Finite Group Databasebeta

← C11×#61052 #14638245

Subgroups — C11×#61052 #14638245

Order 2816.

2722 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#577C211yesmaximal, characteristic, complemented
2C22×C11×#135C211yesmaximal, characteristic, complemented
3C11×#3487C211yesmaximal, characteristic, complemented
4C11×#3485C211yesmaximal, characteristic, complemented
5C11×#3284C214yesmaximal, complemented
6C11×#3282C214yesmaximal, complemented
7C11×#3269C214yesmaximal, complemented
8C11×#3268C214yesmaximal, complemented
9C11×#3154C211yesmaximal, characteristic, complemented
10C11×#3057C211yesmaximal, characteristic, complemented
11C11×#3050C211yesmaximal, characteristic, complemented
12C11×#3044C211yesmaximal, characteristic, complemented
13C11×#3041C211yesmaximal, characteristic, complemented
14C11×#3011C211yesmaximal, characteristic, complemented
15C11×#3008C211yesmaximal, characteristic, complemented
16C11×#3005C211yesmaximal, characteristic, complemented
17C11×#3005C211yesmaximal, characteristic, complemented
18C11×#2949C211yesmaximal, characteristic, complemented
19C11×#2929C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2211yescharacteristic
21C2×C11×H(5,𝔽2)C2211yescharacteristic
22C22×C11×#41C2211yescharacteristic
23C22×C11×#41C2211yescharacteristic, complemented
24C11×#577—28no—
25C2×C11×#137C2211yescharacteristic
26C2×C11×#137C2212yescomplemented
27C2×C11×#137C2211yescharacteristic, complemented
28C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
29C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
30C2×C11×AGL(1,ℤ/8)C2212yescomplemented
31C2×C11×#135—28no—
32C2×C11×#135C2211yescharacteristic
33C2×C11×#135C2214yescomplemented
34C2×C11×#135C2214yescomplemented
35C2×C11×#135C2212yescomplemented
36C22×C11×Q16C2211yescharacteristic, complemented
37C22×C11×SD16C2211yescharacteristic
38C22×C11×SD16C2211yescharacteristic, complemented
39C22×C11×SD16C2212yescomplemented
40C22×C11×D8C2211yescharacteristic
41C2×C11×#131C2211yescharacteristic
42C23×C8×C11C2211yescharacteristic, complemented
43C11×#550—22no—
44C11×#550C2214yescomplemented
45C11×#548—22no—
46C11×#548C2214yescomplemented
47C11×#547—22no—
48C11×#547C2214yescomplemented
49C11×#546—22no—
50C11×#546C2214yescomplemented
51C11×#536C2211yescharacteristic
52C11×#536C2211yescharacteristic
53C11×#535—22no—
54C11×#535C2211yescharacteristic
55C11×#535C2211yescharacteristic, complemented
56C11×#534—22no—
57C11×#525—22no—
58C11×#525C2211yescharacteristic
59C11×#525C2211yescharacteristic
60C11×#525C2211yescharacteristic, complemented
61C2×C11×#123—22no—
62C11×#519C2211yescharacteristic, complemented
63C11×#518C2211yescharacteristic
64C11×#497C2212yescomplemented
65C11×#496C2212yescomplemented
66C11×#495C2212yescomplemented
67C11×#492C2212yescomplemented
68C11×#468C2214yescomplemented
69C11×#467C2212yescomplemented
70C11×#466C2212yescomplemented
71C11×#465C2212yescomplemented
72C11×#465C2214yescomplemented
73C11×#465C2212yescomplemented
74C11×#464C2214yescomplemented
75C11×#463C2214yescomplemented
76C11×#462C2214yescomplemented
77C11×#459C2214yescomplemented
78C11×#452C2214yescomplemented
79C11×#452C2214yescomplemented
80C11×#452C2214yescomplemented
81C11×#451C2214yescomplemented
82C11×#449C2214yescomplemented
83C11×#449C2214yescomplemented
84C11×#449C2214yescomplemented
85C11×#447C2214yescomplemented
86C11×#440C2214yescomplemented
87C4×C11×SD16C2214yescomplemented
88C11×#435C2214yescomplemented
89C8×D4×C11C2214yescomplemented
90C11×#427C2211yescharacteristic, complemented
