Finite Group Databasebeta

← C11×#60559 #14637752

Subgroups — C11×#60559 #14637752

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3444C211yesmaximal, characteristic, complemented
2C2×C4×C11×#41C211yesmaximal, characteristic, complemented
3C11×#3116C212yesmaximal, complemented
4C11×#3115C212yesmaximal, complemented
5C11×#3111C214yesmaximal, complemented
6C11×#3107C212yesmaximal, complemented
7C11×#3106C212yesmaximal, complemented
8C11×#3102C214yesmaximal, complemented
9C11×#3093C212yesmaximal, complemented
10C11×#3078C211yesmaximal, characteristic, complemented
11C11×#3077C211yesmaximal, characteristic, complemented
12C11×#3037C211yesmaximal, characteristic, complemented
13C11×#3036C211yesmaximal, characteristic, complemented
14C11×#3005C212yesmaximal, complemented
15C4×C11×#137C212yesmaximal, complemented
16C4×C11×AGL(1,ℤ/8)C212yesmaximal, complemented
17C11×#2920C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C2×C11×#137C2212yes—
20C2×C11×AGL(1,ℤ/8)C2212yes—
21C11×#533C2211yescharacteristic
22C11×#533C2211yescharacteristic, complemented
23C11×#533C2211yescharacteristic, complemented
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic, complemented
26C11×#532C2211yescharacteristic, complemented
27C11×#529—21no—
28C11×#529—21no—
29C11×#529—21no—
30C11×#529—21no—
31C11×#529C2212yescomplemented
32C11×#529C2212yescomplemented
33C11×#525—21no—
34C11×#525—21no—
35C11×#525C2212yes—
36C4×C11×#41—21no—
37C4×C11×#41—21no—
38C4×C11×#41—21no—
39C4×C11×#41—21no—
40C4×C11×#41—21no—
41C4×C11×#41—21no—
42C4×C11×#41C2212yes—
43C4×C11×#41C2212yes—
44C4×C11×#41C2212yes—
45C4×C11×#41C2212yes—
46C4×C11×#41C2212yes—
47C2×C4×Q8×C11C2211yescharacteristic
48C2×C4×Q8×C11C2211yescharacteristic
49C2×C4×D4×C11—21no—
50C2×C4×D4×C11—21no—
51C2×C4×D4×C11C2211yescharacteristic
52C2×C4×D4×C11C2211yescharacteristic
53C2×C11×#117—21no—
54C2×C11×#117C2211yescharacteristic
55C22×C42×C11—21no—
56C22×C42×C11C2211yescharacteristic
57C11×#485C2214yescomplemented
58C11×#485C2214yescomplemented
59C11×#482C2214yescomplemented
60C11×#482C2214yescomplemented
61C11×#479C2214yescomplemented
62C11×#478C2214yescomplemented
63C11×#477C2212yescomplemented
64C11×#476C2212yescomplemented
65C11×#475C2212yescomplemented
66C11×#474C2212yescomplemented
67C11×#464C2214yescomplemented
68C11×#463C2214yescomplemented
69C11×#462C2212yescomplemented
70C11×#461C2212yescomplemented
71C11×#460C2212yescomplemented
72C11×#459C2212yescomplemented
73C11×#452C2214yes—
74C11×#452C2214yes—
75C11×#449C2214yes—
76C11×#449C2214yes—
77C11×#442C2214yescomplemented
78C11×#441C2214yescomplemented
79C11×#440C2214yescomplemented
80C11×#440C2214yescomplemented
81C4×C11×Q16C2214yescomplemented
82C4×C11×SD16C2214yescomplemented
83C4×C11×SD16C2214yescomplemented
84C4×C11×D8C2214yescomplemented
85C11×#432C2212yescomplemented
86C11×#432C2212yescomplemented
87C11×#431C2212yescomplemented
88C11×#431C2212yescomplemented
89C11×#428C2212yes—
90C11×#428C2212yes—
91C11×#423C2211yescharacteristic
92C11×#423C2211yescharacteristic
93C11×#419C2212yes—
94C11×#418C2212yes—
95C11×#417C2212yes—
96C11×#417C2212yes—
97C11×#407C2212yes—
