Finite Group Databasebeta

← C11×#60756 #14637949

Subgroups — C11×#60756 #14637949

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3488C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic, complemented
3C11×#3199C214yesmaximal, complemented
4C11×#3198C214yesmaximal, complemented
5C11×#3194C212yesmaximal, complemented
6C11×#3192C212yesmaximal, complemented
7C11×#3188C212yesmaximal, complemented
8C11×#3186C212yesmaximal, complemented
9C11×#3096C212yesmaximal, complemented
10C11×#3094C211yesmaximal, characteristic, complemented
11C11×#3091C211yesmaximal, characteristic, complemented
12C11×#3062C212yesmaximal, complemented
13C11×#3058C212yesmaximal, complemented
14C11×#3008C212yesmaximal, complemented
15C11×#3003C211yesmaximal, characteristic, complemented
16C2×C11×#447C211yesmaximal, characteristic, complemented
17C11×#2880C211yesmaximal, characteristic, complemented
18C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic, complemented
21C2×C11×AGL(1,ℤ/8)C2212yescomplemented
22C22×C11×D8C2212yescomplemented
23C2×C11×#131C2212yescomplemented
24C11×#550—21no—
25C11×#548—21no—
26C11×#546—22no—
27C11×#546—21no—
28D42×C11—21no—
29D42×C11—22no—
30C11×#537C2211yescharacteristic, complemented
31C11×#537C2212yescomplemented
32C11×#535—22no—
33C11×#535—21no—
34C11×#535—21no—
35C11×#535C2212yes—
36C11×#535C2214yescomplemented
37C11×#535C2212yescomplemented
38C11×#535C2211yescharacteristic, complemented
39C11×#535C2212yescomplemented
40C2×C11×#127—21no—
41C2×C11×#124—21no—
42C11×#525C2211yescharacteristic
43C11×#525C2212yescomplemented
44C2×C11×#121C2211yescharacteristic
45C2×C11×#121C2212yescomplemented
46C2×C11×#121C2212yescomplemented
47C2×C11×#121C2212yescomplemented
48C2×C11×#120—22no—
49C11×#520C2211yescharacteristic, complemented
50C2×C11×#117C2211yescharacteristic, complemented
51C11×#485C2212yescomplemented
52C11×#484C2211yescharacteristic, complemented
53C11×#483C2211yescharacteristic, complemented
54C11×#482C2214yescomplemented
55C11×#482C2212yescomplemented
56C11×#482C2214yescomplemented
57C11×#482C2214yescomplemented
58C11×#481C2212yescomplemented
59C11×#481C2211yescharacteristic, complemented
60C11×#481C2214yescomplemented
61C11×#480C2211yescharacteristic, complemented
62C11×#480C2212yescomplemented
63C11×#480C2214yescomplemented
64C11×#469C2214yescomplemented
65C11×#469C2214yescomplemented
66C11×#469C2214yescomplemented
67C11×#468C2214yescomplemented
68C11×#466C2214yescomplemented
69C11×#466C2214yescomplemented
70C11×#466C2214yescomplemented
71C11×#465C2214yescomplemented
72C11×#450C2212yescomplemented
73C11×#450C2212yescomplemented
74C11×#449C2214yescomplemented
75C11×#449C2214yescomplemented
76C11×#447C2212yescomplemented
77C11×#447C2212yescomplemented
78C11×#447C2212yescomplemented
79C11×#447C2214yescomplemented
80C11×#447C2212yescomplemented
81C11×#447C2214yescomplemented
82C11×#447C2214yescomplemented
83C11×#428C2212yescomplemented
84C11×#427C2212yescomplemented
85C11×#418C2212yescomplemented
86C11×#418C2212yescomplemented
87C11×#416C2212yescomplemented
88C2×C11×#102C2212yescomplemented
89C11×#408C2214yescomplemented
90C11×#408C2212yescomplemented
91C11×#407C2211yescharacteristic, complemented
92C11×#407C2212yescomplemented
93C2×C11×C22⋊C8C2211yescharacteristic, complemented
94C2×C11×C22⋊C8C2212yescomplemented
95C25×C11—21no—
96C11×H(5,𝔽2)—44no—
97C2×C11×#41—21no—
98C2×C11×#41—44no—
99C2×C11×#41D412yes—
100C2×C11×#41D411yescharacteristic
101C2×C11×#41D411yescharacteristic
102C2×C11×#41C2311yescharacteristic
103C2×C11×#41C2311yescharacteristic
104C2×C11×#41C2311yescharacteristic
105C2×C11×#41C2312yes—