91C11×#424C2211yescharacteristic, complemented
92C11×#419C2211yescharacteristic, complemented
93C11×#419C2211yescharacteristic, complemented
94C11×#418C2211yescharacteristic
95C11×#418C2211yescharacteristic, complemented
96C11×#416C2211yescharacteristic
97C11×#416C2211yescharacteristic, complemented
98C11×#408C2211yescharacteristic
99C11×#407C2211yescharacteristic, complemented
100C11×#405C2211yescharacteristic, complemented
101C11×2−1+4—24no—
102C11×2−1+4—42no—
103C11×H(5,𝔽2)—24no—
104C11×H(5,𝔽2)—42no—
105C2×C11×#41—21no—
106C2×C11×#41—22no—
107C2×C11×#41—21no—
108C2×C11×#41—22no—
109C2×C11×#41—22no—
110C2×C11×#41—24no—
111C2×C11×#41—24no—
112C2×C11×#41—42no—
113C2×C11×#41—42no—
114C2×C11×#41C2311yescharacteristic
115C2×C11×#41C2311yescharacteristic
116C2×C11×#41C2314yes—
117C2×C11×#41C2312yes—
118C2×C11×#41C2314yes—
119C2×C11×#41C2312yes—
120C2×C11×#41C2311yescharacteristic
121C22×Q8×C11—21no—
122C22×Q8×C11C2311yescharacteristic
123C22×Q8×C11C2312yes—
124C22×Q8×C11C2311yescharacteristic
125C22×D4×C11—21no—
126C22×D4×C11—21no—
127C22×D4×C11—22no—
128C22×D4×C11—21no—
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C22×D4×C11C2311yescharacteristic
132C23×C4×C11—21no—
133C23×C4×C11—21no—
134C23×C4×C11C2311yescharacteristic
135C11×#137—24no—
136C11×#137—28no—
137C11×#137—42no—
138C11×AGL(1,ℤ/8)—24no—
139C11×AGL(1,ℤ/8)—28no—
140C11×AGL(1,ℤ/8)—42no—
141C11×#135—216no—
142C11×#135—216no—
143C11×#135—28no—
144C11×#135—24no—
145C2×C11×Q16—24no—
146C2×C11×Q16C2311yescharacteristic
147C2×C11×Q16C2314yes—
148C2×C11×Q16C2312yes—
149C2×C11×Q16C2312yes—
150C2×C11×SD16—28no—
151C2×C11×SD16—24no—
152C2×C11×SD16D418yescomplemented
153C2×C11×SD16C2311yescharacteristic
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2311yescharacteristic
156C2×C11×SD16C2312yes—
157C2×C11×SD16C2312yes—
158C2×C11×SD16C2312yes—
159C2×C11×SD16C2312yes—
160C2×C11×SD16C2312yes—
161C2×C11×SD16C2312yes—
162C2×C11×SD16C2312yes—
163C2×C11×D8—24no—
164C2×C11×D8C2311yescharacteristic
165C2×C11×D8C2314yes—
166C2×C11×D8C2312yes—
167C2×C11×D8C2312yes—
168C11×#131—24no—
169C2×C11×M16C2311yescharacteristic
170C2×C11×M16C2311yescharacteristic
171C2×C11×M16C2312yes—
172C22×C8×C11—24no—
173C22×C8×C11C2311yescharacteristic
174C22×C8×C11C2312yes—
175C22×C8×C11C2312yes—
176C22×C8×C11C2312yes—
177C22×C8×C11C2311yescharacteristic
178C11×C4⋊Q8—21no—
179C11×C4⋊Q8C2312yes—
180C11×#127—24no—
181C11×#127—21no—
182C11×#127C2312yes—
183C11×#124—21no—
184C11×#124—21no—
185C11×#124—24no—
186C11×#124C2312yes—
187C11×#124C2312yes—
188C11×#123—22no—
189C11×#123—21no—
190C11×#123—21no—
191C11×#123—24no—
192C11×#123—22no—
193C11×#123—24no—
194C11×#123—24no—
195C11×#123D412yes—
196C11×C22⋊Q8—24no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8D412yes—
199C11×C22⋊Q8C2312yes—
200C11×C22⋊Q8C2312yes—
201C11×C22⋊Q8C2314yes—
202C11×#121—24no—
203C11×#121—24no—
204C11×#121—22no—
205C11×#121—24no—
206C11×#121—24no—
207C11×#121—24no—
208C11×#121D412yes—
209C11×#121C2312yes—
210C11×#121C2312yes—
211C11×#121C2314yes—
212C11×#120—21no—
213C11×#120—21no—
214C11×#120—22no—
215C11×#120—24no—
216C11×#120—22no—
217C11×#120D412yes—
218C4×Q8×C11—22no—
219C4×Q8×C11C2314yes—
220C4×D4×C11—22no—
221C4×D4×C11—22no—
222C4×D4×C11—22no—
223C4×D4×C11—24no—
224C4×D4×C11—24no—
225C4×D4×C11C2314yes—
226C4×D4×C11C2314yes—
227C11×#117—22no—
228C11×#117C2311yescharacteristic
229C11×#117C2311yescharacteristic
230C11×#117C2311yescharacteristic
231C2×C11×C4⋊C4—24no—
232C2×C11×C22⋊C4—22no—
233C2×C11×C22⋊C4—24no—
234C11×#107C2312yes—
235C11×#106C2312yes—
