Finite Group Databasebeta

← C11×#60170 #14637363

Subgroups — C11×#60170 #14637363

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C211yesmaximal, characteristic
2C11×#3428C211yesmaximal, characteristic, complemented
3C2×C11×#520C211yesmaximal, characteristic, complemented
4C11×#2952C214yesmaximal, complemented
5C11×#2951C214yesmaximal, complemented
6C11×#2947C214yesmaximal, complemented
7C11×#2946C214yesmaximal, complemented
8C4×C11×#137C214yesmaximal, complemented
9C4×C11×AGL(1,ℤ/8)C214yesmaximal, complemented
10C2×C11×#428C211yesmaximal, characteristic, complemented
11C11×#2896C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C11×#2873C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C22×C11×#41C2211yescharacteristic
16C11×#575C4116yescomplemented
17C2×C11×#137C2212yes—
18C2×C11×#137C2212yes—
19C2×C11×AGL(1,ℤ/8)C2212yes—
20C2×C11×AGL(1,ℤ/8)C2212yes—
21C2×C11×#135C2214yes—
22C22×C11×M16C2211yescharacteristic
23C22×C11×M16C2211yescharacteristic
24C11×#520—22no—
25C11×#520—22no—
26C11×#520—21no—
27C11×#520—21no—
28C11×#520C2214yes—
29C11×#520C2214yescomplemented
30C11×#520C2212yescomplemented
31C11×#520C2212yescomplemented
32C11×#519C2212yescomplemented
33C11×#518—22no—
34C11×#518C2212yescomplemented
35C4×C11×#41—22no—
36C4×C11×#41C2214yes—
37C2×C4×Q8×C11C2212yescomplemented
38C2×C4×D4×C11—22no—
39C2×C4×D4×C11C2212yescomplemented
40C2×C11×#117—22no—
41C2×C11×#117—21no—
42C2×C11×#117C2211yescharacteristic
43C2×C11×#117C2211yescharacteristic
44C22×C11×C4⋊C4—21no—
45C22×C11×C4⋊C4C2211yescharacteristic
46C11×#442C2218yescomplemented
47C11×#441C2218yescomplemented
48C11×#440C2218yescomplemented
49C11×#440C2218yescomplemented
50C4×C11×Q16C2218yescomplemented
51C4×C11×SD16C2218yescomplemented
52C4×C11×SD16C2218yescomplemented
53C4×C11×D8C2218yescomplemented
54C11×#428C2214yescomplemented
55C11×#428C2214yescomplemented
56C2×C11×#107C2212yescomplemented
57C2×C11×#106C2212yescomplemented
58C11×#419C2212yescomplemented
59C11×#418C2212yescomplemented
60C11×#417C2214yes—
61C11×#417C2214yescomplemented
62C11×#417C2212yescomplemented
63C11×#417C2212yescomplemented
64C11×#416C2214yes—
65C2×C11×#103C2212yescomplemented
66C2×C11×#102C2212yescomplemented
67C11×#405C2214yescomplemented
68C11×#405C2214yescomplemented
69C4×C11×M16C2214yescomplemented
70C2×C11×#41—21no—
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—21no—
74C2×C11×#41—24no—
75C2×C11×#41—24no—
76C2×C11×#41C2×C418yescomplemented
77C2×C11×#41C2×C418yescomplemented
78C2×C11×#41C2312yes—
79C2×C11×#41C2312yes—
80C2×C11×#41C2312yes—
81C2×C11×#41C2312yes—
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11—22no—
92C23×C4×C11C2311yescharacteristic
93C11×#137C2×C4116yescomplemented
94C11×#137C2×C4116yescomplemented
95C11×AGL(1,ℤ/8)C2×C4116yescomplemented
96C11×AGL(1,ℤ/8)C2×C4116yescomplemented
97C11×#135C2×C4132yescomplemented
