Finite Group Databasebeta

← C11×#32919 #14610112

Subgroups — C11×#32919 #14610112

Order 2816.

1448 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#520C211yesmaximal, characteristic, complemented
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C11×#463C211yesmaximal, characteristic, complemented
4C2×C11×#452C211yesmaximal, characteristic, complemented
5C2×C11×#449C211yesmaximal, characteristic
6C11×#2620C211yesmaximal, characteristic, complemented
7C11×#1880C211yesmaximal, characteristic, complemented
8C11×#1879C211yesmaximal, characteristic, complemented
9C11×#1878C211yesmaximal, characteristic, complemented
10C11×#1877C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C11×#1872C211yesmaximal, characteristic, complemented
13C11×#1803C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C11×#520—24no—
25C11×#520—24no—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117—21no—
33C2×C11×#117C2211yescharacteristic
34C22×C11×C4⋊C4—21no—
35C22×C11×C4⋊C4C2211yescharacteristic
36C11×#464—24no—
37C11×#463—24no—
38C11×#452—24no—
39C11×#449—24no—
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C11×#396—21no—
53C11×#396—21no—
54C11×#394—21no—
55C11×#394—21no—
56C11×#391C2211yescharacteristic
57C11×#390C2211yescharacteristic
58C11×#384C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
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×#41D414yes—
71C22×Q8×C11C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11C2311yescharacteristic
76C22×D4×C11C2311yescharacteristic
77C23×C4×C11—21no—
78C23×C4×C11—21no—
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C23×C4×C11C2311yescharacteristic
82C2×C11×Q16—22no—
83C2×C11×Q16—22no—
84C2×C11×Q16—22no—
85C2×C11×SD16—22no—
86C2×C11×SD16—22no—
87C2×C11×SD16—22no—
88C2×C11×SD16—22no—
89C2×C11×SD16—22no—
90C2×C11×SD16—22no—
91C2×C11×D8—22no—
92C2×C11×D8—22no—
93C2×C11×D8—22no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×#124—22no—
99C11×#124—22no—
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8—22no—
102C11×#121—22no—
103C11×#121—22no—
104C4×Q8×C11—22no—
105C4×Q8×C11—22no—
106C4×Q8×C11—22no—
107C4×Q8×C11D414yescomplemented
108C4×D4×C11—28no—
109C4×D4×C11—28no—
110C4×D4×C11—22no—
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C4×D4×C11D414yescomplemented
114C11×#117—28no—
115C11×#117—22no—
116C11×#117—22no—
117C2×C11×C4⋊C4—28no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—22no—
122C2×C11×C4⋊C4—22no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4D411yescharacteristic
127C2×C11×C4⋊C4D411yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C11×C22⋊C4D411yescharacteristic
142C2×C42×C11—21no—
143C2×C42×C11—21no—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C11×C4⋊C8—22no—
147C11×C4⋊C8—22no—
148C11×#103—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×C22⋊C8—22no—
157C11×C22⋊C8—22no—
158C11×#95—21no—
159C11×#95—21no—
160#32919C1111yesmaximal, characteristic, direct product factor, Sylow
161C24×C11—21no—
162C24×C11—21no—
163C24×C11C2×D411yescharacteristic
164C11×#41—28no—
165C11×#41—28no—
166C11×#41—28no—
167C11×#41—28no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
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×C11C2×D412yes—
178C2×Q8×C11C2×D412yes—
179C2×Q8×C11#4112yes—
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—42no—
193C2×D4×C11—81no—
194C2×D4×C11—81no—
195C2×D4×C11C2×D412yes—
196C2×D4×C11C2×D412yes—
197C2×D4×C11#4112yes—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