236C11×C4⋊C8C2314yes—
237C11×#103C2312yes—
238C11×#103C2312yes—
239C11×#103C2314yes—
240C11×#103C2314yes—
241C11×#102C2312yes—
242C11×#102C2312yes—
243C11×#102C2314yes—
244C11×#102C2314yes—
245C11×C22⋊C8C2314yes—
246C11×C22⋊C8C2314yes—
247C11×#97C2312yes—
248C4×C8×C11C2312yes—
249#61052C1111yesmaximal, characteristic, direct product factor, Sylow
250C24×C11—21no—
251C24×C11—22no—
252C24×C11—21no—
253C24×C11C2×D411yescharacteristic
254C11×#41—22no—
255C11×#41—22no—
256C11×#41—28no—
257C11×#41—24no—
258C11×#41—28no—
259C11×#41—24no—
260C11×#41—22no—
261C11×#41—22no—
262C11×#41—22no—
263C11×#41—22no—
264C11×#41—44no—
265C11×#41—44no—
266C11×#41—42no—
267C11×#41—42no—
268C11×#41—48no—
269C11×#41—48no—
270C11×#41—48no—
271C11×#41—44no—
272C11×#41—44no—
273C2×Q8×C11—21no—
274C2×Q8×C11—22no—
275C2×Q8×C11—21no—
276C2×Q8×C11—22no—
277C2×Q8×C11—24no—
278C2×Q8×C11—22no—
279C2×Q8×C11—22no—
280C2×Q8×C11—42no—
281C2×Q8×C11—44no—
282C2×Q8×C11C2×D414yes—
283C2×Q8×C11C2×D411yescharacteristic
284C2×Q8×C11C2411yescharacteristic
285C2×Q8×C11C2412yes—
286C2×Q8×C11C2411yescharacteristic
287C2×Q8×C11C2412yes—
288C2×D4×C11—24no—
289C2×D4×C11—21no—
290C2×D4×C11—24no—
291C2×D4×C11—21no—
292C2×D4×C11—22no—
293C2×D4×C11—24no—
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—24no—
297C2×D4×C11—22no—
298C2×D4×C11—21no—
299C2×D4×C11—22no—
300C2×D4×C11—22no—
301C2×D4×C11—21no—
302C2×D4×C11—24no—
303C2×D4×C11—22no—
304C2×D4×C11—22no—
305C2×D4×C11—42no—
306C2×D4×C11—44no—
307C2×D4×C11—44no—
308C2×D4×C11—48no—
309C2×D4×C11—44no—
310C2×D4×C11C2×D412yes—
311C2×D4×C11C2×D411yescharacteristic
312C2×D4×C11C2×D414yes—
313C2×D4×C11C2×D414yes—
314C2×D4×C11C2411yescharacteristic
315C2×D4×C11C2412yes—
316C2×D4×C11C2411yescharacteristic
317C2×D4×C11C2412yes—
318C22×C4×C11—21no—
319C22×C4×C11—22no—
320C22×C4×C11—22no—
321C22×C4×C11—22no—
322C22×C4×C11—21no—
323C22×C4×C11—24no—
324C22×C4×C11—22no—
325C22×C4×C11—22no—
326C22×C4×C11—21no—
327C22×C4×C11—24no—
328C22×C4×C11—21no—
329C22×C4×C11—24no—
330C22×C4×C11—44no—
331C22×C4×C11—44no—
332C22×C4×C11C2×D412yes—
333C22×C4×C11C2×D411yescharacteristic
334C22×C4×C11C2412yes—
335C22×C4×C11C2412yes—
336C22×C4×C11C2411yescharacteristic
337C11×Q16—22no—
338C11×Q16—28no—
339C11×Q16—24no—
340C11×Q16—42no—
341C11×SD16—22no—
342C11×SD16—24no—
343C11×SD16—24no—
344C11×SD16—22no—
345C11×SD16—24no—
346C11×SD16—24no—
347C11×SD16—42no—
348C11×SD16—42no—
349C11×SD16C2×D418yes—
350C11×SD16C2×D418yes—
351C11×D8—22no—
352C11×D8—28no—
353C11×D8—24no—
354C11×D8—42no—
355C11×M16—24no—
356C11×M16—22no—
357C11×M16—22no—
358C2×C8×C11—24no—
359C2×C8×C11—24no—
360C2×C8×C11—24no—
361C2×C8×C11—22no—
362C2×C8×C11C2×D414yes—
363C2×C8×C11C2412yes—
364C2×C8×C11C2412yes—
365C2×C8×C11C2412yes—
366C2×C8×C11C2411yescharacteristic
367C2×C8×C11C2411yescharacteristic
368C11×C4⋊C4—22no—
369C11×C4⋊C4—24no—
370C11×C4⋊C4—24no—
371C11×C4⋊C4—24no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4C2×D414yes—
374C11×C4⋊C4C2×D412yes—
375C11×C4⋊C4C2412yes—
376C11×C4⋊C4C2412yes—
377C11×C22⋊C4—21no—
378C11×C22⋊C4—24no—
379C11×C22⋊C4—21no—
380C11×C22⋊C4—22no—
381C11×C22⋊C4—22no—
382C11×C22⋊C4—22no—
383C11×C22⋊C4—24no—
384C11×C22⋊C4—24no—
385C11×C22⋊C4—22no—
386C11×C22⋊C4—24no—
387C11×C22⋊C4—24no—
388C11×C22⋊C4C2×D412yes—
389C11×C22⋊C4C2×D414yes—
390C11×C22⋊C4C2×D414yes—
391C42×C11—24no—
392C42×C11—21no—
393C42×C11—21no—
394C42×C11C2412yes—
395C2×#577C2×C1111yescharacteristic, complemented
396C22×#135C2×C1111yescharacteristic, complemented
397#3487C2×C1111yescharacteristic, complemented