106C2×C11×#41C2312yescomplemented
107C22×Q8×C11D411yescharacteristic
108C22×D4×C11—22no—
109C22×D4×C11—22no—
110C22×D4×C11—21no—
111C22×D4×C11—22no—
112C22×D4×C11—21no—
113C22×D4×C11—22no—
114C22×D4×C11—21no—
115C22×D4×C11—21no—
116C22×D4×C11—21no—
117C22×D4×C11—44no—
118C22×D4×C11D412yes—
119C22×D4×C11D411yescharacteristic
120C22×D4×C11C2311yescharacteristic
121C22×D4×C11C2312yes—
122C22×D4×C11C2312yes—
123C22×D4×C11C2312yes—
124C22×D4×C11C2312yescomplemented
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C11×AGL(1,ℤ/8)—44no—
128C2×C11×SD16C2314yes—
129C2×C11×D8—44no—
130C2×C11×D8C2314yes—
131C2×C11×D8C2314yes—
132C2×C11×D8C2314yes—
133C11×#131—44no—
134C2×C11×M16C2312yes—
135C2×C11×M16C2314yescomplemented
136C22×C8×C11C2312yes—
137C22×C8×C11C2314yescomplemented
138C11×#127—22no—
139C11×#127—22no—
140C11×#127—24no—
141C11×#127—21no—
142C11×#127—22no—
143C11×#124—22no—
144C11×#124—22no—
145C11×#124—24no—
146C11×#124—21no—
147C11×#124—22no—
148C11×#123—21no—
149C11×#123—22no—
150C11×C22⋊Q8—22no—
151C11×C22⋊Q8—21no—
152C11×C22⋊Q8C2311yescharacteristic
153C11×C22⋊Q8C2311yescharacteristic
154C11×C22⋊Q8C2312yescomplemented
155C11×#121—22no—
156C11×#121—22no—
157C11×#121—22no—
158C11×#121—22no—
159C11×#121—21no—
160C11×#121—21no—
161C11×#121—21no—
162C11×#121—22no—
163C11×#121—22no—
164C11×#121—22no—
165C11×#121—22no—
166C11×#121—22no—
167C11×#121—22no—
168C11×#121C2312yes—
169C11×#121C2312yes—
170C11×#121C2311yescharacteristic
171C11×#121C2314yes—
172C11×#121C2314yes—
173C11×#121C2314yes—
174C11×#121C2314yes—
175C11×#121C2311yescharacteristic
176C11×#121C2312yescomplemented
177C11×#121C2312yescomplemented
178C11×#121C2312yescomplemented
179C11×#120—21no—
180C11×#120—22no—
181C11×#120—24no—
182C11×#120—24no—
183C11×#120—24no—
184C11×#120—24no—
185C11×#120—22no—
186C11×#120—22no—
187C11×#120—22no—
188C4×Q8×C11—21no—
189C4×D4×C11—21no—
190C4×D4×C11—22no—
191C4×D4×C11—21no—
192C4×D4×C11—21no—
193C4×D4×C11—22no—
194C4×D4×C11—22no—
195C11×#117—21no—
196C11×#117—21no—
197C11×#117C2312yes—
198C11×#117C2312yes—
199C11×#117C2311yescharacteristic
200C11×#117C2312yescomplemented
201C2×C11×C4⋊C4C2311yescharacteristic
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2311yescharacteristic
204C2×C11×C4⋊C4C2312yescomplemented
205C2×C11×C22⋊C4—21no—
206C2×C11×C22⋊C4—22no—
207C2×C11×C22⋊C4—22no—
208C2×C11×C22⋊C4—21no—
209C2×C11×C22⋊C4—22no—
210C2×C42×C11—21no—
211C11×#107C2312yescomplemented
212C11×#107C2312yescomplemented
213C11×#107C2314yescomplemented
214C11×#106C2312yescomplemented
215C11×#106C2312yescomplemented
216C11×#106C2314yescomplemented
217C11×#103C2312yescomplemented
218C11×#103C2312yescomplemented
219C11×#102C2314yes—
220C11×#102C2314yes—
221C11×#102C2314yes—
222C11×#102C2314yes—
223C11×#102C2312yescomplemented
224C11×#102C2312yescomplemented
225C11×#102C2314yescomplemented
226C11×#102C2314yescomplemented
227C11×C22⋊C8C2311yescharacteristic
228C11×C22⋊C8C2311yescharacteristic
229C11×C22⋊C8C2312yes—
230C11×C22⋊C8C2312yes—
231C11×C22⋊C8C2312yes—
232C11×C22⋊C8C2314yescomplemented
233C11×C22⋊C8C2314yescomplemented
234#60756C1111yesmaximal, characteristic, direct product factor, Sylow
235C24×C11—22no—
236C24×C11—21no—
237C24×C11—22no—
238C24×C11—22no—
239C24×C11—22no—
240C24×C11—44no—
241C24×C11—82no—
242C24×C11—82no—
243C24×C11C2×D411yescharacteristic
244C24×C11C2×D412yes—
245C11×#41—24no—
246C11×#41—24no—
247C11×#41—24no—
248C11×#41—44no—
249C11×#41—44no—
250C11×#41—42no—
251C11×#41—42no—
252C11×#41—44no—
253C11×#41—44no—
254C2×Q8×C11—42no—
255C2×Q8×C11C2×D411yescharacteristic
256C2×Q8×C11C2×D411yescharacteristic