98C4×C11×M16C2212yes—
99C2×C11×#41—24no—
100C2×C11×#41—24no—
101C2×C11×#41—21no—
102C2×C11×#41—21no—
103C2×C11×#41—21no—
104C2×C11×#41—21no—
105C2×C11×#41C2312yes—
106C2×C11×#41C2312yes—
107C2×C11×#41C2312yes—
108C22×Q8×C11C2311yescharacteristic
109C22×D4×C11—21no—
110C22×D4×C11C2311yescharacteristic
111C23×C4×C11—21no—
112C23×C4×C11—21no—
113C23×C4×C11—21no—
114C23×C4×C11D411yescharacteristic
115C23×C4×C11D411yescharacteristic
116C23×C4×C11C2311yescharacteristic
117C11×#137—28no—
118C11×AGL(1,ℤ/8)—28no—
119C2×C11×Q16C2314yes—
120C2×C11×SD16C2314yes—
121C2×C11×SD16C2314yes—
122C2×C11×D8C2314yes—
123C2×C11×M16C2312yes—
124C2×C11×M16C2312yes—
125C11×C4⋊Q8C2311yescharacteristic
126C11×C4⋊Q8C2311yescharacteristic
127C11×C4⋊Q8C2311yescharacteristic
128C11×#127C2311yescharacteristic
129C11×#126—22no—
130C11×#126—22no—
131C11×#125—21no—
132C11×#125—21no—
133C11×#125C2312yes—
134C11×#124—21no—
135C11×#124—21no—
136C11×#124C2312yes—
137C11×#123—22no—
138C11×#123—22no—
139C11×#123—22no—
140C11×C22⋊Q8—21no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8—21no—
143C11×C22⋊Q8—21no—
144C11×C22⋊Q8C2312yes—
145C11×C22⋊Q8C2312yes—
146C11×#121—21no—
147C11×#121—21no—
148C11×#121—21no—
149C11×#121—21no—
150C11×#121C2312yes—
151C11×#121C2312yes—
152C11×#120—22no—
153C4×Q8×C11—21no—
154C4×Q8×C11—21no—
155C4×Q8×C11—21no—
156C4×Q8×C11—21no—
157C4×Q8×C11—21no—
158C4×Q8×C11—21no—
159C4×Q8×C11—21no—
160C4×Q8×C11—21no—
161C4×Q8×C11C2312yes—
162C4×Q8×C11C2312yes—
163C4×Q8×C11C2312yes—
164C4×Q8×C11C2312yes—
165C4×Q8×C11C2312yes—
166C4×Q8×C11C2312yes—
167C4×D4×C11—22no—
168C4×D4×C11—22no—
169C4×D4×C11—22no—
170C4×D4×C11—22no—
171C4×D4×C11—22no—
172C4×D4×C11—22no—
173C4×D4×C11—22no—
174C4×D4×C11—22no—
175C4×D4×C11—22no—
176C4×D4×C11—22no—
177C4×D4×C11—22no—
178C4×D4×C11—22no—
179C4×D4×C11—22no—
180C4×D4×C11—22no—
181C4×D4×C11—21no—
182C4×D4×C11—21no—
183C4×D4×C11—21no—
184C4×D4×C11—21no—
185C4×D4×C11—21no—
186C4×D4×C11—21no—
187C4×D4×C11—21no—
188C4×D4×C11—21no—
189C4×D4×C11C2312yes—
190C4×D4×C11C2312yes—
191C4×D4×C11C2312yes—
192C4×D4×C11C2312yes—
193C4×D4×C11C2312yes—
194C4×D4×C11C2312yes—
195C11×#117—21no—
196C11×#117—21no—
197C11×#117—21no—
198C11×#117—21no—
199C11×#117—22no—
200C11×#117—22no—
201C11×#117—22no—
202C11×#117—22no—
203C11×#117—22no—
204C11×#117—22no—
205C11×#117—22no—
206C11×#117C2312yes—
207C11×#117C2312yes—
208C11×#117C2312yes—
209C2×C11×C4⋊C4—21no—
210C2×C11×C4⋊C4—21no—
211C2×C11×C4⋊C4C2311yescharacteristic
212C2×C11×C4⋊C4C2311yescharacteristic
213C2×C11×C22⋊C4—21no—
214C2×C11×C22⋊C4—21no—
215C2×C11×C22⋊C4—21no—
216C2×C42×C11—21no—
217C2×C42×C11—21no—
218C2×C42×C11—21no—
219C2×C42×C11—22no—
220C2×C42×C11—22no—
221C2×C42×C11—22no—
222C2×C42×C11—22no—
223C2×C42×C11—22no—
224C2×C42×C11D411yescharacteristic
225C2×C42×C11D411yescharacteristic
226C2×C42×C11D411yescharacteristic
227C2×C42×C11D411yescharacteristic
228C2×C42×C11D411yescharacteristic
229C2×C42×C11D411yescharacteristic
230C2×C42×C11C2311yescharacteristic
231C2×C42×C11C2311yescharacteristic
232C2×C42×C11C2311yescharacteristic
233C2×C42×C11C2311yescharacteristic
234C2×C42×C11C2311yescharacteristic
