Finite Group Databasebeta

← C11×#23011 #14600204

Subgroups — C11×#23011 #14600204

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2367C211yesmaximal, characteristic, complemented
5D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#1959C211yesmaximal, characteristic, complemented
7C11×#1947C211yesmaximal, characteristic, complemented
8C11×#1936C211yesmaximal, characteristic, complemented
9C11×#1933C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1862C211yesmaximal, characteristic, complemented
14C11×#1771C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4—21no—
25C11×#463C418yescomplemented
26C11×#440—24no—
27C4×C11×D8—24no—
28C2×C11×#107C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#388—21no—
47C11×#388—21no—
48C11×#385—21no—
49C11×#385—21no—
50C11×#385—21no—
51C11×#384C2211yescharacteristic
52C11×#380—21no—
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16C2×C414yescomplemented
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8C2×C414yes—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×#124—22no—
80C11×#124C2×C414yescomplemented
81C4×Q8×C11—22no—
82C4×Q8×C11—41no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—41no—
88C4×D4×C11—41no—
89C4×D4×C11—41no—
90C4×D4×C11C2×C414yescomplemented
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—44no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#107—22no—
118C11×#107—22no—
119C11×C4⋊C8C2×C414yescomplemented
120C11×#103—22no—
121C11×#103—41no—
122C11×#103C2×C414yescomplemented
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—41no—
126C11×#102C2×C414yescomplemented
127C11×#102D414yes—
128C11×#97—22no—
129C11×#97—22no—
130C4×C8×C11—22no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#23011C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C412yes—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C22×C412yes—
156C2×D4×C11C22×C412yes—
157C2×D4×C11C2×D412yes—
158C2×D4×C11#4112yes—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—81no—
175C22×C4×C11—81no—
176C22×C4×C11—81no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C11×SD16—28no—
185C11×D8—28no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C22×C412yes—
196C2×C8×C11C22×C412yes—
197C2×C8×C11C2×D412yes—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—41no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—81no—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4C2×D412yes—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—81no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—42no—
228C42×C11—81no—
229C42×C11C22×C412yes—
230C42×C11#4112yes—
231C2×#463C2×C1111yescharacteristic
232C2×#440C2×C1111yescharacteristic, complemented
233C2×C4×D8C2×C1111yescharacteristic
234#2367C2×C1111yescharacteristic, complemented
235D4×C4⋊C4C2×C1111yescharacteristic, complemented
236#1959C2×C1111yescharacteristic, complemented
237#1947C2×C1111yescharacteristic, complemented
238#1936C2×C1111yescharacteristic, complemented
239#1933C2×C1111yescharacteristic, complemented
240#1879C2×C1111yescharacteristic
241#1877C2×C1111yescharacteristic, complemented
242#1863C2×C1111yescharacteristic, complemented
243#1862C2×C1111yescharacteristic, complemented
244#1771C2×C1111yescharacteristic, complemented
245#1762C2×C1111yescharacteristic, complemented
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11C22×D411yescharacteristic
261Q8×C11—22no—
262Q8×C11—22no—
263Q8×C11—41no—
264Q8×C11—41no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11C4×D414yes—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—48no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—84no—
308C2×C4×C11—84no—
309C2×C4×C11—84no—
310C2×C4×C11C4×D412yes—
311C2×C4×C11C4×D412yes—
312C2×C4×C11AGL(1,ℤ/8)12yes—
313C2×C4×C11C23×C411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×C4×C112−1+411yescharacteristic
319C8×C11—22no—
320C8×C11—22no—
321C8×C11—22no—
322C8×C11—41no—
323C22×SD16C22×C1111yescharacteristic
324C22×D8C22×C1111yescharacteristic
325C2×#124C22×C1111yescharacteristic
326C2×C4×Q8C22×C1111yescharacteristic
327C2×C4×D4C22×C1111yescharacteristic
328C2×C4×D4C22×C1111yescharacteristic
329C2×C4×D4C22×C1111yescharacteristic
330C2×C4×D4C22×C1111yescharacteristic
331C22×C4⋊C4—21no—
332#463C4×C1118yescomplemented
333#440—24no—
334C4×D8—24no—
335C2×#107C22×C1111yescharacteristic
336C2×#107C22×C1111yescharacteristic
337C2×C4⋊C8C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#102C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#102C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#97C22×C1111yescharacteristic
347C2×#97C22×C1111yescharacteristic
348C2×C4×C8C22×C1111yescharacteristic
349#391C22×C1111yescharacteristic
350#390C22×C1111yescharacteristic
351#389C22×C1111yescharacteristic
352#389C22×C1111yescharacteristic
353#388—21no—
354#388—21no—
355#385—21no—
356#385—21no—
357#385—21no—
358#384C22×C1111yescharacteristic
359#380—21no—
360C4×C4⋊C4C22×C1111yescharacteristic
361C4×C4⋊C4C22×C1111yescharacteristic
362C4×C22⋊C4—21no—
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369C22×C11—24no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11C2×C4×D411yescharacteristic
384C22×C11D4211yescharacteristic
385C22×C11#54811yescharacteristic
386C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
387C22×C11#57511yescharacteristic
388C22×C11#57611yescharacteristic
