Finite Group Databasebeta

← C11×#22889 #14600082

Subgroups — C11×#22889 #14600082

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3002C211yesmaximal, characteristic
2C2×C11×#443C211yesmaximal, characteristic, complemented
3C11×#2933C211yesmaximal, characteristic, complemented
4C2×C11×#421C211yesmaximal, characteristic, complemented
5C11×#2880C211yesmaximal, characteristic, complemented
6C11×#1975C211yesmaximal, characteristic, complemented
7C11×#1937C211yesmaximal, characteristic, complemented
8C11×#1929C211yesmaximal, characteristic, complemented
9C11×#1897C211yesmaximal, characteristic, complemented
10C11×#1876C211yesmaximal, characteristic, complemented
11C11×#1876C211yesmaximal, characteristic, complemented
12C11×#1866C211yesmaximal, characteristic, complemented
13C11×#1855C211yesmaximal, characteristic, complemented
14C11×#1765C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C2×C11×#135C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic
20C2×C11×#131C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic, complemented
22C22×C11×M16C2211yescharacteristic
23C11×#525C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C11×#452C411yescharacteristic, complemented
26C11×#452C411yescharacteristic, complemented
27C11×#451C411yescharacteristic, complemented
28C11×#450C411yescharacteristic, complemented
29C11×#449C411yescharacteristic, complemented
30C11×#449C411yescharacteristic, complemented
31C11×#448C411yescharacteristic, complemented
32C11×#447C411yescharacteristic, complemented
33C11×#443—24no—
34C11×#436—21no—
35C11×#435—21no—
36C11×#435—21no—
37C8×D4×C11—21no—
38C2×C11×#108C2211yescharacteristic, complemented
39C2×C11×#108C2211yescharacteristic, complemented
40C11×#424C2211yescharacteristic, complemented
41C11×#421—24no—
42C2×C11×#104C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic, complemented
47C2×C11×#104C2211yescharacteristic, complemented
48C11×#416C2211yescharacteristic
49C11×#416C2211yescharacteristic
50C11×#408—21no—
51C11×#408—21no—
52C11×#408C2211yescharacteristic
53C11×#408C2211yescharacteristic
54C11×#408C2211yescharacteristic, complemented
55C11×#407—21no—
56C11×#407C2211yescharacteristic
57C2×C11×C22⋊C8—21no—
58C2×C11×C22⋊C8C2211yescharacteristic
59C2×C11×C22⋊C8C2211yescharacteristic
60C11×#405C2211yescharacteristic, complemented
61C2×C11×#97C2211yescharacteristic, complemented
62C2×C4×C8×C11C2211yescharacteristic, complemented
63C11×#341C2211yescharacteristic, complemented
64C11×#341C2211yescharacteristic, complemented
65C11×#339C2211yescharacteristic, complemented
66C11×#339C2211yescharacteristic, complemented
67C11×#336C2211yescharacteristic, complemented
68C11×#336C2211yescharacteristic, complemented
69C2×C11×#41—21no—
70C2×C11×#41—21no—
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41C2×C411yescharacteristic
76C2×C11×#41C2×C411yescharacteristic
77C2×C11×#41C2311yescharacteristic
78C2×C11×#41C2311yescharacteristic
79C2×C11×#41C2311yescharacteristic
80C22×Q8×C11C2×C411yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11C2×C411yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C11×#135—22no—
86C11×#135—22no—
87C11×#135—41no—
88C11×#135—41no—
89C2×C11×Q16C2×C411yescharacteristic
90C2×C11×Q16C2×C411yescharacteristic
91C2×C11×SD16C2×C411yescharacteristic
92C2×C11×SD16C2×C411yescharacteristic
93C2×C11×SD16C2×C411yescharacteristic
