Finite Group Databasebeta

← C11×#61070 #14638263

Subgroups — C11×#61070 #14638263

Order 2816.

2830 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
1C2×C11×#575C212yesmaximal, complemented
2D4×C11×#41C211yesmaximal, characteristic, complemented
3C2×C11×#550C211yesmaximal, characteristic, complemented
4C11×#3287C212yesmaximal, complemented
5C11×#3284C212yesmaximal, complemented
6C11×#3278C212yesmaximal, complemented
7C11×#3274C212yesmaximal, complemented
8C11×#3271C214yesmaximal, complemented
9C11×#3268C214yesmaximal, complemented
10C11×#3151C211yesmaximal, characteristic, complemented
11C11×#3055C212yesmaximal, complemented
12C11×#3038C211yesmaximal, characteristic, complemented
13C11×#3037C211yesmaximal, characteristic, complemented
14C11×#3006C212yesmaximal, complemented
15C11×#3005C212yesmaximal, complemented
16C4×C11×#137C211yesmaximal, characteristic, complemented
17D4×C11×M16C211yesmaximal, characteristic, complemented
18C22×C11×#41C2212yes—
19C22×C11×#41C2212yescomplemented
20C11×#575—216no—
21C2×C11×#137C2211yescharacteristic
22C2×C11×#137C2212yescomplemented
23C2×C11×#137C2214yescomplemented
24C2×C11×AGL(1,ℤ/8)C2212yes—
25C2×C11×AGL(1,ℤ/8)C2212yescomplemented
26C2×C11×AGL(1,ℤ/8)C2214yescomplemented
27C2×C11×AGL(1,ℤ/8)C2212yescomplemented
28C2×C11×#135C2214yescomplemented
29C2×C11×#135C2214yescomplemented
30C22×C11×M16C2212yescomplemented
31C11×#550—21no—
32C11×#550—21no—
33C11×#550—22no—
34C11×#550C2212yes—
35C11×#550C2214yescomplemented
36C11×#550C2212yescomplemented
37C11×#550C2211yescharacteristic, complemented
38D4×Q8×C11C2211yescharacteristic, complemented
39C11×#548C2212yescomplemented
40C11×#547—21no—
41C11×#547C2211yescharacteristic, complemented
42C11×#546—22no—
43C11×#546C2212yescomplemented
44D42×C11—21no—
45D42×C11C2211yescharacteristic, complemented
46C11×#532—21no—
47C11×#532C2211yescharacteristic
48C2×C11×#127—21no—
49C2×C11×#127C2211yescharacteristic, complemented
50C11×#525—22no—
51C11×#525C2212yes—
52C2×C11×#121—22no—
53C2×C11×#121C2212yescomplemented
54C4×C11×#41C2211yescharacteristic
55C2×C4×Q8×C11C2211yescharacteristic, complemented
56C2×C4×D4×C11—21no—
57C2×C4×D4×C11—21no—
58C2×C4×D4×C11C2211yescharacteristic
59C11×#496C2214yescomplemented
60C11×#493C2212yescomplemented
61C11×#492C2212yescomplemented
62C11×#469C2214yescomplemented
63C11×#468C2214yescomplemented
64C11×#466C2214yescomplemented
65C11×#465C2214yescomplemented
66C11×#464C2214yescomplemented
67C11×#462C2212yescomplemented
68C11×#460C2212yescomplemented
69C11×#460C2212yescomplemented
70C11×#460C2212yescomplemented
71C11×#459C2212yescomplemented
72C11×#459C2212yescomplemented
73C11×#452C2214yescomplemented
74C11×#452C2214yescomplemented
75C11×#449C2214yescomplemented
76C11×#449C2214yescomplemented
77C11×#449C2214yescomplemented
78C11×#449C2214yescomplemented
79C11×#448C2214yescomplemented
80C11×#447C2214yescomplemented
81C11×#441C2212yescomplemented
82C11×#440C2212yescomplemented
83C4×C11×Q16C2212yescomplemented
84C4×C11×SD16C2212yescomplemented
85C11×#436C2212yescomplemented
86C11×#435C2214yescomplemented
87C8×D4×C11C2212yescomplemented
88C11×#428C2211yescharacteristic, complemented
89C11×#423C2211yescharacteristic, complemented
90C11×#419C2211yescharacteristic, complemented
91C11×#418C2212yescomplemented
92C11×#417C2211yescharacteristic
93C11×#417C2212yescomplemented
94C11×#407C2212yescomplemented
95C4×C11×M16C2211yescharacteristic, complemented