98C2×C11×Q16C2314yes—
99C2×C11×SD16C2314yes—
100C2×C11×SD16C2314yes—
101C2×C11×D8C2314yes—
102C2×C11×M16—24no—
103C2×C11×M16C2×C418yescomplemented
104C2×C11×M16C2312yes—
105C2×C11×M16C2312yes—
106C2×C11×M16C2312yes—
107C2×C11×M16C2312yes—
108C22×C8×C11C2312yes—
109C22×C8×C11C2312yes—
110C4×Q8×C11—22no—
111C4×Q8×C11—22no—
112C4×Q8×C11—24no—
113C4×Q8×C11C2318yes—
114C4×Q8×C11C2314yes—
115C4×Q8×C11C2314yes—
116C4×D4×C11—24no—
117C4×D4×C11—24no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—28no—
121C4×D4×C11—28no—
122C4×D4×C11—24no—
123C4×D4×C11—24no—
124C4×D4×C11—24no—
125C4×D4×C11C2318yes—
126C4×D4×C11C2314yes—
127C4×D4×C11C2314yes—
128C11×#117—21no—
129C11×#117—21no—
130C11×#117—24no—
131C11×#117—24no—
132C11×#117—22no—
133C11×#117—22no—
134C11×#117—24no—
135C11×#117—24no—
136C11×#117D412yes—
137C11×#117D412yes—
138C11×#117C2312yes—
139C11×#117C2312yes—
140C11×#117C2312yes—
141C11×#117C2312yes—
142C2×C11×C4⋊C4—21no—
143C2×C11×C4⋊C4—22no—
144C2×C11×C4⋊C4—21no—
145C2×C11×C4⋊C4—21no—
146C2×C11×C4⋊C4—24no—
147C2×C11×C4⋊C4—24no—
148C2×C11×C4⋊C4—22no—
149C2×C11×C4⋊C4—22no—
150C2×C11×C4⋊C4D411yescharacteristic
151C2×C11×C4⋊C4D411yescharacteristic
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—22no—
159C2×C11×C22⋊C4—24no—
160C2×C11×C22⋊C4D412yes—
161C2×C42×C11—22no—
162C2×C42×C11—21no—
163C2×C42×C11—24no—
164C2×C42×C11C2312yes—
165C11×#107C2318yes—
166C11×#106C2318yes—
167C11×#103C2318yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#102C2318yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173C11×#97C2318yes—
174C4×C8×C11C2318yes—
175#60170C1111yesmaximal, characteristic, direct product factor, Sylow
176C24×C11—21no—
177C24×C11—21no—
178C24×C11C2×D411yescharacteristic
179C11×#41—28no—
180C11×#41—28no—
181C11×#41—28no—
182C11×#41—28no—
183C11×#41—24no—
184C11×#41—24no—
185C11×#41—24no—
186C11×#41—24no—
187C11×#41C22×C418yes—
188C11×#41C22×C418yes—
189C11×#41C22×C418yes—
190C11×#41C22×C418yescomplemented
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11C22×C414yes—
196C2×Q8×C11C22×C414yescomplemented
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11C22×C414yes—
210C2×D4×C11C22×C414yescomplemented
211C2×D4×C11C2412yes—
212C2×D4×C11C2412yes—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—28no—
216C22×C4×C11—28no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—24no—
227C22×C4×C11—24no—
228C22×C4×C11—28no—
229C22×C4×C11—84no—
230C22×C4×C11—82no—
231C22×C4×C11C22×C414yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11#4114yes—
238C22×C4×C11C2411yescharacteristic
239C22×C4×C11C2411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C11×Q16C22×C4116yescomplemented
242C11×SD16C22×C4116yescomplemented
243C11×SD16C22×C4116yescomplemented
244C11×D8C22×C4116yescomplemented
245C11×M16—24no—
246C11×M16—24no—
247C11×M16C22×C418yes—