398#3485C2×C1111yescharacteristic, complemented
399#3284C2×C1114yescomplemented
400#3282C2×C1114yescomplemented
401#3269C2×C1114yescomplemented
402#3268C2×C1114yescomplemented
403#3154C2×C1111yescharacteristic, complemented
404#3057C2×C1111yescharacteristic, complemented
405#3050C2×C1111yescharacteristic, complemented
406#3044C2×C1111yescharacteristic, complemented
407#3041C2×C1111yescharacteristic, complemented
408#3011C2×C1111yescharacteristic, complemented
409#3008C2×C1111yescharacteristic, complemented
410#3005C2×C1111yescharacteristic, complemented
411#3005C2×C1111yescharacteristic, complemented
412#2949C2×C1111yescharacteristic, complemented
413#2929C2×C1111yescharacteristic, complemented
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—24no—
417C23×C11—21no—
418C23×C11—22no—
419C23×C11—21no—
420C23×C11—42no—
421C23×C11—44no—
422C23×C11—42no—
423C23×C11—82no—
424C23×C11—82no—
425C23×C11—84no—
426C23×C11C22×D412yes—
427C23×C11C22×D412yes—
428C23×C11C22×D411yescharacteristic
429Q8×C11—24no—
430Q8×C11—22no—
431Q8×C11—22no—
432Q8×C11—21no—
433Q8×C11—22no—
434Q8×C11—21no—
435Q8×C11—21no—
436Q8×C11—22no—
437Q8×C11—21no—
438Q8×C11—44no—
439Q8×C11—42no—
440Q8×C11C22×D414yes—
441D4×C11—24no—
442D4×C11—24no—
443D4×C11—22no—
444D4×C11—21no—
445D4×C11—22no—
446D4×C11—21no—
447D4×C11—22no—
448D4×C11—21no—
449D4×C11—22no—
450D4×C11—21no—
451D4×C11—44no—
452D4×C11—44no—
453D4×C11—48no—
454D4×C11—44no—
455D4×C11—44no—
456D4×C11—48no—
457D4×C11—42no—
458D4×C11—42no—
459D4×C11—42no—
460D4×C11—84no—
461D4×C11—82no—
462D4×C11—84no—
463D4×C11—82no—
464D4×C11C22×D414yes—
465C2×C4×C11—22no—
466C2×C4×C11—24no—
467C2×C4×C11—22no—
468C2×C4×C11—24no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—22no—
477C2×C4×C11—21no—
478C2×C4×C11—48no—
479C2×C4×C11—44no—
480C2×C4×C11—48no—
481C2×C4×C11—44no—
482C2×C4×C11—44no—
483C2×C4×C11—42no—
484C2×C4×C11—42no—
485C2×C4×C11—42no—
486C2×C4×C11—84no—
487C2×C4×C11C22×D414yes—
488C2×C4×C11C22×D412yes—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C22×D411yescharacteristic
491C2×C4×C11C22×D412yes—
492C2×C4×C11H(5,𝔽2)12yes—
493C2×C4×C11C2511yescharacteristic
494C8×C11—22no—
495C8×C11—22no—
496C8×C11—22no—
497C8×C11C22×D412yes—
498C8×C11C22×D412yes—
499C2×2−1+4C22×C1111yescharacteristic
500C2×H(5,𝔽2)C22×C1111yescharacteristic
501C22×#41C22×C1111yescharacteristic
502C22×#41C22×C1111yescharacteristic, complemented
503#577—28no—
504C2×#137C22×C1111yescharacteristic
505C2×#137C22×C1112yescomplemented
506C2×#137C22×C1111yescharacteristic, complemented
507C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
508C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
509C2×AGL(1,ℤ/8)C22×C1112yescomplemented
510C2×#135—28no—
511C2×#135C22×C1111yescharacteristic
512C2×#135C22×C1114yescomplemented
513C2×#135C22×C1114yescomplemented
514C2×#135C22×C1112yescomplemented
515C22×Q16C22×C1111yescharacteristic, complemented
516C22×SD16C22×C1111yescharacteristic
517C22×SD16C22×C1111yescharacteristic, complemented
518C22×SD16C22×C1112yescomplemented
519C22×D8C22×C1111yescharacteristic
520C2×#131C22×C1111yescharacteristic
521C23×C8C22×C1111yescharacteristic, complemented
522#550—22no—
523#550C22×C1114yescomplemented
524#548—22no—
525#548C22×C1114yescomplemented
526#547—22no—
527#547C22×C1114yescomplemented
528#546—22no—
529#546C22×C1114yescomplemented
530#536C22×C1111yescharacteristic
531#536C22×C1111yescharacteristic
532#535—22no—
533#535C22×C1111yescharacteristic
534#535C22×C1111yescharacteristic, complemented
535#534—22no—