389C22×C11#57811yescharacteristic
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11C2×C4×D411yescharacteristic
403C4×C11#52011yescharacteristic
404C4×C11#54711yescharacteristic
405C4×C11#55311yescharacteristic
406C22×Q8C23×C1111yescharacteristic
407C22×D4C23×C1111yescharacteristic
408C22×D4C23×C1111yescharacteristic
409C23×C4—21no—
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16C2×C4×C1114yescomplemented
416C2×D8—22no—
417C2×D8—22no—
418C2×D8C2×C4×C1114yes—
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423#124—22no—
424#124C2×C4×C1114yescomplemented
425C4×Q8—22no—
426C4×Q8—41no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—41no—
432C4×D4—41no—
433C4×D4—41no—
434C4×D4C2×C4×C1114yescomplemented
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—44no—
441C2×C4⋊C4D4×C1111yescharacteristic
442C2×C4⋊C4D4×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C4⋊C4C23×C1111yescharacteristic
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C23×C1111yescharacteristic
459C2×C42C23×C1111yescharacteristic
460C2×C42C23×C1111yescharacteristic
461#107—22no—
462#107—22no—
463C4⋊C8C2×C4×C1114yescomplemented
464#103—22no—
465#103—41no—
466#103C2×C4×C1114yescomplemented
467#102—22no—
468#102—22no—
469#102—41no—
470#102C2×C4×C1114yescomplemented
471#102D4×C1114yes—
472#97—22no—
473#97—22no—
474C4×C8—22no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95D4×C1111yescharacteristic
481#95D4×C1111yescharacteristic
482C2×C11—44no—
483C2×C11—82no—
484C2×C11#236111yescharacteristic
485C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
486C2×C11#295111yescharacteristic
487C2×C11#326411yescharacteristic
488C2×C11#326911yescharacteristic
489C2×C11#336711yescharacteristic
490C2×C11#337011yescharacteristic
491C24—21no—
492C24—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×C4×C1112yes—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4C22×C4×C1112yes—
508C2×D4C22×C4×C1112yes—
509C2×D4C2×D4×C1112yes—
510C2×D4C11×#4112yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C24×C1111yescharacteristic
536SD16—28no—
537D8—28no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8C22×C4×C1112yes—
548C2×C8C22×C4×C1112yes—
549C2×C8C2×D4×C1112yes—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—41no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4C22×C4×C1112yes—
566C4⋊C4C2×D4×C1112yes—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—81no—
581C42C22×C4×C1112yes—
582C42C11×#4112yes—
583C11#2301111yescharacteristic, direct product factor, Sylow
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C22×D4×C1111yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4C4×D4×C1114yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—48no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4C4×D4×C1112yes—
649C2×C4C4×D4×C1112yes—
650C2×C4C11×AGL(1,ℤ/8)12yes—
651C2×C4C23×C4×C1111yescharacteristic
652C2×C4C22×D4×C1111yescharacteristic
653C2×C4C2×C11×#4111yescharacteristic
654C2×C4C2×C11×#4111yescharacteristic
655C2×C4C11×H(5,𝔽2)11yescharacteristic
656C2×C4C11×2−1+411yescharacteristic
657C8—22no—
658C8—22no—
659C8—22no—
660C8—41no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×C4×D4×C1111yescharacteristic
676C22D42×C1111yescharacteristic
677C22C11×#54811yescharacteristic
678C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
679C22C11×#57511yescharacteristic
680C22C11×#57611yescharacteristic
681C22C11×#57811yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—41no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4C2×C4×D4×C1111yescharacteristic
695C4C11×#52011yescharacteristic
696C4C11×#54711yescharacteristic
697C4C11×#55311yescharacteristic
698C2—44no—
699C2—82no—
700C2C11×#236111yescharacteristic
701C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
702C2C11×#295111yescharacteristic
703C2C11×#326411yescharacteristic
704C2C11×#326911yescharacteristic
705C2C11×#336711yescharacteristic
706C2C11×#337011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×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
2. C2×C11×#440C2semidirect
4. C11×#2367C2semidirect
5. D4×C11×C4⋊C4C2semidirect
6. C11×#1959C2semidirect
7. C11×#1947C2semidirect
8. C11×#1936C2semidirect
9. C11×#1933C2semidirect
11. C11×#1877C2semidirect
12. C11×#1863C2semidirect
13. C11×#1862C2semidirect
14. C11×#1771C2semidirect
15. C11×#1762C2semidirect
25. C11×#463C4semidirect
71. C2×C11×SD16C2×C4semidirect
80. C11×#124C2×C4semidirect
90. C4×D4×C11C2×C4semidirect
119. C11×C4⋊C8C2×C4semidirect
122. C11×#103C2×C4semidirect
126. C11×#102C2×C4semidirect
138. #23011C11direct (N × H)
232. C2×#440C2×C11semidirect
234. #2367C2×C11semidirect
235. D4×C4⋊C4C2×C11semidirect
236. #1959C2×C11semidirect
237. #1947C2×C11semidirect
238. #1936C2×C11semidirect
239. #1933C2×C11semidirect
241. #1877C2×C11semidirect
242. #1863C2×C11semidirect
243. #1862C2×C11semidirect
244. #1771C2×C11semidirect
245. #1762C2×C11semidirect
332. #463C4×C11semidirect
415. C2×SD16C2×C4×C11semidirect
424. #124C2×C4×C11semidirect
434. C4×D4C2×C4×C11semidirect
463. C4⋊C8C2×C4×C11semidirect
466. #103C2×C4×C11semidirect
470. #102C2×C4×C11semidirect
583. C11#23011direct (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×#4402
C2×C4×C11×D82
C11×#23672
D4×C11×C4⋊C42
C11×#19592
C11×#19472
C11×#19362
C11×#19332
C11×#18792
C11×#18772
C11×#18632
C11×#18622
C11×#17712
C11×#17622
#2301111