Finite Group Databasebeta

← C11×#22420 #14599613

Subgroups — C11×#22420 #14599613

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic, complemented
5C11×#2352C211yesmaximal, characteristic, complemented
6C11×#1981C211yesmaximal, characteristic, complemented
7C11×#1960C211yesmaximal, characteristic, complemented
8C11×#1894C211yesmaximal, characteristic, complemented
9C11×#1892C211yesmaximal, characteristic, complemented
10C11×#1873C211yesmaximal, characteristic, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C11×#1804C211yesmaximal, characteristic, complemented
13C11×#1788C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#547—24no—
21C11×#547C418yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×C11×C4⋊C4—21no—
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#435—24no—
34C2×C11×C4⋊C8C2211yescharacteristic
35C11×#417—24no—
36C11×#416—24no—
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×#97C2211yescharacteristic
52C11×#388—21no—
53C11×#387—21no—
54C11×#386—21no—
55C11×#382C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#380C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59C4×C11×C22⋊C4—21no—
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#340C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41C2×C414yes—
75C2×C11×#41C2×C414yescomplemented
76C22×Q8×C11C2311yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C2×C11×M16—22no—
89C2×C11×M16—22no—
90C2×C11×M16—41no—
91C22×C8×C11—22no—
92C22×C8×C11—22no—
93C22×C8×C11—41no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×C4⋊Q8—22no—
99C11×C4⋊Q8C2×C414yescomplemented
100C11×#123—28no—
101C11×#123—28no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8C2×C414yes—
105C11×C22⋊Q8C2×C414yescomplemented
106C11×#121—28no—
107C4×D4×C11—22no—
108C4×D4×C11C2×C414yes—
109C4×D4×C11C2×C414yescomplemented
110C4×D4×C11D414yes—
111C11×#117—22no—
112C11×#117—41no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—28no—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—41no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4D411yescharacteristic
134C2×C11×C22⋊C4D411yescharacteristic
135C2×C42×C11—21no—
136C2×C42×C11—21no—
137C2×C42×C11C2311yescharacteristic
138C11×C4⋊C8—22no—
139C11×#103—22no—
140C11×#103—22no—
141C11×#103—22no—
142C11×#103—22no—
143C11×#103—41no—
144C11×#103—41no—
145C11×#103—41no—
146C11×#103—41no—
147C11×#102—22no—
148C11×#102—22no—
149C11×#102—22no—
150C11×#102D414yescomplemented
151C11×C22⋊C8—22no—
152C11×C22⋊C8—22no—
153C11×#97—22no—
154C11×#95—21no—
155C11×#95—21no—
156C11×#95—21no—
157C11×#95—21no—
158C11×#95—21no—
159#22420C1111yesmaximal, characteristic, direct product factor, Sylow
160C24×C11—21no—
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D411yescharacteristic
163C11×#41—28no—
164C11×#41—28no—
165C11×#41—44no—
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11C22×C412yes—
182C2×Q8×C11C22×C412yes—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—41no—
189C2×D4×C11—41no—
190C2×D4×C11—42no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—42no—
194C2×D4×C11C22⋊C414yes—
195C2×D4×C11C22×C412yes—
196C2×D4×C11C2×D412yes—
197C2×D4×C11#4112yes—
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—24no—
211C22×C4×C11—24no—
212C22×C4×C11—24no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—81no—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2411yescharacteristic