235C2×C42×C11C2311yescharacteristic
236C11×#107C2314yes—
237C11×#107C2314yes—
238C11×#106C2314yes—
239C11×#106C2314yes—
240C11×C4⋊C8C2312yes—
241C11×C4⋊C8C2312yes—
242C11×C4⋊C8C2312yes—
243C11×C4⋊C8C2312yes—
244C11×#103C2314yes—
245C11×#103C2314yes—
246C11×#103C2314yes—
247C11×#103C2314yes—
248C11×#102C2314yes—
249C11×#102C2314yes—
250C11×#102C2314yes—
251C11×#102C2314yes—
252C11×C22⋊C8C2314yes—
253C11×C22⋊C8C2314yes—
254C11×#97C2314yes—
255C4×C8×C11C2314yes—
256#60559C1111yesmaximal, characteristic, direct product factor, Sylow
257C24×C11—21no—
258C24×C11C2×D411yescharacteristic
259C11×#41—28no—
260C11×#41—28no—
261C11×#41—24no—
262C11×#41—24no—
263C11×#41—24no—
264C11×#41—24no—
265C11×#41—24no—
266C11×#41—24no—
267C11×#41—44no—
268C11×#41—44no—
269C2×Q8×C11—21no—
270C2×Q8×C11—21no—
271C2×Q8×C11—21no—
272C2×Q8×C11—22no—
273C2×Q8×C11#4114yescomplemented
274C2×Q8×C11C2412yes—
275C2×Q8×C11C2412yes—
276C2×D4×C11—28no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—21no—
283C2×D4×C11—21no—
284C2×D4×C11—21no—
285C2×D4×C11—22no—
286C2×D4×C11#4114yescomplemented
287C2×D4×C11C2412yes—
288C2×D4×C11C2412yes—
289C22×C4×C11—28no—
290C22×C4×C11—21no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—21no—
296C22×C4×C11—21no—
297C22×C4×C11—22no—
298C22×C4×C11—22no—
299C22×C4×C11—22no—
300C22×C4×C11—22no—
301C22×C4×C11—22no—
302C22×C4×C11—22no—
303C22×C4×C11—22no—
304C22×C4×C11—42no—
305C22×C4×C11—42no—
306C22×C4×C11—44no—
307C22×C4×C11—44no—
308C22×C4×C11C2×D411yescharacteristic
309C22×C4×C11C2×D411yescharacteristic
310C22×C4×C11C2×D411yescharacteristic
311C22×C4×C11C2×D411yescharacteristic
312C22×C4×C11C2×D411yescharacteristic
313C22×C4×C11C2×D411yescharacteristic
314C22×C4×C11C2×D411yescharacteristic
315C22×C4×C11C2×D411yescharacteristic
316C22×C4×C11C2×D411yescharacteristic
317C22×C4×C11C2×D411yescharacteristic
318C22×C4×C11C2×D411yescharacteristic
319C22×C4×C11C2×D411yescharacteristic
320C22×C4×C11C2×D411yescharacteristic
321C22×C4×C11C2×D411yescharacteristic
322C22×C4×C11C2×D411yescharacteristic
323C22×C4×C11C2411yescharacteristic
324C22×C4×C11C2411yescharacteristic
325C22×C4×C11C2411yescharacteristic
326C11×Q16—28no—
327C11×SD16—28no—
328C11×SD16—28no—
329C11×D8—28no—
330C11×M16—24no—
331C11×M16—24no—
332C2×C8×C11C2414yes—
333C2×C8×C11C2414yes—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—22no—
336C11×C4⋊C4—22no—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—21no—
339C11×C4⋊C4—21no—
340C11×C4⋊C4—21no—
341C11×C4⋊C4—21no—
342C11×C4⋊C4—21no—
343C11×C4⋊C4—21no—
344C11×C4⋊C4—22no—
345C11×C4⋊C4—22no—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4C2412yes—
351C11×C4⋊C4C2412yes—
352C11×C4⋊C4C2412yes—
353C11×C4⋊C4C2412yes—
354C11×C22⋊C4—22no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—22no—
357C11×C22⋊C4—22no—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—22no—
368C11×C22⋊C4—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—22no—
373C42×C11—22no—
374C42×C11—22no—
375C42×C11—22no—
376C42×C11—22no—
377C42×C11—22no—
378C42×C11C2×D411yescharacteristic
379C42×C11C2×D411yescharacteristic
380C42×C11C2×D411yescharacteristic
