Finite Group Databasebeta

← C11×#24165 #14601358

Subgroups — C11×#24165 #14601358

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#541C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C11×#462C211yesmaximal, characteristic, complemented
4C11×#2323C211yesmaximal, characteristic
5C11×#2036C211yesmaximal, characteristic
6C11×#2035C211yesmaximal, characteristic
7C11×#2001C211yesmaximal, characteristic
8C11×#2001C211yesmaximal, characteristic
9C11×#1989C211yesmaximal, characteristic, complemented
10C11×#1981C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1878C211yesmaximal, characteristic, complemented
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1863C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C11×#541—24no—
19C11×#541—24no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#126—21no—
22C2×C11×#126—21no—
23C2×C11×#125—21no—
24C2×C11×#125—21no—
25C2×C11×#125C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C11×#479—24no—
34C11×#462—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#389—21no—
51C11×#389C2211yescharacteristic
52C11×#388—21no—
53C11×#388—21no—
54C11×#387—21no—
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C2×C11×Q16—22no—
68C2×C11×Q16—22no—
69C2×C11×Q16—22no—
70C2×C11×Q16—22no—
71C2×C11×Q16—41no—
72C2×C11×Q16—41no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8D414yes—
79C11×#126—28no—
80C11×#126—28no—
81C11×#125—28no—
82C11×#125—28no—
83C11×#125—22no—
84C11×#125D414yes—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C11×#117—22no—
98C11×#117—22no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11—21no—
124C2×C42×C11—21no—
125C2×C42×C11—21no—
126C2×C42×C11—21no—
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#106—22no—
131C11×C4⋊C8—22no—
132C11×C4⋊C8—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—22no—
139C11×#103—41no—
140C11×#103—41no—
141C11×C22⋊C8—41no—
142C11×C22⋊C8—41no—
143C11×#95—21no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24165C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11C2×D411yescharacteristic
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11C2×D412yes—
166C2×Q8×C11C2×D412yes—
167C2×Q8×C11#4112yes—
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×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C11×Q16—44no—
189C11×Q16—44no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—81no—
222C11×C4⋊C4C2×D412yes—
223C11×C4⋊C4C2×D412yes—
224C11×C4⋊C4#4112yes—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—81no—
231C42×C11—24no—
232C42×C11—24no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—42no—
236C42×C11—81no—
237C42×C11C2×D412yes—
238C42×C11C2×D412yes—
239C2×#541C2×C1111yescharacteristic
240C2×#479C2×C1111yescharacteristic, complemented
241C2×#462C2×C1111yescharacteristic, complemented
242#2323C2×C1111yescharacteristic
243#2036C2×C1111yescharacteristic
244#2035C2×C1111yescharacteristic
245#2001C2×C1111yescharacteristic
246#2001C2×C1111yescharacteristic
247#1989C2×C1111yescharacteristic, complemented
248#1981C2×C1111yescharacteristic, complemented
249#1878C2×C1111yescharacteristic, complemented
250#1878C2×C1111yescharacteristic, complemented
251#1865C2×C1111yescharacteristic, complemented
252#1863C2×C1111yescharacteristic, complemented
253#1798C2×C1111yescharacteristic
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11C22×D411yescharacteristic
262Q8×C11—22no—
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11#12012yes—
316C2×C4×C11#12012yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C112−1+411yescharacteristic
323C8×C11—41no—
324C8×C11—41no—
325C8×C11—41no—
326C8×C11—41no—
327C22×Q16C22×C1111yescharacteristic
328C22×Q16C22×C1111yescharacteristic
329#541—24no—
330#541—24no—
331C2×C4⋊Q8C22×C1111yescharacteristic
332C2×#126—21no—
333C2×#126—21no—
334C2×#125—21no—
335C2×#125—21no—
336C2×#125C22×C1111yescharacteristic
337C2×C22⋊Q8C22×C1111yescharacteristic
338C2×C22⋊Q8C22×C1111yescharacteristic
339C2×C22⋊Q8C22×C1111yescharacteristic
340C2×C4×Q8C22×C1111yescharacteristic
341C2×C4×Q8C22×C1111yescharacteristic
342C2×C4×Q8C22×C1111yescharacteristic
343C2×#117C22×C1111yescharacteristic
344#479—24no—
345#462—24no—
346C2×#107C22×C1111yescharacteristic
347C2×#106C22×C1111yescharacteristic
348C2×C4⋊C8C22×C1111yescharacteristic
349C2×C4⋊C8C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×#103C22×C1111yescharacteristic
358C2×C22⋊C8C22×C1111yescharacteristic
359C2×C22⋊C8C22×C1111yescharacteristic
360#391C22×C1111yescharacteristic
361#389—21no—