257C2×Q8×C11C2×D412yes—
258C2×Q8×C11C2411yescharacteristic
259C2×D4×C11—21no—
260C2×D4×C11—22no—
261C2×D4×C11—21no—
262C2×D4×C11—22no—
263C2×D4×C11—21no—
264C2×D4×C11—22no—
265C2×D4×C11—24no—
266C2×D4×C11—24no—
267C2×D4×C11—24no—
268C2×D4×C11—24no—
269C2×D4×C11—22no—
270C2×D4×C11—22no—
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—21no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—24no—
278C2×D4×C11—24no—
279C2×D4×C11—24no—
280C2×D4×C11—44no—
281C2×D4×C11—44no—
282C2×D4×C11—42no—
283C2×D4×C11—44no—
284C2×D4×C11—44no—
285C2×D4×C11—44no—
286C2×D4×C11—44no—
287C2×D4×C11—44no—
288C2×D4×C11—48no—
289C2×D4×C11—44no—
290C2×D4×C11—84no—
291C2×D4×C11—84no—
292C2×D4×C11—82no—
293C2×D4×C11—84no—
294C2×D4×C11C2×D412yes—
295C2×D4×C11C2×D411yescharacteristic
296C2×D4×C11C2×D412yes—
297C2×D4×C11C2×D411yescharacteristic
298C2×D4×C11C2×D412yes—
299C2×D4×C11C2×D412yes—
300C2×D4×C11C2×D412yes—
301C2×D4×C11C2414yes—
302C2×D4×C11C2412yes—
303C2×D4×C11C2411yescharacteristic
304C22×C4×C11—24no—
305C22×C4×C11—21no—
306C22×C4×C11—21no—
307C22×C4×C11—21no—
308C22×C4×C11—22no—
309C22×C4×C11—21no—
310C22×C4×C11—22no—
311C22×C4×C11—44no—
312C22×C4×C11C2×D411yescharacteristic
313C22×C4×C11C2×D411yescharacteristic
314C22×C4×C11C2×D411yescharacteristic
315C22×C4×C11C2×D412yes—
316C22×C4×C11C2×D412yes—
317C22×C4×C11C2×D412yes—
318C22×C4×C11C2411yescharacteristic
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2412yes—
321C22×C4×C11C2412yes—
322C22×C4×C11C2411yescharacteristic
323C11×SD16—44no—
324C11×D8—44no—
325C11×D8—44no—
326C11×D8—44no—
327C11×M16—24no—
328C11×M16—44no—
329C2×C8×C11—24no—
330C2×C8×C11—44no—
331C2×C8×C11C2414yes—
332C2×C8×C11C2412yes—
333C2×C8×C11C2412yes—
334C11×C4⋊C4—21no—
335C11×C4⋊C4—21no—
336C11×C4⋊C4—21no—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—21no—
339C11×C4⋊C4—21no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4C2412yes—
342C11×C4⋊C4C2411yescharacteristic
343C11×C4⋊C4C2411yescharacteristic
344C11×C4⋊C4C2412yes—
345C11×C4⋊C4C2412yes—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—22no—
348C11×C22⋊C4—21no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—21no—
351C11×C22⋊C4—21no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—21no—
355C11×C22⋊C4—24no—
356C11×C22⋊C4—24no—
357C11×C22⋊C4—24no—
358C11×C22⋊C4—24no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—21no—
363C11×C22⋊C4—22no—
364C42×C11—22no—
365C42×C11—22no—
366C42×C11—21no—
367C42×C11—22no—
368#3488C2×C1111yescharacteristic, complemented
369C2×#535C2×C1111yescharacteristic, complemented
370#3199C2×C1114yescomplemented
371#3198C2×C1114yescomplemented
372#3194C2×C1112yescomplemented
373#3192C2×C1112yescomplemented
374#3188C2×C1112yescomplemented
375#3186C2×C1112yescomplemented
376#3096C2×C1112yescomplemented
377#3094C2×C1111yescharacteristic, complemented
378#3091C2×C1111yescharacteristic, complemented
379#3062C2×C1112yescomplemented
380#3058C2×C1112yescomplemented
381#3008C2×C1112yescomplemented
382#3003C2×C1111yescharacteristic, complemented
383C2×#447C2×C1111yescharacteristic, complemented
384#2880C2×C1111yescharacteristic, complemented
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—24no—
388C23×C11—22no—
389C23×C11—21no—
390C23×C11—24no—
391C23×C11—41no—
392C23×C11—42no—
393C23×C11—42no—
394C23×C11—44no—
395C23×C11—44no—
396C23×C11—44no—
397C23×C11—44no—
398C23×C11—44no—
399C23×C11—44no—
400C23×C11—42no—
401C23×C11—82no—
402C23×C11—82no—
403C23×C11—82no—
404C23×C11—82no—
405C23×C11—81no—
406C23×C11—82no—
407C23×C11—81no—
408C23×C11—82no—
409C23×C11—816no—
410C23×C11C22×D411yescharacteristic