381C42×C11C2×D411yescharacteristic
382C42×C11C2×D411yescharacteristic
383C42×C11C2×D411yescharacteristic
384C42×C11C2×D411yescharacteristic
385C42×C11C2×D411yescharacteristic
386C42×C11C2×D411yescharacteristic
387C42×C11C2×D411yescharacteristic
388C42×C11C2×D411yescharacteristic
389C42×C11C2×D411yescharacteristic
390C42×C11C2411yescharacteristic
391C42×C11C2411yescharacteristic
392C42×C11C2411yescharacteristic
393C42×C11C2411yescharacteristic
394#3444C2×C1111yescharacteristic, complemented
395C2×C4×#41C2×C1111yescharacteristic, complemented
396#3116C2×C1112yescomplemented
397#3115C2×C1112yescomplemented
398#3111C2×C1114yescomplemented
399#3107C2×C1112yescomplemented
400#3106C2×C1112yescomplemented
401#3102C2×C1114yescomplemented
402#3093C2×C1112yescomplemented
403#3078C2×C1111yescharacteristic, complemented
404#3077C2×C1111yescharacteristic, complemented
405#3037C2×C1111yescharacteristic, complemented
406#3036C2×C1111yescharacteristic, complemented
407#3005C2×C1112yescomplemented
408C4×#137C2×C1112yescomplemented
409C4×AGL(1,ℤ/8)C2×C1112yescomplemented
410#2920C2×C1111yescharacteristic, complemented
411C23×C11—22no—
412C23×C11—24no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—42no—
418C23×C11—42no—
419C23×C11C22×D411yescharacteristic
420C23×C11C22×D411yescharacteristic
421C23×C11C22×D411yescharacteristic
422Q8×C11—24no—
423Q8×C11—22no—
424Q8×C11—22no—
425Q8×C11—22no—
426Q8×C11—42no—
427Q8×C11—42no—
428Q8×C11C2×#4114yes—
429D4×C11—28no—
430D4×C11—28no—
431D4×C11—24no—
432D4×C11—22no—
433D4×C11—22no—
434D4×C11—22no—
435D4×C11—42no—
436D4×C11—44no—
437D4×C11—44no—
438D4×C11—44no—
439D4×C11—42no—
440D4×C11C2×#4114yes—
441C2×C4×C11—28no—
442C2×C4×C11—28no—
443C2×C4×C11—22no—
444C2×C4×C11—24no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—44no—
470C2×C4×C11—44no—
471C2×C4×C11—44no—
472C2×C4×C11—42no—
473C2×C4×C11—42no—
474C2×C4×C11—44no—
475C2×C4×C11—44no—
476C2×C4×C11—44no—
477C2×C4×C11—44no—
478C2×C4×C11C22×D411yescharacteristic
479C2×C4×C11C22×D411yescharacteristic
480C2×C4×C11C22×D411yescharacteristic
481C2×C4×C11C22×D411yescharacteristic
482C2×C4×C11C22×D411yescharacteristic
483C2×C4×C11C22×D411yescharacteristic
484C2×C4×C11C22×D411yescharacteristic
485C2×C4×C11C22×D411yescharacteristic
486C2×C4×C11C22×D411yescharacteristic
487C2×C4×C11C22×D411yescharacteristic
488C2×C4×C11C22×D411yescharacteristic
489C2×C4×C11C2×#4112yes—
490C2×C4×C11C2×#4112yes—
491C2×C4×C11C2511yescharacteristic
492C8×C11—24no—
493C8×C11—24no—
494C22×#41C22×C1111yescharacteristic
495C2×#137C22×C1112yes—
496C2×AGL(1,ℤ/8)C22×C1112yes—
497#533C22×C1111yescharacteristic
498#533C22×C1111yescharacteristic, complemented
499#533C22×C1111yescharacteristic, complemented
500#532C22×C1111yescharacteristic
501#532C22×C1111yescharacteristic, complemented
502#532C22×C1111yescharacteristic, complemented
503#529—21no—
504#529—21no—
505#529—21no—
506#529—21no—
507#529C22×C1112yescomplemented
508#529C22×C1112yescomplemented
509#525—21no—
510#525—21no—
511#525C22×C1112yes—
512C4×#41—21no—
513C4×#41—21no—
514C4×#41—21no—
515C4×#41—21no—
516C4×#41—21no—
517C4×#41—21no—
518C4×#41C22×C1112yes—
519C4×#41C22×C1112yes—
