Finite Group Databasebeta

← C11×#22582 #14599775

Subgroups — C11×#22582 #14599775

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#417C211yesmaximal, characteristic
2C11×#2344C211yesmaximal, characteristic, complemented
3C11×#2339C211yesmaximal, characteristic
4C11×#1935C211yesmaximal, characteristic, complemented
5C11×#1933C211yesmaximal, characteristic, complemented
6C11×#1928C211yesmaximal, characteristic, complemented
7C11×#1927C211yesmaximal, characteristic, complemented
8C11×#1864C211yesmaximal, characteristic, complemented
9C11×#1862C211yesmaximal, characteristic, complemented
10C11×#1824C211yesmaximal, characteristic, complemented
11C11×#1809C211yesmaximal, characteristic, complemented
12C11×#1788C211yesmaximal, characteristic
13C11×#1762C211yesmaximal, characteristic, complemented
14C4×C11×#102C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C11×#417C418yescomplemented
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#391C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#387—21no—
41C11×#387—21no—
42C11×#386—21no—
43C11×#386—21no—
44C11×#381—21no—
45C11×#381—21no—
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51C2×C11×#95—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yes—
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C2×C11×M16—41no—
75C2×C11×M16—41no—
76C2×C11×M16C2×C414yescomplemented
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C11×#117—44no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2×C414yescomplemented
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C11×#107—41no—
108C11×#106—41no—
109C11×#103—41no—
110C11×#103—41no—
111C11×#103C2×C414yescomplemented
112C11×#103C2×C414yescomplemented
113C11×#102—22no—
114C11×#102—22no—
115C11×#102C2×C414yes—
116C11×#102C2×C414yes—
117C11×C22⋊C8—22no—
118C11×#97—41no—
119C4×C8×C11—41no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95D411yescharacteristic
131C11×#95D411yescharacteristic
132#22582C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C11×#41—28no—
136C11×#41—44no—
137C11×#41—44no—
138C11×#41—44no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C2×D4×C11—24no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11C22×C412yes—
152C2×D4×C11#4112yes—
153C2×D4×C11#4112yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
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—21no—
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—42no—
175C22×C4×C11—81no—
176C22×C4×C11—81no—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11#4112yes—
184C22×C4×C11C2411yescharacteristic
185C11×M16—44no—
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×C11—21no—
196C2×C8×C11C22×C412yes—
197C2×C8×C11C22×C412yes—
198C11×C4⋊C4—24no—
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—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4C22×C412yes—
212C11×C4⋊C4C22×C412yes—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—81no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—42no—
224C42×C11—42no—
225C2×#417C2×C1111yescharacteristic
226#2344C2×C1111yescharacteristic, complemented
227#2339C2×C1111yescharacteristic
228#1935C2×C1111yescharacteristic, complemented
229#1933C2×C1111yescharacteristic, complemented
230#1928C2×C1111yescharacteristic, complemented
231#1927C2×C1111yescharacteristic, complemented
232#1864C2×C1111yescharacteristic, complemented
233#1862C2×C1111yescharacteristic, complemented
234#1824C2×C1111yescharacteristic, complemented
235#1809C2×C1111yescharacteristic, complemented
236#1788C2×C1111yescharacteristic
237#1762C2×C1111yescharacteristic, complemented
238C4×#102C2×C1111yescharacteristic, complemented
239#1753C2×C1111yescharacteristic, complemented
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11C4×D412yes—
254C23×C11C22×D411yescharacteristic
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—41no—