94C2×C11×SD16C2×C411yescharacteristic
95C2×C11×D8C2×C411yescharacteristic
96C2×C11×D8C2×C411yescharacteristic
97C11×#131—22no—
98C11×#131—22no—
99C11×#131—22no—
100C11×#131—41no—
101C11×#131—41no—
102C11×#131—41no—
103C2×C11×M16—21no—
104C2×C11×M16—21no—
105C2×C11×M16—21no—
106C2×C11×M16—21no—
107C2×C11×M16—22no—
108C2×C11×M16—41no—
109C2×C11×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C2×C11×M16C2311yescharacteristic
112C2×C11×M16C2311yescharacteristic
113C22×C8×C11—21no—
114C22×C8×C11—21no—
115C22×C8×C11—21no—
116C22×C8×C11—21no—
117C22×C8×C11C2311yescharacteristic
118C22×C8×C11C2311yescharacteristic
119C22×C8×C11C2311yescharacteristic
120C22×C8×C11C2311yescharacteristic
121C11×#123—21no—
122C11×C22⋊Q8C2×C411yescharacteristic
123C11×C22⋊Q8C2×C411yescharacteristic
124C11×#121C2×C411yescharacteristic
125C11×#121C2×C411yescharacteristic
126C11×#120—21no—
127C4×D4×C11—21no—
128C4×D4×C11—21no—
129C11×#117—22no—
130C11×#117—41no—
131C11×#117C2311yescharacteristic
132C2×C11×C4⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C42×C11C2311yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C11×#108—22no—
137C11×#108—41no—
138C11×C4⋊C8—21no—
139C11×C4⋊C8—21no—
140C11×#104—22no—
141C11×#104—22no—
142C11×#104—22no—
143C11×#104—22no—
144C11×#104—41no—
145C11×#104D414yescomplemented
146C11×#103C2×C411yescharacteristic
147C11×#103C2×C411yescharacteristic
148C11×#103C2×C411yescharacteristic
149C11×#103C2×C411yescharacteristic
150C11×#102C2×C411yescharacteristic
151C11×#102C2×C411yescharacteristic
152C11×#102C2×C411yescharacteristic
153C11×#102C2×C411yescharacteristic
154C11×C22⋊C8—21no—
155C11×C22⋊C8—21no—
156C11×C22⋊C8—21no—
157C11×C22⋊C8—21no—
158C11×C22⋊C8—21no—
159C11×C22⋊C8—21no—
160C11×C22⋊C8—21no—
161C11×C22⋊C8—21no—
162C11×C22⋊C8C2×C411yescharacteristic
163C11×C22⋊C8C2×C411yescharacteristic
164C11×C22⋊C8C2×C411yescharacteristic
165C11×C22⋊C8C2×C411yescharacteristic
166C11×C22⋊C8D411yescharacteristic
167C11×C22⋊C8D411yescharacteristic
168C11×C22⋊C8D411yescharacteristic
169C11×C22⋊C8D411yescharacteristic
170C11×#97—21no—
171C11×#97—41no—
172C4×C8×C11—21no—
173C4×C8×C11—22no—
174#22889C1111yesmaximal, characteristic, direct product factor, Sylow
175C24×C11—21no—
176C24×C11#4111yescharacteristic
177C11×#41—21no—
178C11×#41—21no—
179C11×#41—22no—
180C11×#41—22no—
181C11×#41—21no—
182C11×#41—21no—
183C11×#41—21no—
184C11×#41—21no—
185C11×#41—21no—
186C11×#41—21no—
187C11×#41—21no—
188C11×#41—21no—
189C11×#41—42no—
190C11×#41—42no—
191C11×#41—41no—
192C11×#41—41no—
193C11×#41—42no—
194C11×#41—42no—
195C11×#41C2×D412yes—
196C11×#41#4112yes—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—41no—
200C2×Q8×C11C22×C411yescharacteristic
201C2×Q8×C11C22×C411yescharacteristic
202C2×Q8×C11C22×C411yescharacteristic
203C2×D4×C11—21no—
204C2×D4×C11—22no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—41no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11C22×C411yescharacteristic
216C2×D4×C11C22×C411yescharacteristic
217C2×D4×C11C22×C411yescharacteristic
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—42no—
231C22×C4×C11—42no—
232C22×C4×C11C22×C411yescharacteristic
233C22×C4×C11C22×C411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11#4111yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C11×Q16—22no—
239C11×Q16—41no—
240C11×SD16—22no—
241C11×SD16—22no—