536#525—22no—
537#525C22×C1111yescharacteristic
538#525C22×C1111yescharacteristic
539#525C22×C1111yescharacteristic, complemented
540C2×#123—22no—
541#519C22×C1111yescharacteristic, complemented
542#518C22×C1111yescharacteristic
543#497C22×C1112yescomplemented
544#496C22×C1112yescomplemented
545#495C22×C1112yescomplemented
546#492C22×C1112yescomplemented
547#468C22×C1114yescomplemented
548#467C22×C1112yescomplemented
549#466C22×C1112yescomplemented
550#465C22×C1112yescomplemented
551#465C22×C1114yescomplemented
552#465C22×C1112yescomplemented
553#464C22×C1114yescomplemented
554#463C22×C1114yescomplemented
555#462C22×C1114yescomplemented
556#459C22×C1114yescomplemented
557#452C22×C1114yescomplemented
558#452C22×C1114yescomplemented
559#452C22×C1114yescomplemented
560#451C22×C1114yescomplemented
561#449C22×C1114yescomplemented
562#449C22×C1114yescomplemented
563#449C22×C1114yescomplemented
564#447C22×C1114yescomplemented
565#440C22×C1114yescomplemented
566C4×SD16C22×C1114yescomplemented
567#435C22×C1114yescomplemented
568C8×D4C22×C1114yescomplemented
569#427C22×C1111yescharacteristic, complemented
570#424C22×C1111yescharacteristic, complemented
571#419C22×C1111yescharacteristic, complemented
572#419C22×C1111yescharacteristic, complemented
573#418C22×C1111yescharacteristic
574#418C22×C1111yescharacteristic, complemented
575#416C22×C1111yescharacteristic
576#416C22×C1111yescharacteristic, complemented
577#408C22×C1111yescharacteristic
578#407C22×C1111yescharacteristic, complemented
579#405C22×C1111yescharacteristic, complemented
580C22×C11—22no—
581C22×C11—22no—
582C22×C11—24no—
583C22×C11—22no—
584C22×C11—22no—
585C22×C11—22no—
586C22×C11—24no—
587C22×C11—44no—
588C22×C11—44no—
589C22×C11—42no—
590C22×C11—44no—
591C22×C11—42no—
592C22×C11—41no—
593C22×C11—42no—
594C22×C11—41no—
595C22×C11—84no—
596C22×C11—84no—
597C22×C11—164no—
598C22×C11D4212yes—
599C22×C11C23×D411yescharacteristic
600C4×C11—24no—
601C4×C11—22no—
602C4×C11—24no—
603C4×C11—22no—
604C4×C11—42no—
605C4×C11—42no—
606C4×C11—41no—
607C4×C11—42no—
608C4×C11—41no—
609C4×C11D4212yes—
610C4×C11C23×D411yescharacteristic
611C4×C11C2×H(5,𝔽2)11yescharacteristic
6122−1+4—24no—
6132−1+4—42no—
614H(5,𝔽2)—24no—
615H(5,𝔽2)—42no—
616C2×#41—21no—
617C2×#41—22no—
618C2×#41—21no—
619C2×#41—22no—
620C2×#41—22no—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—42no—
624C2×#41—42no—
625C2×#41C23×C1111yescharacteristic
626C2×#41C23×C1111yescharacteristic
627C2×#41C23×C1114yes—
628C2×#41C23×C1112yes—
629C2×#41C23×C1114yes—
630C2×#41C23×C1112yes—
631C2×#41C23×C1111yescharacteristic
632C22×Q8—21no—
633C22×Q8C23×C1111yescharacteristic
634C22×Q8C23×C1112yes—
635C22×Q8C23×C1111yescharacteristic
636C22×D4—21no—
637C22×D4—21no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4C23×C1111yescharacteristic
641C22×D4C23×C1112yes—
642C22×D4C23×C1111yescharacteristic
643C23×C4—21no—
644C23×C4—21no—
645C23×C4C23×C1111yescharacteristic
646#137—24no—
647#137—28no—
648#137—42no—
649AGL(1,ℤ/8)—24no—
650AGL(1,ℤ/8)—28no—
651AGL(1,ℤ/8)—42no—
652#135—216no—
653#135—216no—
654#135—28no—
655#135—24no—
656C2×Q16—24no—
657C2×Q16C23×C1114yes—
658C2×Q16C23×C1111yescharacteristic
659C2×Q16C23×C1112yes—
660C2×Q16C23×C1112yes—
661C2×SD16—28no—
662C2×SD16—24no—
663C2×SD16D4×C1118yescomplemented
664C2×SD16C23×C1111yescharacteristic
665C2×SD16C23×C1112yes—
666C2×SD16C23×C1112yes—
667C2×SD16C23×C1112yes—
668C2×SD16C23×C1112yes—
669C2×SD16C23×C1111yescharacteristic
670C2×SD16C23×C1112yes—
671C2×SD16C23×C1112yes—
672C2×SD16C23×C1112yes—