96C2×C11×#41—22no—
97C2×C11×#41—22no—
98C2×C11×#41—22no—
99C2×C11×#41—22no—
100C2×C11×#41—28no—
101C2×C11×#41—28no—
102C2×C11×#41—44no—
103C2×C11×#41—44no—
104C2×C11×#41C2312yes—
105C2×C11×#41C2312yes—
106C2×C11×#41C2312yes—
107C2×C11×#41C2314yes—
108C2×C11×#41C2314yes—
109C2×C11×#41C2311yescharacteristic
110C22×Q8×C11C2312yes—
111C22×Q8×C11C2311yescharacteristic
112C22×D4×C11—22no—
113C22×D4×C11—22no—
114C22×D4×C11—22no—
115C22×D4×C11—21no—
116C22×D4×C11—21no—
117C22×D4×C11—21no—
118C22×D4×C11D411yescharacteristic
119C22×D4×C11C2312yes—
120C22×D4×C11C2312yes—
121C23×C4×C11—22no—
122C23×C4×C11—22no—
123C23×C4×C11C2312yes—
124C11×#137—28no—
125C11×#137—216no—
126C11×#137D418yescomplemented
127C11×AGL(1,ℤ/8)—28no—
128C11×AGL(1,ℤ/8)—216no—
129C11×AGL(1,ℤ/8)—28no—
130C11×AGL(1,ℤ/8)—44no—
131C11×#135—216no—
132C11×#135—216no—
133C2×C11×Q16C2314yes—
134C2×C11×Q16C2312yes—
135C2×C11×SD16C2314yes—
136C2×C11×SD16C2314yes—
137C2×C11×SD16C2314yes—
138C2×C11×SD16C2314yes—
139C2×C11×SD16C2312yes—
140C2×C11×D8C2314yes—
141C2×C11×D8C2314yes—
142C2×C11×D8C2314yes—
143C2×C11×M16—28no—
144C2×C11×M16C2311yescharacteristic
145C2×C11×M16C2312yes—
146C2×C11×M16C2314yes—
147C2×C11×M16C2311yescharacteristic
148C22×C8×C11C2314yes—
149C11×C4⋊Q8—21no—
150C11×C4⋊Q8C2311yescharacteristic
151C11×#127—22no—
152C11×#127—22no—
153C11×#127—24no—
154C11×#127—21no—
155C11×#127—21no—
156C11×#127—21no—
157C11×#127C2312yes—
158C11×#127C2311yescharacteristic
159C11×#127C2312yes—
160C11×#124—22no—
161C11×#124C2312yes—
162C11×#123—22no—
163C11×#123—22no—
164C11×#123—22no—
165C11×C22⋊Q8—22no—
166C11×C22⋊Q8—22no—
167C11×C22⋊Q8C2312yes—
168C11×C22⋊Q8C2312yes—
169C11×#121—22no—
170C11×#121—21no—
171C11×#121—22no—
172C11×#121—22no—
173C11×#121—21no—
174C11×#121—21no—
175C11×#121—21no—
176C11×#121—24no—
177C11×#121—24no—
178C11×#121—24no—
179C11×#121—24no—
180C11×#121—22no—
181C11×#121—22no—
182C11×#121C2314yes—
183C11×#121C2314yes—
184C11×#121C2312yes—
185C11×#121C2312yes—
186C11×#120—22no—
187C11×#120—22no—
188C11×#120—22no—
189C4×Q8×C11—21no—
190C4×Q8×C11—21no—
191C4×Q8×C11C2312yes—
192C4×Q8×C11C2312yes—
193C4×Q8×C11C2311yescharacteristic
194C4×Q8×C11C2311yescharacteristic
195C4×D4×C11—21no—
196C4×D4×C11—22no—
197C4×D4×C11—21no—
198C4×D4×C11—21no—
199C4×D4×C11—22no—
200C4×D4×C11—21no—
201C4×D4×C11—22no—
202C4×D4×C11—22no—
203C4×D4×C11—24no—
204C4×D4×C11—22no—
205C4×D4×C11—21no—
206C4×D4×C11—21no—
207C4×D4×C11D411yescharacteristic
208C4×D4×C11D412yes—
209C4×D4×C11D411yescharacteristic
210C4×D4×C11C2311yescharacteristic
211C4×D4×C11C2311yescharacteristic
212C4×D4×C11C2311yescharacteristic
213C4×D4×C11C2312yes—
214C4×D4×C11C2311yescharacteristic
215C11×#117—21no—
216C11×#117C2311yescharacteristic
217C2×C11×C4⋊C4—21no—
218C2×C11×C4⋊C4—21no—
219C2×C11×C4⋊C4D411yescharacteristic
220C2×C11×C4⋊C4C2311yescharacteristic
221C2×C11×C22⋊C4—22no—
222C2×C11×C22⋊C4—22no—
223C2×C11×C22⋊C4D412yes—
224C2×C42×C11—21no—
225C2×C42×C11—21no—
226C2×C42×C11C2311yescharacteristic
227C11×#107C2312yes—
228C11×#106C2312yes—
229C11×C4⋊C8C2312yes—
230C11×C4⋊C8C2312yes—
231C11×#103C2312yes—
232C11×#103C2314yes—
233C11×#103C2312yes—
234C11×#103C2312yes—
235C11×#102C2312yes—
236C11×#102C2314yes—
237C11×#102C2314yes—
238C11×#102C2314yes—
239C11×C22⋊C8C2314yes—
240C11×C22⋊C8C2314yes—
241C11×#97C2312yes—
242C4×C8×C11C2312yes—
243#61070C1111yesmaximal, characteristic, direct product factor, Sylow
244C24×C11—22no—
245C24×C11—22no—
