Finite Group Databasebeta

← C11×#24365 #14601558

Subgroups — C11×#24365 #14601558

Order 2816.

1454 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
1C22×C11×#135C211yesmaximal, characteristic
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C2×C11×#452C211yesmaximal, characteristic, complemented
5C11×#2432C211yesmaximal, characteristic, complemented
6C11×#2339C211yesmaximal, characteristic, complemented
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#2016C211yesmaximal, characteristic, complemented
10C11×#2015C211yesmaximal, characteristic, complemented
11C11×#1892C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1877C211yesmaximal, characteristic, complemented
14C11×#1850C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C2×C11×#135—24no—
19C2×C11×#135—24no—
20C2×C11×#135—24no—
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C23×C8×C11C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C2×C11×#124C2211yescharacteristic
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C11×#463—24no—
34C11×#461—24no—
35C11×#452—24no—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C11×#394—21no—
48C11×#394—21no—
49C11×#391C2211yescharacteristic
50C11×#391C2211yescharacteristic
51C11×#391C2211yescharacteristic
52C11×#390C2211yescharacteristic
53C11×#386—21no—
54C11×#386—21no—
55C11×#385—21no—
56C11×#385—21no—
57C11×#381—21no—
58C11×#380C2211yescharacteristic
59C4×C11×C22⋊C4C2211yescharacteristic
60C2×C11×#95—21no—
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41D414yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C11×#135—232no—
90C2×C11×Q16—22no—
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—22no—
94C2×C11×Q16—41no—
95C2×C11×Q16—41no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—22no—
100C2×C11×SD16—22no—
101C2×C11×SD16—22no—
102C2×C11×SD16—22no—
103C2×C11×SD16—22no—
104C2×C11×SD16D414yes—
105C2×C11×D8—22no—
106C2×C11×D8—22no—
107C2×C11×D8D414yes—
108C22×C8×C11—22no—
109C22×C8×C11—22no—
110C22×C8×C11—22no—
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2311yescharacteristic
115C11×C4⋊Q8—22no—
116C11×C4⋊Q8—41no—
117C11×#124—22no—
118C11×#124—41no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—41no—
124C4×D4×C11—41no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4D411yescharacteristic
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143C11×C4⋊C8—22no—
144C11×C4⋊C8—22no—
145C11×#103—22no—
146C11×#103—22no—
147C11×#103—22no—
148C11×#103—22no—
149C11×#103—41no—
150C11×#102—22no—
151C11×#102—22no—
152C11×#102—41no—
153C11×C22⋊C8—22no—
154C11×#95—21no—
155C11×#95—21no—
156C11×#95—21no—
157C11×#95—21no—
158C11×#95—21no—
159C11×#95—21no—
160C11×#95—21no—
161C11×#95D411yescharacteristic
162C11×#95D411yescharacteristic
163#24365C1111yesmaximal, characteristic, direct product factor, Sylow
164C24×C11—21no—
165C24×C11—21no—
166C24×C11C2×D411yescharacteristic
167C11×#41—28no—
168C11×#41—28no—
169C11×#41—44no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
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×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11C2×D412yes—
192C2×Q8×C11C2×D412yes—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—42no—
203C2×D4×C11—42no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11C2×D412yes—
208C2×D4×C11C2×D412yes—
209C2×D4×C11C2×D412yes—
210C2×D4×C11C2×D412yes—
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—24no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11—42no—
229C22×C4×C11—42no—
230C22×C4×C11—42no—
231C22×C4×C11—81no—
232C22×C4×C11—81no—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11#4112yes—
240C22×C4×C11C2411yescharacteristic
241C11×Q16—28no—
242C11×Q16—44no—
243C11×SD16—28no—
244C11×SD16—28no—
245C11×SD16—44no—
246C11×D8—28no—
247C2×C8×C11—28no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11C2×D412yes—
259C2×C8×C11C2×D412yes—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—42no—
267C11×C4⋊C4—42no—
268C11×C4⋊C4—42no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—41no—
271C11×C22⋊C4—42no—
272C11×C22⋊C4—42no—
273C11×C22⋊C4—42no—
274C11×C22⋊C4—42no—
275C11×C22⋊C4—42no—
276C11×C22⋊C4—42no—
277C11×C22⋊C4—42no—
278C11×C22⋊C4—81no—
279C42×C11—21no—
280C42×C11—21no—
281C42×C11—21no—
282C42×C11—21no—
283C22×#135C2×C1111yescharacteristic
284C2×#463C2×C1111yescharacteristic, complemented
285C2×#461C2×C1111yescharacteristic, complemented
286C2×#452C2×C1111yescharacteristic, complemented
287#2432C2×C1111yescharacteristic, complemented
288#2339C2×C1111yescharacteristic, complemented
289#2056C2×C1111yescharacteristic, complemented