673C2×SD16C23×C1112yes—
674C2×D8—24no—
675C2×D8C23×C1114yes—
676C2×D8C23×C1111yescharacteristic
677C2×D8C23×C1112yes—
678C2×D8C23×C1112yes—
679#131—24no—
680C2×M16C23×C1111yescharacteristic
681C2×M16C23×C1112yes—
682C2×M16C23×C1111yescharacteristic
683C22×C8—24no—
684C22×C8C23×C1111yescharacteristic
685C22×C8C23×C1112yes—
686C22×C8C23×C1112yes—
687C22×C8C23×C1112yes—
688C22×C8C23×C1111yescharacteristic
689C4⋊Q8—21no—
690C4⋊Q8C23×C1112yes—
691#127—24no—
692#127—21no—
693#127C23×C1112yes—
694#124—21no—
695#124—21no—
696#124—24no—
697#124C23×C1112yes—
698#124C23×C1112yes—
699#123—22no—
700#123—21no—
701#123—21no—
702#123—24no—
703#123—22no—
704#123—24no—
705#123—24no—
706#123D4×C1112yes—
707C22⋊Q8—24no—
708C22⋊Q8—22no—
709C22⋊Q8D4×C1112yes—
710C22⋊Q8C23×C1112yes—
711C22⋊Q8C23×C1112yes—
712C22⋊Q8C23×C1114yes—
713#121—24no—
714#121—24no—
715#121—22no—
716#121—24no—
717#121—24no—
718#121—24no—
719#121D4×C1112yes—
720#121C23×C1112yes—
721#121C23×C1112yes—
722#121C23×C1114yes—
723#120—21no—
724#120—21no—
725#120—22no—
726#120—24no—
727#120—22no—
728#120D4×C1112yes—
729C4×Q8—22no—
730C4×Q8C23×C1114yes—
731C4×D4—22no—
732C4×D4—22no—
733C4×D4—22no—
734C4×D4—24no—
735C4×D4—24no—
736C4×D4C23×C1114yes—
737C4×D4C23×C1114yes—
738#117—22no—
739#117C23×C1111yescharacteristic
740#117C23×C1111yescharacteristic
741#117C23×C1111yescharacteristic
742C2×C4⋊C4—24no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—24no—
745#107C23×C1112yes—
746#106C23×C1112yes—
747C4⋊C8C23×C1114yes—
748#103C23×C1112yes—
749#103C23×C1112yes—
750#103C23×C1114yes—
751#103C23×C1114yes—
752#102C23×C1112yes—
753#102C23×C1112yes—
754#102C23×C1114yes—
755#102C23×C1114yes—
756C22⋊C8C23×C1114yes—
757C22⋊C8C23×C1114yes—
758#97C23×C1112yes—
759C4×C8C23×C1112yes—
760C2×C11—22no—
761C2×C11—42no—
762C2×C11—42no—
763C2×C11—44no—
764C2×C11—81no—
765C2×C11—82no—
766C2×C11—81no—
767C2×C11C2×D4211yescharacteristic
768C2×C11#358412yes—
769C24—21no—
770C24—22no—
771C24—21no—
772C24C2×D4×C1111yescharacteristic
773#41—22no—
774#41—22no—
775#41—28no—
776#41—24no—
777#41—28no—
778#41—24no—
779#41—22no—
780#41—22no—
781#41—22no—
782#41—22no—
783#41—44no—
784#41—44no—
785#41—42no—
786#41—42no—
787#41—48no—
788#41—48no—
789#41—48no—
790#41—44no—
791#41—44no—
792C2×Q8—21no—
793C2×Q8—22no—
794C2×Q8—21no—
795C2×Q8—22no—
796C2×Q8—24no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—42no—
800C2×Q8—44no—
801C2×Q8C2×D4×C1114yes—
802C2×Q8C2×D4×C1111yescharacteristic
803C2×Q8C24×C1111yescharacteristic
804C2×Q8C24×C1112yes—
805C2×Q8C24×C1111yescharacteristic
806C2×Q8C24×C1112yes—
807C2×D4—24no—
808C2×D4—21no—
809C2×D4—24no—
810C2×D4—21no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—24no—
816C2×D4—22no—
817C2×D4—21no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—42no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—48no—
828C2×D4—44no—
829C2×D4C2×D4×C1112yes—
830C2×D4C2×D4×C1111yescharacteristic
831C2×D4C2×D4×C1114yes—
832C2×D4C2×D4×C1114yes—
833C2×D4C24×C1111yescharacteristic
834C2×D4C24×C1112yes—
835C2×D4C24×C1111yescharacteristic
836C2×D4C24×C1112yes—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—24no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—24no—
847C22×C4—21no—
848C22×C4—24no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4C2×D4×C1112yes—
852C22×C4C2×D4×C1111yescharacteristic
853C22×C4C24×C1112yes—
854C22×C4C24×C1112yes—
855C22×C4C24×C1111yescharacteristic
856Q16—28no—
857Q16—24no—
858Q16—22no—
859Q16—42no—
860SD16—24no—
861SD16—24no—
862SD16—22no—
863SD16—24no—
864SD16—24no—