246C24×C11C2×D412yes—
247C11×#41—22no—
248C11×#41—24no—
249C11×#41—28no—
250C11×#41—28no—
251C11×#41—24no—
252C11×#41—24no—
253C11×#41—24no—
254C11×#41—48no—
255C11×#41—44no—
256C11×#41—42no—
257C11×#41—44no—
258C11×#41—42no—
259C11×#41—48no—
260C11×#41—48no—
261C11×#41—48no—
262C11×#41C2×D414yes—
263C2×Q8×C11—21no—
264C2×Q8×C11—22no—
265C2×Q8×C11—22no—
266C2×Q8×C11—24no—
267C2×Q8×C11—42no—
268C2×Q8×C11C2×D414yescomplemented
269C2×Q8×C11C2412yes—
270C2×Q8×C11C2411yescharacteristic
271C2×Q8×C11C2412yes—
272C2×D4×C11—21no—
273C2×D4×C11—24no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—24no—
279C2×D4×C11—24no—
280C2×D4×C11—22no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—24no—
284C2×D4×C11—21no—
285C2×D4×C11—22no—
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—22no—
289C2×D4×C11—21no—
290C2×D4×C11—22no—
291C2×D4×C11—22no—
292C2×D4×C11—24no—
293C2×D4×C11—42no—
294C2×D4×C11—42no—
295C2×D4×C11—48no—
296C2×D4×C11—44no—
297C2×D4×C11—48no—
298C2×D4×C11—44no—
299C2×D4×C11—82no—
300C2×D4×C11—84no—
301C2×D4×C11C2×D411yescharacteristic
302C2×D4×C11C2×D411yescharacteristic
303C2×D4×C11C2×D412yes—
304C2×D4×C11C2412yes—
305C2×D4×C11C2414yes—
306C2×D4×C11C2411yescharacteristic
307C22×C4×C11—21no—
308C22×C4×C11—21no—
309C22×C4×C11—24no—
310C22×C4×C11—24no—
311C22×C4×C11—21no—
312C22×C4×C11—22no—
313C22×C4×C11—21no—
314C22×C4×C11—22no—
315C22×C4×C11—22no—
316C22×C4×C11—24no—
317C22×C4×C11—24no—
318C22×C4×C11—22no—
319C22×C4×C11—21no—
320C22×C4×C11—48no—
321C22×C4×C11—48no—
322C22×C4×C11C2×D411yescharacteristic
323C22×C4×C11C2×D412yes—
324C22×C4×C11C2×D412yes—
325C22×C4×C11C2×D412yes—
326C22×C4×C11C2×D411yescharacteristic
327C22×C4×C11C2412yes—
328C22×C4×C11C2412yes—
329C22×C4×C11C2411yescharacteristic
330C11×Q16—28no—
331C11×Q16C2×D418yescomplemented
332C11×SD16—28no—
333C11×SD16—28no—
334C11×SD16—28no—
335C11×SD16—44no—
336C11×SD16C2×D418yescomplemented
337C11×D8—28no—
338C11×D8—28no—
339C11×D8—44no—
340C11×M16—28no—
341C11×M16—24no—
342C11×M16—22no—
343C11×M16C2×D414yescomplemented
344C2×C8×C11—28no—
345C2×C8×C11C2412yes—
346C2×C8×C11C2414yes—
347C2×C8×C11C2412yes—
348C11×C4⋊C4—21no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—22no—
351C11×C4⋊C4—22no—
352C11×C4⋊C4—21no—
353C11×C4⋊C4—21no—
354C11×C4⋊C4—21no—
355C11×C4⋊C4—21no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4C2×D411yescharacteristic
358C11×C4⋊C4C2×D411yescharacteristic
359C11×C4⋊C4C2×D412yes—
360C11×C4⋊C4C2411yescharacteristic
361C11×C4⋊C4C2411yescharacteristic
362C11×C4⋊C4C2412yes—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—21no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—22no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—21no—
371C11×C22⋊C4—21no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4C2×D412yes—
375C11×C22⋊C4C2×D412yes—
376C11×C22⋊C4C2×D412yes—
377C11×C22⋊C4C2×D412yes—
378C42×C11—21no—
379C42×C11—21no—
380C42×C11—21no—
381C42×C11—22no—
382C42×C11—22no—
383C42×C11C2×D411yescharacteristic
384C42×C11C2×D411yescharacteristic
385C42×C11C2411yescharacteristic
386C42×C11C2411yescharacteristic
387C2×#575C2×C1112yescomplemented
388D4×#41C2×C1111yescharacteristic, complemented
389C2×#550C2×C1111yescharacteristic, complemented
390#3287C2×C1112yescomplemented
391#3284C2×C1112yescomplemented
392#3278C2×C1112yescomplemented
393#3274C2×C1112yescomplemented
394#3271C2×C1114yescomplemented
395#3268C2×C1114yescomplemented
396#3151C2×C1111yescharacteristic, complemented