248C11×M16C22×C418yescomplemented
249C2×C8×C11—24no—
250C2×C8×C11C22×C418yescomplemented
251C2×C8×C11C2414yes—
252C2×C8×C11C2414yes—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—28no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4C2×D412yes—
262C11×C4⋊C4C2×D412yes—
263C11×C4⋊C4C2×D412yes—
264C11×C4⋊C4C2×D412yes—
265C11×C4⋊C4C2412yes—
266C11×C4⋊C4C2414yes—
267C11×C4⋊C4C2412yes—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—28no—
273C11×C22⋊C4C2×D414yes—
274C11×C22⋊C4C2×D414yes—
275C42×C11—22no—
276C42×C11—24no—
277C42×C11—24no—
278C42×C11—28no—
279C42×C11—22no—
280C42×C11C2×D414yes—
281C42×C11C2414yes—
282C2×#575C2×C1111yescharacteristic
283#3428C2×C1111yescharacteristic, complemented
284C2×#520C2×C1111yescharacteristic, complemented
285#2952C2×C1114yescomplemented
286#2951C2×C1114yescomplemented
287#2947C2×C1114yescomplemented
288#2946C2×C1114yescomplemented
289C4×#137C2×C1114yescomplemented
290C4×AGL(1,ℤ/8)C2×C1114yescomplemented
291C2×#428C2×C1111yescharacteristic, complemented
292#2896C2×C1111yescharacteristic, complemented
293C2×#417C2×C1111yescharacteristic, complemented
294#2873C2×C1111yescharacteristic, complemented
295C23×C11—24no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—81no—
304C23×C11—81no—
305C23×C11C4×D414yes—
306C23×C11C22×D411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C22×D411yescharacteristic
309Q8×C11—24no—
310Q8×C11—24no—
311Q8×C11—22no—
312Q8×C11—22no—
313Q8×C11C23×C414yes—
314Q8×C11C23×C414yes—
315D4×C11—28no—
316D4×C11—28no—
317D4×C11—28no—
318D4×C11—28no—
319D4×C11—24no—
320D4×C11—24no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11C23×C414yes—
324D4×C11C23×C414yes—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—28no—
330C2×C4×C11—28no—
331C2×C4×C11—28no—
332C2×C4×C11—28no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—44no—
339C2×C4×C11—84no—
340C2×C4×C11—84no—
341C2×C4×C11—88no—
342C2×C4×C11—81no—
343C2×C4×C11—81no—
344C2×C4×C11—82no—
345C2×C4×C11—82no—
346C2×C4×C11C4×D414yes—
347C2×C4×C11C4×D414yes—
348C2×C4×C11C4×D414yes—
349C2×C4×C11C23×C412yes—
350C2×C4×C11C23×C412yes—
351C2×C4×C11C23×C412yes—
352C2×C4×C11C22×D414yes—
353C2×C4×C11C22×D414yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4112yes—
358C2×C4×C11C2×#4112yes—
359C2×C4×C11C2×#4112yes—
360C2×C4×C11C2511yescharacteristic
361C8×C11—24no—
362C8×C11C23×C418yes—
363C22×#41C22×C1111yescharacteristic
364C22×#41C22×C1111yescharacteristic
365#575C4×C11116yescomplemented
366C2×#137C22×C1112yes—
367C2×#137C22×C1112yes—
368C2×AGL(1,ℤ/8)C22×C1112yes—
369C2×AGL(1,ℤ/8)C22×C1112yes—
370C2×#135C22×C1114yes—
371C22×M16C22×C1111yescharacteristic
372C22×M16C22×C1111yescharacteristic
373#520—22no—
374#520—22no—
375#520—21no—
376#520—21no—
377#520C22×C1114yes—
378#520C22×C1114yescomplemented
379#520C22×C1112yescomplemented
380#520C22×C1112yescomplemented