258Q8×C11—41no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—48no—
263D4×C11#11714yescomplemented
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—48no—
285C2×C4×C11—48no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
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—84no—
305C2×C4×C11—84no—
306C2×C4×C11C4×D412yes—
307C2×C4×C11AGL(1,ℤ/8)12yes—
308C2×C4×C11C23×C411yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C8×C11—22no—
315C8×C11—22no—
316C8×C11—41no—
317C8×C11—41no—
318C22×#41C22×C1111yescharacteristic
319C22×M16C22×C1111yescharacteristic
320C2×C4×D4C22×C1111yescharacteristic
321C2×C4×D4C22×C1111yescharacteristic
322C2×#117—21no—
323C22×C4⋊C4C22×C1111yescharacteristic
324C2×#107C22×C1111yescharacteristic
325C2×#106C22×C1111yescharacteristic
326#417C4×C1118yescomplemented
327C2×#103C22×C1111yescharacteristic
328C2×#103C22×C1111yescharacteristic
329C2×#103C22×C1111yescharacteristic
330C2×#103C22×C1111yescharacteristic
331C2×#102C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×#102C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×C22⋊C8C22×C1111yescharacteristic
336C2×#97C22×C1111yescharacteristic
337C2×C4×C8C22×C1111yescharacteristic
338#391C22×C1111yescharacteristic
339#391C22×C1111yescharacteristic
340#389C22×C1111yescharacteristic
341#389C22×C1111yescharacteristic
342#387—21no—
343#387—21no—
344#386—21no—
345#386—21no—
346#381—21no—
347#381—21no—
348#380C22×C1111yescharacteristic
349#380C22×C1111yescharacteristic
350C4×C4⋊C4C22×C1111yescharacteristic
351C4×C4⋊C4C22×C1111yescharacteristic
352C4×C22⋊C4C22×C1111yescharacteristic
353C2×#95—21no—
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#336C22×C1111yescharacteristic
361#336C22×C1111yescharacteristic
362C22×C11—22no—
363C22×C11—24no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—41no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—41no—
376C22×C11C2×C4×D411yescharacteristic
377C22×C11#54611yescharacteristic
378C22×C11#54611yescharacteristic
379C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C11#57511yescharacteristic
381C22×C11#57711yescharacteristic
382C22×C11#57811yescharacteristic
383C4×C11—22no—
384C4×C11—22no—
385C4×C11—41no—
386C4×C11—42no—
387C4×C11—42no—
388C4×C11—42no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11—81no—
395C4×C11C2×#11711yescharacteristic
396C4×C11#51811yescharacteristic
397C4×C11#55111yescharacteristic
398C4×C11#55111yescharacteristic
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—41no—
403C2×#41—41no—
404C2×#41C2×C4×C1114yes—
405C22×Q8C23×C1111yescharacteristic
406C22×D4—21no—
407C22×D4C23×C1111yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C23×C4—21no—
411C23×C4—21no—
412C23×C4C23×C1111yescharacteristic
413C2×M16—41no—
414C2×M16—41no—
415C2×M16C2×C4×C1114yescomplemented
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—41no—
423C4×D4—41no—
424#117—44no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4C2×C4×C1114yescomplemented
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4D4×C1111yescharacteristic
441C2×C22⋊C4D4×C1111yescharacteristic
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C1111yescharacteristic
445C2×C42C23×C1111yescharacteristic
446#107—41no—
447#106—41no—
448#103—41no—
449#103—41no—
450#103C2×C4×C1114yescomplemented
451#103C2×C4×C1114yescomplemented
452#102—22no—
453#102—22no—
454#102C2×C4×C1114yes—
455#102C2×C4×C1114yes—
456C22⋊C8—22no—
457#97—41no—
458C4×C8—41no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95D4×C1111yescharacteristic
470#95D4×C1111yescharacteristic
471C2×C11—42no—
472C2×C11—44no—
473C2×C11#234211yescharacteristic
474C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
475C2×C11#294711yescharacteristic
476C2×C11#330611yescharacteristic
477C2×C11#331511yescharacteristic
478C2×C11#332311yescharacteristic