397#3055C2×C1112yescomplemented
398#3038C2×C1111yescharacteristic, complemented
399#3037C2×C1111yescharacteristic, complemented
400#3006C2×C1112yescomplemented
401#3005C2×C1112yescomplemented
402C4×#137C2×C1111yescharacteristic, complemented
403D4×M16C2×C1111yescharacteristic, complemented
404C23×C11—21no—
405C23×C11—24no—
406C23×C11—22no—
407C23×C11—24no—
408C23×C11—42no—
409C23×C11—42no—
410C23×C11—44no—
411C23×C11—44no—
412C23×C11—44no—
413C23×C11—44no—
414C23×C11—44no—
415C23×C11—82no—
416C23×C11C22×D412yes—
417C23×C11C22×D412yes—
418C23×C11C22×D411yescharacteristic
419Q8×C11—24no—
420Q8×C11—22no—
421Q8×C11—21no—
422Q8×C11—22no—
423Q8×C11—22no—
424Q8×C11—44no—
425Q8×C11C22×D412yes—
426Q8×C11C22×D414yes—
427D4×C11—24no—
428D4×C11—22no—
429D4×C11—22no—
430D4×C11—22no—
431D4×C11—24no—
432D4×C11—21no—
433D4×C11—22no—
434D4×C11—24no—
435D4×C11—42no—
436D4×C11—44no—
437D4×C11—44no—
438D4×C11—48no—
439D4×C11—48no—
440D4×C11—44no—
441D4×C11—44no—
442D4×C11—44no—
443D4×C11—44no—
444D4×C11—44no—
445D4×C11—42no—
446D4×C11—44no—
447D4×C11—81no—
448D4×C11—82no—
449D4×C11—82no—
450D4×C11—82no—
451D4×C11—84no—
452D4×C11—84no—
453D4×C11C22×D412yes—
454C2×C4×C11—24no—
455C2×C4×C11—24no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—24no—
459C2×C4×C11—24no—
460C2×C4×C11—24no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—41no—
471C2×C4×C11—44no—
472C2×C4×C11—48no—
473C2×C4×C11—48no—
474C2×C4×C11—44no—
475C2×C4×C11—44no—
476C2×C4×C11—42no—
477C2×C4×C11—44no—
478C2×C4×C11—42no—
479C2×C4×C11—81no—
480C2×C4×C11C22×D411yescharacteristic
481C2×C4×C11C22×D411yescharacteristic
482C2×C4×C11C22×D411yescharacteristic
483C2×C4×C11C22×D412yes—
484C2×C4×C11C22×D412yes—
485C2×C4×C11C22×D411yescharacteristic
486C2×C4×C11C22×D412yes—
487C2×C4×C11C22×D411yescharacteristic
488C2×C4×C11H(5,𝔽2)12yes—
489C2×C4×C11C2511yescharacteristic
490C8×C11—24no—
491C8×C11—22no—
492C8×C11C22×D414yes—
493C22×#41C22×C1112yes—
494C22×#41C22×C1112yescomplemented
495#575—216no—
496C2×#137C22×C1111yescharacteristic
497C2×#137C22×C1112yescomplemented
498C2×#137C22×C1114yescomplemented
499C2×AGL(1,ℤ/8)C22×C1112yes—
500C2×AGL(1,ℤ/8)C22×C1112yescomplemented
501C2×AGL(1,ℤ/8)C22×C1114yescomplemented
502C2×AGL(1,ℤ/8)C22×C1112yescomplemented
503C2×#135C22×C1114yescomplemented
504C2×#135C22×C1114yescomplemented
505C22×M16C22×C1112yescomplemented
506#550—21no—
507#550—21no—
508#550—22no—
509#550C22×C1112yes—
510#550C22×C1114yescomplemented
511#550C22×C1112yescomplemented
512#550C22×C1111yescharacteristic, complemented
513D4×Q8C22×C1111yescharacteristic, complemented
514#548C22×C1112yescomplemented
515#547—21no—
516#547C22×C1111yescharacteristic, complemented
517#546—22no—
518#546C22×C1112yescomplemented
519D42—21no—
520D42C22×C1111yescharacteristic, complemented
521#532—21no—
522#532C22×C1111yescharacteristic
523C2×#127—21no—
524C2×#127C22×C1111yescharacteristic, complemented
525#525—22no—
526#525C22×C1112yes—
527C2×#121—22no—
528C2×#121C22×C1112yescomplemented
529C4×#41C22×C1111yescharacteristic
530C2×C4×Q8C22×C1111yescharacteristic, complemented
531C2×C4×D4—21no—
532C2×C4×D4—21no—
533C2×C4×D4C22×C1111yescharacteristic
534#496C22×C1114yescomplemented
535#493C22×C1112yescomplemented
536#492C22×C1112yescomplemented
537#469C22×C1114yescomplemented
538#468C22×C1114yescomplemented
539#466C22×C1114yescomplemented
540#465C22×C1114yescomplemented
541#464C22×C1114yescomplemented
542#462C22×C1112yescomplemented