411C23×C11C22×D412yes—
412C23×C11C22×D412yes—
413C23×C11C22×D411yescharacteristic
414C23×C11C22×D411yescharacteristic
415Q8×C11—22no—
416Q8×C11—22no—
417Q8×C11—22no—
418Q8×C11—42no—
419D4×C11—24no—
420D4×C11—24no—
421D4×C11—22no—
422D4×C11—22no—
423D4×C11—24no—
424D4×C11—24no—
425D4×C11—22no—
426D4×C11—24no—
427D4×C11—42no—
428D4×C11—42no—
429D4×C11—42no—
430D4×C11—44no—
431D4×C11—44no—
432D4×C11—44no—
433D4×C11—44no—
434D4×C11—42no—
435D4×C11—42no—
436D4×C11—44no—
437D4×C11—44no—
438D4×C11—42no—
439D4×C11—82no—
440D4×C11—81no—
441D4×C11—84no—
442D4×C11—84no—
443D4×C11—84no—
444D4×C11—84no—
445D4×C11—82no—
446D4×C11—82no—
447D4×C11—82no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—24no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—24no—
455C2×C4×C11—21no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—21no—
459C2×C4×C11—22no—
460C2×C4×C11—21no—
461C2×C4×C11—42no—
462C2×C4×C11—42no—
463C2×C4×C11—42no—
464C2×C4×C11—44no—
465C2×C4×C11—42no—
466C2×C4×C11—42no—
467C2×C4×C11—42no—
468C2×C4×C11—81no—
469C2×C4×C11—82no—
470C2×C4×C11C22×D411yescharacteristic
471C2×C4×C11C22×D412yes—
472C2×C4×C11C22×D412yes—
473C2×C4×C11C22×D411yescharacteristic
474C2×C4×C11C22×D411yescharacteristic
475C2×C4×C11H(5,𝔽2)14yes—
476C2×C4×C11C2511yescharacteristic
477C8×C11—22no—
478C8×C11—22no—
479C8×C11—24no—
480C2×H(5,𝔽2)C22×C1111yescharacteristic, complemented
481C22×#41C22×C1111yescharacteristic
482C23×D4C22×C1111yescharacteristic, complemented
483C2×AGL(1,ℤ/8)C22×C1112yescomplemented
484C22×D8C22×C1112yescomplemented
485C2×#131C22×C1112yescomplemented
486#550—21no—
487#548—21no—
488#546—22no—
489#546—21no—
490D42—21no—
491D42—22no—
492#537C22×C1111yescharacteristic, complemented
493#537C22×C1112yescomplemented
494#535—22no—
495#535—21no—
496#535—21no—
497#535C22×C1112yes—
498#535C22×C1114yescomplemented
499#535C22×C1112yescomplemented
500#535C22×C1111yescharacteristic, complemented
501#535C22×C1112yescomplemented
502C2×#127—21no—
503C2×#124—21no—
504#525C22×C1111yescharacteristic
505#525C22×C1112yescomplemented
506C2×#121C22×C1111yescharacteristic
507C2×#121C22×C1112yescomplemented
508C2×#121C22×C1112yescomplemented
509C2×#121C22×C1112yescomplemented
510C2×#120—22no—
511#520C22×C1111yescharacteristic, complemented
512C2×#117C22×C1111yescharacteristic, complemented
513#485C22×C1112yescomplemented
514#484C22×C1111yescharacteristic, complemented
515#483C22×C1111yescharacteristic, complemented
516#482C22×C1112yescomplemented
517#482C22×C1114yescomplemented
518#482C22×C1114yescomplemented
519#482C22×C1114yescomplemented
520#481C22×C1111yescharacteristic, complemented
521#481C22×C1112yescomplemented
522#481C22×C1114yescomplemented
523#480C22×C1111yescharacteristic, complemented
524#480C22×C1112yescomplemented
525#480C22×C1114yescomplemented
526#469C22×C1114yescomplemented
527#469C22×C1114yescomplemented
528#469C22×C1114yescomplemented
529#468C22×C1114yescomplemented
530#466C22×C1114yescomplemented
531#466C22×C1114yescomplemented
532#466C22×C1114yescomplemented
533#465C22×C1114yescomplemented
534#450C22×C1112yescomplemented
535#450C22×C1112yescomplemented
536#449C22×C1114yescomplemented
537#449C22×C1114yescomplemented
538#447C22×C1112yescomplemented
539#447C22×C1112yescomplemented
540#447C22×C1112yescomplemented
541#447C22×C1114yescomplemented
542#447C22×C1112yescomplemented
543#447C22×C1114yescomplemented
544#447C22×C1114yescomplemented
545#428C22×C1112yescomplemented
546#427C22×C1112yescomplemented
547#418C22×C1112yescomplemented
548#418C22×C1112yescomplemented
549#416C22×C1112yescomplemented
550C2×#102C22×C1112yescomplemented