520C4×#41C22×C1112yes—
521C4×#41C22×C1112yes—
522C4×#41C22×C1112yes—
523C2×C4×Q8C22×C1111yescharacteristic
524C2×C4×Q8C22×C1111yescharacteristic
525C2×C4×D4—21no—
526C2×C4×D4—21no—
527C2×C4×D4C22×C1111yescharacteristic
528C2×C4×D4C22×C1111yescharacteristic
529C2×#117—21no—
530C2×#117C22×C1111yescharacteristic
531C22×C42—21no—
532C22×C42C22×C1111yescharacteristic
533#485C22×C1114yescomplemented
534#485C22×C1114yescomplemented
535#482C22×C1114yescomplemented
536#482C22×C1114yescomplemented
537#479C22×C1114yescomplemented
538#478C22×C1114yescomplemented
539#477C22×C1112yescomplemented
540#476C22×C1112yescomplemented
541#475C22×C1112yescomplemented
542#474C22×C1112yescomplemented
543#464C22×C1114yescomplemented
544#463C22×C1114yescomplemented
545#462C22×C1112yescomplemented
546#461C22×C1112yescomplemented
547#460C22×C1112yescomplemented
548#459C22×C1112yescomplemented
549#452C22×C1114yes—
550#452C22×C1114yes—
551#449C22×C1114yes—
552#449C22×C1114yes—
553#442C22×C1114yescomplemented
554#441C22×C1114yescomplemented
555#440C22×C1114yescomplemented
556#440C22×C1114yescomplemented
557C4×Q16C22×C1114yescomplemented
558C4×SD16C22×C1114yescomplemented
559C4×SD16C22×C1114yescomplemented
560C4×D8C22×C1114yescomplemented
561#432C22×C1112yescomplemented
562#432C22×C1112yescomplemented
563#431C22×C1112yescomplemented
564#431C22×C1112yescomplemented
565#428C22×C1112yes—
566#428C22×C1112yes—
567#423C22×C1111yescharacteristic
568#423C22×C1111yescharacteristic
569#419C22×C1112yes—
570#418C22×C1112yes—
571#417C22×C1112yes—
572#417C22×C1112yes—
573#407C22×C1112yes—
574C4×M16C22×C1112yes—
575C22×C11—21no—
576C22×C11—21no—
577C22×C11—21no—
578C22×C11—21no—
579C22×C11—24no—
580C22×C11—21no—
581C22×C11—21no—
582C22×C11—21no—
583C22×C11—21no—
584C22×C11—44no—
585C22×C11—48no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11#52512yes—
592C22×C11C23×D411yescharacteristic
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—24no—
596C4×C11—21no—
597C4×C11—21no—
598C4×C11—21no—
599C4×C11—21no—
600C4×C11—21no—
601C4×C11—21no—
602C4×C11—42no—
603C4×C11—42no—
604C4×C11—42no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11#52512yes—
608C4×C11#57512yes—
609C4×C11#57512yes—
610C4×C11C22×#4111yescharacteristic
611C4×C11C22×#4111yescharacteristic
612C2×#41—24no—
613C2×#41—24no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41C23×C1112yes—
619C2×#41C23×C1112yes—
620C2×#41C23×C1112yes—
621C22×Q8C23×C1111yescharacteristic
622C22×D4—21no—
623C22×D4C23×C1111yescharacteristic
624C23×C4—21no—
625C23×C4—21no—
626C23×C4—21no—
627C23×C4D4×C1111yescharacteristic
628C23×C4D4×C1111yescharacteristic
629C23×C4C23×C1111yescharacteristic
630#137—28no—
631AGL(1,ℤ/8)—28no—
632C2×Q16C23×C1114yes—
633C2×SD16C23×C1114yes—
634C2×SD16C23×C1114yes—
635C2×D8C23×C1114yes—
636C2×M16C23×C1112yes—
637C2×M16C23×C1112yes—
638C4⋊Q8C23×C1111yescharacteristic
639C4⋊Q8C23×C1111yescharacteristic
640C4⋊Q8C23×C1111yescharacteristic
641#127C23×C1111yescharacteristic
642#126—22no—
643#126—22no—
644#125—21no—
645#125—21no—
646#125C23×C1112yes—
647#124—21no—
648#124—21no—
649#124C23×C1112yes—
650#123—22no—