865SD16—22no—
866SD16—42no—
867SD16—42no—
868SD16C2×D4×C1118yes—
869SD16C2×D4×C1118yes—
870D8—28no—
871D8—24no—
872D8—22no—
873D8—42no—
874M16—22no—
875M16—22no—
876M16—24no—
877C2×C8—22no—
878C2×C8—24no—
879C2×C8—24no—
880C2×C8—24no—
881C2×C8C2×D4×C1114yes—
882C2×C8C24×C1112yes—
883C2×C8C24×C1112yes—
884C2×C8C24×C1112yes—
885C2×C8C24×C1111yescharacteristic
886C2×C8C24×C1111yescharacteristic
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4C2×D4×C1114yes—
893C4⋊C4C2×D4×C1112yes—
894C4⋊C4C24×C1112yes—
895C4⋊C4C24×C1112yes—
896C22⋊C4—21no—
897C22⋊C4—24no—
898C22⋊C4—21no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—22no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4C2×D4×C1112yes—
908C22⋊C4C2×D4×C1114yes—
909C22⋊C4C2×D4×C1114yes—
910C42—24no—
911C42—21no—
912C42—21no—
913C42C24×C1112yes—
914C11#6105211yescharacteristic, direct product factor, Sylow
915C23—22no—
916C23—22no—
917C23—24no—
918C23—21no—
919C23—22no—
920C23—21no—
921C23—42no—
922C23—44no—
923C23—42no—
924C23—82no—
925C23—82no—
926C23—84no—
927C23C22×D4×C1112yes—
928C23C22×D4×C1112yes—
929C23C22×D4×C1111yescharacteristic
930Q8—24no—
931Q8—22no—
932Q8—22no—
933Q8—21no—
934Q8—22no—
935Q8—21no—
936Q8—21no—
937Q8—22no—
938Q8—21no—
939Q8—44no—
940Q8—42no—
941Q8C22×D4×C1114yes—
942D4—24no—
943D4—24no—
944D4—22no—
945D4—21no—
946D4—22no—
947D4—21no—
948D4—22no—
949D4—21no—
950D4—22no—
951D4—21no—
952D4—44no—
953D4—44no—
954D4—48no—
955D4—44no—
956D4—44no—
957D4—48no—
958D4—42no—
959D4—42no—
960D4—42no—
961D4—84no—
962D4—82no—
963D4—84no—
964D4—82no—
965D4C22×D4×C1114yes—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—48no—
980C2×C4—44no—
981C2×C4—48no—
982C2×C4—44no—
983C2×C4—44no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—84no—
988C2×C4C22×D4×C1114yes—
989C2×C4C22×D4×C1112yes—
990C2×C4C22×D4×C1112yes—
991C2×C4C22×D4×C1111yescharacteristic
992C2×C4C22×D4×C1112yes—
993C2×C4C11×H(5,𝔽2)12yes—
994C2×C4C25×C1111yescharacteristic
995C8—22no—
996C8—22no—
997C8—22no—
998C8C22×D4×C1112yes—
999C8C22×D4×C1112yes—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—24no—
1004C22—22no—
1005C22—24no—
1006C22—22no—
1007C22—44no—
1008C22—44no—
1009C22—41no—
1010C22—42no—
1011C22—41no—
1012C22—42no—
1013C22—44no—
1014C22—42no—
1015C22—84no—
1016C22—84no—
1017C22—164no—
1018C22D42×C1112yes—
1019C22C23×D4×C1111yescharacteristic
1020C4—22no—
1021C4—24no—
1022C4—22no—
1023C4—24no—
1024C4—41no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—42no—
1029C4D42×C1112yes—
1030C4C23×D4×C1111yescharacteristic
1031C4C2×C11×H(5,𝔽2)11yescharacteristic
1032C2—22no—
1033C2—42no—
1034C2—42no—
1035C2—44no—
1036C2—82no—
1037C2—81no—
1038C2—81no—
1039C2C2×D42×C1111yescharacteristic
1040C2C11×#358412yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#525 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#577C2semidirect
2. C22×C11×#135C2semidirect
3. C11×#3487C2semidirect
4. C11×#3485C2semidirect
5. C11×#3284C2semidirect
6. C11×#3282C2semidirect
7. C11×#3269C2semidirect
8. C11×#3268C2semidirect
9. C11×#3154C2semidirect
10. C11×#3057C2semidirect
11. C11×#3050C2semidirect
12. C11×#3044C2semidirect
13. C11×#3041C2semidirect
14. C11×#3011C2semidirect
15. C11×#3008C2semidirect
16. C11×#3005C2semidirect
17. C11×#3005C2semidirect
18. C11×#2949C2semidirect
19. C11×#2929C2semidirect
23. C22×C11×#41C22semidirect
26. C2×C11×#137C22semidirect
27. C2×C11×#137C22semidirect
30. C2×C11×AGL(1,ℤ/8)C22semidirect
33. C2×C11×#135C22semidirect
34. C2×C11×#135C22semidirect
35. C2×C11×#135C22semidirect