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—24no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—81no—
215C22×C4×C11—81no—
216C22×C4×C11—81no—
217C22×C4×C11—81no—
218C22×C4×C11—81no—
219C22×C4×C11—81no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D412yes—
226C22×C4×C11#4112yes—
227C22×C4×C11C2411yescharacteristic
228C11×Q16—44no—
229C11×SD16—44no—
230C11×SD16—44no—
231C11×D8—44no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
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—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—42no—
256C11×C4⋊C4—81no—
257C11×C4⋊C4—81no—
258C11×C4⋊C4C2×D412yes—
259C11×C4⋊C4C2×D412yes—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—22no—
264C11×C22⋊C4—42no—
265C11×C22⋊C4—42no—
266C11×C22⋊C4—42no—
267C11×C22⋊C4—42no—
268C11×C22⋊C4—81no—
269C11×C22⋊C4—81no—
270C42×C11—24no—
271C42×C11—24no—
272C42×C11—21no—
273C42×C11—21no—
274C42×C11C2×D412yes—
275C42×C11C2×D412yes—
276C2×#520C2×C1111yescharacteristic, complemented
277C2×#464C2×C1111yescharacteristic, complemented
278C2×#463C2×C1111yescharacteristic, complemented
279C2×#452C2×C1111yescharacteristic, complemented
280C2×#449C2×C1111yescharacteristic
281#2620C2×C1111yescharacteristic, complemented
282#1880C2×C1111yescharacteristic, complemented
283#1879C2×C1111yescharacteristic, complemented
284#1878C2×C1111yescharacteristic, complemented
285#1877C2×C1111yescharacteristic, complemented
286#1874C2×C1111yescharacteristic, complemented
287#1872C2×C1111yescharacteristic, complemented
288#1803C2×C1111yescharacteristic, complemented
289#1802C2×C1111yescharacteristic, complemented
290#1798C2×C1111yescharacteristic, complemented
291C23×C11—21no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—21no—
295C23×C11—22no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11#12112yes—
312C23×C11C22×D411yescharacteristic
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—41no—
317Q8×C11—41no—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11#12114yes—
321D4×C11—216no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—22no—
325D4×C11—41no—
326D4×C11—41no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—84no—
330D4×C11#12114yes—
331C2×C4×C11—216no—
332C2×C4×C11—22no—
333C2×C4×C11—21no—
334C2×C4×C11—22no—
335C2×C4×C11—21no—
336C2×C4×C11—22no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
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—84no—
367C2×C4×C11—84no—
368C2×C4×C11—84no—
369C2×C4×C11#12012yes—
370C2×C4×C11#12012yes—
371C2×C4×C11#12112yes—
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C2×#4111yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11C2×#4111yescharacteristic
378C8×C11—41no—
379C8×C11—41no—
380C8×C11—41no—
381C8×C11—41no—
382C22×#41C22×C1111yescharacteristic
383C22×Q16C22×C1111yescharacteristic
384C22×SD16C22×C1111yescharacteristic
385C22×SD16C22×C1111yescharacteristic
386C22×D8C22×C1111yescharacteristic
387C2×#124C22×C1111yescharacteristic
388C2×C22⋊Q8C22×C1111yescharacteristic
389C2×#121C22×C1111yescharacteristic
390#520—24no—
391#520—24no—
392C2×C4×Q8C22×C1111yescharacteristic
393C2×C4×Q8C22×C1111yescharacteristic
394C2×C4×D4—21no—
395C2×C4×D4—21no—
396C2×C4×D4C22×C1111yescharacteristic
397C2×C4×D4C22×C1111yescharacteristic
398C2×#117—21no—
399C2×#117C22×C1111yescharacteristic
400C22×C4⋊C4—21no—
401C22×C4⋊C4C22×C1111yescharacteristic
402#464—24no—
403#463—24no—
404#452—24no—
405#449—24no—
406C2×C4⋊C8C22×C1111yescharacteristic
407C2×C4⋊C8C22×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
418#396—21no—
419#396—21no—
420#394—21no—
421#394—21no—