551#408C22×C1114yescomplemented
552#408C22×C1112yescomplemented
553#407C22×C1111yescharacteristic, complemented
554#407C22×C1112yescomplemented
555C2×C22⋊C8C22×C1111yescharacteristic, complemented
556C2×C22⋊C8C22×C1112yescomplemented
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—21no—
561C22×C11—22no—
562C22×C11—22no—
563C22×C11—21no—
564C22×C11—21no—
565C22×C11—22no—
566C22×C11—22no—
567C22×C11—22no—
568C22×C11—22no—
569C22×C11—21no—
570C22×C11—44no—
571C22×C11—44no—
572C22×C11—42no—
573C22×C11—41no—
574C22×C11—42no—
575C22×C11—41no—
576C22×C11—44no—
577C22×C11—42no—
578C22×C11—41no—
579C22×C11—44no—
580C22×C11—84no—
581C22×C11—88no—
582C22×C11—88no—
583C22×C11—88no—
584C22×C11—162no—
585C22×C11—164no—
586C22×C11#53412yes—
587C22×C11#57612yes—
588C22×C11C23×D411yescharacteristic
589C4×C11—21no—
590C4×C11—21no—
591C4×C11—22no—
592C4×C11—22no—
593C4×C11—42no—
594C4×C11—41no—
595C4×C11—41no—
596C4×C11—42no—
597C4×C11—41no—
598C4×C11—42no—
599C4×C11#53412yes—
600C4×C11C2×H(5,𝔽2)12yes—
601C25—21no—
602H(5,𝔽2)—44no—
603C2×#41—21no—
604C2×#41—44no—
605C2×#41D4×C1112yes—
606C2×#41D4×C1111yescharacteristic
607C2×#41D4×C1111yescharacteristic
608C2×#41C23×C1111yescharacteristic
609C2×#41C23×C1111yescharacteristic
610C2×#41C23×C1111yescharacteristic
611C2×#41C23×C1112yes—
612C2×#41C23×C1112yescomplemented
613C22×Q8D4×C1111yescharacteristic
614C22×D4—22no—
615C22×D4—22no—
616C22×D4—21no—
617C22×D4—22no—
618C22×D4—21no—
619C22×D4—22no—
620C22×D4—21no—
621C22×D4—21no—
622C22×D4—21no—
623C22×D4—44no—
624C22×D4D4×C1112yes—
625C22×D4D4×C1111yescharacteristic
626C22×D4C23×C1111yescharacteristic
627C22×D4C23×C1112yes—
628C22×D4C23×C1112yes—
629C22×D4C23×C1112yes—
630C22×D4C23×C1112yescomplemented
631C23×C4C23×C1111yescharacteristic
632C23×C4C23×C1112yes—
633AGL(1,ℤ/8)—44no—
634C2×SD16C23×C1114yes—
635C2×D8—44no—
636C2×D8C23×C1114yes—
637C2×D8C23×C1114yes—
638C2×D8C23×C1114yes—
639#131—44no—
640C2×M16C23×C1112yes—
641C2×M16C23×C1114yescomplemented
642C22×C8C23×C1112yes—
643C22×C8C23×C1114yescomplemented
644#127—22no—
645#127—22no—
646#127—24no—
647#127—21no—
648#127—22no—
649#124—22no—
650#124—22no—
651#124—24no—
652#124—21no—
653#124—22no—
654#123—21no—
655#123—22no—
656C22⋊Q8—22no—
657C22⋊Q8—21no—
658C22⋊Q8C23×C1111yescharacteristic
659C22⋊Q8C23×C1111yescharacteristic
660C22⋊Q8C23×C1112yescomplemented
661#121—22no—
662#121—22no—
663#121—22no—
664#121—22no—
665#121—21no—
666#121—21no—
667#121—21no—
668#121—22no—
669#121—22no—
670#121—22no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121C23×C1112yes—
675#121C23×C1112yes—
676#121C23×C1111yescharacteristic
677#121C23×C1114yes—
678#121C23×C1114yes—
679#121C23×C1114yes—
680#121C23×C1114yes—
681#121C23×C1111yescharacteristic
682#121C23×C1112yescomplemented
683#121C23×C1112yescomplemented
684#121C23×C1112yescomplemented
685#120—21no—
686#120—22no—
687#120—24no—
688#120—24no—
689#120—24no—
690#120—24no—
691#120—22no—
692#120—22no—
693#120—22no—
694C4×Q8—21no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—22no—
701#117—21no—
702#117—21no—
703#117C23×C1112yes—
704#117C23×C1112yes—
705#117C23×C1111yescharacteristic
706#117C23×C1112yescomplemented
707C2×C4⋊C4C23×C1111yescharacteristic
708C2×C4⋊C4C23×C1111yescharacteristic
709C2×C4⋊C4C23×C1111yescharacteristic
710C2×C4⋊C4C23×C1112yescomplemented
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—22no—
716C2×C42—21no—
717#107C23×C1112yescomplemented
718#107C23×C1112yescomplemented
719#107C23×C1114yescomplemented
720#106C23×C1112yescomplemented
721#106C23×C1112yescomplemented
722#106C23×C1114yescomplemented
