Finite Group Databasebeta

← C11×#24738 #14601931

Subgroups — C11×#24738 #14601931

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4C2×C11×#442C211yesmaximal, characteristic, complemented
5C11×#2544C211yesmaximal, characteristic, complemented
6D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
7C11×#2066C211yesmaximal, characteristic, complemented
8C11×#2065C211yesmaximal, characteristic, complemented
9C11×#2042C211yesmaximal, characteristic, complemented
10C11×#2041C211yesmaximal, characteristic, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C11×#1940C211yesmaximal, characteristic, complemented
13C11×#1879C211yesmaximal, characteristic, complemented
14C11×#1877C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C4⋊C4—21no—
27C11×#463—24no—
28C11×#463—24no—
29C11×#459—24no—
30C11×#442—24no—
31C2×C11×#106C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#97C2211yescharacteristic
46C11×#394—21no—
47C11×#394—21no—
48C11×#391C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#389C2211yescharacteristic
52C11×#386—21no—
53C11×#386—21no—
54C11×#385—21no—
55C11×#385—21no—
56C11×#384C2211yescharacteristic
57C11×#380—21no—
58C4×C11×C4⋊C4C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×D8—22no—
77C2×C11×D8—22no—
78C2×C11×D8—22no—
79C2×C11×D8—22no—
80C2×C11×D8—22no—
81C2×C11×D8D414yes—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×#127—22no—
87C11×#127—41no—
88C11×#124—22no—
89C11×#124—22no—
90C11×#124—22no—
91C11×#124—41no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—41no—
98C4×D4×C11—41no—
99C4×D4×C11D414yescomplemented
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—44no—
105C2×C11×C4⋊C4D411yescharacteristic
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C11×#106—22no—
125C11×C4⋊C8—22no—
126C11×C4⋊C8—22no—
127C11×C4⋊C8—22no—
128C11×#103—22no—
129C11×#103—22no—
130C11×#103—41no—
131C11×#102—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—22no—
136C11×#102—22no—
137C11×#102—41no—
138C11×#97—22no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95D411yescharacteristic
144C11×#95D411yescharacteristic
145#24738C1111yesmaximal, characteristic, direct product factor, Sylow
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11C2×D412yes—
176C2×D4×C11C2×D412yes—
177C2×D4×C11C2×D412yes—
178C2×D4×C11#4112yes—
179C22×C4×C11—21no—
180C22×C4×C11—24no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—81no—
193C22×C4×C11—81no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C11×SD16—44no—
204C11×D8—28no—
205C11×D8—44no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11C2×D412yes—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—41no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—42no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4—81no—
231C11×C4⋊C4C2×D412yes—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—81no—
241C11×C22⋊C4—81no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—21no—
245C42×C11—21no—
246C42×C11C2×D412yes—
247C42×C11#4112yes—
248C2×#463C2×C1111yescharacteristic, complemented
249C2×#463C2×C1111yescharacteristic, complemented
250C2×#459C2×C1111yescharacteristic
251C2×#442C2×C1111yescharacteristic, complemented
252#2544C2×C1111yescharacteristic, complemented
253D4×C4⋊C4C2×C1111yescharacteristic, complemented
254#2066C2×C1111yescharacteristic, complemented
255#2065C2×C1111yescharacteristic, complemented
256#2042C2×C1111yescharacteristic, complemented
257#2041C2×C1111yescharacteristic, complemented
258#1959C2×C1111yescharacteristic, complemented
259#1940C2×C1111yescharacteristic, complemented
260#1879C2×C1111yescharacteristic, complemented
261#1877C2×C1111yescharacteristic, complemented
262#1802C2×C1111yescharacteristic, complemented
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11C22×D411yescharacteristic
285Q8×C11—41no—
286Q8×C11—41no—
287Q8×C11—41no—