290#2055C2×C1111yescharacteristic, complemented
291#2016C2×C1111yescharacteristic, complemented
292#2015C2×C1111yescharacteristic, complemented
293#1892C2×C1111yescharacteristic, complemented
294#1879C2×C1111yescharacteristic, complemented
295#1877C2×C1111yescharacteristic, complemented
296#1850C2×C1111yescharacteristic, complemented
297#1788C2×C1111yescharacteristic, complemented
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—22no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11#12112yes—
319C23×C11C22×D411yescharacteristic
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—41no—
325Q8×C11—41no—
326Q8×C11—41no—
327Q8×C11—41no—
328Q8×C11—41no—
329Q8×C11—41no—
330Q8×C11—41no—
331Q8×C11—41no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—48no—
339D4×C11—41no—
340D4×C11—41no—
341D4×C11#12014yes—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—22no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—48no—
362C2×C4×C11—48no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
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—84no—
380C2×C4×C11—84no—
381C2×C4×C11#12112yes—
382C2×C4×C11#13512yescomplemented
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C2×#4111yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C2×C4×C11H(5,𝔽2)11yescharacteristic
389C8×C11—22no—
390C8×C11—22no—
391C8×C11—41no—
392C8×C11—41no—
393C22×#41C22×C1111yescharacteristic
394C22×#41C22×C1111yescharacteristic
395C2×#135—24no—
396C2×#135—24no—
397C2×#135—24no—
398C22×Q16C22×C1111yescharacteristic
399C22×Q16C22×C1111yescharacteristic
400C22×SD16C22×C1111yescharacteristic
401C22×SD16C22×C1111yescharacteristic
402C22×SD16C22×C1111yescharacteristic
403C22×D8C22×C1111yescharacteristic
404C23×C8C22×C1111yescharacteristic
405C2×C4⋊Q8C22×C1111yescharacteristic
406C2×#124C22×C1111yescharacteristic
407C2×C22⋊Q8C22×C1111yescharacteristic
408C2×C4×D4C22×C1111yescharacteristic
409C2×C4×D4C22×C1111yescharacteristic
410#463—24no—
411#461—24no—
412#452—24no—
413C2×C4⋊C8C22×C1111yescharacteristic
414C2×C4⋊C8C22×C1111yescharacteristic
415C2×#103C22×C1111yescharacteristic
416C2×#103C22×C1111yescharacteristic
417C2×#103C22×C1111yescharacteristic
418C2×#103C22×C1111yescharacteristic
419C2×#103C22×C1111yescharacteristic
420C2×#102C22×C1111yescharacteristic
421C2×#102C22×C1111yescharacteristic
422C2×#102C22×C1111yescharacteristic
423C2×C22⋊C8C22×C1111yescharacteristic
424#394—21no—
425#394—21no—
426#391C22×C1111yescharacteristic
427#391C22×C1111yescharacteristic
428#391C22×C1111yescharacteristic
429#390C22×C1111yescharacteristic
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#381—21no—
435#380C22×C1111yescharacteristic
436C4×C22⋊C4C22×C1111yescharacteristic
437C2×#95—21no—
438#340C22×C1111yescharacteristic
439#340C22×C1111yescharacteristic
440#336C22×C1111yescharacteristic
441#336C22×C1111yescharacteristic
442C22×C11—22no—
443C22×C11—24no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—42no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11C2×#12111yescharacteristic
464C22×C11D4211yescharacteristic
465C22×C11D4211yescharacteristic
466C22×C11C2×#13511yescharacteristic
467C22×C11#57511yescharacteristic
468C22×C11#57711yescharacteristic
469C22×C11#57811yescharacteristic
470C4×C11—22no—
471C4×C11—22no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—41no—
475C4×C11—41no—
476C4×C11—41no—
477C4×C11—81no—
478C4×C11—81no—
479C4×C11—81no—
480C4×C11—81no—
481C4×C11C2×#12011yescharacteristic
482C4×C11#53411yescharacteristic
483C4×C11#54611yescharacteristic
484C4×C11#54611yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41D4×C1114yes—
497C22×Q8C23×C1111yescharacteristic
498C22×Q8C23×C1111yescharacteristic
499C22×Q8C23×C1111yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C23×C1111yescharacteristic
503C22×D4C23×C1111yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C1111yescharacteristic
509#135—232no—
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16D4×C1114yes—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8D4×C1114yes—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8C23×C1111yescharacteristic
532C22×C8C23×C1111yescharacteristic
533C22×C8C23×C1111yescharacteristic
534C22×C8C23×C1111yescharacteristic
535C4⋊Q8—22no—
536C4⋊Q8—41no—
537#124—22no—
538#124—41no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—41no—
544C4×D4—41no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4C23×C1111yescharacteristic
549C2×C4⋊C4C23×C1111yescharacteristic
550C2×C4⋊C4C23×C1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C1111yescharacteristic