723#103C23×C1112yescomplemented
724#103C23×C1112yescomplemented
725#102C23×C1114yes—
726#102C23×C1114yes—
727#102C23×C1114yes—
728#102C23×C1114yes—
729#102C23×C1112yescomplemented
730#102C23×C1112yescomplemented
731#102C23×C1114yescomplemented
732#102C23×C1114yescomplemented
733C22⋊C8C23×C1111yescharacteristic
734C22⋊C8C23×C1111yescharacteristic
735C22⋊C8C23×C1112yes—
736C22⋊C8C23×C1112yes—
737C22⋊C8C23×C1112yes—
738C22⋊C8C23×C1114yescomplemented
739C22⋊C8C23×C1114yescomplemented
740C2×C11—22no—
741C2×C11—22no—
742C2×C11—41no—
743C2×C11—42no—
744C2×C11—42no—
745C2×C11—84no—
746C2×C11—82no—
747C2×C11—81no—
748C2×C11C2×#53411yescharacteristic
749C2×C11C2×#57611yescharacteristic
750C2×C11#358511yescharacteristic
751C24—22no—
752C24—21no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—44no—
757C24—82no—
758C24—82no—
759C24C2×D4×C1111yescharacteristic
760C24C2×D4×C1112yes—
761#41—24no—
762#41—24no—
763#41—24no—
764#41—44no—
765#41—44no—
766#41—42no—
767#41—42no—
768#41—44no—
769#41—44no—
770C2×Q8—42no—
771C2×Q8C2×D4×C1111yescharacteristic
772C2×Q8C2×D4×C1111yescharacteristic
773C2×Q8C2×D4×C1112yes—
774C2×Q8C24×C1111yescharacteristic
775C2×D4—21no—
776C2×D4—22no—
777C2×D4—21no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—22no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—42no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—48no—
805C2×D4—44no—
806C2×D4—84no—
807C2×D4—84no—
808C2×D4—82no—
809C2×D4—84no—
810C2×D4C2×D4×C1112yes—
811C2×D4C2×D4×C1111yescharacteristic
812C2×D4C2×D4×C1112yes—
813C2×D4C2×D4×C1111yescharacteristic
814C2×D4C2×D4×C1112yes—
815C2×D4C2×D4×C1112yes—
816C2×D4C2×D4×C1112yes—
817C2×D4C24×C1114yes—
818C2×D4C24×C1112yes—
819C2×D4C24×C1111yescharacteristic
820C22×C4—24no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—44no—
828C22×C4C2×D4×C1111yescharacteristic
829C22×C4C2×D4×C1111yescharacteristic
830C22×C4C2×D4×C1111yescharacteristic
831C22×C4C2×D4×C1112yes—
832C22×C4C2×D4×C1112yes—
833C22×C4C2×D4×C1112yes—
834C22×C4C24×C1111yescharacteristic
835C22×C4C24×C1111yescharacteristic
836C22×C4C24×C1112yes—
837C22×C4C24×C1112yes—
838C22×C4C24×C1111yescharacteristic
839SD16—44no—
840D8—44no—
841D8—44no—
842D8—44no—
843M16—24no—
844M16—44no—
845C2×C8—24no—
846C2×C8—44no—
847C2×C8C24×C1114yes—
848C2×C8C24×C1112yes—
849C2×C8C24×C1112yes—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—22no—
857C4⋊C4C24×C1112yes—
858C4⋊C4C24×C1111yescharacteristic
859C4⋊C4C24×C1111yescharacteristic
860C4⋊C4C24×C1112yes—
861C4⋊C4C24×C1112yes—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—21no—
865C22⋊C4—22no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—21no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—22no—
880C42—22no—
881C42—22no—
882C42—21no—
883C42—22no—
884C11#6075611yescharacteristic, direct product factor, Sylow
885C23—22no—
886C23—22no—
887C23—24no—
888C23—22no—
889C23—21no—
890C23—24no—
891C23—41no—
892C23—42no—
893C23—42no—
894C23—44no—
895C23—44no—
896C23—44no—
897C23—44no—
898C23—44no—
899C23—44no—
900C23—42no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—81no—
906C23—82no—
907C23—81no—
908C23—82no—
909C23—816no—
910C23C22×D4×C1111yescharacteristic
911C23C22×D4×C1112yes—
912C23C22×D4×C1112yes—
913C23C22×D4×C1111yescharacteristic
914C23C22×D4×C1111yescharacteristic
915Q8—22no—
916Q8—22no—
917Q8—22no—
918Q8—42no—
919D4—24no—
920D4—24no—
921D4—22no—
922D4—22no—
923D4—24no—
924D4—24no—
925D4—22no—
926D4—24no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—44no—
931D4—44no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—44no—
937D4—44no—
938D4—42no—
