Finite Group Databasebeta

← C11×#16299 #14593492

Subgroups — C11×#16299 #14593492

Order 2816.

1554 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#395C211yesmaximal, characteristic, complemented
2C2×C11×#393C211yesmaximal, characteristic
3C2×C11×#381C211yesmaximal, characteristic
4C2×C11×#380C211yesmaximal, characteristic
5C11×#1446C211yesmaximal, characteristic, complemented
6C11×#1445C211yesmaximal, characteristic, complemented
7C11×#1443C211yesmaximal, characteristic, complemented
8C11×#1442C211yesmaximal, characteristic, complemented
9C11×#1442C211yesmaximal, characteristic, complemented
10C11×#1441C211yesmaximal, characteristic, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C11×#1439C211yesmaximal, characteristic
13C11×#1439C211yesmaximal, characteristic
14C11×#1439C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C11×#395—24no—
30C11×#393—24no—
31C11×#381—24no—
32C11×#380—24no—
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C25×C11C2311yescharacteristic
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—41no—
60C22×Q8×C11—41no—
61C22×Q8×C11—41no—
62C22×Q8×C11—41no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11Q814yescomplemented
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
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—22no—
91C2×C11×C4⋊C4—22no—
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×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—41no—
109C2×C11×C22⋊C4—41no—
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⋊C4D414yes—
117C11×#95—22no—
118C11×#95—22no—
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#16299C1111yesmaximal, 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
156C2×Q8×C11—44no—
157C2×Q8×C11—44no—
158C2×Q8×C11—44no—
159C2×Q8×C11—44no—
160C2×Q8×C11—44no—
161C2×Q8×C11—44no—
162C2×Q8×C11—44no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—28no—
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—28no—
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—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—44no—
254C22×C4×C11—44no—
255C22×C4×C11—44no—
256C22×C4×C11—44no—
257C22×C4×C11—44no—
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×Q812yes—
264C22×C4×C11C2×Q812yes—
265C22×C4×C11#4112yes—
266C22×C4×C11#4112yes—
267C22×C4×C11#4112yes—
268C11×C4⋊C4—44no—
269C11×C4⋊C4—44no—
270C11×C4⋊C4—44no—
271C11×C4⋊C4—44no—
272C11×C4⋊C4—44no—
273C11×C22⋊C4—44no—
274C11×C22⋊C4—44no—
275C11×C22⋊C4—44no—
276C11×C22⋊C4—44no—
277C11×C22⋊C4—44no—
278C11×C22⋊C4—44no—
279C2×#395C2×C1111yescharacteristic, complemented
280C2×#393C2×C1111yescharacteristic
281C2×#381C2×C1111yescharacteristic
282C2×#380C2×C1111yescharacteristic
283#1446C2×C1111yescharacteristic, complemented
284#1445C2×C1111yescharacteristic, complemented
285#1443C2×C1111yescharacteristic, complemented
286#1442C2×C1111yescharacteristic, complemented
287#1442C2×C1111yescharacteristic, complemented
288#1441C2×C1111yescharacteristic, complemented
289#1441C2×C1111yescharacteristic, complemented
290#1439C2×C1111yescharacteristic
291#1439C2×C1111yescharacteristic
292#1439C2×C1111yescharacteristic
293C22⋊#95C2×C1111yescharacteristic
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—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
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—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11C22⋊Q814yes—
329C23×C11C22×D411yescharacteristic
330C23×C11C22×D411yescharacteristic
331C23×C11C22×Q811yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C11H(5,𝔽2)11yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C112−1+411yescharacteristic
342C23×C112−1+411yescharacteristic
343C23×C112−1+411yescharacteristic
344Q8×C11—416no—
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—416no—
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×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11C22⋊Q814yes—
444C23×Q8C22×C1111yescharacteristic
445C24×C4C22×C1111yescharacteristic
446C22×C4⋊C4C22×C1111yescharacteristic