651#123—22no—
652#123—22no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8C23×C1112yes—
658C22⋊Q8C23×C1112yes—
659#121—21no—
660#121—21no—
661#121—21no—
662#121—21no—
663#121C23×C1112yes—
664#121C23×C1112yes—
665#120—22no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—21no—
670C4×Q8—21no—
671C4×Q8—21no—
672C4×Q8—21no—
673C4×Q8—21no—
674C4×Q8C23×C1112yes—
675C4×Q8C23×C1112yes—
676C4×Q8C23×C1112yes—
677C4×Q8C23×C1112yes—
678C4×Q8C23×C1112yes—
679C4×Q8C23×C1112yes—
680C4×D4—22no—
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—22no—
689C4×D4—22no—
690C4×D4—22no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—21no—
695C4×D4—21no—
696C4×D4—21no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4C23×C1112yes—
703C4×D4C23×C1112yes—
704C4×D4C23×C1112yes—
705C4×D4C23×C1112yes—
706C4×D4C23×C1112yes—
707C4×D4C23×C1112yes—
708#117—21no—
709#117—21no—
710#117—21no—
711#117—21no—
712#117—22no—
713#117—22no—
714#117—22no—
715#117—22no—
716#117—22no—
717#117—22no—
718#117—22no—
719#117C23×C1112yes—
720#117C23×C1112yes—
721#117C23×C1112yes—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4C23×C1111yescharacteristic
725C2×C4⋊C4C23×C1111yescharacteristic
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—22no—
737C2×C42D4×C1111yescharacteristic
738C2×C42D4×C1111yescharacteristic
739C2×C42D4×C1111yescharacteristic
740C2×C42D4×C1111yescharacteristic
741C2×C42D4×C1111yescharacteristic
742C2×C42D4×C1111yescharacteristic
743C2×C42C23×C1111yescharacteristic
744C2×C42C23×C1111yescharacteristic
745C2×C42C23×C1111yescharacteristic
746C2×C42C23×C1111yescharacteristic
747C2×C42C23×C1111yescharacteristic
748C2×C42C23×C1111yescharacteristic
749#107C23×C1114yes—
750#107C23×C1114yes—
751#106C23×C1114yes—
752#106C23×C1114yes—
753C4⋊C8C23×C1112yes—
754C4⋊C8C23×C1112yes—
755C4⋊C8C23×C1112yes—
756C4⋊C8C23×C1112yes—
757#103C23×C1114yes—
758#103C23×C1114yes—
759#103C23×C1114yes—
760#103C23×C1114yes—
761#102C23×C1114yes—
762#102C23×C1114yes—
763#102C23×C1114yes—
764#102C23×C1114yes—
765C22⋊C8C23×C1114yes—
766C22⋊C8C23×C1114yes—
767#97C23×C1114yes—
768C4×C8C23×C1114yes—
769C2×C11—22no—
770C2×C11—41no—
771C2×C11—41no—
772C2×C11—44no—
773C2×C11—82no—
774C2×C11C2×#52511yescharacteristic
775C2×C11C2×#57511yescharacteristic
776C2×C11C2×#57511yescharacteristic
777C24—21no—
778C24C2×D4×C1111yescharacteristic
779#41—28no—
780#41—28no—
781#41—24no—
782#41—24no—
783#41—24no—
784#41—24no—
785#41—24no—
786#41—24no—
787#41—44no—
788#41—44no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—22no—
793C2×Q8C11×#4114yescomplemented
794C2×Q8C24×C1112yes—
795C2×Q8C24×C1112yes—
796C2×D4—28no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—22no—
806C2×D4C11×#4114yescomplemented
807C2×D4C24×C1112yes—
808C2×D4C24×C1112yes—
809C22×C4—28no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4C2×D4×C1111yescharacteristic
829C22×C4C2×D4×C1111yescharacteristic
830C22×C4C2×D4×C1111yescharacteristic
831C22×C4C2×D4×C1111yescharacteristic
832C22×C4C2×D4×C1111yescharacteristic
833C22×C4C2×D4×C1111yescharacteristic
834C22×C4C2×D4×C1111yescharacteristic
835C22×C4C2×D4×C1111yescharacteristic