242C11×SD16—41no—
243C11×SD16—41no—
244C11×D8—22no—
245C11×D8—41no—
246C11×M16—21no—
247C11×M16—21no—
248C11×M16—21no—
249C11×M16—21no—
250C11×M16—21no—
251C11×M16—21no—
252C11×M16—21no—
253C11×M16—42no—
254C11×M16—42no—
255C11×M16—42no—
256C11×M16—42no—
257C11×M16C2×D412yes—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—42no—
271C2×C8×C11—42no—
272C2×C8×C11—42no—
273C2×C8×C11—42no—
274C2×C8×C11C22×C411yescharacteristic
275C2×C8×C11C22×C411yescharacteristic
276C2×C8×C11C22×C411yescharacteristic
277C2×C8×C11C22×C411yescharacteristic
278C2×C8×C11C2×D411yescharacteristic
279C2×C8×C11C2×D411yescharacteristic
280C2×C8×C11C2×D411yescharacteristic
281C2×C8×C11C2×D411yescharacteristic
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—42no—
285C11×C4⋊C4C22×C411yescharacteristic
286C11×C4⋊C4C22×C411yescharacteristic
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—42no—
293C42×C11—21no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11C2×D412yes—
298#3002C2×C1111yescharacteristic
299C2×#443C2×C1111yescharacteristic, complemented
300#2933C2×C1111yescharacteristic, complemented
301C2×#421C2×C1111yescharacteristic, complemented
302#2880C2×C1111yescharacteristic, complemented
303#1975C2×C1111yescharacteristic, complemented
304#1937C2×C1111yescharacteristic, complemented
305#1929C2×C1111yescharacteristic, complemented
306#1897C2×C1111yescharacteristic, complemented
307#1876C2×C1111yescharacteristic, complemented
308#1876C2×C1111yescharacteristic, complemented
309#1866C2×C1111yescharacteristic, complemented
310#1855C2×C1111yescharacteristic, complemented
311#1765C2×C1111yescharacteristic, complemented
312#1750C2×C1111yescharacteristic, complemented
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—81no—
323C23×C11C4×D411yescharacteristic
324C23×C11C4×D411yescharacteristic
325C23×C11C2×#4111yescharacteristic
326Q8×C11—21no—
327Q8×C11—21no—
328Q8×C11—21no—
329Q8×C11—21no—
330Q8×C11—21no—
331Q8×C11—42no—
332Q8×C11C4×D412yes—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—21no—
336D4×C11—21no—
337D4×C11—21no—
338D4×C11—21no—
339D4×C11—21no—
340D4×C11—42no—
341D4×C11—42no—
342D4×C11—42no—
343D4×C11—42no—
344D4×C11—41no—
345D4×C11—41no—
346D4×C11—41no—
347D4×C11—41no—
348D4×C11—81no—
349D4×C11C4×D412yes—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—22no—
359C2×C4×C11—21no—
360C2×C4×C11—22no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—22no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
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×C11C4×D411yescharacteristic
381C2×C4×C11C4×D411yescharacteristic
382C2×C4×C11C23×C411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C2×#4111yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C8×C11—21no—
389C8×C11—21no—
390C8×C11—21no—
391C8×C11—21no—
392C8×C11—21no—
393C8×C11—21no—
394C8×C11—22no—
395C8×C11—21no—
396C8×C11—21no—
397C8×C11—41no—
398C8×C11—41no—
399C8×C11—41no—
400C22×#41C22×C1111yescharacteristic
401C2×#135C22×C1111yescharacteristic
402C2×#135C22×C1111yescharacteristic
403C2×#131C22×C1111yescharacteristic
404C2×#131C22×C1111yescharacteristic
405C2×#131C22×C1111yescharacteristic, complemented
406C22×M16C22×C1111yescharacteristic
407#525C22×C1111yescharacteristic
408C2×#117C22×C1111yescharacteristic
409#452C4×C1111yescharacteristic, complemented
410#452C4×C1111yescharacteristic, complemented