447C22×C4⋊C4C22×C1111yescharacteristic
448C22×C4⋊C4C22×C1111yescharacteristic
449C22×C4⋊C4C22×C1111yescharacteristic
450C22×C4⋊C4C22×C1111yescharacteristic
451C22×C22⋊C4C22×C1111yescharacteristic
452C22×C22⋊C4C22×C1111yescharacteristic
453C22×C22⋊C4C22×C1111yescharacteristic
454C22×C22⋊C4C22×C1111yescharacteristic
455C22×C22⋊C4C22×C1111yescharacteristic
456C22×C22⋊C4C22×C1111yescharacteristic
457#395—24no—
458#393—24no—
459#381—24no—
460#380—24no—
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
478C2×#95C22×C1111yescharacteristic
479C2×#95C22×C1111yescharacteristic
480C2×#95C22×C1111yescharacteristic
481C2×#95C22×C1111yescharacteristic
482C2×#95C22×C1111yescharacteristic
483C22×C11—24no—
484C22×C11—24no—
485C22×C11—24no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11C2×C22⋊Q811yescharacteristic
499C22×C11C2×C22⋊Q811yescharacteristic
500C22×C11#53311yescharacteristic
501C22×C11#53411yescharacteristic
502C22×C11#53511yescharacteristic
503C22×C11#53611yescharacteristic
504C22×C11#53611yescharacteristic
505C22×C11#53811yescharacteristic
506C22×C11#53811yescharacteristic
507C22×C11#53911yescharacteristic
508C22×C11#53911yescharacteristic
509C22×C11#54211yescharacteristic
510C22×C11#54211yescharacteristic
511C22×C11#54211yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54311yescharacteristic
514C22×C11#54411yescharacteristic
515C22×C11#54411yescharacteristic
516C22×C11#54411yescharacteristic
517C22×C11D4211yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54611yescharacteristic
520C22×C11#54611yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54711yescharacteristic
523C22×C11#54811yescharacteristic
524C22×C11#55111yescharacteristic
525C22×C11#55111yescharacteristic
526C22×C11#55211yescharacteristic
527C22×C11#55511yescharacteristic
528C22×C11#55611yescharacteristic
529C22×C11#56011yescharacteristic
530C22×C11#56211yescharacteristic
531C22×C11#56211yescharacteristic
532C22×C11#56311yescharacteristic
533C4×C11—24no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—81no—
542C4×C11—81no—
543C4×C11—81no—
544C4×C11—81no—
545C4×C11—81no—
546C4×C11—81no—
547C25C23×C1111yescharacteristic
548C22×Q8—22no—
549C22×Q8—22no—
550C22×Q8—22no—
551C22×Q8—41no—
552C22×Q8—41no—
553C22×Q8—41no—
554C22×Q8—41no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—41no—
560C23×C4—41no—
561C23×C4Q8×C1114yescomplemented
562C23×C4C23×C1111yescharacteristic
563C23×C4C23×C1111yescharacteristic
564C23×C4C23×C1111yescharacteristic
565C23×C4C23×C1111yescharacteristic
566C23×C4C23×C1111yescharacteristic
567C23×C4C23×C1111yescharacteristic
568C23×C4C23×C1111yescharacteristic
569C23×C4C23×C1111yescharacteristic
570C23×C4C23×C1111yescharacteristic
571C23×C4C23×C1111yescharacteristic
572C23×C4C23×C1111yescharacteristic
573C23×C4C23×C1111yescharacteristic
574C23×C4C23×C1111yescharacteristic
575C23×C4C23×C1111yescharacteristic
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
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—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4D4×C1114yes—
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—22no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95D4×C1114yes—
631C2×C11—44no—
632C2×C11#243711yescharacteristic
633C2×C11#243811yescharacteristic
634C2×C11#243911yescharacteristic
635C2×C11#262711yescharacteristic
636C2×C11#262811yescharacteristic
637C2×C11#266511yescharacteristic
638C2×C11#267411yescharacteristic
639C2×C11#267811yescharacteristic
640C2×C11#268611yescharacteristic
641C2×C11#268711yescharacteristic
642C2×C11#269611yescharacteristic
643C2×C11#270011yescharacteristic
644C2×C11#273711yescharacteristic
645C2×C11#274511yescharacteristic
646C2×C11#284111yescharacteristic
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24C2×D4×C1112yes—
660C24C2×Q8×C1112yes—
661C24C11×#4112yes—
662C24C24×C1111yescharacteristic
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—44no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—28no—