836C22×C4C2×D4×C1111yescharacteristic
837C22×C4C2×D4×C1111yescharacteristic
838C22×C4C2×D4×C1111yescharacteristic
839C22×C4C2×D4×C1111yescharacteristic
840C22×C4C2×D4×C1111yescharacteristic
841C22×C4C2×D4×C1111yescharacteristic
842C22×C4C2×D4×C1111yescharacteristic
843C22×C4C24×C1111yescharacteristic
844C22×C4C24×C1111yescharacteristic
845C22×C4C24×C1111yescharacteristic
846Q16—28no—
847SD16—28no—
848SD16—28no—
849D8—28no—
850M16—24no—
851M16—24no—
852C2×C8C24×C1114yes—
853C2×C8C24×C1114yes—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4C24×C1112yes—
871C4⋊C4C24×C1112yes—
872C4⋊C4C24×C1112yes—
873C4⋊C4C24×C1112yes—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—22no—
898C42C2×D4×C1111yescharacteristic
899C42C2×D4×C1111yescharacteristic
900C42C2×D4×C1111yescharacteristic
901C42C2×D4×C1111yescharacteristic
902C42C2×D4×C1111yescharacteristic
903C42C2×D4×C1111yescharacteristic
904C42C2×D4×C1111yescharacteristic
905C42C2×D4×C1111yescharacteristic
906C42C2×D4×C1111yescharacteristic
907C42C2×D4×C1111yescharacteristic
908C42C2×D4×C1111yescharacteristic
909C42C2×D4×C1111yescharacteristic
910C42C24×C1111yescharacteristic
911C42C24×C1111yescharacteristic
912C42C24×C1111yescharacteristic
913C42C24×C1111yescharacteristic
914C11#6055911yescharacteristic, direct product factor, Sylow
915C23—22no—
916C23—24no—
917C23—22no—
918C23—22no—
919C23—41no—
920C23—41no—
921C23—42no—
922C23—42no—
923C23C22×D4×C1111yescharacteristic
924C23C22×D4×C1111yescharacteristic
925C23C22×D4×C1111yescharacteristic
926Q8—24no—
927Q8—22no—
928Q8—22no—
929Q8—22no—
930Q8—42no—
931Q8—42no—
932Q8C2×C11×#4114yes—
933D4—28no—
934D4—28no—
935D4—24no—
936D4—22no—
937D4—22no—
938D4—22no—
939D4—42no—
940D4—44no—
941D4—44no—
942D4—44no—
943D4—42no—
944D4C2×C11×#4114yes—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4C22×D4×C1111yescharacteristic
983C2×C4C22×D4×C1111yescharacteristic
984C2×C4C22×D4×C1111yescharacteristic
985C2×C4C22×D4×C1111yescharacteristic
986C2×C4C22×D4×C1111yescharacteristic
987C2×C4C22×D4×C1111yescharacteristic
988C2×C4C22×D4×C1111yescharacteristic
989C2×C4C22×D4×C1111yescharacteristic
990C2×C4C22×D4×C1111yescharacteristic
991C2×C4C22×D4×C1111yescharacteristic
992C2×C4C22×D4×C1111yescharacteristic
993C2×C4C2×C11×#4112yes—
994C2×C4C2×C11×#4112yes—
995C2×C4C25×C1111yescharacteristic
996C8—24no—
997C8—24no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—24no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—44no—
1008C22—48no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22C11×#52512yes—
1015C22C23×D4×C1111yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—24no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—21no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4C11×#52512yes—
1031C4C11×#57512yes—
1032C4C11×#57512yes—
1033C4C22×C11×#4111yescharacteristic
1034C4C22×C11×#4111yescharacteristic
1035C2—22no—
1036C2—41no—
1037C2—41no—
1038C2—44no—
1039C2—82no—
1040C2C2×C11×#52511yescharacteristic
1041C2C2×C11×#57511yescharacteristic
1042C2C2×C11×#57511yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3444C2semidirect
2. C2×C4×C11×#41C2semidirect