381#519C22×C1112yescomplemented
382#518—22no—
383#518C22×C1112yescomplemented
384C4×#41—22no—
385C4×#41C22×C1114yes—
386C2×C4×Q8C22×C1112yescomplemented
387C2×C4×D4—22no—
388C2×C4×D4C22×C1112yescomplemented
389C2×#117—22no—
390C2×#117—21no—
391C2×#117C22×C1111yescharacteristic
392C2×#117C22×C1111yescharacteristic
393C22×C4⋊C4—21no—
394C22×C4⋊C4C22×C1111yescharacteristic
395#442C22×C1118yescomplemented
396#441C22×C1118yescomplemented
397#440C22×C1118yescomplemented
398#440C22×C1118yescomplemented
399C4×Q16C22×C1118yescomplemented
400C4×SD16C22×C1118yescomplemented
401C4×SD16C22×C1118yescomplemented
402C4×D8C22×C1118yescomplemented
403#428C22×C1114yescomplemented
404#428C22×C1114yescomplemented
405C2×#107C22×C1112yescomplemented
406C2×#106C22×C1112yescomplemented
407#419C22×C1112yescomplemented
408#418C22×C1112yescomplemented
409#417C22×C1114yes—
410#417C22×C1114yescomplemented
411#417C22×C1112yescomplemented
412#417C22×C1112yescomplemented
413#416C22×C1114yes—
414C2×#103C22×C1112yescomplemented
415C2×#102C22×C1112yescomplemented
416#405C22×C1114yescomplemented
417#405C22×C1114yescomplemented
418C4×M16C22×C1114yescomplemented
419C22×C11—21no—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11—21no—
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—24no—
426C22×C11—24no—
427C22×C11—44no—
428C22×C11—48no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—84no—
434C22×C11C2×C4×D412yes—
435C22×C11C2×C4×D412yes—
436C22×C11C2×C4×D412yes—
437C22×C11C23×D411yescharacteristic
438C4×C11—24no—
439C4×C11—24no—
440C4×C11—24no—
441C4×C11—24no—
442C4×C11—44no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11C2×C4×D412yes—
446C4×C11C2×C4×D412yes—
447C4×C11C2×C4×D412yes—
448C4×C11C24×C411yescharacteristic
449C4×C11C22×#4111yescharacteristic
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—24no—
455C2×#41—24no—
456C2×#41C2×C4×C1118yescomplemented
457C2×#41C2×C4×C1118yescomplemented
458C2×#41C23×C1112yes—
459C2×#41C23×C1112yes—
460C2×#41C23×C1112yes—
461C2×#41C23×C1112yes—
462C22×Q8C23×C1111yescharacteristic
463C22×Q8C23×C1111yescharacteristic
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C1111yescharacteristic
467C22×D4C23×C1111yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—22no—
472C23×C4C23×C1111yescharacteristic
473#137C2×C4×C11116yescomplemented
474#137C2×C4×C11116yescomplemented
475AGL(1,ℤ/8)C2×C4×C11116yescomplemented
476AGL(1,ℤ/8)C2×C4×C11116yescomplemented
477#135C2×C4×C11132yescomplemented
478C2×Q16C23×C1114yes—
479C2×SD16C23×C1114yes—
480C2×SD16C23×C1114yes—
481C2×D8C23×C1114yes—
482C2×M16—24no—
483C2×M16C2×C4×C1118yescomplemented
484C2×M16C23×C1112yes—
485C2×M16C23×C1112yes—
486C2×M16C23×C1112yes—
487C2×M16C23×C1112yes—
488C22×C8C23×C1112yes—
489C22×C8C23×C1112yes—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8—24no—
493C4×Q8C23×C1118yes—
494C4×Q8C23×C1114yes—