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—28no—
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—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4C2×D4×C1112yes—
766C22×C4C2×D4×C1112yes—
767C22×C4C2×D4×C1112yes—
768C22×C4C2×D4×C1112yes—
769C22×C4C2×D4×C1112yes—
770C22×C4C2×Q8×C1112yes—
771C22×C4C2×Q8×C1112yes—
772C22×C4C11×#4112yes—
773C22×C4C11×#4112yes—
774C22×C4C11×#4112yes—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C11#1629911yescharacteristic, direct product factor, Sylow
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23C11×C22⋊Q814yes—
822C23C22×D4×C1111yescharacteristic
823C23C22×D4×C1111yescharacteristic
824C23C22×Q8×C1111yescharacteristic
825C23C2×C11×#4111yescharacteristic
826C23C2×C11×#4111yescharacteristic
827C23C2×C11×#4111yescharacteristic
828C23C2×C11×#4111yescharacteristic
829C23C11×H(5,𝔽2)11yescharacteristic
830C23C11×H(5,𝔽2)11yescharacteristic
831C23C11×H(5,𝔽2)11yescharacteristic
832C23C11×H(5,𝔽2)11yescharacteristic
833C23C11×H(5,𝔽2)11yescharacteristic
834C23C11×2−1+411yescharacteristic
835C23C11×2−1+411yescharacteristic
836C23C11×2−1+411yescharacteristic
837Q8—416no—
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—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—416no—
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×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4C11×C22⋊Q814yes—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22C2×C11×C22⋊Q811yescharacteristic
953C22C2×C11×C22⋊Q811yescharacteristic
954C22C11×#53311yescharacteristic
955C22C11×#53411yescharacteristic
956C22C11×#53511yescharacteristic
957C22C11×#53611yescharacteristic
958C22C11×#53611yescharacteristic
959C22C11×#53811yescharacteristic
960C22C11×#53811yescharacteristic
961C22C11×#53911yescharacteristic
962C22C11×#53911yescharacteristic
963C22C11×#54211yescharacteristic
964C22C11×#54211yescharacteristic
965C22C11×#54211yescharacteristic
966C22C11×#54211yescharacteristic
967C22C11×#54311yescharacteristic
968C22C11×#54411yescharacteristic
969C22C11×#54411yescharacteristic
970C22C11×#54411yescharacteristic
971C22D42×C1111yescharacteristic
972C22C11×#54611yescharacteristic
973C22C11×#54611yescharacteristic
974C22C11×#54611yescharacteristic
975C22C11×#54611yescharacteristic
976C22C11×#54711yescharacteristic
977C22C11×#54811yescharacteristic
978C22C11×#55111yescharacteristic
979C22C11×#55111yescharacteristic
980C22C11×#55211yescharacteristic
981C22C11×#55511yescharacteristic
982C22C11×#55611yescharacteristic
983C22C11×#56011yescharacteristic
984C22C11×#56211yescharacteristic
985C22C11×#56211yescharacteristic
986C22C11×#56311yescharacteristic
987C4—24no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C4—81no—
1000C4—81no—
1001C2—44no—
1002C2C11×#243711yescharacteristic
1003C2C11×#243811yescharacteristic
1004C2C11×#243911yescharacteristic
1005C2C11×#262711yescharacteristic
1006C2C11×#262811yescharacteristic
1007C2C11×#266511yescharacteristic
1008C2C11×#267411yescharacteristic
1009C2C11×#267811yescharacteristic
1010C2C11×#268611yescharacteristic
1011C2C11×#268711yescharacteristic
1012C2C11×#269611yescharacteristic
1013C2C11×#270011yescharacteristic
1014C2C11×#273711yescharacteristic
1015C2C11×#274511yescharacteristic
1016C2C11×#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×#395C2semidirect
5. C11×#1446C2semidirect
6. C11×#1445C2semidirect
7. C11×#1443C2semidirect
8. C11×#1442C2semidirect
9. C11×#1442C2semidirect
10. C11×#1441C2semidirect
11. C11×#1441C2semidirect
69. C23×C4×C11Q8semidirect
139. #16299C11direct (N × H)
279. C2×#395C2×C11semidirect
283. #1446C2×C11semidirect
284. #1445C2×C11semidirect
285. #1443C2×C11semidirect
286. #1442C2×C11semidirect
287. #1442C2×C11semidirect
288. #1441C2×C11semidirect
289. #1441C2×C11semidirect
561. C23×C4Q8×C11semidirect
786. C11#16299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3952
C2×C11×#3932
C2×C11×#3812
C2×C11×#3802
C11×#14462
C11×#14452
C11×#14432
C11×#14422
C11×#14412
C11×#14392
C11×C22⋊#952
#1629911