939D4—82no—
940D4—81no—
941D4—84no—
942D4—84no—
943D4—82no—
944D4—82no—
945D4—82no—
946D4—84no—
947D4—84no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—44no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—81no—
969C2×C4—82no—
970C2×C4C22×D4×C1111yescharacteristic
971C2×C4C22×D4×C1112yes—
972C2×C4C22×D4×C1112yes—
973C2×C4C22×D4×C1111yescharacteristic
974C2×C4C22×D4×C1111yescharacteristic
975C2×C4C11×H(5,𝔽2)14yes—
976C2×C4C25×C1111yescharacteristic
977C8—22no—
978C8—22no—
979C8—24no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—21no—
990C22—22no—
991C22—22no—
992C22—21no—
993C22—44no—
994C22—42no—
995C22—41no—
996C22—44no—
997C22—42no—
998C22—41no—
999C22—44no—
1000C22—44no—
1001C22—42no—
1002C22—41no—
1003C22—84no—
1004C22—88no—
1005C22—88no—
1006C22—88no—
1007C22—162no—
1008C22—164no—
1009C22C11×#53412yes—
1010C22C11×#57612yes—
1011C22C23×D4×C1111yescharacteristic
1012C4—21no—
1013C4—21no—
1014C4—22no—
1015C4—22no—
1016C4—41no—
1017C4—42no—
1018C4—41no—
1019C4—42no—
1020C4—42no—
1021C4—41no—
1022C4C11×#53412yes—
1023C4C2×C11×H(5,𝔽2)12yes—
1024C2—22no—
1025C2—22no—
1026C2—41no—
1027C2—42no—
1028C2—42no—
1029C2—84no—
1030C2—82no—
1031C2—81no—
1032C2C2×C11×#53411yescharacteristic
1033C2C2×C11×#57611yescharacteristic
1034C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3488C2semidirect
2. C2×C11×#535C2semidirect
3. C11×#3199C2semidirect
4. C11×#3198C2semidirect
5. C11×#3194C2semidirect
6. C11×#3192C2semidirect
7. C11×#3188C2semidirect
8. C11×#3186C2semidirect
9. C11×#3096C2semidirect
10. C11×#3094C2semidirect
11. C11×#3091C2semidirect
12. C11×#3062C2semidirect
13. C11×#3058C2semidirect
14. C11×#3008C2semidirect
15. C11×#3003C2semidirect
16. C2×C11×#447C2semidirect
17. C11×#2880C2semidirect
18. C2×C11×H(5,𝔽2)C22semidirect
20. C23×D4×C11C22semidirect
21. C2×C11×AGL(1,ℤ/8)C22semidirect
22. C22×C11×D8C22semidirect
23. C2×C11×#131C22semidirect
30. C11×#537C22semidirect
31. C11×#537C22semidirect
36. C11×#535C22semidirect
37. C11×#535C22semidirect
38. C11×#535C22semidirect
39. C11×#535C22semidirect
43. C11×#525C22semidirect
45. C2×C11×#121C22semidirect
46. C2×C11×#121C22semidirect
47. C2×C11×#121C22semidirect
49. C11×#520C22semidirect
50. C2×C11×#117C22semidirect
51. C11×#485C22semidirect
52. C11×#484C22semidirect
53. C11×#483C22semidirect
54. C11×#482C22semidirect
55. C11×#482C22semidirect
56. C11×#482C22semidirect
57. C11×#482C22semidirect
58. C11×#481C22semidirect
59. C11×#481C22semidirect
60. C11×#481C22semidirect
61. C11×#480C22semidirect
62. C11×#480C22semidirect
63. C11×#480C22semidirect
64. C11×#469C22semidirect
65. C11×#469C22semidirect
66. C11×#469C22semidirect
67. C11×#468C22semidirect
68. C11×#466C22semidirect
69. C11×#466C22semidirect
70. C11×#466C22semidirect
71. C11×#465C22semidirect
72. C11×#450C22semidirect
73. C11×#450C22semidirect
74. C11×#449C22semidirect
75. C11×#449C22semidirect
76. C11×#447C22semidirect
77. C11×#447C22semidirect
78. C11×#447C22semidirect
79. C11×#447C22semidirect
80. C11×#447C22semidirect
81. C11×#447C22semidirect
82. C11×#447C22semidirect
83. C11×#428C22semidirect
84. C11×#427C22semidirect
85. C11×#418C22semidirect
86. C11×#418C22semidirect
87. C11×#416C22semidirect
88. C2×C11×#102C22semidirect
89. C11×#408C22semidirect
90. C11×#408C22semidirect
91. C11×#407C22semidirect
92. C11×#407C22semidirect
93. C2×C11×C22⋊C8C22semidirect
94. C2×C11×C22⋊C8C22semidirect
106. C2×C11×#41C23semidirect
124. C22×D4×C11C23semidirect
135. C2×C11×M16C23semidirect
137. C22×C8×C11C23semidirect
154. C11×C22⋊Q8C23semidirect
176. C11×#121C23semidirect
177. C11×#121C23semidirect