3. C11×#3116C2semidirect
4. C11×#3115C2semidirect
5. C11×#3111C2semidirect
6. C11×#3107C2semidirect
7. C11×#3106C2semidirect
8. C11×#3102C2semidirect
9. C11×#3093C2semidirect
10. C11×#3078C2semidirect
11. C11×#3077C2semidirect
12. C11×#3037C2semidirect
13. C11×#3036C2semidirect
14. C11×#3005C2semidirect
15. C4×C11×#137C2semidirect
16. C4×C11×AGL(1,ℤ/8)C2semidirect
17. C11×#2920C2semidirect
22. C11×#533C22semidirect
23. C11×#533C22semidirect
25. C11×#532C22semidirect
26. C11×#532C22semidirect
31. C11×#529C22semidirect
32. C11×#529C22semidirect
57. C11×#485C22semidirect
58. C11×#485C22semidirect
59. C11×#482C22semidirect
60. C11×#482C22semidirect
61. C11×#479C22semidirect
62. C11×#478C22semidirect
63. C11×#477C22semidirect
64. C11×#476C22semidirect
65. C11×#475C22semidirect
66. C11×#474C22semidirect
67. C11×#464C22semidirect
68. C11×#463C22semidirect
69. C11×#462C22semidirect
70. C11×#461C22semidirect
71. C11×#460C22semidirect
72. C11×#459C22semidirect
77. C11×#442C22semidirect
78. C11×#441C22semidirect
79. C11×#440C22semidirect
80. C11×#440C22semidirect
81. C4×C11×Q16C22semidirect
82. C4×C11×SD16C22semidirect
83. C4×C11×SD16C22semidirect
84. C4×C11×D8C22semidirect
85. C11×#432C22semidirect
86. C11×#432C22semidirect
87. C11×#431C22semidirect
88. C11×#431C22semidirect
256. #60559C11direct (N × H)
273. C2×Q8×C11#41semidirect
286. C2×D4×C11#41semidirect
394. #3444C2×C11semidirect
395. C2×C4×#41C2×C11semidirect
396. #3116C2×C11semidirect
397. #3115C2×C11semidirect
398. #3111C2×C11semidirect
399. #3107C2×C11semidirect
400. #3106C2×C11semidirect
401. #3102C2×C11semidirect
402. #3093C2×C11semidirect
403. #3078C2×C11semidirect
404. #3077C2×C11semidirect
405. #3037C2×C11semidirect
406. #3036C2×C11semidirect
407. #3005C2×C11semidirect
408. C4×#137C2×C11semidirect
409. C4×AGL(1,ℤ/8)C2×C11semidirect
410. #2920C2×C11semidirect
498. #533C22×C11semidirect
499. #533C22×C11semidirect
501. #532C22×C11semidirect
502. #532C22×C11semidirect
507. #529C22×C11semidirect
508. #529C22×C11semidirect
533. #485C22×C11semidirect
534. #485C22×C11semidirect
535. #482C22×C11semidirect
536. #482C22×C11semidirect
537. #479C22×C11semidirect
538. #478C22×C11semidirect
539. #477C22×C11semidirect
540. #476C22×C11semidirect
541. #475C22×C11semidirect
542. #474C22×C11semidirect
543. #464C22×C11semidirect
544. #463C22×C11semidirect
545. #462C22×C11semidirect
546. #461C22×C11semidirect
547. #460C22×C11semidirect
548. #459C22×C11semidirect
553. #442C22×C11semidirect
554. #441C22×C11semidirect
555. #440C22×C11semidirect
556. #440C22×C11semidirect
557. C4×Q16C22×C11semidirect
558. C4×SD16C22×C11semidirect
559. C4×SD16C22×C11semidirect
560. C4×D8C22×C11semidirect
561. #432C22×C11semidirect
562. #432C22×C11semidirect
563. #431C22×C11semidirect
564. #431C22×C11semidirect
793. C2×Q8C11×#41semidirect
806. C2×D4C11×#41semidirect
914. C11#60559direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34442
C2×C4×C11×#412
C11×#31162
C11×#31152
C11×#31112
C11×#31072
C11×#31062
C11×#31022
C11×#30932
C11×#30782
C11×#30772
C11×#30372
C11×#30362
C11×#30052
C4×C11×#1372
C4×C11×AGL(1,ℤ/8)2
C11×#29202
#6055911