234C11×M16—44no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—44no—
247C2×C8×C11C2×D412yes—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—42no—
261C11×C4⋊C4C22⋊C414yes—
262C11×C4⋊C4C22×C412yes—
263C11×C4⋊C4C2×D412yes—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—42no—
268C11×C22⋊C4—42no—
269C11×C22⋊C4—81no—
270C11×C22⋊C4C22⋊C414yes—
271C11×C22⋊C4C22⋊C414yes—
272C42×C11—42no—
273C42×C11—81no—
274C42×C11C22×C412yes—
275C42×C11C2×D412yes—
276C2×#547C2×C1111yescharacteristic
277C2×#435C2×C1111yescharacteristic, complemented
278C2×#417C2×C1111yescharacteristic, complemented
279C2×#416C2×C1111yescharacteristic, complemented
280#2352C2×C1111yescharacteristic, complemented
281#1981C2×C1111yescharacteristic, complemented
282#1960C2×C1111yescharacteristic, complemented
283#1894C2×C1111yescharacteristic, complemented
284#1892C2×C1111yescharacteristic, complemented
285#1873C2×C1111yescharacteristic, complemented
286#1872C2×C1111yescharacteristic, complemented
287#1804C2×C1111yescharacteristic, complemented
288#1788C2×C1111yescharacteristic, complemented
289#1788C2×C1111yescharacteristic, complemented
290#1762C2×C1111yescharacteristic, complemented
291C23×C11—22no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C2×C22⋊C412yes—
311C23×C11C2×C22⋊C412yes—
312C23×C11C22×D411yescharacteristic
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—41no—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11—41no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—44no—
325D4×C11—48no—
326D4×C11—48no—
327D4×C11C4×D414yes—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
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—48no—
349C2×C4×C11—48no—
350C2×C4×C11—48no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—84no—
369C2×C4×C11C2×C22⋊C412yes—
370C2×C4×C11C2×C22⋊C412yes—
371C2×C4×C11C2×C22⋊C412yes—
372C2×C4×C11C2×C22⋊C412yes—
373C2×C4×C11C23×C411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11H(5,𝔽2)11yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C8×C11—22no—
380C8×C11—41no—
381C8×C11—41no—
382C8×C11—41no—
383C22×#41C22×C1111yescharacteristic
384C22×#41C22×C1111yescharacteristic
385C22×M16C22×C1111yescharacteristic
386C23×C8C22×C1111yescharacteristic
387#547—24no—
388#547C4×C1118yescomplemented
389C2×C4⋊Q8C22×C1111yescharacteristic
390C2×#123—21no—
391C2×#123—21no—
392C2×C22⋊Q8C22×C1111yescharacteristic
393C2×C22⋊Q8C22×C1111yescharacteristic
394C2×#121—21no—
395C2×C4×D4C22×C1111yescharacteristic
396C2×C4×D4C22×C1111yescharacteristic
397C2×#117C22×C1111yescharacteristic
398C22×C4⋊C4—21no—
399C22×C4⋊C4C22×C1111yescharacteristic
400#435—24no—
401C2×C4⋊C8C22×C1111yescharacteristic
402#417—24no—
403#416—24no—
404C2×#103C22×C1111yescharacteristic
405C2×#103C22×C1111yescharacteristic
406C2×#103C22×C1111yescharacteristic
407C2×#103C22×C1111yescharacteristic
408C2×#103C22×C1111yescharacteristic
409C2×#103C22×C1111yescharacteristic
410C2×#103C22×C1111yescharacteristic
411C2×#103C22×C1111yescharacteristic
412C2×#102C22×C1111yescharacteristic
413C2×#102C22×C1111yescharacteristic
414C2×#102C22×C1111yescharacteristic
415C2×#102C22×C1111yescharacteristic
416C2×C22⋊C8C22×C1111yescharacteristic
417C2×C22⋊C8C22×C1111yescharacteristic
418C2×#97C22×C1111yescharacteristic
419#388—21no—
420#387—21no—
421#386—21no—
422#382C22×C1111yescharacteristic
423#380C22×C1111yescharacteristic
424#380C22×C1111yescharacteristic