495C4×Q8C23×C1114yes—
496C4×D4—24no—
497C4×D4—24no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—28no—
501C4×D4—28no—
502C4×D4—24no—
503C4×D4—24no—
504C4×D4—24no—
505C4×D4C23×C1118yes—
506C4×D4C23×C1114yes—
507C4×D4C23×C1114yes—
508#117—21no—
509#117—21no—
510#117—24no—
511#117—24no—
512#117—22no—
513#117—22no—
514#117—24no—
515#117—24no—
516#117D4×C1112yes—
517#117D4×C1112yes—
518#117C23×C1112yes—
519#117C23×C1112yes—
520#117C23×C1112yes—
521#117C23×C1112yes—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4D4×C1111yescharacteristic
531C2×C4⋊C4D4×C1111yescharacteristic
532C2×C4⋊C4C23×C1112yes—
533C2×C4⋊C4C23×C1112yes—
534C2×C4⋊C4C23×C1112yes—
535C2×C4⋊C4C23×C1111yescharacteristic
536C2×C4⋊C4C23×C1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4D4×C1112yes—
541C2×C42—22no—
542C2×C42—21no—
543C2×C42—24no—
544C2×C42C23×C1112yes—
545#107C23×C1118yes—
546#106C23×C1118yes—
547#103C23×C1118yes—
548#103C23×C1114yes—
549#103C23×C1114yes—
550#102C23×C1118yes—
551#102C23×C1114yes—
552#102C23×C1114yes—
553#97C23×C1118yes—
554C4×C8C23×C1118yes—
555C2×C11—22no—
556C2×C11—22no—
557C2×C11—22no—
558C2×C11—44no—
559C2×C11—44no—
560C2×C11C22×C4×D411yescharacteristic
561C2×C11#358511yescharacteristic
562C2×C11#358611yescharacteristic
563C24—21no—
564C24—21no—
565C24C2×D4×C1111yescharacteristic
566#41—28no—
567#41—28no—
568#41—28no—
569#41—28no—
570#41—24no—
571#41—24no—
572#41—24no—
573#41—24no—
574#41C22×C4×C1118yes—
575#41C22×C4×C1118yes—
576#41C22×C4×C1118yes—
577#41C22×C4×C1118yescomplemented
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8C22×C4×C1114yes—
583C2×Q8C22×C4×C1114yescomplemented
584C2×Q8C24×C1112yes—
585C2×Q8C24×C1112yes—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4C22×C4×C1114yes—
597C2×D4C22×C4×C1114yescomplemented
598C2×D4C24×C1112yes—
599C2×D4C24×C1112yes—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—28no—
616C22×C4—84no—
617C22×C4—82no—
618C22×C4C22×C4×C1114yes—
619C22×C4C2×D4×C1112yes—
620C22×C4C2×D4×C1112yes—
621C22×C4C2×D4×C1111yescharacteristic
622C22×C4C2×D4×C1111yescharacteristic
623C22×C4C2×D4×C1111yescharacteristic
624C22×C4C11×#4114yes—
625C22×C4C24×C1111yescharacteristic
626C22×C4C24×C1111yescharacteristic
627C22×C4C24×C1111yescharacteristic
628Q16C22×C4×C11116yescomplemented
629SD16C22×C4×C11116yescomplemented
630SD16C22×C4×C11116yescomplemented
631D8C22×C4×C11116yescomplemented
632M16—24no—
633M16—24no—
634M16C22×C4×C1118yes—
635M16C22×C4×C1118yescomplemented
636C2×C8—24no—
637C2×C8C22×C4×C1118yescomplemented
638C2×C8C24×C1114yes—
639C2×C8C24×C1114yes—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—28no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4C2×D4×C1112yes—
649C4⋊C4C2×D4×C1112yes—
650C4⋊C4C2×D4×C1112yes—
651C4⋊C4C2×D4×C1112yes—
652C4⋊C4C24×C1112yes—
653C4⋊C4C24×C1114yes—