422#391C22×C1111yescharacteristic
423#390C22×C1111yescharacteristic
424#384C22×C1111yescharacteristic
425#340C22×C1111yescharacteristic
426#340C22×C1111yescharacteristic
427#340C22×C1111yescharacteristic
428#340C22×C1111yescharacteristic
429#336C22×C1111yescharacteristic
430#336C22×C1111yescharacteristic
431C22×C11—22no—
432C22×C11—24no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—41no—
436C22×C11—42no—
437C22×C11—41no—
438C22×C11—42no—
439C22×C11—41no—
440C22×C11—42no—
441C22×C11—41no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—81no—
446C22×C11—81no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11—81no—
452C22×C11C2×#12011yescharacteristic
453C22×C11C2×#12111yescharacteristic
454C22×C11#52511yescharacteristic
455C22×C11#57611yescharacteristic
456C22×C11#57711yescharacteristic
457C22×C11#57711yescharacteristic
458C22×C11#57811yescharacteristic
459C4×C11—22no—
460C4×C11—24no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—41no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—41no—
467C4×C11—81no—
468C4×C11—81no—
469C4×C11—81no—
470C4×C11C2×#12111yescharacteristic
471C4×C11C2×#12111yescharacteristic
472C4×C11#52511yescharacteristic
473C4×C11#52511yescharacteristic
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41D4×C1114yes—
480C22×Q8C23×C1111yescharacteristic
481C22×Q8C23×C1111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C23×C1111yescharacteristic
485C22×D4C23×C1111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C23×C1111yescharacteristic
491C2×Q16—22no—
492C2×Q16—22no—
493C2×Q16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—22no—
503C22×C8C23×C1111yescharacteristic
504C22×C8C23×C1111yescharacteristic
505C22×C8C23×C1111yescharacteristic
506C22×C8C23×C1111yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511#121—22no—
512#121—22no—
513C4×Q8—22no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×Q8D4×C1114yescomplemented
517C4×D4—28no—
518C4×D4—28no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4D4×C1114yescomplemented
523#117—28no—
524#117—22no—
525#117—22no—
526C2×C4⋊C4—28no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4D4×C1111yescharacteristic
536C2×C4⋊C4D4×C1111yescharacteristic
537C2×C4⋊C4C23×C1111yescharacteristic
538C2×C4⋊C4C23×C1111yescharacteristic
539C2×C4⋊C4C23×C1111yescharacteristic
540C2×C4⋊C4C23×C1111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C1111yescharacteristic
550C2×C22⋊C4D4×C1111yescharacteristic
551C2×C42—21no—
552C2×C42—21no—
553C2×C42C23×C1111yescharacteristic
554C2×C42C23×C1111yescharacteristic
555C4⋊C8—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103—22no—
560#103—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565C22⋊C8—22no—
566C22⋊C8—22no—
567#95—21no—
568#95—21no—
569C2×C11—42no—
570C2×C11—44no—
571C2×C11—161no—
572C2×C11#284711yescharacteristic
573C2×C11#301211yescharacteristic
574C2×C11#301311yescharacteristic
575C2×C11#304511yescharacteristic
576C2×C11#304611yescharacteristic
577C2×C11#312411yescharacteristic
578C2×C11#312511yescharacteristic
579C24—21no—
580C24—21no—
581C24C2×D4×C1111yescharacteristic
582#41—28no—
583#41—28no—
584#41—28no—
585#41—28no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C1112yes—
596C2×Q8C2×D4×C1112yes—
597C2×Q8C11×#4112yes—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4C2×D4×C1112yes—
614C2×D4C2×D4×C1112yes—
615C2×D4C11×#4112yes—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C2×D4×C1111yescharacteristic
639C22×C4C2×D4×C1111yescharacteristic
640C22×C4C2×D4×C1111yescharacteristic