36. C22×C11×Q16C22semidirect
38. C22×C11×SD16C22semidirect
39. C22×C11×SD16C22semidirect
42. C23×C8×C11C22semidirect
44. C11×#550C22semidirect
46. C11×#548C22semidirect
48. C11×#547C22semidirect
50. C11×#546C22semidirect
55. C11×#535C22semidirect
60. C11×#525C22semidirect
62. C11×#519C22semidirect
64. C11×#497C22semidirect
65. C11×#496C22semidirect
66. C11×#495C22semidirect
67. C11×#492C22semidirect
68. C11×#468C22semidirect
69. C11×#467C22semidirect
70. C11×#466C22semidirect
71. C11×#465C22semidirect
72. C11×#465C22semidirect
73. C11×#465C22semidirect
74. C11×#464C22semidirect
75. C11×#463C22semidirect
76. C11×#462C22semidirect
77. C11×#459C22semidirect
78. C11×#452C22semidirect
79. C11×#452C22semidirect
80. C11×#452C22semidirect
81. C11×#451C22semidirect
82. C11×#449C22semidirect
83. C11×#449C22semidirect
84. C11×#449C22semidirect
85. C11×#447C22semidirect
86. C11×#440C22semidirect
87. C4×C11×SD16C22semidirect
88. C11×#435C22semidirect
89. C8×D4×C11C22semidirect
90. C11×#427C22semidirect
91. C11×#424C22semidirect
92. C11×#419C22semidirect
93. C11×#419C22semidirect
95. C11×#418C22semidirect
97. C11×#416C22semidirect
99. C11×#407C22semidirect
100. C11×#405C22semidirect
152. C2×C11×SD16D4semidirect
249. #61052C11direct (N × H)
395. C2×#577C2×C11semidirect
396. C22×#135C2×C11semidirect
397. #3487C2×C11semidirect
398. #3485C2×C11semidirect
399. #3284C2×C11semidirect
400. #3282C2×C11semidirect
401. #3269C2×C11semidirect
402. #3268C2×C11semidirect
403. #3154C2×C11semidirect
404. #3057C2×C11semidirect
405. #3050C2×C11semidirect
406. #3044C2×C11semidirect
407. #3041C2×C11semidirect
408. #3011C2×C11semidirect
409. #3008C2×C11semidirect
410. #3005C2×C11semidirect
411. #3005C2×C11semidirect
412. #2949C2×C11semidirect
413. #2929C2×C11semidirect
502. C22×#41C22×C11semidirect
505. C2×#137C22×C11semidirect
506. C2×#137C22×C11semidirect
509. C2×AGL(1,ℤ/8)C22×C11semidirect
512. C2×#135C22×C11semidirect
513. C2×#135C22×C11semidirect
514. C2×#135C22×C11semidirect
515. C22×Q16C22×C11semidirect
517. C22×SD16C22×C11semidirect
518. C22×SD16C22×C11semidirect
521. C23×C8C22×C11semidirect
523. #550C22×C11semidirect
525. #548C22×C11semidirect
527. #547C22×C11semidirect
529. #546C22×C11semidirect
534. #535C22×C11semidirect
539. #525C22×C11semidirect
541. #519C22×C11semidirect
543. #497C22×C11semidirect
544. #496C22×C11semidirect
545. #495C22×C11semidirect
546. #492C22×C11semidirect
547. #468C22×C11semidirect
548. #467C22×C11semidirect
549. #466C22×C11semidirect
550. #465C22×C11semidirect
551. #465C22×C11semidirect
552. #465C22×C11semidirect
553. #464C22×C11semidirect
554. #463C22×C11semidirect
555. #462C22×C11semidirect
556. #459C22×C11semidirect
557. #452C22×C11semidirect
558. #452C22×C11semidirect
559. #452C22×C11semidirect
560. #451C22×C11semidirect
561. #449C22×C11semidirect
562. #449C22×C11semidirect
563. #449C22×C11semidirect
564. #447C22×C11semidirect
565. #440C22×C11semidirect
566. C4×SD16C22×C11semidirect
567. #435C22×C11semidirect
568. C8×D4C22×C11semidirect
569. #427C22×C11semidirect
570. #424C22×C11semidirect
571. #419C22×C11semidirect
572. #419C22×C11semidirect
574. #418C22×C11semidirect
576. #416C22×C11semidirect
578. #407C22×C11semidirect
579. #405C22×C11semidirect
663. C2×SD16D4×C11semidirect
914. C11#61052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5772
C22×C11×#1352
C11×#34872
C11×#34852
C11×#32842
C11×#32822
C11×#32692
C11×#32682
C11×#31542
C11×#30572
C11×#30502
C11×#30442
C11×#30412
C11×#30112
C11×#30082
C11×#30052
C11×#29492
C11×#29292
#6105211