411#451C4×C1111yescharacteristic, complemented
412#450C4×C1111yescharacteristic, complemented
413#449C4×C1111yescharacteristic, complemented
414#449C4×C1111yescharacteristic, complemented
415#448C4×C1111yescharacteristic, complemented
416#447C4×C1111yescharacteristic, complemented
417#443—24no—
418#436—21no—
419#435—21no—
420#435—21no—
421C8×D4—21no—
422C2×#108C22×C1111yescharacteristic, complemented
423C2×#108C22×C1111yescharacteristic, complemented
424#424C22×C1111yescharacteristic, complemented
425#421—24no—
426C2×#104C22×C1111yescharacteristic
427C2×#104C22×C1111yescharacteristic
428C2×#104C22×C1111yescharacteristic
429C2×#104C22×C1111yescharacteristic
430C2×#104C22×C1111yescharacteristic, complemented
431C2×#104C22×C1111yescharacteristic, complemented
432#416C22×C1111yescharacteristic
433#416C22×C1111yescharacteristic
434#408—21no—
435#408—21no—
436#408C22×C1111yescharacteristic
437#408C22×C1111yescharacteristic
438#408C22×C1111yescharacteristic, complemented
439#407—21no—
440#407C22×C1111yescharacteristic
441C2×C22⋊C8—21no—
442C2×C22⋊C8C22×C1111yescharacteristic
443C2×C22⋊C8C22×C1111yescharacteristic
444#405C22×C1111yescharacteristic, complemented
445C2×#97C22×C1111yescharacteristic, complemented
446C2×C4×C8C22×C1111yescharacteristic, complemented
447#341C22×C1111yescharacteristic, complemented
448#341C22×C1111yescharacteristic, complemented
449#339C22×C1111yescharacteristic, complemented
450#339C22×C1111yescharacteristic, complemented
451#336C22×C1111yescharacteristic, complemented
452#336C22×C1111yescharacteristic, complemented
453C22×C11—21no—
454C22×C11—21no—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—22no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—21no—
461C22×C11—21no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11—41no—
470C22×C11—81no—
471C22×C11—81no—
472C22×C11—84no—
473C22×C11C2×C4×D411yescharacteristic
474C22×C11#54611yescharacteristic
475C22×C11#55111yescharacteristic
476C4×C11—21no—
477C4×C11—21no—
478C4×C11—22no—
479C4×C11—42no—
480C4×C11—41no—
481C4×C11—41no—
482C4×C11—41no—
483C4×C11—41no—
484C4×C11—81no—
485C4×C11C2×C4×D411yescharacteristic
486C4×C11#51811yescharacteristic
487C4×C11D4211yescharacteristic
488C4×C11#54611yescharacteristic
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41C2×C4×C1111yescharacteristic
496C2×#41C2×C4×C1111yescharacteristic
497C2×#41C23×C1111yescharacteristic
498C2×#41C23×C1111yescharacteristic
499C2×#41C23×C1111yescharacteristic
500C22×Q8C2×C4×C1111yescharacteristic
501C22×D4—21no—
502C22×D4C2×C4×C1111yescharacteristic
503C23×C4—21no—
504C23×C4C23×C1111yescharacteristic
505#135—22no—
506#135—22no—
507#135—41no—
508#135—41no—
509C2×Q16C2×C4×C1111yescharacteristic
510C2×Q16C2×C4×C1111yescharacteristic
511C2×SD16C2×C4×C1111yescharacteristic
512C2×SD16C2×C4×C1111yescharacteristic
513C2×SD16C2×C4×C1111yescharacteristic
514C2×SD16C2×C4×C1111yescharacteristic
515C2×D8C2×C4×C1111yescharacteristic
516C2×D8C2×C4×C1111yescharacteristic
517#131—22no—
518#131—22no—
519#131—22no—
520#131—41no—
521#131—41no—
522#131—41no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16—21no—
527C2×M16—22no—
528C2×M16—41no—
529C2×M16C23×C1111yescharacteristic
530C2×M16C23×C1111yescharacteristic
531C2×M16C23×C1111yescharacteristic
532C2×M16C23×C1111yescharacteristic
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C1111yescharacteristic