543#460C22×C1112yescomplemented
544#460C22×C1112yescomplemented
545#460C22×C1112yescomplemented
546#459C22×C1112yescomplemented
547#459C22×C1112yescomplemented
548#452C22×C1114yescomplemented
549#452C22×C1114yescomplemented
550#449C22×C1114yescomplemented
551#449C22×C1114yescomplemented
552#449C22×C1114yescomplemented
553#449C22×C1114yescomplemented
554#448C22×C1114yescomplemented
555#447C22×C1114yescomplemented
556#441C22×C1112yescomplemented
557#440C22×C1112yescomplemented
558C4×Q16C22×C1112yescomplemented
559C4×SD16C22×C1112yescomplemented
560#436C22×C1112yescomplemented
561#435C22×C1114yescomplemented
562C8×D4C22×C1112yescomplemented
563#428C22×C1111yescharacteristic, complemented
564#423C22×C1111yescharacteristic, complemented
565#419C22×C1111yescharacteristic, complemented
566#418C22×C1112yescomplemented
567#417C22×C1111yescharacteristic
568#417C22×C1112yescomplemented
569#407C22×C1112yescomplemented
570C4×M16C22×C1111yescharacteristic, complemented
571C22×C11—21no—
572C22×C11—21no—
573C22×C11—22no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—22no—
577C22×C11—22no—
578C22×C11—22no—
579C22×C11—22no—
580C22×C11—41no—
581C22×C11—41no—
582C22×C11—44no—
583C22×C11—42no—
584C22×C11—44no—
585C22×C11—42no—
586C22×C11—44no—
587C22×C11—42no—
588C22×C11—84no—
589C22×C11—88no—
590C22×C11—88no—
591C22×C11D4212yes—
592C22×C11C23×D411yescharacteristic
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—22no—
598C4×C11—24no—
599C4×C11—21no—
600C4×C11—42no—
601C4×C11—41no—
602C4×C11—42no—
603C4×C11—41no—
604C4×C11D4212yes—
605C4×C11#57512yescomplemented
606C4×C11C23×D411yescharacteristic
607C4×C11C2×H(5,𝔽2)11yescharacteristic
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—22no—
611C2×#41—22no—
612C2×#41—28no—
613C2×#41—28no—
614C2×#41—44no—
615C2×#41—44no—
616C2×#41C23×C1112yes—
617C2×#41C23×C1112yes—
618C2×#41C23×C1112yes—
619C2×#41C23×C1114yes—
620C2×#41C23×C1114yes—
621C2×#41C23×C1111yescharacteristic
622C22×Q8C23×C1112yes—
623C22×Q8C23×C1111yescharacteristic
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4—21no—
630C22×D4D4×C1111yescharacteristic
631C22×D4C23×C1112yes—
632C22×D4C23×C1112yes—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4C23×C1112yes—
636#137—28no—
637#137—216no—
638#137D4×C1118yescomplemented
639AGL(1,ℤ/8)—28no—
640AGL(1,ℤ/8)—216no—
641AGL(1,ℤ/8)—28no—
642AGL(1,ℤ/8)—44no—
643#135—216no—
644#135—216no—
645C2×Q16C23×C1114yes—
646C2×Q16C23×C1112yes—
647C2×SD16C23×C1114yes—
648C2×SD16C23×C1114yes—
649C2×SD16C23×C1114yes—
650C2×SD16C23×C1114yes—
651C2×SD16C23×C1112yes—
652C2×D8C23×C1114yes—
653C2×D8C23×C1114yes—
654C2×D8C23×C1114yes—
655C2×M16—28no—
656C2×M16C23×C1112yes—
657C2×M16C23×C1114yes—
658C2×M16C23×C1111yescharacteristic
659C2×M16C23×C1111yescharacteristic
660C22×C8C23×C1114yes—
661C4⋊Q8—21no—
662C4⋊Q8C23×C1111yescharacteristic
663#127—22no—
664#127—22no—
665#127—24no—
666#127—21no—
667#127—21no—
668#127—21no—
669#127C23×C1112yes—
670#127C23×C1112yes—
671#127C23×C1111yescharacteristic
672#124—22no—
673#124C23×C1112yes—
674#123—22no—
675#123—22no—
676#123—22no—
677C22⋊Q8—22no—
678C22⋊Q8—22no—
679C22⋊Q8C23×C1112yes—
680C22⋊Q8C23×C1112yes—
681#121—22no—
682#121—21no—
683#121—22no—
684#121—22no—
685#121—21no—
686#121—21no—
687#121—21no—
688#121—24no—
689#121—24no—
690#121—24no—
691#121—24no—
692#121—22no—
693#121—22no—
694#121C23×C1114yes—
695#121C23×C1114yes—
696#121C23×C1112yes—
697#121C23×C1112yes—