178. C11×#121C23semidirect
200. C11×#117C23semidirect
204. C2×C11×C4⋊C4C23semidirect
211. C11×#107C23semidirect
212. C11×#107C23semidirect
213. C11×#107C23semidirect
214. C11×#106C23semidirect
215. C11×#106C23semidirect
216. C11×#106C23semidirect
217. C11×#103C23semidirect
218. C11×#103C23semidirect
223. C11×#102C23semidirect
224. C11×#102C23semidirect
225. C11×#102C23semidirect
226. C11×#102C23semidirect
232. C11×C22⋊C8C23semidirect
233. C11×C22⋊C8C23semidirect
234. #60756C11direct (N × H)
368. #3488C2×C11semidirect
369. C2×#535C2×C11semidirect
370. #3199C2×C11semidirect
371. #3198C2×C11semidirect
372. #3194C2×C11semidirect
373. #3192C2×C11semidirect
374. #3188C2×C11semidirect
375. #3186C2×C11semidirect
376. #3096C2×C11semidirect
377. #3094C2×C11semidirect
378. #3091C2×C11semidirect
379. #3062C2×C11semidirect
380. #3058C2×C11semidirect
381. #3008C2×C11semidirect
382. #3003C2×C11semidirect
383. C2×#447C2×C11semidirect
384. #2880C2×C11semidirect
480. C2×H(5,𝔽2)C22×C11semidirect
482. C23×D4C22×C11semidirect
483. C2×AGL(1,ℤ/8)C22×C11semidirect
484. C22×D8C22×C11semidirect
485. C2×#131C22×C11semidirect
492. #537C22×C11semidirect
493. #537C22×C11semidirect
498. #535C22×C11semidirect
499. #535C22×C11semidirect
500. #535C22×C11semidirect
501. #535C22×C11semidirect
505. #525C22×C11semidirect
507. C2×#121C22×C11semidirect
508. C2×#121C22×C11semidirect
509. C2×#121C22×C11semidirect
511. #520C22×C11semidirect
512. C2×#117C22×C11semidirect
513. #485C22×C11semidirect
514. #484C22×C11semidirect
515. #483C22×C11semidirect
516. #482C22×C11semidirect
517. #482C22×C11semidirect
518. #482C22×C11semidirect
519. #482C22×C11semidirect
520. #481C22×C11semidirect
521. #481C22×C11semidirect
522. #481C22×C11semidirect
523. #480C22×C11semidirect
524. #480C22×C11semidirect
525. #480C22×C11semidirect
526. #469C22×C11semidirect
527. #469C22×C11semidirect
528. #469C22×C11semidirect
529. #468C22×C11semidirect
530. #466C22×C11semidirect
531. #466C22×C11semidirect
532. #466C22×C11semidirect
533. #465C22×C11semidirect
534. #450C22×C11semidirect
535. #450C22×C11semidirect
536. #449C22×C11semidirect
537. #449C22×C11semidirect
538. #447C22×C11semidirect
539. #447C22×C11semidirect
540. #447C22×C11semidirect
541. #447C22×C11semidirect
542. #447C22×C11semidirect
543. #447C22×C11semidirect
544. #447C22×C11semidirect
545. #428C22×C11semidirect
546. #427C22×C11semidirect
547. #418C22×C11semidirect
548. #418C22×C11semidirect
549. #416C22×C11semidirect
550. C2×#102C22×C11semidirect
551. #408C22×C11semidirect
552. #408C22×C11semidirect
553. #407C22×C11semidirect
554. #407C22×C11semidirect
555. C2×C22⋊C8C22×C11semidirect
556. C2×C22⋊C8C22×C11semidirect
612. C2×#41C23×C11semidirect
630. C22×D4C23×C11semidirect
641. C2×M16C23×C11semidirect
643. C22×C8C23×C11semidirect
660. C22⋊Q8C23×C11semidirect
682. #121C23×C11semidirect
683. #121C23×C11semidirect
684. #121C23×C11semidirect
706. #117C23×C11semidirect
710. C2×C4⋊C4C23×C11semidirect
717. #107C23×C11semidirect
718. #107C23×C11semidirect
719. #107C23×C11semidirect
720. #106C23×C11semidirect
721. #106C23×C11semidirect
722. #106C23×C11semidirect
723. #103C23×C11semidirect
724. #103C23×C11semidirect
729. #102C23×C11semidirect
730. #102C23×C11semidirect
731. #102C23×C11semidirect
732. #102C23×C11semidirect
738. C22⋊C8C23×C11semidirect
739. C22⋊C8C23×C11semidirect
884. C11#60756direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34882
C2×C11×#5352
C11×#31992
C11×#31982
C11×#31942
C11×#31922
C11×#31882
C11×#31862
C11×#30962
C11×#30942
C11×#30912
C11×#30622
C11×#30582
C11×#30082
C11×#30032
C2×C11×#4472
C11×#28802
#6075611