654C4⋊C4C24×C1112yes—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—28no—
660C22⋊C4C2×D4×C1114yes—
661C22⋊C4C2×D4×C1114yes—
662C42—22no—
663C42—24no—
664C42—24no—
665C42—28no—
666C42—22no—
667C42C2×D4×C1114yes—
668C42C24×C1114yes—
669C11#6017011yescharacteristic, direct product factor, Sylow
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—81no—
679C23—81no—
680C23C4×D4×C1114yes—
681C23C22×D4×C1111yescharacteristic
682C23C22×D4×C1111yescharacteristic
683C23C22×D4×C1111yescharacteristic
684Q8—24no—
685Q8—24no—
686Q8—22no—
687Q8—22no—
688Q8C23×C4×C1114yes—
689Q8C23×C4×C1114yes—
690D4—28no—
691D4—28no—
692D4—28no—
693D4—28no—
694D4—24no—
695D4—24no—
696D4—22no—
697D4—22no—
698D4C23×C4×C1114yes—
699D4C23×C4×C1114yes—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4—88no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4C4×D4×C1114yes—
722C2×C4C4×D4×C1114yes—
723C2×C4C4×D4×C1114yes—
724C2×C4C23×C4×C1112yes—
725C2×C4C23×C4×C1112yes—
726C2×C4C23×C4×C1112yes—
727C2×C4C22×D4×C1114yes—
728C2×C4C22×D4×C1114yes—
729C2×C4C22×D4×C1111yescharacteristic
730C2×C4C22×D4×C1111yescharacteristic
731C2×C4C22×D4×C1111yescharacteristic
732C2×C4C2×C11×#4112yes—
733C2×C4C2×C11×#4112yes—
734C2×C4C2×C11×#4112yes—
735C2×C4C25×C1111yescharacteristic
736C8—24no—
737C8C23×C4×C1118yes—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—24no—
745C22—24no—
746C22—44no—
747C22—48no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—84no—
753C22C2×C4×D4×C1112yes—
754C22C2×C4×D4×C1112yes—
755C22C2×C4×D4×C1112yes—
756C22C23×D4×C1111yescharacteristic
757C4—24no—
758C4—24no—
759C4—24no—
760C4—24no—
761C4—44no—
762C4—42no—
763C4—42no—
764C4C2×C4×D4×C1112yes—
765C4C2×C4×D4×C1112yes—
766C4C2×C4×D4×C1112yes—
767C4C24×C4×C1111yescharacteristic
768C4C22×C11×#4111yescharacteristic
769C2—22no—
770C2—22no—
771C2—22no—
772C2—44no—
773C2—44no—
774C2C22×C4×D4×C1111yescharacteristic
775C2C11×#358511yescharacteristic
776C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutatorC4C24×C4×C11
Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#575C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3428C2semidirect
3. C2×C11×#520C2semidirect
4. C11×#2952C2semidirect
5. C11×#2951C2semidirect
6. C11×#2947C2semidirect
7. C11×#2946C2semidirect
8. C4×C11×#137C2semidirect
9. C4×C11×AGL(1,ℤ/8)C2semidirect
10. C2×C11×#428C2semidirect
11. C11×#2896C2semidirect
12. C2×C11×#417C2semidirect
13. C11×#2873C2semidirect
16. C11×#575C4semidirect
29. C11×#520C22semidirect
30. C11×#520C22semidirect
31. C11×#520C22semidirect
32. C11×#519C22semidirect
34. C11×#518C22semidirect
37. C2×C4×Q8×C11C22semidirect
39. C2×C4×D4×C11C22semidirect
46. C11×#442C22semidirect
47. C11×#441C22semidirect
48. C11×#440C22semidirect
49. C11×#440C22semidirect
50. C4×C11×Q16C22semidirect
51. C4×C11×SD16C22semidirect
52. C4×C11×SD16C22semidirect
53. C4×C11×D8C22semidirect