698#120—22no—
699#120—22no—
700#120—22no—
701C4×Q8—21no—
702C4×Q8—21no—
703C4×Q8C23×C1112yes—
704C4×Q8C23×C1112yes—
705C4×Q8C23×C1111yescharacteristic
706C4×Q8C23×C1111yescharacteristic
707C4×D4—21no—
708C4×D4—22no—
709C4×D4—21no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—22no—
714C4×D4—22no—
715C4×D4—24no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—21no—
719C4×D4D4×C1111yescharacteristic
720C4×D4D4×C1112yes—
721C4×D4D4×C1111yescharacteristic
722C4×D4C23×C1111yescharacteristic
723C4×D4C23×C1111yescharacteristic
724C4×D4C23×C1111yescharacteristic
725C4×D4C23×C1112yes—
726C4×D4C23×C1111yescharacteristic
727#117—21no—
728#117C23×C1111yescharacteristic
729C2×C4⋊C4—21no—
730C2×C4⋊C4—21no—
731C2×C4⋊C4D4×C1111yescharacteristic
732C2×C4⋊C4C23×C1111yescharacteristic
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4D4×C1112yes—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42C23×C1111yescharacteristic
739#107C23×C1112yes—
740#106C23×C1112yes—
741C4⋊C8C23×C1112yes—
742C4⋊C8C23×C1112yes—
743#103C23×C1112yes—
744#103C23×C1114yes—
745#103C23×C1112yes—
746#103C23×C1112yes—
747#102C23×C1112yes—
748#102C23×C1114yes—
749#102C23×C1114yes—
750#102C23×C1114yes—
751C22⋊C8C23×C1114yes—
752C22⋊C8C23×C1114yes—
753#97C23×C1112yes—
754C4×C8C23×C1112yes—
755C2×C11—22no—
756C2×C11—42no—
757C2×C11—42no—
758C2×C11—42no—
759C2×C11—84no—
760C2×C11—82no—
761C2×C11C2×D4211yescharacteristic
762C2×C11C2×#57511yescharacteristic
763C2×C11#358511yescharacteristic
764C24—22no—
765C24—22no—
766C24C2×D4×C1112yes—
767#41—22no—
768#41—24no—
769#41—28no—
770#41—28no—
771#41—24no—
772#41—24no—
773#41—24no—
774#41—48no—
775#41—44no—
776#41—42no—
777#41—44no—
778#41—42no—
779#41—48no—
780#41—48no—
781#41—48no—
782#41C2×D4×C1114yes—
783C2×Q8—21no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—42no—
788C2×Q8C2×D4×C1114yescomplemented
789C2×Q8C24×C1112yes—
790C2×Q8C24×C1111yescharacteristic
791C2×Q8C24×C1112yes—
792C2×D4—21no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—21no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—21no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—48no—
816C2×D4—44no—
817C2×D4—48no—
818C2×D4—44no—
819C2×D4—82no—
820C2×D4—84no—
821C2×D4C2×D4×C1111yescharacteristic
822C2×D4C2×D4×C1111yescharacteristic
823C2×D4C2×D4×C1112yes—
824C2×D4C24×C1112yes—
825C2×D4C24×C1114yes—
826C2×D4C24×C1111yescharacteristic
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4C2×D4×C1111yescharacteristic
843C22×C4C2×D4×C1112yes—
844C22×C4C2×D4×C1112yes—
845C22×C4C2×D4×C1112yes—
846C22×C4C2×D4×C1111yescharacteristic
847C22×C4C24×C1112yes—
848C22×C4C24×C1112yes—
849C22×C4C24×C1111yescharacteristic
850Q16—28no—
851Q16C2×D4×C1118yescomplemented
852SD16—28no—
853SD16—28no—
854SD16—28no—
855SD16—44no—
856SD16C2×D4×C1118yescomplemented
857D8—28no—
858D8—28no—
859D8—44no—
860M16—24no—
861M16—22no—
862M16—28no—
863M16C2×D4×C1114yescomplemented
864C2×C8—28no—
865C2×C8C24×C1112yes—
866C2×C8C24×C1114yes—
867C2×C8C24×C1112yes—
868C4⋊C4—21no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—22no—
877C4⋊C4C2×D4×C1111yescharacteristic
878C4⋊C4C2×D4×C1111yescharacteristic
879C4⋊C4C2×D4×C1112yes—
880C4⋊C4C24×C1111yescharacteristic
881C4⋊C4C24×C1111yescharacteristic
882C4⋊C4C24×C1112yes—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4C2×D4×C1112yes—
895C22⋊C4C2×D4×C1112yes—
896C22⋊C4C2×D4×C1112yes—
897C22⋊C4C2×D4×C1112yes—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—22no—