641C22×C4C2×D4×C1111yescharacteristic
642C22×C4C2×D4×C1111yescharacteristic
643C22×C4C2×D4×C1112yes—
644C22×C4C11×#4112yes—
645C22×C4C24×C1111yescharacteristic
646Q16—44no—
647SD16—44no—
648SD16—44no—
649D8—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—22no—
665C4⋊C4—24no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—42no—
674C4⋊C4—81no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C1112yes—
677C4⋊C4C2×D4×C1112yes—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C42—24no—
689C42—24no—
690C42—21no—
691C42—21no—
692C42C2×D4×C1112yes—
693C42C2×D4×C1112yes—
694C11#3291911yescharacteristic, direct product factor, Sylow
695C23—21no—
696C23—22no—
697C23—22no—
698C23—21no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C11×#12112yes—
716C23C22×D4×C1111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8C11×#12114yes—
725D4—216no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—84no—
734D4C11×#12114yes—
735C2×C4—216no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
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—84no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4C11×#12012yes—
774C2×C4C11×#12012yes—
775C2×C4C11×#12112yes—
776C2×C4C22×D4×C1111yescharacteristic
777C2×C4C22×D4×C1111yescharacteristic
778C2×C4C22×D4×C1111yescharacteristic
779C2×C4C2×C11×#4111yescharacteristic
780C2×C4C2×C11×#4111yescharacteristic
781C2×C4C2×C11×#4111yescharacteristic
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—24no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×C11×#12011yescharacteristic
808C22C2×C11×#12111yescharacteristic
809C22C11×#52511yescharacteristic
810C22C11×#57611yescharacteristic
811C22C11×#57711yescharacteristic
812C22C11×#57711yescharacteristic
813C22C11×#57811yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—24no—
818C4—41no—
819C4—42no—
820C4—42no—
821C4—41no—
822C4—81no—
823C4—81no—
824C4—81no—
825C4C2×C11×#12111yescharacteristic
826C4C2×C11×#12111yescharacteristic
827C4C11×#52511yescharacteristic
828C4C11×#52511yescharacteristic
829C2—42no—
830C2—44no—
831C2—161no—
832C2C11×#284711yescharacteristic
833C2C11×#301211yescharacteristic
834C2C11×#301311yescharacteristic
835C2C11×#304511yescharacteristic
836C2C11×#304611yescharacteristic
837C2C11×#312411yescharacteristic
838C2C11×#312511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
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
1. C2×C11×#520C2semidirect
2. C2×C11×#464C2semidirect
3. C2×C11×#463C2semidirect
4. C2×C11×#452C2semidirect
6. C11×#2620C2semidirect
7. C11×#1880C2semidirect
8. C11×#1879C2semidirect
9. C11×#1878C2semidirect
10. C11×#1877C2semidirect
11. C11×#1874C2semidirect
12. C11×#1872C2semidirect
13. C11×#1803C2semidirect
14. C11×#1802C2semidirect
15. C11×#1798C2semidirect
107. C4×Q8×C11D4semidirect
113. C4×D4×C11D4semidirect
160. #32919C11direct (N × H)
276. C2×#520C2×C11semidirect
277. C2×#464C2×C11semidirect
278. C2×#463C2×C11semidirect
279. C2×#452C2×C11semidirect
281. #2620C2×C11semidirect
282. #1880C2×C11semidirect
283. #1879C2×C11semidirect
284. #1878C2×C11semidirect
285. #1877C2×C11semidirect
286. #1874C2×C11semidirect
287. #1872C2×C11semidirect
288. #1803C2×C11semidirect
289. #1802C2×C11semidirect
290. #1798C2×C11semidirect
516. C4×Q8D4×C11semidirect
522. C4×D4D4×C11semidirect
694. C11#32919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5202
C2×C11×#4642
C2×C11×#4632
C2×C11×#4522
C2×C11×#4492
C11×#26202
C11×#18802
C11×#18792
C11×#18782
C11×#18772
C11×#18742
C11×#18722
C11×#18032
C11×#18022
C11×#17982
#3291911