560C2×C22⋊C4D4×C1111yescharacteristic
561C2×C42C23×C1111yescharacteristic
562C2×C42C23×C1111yescharacteristic
563C4⋊C8—22no—
564C4⋊C8—22no—
565#103—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—41no—
570#102—22no—
571#102—22no—
572#102—41no—
573C22⋊C8—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581#95D4×C1111yescharacteristic
582#95D4×C1111yescharacteristic
583C2×C11—42no—
584C2×C11—44no—
585C2×C11—82no—
586C2×C11#241011yescharacteristic
587C2×C11#303511yescharacteristic
588C2×C11#304611yescharacteristic
589C2×C11#326711yescharacteristic
590C2×C11#326911yescharacteristic
591C2×C11#328211yescharacteristic
592C2×C11#328311yescharacteristic
593C24—21no—
594C24—21no—
595C24C2×D4×C1111yescharacteristic
596#41—28no—
597#41—28no—
598#41—44no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—44no—
603#41—44no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8C2×D4×C1112yes—
621C2×Q8C2×D4×C1112yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4C2×D4×C1112yes—
637C2×D4C2×D4×C1112yes—
638C2×D4C2×D4×C1112yes—
639C2×D4C2×D4×C1112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C1111yescharacteristic
663C22×C4C2×D4×C1111yescharacteristic
664C22×C4C2×D4×C1111yescharacteristic
665C22×C4C2×D4×C1111yescharacteristic
666C22×C4C2×D4×C1112yes—
667C22×C4C2×D4×C1111yescharacteristic
668C22×C4C11×#4112yes—
669C22×C4C24×C1111yescharacteristic
670Q16—28no—
671Q16—44no—
672SD16—28no—
673SD16—28no—
674SD16—44no—
675D8—28no—
676C2×C8—28no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8C2×D4×C1112yes—
688C2×C8C2×D4×C1112yes—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C22⋊C4—22no—
699C22⋊C4—41no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C11#2436511yescharacteristic, direct product factor, Sylow
713C23—22no—
714C23—22no—
715C23—22no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23C11×#12112yes—
734C23C22×D4×C1111yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—22no—
738Q8—22no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—48no—
753D4—48no—
754D4—41no—
755D4—41no—
756D4C11×#12014yes—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—48no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
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—84no—
795C2×C4—84no—
796C2×C4C11×#12112yes—
797C2×C4C11×#13512yescomplemented
798C2×C4C22×D4×C1111yescharacteristic
799C2×C4C22×D4×C1111yescharacteristic
800C2×C4C22×D4×C1111yescharacteristic
801C2×C4C2×C11×#4111yescharacteristic
802C2×C4C11×H(5,𝔽2)11yescharacteristic
803C2×C4C11×H(5,𝔽2)11yescharacteristic
804C8—22no—
805C8—22no—
806C8—41no—
807C8—41no—
808C22—22no—
809C22—24no—
810C22—22no—
811C22—22no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22C2×C11×#12111yescharacteristic
830C22D42×C1111yescharacteristic
831C22D42×C1111yescharacteristic
832C22C2×C11×#13511yescharacteristic
833C22C11×#57511yescharacteristic
834C22C11×#57711yescharacteristic
835C22C11×#57811yescharacteristic
836C4—22no—
837C4—22no—
838C4—42no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4C2×C11×#12011yescharacteristic
848C4C11×#53411yescharacteristic
849C4C11×#54611yescharacteristic
850C4C11×#54611yescharacteristic
851C2—42no—
852C2—44no—
853C2—82no—
854C2C11×#241011yescharacteristic
855C2C11×#303511yescharacteristic
856C2C11×#304611yescharacteristic
857C2C11×#326711yescharacteristic
858C2C11×#326911yescharacteristic
859C2C11×#328211yescharacteristic
860C2C11×#328311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#135C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#463C2semidirect
3. C2×C11×#461C2semidirect
4. C2×C11×#452C2semidirect
5. C11×#2432C2semidirect
6. C11×#2339C2semidirect
7. C11×#2056C2semidirect
8. C11×#2055C2semidirect
9. C11×#2016C2semidirect
10. C11×#2015C2semidirect
11. C11×#1892C2semidirect
12. C11×#1879C2semidirect
13. C11×#1877C2semidirect
14. C11×#1850C2semidirect
15. C11×#1788C2semidirect
163. #24365C11direct (N × H)
284. C2×#463C2×C11semidirect
285. C2×#461C2×C11semidirect
286. C2×#452C2×C11semidirect
287. #2432C2×C11semidirect
288. #2339C2×C11semidirect
289. #2056C2×C11semidirect
290. #2055C2×C11semidirect
291. #2016C2×C11semidirect
292. #2015C2×C11semidirect
293. #1892C2×C11semidirect
294. #1879C2×C11semidirect
295. #1877C2×C11semidirect
296. #1850C2×C11semidirect
297. #1788C2×C11semidirect
382. C2×C4×C11#135semidirect
712. C11#24365direct (N × H)
797. C2×C4C11×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C2×C11×#4632
C2×C11×#4612
C2×C11×#4522
C11×#24322
C11×#23392
C11×#20562
C11×#20552
C11×#20162
C11×#20152
C11×#18922
C11×#18792
C11×#18772
C11×#18502
C11×#17882
#2436511