Finite Group Databasebeta

← C11×#61067 #14638260

Subgroups — C11×#61067 #14638260

Order 2816.

2778 conjugacy classes of subgroups.

The subgroup lattice has 1032 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×#547C211yesmaximal, characteristic, complemented
4C11×#3284C212yesmaximal, complemented
5C11×#3283C212yesmaximal, complemented
6C11×#3276C212yesmaximal, complemented
7C11×#3272C212yesmaximal, complemented
8C11×#3269C214yesmaximal, complemented
9C11×#3267C214yesmaximal, complemented
10C11×#3152C211yesmaximal, characteristic, complemented
11C11×#3056C212yesmaximal, complemented
12C11×#3039C211yesmaximal, characteristic, complemented
13C11×#3036C211yesmaximal, characteristic, complemented
14C11×#3007C212yesmaximal, complemented
15C11×#3005C212yesmaximal, complemented
16C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
17D4×C11×M16C211yesmaximal, characteristic, complemented
18C22×C11×#41C2212yes—
19C22×C11×#41C2212yescomplemented
20C11×#575—216no—
21C2×C11×#137C2212yes—
22C2×C11×#137C2212yescomplemented
23C2×C11×#137C2214yescomplemented
24C2×C11×#137C2212yescomplemented
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×AGL(1,ℤ/8)C2212yescomplemented
27C2×C11×AGL(1,ℤ/8)C2214yescomplemented
28C2×C11×#135C2214yescomplemented
29C2×C11×#135C2214yescomplemented
30C22×C11×M16C2212yescomplemented
31C11×#550C2211yescharacteristic, complemented
32D4×Q8×C11C2211yescharacteristic, complemented
33C11×#548C2212yescomplemented
34C11×#547—21no—
35C11×#547—21no—
36C11×#547—22no—
37C11×#547—21no—
38C11×#547C2212yes—
39C11×#547C2214yescomplemented
40C11×#547C2212yescomplemented
41C11×#547C2211yescharacteristic, complemented
42C11×#546—22no—
43C11×#546C2212yescomplemented
44D42×C11—21no—
45D42×C11C2211yescharacteristic, complemented
46C11×#532—21no—
47C11×#532C2211yescharacteristic
48C2×C11×C4⋊Q8C2211yescharacteristic, complemented
49C11×#525—22no—
50C11×#525C2212yes—
51C2×C11×#123—22no—
52C2×C11×C22⋊Q8C2212yescomplemented
53C2×C11×#121—21no—
54C4×C11×#41C2211yescharacteristic
55C2×C4×D4×C11—21no—
56C2×C4×D4×C11C2211yescharacteristic
57C2×C4×D4×C11C2211yescharacteristic, complemented
58C22×C11×C4⋊C4—21no—
59C11×#497C2214yescomplemented
60C11×#494C2212yescomplemented
61C11×#492C2212yescomplemented
62C11×#470C2214yescomplemented
63C11×#468C2214yescomplemented
64C11×#467C2214yescomplemented
65C11×#465C2214yescomplemented
66C11×#463C2214yescomplemented
67C11×#462C2212yescomplemented
68C11×#462C2212yescomplemented
69C11×#461C2212yescomplemented
70C11×#461C2212yescomplemented
71C11×#461C2212yescomplemented
72C11×#459C2212yescomplemented
73C11×#452C2214yescomplemented
74C11×#452C2214yescomplemented
75C11×#452C2214yescomplemented
76C11×#452C2214yescomplemented