362#389C22×C1111yescharacteristic
363#388—21no—
364#388—21no—
365#387—21no—
366#380C22×C1111yescharacteristic
367C4×C4⋊C4C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11C2×#12011yescharacteristic
382C22×C11#52511yescharacteristic
383C22×C11#53711yescharacteristic
384C22×C11#57711yescharacteristic
385C22×C11#57811yescharacteristic
386C22×C11#57811yescharacteristic
387C22×C11#57811yescharacteristic
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—42no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—42no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11#54611yescharacteristic
402C4×C11#54711yescharacteristic
403C4×C11#54811yescharacteristic
404C4×C11#55011yescharacteristic
405C22×Q8C23×C1111yescharacteristic
406C22×Q8C23×C1111yescharacteristic
407C22×Q8C23×C1111yescharacteristic
408C23×C4C23×C1111yescharacteristic
409C2×Q16—22no—
410C2×Q16—22no—
411C2×Q16—22no—
412C2×Q16—22no—
413C2×Q16—41no—
414C2×Q16—41no—
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419C4⋊Q8—22no—
420C4⋊Q8D4×C1114yes—
421#126—28no—
422#126—28no—
423#125—28no—
424#125—28no—
425#125—22no—
426#125D4×C1114yes—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8—22no—
439#117—22no—
440#117—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4D4×C1111yescharacteristic
453C2×C4⋊C4D4×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4D4×C1111yescharacteristic
464C2×C22⋊C4D4×C1111yescharacteristic
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C23×C1111yescharacteristic
470C2×C42C23×C1111yescharacteristic
471#107—22no—
472#106—22no—
473C4⋊C8—22no—
474C4⋊C8—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—41no—
482#103—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490C2×C11—81no—
491C2×C11#240711yescharacteristic
492C2×C11#301111yescharacteristic
493C2×C11#301311yescharacteristic
494C2×C11#312011yescharacteristic
495C2×C11#312711yescharacteristic
496C2×C11#325811yescharacteristic
497C2×C11#326111yescharacteristic
498C24C2×D4×C1111yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8C2×D4×C1112yes—
515C2×Q8C2×D4×C1112yes—
516C2×Q8C11×#4112yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C24×C1111yescharacteristic
537Q16—44no—
538Q16—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4C2×D4×C1112yes—
572C4⋊C4C2×D4×C1112yes—
573C4⋊C4C11×#4112yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—81no—
580C42—24no—
581C42—24no—
582C42—21no—
583C42—21no—
584C42—42no—
585C42—81no—
586C42C2×D4×C1112yes—
587C42C2×D4×C1112yes—
588C11#2416511yescharacteristic, direct product factor, Sylow
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C22×D4×C1111yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—22no—
600Q8—22no—
601Q8—22no—
602Q8—22no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4C11×#12012yes—
651C2×C4C11×#12012yes—
652C2×C4C22×D4×C1111yescharacteristic
653C2×C4C22×D4×C1111yescharacteristic
654C2×C4C2×C11×#4111yescharacteristic
655C2×C4C2×C11×#4111yescharacteristic
656C2×C4C11×H(5,𝔽2)11yescharacteristic
657C2×C4C11×2−1+411yescharacteristic
658C8—41no—
659C8—41no—
660C8—41no—
661C8—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×C11×#12011yescharacteristic
670C22C11×#52511yescharacteristic
671C22C11×#53711yescharacteristic
672C22C11×#57711yescharacteristic
673C22C11×#57811yescharacteristic
674C22C11×#57811yescharacteristic
675C22C11×#57811yescharacteristic
676C4—22no—
677C4—22no—
678C4—41no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4C11×#54611yescharacteristic
690C4C11×#54711yescharacteristic
691C4C11×#54811yescharacteristic
692C4C11×#55011yescharacteristic
693C2—81no—
694C2C11×#240711yescharacteristic
695C2C11×#301111yescharacteristic
696C2C11×#301311yescharacteristic
697C2C11×#312011yescharacteristic
698C2C11×#312711yescharacteristic
699C2C11×#325811yescharacteristic
700C2C11×#326111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
3. C2×C11×#462C2semidirect
9. C11×#1989C2semidirect
10. C11×#1981C2semidirect
11. C11×#1878C2semidirect
12. C11×#1878C2semidirect
13. C11×#1865C2semidirect
14. C11×#1863C2semidirect
148. #24165C11direct (N × H)
240. C2×#479C2×C11semidirect
241. C2×#462C2×C11semidirect
247. #1989C2×C11semidirect
248. #1981C2×C11semidirect
249. #1878C2×C11semidirect
250. #1878C2×C11semidirect
251. #1865C2×C11semidirect
252. #1863C2×C11semidirect
588. C11#24165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C2×C11×#4792
C2×C11×#4622
C11×#23232
C11×#20362
C11×#20352
C11×#20012
C11×#19892
C11×#19812
C11×#18782
C11×#18652
C11×#18632
C11×#17982
#2416511