Finite Group Databasebeta

← C11×#13876 #14591069

Subgroups — C11×#13876 #14591069

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#388C212yesmaximal
2C2×C11×#384C211yesmaximal, characteristic, complemented
3C2×C11×#380C211yesmaximal, characteristic
4C2×C11×#380C211yesmaximal, characteristic
5C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
7C11×#1442C212yesmaximal, complemented
8C11×#1439C212yesmaximal
9C11×#1436C212yesmaximal, complemented
10C11×C4⋊#95C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2212yes—
24C22×C42×C11C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C11×#388—28no—
27C11×#384—24no—
28C11×#380—24no—
29C11×#380—24no—
30C4×C11×C4⋊C4—24no—
31C4×C11×C22⋊C4C418yescomplemented
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C2×C11×#95C2212yes—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C25×C11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11C2×C414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—42no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C4⋊C4D414yes—
76C2×C11×C4⋊C4D414yes—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—42no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C11×C22⋊C4D414yes—
88C2×C11×C22⋊C4Q814yes—
89C2×C42×C11—22no—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C42×C11—24no—
94C2×C42×C11—24no—
95C2×C42×C11—42no—
96C2×C42×C11C2×C414yes—
97C2×C42×C11C2×C414yes—
98C11×#95—24no—
99C11×#95—24no—
100C11×#95—24no—
101C11×#95—24no—
102C11×#95—24no—
103C11×#95—24no—
104C11×#95—42no—
105C11×#95C2×C414yes—
106C11×#95C2×C414yes—
107#13876C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—21no—
119C24×C11—21no—
120C24×C11C22×C412yes—
121C24×C11C2×D412yes—
122C24×C11C2×Q812yes—
123C24×C11C2411yescharacteristic
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—28no—
161C22×C4×C11—28no—
162C22×C4×C11—28no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—44no—
178C22×C4×C11—44no—
179C22×C4×C11—44no—
180C22×C4×C11—44no—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C22×C412yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×Q812yes—
194C22×C4×C11C2×Q812yes—
195C22×C4×C11#4112yes—
196C22×C4×C11#4112yes—
197C22×C4×C11#4112yes—
198C22×C4×C11#4112yes—
199C22×C4×C11#4112yes—
200C22×C4×C11#4112yes—
201C11×C4⋊C4—28no—
202C11×C4⋊C4—28no—
203C11×C4⋊C4—48no—
204C11×C4⋊C4—48no—
205C11×C4⋊C4—44no—
206C11×C4⋊C4—44no—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—48no—
209C11×C22⋊C4—48no—
210C11×C22⋊C4C4⋊C4116yescomplemented
211C42×C11—28no—
212C42×C11—28no—
213C42×C11—48no—
214C2×#388C2×C1112yes—
215C2×#384C2×C1111yescharacteristic, complemented
216C2×#380C2×C1111yescharacteristic
217C2×#380C2×C1111yescharacteristic
218C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
219C2×C4×C22⋊C4C2×C1111yescharacteristic
220#1442C2×C1112yescomplemented
221#1439C2×C1112yes—
222#1436C2×C1112yescomplemented
223C4⋊#95C2×C1111yescharacteristic, complemented
224C4⋊#95C2×C1111yescharacteristic, complemented
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11C2×C4⋊C414yes—
260C23×C11C23×C411yescharacteristic
261C23×C11C22×D411yescharacteristic
262C23×C11C22×D411yescharacteristic
263C23×C11C22×D411yescharacteristic
264C23×C11C22×Q811yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11C2×#4111yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C11H(5,𝔽2)11yescharacteristic
273C23×C112−1+411yescharacteristic
274C23×C112−1+411yescharacteristic
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—41no—
315C2×C4×C11—42no—
316C2×C4×C11—41no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—416no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11C2×C4⋊C414yes—
337C2×C4×C11C2×C4⋊C414yes—
338C2×C4×C11#11714yes—
339C2×C4×C11#11714yes—
340C2×C4×C11C4×D414yes—
341C2×C4×C11C4×D414yes—
342C2×C4×C11#12114yes—
343C2×C4×C11#12314yes—
344C2×C4×C11#12414yes—
345C2×C4×C11#12614yes—
346C24×C4C22×C1111yescharacteristic
347C22×C4⋊C4C22×C1111yescharacteristic
348C22×C4⋊C4C22×C1111yescharacteristic
349C22×C4⋊C4C22×C1112yes—
350C22×C4⋊C4C22×C1112yes—