77C11×#451C2214yescomplemented
78C11×#450C2214yescomplemented
79C11×#449C2214yescomplemented
80C11×#449C2214yescomplemented
81C11×#442C2212yescomplemented
82C11×#440C2212yescomplemented
83C4×C11×SD16C2212yescomplemented
84C4×C11×D8C2212yescomplemented
85C11×#436C2212yescomplemented
86C11×#435C2214yescomplemented
87C8×D4×C11C2212yescomplemented
88C11×#428C2211yescharacteristic, complemented
89C11×#423C2211yescharacteristic, complemented
90C11×#419C2212yescomplemented
91C11×#418C2211yescharacteristic, complemented
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×#41C2314yes—
107C2×C11×#41C2314yes—
108C2×C11×#41C2312yes—
109C2×C11×#41C2311yescharacteristic
110C22×Q8×C11C2312yes—
111C22×Q8×C11C2312yes—
112C22×D4×C11—22no—
113C22×D4×C11—22no—
114C22×D4×C11—21no—
115C22×D4×C11D411yescharacteristic
116C22×D4×C11C2312yes—
117C22×D4×C11C2311yescharacteristic
118C23×C4×C11—21no—
119C23×C4×C11—22no—
120C23×C4×C11—22no—
121C23×C4×C11C2312yes—
122C11×#137—28no—
123C11×#137—216no—
124C11×#137—28no—
125C11×#137—44no—
126C11×AGL(1,ℤ/8)—28no—
127C11×AGL(1,ℤ/8)—216no—
128C11×AGL(1,ℤ/8)D418yescomplemented
129C11×#135—216no—
130C11×#135—216no—
131C2×C11×Q16C2314yes—
132C2×C11×Q16C2314yes—
133C2×C11×Q16C2314yes—
134C2×C11×SD16C2314yes—
135C2×C11×SD16C2314yes—
136C2×C11×SD16C2314yes—
137C2×C11×SD16C2314yes—
138C2×C11×SD16C2312yes—
139C2×C11×D8C2314yes—
140C2×C11×D8C2312yes—
141C2×C11×M16—28no—
142C2×C11×M16C2311yescharacteristic
143C2×C11×M16C2312yes—
144C2×C11×M16C2314yes—
145C2×C11×M16C2311yescharacteristic
146C22×C8×C11C2314yes—
147C11×C4⋊Q8—21no—
148C11×C4⋊Q8—21no—
149C11×C4⋊Q8—21no—
150C11×C4⋊Q8C2312yes—
151C11×C4⋊Q8C2311yescharacteristic
152C11×C4⋊Q8C2312yes—
153C11×#127—21no—
154C11×#127C2311yescharacteristic
155C11×#124—22no—
156C11×#124C2312yes—
157C11×#123—22no—
158C11×#123—22no—
159C11×#123—24no—
160C11×#123—24no—
161C11×#123—24no—
162C11×#123—24no—
163C11×#123—22no—
164C11×C22⋊Q8—22no—
165C11×C22⋊Q8—22no—
166C11×C22⋊Q8—22no—
167C11×C22⋊Q8—22no—
168C11×C22⋊Q8C2314yes—
169C11×C22⋊Q8C2314yes—
170C11×C22⋊Q8C2312yes—
171C11×C22⋊Q8C2312yes—
172C11×#121—22no—
173C11×#121—22no—
174C11×#121—24no—
175C11×#121—22no—
176C11×#121—21no—
177C11×#121—21no—
178C11×#121—21no—
179C11×#121—21no—
180C11×#121—22no—
181C11×#121—22no—
182C11×#121C2312yes—
183C11×#121C2312yes—
184C11×#120—22no—
185C11×#120—22no—
186C11×#120—22no—
187C4×Q8×C11C2311yescharacteristic
188C4×Q8×C11C2311yescharacteristic
189C4×D4×C11—21no—
190C4×D4×C11—22no—
191C4×D4×C11—21no—
192C4×D4×C11—21no—
193C4×D4×C11—22no—
194C4×D4×C11—21no—
195C4×D4×C11—22no—
196C4×D4×C11—21no—
197C4×D4×C11—21no—
198C4×D4×C11—21no—
199C4×D4×C11—21no—
200C4×D4×C11D411yescharacteristic
201C4×D4×C11D412yes—
202C4×D4×C11D411yescharacteristic