479C2×C11#333011yescharacteristic
480C24—21no—
481C24C2×D4×C1111yescharacteristic
482#41—28no—
483#41—44no—
484#41—44no—
485#41—44no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8C22×C4×C1112yes—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4C22×C4×C1112yes—
499C2×D4C11×#4112yes—
500C2×D4C11×#4112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4C22×C4×C1112yes—
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C11×#4112yes—
531C22×C4C24×C1111yescharacteristic
532M16—44no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8C22×C4×C1112yes—
544C2×C8C22×C4×C1112yes—
545C4⋊C4—24no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4C22×C4×C1112yes—
559C4⋊C4C22×C4×C1112yes—
560C22⋊C4—22no—
561C22⋊C4—41no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—42no—
572C11#2258211yescharacteristic, direct product factor, Sylow
573C23—22no—
574C23—22no—
575C23—22no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23C4×D4×C1112yes—
587C23C22×D4×C1111yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4—48no—
596D4C11×#11714yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—48no—
618C2×C4—48no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4C4×D4×C1112yes—
640C2×C4C11×AGL(1,ℤ/8)12yes—
641C2×C4C23×C4×C1111yescharacteristic
642C2×C4C2×C11×#4111yescharacteristic
643C2×C4C2×C11×#4111yescharacteristic
644C2×C4C2×C11×#4111yescharacteristic
645C2×C4C11×H(5,𝔽2)11yescharacteristic
646C2×C4C11×H(5,𝔽2)11yescharacteristic
647C8—22no—
648C8—22no—
649C8—41no—
650C8—41no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—24no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22C2×C4×D4×C1111yescharacteristic
666C22C11×#54611yescharacteristic
667C22C11×#54611yescharacteristic
668C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
669C22C11×#57511yescharacteristic
670C22C11×#57711yescharacteristic
671C22C11×#57811yescharacteristic
672C4—22no—
673C4—22no—
674C4—42no—
675C4—42no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—42no—
680C4—81no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4C2×C11×#11711yescharacteristic
685C4C11×#51811yescharacteristic
686C4C11×#55111yescharacteristic
687C4C11×#55111yescharacteristic
688C2—42no—
689C2—44no—
690C2C11×#234211yescharacteristic
691C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
692C2C11×#294711yescharacteristic
693C2C11×#330611yescharacteristic
694C2C11×#331511yescharacteristic
695C2C11×#332311yescharacteristic
696C2C11×#333011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×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. C11×#2344C2semidirect
4. C11×#1935C2semidirect
5. C11×#1933C2semidirect
6. C11×#1928C2semidirect
7. C11×#1927C2semidirect
8. C11×#1864C2semidirect
9. C11×#1862C2semidirect
10. C11×#1824C2semidirect
11. C11×#1809C2semidirect
13. C11×#1762C2semidirect
14. C4×C11×#102C2semidirect
15. C11×#1753C2semidirect
24. C11×#417C4semidirect
76. C2×C11×M16C2×C4semidirect
90. C2×C11×C4⋊C4C2×C4semidirect
111. C11×#103C2×C4semidirect
112. C11×#103C2×C4semidirect
132. #22582C11direct (N × H)
226. #2344C2×C11semidirect
228. #1935C2×C11semidirect
229. #1933C2×C11semidirect
230. #1928C2×C11semidirect
231. #1927C2×C11semidirect
232. #1864C2×C11semidirect
233. #1862C2×C11semidirect
234. #1824C2×C11semidirect
235. #1809C2×C11semidirect
237. #1762C2×C11semidirect
238. C4×#102C2×C11semidirect
239. #1753C2×C11semidirect
263. D4×C11#117semidirect
326. #417C4×C11semidirect
415. C2×M16C2×C4×C11semidirect
429. C2×C4⋊C4C2×C4×C11semidirect
450. #103C2×C4×C11semidirect
451. #103C2×C4×C11semidirect
572. C11#22582direct (N × H)
596. D4C11×#117semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4172
C11×#23442
C11×#23392
C11×#19352
C11×#19332
C11×#19282
C11×#19272
C11×#18642
C11×#18622
C11×#18242
C11×#18092
C11×#17882
C11×#17622
C4×C11×#1022
C11×#17532
#2258211