425C4×C4⋊C4C22×C1111yescharacteristic
426C4×C22⋊C4—21no—
427#340C22×C1111yescharacteristic
428#340C22×C1111yescharacteristic
429#340C22×C1111yescharacteristic
430#340C22×C1111yescharacteristic
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—24no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—42no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—42no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—42no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11C22×C22⋊C411yescharacteristic
453C22×C11D4211yescharacteristic
454C22×C11#54611yescharacteristic
455C22×C11#57511yescharacteristic
456C22×C11#57511yescharacteristic
457C22×C11#57711yescharacteristic
458C22×C11#57811yescharacteristic
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—81no—
468C4×C11—81no—
469C4×C11—81no—
470C4×C11C2×C4×D411yescharacteristic
471C4×C11#51811yescharacteristic
472C4×C11D4211yescharacteristic
473C4×C11#54611yescharacteristic
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—41no—
481C2×#41—41no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41C2×C4×C1114yes—
485C2×#41C2×C4×C1114yescomplemented
486C22×Q8C23×C1111yescharacteristic
487C22×Q8C23×C1111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4D4×C1111yescharacteristic
491C22×D4C23×C1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C1111yescharacteristic
497C23×C4C23×C1111yescharacteristic
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8C23×C1111yescharacteristic
505C22×C8C23×C1111yescharacteristic
506C22×C8C23×C1111yescharacteristic
507C22×C8C23×C1111yescharacteristic
508C4⋊Q8—22no—
509C4⋊Q8C2×C4×C1114yescomplemented
510#123—28no—
511#123—28no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8C2×C4×C1114yes—
515C22⋊Q8C2×C4×C1114yescomplemented
516#121—28no—
517C4×D4—22no—
518C4×D4C2×C4×C1114yes—
519C4×D4C2×C4×C1114yescomplemented
520C4×D4D4×C1114yes—
521#117—22no—
522#117—41no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4D4×C1111yescharacteristic
532C2×C4⋊C4C23×C1111yescharacteristic
533C2×C4⋊C4C23×C1111yescharacteristic
534C2×C4⋊C4C23×C1111yescharacteristic
535C2×C4⋊C4C23×C1111yescharacteristic
536C2×C4⋊C4C23×C1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4D4×C1111yescharacteristic
544C2×C22⋊C4D4×C1111yescharacteristic
545C2×C42—21no—
546C2×C42—21no—
547C2×C42C23×C1111yescharacteristic
548C4⋊C8—22no—
549#103—22no—
550#103—22no—
551#103—22no—
552#103—22no—
553#103—41no—
554#103—41no—
555#103—41no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102D4×C1114yescomplemented
561C22⋊C8—22no—
562C22⋊C8—22no—
563#97—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569C2×C11—42no—
570C2×C11—42no—
571C2×C11—44no—
572C2×C11D4×C22⋊C411yescharacteristic
573C2×C11#289611yescharacteristic
574C2×C11#289811yescharacteristic
575C2×C11#326711yescharacteristic
576C2×C11#326911yescharacteristic
577C2×C11#330711yescharacteristic
578C2×C11#331511yescharacteristic
579C24—21no—
580C24C2×D4×C1111yescharacteristic
581C24C2×D4×C1111yescharacteristic
582#41—28no—
583#41—28no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8C22×C4×C1112yes—
601C2×Q8C22×C4×C1112yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4C11×C22⋊C414yes—
614C2×D4C22×C4×C1112yes—
615C2×D4C2×D4×C1112yes—
616C2×D4C11×#4112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4C22×C4×C1112yes—
645C22×C4C22×C4×C1112yes—
646C22×C4C2×D4×C1111yescharacteristic
647C22×C4C2×D4×C1111yescharacteristic
