Finite Group Databasebeta

← C11×#16302 #14593495

Subgroups — C11×#16302 #14593495

Order 2816.

1490 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×#398C211yesmaximal, characteristic, complemented
2C2×C11×#396C211yesmaximal, characteristic
3C2×C11×#381C211yesmaximal, characteristic
4C2×C11×#380C211yesmaximal, characteristic
5C11×#1445C211yesmaximal, characteristic, complemented
6C11×#1444C211yesmaximal, characteristic, complemented
7C11×#1442C211yesmaximal, characteristic, complemented
8C11×#1442C211yesmaximal, characteristic, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C11×#1441C211yesmaximal, characteristic, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C11×#1439C211yesmaximal, characteristic
13C11×#1439C211yesmaximal, characteristic
14C11×#1439C211yesmaximal, 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×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C11×#398—24no—
32C11×#396—24no—
33C11×#381—24no—
34C11×#380—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—22no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11Q814yes—
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—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
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⋊C4—41no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4—41no—
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—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4—41no—
113C2×C11×C22⋊C4—41no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4D414yes—
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—41no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95—41no—
133C11×#95—41no—
134C11×#95—41no—
135C11×#95—41no—
136C11×#95—41no—
137C11×#95—41no—
138C11×#95D414yes—
139#16302C1111yesmaximal, 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×D412yes—
153C24×C11C2×Q812yes—
154C24×C11#4112yes—
155C24×C11C2411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—28no—
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—28no—
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—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—44no—
247C22×C4×C11—44no—
248C22×C4×C11—44no—
249C22×C4×C11—44no—
250C22×C4×C11—44no—
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×Q812yes—
257C22×C4×C11C2×Q812yes—
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×C4⋊C4—44no—
269C11×C22⋊C4—44no—
270C11×C22⋊C4—44no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C11×C22⋊C4—44no—
274C11×C22⋊C4—44no—
275C2×#398C2×C1111yescharacteristic, complemented
276C2×#396C2×C1111yescharacteristic
277C2×#381C2×C1111yescharacteristic
278C2×#380C2×C1111yescharacteristic
279#1445C2×C1111yescharacteristic, complemented
280#1444C2×C1111yescharacteristic, complemented
281#1442C2×C1111yescharacteristic, complemented
282#1442C2×C1111yescharacteristic, complemented
283#1441C2×C1111yescharacteristic, complemented
284#1441C2×C1111yescharacteristic, complemented
285#1441C2×C1111yescharacteristic, complemented
286#1439C2×C1111yescharacteristic
287#1439C2×C1111yescharacteristic
288#1439C2×C1111yescharacteristic
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×C11C22⋊Q814yes—
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C22×Q811yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C112−1+411yescharacteristic
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—416no—
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—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×C4⋊C4C22×C1111yescharacteristic
448C22×C22⋊C4C22×C1111yescharacteristic
449C22×C22⋊C4C22×C1111yescharacteristic
450C22×C22⋊C4C22×C1111yescharacteristic
451C22×C22⋊C4C22×C1111yescharacteristic
452C22×C22⋊C4C22×C1111yescharacteristic
453C22×C22⋊C4C22×C1111yescharacteristic
454#398—24no—
455#396—24no—
456#381—24no—
457#380—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×C11C2×C22⋊Q811yescharacteristic
495C22×C11#53311yescharacteristic
496C22×C11#53411yescharacteristic
497C22×C11#53611yescharacteristic
498C22×C11#53711yescharacteristic
499C22×C11#53711yescharacteristic
500C22×C11#53911yescharacteristic
501C22×C11#53911yescharacteristic
502C22×C11#53911yescharacteristic
503C22×C11#53911yescharacteristic
504C22×C11#54011yescharacteristic
505C22×C11#54011yescharacteristic
506C22×C11#54011yescharacteristic
507C22×C11#54111yescharacteristic
508C22×C11#54311yescharacteristic
509C22×C11#54411yescharacteristic
510C22×C11#54411yescharacteristic
511C22×C11#54411yescharacteristic
512C22×C11D4211yescharacteristic
513C22×C11#54611yescharacteristic
514C22×C11#54611yescharacteristic
515C22×C11#54611yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54711yescharacteristic
518C22×C11#54811yescharacteristic
519C22×C11#55111yescharacteristic
520C22×C11#55111yescharacteristic
521C22×C11#55211yescharacteristic
522C22×C11#55511yescharacteristic
523C22×C11#55611yescharacteristic
524C22×C11#56011yescharacteristic
525C22×C11#56211yescharacteristic
526C22×C11#56211yescharacteristic