538C22×C8C23×C1111yescharacteristic
539C22×C8C23×C1111yescharacteristic
540C22×C8C23×C1111yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C1111yescharacteristic
543C22⋊Q8C2×C4×C1111yescharacteristic
544#121C2×C4×C1111yescharacteristic
545#121C2×C4×C1111yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117—22no—
550#117—41no—
551#117C23×C1111yescharacteristic
552C2×C4⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C42C23×C1111yescharacteristic
555C2×C42C23×C1111yescharacteristic
556#108—22no—
557#108—41no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#104—22no—
561#104—22no—
562#104—22no—
563#104—22no—
564#104—41no—
565#104D4×C1114yescomplemented
566#103C2×C4×C1111yescharacteristic
567#103C2×C4×C1111yescharacteristic
568#103C2×C4×C1111yescharacteristic
569#103C2×C4×C1111yescharacteristic
570#102C2×C4×C1111yescharacteristic
571#102C2×C4×C1111yescharacteristic
572#102C2×C4×C1111yescharacteristic
573#102C2×C4×C1111yescharacteristic
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8C2×C4×C1111yescharacteristic
583C22⋊C8C2×C4×C1111yescharacteristic
584C22⋊C8C2×C4×C1111yescharacteristic
585C22⋊C8C2×C4×C1111yescharacteristic
586C22⋊C8D4×C1111yescharacteristic
587C22⋊C8D4×C1111yescharacteristic
588C22⋊C8D4×C1111yescharacteristic
589C22⋊C8D4×C1111yescharacteristic
590#97—21no—
591#97—41no—
592C4×C8—21no—
593C4×C8—22no—
594C2×C11—21no—
595C2×C11—21no—
596C2×C11—41no—
597C2×C11—41no—
598C2×C11—42no—
599C2×C11—81no—
600C2×C11—81no—
601C2×C11#235811yescharacteristic
602C2×C11#295511yescharacteristic
603C2×C11#295711yescharacteristic
604C24—21no—
605C24C11×#4111yescharacteristic
606#41—21no—
607#41—21no—
608#41—22no—
609#41—22no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41C2×D4×C1112yes—
625#41C11×#4112yes—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—41no—
629C2×Q8C22×C4×C1111yescharacteristic
630C2×Q8C22×C4×C1111yescharacteristic
631C2×Q8C22×C4×C1111yescharacteristic
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4C22×C4×C1111yescharacteristic
645C2×D4C22×C4×C1111yescharacteristic
646C2×D4C22×C4×C1111yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4C22×C4×C1111yescharacteristic
662C22×C4C22×C4×C1111yescharacteristic
663C22×C4C2×D4×C1111yescharacteristic
664C22×C4C2×D4×C1111yescharacteristic
665C22×C4C11×#4111yescharacteristic
666C22×C4C24×C1111yescharacteristic
667Q16—22no—
668Q16—41no—
669SD16—22no—
670SD16—22no—
671SD16—41no—
672SD16—41no—
673D8—22no—
674D8—41no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—42no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16C2×D4×C1112yes—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8C22×C4×C1111yescharacteristic
704C2×C8C22×C4×C1111yescharacteristic
705C2×C8C22×C4×C1111yescharacteristic
706C2×C8C22×C4×C1111yescharacteristic
707C2×C8C2×D4×C1111yescharacteristic
708C2×C8C2×D4×C1111yescharacteristic
709C2×C8C2×D4×C1111yescharacteristic
710C2×C8C2×D4×C1111yescharacteristic
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—42no—
714C4⋊C4C22×C4×C1111yescharacteristic
715C4⋊C4C22×C4×C1111yescharacteristic
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—42no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42C2×D4×C1112yes—
727C11#2288911yescharacteristic, direct product factor, Sylow
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C1111yescharacteristic
739C23C4×D4×C1111yescharacteristic