288Q8×C11—41no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11—41no—
300D4×C11—84no—
301D4×C11—84no—
302D4×C11#12114yes—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—48no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—84no—
335C2×C4×C11—84no—
336C2×C4×C11—84no—
337C2×C4×C11#12112yes—
338C2×C4×C11#12112yes—
339C2×C4×C11AGL(1,ℤ/8)12yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C112−1+411yescharacteristic
346C8×C11—22no—
347C8×C11—41no—
348C8×C11—41no—
349C8×C11—41no—
350C22×SD16C22×C1111yescharacteristic
351C22×D8C22×C1111yescharacteristic
352C22×D8C22×C1111yescharacteristic
353C2×#127C22×C1111yescharacteristic
354C2×#124C22×C1111yescharacteristic
355C2×#124C22×C1111yescharacteristic
356C2×C4×D4C22×C1111yescharacteristic
357C2×C4×D4C22×C1111yescharacteristic
358C2×C4×D4C22×C1111yescharacteristic
359C2×C4×D4C22×C1111yescharacteristic
360C22×C4⋊C4—21no—
361#463—24no—
362#463—24no—
363#459—24no—
364#442—24no—
365C2×#106C22×C1111yescharacteristic
366C2×C4⋊C8C22×C1111yescharacteristic
367C2×C4⋊C8C22×C1111yescharacteristic
368C2×C4⋊C8C22×C1111yescharacteristic
369C2×#103C22×C1111yescharacteristic
370C2×#103C22×C1111yescharacteristic
371C2×#103C22×C1111yescharacteristic
372C2×#102C22×C1111yescharacteristic
373C2×#102C22×C1111yescharacteristic
374C2×#102C22×C1111yescharacteristic
375C2×#102C22×C1111yescharacteristic
376C2×#102C22×C1111yescharacteristic
377C2×#102C22×C1111yescharacteristic
378C2×#102C22×C1111yescharacteristic
379C2×#97C22×C1111yescharacteristic
380#394—21no—
381#394—21no—
382#391C22×C1111yescharacteristic
383#390C22×C1111yescharacteristic
384#389C22×C1111yescharacteristic
385#389C22×C1111yescharacteristic
386#386—21no—
387#386—21no—
388#385—21no—
389#385—21no—
390#384C22×C1111yescharacteristic
391#380—21no—
392C4×C4⋊C4C22×C1111yescharacteristic
393#340C22×C1111yescharacteristic
394#340C22×C1111yescharacteristic
395#336C22×C1111yescharacteristic
396#336C22×C1111yescharacteristic
397C22×C11—24no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11C2×#12111yescharacteristic
419C22×C11D4211yescharacteristic
420C22×C11#54811yescharacteristic
421C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
422C22×C11#57511yescharacteristic
423C22×C11#57611yescharacteristic
424C22×C11#57711yescharacteristic
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—22no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—42no—
432C4×C11—81no—
433C4×C11—81no—
434C4×C11—81no—
435C4×C11—81no—
436C4×C11C2×#12111yescharacteristic
437C4×C11#53711yescharacteristic
438C4×C11#54711yescharacteristic
439C4×C11#55311yescharacteristic
440C22×Q8C23×C1111yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4C23×C1111yescharacteristic
444C22×D4C23×C1111yescharacteristic
445C22×D4C23×C1111yescharacteristic
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—21no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×D8—22no—
454C2×D8—22no—
455C2×D8—22no—
456C2×D8—22no—
457C2×D8—22no—
458C2×D8D4×C1114yes—
459C22×C8C23×C1111yescharacteristic
460C22×C8C23×C1111yescharacteristic
461C22×C8C23×C1111yescharacteristic
462C22×C8C23×C1111yescharacteristic
463#127—22no—
464#127—41no—
465#124—22no—
466#124—22no—
467#124—22no—
468#124—41no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
476C4×D4D4×C1114yescomplemented
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—44no—
482C2×C4⋊C4D4×C1111yescharacteristic
483C2×C4⋊C4D4×C1111yescharacteristic
484C2×C4⋊C4C23×C1111yescharacteristic
485C2×C4⋊C4C23×C1111yescharacteristic
486C2×C4⋊C4C23×C1111yescharacteristic
487C2×C4⋊C4C23×C1111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C42C23×C1111yescharacteristic
499C2×C42C23×C1111yescharacteristic
500C2×C42C23×C1111yescharacteristic
501#106—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505#103—22no—
506#103—22no—
507#103—41no—
508#102—22no—
509#102—22no—
510#102—22no—
511#102—22no—
512#102—22no—