351C22×C4⋊C4C22×C1111yescharacteristic
352C22×C4⋊C4C22×C1111yescharacteristic
353C22×C22⋊C4C22×C1112yes—
354C22×C22⋊C4C22×C1112yes—
355C22×C22⋊C4C22×C1111yescharacteristic
356C22×C22⋊C4C22×C1111yescharacteristic
357C22×C42C22×C1112yes—
358C22×C42C22×C1111yescharacteristic
359C22×C42C22×C1111yescharacteristic
360#388—28no—
361#384—24no—
362#380—24no—
363#380—24no—
364C4×C4⋊C4—24no—
365C4×C22⋊C4C4×C1118yescomplemented
366C2×#95C22×C1112yes—
367C2×#95C22×C1112yes—
368C2×#95C22×C1112yes—
369C2×#95C22×C1112yes—
370C2×#95C22×C1112yes—
371C2×#95C22×C1112yes—
372C2×#95C22×C1112yes—
373C2×#95C22×C1111yescharacteristic
374C2×#95C22×C1111yescharacteristic
375C22×C11—24no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11C22×C4⋊C411yescharacteristic
391C22×C11C2×#11711yescharacteristic
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11#52011yescharacteristic
396C22×C11#52011yescharacteristic
397C22×C11C2×#12111yescharacteristic
398C22×C11C2×#12311yescharacteristic
399C22×C11C2×#12411yescharacteristic
400C22×C11C2×#12611yescharacteristic
401C22×C11#53211yescharacteristic
402C22×C11#53211yescharacteristic
403C22×C11#53311yescharacteristic
404C22×C11#53311yescharacteristic
405C22×C11#54011yescharacteristic
406C22×C11#54111yescharacteristic
407C22×C11#54211yescharacteristic
408C22×C11#54211yescharacteristic
409C22×C11D4211yescharacteristic
410C22×C11D4211yescharacteristic
411C22×C11#54611yescharacteristic
412C22×C11#54711yescharacteristic
413C22×C11#54711yescharacteristic
414C22×C11#54711yescharacteristic
415C22×C11#54811yescharacteristic
416C22×C11D4×Q811yescharacteristic
417C22×C11D4×Q811yescharacteristic
418C22×C11#55011yescharacteristic
419C22×C11#55211yescharacteristic
420C22×C11#55311yescharacteristic
421C22×C11#55411yescharacteristic
422C22×C11#55411yescharacteristic
423C22×C11#55511yescharacteristic
424C22×C11#55611yescharacteristic
425C4×C11—24no—
426C4×C11—24no—
427C4×C11—24no—
428C4×C11—42no—
429C4×C11—44no—
430C4×C11—44no—
431C4×C11—42no—
432C4×C11—82no—
433C4×C11—82no—
434C4×C11#38818yescomplemented
435C25C23×C1111yescharacteristic
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4C2×C4×C1114yes—
443C23×C4C23×C1112yes—
444C23×C4C23×C1112yes—
445C23×C4C23×C1111yescharacteristic
446C23×C4C23×C1111yescharacteristic
447C23×C4C23×C1112yes—
448C23×C4C23×C1112yes—
449C23×C4C23×C1111yescharacteristic
450C23×C4C23×C1111yescharacteristic
451C23×C4C23×C1111yescharacteristic
452C23×C4C23×C1111yescharacteristic
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4D4×C1114yes—
470C2×C4⋊C4D4×C1114yes—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4C2×C4×C1114yes—
480C2×C22⋊C4C2×C4×C1114yes—
481C2×C22⋊C4D4×C1114yes—
482C2×C22⋊C4Q8×C1114yes—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—24no—
488C2×C42—24no—
489C2×C42—42no—
490C2×C42C2×C4×C1114yes—
491C2×C42C2×C4×C1114yes—
492#95—24no—
493#95—24no—
494#95—24no—
495#95—24no—
496#95—24no—
497#95—24no—
498#95—42no—
499#95C2×C4×C1114yes—
500#95C2×C4×C1114yes—
501C2×C11—44no—
502C2×C11#228511yescharacteristic
503C2×C11C2×#38811yescharacteristic
504C2×C11#231411yescharacteristic
505C2×C11D4×C4⋊C411yescharacteristic
506C2×C11D4×C4⋊C411yescharacteristic
507C2×C11#235211yescharacteristic
508C2×C11#235411yescharacteristic
509C2×C11#242211yescharacteristic
510C2×C11#242311yescharacteristic
511C2×C11#242811yescharacteristic
512C2×C11#242911yescharacteristic
513C2×C11#249111yescharacteristic
514C2×C11#249211yescharacteristic
515C2×C11#249611yescharacteristic
516C2×C11#249711yescharacteristic
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24C22×C4×C1112yes—
530C24C2×D4×C1112yes—
531C24C2×Q8×C1112yes—
532C24C24×C1111yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4C22×C4×C1112yes—
591C22×C4C22×C4×C1112yes—
592C22×C4C22×C4×C1112yes—
593C22×C4C22×C4×C1112yes—
594C22×C4C22×C4×C1112yes—
595C22×C4C22×C4×C1112yes—
596C22×C4C2×D4×C1114yes—
597C22×C4C2×D4×C1114yes—
598C22×C4C2×D4×C1112yes—
599C22×C4C2×D4×C1112yes—
600C22×C4C2×D4×C1112yes—
601C22×C4C2×D4×C1112yes—