902C42—22no—
903C42C2×D4×C1111yescharacteristic
904C42C2×D4×C1111yescharacteristic
905C42C24×C1111yescharacteristic
906C42C24×C1111yescharacteristic
907C11#6107011yescharacteristic, direct product factor, Sylow
908C23—21no—
909C23—24no—
910C23—22no—
911C23—24no—
912C23—42no—
913C23—42no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—82no—
920C23C22×D4×C1112yes—
921C23C22×D4×C1112yes—
922C23C22×D4×C1111yescharacteristic
923Q8—24no—
924Q8—22no—
925Q8—21no—
926Q8—22no—
927Q8—22no—
928Q8—44no—
929Q8C22×D4×C1112yes—
930Q8C22×D4×C1114yes—
931D4—24no—
932D4—22no—
933D4—22no—
934D4—24no—
935D4—22no—
936D4—21no—
937D4—22no—
938D4—24no—
939D4—42no—
940D4—44no—
941D4—44no—
942D4—48no—
943D4—48no—
944D4—44no—
945D4—44no—
946D4—44no—
947D4—44no—
948D4—44no—
949D4—42no—
950D4—44no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4—84no—
956D4—84no—
957D4C22×D4×C1112yes—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—41no—
975C2×C4—44no—
976C2×C4—48no—
977C2×C4—48no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—42no—
983C2×C4—81no—
984C2×C4C22×D4×C1111yescharacteristic
985C2×C4C22×D4×C1111yescharacteristic
986C2×C4C22×D4×C1111yescharacteristic
987C2×C4C22×D4×C1112yes—
988C2×C4C22×D4×C1112yes—
989C2×C4C22×D4×C1111yescharacteristic
990C2×C4C22×D4×C1112yes—
991C2×C4C22×D4×C1111yescharacteristic
992C2×C4C11×H(5,𝔽2)12yes—
993C2×C4C25×C1111yescharacteristic
994C8—24no—
995C8—22no—
996C8C22×D4×C1114yes—
997C22—21no—
998C22—21no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—41no—
1007C22—41no—
1008C22—44no—
1009C22—42no—
1010C22—44no—
1011C22—42no—
1012C22—44no—
1013C22—42no—
1014C22—84no—
1015C22—88no—
1016C22—88no—
1017C22D42×C1112yes—
1018C22C23×D4×C1111yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—24no—
1023C4—21no—
1024C4—21no—
1025C4—21no—
1026C4—42no—
1027C4—41no—
1028C4—42no—
1029C4—41no—
1030C4D42×C1112yes—
1031C4C11×#57512yescomplemented
1032C4C23×D4×C1111yescharacteristic
1033C4C2×C11×H(5,𝔽2)11yescharacteristic
1034C2—22no—
1035C2—42no—
1036C2—42no—
1037C2—42no—
1038C2—84no—
1039C2—82no—
1040C2C2×D42×C1111yescharacteristic
1041C2C2×C11×#57511yescharacteristic
1042C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#575C2semidirect
2. D4×C11×#41C2semidirect
3. C2×C11×#550C2semidirect
4. C11×#3287C2semidirect
5. C11×#3284C2semidirect
6. C11×#3278C2semidirect
7. C11×#3274C2semidirect
8. C11×#3271C2semidirect
9. C11×#3268C2semidirect
10. C11×#3151C2semidirect
11. C11×#3055C2semidirect
12. C11×#3038C2semidirect
13. C11×#3037C2semidirect
14. C11×#3006C2semidirect
15. C11×#3005C2semidirect
16. C4×C11×#137C2semidirect
17. D4×C11×M16C2semidirect
19. C22×C11×#41C22semidirect
22. C2×C11×#137C22semidirect
23. C2×C11×#137C22semidirect
25. C2×C11×AGL(1,ℤ/8)C22semidirect
26. C2×C11×AGL(1,ℤ/8)C22semidirect
27. C2×C11×AGL(1,ℤ/8)C22semidirect
28. C2×C11×#135C22semidirect
29. C2×C11×#135C22semidirect
30. C22×C11×M16C22semidirect
35. C11×#550C22semidirect
36. C11×#550C22semidirect
37. C11×#550C22semidirect
38. D4×Q8×C11C22semidirect
39. C11×#548C22semidirect
41. C11×#547C22semidirect
43. C11×#546C22semidirect
45. D42×C11C22semidirect
49. C2×C11×#127C22semidirect
53. C2×C11×#121C22semidirect
55. C2×C4×Q8×C11C22semidirect
59. C11×#496C22semidirect
60. C11×#493C22semidirect
61. C11×#492C22semidirect
62. C11×#469C22semidirect
63. C11×#468C22semidirect
64. C11×#466C22semidirect
65. C11×#465C22semidirect
66. C11×#464C22semidirect