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—81no—
537C4×C11—81no—
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—22no—
547C23×C4—41no—
548C23×C4—41no—
549C23×C4Q8×C1114yes—
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—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
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⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
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—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4D4×C1114yes—
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—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95D4×C1114yes—
626C2×C11—44no—
627C2×C11#243711yescharacteristic
628C2×C11#243811yescharacteristic
629C2×C11#243911yescharacteristic
630C2×C11#262711yescharacteristic
631C2×C11#262911yescharacteristic
632C2×C11#266711yescharacteristic
633C2×C11#267111yescharacteristic
634C2×C11#268111yescharacteristic
635C2×C11#268911yescharacteristic
636C2×C11#269311yescharacteristic
637C2×C11#269911yescharacteristic
638C2×C11#270711yescharacteristic
639C2×C11#274011yescharacteristic
640C2×C11#274411yescharacteristic
641C2×C11#284111yescharacteristic
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×D4×C1112yes—
655C24C2×Q8×C1112yes—
656C24C11×#4112yes—
657C24C24×C1111yescharacteristic
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—28no—
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—28no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4C2×D4×C1112yes—
754C22×C4C2×D4×C1112yes—
755C22×C4C2×D4×C1112yes—
756C22×C4C2×D4×C1112yes—
757C22×C4C2×D4×C1112yes—
758C22×C4C2×Q8×C1112yes—
759C22×C4C2×Q8×C1112yes—
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—
770C4⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C11#1630211yescharacteristic, 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×C22⋊Q814yes—
813C23C22×D4×C1111yescharacteristic
814C23C22×D4×C1111yescharacteristic
815C23C22×Q8×C1111yescharacteristic
816C23C2×C11×#4111yescharacteristic
817C23C2×C11×#4111yescharacteristic
818C23C2×C11×#4111yescharacteristic
819C23C2×C11×#4111yescharacteristic
820C23C11×H(5,𝔽2)11yescharacteristic
821C23C11×H(5,𝔽2)11yescharacteristic
822C23C11×H(5,𝔽2)11yescharacteristic
823C23C11×H(5,𝔽2)11yescharacteristic
824C23C11×H(5,𝔽2)11yescharacteristic
825C23C11×2−1+411yescharacteristic
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—416no—
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—
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
943C22C2×C11×C22⋊Q811yescharacteristic
944C22C11×#53311yescharacteristic
945C22C11×#53411yescharacteristic
946C22C11×#53611yescharacteristic
947C22C11×#53711yescharacteristic
948C22C11×#53711yescharacteristic
949C22C11×#53911yescharacteristic
950C22C11×#53911yescharacteristic
951C22C11×#53911yescharacteristic
952C22C11×#53911yescharacteristic
953C22C11×#54011yescharacteristic
954C22C11×#54011yescharacteristic
955C22C11×#54011yescharacteristic
956C22C11×#54111yescharacteristic
957C22C11×#54311yescharacteristic
958C22C11×#54411yescharacteristic
959C22C11×#54411yescharacteristic
960C22C11×#54411yescharacteristic
961C22D42×C1111yescharacteristic
962C22C11×#54611yescharacteristic
963C22C11×#54611yescharacteristic
964C22C11×#54611yescharacteristic
965C22C11×#54611yescharacteristic
966C22C11×#54711yescharacteristic
967C22C11×#54811yescharacteristic
968C22C11×#55111yescharacteristic
969C22C11×#55111yescharacteristic
970C22C11×#55211yescharacteristic
971C22C11×#55511yescharacteristic
972C22C11×#55611yescharacteristic
973C22C11×#56011yescharacteristic
974C22C11×#56211yescharacteristic
975C22C11×#56211yescharacteristic
976C22C11×#56311yescharacteristic
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C4—81no—
990C4—81no—
991C2—44no—
992C2C11×#243711yescharacteristic
993C2C11×#243811yescharacteristic
994C2C11×#243911yescharacteristic
995C2C11×#262711yescharacteristic
996C2C11×#262911yescharacteristic
997C2C11×#266711yescharacteristic
998C2C11×#267111yescharacteristic
999C2C11×#268111yescharacteristic
1000C2C11×#268911yescharacteristic
1001C2C11×#269311yescharacteristic
1002C2C11×#269911yescharacteristic
1003C2C11×#270711yescharacteristic
1004C2C11×#274011yescharacteristic
1005C2C11×#274411yescharacteristic
1006C2C11×#284111yescharacteristic
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×#398C2semidirect
5. C11×#1445C2semidirect
6. C11×#1444C2semidirect
7. C11×#1442C2semidirect
8. C11×#1442C2semidirect
9. C11×#1441C2semidirect
10. C11×#1441C2semidirect
11. C11×#1441C2semidirect
139. #16302C11direct (N × H)
275. C2×#398C2×C11semidirect
279. #1445C2×C11semidirect
280. #1444C2×C11semidirect
281. #1442C2×C11semidirect
282. #1442C2×C11semidirect
283. #1441C2×C11semidirect
284. #1441C2×C11semidirect
285. #1441C2×C11semidirect
777. C11#16302direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3982
C2×C11×#3962
C2×C11×#3812
C2×C11×#3802
C11×#14452
C11×#14442
C11×#14422
C11×#14412
C11×#14392
C11×C22⋊#952
#1630211