602C22×C4C2×Q8×C1112yes—
603C22×C4C2×Q8×C1112yes—
604C22×C4C11×#4112yes—
605C22×C4C11×#4112yes—
606C22×C4C11×#4112yes—
607C22×C4C11×#4112yes—
608C22×C4C11×#4112yes—
609C22×C4C11×#4112yes—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C22⋊C4—28no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4C11×C4⋊C4116yescomplemented
620C42—28no—
621C42—28no—
622C42—48no—
623C11#1387611yescharacteristic, direct product factor, Sylow
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C11×C4⋊C414yes—
659C23C23×C4×C1111yescharacteristic
660C23C22×D4×C1111yescharacteristic
661C23C22×D4×C1111yescharacteristic
662C23C22×D4×C1111yescharacteristic
663C23C22×Q8×C1111yescharacteristic
664C23C2×C11×#4111yescharacteristic
665C23C2×C11×#4111yescharacteristic
666C23C2×C11×#4111yescharacteristic
667C23C2×C11×#4111yescharacteristic
668C23C2×C11×#4111yescharacteristic
669C23C2×C11×#4111yescharacteristic
670C23C11×H(5,𝔽2)11yescharacteristic
671C23C11×H(5,𝔽2)11yescharacteristic
672C23C11×2−1+411yescharacteristic
673C23C11×2−1+411yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C2×C11×C4⋊C414yes—
736C2×C4C2×C11×C4⋊C414yes—
737C2×C4C11×#11714yes—
738C2×C4C11×#11714yes—
739C2×C4C4×D4×C1114yes—
740C2×C4C4×D4×C1114yes—
741C2×C4C11×#12114yes—
742C2×C4C11×#12314yes—
743C2×C4C11×#12414yes—
744C2×C4C11×#12614yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C11×C4⋊C411yescharacteristic
761C22C2×C11×#11711yescharacteristic
762C22C2×C11×#11711yescharacteristic
763C22C2×C4×D4×C1111yescharacteristic
764C22C2×C4×D4×C1111yescharacteristic
765C22C11×#52011yescharacteristic
766C22C11×#52011yescharacteristic
767C22C2×C11×#12111yescharacteristic
768C22C2×C11×#12311yescharacteristic
769C22C2×C11×#12411yescharacteristic
770C22C2×C11×#12611yescharacteristic
771C22C11×#53211yescharacteristic
772C22C11×#53211yescharacteristic
773C22C11×#53311yescharacteristic
774C22C11×#53311yescharacteristic
775C22C11×#54011yescharacteristic
776C22C11×#54111yescharacteristic
777C22C11×#54211yescharacteristic
778C22C11×#54211yescharacteristic
779C22D42×C1111yescharacteristic
780C22D42×C1111yescharacteristic
781C22C11×#54611yescharacteristic
782C22C11×#54711yescharacteristic
783C22C11×#54711yescharacteristic
784C22C11×#54711yescharacteristic
785C22C11×#54811yescharacteristic
786C22D4×Q8×C1111yescharacteristic
787C22D4×Q8×C1111yescharacteristic
788C22C11×#55011yescharacteristic
789C22C11×#55211yescharacteristic
790C22C11×#55311yescharacteristic
791C22C11×#55411yescharacteristic
792C22C11×#55411yescharacteristic
793C22C11×#55511yescharacteristic
794C22C11×#55611yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—44no—
799C4—44no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4C11×#38818yescomplemented
805C2—44no—
806C2C11×#228511yescharacteristic
807C2C2×C11×#38811yescharacteristic
808C2C11×#231411yescharacteristic
809C2D4×C11×C4⋊C411yescharacteristic
810C2D4×C11×C4⋊C411yescharacteristic
811C2C11×#235211yescharacteristic
812C2C11×#235411yescharacteristic
813C2C11×#242211yescharacteristic
814C2C11×#242311yescharacteristic
815C2C11×#242811yescharacteristic
816C2C11×#242911yescharacteristic
817C2C11×#249111yescharacteristic
818C2C11×#249211yescharacteristic
819C2C11×#249611yescharacteristic
820C2C11×#249711yescharacteristic
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. C2×C11×#384C2semidirect
5. C2×C4×C11×C4⋊C4C2semidirect
7. C11×#1442C2semidirect
9. C11×#1436C2semidirect
10. C11×C4⋊#95C2semidirect
11. C11×C4⋊#95C2semidirect
31. C4×C11×C22⋊C4C4semidirect
107. #13876C11direct (N × H)
210. C11×C22⋊C4C4⋊C4semidirect
215. C2×#384C2×C11semidirect
218. C2×C4×C4⋊C4C2×C11semidirect
220. #1442C2×C11semidirect
222. #1436C2×C11semidirect
223. C4⋊#95C2×C11semidirect
224. C4⋊#95C2×C11semidirect
365. C4×C22⋊C4C4×C11semidirect
434. C4×C11#388semidirect
619. C22⋊C4C11×C4⋊C4semidirect
623. C11#13876direct (N × H)
804. C4C11×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#3882
C2×C11×#3842
C2×C11×#3802
C2×C4×C11×C4⋊C42
C2×C4×C11×C22⋊C42
C11×#14422
C11×#14392
C11×#14362
C11×C4⋊#952
#1387611