semidirect
6. C11×#1443C2semidirect
7. C11×#1442C2semidirect
8. C11×#1441C2semidirect
13. C11×C4⋊#95C2semidirect
14. C11×#1434C2semidirect
139. #15515C11direct (N × H)
275. C2×#400C2×C11semidirect
276. C2×#398C2×C11semidirect
279. #1444C2×C11semidirect
280. #1443C2×C11semidirect
281. #1442C2×C11semidirect
282. #1441C2×C11semidirect
287. C4⋊#95C2×C11semidirect
288. #1434C2×C11semidirect
777. C11#15515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4002
C2×C11×#3982
C2×C11×#3852
C11×#14442
C11×#14432
C11×#14422
C11×#14412
C11×#14392
C11×#14372
C11×C4⋊#952
C11×#14342
C11×C22⋊#952
#1551511