648C22×C4C2×D4×C1111yescharacteristic
649C22×C4C2×D4×C1111yescharacteristic
650C22×C4C2×D4×C1112yes—
651C22×C4C2×D4×C1112yes—
652C22×C4C24×C1111yescharacteristic
653M16—44no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—44no—
666C2×C8C2×D4×C1112yes—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—42no—
680C4⋊C4C11×C22⋊C414yes—
681C4⋊C4C22×C4×C1112yes—
682C4⋊C4C2×D4×C1112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—81no—
689C22⋊C4C11×C22⋊C414yes—
690C22⋊C4C11×C22⋊C414yes—
691C42—42no—
692C42—81no—
693C42C22×C4×C1112yes—
694C42C2×D4×C1112yes—
695C11#2242011yescharacteristic, direct product factor, Sylow
696C23—22no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C11×C22⋊C412yes—
716C23C2×C11×C22⋊C412yes—
717C23C22×D4×C1111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4C4×D4×C1114yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—48no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4C2×C11×C22⋊C412yes—
775C2×C4C2×C11×C22⋊C412yes—
776C2×C4C2×C11×C22⋊C412yes—
777C2×C4C2×C11×C22⋊C412yes—
778C2×C4C23×C4×C1111yescharacteristic
779C2×C4C22×D4×C1111yescharacteristic
780C2×C4C22×D4×C1111yescharacteristic
781C2×C4C2×C11×#4111yescharacteristic
782C2×C4C11×H(5,𝔽2)11yescharacteristic
783C2×C4C11×H(5,𝔽2)11yescharacteristic
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22C22×C11×C22⋊C411yescharacteristic
810C22D42×C1111yescharacteristic
811C22C11×#54611yescharacteristic
812C22C11×#57511yescharacteristic
813C22C11×#57511yescharacteristic
814C22C11×#57711yescharacteristic
815C22C11×#57811yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4C2×C4×D4×C1111yescharacteristic
828C4C11×#51811yescharacteristic
829C4D42×C1111yescharacteristic
830C4C11×#54611yescharacteristic
831C2—42no—
832C2—42no—
833C2—44no—
834C2D4×C11×C22⋊C411yescharacteristic
835C2C11×#289611yescharacteristic
836C2C11×#289811yescharacteristic
837C2C11×#326711yescharacteristic
838C2C11×#326911yescharacteristic
839C2C11×#330711yescharacteristic
840C2C11×#331511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#435C2semidirect
3. C2×C11×#417C2semidirect
4. C2×C11×#416C2semidirect
5. C11×#2352C2semidirect
6. C11×#1981C2semidirect
7. C11×#1960C2semidirect
8. C11×#1894C2semidirect
9. C11×#1892C2semidirect
10. C11×#1873C2semidirect
11. C11×#1872C2semidirect
12. C11×#1804C2semidirect
13. C11×#1788C2semidirect
14. C11×#1788C2semidirect
15. C11×#1762C2semidirect
21. C11×#547C4semidirect
75. C2×C11×#41C2×C4semidirect
99. C11×C4⋊Q8C2×C4semidirect
105. C11×C22⋊Q8C2×C4semidirect
109. C4×D4×C11C2×C4semidirect
150. C11×#102D4semidirect
159. #22420C11direct (N × H)
277. C2×#435C2×C11semidirect
278. C2×#417C2×C11semidirect
279. C2×#416C2×C11semidirect
280. #2352C2×C11semidirect
281. #1981C2×C11semidirect
282. #1960C2×C11semidirect
283. #1894C2×C11semidirect
284. #1892C2×C11semidirect
285. #1873C2×C11semidirect
286. #1872C2×C11semidirect
287. #1804C2×C11semidirect
288. #1788C2×C11semidirect
289. #1788C2×C11semidirect
290. #1762C2×C11semidirect
388. #547C4×C11semidirect
485. C2×#41C2×C4×C11semidirect
509. C4⋊Q8C2×C4×C11semidirect
515. C22⋊Q8C2×C4×C11semidirect
519. C4×D4C2×C4×C11semidirect
560. #102D4×C11semidirect
695. C11#22420direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4352
C2×C11×#4172
C2×C11×#4162
C11×#23522
C11×#19812
C11×#19602
C11×#18942
C11×#18922
C11×#18732
C11×#18722
C11×#18042
C11×#17882
C11×#17622
#2242011