740C23C2×C11×#4111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C1112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C1112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C1111yescharacteristic
796C2×C4C4×D4×C1111yescharacteristic
797C2×C4C23×C4×C1111yescharacteristic
798C2×C4C22×D4×C1111yescharacteristic
799C2×C4C22×D4×C1111yescharacteristic
800C2×C4C2×C11×#4111yescharacteristic
801C2×C4C11×H(5,𝔽2)11yescharacteristic
802C2×C4C11×H(5,𝔽2)11yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C1111yescharacteristic
836C22C11×#54611yescharacteristic
837C22C11×#55111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C1111yescharacteristic
848C4C11×#51811yescharacteristic
849C4D42×C1111yescharacteristic
850C4C11×#54611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C11×#235811yescharacteristic
859C2C11×#295511yescharacteristic
860C2C11×#295711yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC11×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#443C2semidirect
3. C11×#2933C2semidirect
4. C2×C11×#421C2semidirect
5. C11×#2880C2semidirect
6. C11×#1975C2semidirect
7. C11×#1937C2semidirect
8. C11×#1929C2semidirect
9. C11×#1897C2semidirect
10. C11×#1876C2semidirect
11. C11×#1876C2semidirect
12. C11×#1866C2semidirect
13. C11×#1855C2semidirect
14. C11×#1765C2semidirect
15. C11×#1750C2semidirect
21. C2×C11×#131C22semidirect
25. C11×#452C4semidirect
26. C11×#452C4semidirect
27. C11×#451C4semidirect
28. C11×#450C4semidirect
29. C11×#449C4semidirect
30. C11×#449C4semidirect
31. C11×#448C4semidirect
32. C11×#447C4semidirect
38. C2×C11×#108C22semidirect
39. C2×C11×#108C22semidirect
40. C11×#424C22semidirect
46. C2×C11×#104C22semidirect
47. C2×C11×#104C22semidirect
54. C11×#408C22semidirect
60. C11×#405C22semidirect
61. C2×C11×#97C22semidirect
62. C2×C4×C8×C11C22semidirect
63. C11×#341C22semidirect
64. C11×#341C22semidirect
65. C11×#339C22semidirect
66. C11×#339C22semidirect
67. C11×#336C22semidirect
68. C11×#336C22semidirect
145. C11×#104D4semidirect
174. #22889C11direct (N × H)
299. C2×#443C2×C11semidirect
300. #2933C2×C11semidirect
301. C2×#421C2×C11semidirect
302. #2880C2×C11semidirect
303. #1975C2×C11semidirect
304. #1937C2×C11semidirect
305. #1929C2×C11semidirect
306. #1897C2×C11semidirect
307. #1876C2×C11semidirect
308. #1876C2×C11semidirect
309. #1866C2×C11semidirect
310. #1855C2×C11semidirect
311. #1765C2×C11semidirect
312. #1750C2×C11semidirect
405. C2×#131C22×C11semidirect
409. #452C4×C11semidirect
410. #452C4×C11semidirect
411. #451C4×C11semidirect
412. #450C4×C11semidirect
413. #449C4×C11semidirect
414. #449C4×C11semidirect
415. #448C4×C11semidirect
416. #447C4×C11semidirect
422. C2×#108C22×C11semidirect
423. C2×#108C22×C11semidirect
424. #424C22×C11semidirect
430. C2×#104C22×C11semidirect
431. C2×#104C22×C11semidirect
438. #408C22×C11semidirect
444. #405C22×C11semidirect
445. C2×#97C22×C11semidirect
446. C2×C4×C8C22×C11semidirect
447. #341C22×C11semidirect
448. #341C22×C11semidirect
449. #339C22×C11semidirect
450. #339C22×C11semidirect
451. #336C22×C11semidirect
452. #336C22×C11semidirect
565. #104D4×C11semidirect
727. C11#22889direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30022
C2×C11×#4432
C11×#29332
C2×C11×#4212
C11×#28802
C11×#19752
C11×#19372
C11×#19292
C11×#18972
C11×#18762
C11×#18662
C11×#18552
C11×#17652
C11×#17502
#2288911