513#102—22no—
514#102—41no—
515#97—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95D4×C1111yescharacteristic
521#95D4×C1111yescharacteristic
522C2×C11—44no—
523C2×C11—82no—
524C2×C11—161no—
525C2×C11#241611yescharacteristic
526C2×C11#303611yescharacteristic
527C2×C11#304511yescharacteristic
528C2×C11#326411yescharacteristic
529C2×C11#326711yescharacteristic
530C2×C11#337011yescharacteristic
531C2×C11#337311yescharacteristic
532C24—21no—
533C24—21no—
534C24—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4C2×D4×C1112yes—
562C2×D4C2×D4×C1112yes—
563C2×D4C2×D4×C1112yes—
564C2×D4C11×#4112yes—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4C2×D4×C1111yescharacteristic
583C22×C4C2×D4×C1111yescharacteristic
584C22×C4C2×D4×C1111yescharacteristic
585C22×C4C2×D4×C1111yescharacteristic
586C22×C4C2×D4×C1111yescharacteristic
587C22×C4C2×D4×C1111yescharacteristic
588C22×C4C24×C1111yescharacteristic
589SD16—44no—
590D8—28no—
591D8—44no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8C2×D4×C1112yes—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—41no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—81no—
617C4⋊C4C2×D4×C1112yes—
618C22⋊C4—24no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42C2×D4×C1112yes—
633C42C11×#4112yes—
634C11#2473811yescharacteristic, direct product factor, Sylow
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
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—
656C23C22×D4×C1111yescharacteristic
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—84no—
673D4—84no—
674D4C11×#12114yes—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—48no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4C11×#12112yes—
710C2×C4C11×#12112yes—
711C2×C4C11×AGL(1,ℤ/8)12yes—
712C2×C4C22×D4×C1111yescharacteristic
713C2×C4C22×D4×C1111yescharacteristic
714C2×C4C2×C11×#4111yescharacteristic
715C2×C4C2×C11×#4111yescharacteristic
716C2×C4C11×H(5,𝔽2)11yescharacteristic
717C2×C4C11×2−1+411yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×C11×#12111yescharacteristic
744C22D42×C1111yescharacteristic
745C22C11×#54811yescharacteristic
746C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
747C22C11×#57511yescharacteristic
748C22C11×#57611yescharacteristic
749C22C11×#57711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—42no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C2×C11×#12111yescharacteristic
762C4C11×#53711yescharacteristic
763C4C11×#54711yescharacteristic
764C4C11×#55311yescharacteristic
765C2—44no—
766C2—82no—
767C2—161no—
768C2C11×#241611yescharacteristic
769C2C11×#303611yescharacteristic
770C2C11×#304511yescharacteristic
771C2C11×#326411yescharacteristic
772C2C11×#326711yescharacteristic
773C2C11×#337011yescharacteristic
774C2C11×#337311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#463C2semidirect
2. C2×C11×#463C2semidirect
4. C2×C11×#442C2semidirect
5. C11×#2544C2semidirect
6. D4×C11×C4⋊C4C2semidirect
7. C11×#2066C2semidirect
8. C11×#2065C2semidirect
9. C11×#2042C2semidirect
10. C11×#2041C2semidirect
11. C11×#1959C2semidirect
12. C11×#1940C2semidirect
13. C11×#1879C2semidirect
14. C11×#1877C2semidirect
15. C11×#1802C2semidirect
99. C4×D4×C11D4semidirect
145. #24738C11direct (N × H)
248. C2×#463C2×C11semidirect
249. C2×#463C2×C11semidirect
251. C2×#442C2×C11semidirect
252. #2544C2×C11semidirect
253. D4×C4⋊C4C2×C11semidirect
254. #2066C2×C11semidirect
255. #2065C2×C11semidirect
256. #2042C2×C11semidirect
257. #2041C2×C11semidirect
258. #1959C2×C11semidirect
259. #1940C2×C11semidirect
260. #1879C2×C11semidirect
261. #1877C2×C11semidirect
262. #1802C2×C11semidirect
476. C4×D4D4×C11semidirect
634. C11#24738direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4592
C2×C11×#4422
C11×#25442
D4×C11×C4⋊C42
C11×#20662
C11×#20652
C11×#20422
C11×#20412
C11×#19592
C11×#19402
C11×#18792
C11×#18772
C11×#18022
#2473811