67. C11×#462C22semidirect
68. C11×#460C22semidirect
69. C11×#460C22semidirect
70. C11×#460C22semidirect
71. C11×#459C22semidirect
72. C11×#459C22semidirect
73. C11×#452C22semidirect
74. C11×#452C22semidirect
75. C11×#449C22semidirect
76. C11×#449C22semidirect
77. C11×#449C22semidirect
78. C11×#449C22semidirect
79. C11×#448C22semidirect
80. C11×#447C22semidirect
81. C11×#441C22semidirect
82. C11×#440C22semidirect
83. C4×C11×Q16C22semidirect
84. C4×C11×SD16C22semidirect
85. C11×#436C22semidirect
86. C11×#435C22semidirect
87. C8×D4×C11C22semidirect
88. C11×#428C22semidirect
89. C11×#423C22semidirect
90. C11×#419C22semidirect
91. C11×#418C22semidirect
93. C11×#417C22semidirect
94. C11×#407C22semidirect
95. C4×C11×M16C22semidirect
126. C11×#137D4semidirect
243. #61070C11direct (N × H)
268. C2×Q8×C11C2×D4semidirect
331. C11×Q16C2×D4semidirect
336. C11×SD16C2×D4semidirect
343. C11×M16C2×D4semidirect
387. C2×#575C2×C11semidirect
388. D4×#41C2×C11semidirect
389. C2×#550C2×C11semidirect
390. #3287C2×C11semidirect
391. #3284C2×C11semidirect
392. #3278C2×C11semidirect
393. #3274C2×C11semidirect
394. #3271C2×C11semidirect
395. #3268C2×C11semidirect
396. #3151C2×C11semidirect
397. #3055C2×C11semidirect
398. #3038C2×C11semidirect
399. #3037C2×C11semidirect
400. #3006C2×C11semidirect
401. #3005C2×C11semidirect
402. C4×#137C2×C11semidirect
403. D4×M16C2×C11semidirect
494. C22×#41C22×C11semidirect
497. C2×#137C22×C11semidirect
498. C2×#137C22×C11semidirect
500. C2×AGL(1,ℤ/8)C22×C11semidirect
501. C2×AGL(1,ℤ/8)C22×C11semidirect
502. C2×AGL(1,ℤ/8)C22×C11semidirect
503. C2×#135C22×C11semidirect
504. C2×#135C22×C11semidirect
505. C22×M16C22×C11semidirect
510. #550C22×C11semidirect
511. #550C22×C11semidirect
512. #550C22×C11semidirect
513. D4×Q8C22×C11semidirect
514. #548C22×C11semidirect
516. #547C22×C11semidirect
518. #546C22×C11semidirect
520. D42C22×C11semidirect
524. C2×#127C22×C11semidirect
528. C2×#121C22×C11semidirect
530. C2×C4×Q8C22×C11semidirect
534. #496C22×C11semidirect
535. #493C22×C11semidirect
536. #492C22×C11semidirect
537. #469C22×C11semidirect
538. #468C22×C11semidirect
539. #466C22×C11semidirect
540. #465C22×C11semidirect
541. #464C22×C11semidirect
542. #462C22×C11semidirect
543. #460C22×C11semidirect
544. #460C22×C11semidirect
545. #460C22×C11semidirect
546. #459C22×C11semidirect
547. #459C22×C11semidirect
548. #452C22×C11semidirect
549. #452C22×C11semidirect
550. #449C22×C11semidirect
551. #449C22×C11semidirect
552. #449C22×C11semidirect
553. #449C22×C11semidirect
554. #448C22×C11semidirect
555. #447C22×C11semidirect
556. #441C22×C11semidirect
557. #440C22×C11semidirect
558. C4×Q16C22×C11semidirect
559. C4×SD16C22×C11semidirect
560. #436C22×C11semidirect
561. #435C22×C11semidirect
562. C8×D4C22×C11semidirect
563. #428C22×C11semidirect
564. #423C22×C11semidirect
565. #419C22×C11semidirect
566. #418C22×C11semidirect
568. #417C22×C11semidirect
569. #407C22×C11semidirect
570. C4×M16C22×C11semidirect
605. C4×C11#575semidirect
638. #137D4×C11semidirect
788. C2×Q8C2×D4×C11semidirect
851. Q16C2×D4×C11semidirect
856. SD16C2×D4×C11semidirect
863. M16C2×D4×C11semidirect
907. C11#61070direct (N × H)
1031. C4C11×#575semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5752
D4×C11×#412
C2×C11×#5502
C11×#32872
C11×#32842
C11×#32782
C11×#32742
C11×#32712
C11×#32682
C11×#31512
C11×#30552
C11×#30382
C11×#30372
C11×#30062
C11×#30052
C4×C11×#1372
D4×C11×M162
#6107011