54. C11×#428C22semidirect
55. C11×#428C22semidirect
56. C2×C11×#107C22semidirect
57. C2×C11×#106C22semidirect
58. C11×#419C22semidirect
59. C11×#418C22semidirect
61. C11×#417C22semidirect
62. C11×#417C22semidirect
63. C11×#417C22semidirect
65. C2×C11×#103C22semidirect
66. C2×C11×#102C22semidirect
67. C11×#405C22semidirect
68. C11×#405C22semidirect
69. C4×C11×M16C22semidirect
76. C2×C11×#41C2×C4semidirect
77. C2×C11×#41C2×C4semidirect
93. C11×#137C2×C4semidirect
94. C11×#137C2×C4semidirect
95. C11×AGL(1,ℤ/8)C2×C4semidirect
96. C11×AGL(1,ℤ/8)C2×C4semidirect
97. C11×#135C2×C4semidirect
103. C2×C11×M16C2×C4semidirect
175. #60170C11direct (N × H)
190. C11×#41C22×C4semidirect
196. C2×Q8×C11C22×C4semidirect
210. C2×D4×C11C22×C4semidirect
241. C11×Q16C22×C4semidirect
242. C11×SD16C22×C4semidirect
243. C11×SD16C22×C4semidirect
244. C11×D8C22×C4semidirect
248. C11×M16C22×C4semidirect
250. C2×C8×C11C22×C4semidirect
283. #3428C2×C11semidirect
284. C2×#520C2×C11semidirect
285. #2952C2×C11semidirect
286. #2951C2×C11semidirect
287. #2947C2×C11semidirect
288. #2946C2×C11semidirect
289. C4×#137C2×C11semidirect
290. C4×AGL(1,ℤ/8)C2×C11semidirect
291. C2×#428C2×C11semidirect
292. #2896C2×C11semidirect
293. C2×#417C2×C11semidirect
294. #2873C2×C11semidirect
365. #575C4×C11semidirect
378. #520C22×C11semidirect
379. #520C22×C11semidirect
380. #520C22×C11semidirect
381. #519C22×C11semidirect
383. #518C22×C11semidirect
386. C2×C4×Q8C22×C11semidirect
388. C2×C4×D4C22×C11semidirect
395. #442C22×C11semidirect
396. #441C22×C11semidirect
397. #440C22×C11semidirect
398. #440C22×C11semidirect
399. C4×Q16C22×C11semidirect
400. C4×SD16C22×C11semidirect
401. C4×SD16C22×C11semidirect
402. C4×D8C22×C11semidirect
403. #428C22×C11semidirect
404. #428C22×C11semidirect
405. C2×#107C22×C11semidirect
406. C2×#106C22×C11semidirect
407. #419C22×C11semidirect
408. #418C22×C11semidirect
410. #417C22×C11semidirect
411. #417C22×C11semidirect
412. #417C22×C11semidirect
414. C2×#103C22×C11semidirect
415. C2×#102C22×C11semidirect
416. #405C22×C11semidirect
417. #405C22×C11semidirect
418. C4×M16C22×C11semidirect
456. C2×#41C2×C4×C11semidirect
457. C2×#41C2×C4×C11semidirect
473. #137C2×C4×C11semidirect
474. #137C2×C4×C11semidirect
475. AGL(1,ℤ/8)C2×C4×C11semidirect
476. AGL(1,ℤ/8)C2×C4×C11semidirect
477. #135C2×C4×C11semidirect
483. C2×M16C2×C4×C11semidirect
577. #41C22×C4×C11semidirect
583. C2×Q8C22×C4×C11semidirect
597. C2×D4C22×C4×C11semidirect
628. Q16C22×C4×C11semidirect
629. SD16C22×C4×C11semidirect
630. SD16C22×C4×C11semidirect
631. D8C22×C4×C11semidirect
635. M16C22×C4×C11semidirect
637. C2×C8C22×C4×C11semidirect
669. C11#60170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C11×#34282
C2×C11×#5202
C11×#29522
C11×#29512
C11×#29472
C11×#29462
C4×C11×#1372
C4×C11×AGL(1,ℤ/8)2
C2×C11×#4282
C11×#28962
C2×C11×#4172
C11×#28732
#6017011