203C4×D4×C11C2312yes—
204C4×D4×C11C2312yes—
205C4×D4×C11C2311yescharacteristic
206C4×D4×C11C2311yescharacteristic
207C4×D4×C11C2311yescharacteristic
208C4×D4×C11C2312yes—
209C4×D4×C11C2311yescharacteristic
210C11×#117—21no—
211C11×#117C2311yescharacteristic
212C2×C11×C4⋊C4—21no—
213C2×C11×C4⋊C4—22no—
214C2×C11×C4⋊C4—21no—
215C2×C11×C4⋊C4—22no—
216C2×C11×C4⋊C4—22no—
217C2×C11×C4⋊C4—24no—
218C2×C11×C4⋊C4—21no—
219C2×C11×C4⋊C4D411yescharacteristic
220C2×C11×C4⋊C4C2311yescharacteristic
221C2×C11×C22⋊C4—22no—
222C2×C11×C22⋊C4—21no—
223C2×C11×C22⋊C4—22no—
224C2×C11×C22⋊C4D412yes—
225C2×C42×C11—21no—
226C2×C42×C11C2311yescharacteristic
227C11×#107C2312yes—
228C11×#106C2312yes—
229C11×C4⋊C8C2312yes—
230C11×C4⋊C8C2312yes—
231C11×#103C2312yes—
232C11×#103C2314yes—
233C11×#103C2314yes—
234C11×#103C2314yes—
235C11×#102C2312yes—
236C11×#102C2314yes—
237C11×#102C2312yes—
238C11×#102C2312yes—
239C11×C22⋊C8C2314yes—
240C11×C22⋊C8C2314yes—
241C11×#97C2312yes—
242C4×C8×C11C2312yes—
243#61067C1111yesmaximal, characteristic, direct product factor, Sylow
244C24×C11—21no—
245C24×C11—22no—
246C24×C11C2×D412yes—
247C11×#41—22no—
248C11×#41—24no—
249C11×#41—28no—
250C11×#41—24no—
251C11×#41—28no—
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—22no—
264C2×Q8×C11—22no—
265C2×Q8×C11—24no—
266C2×Q8×C11—24no—
267C2×Q8×C11—24no—
268C2×Q8×C11—42no—
269C2×Q8×C11C2412yes—
270C2×Q8×C11C2414yes—
271C2×Q8×C11C2411yescharacteristic
272C2×D4×C11—21no—
273C2×D4×C11—24no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—24no—
278C2×D4×C11—24no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—21no—
282C2×D4×C11—21no—
283C2×D4×C11—22no—
284C2×D4×C11—21no—
285C2×D4×C11—22no—
286C2×D4×C11—42no—
287C2×D4×C11—42no—
288C2×D4×C11—48no—
289C2×D4×C11—44no—
290C2×D4×C11—48no—
291C2×D4×C11C2×D411yescharacteristic
292C2×D4×C11C2×D411yescharacteristic
293C2×D4×C11C2×D412yes—
294C2×D4×C11C2×D414yescomplemented
295C2×D4×C11C2412yes—
296C2×D4×C11C2412yes—
297C2×D4×C11C2411yescharacteristic
298C22×C4×C11—21no—
299C22×C4×C11—24no—
300C22×C4×C11—24no—
301C22×C4×C11—21no—
302C22×C4×C11—22no—
303C22×C4×C11—22no—
304C22×C4×C11—21no—
305C22×C4×C11—22no—
306C22×C4×C11—22no—
307C22×C4×C11—22no—
308C22×C4×C11—24no—
309C22×C4×C11—24no—
310C22×C4×C11—22no—
311C22×C4×C11—22no—
312C22×C4×C11—21no—
313C22×C4×C11—48no—
314C22×C4×C11—48no—
315C22×C4×C11—44no—
316C22×C4×C11C2×D411yescharacteristic
317C22×C4×C11C2×D412yes—
318C22×C4×C11C2×D412yes—
319C22×C4×C11C2×D412yes—
320C22×C4×C11C2×D411yescharacteristic
321C22×C4×C11C2412yes—
322C22×C4×C11C2412yes—
323C22×C4×C11C2411yescharacteristic
324C11×Q16—28no—
325C11×Q16—28no—
326C11×Q16—44no—
327C11×SD16—28no—
328C11×SD16—28no—
329C11×SD16—28no—
330C11×SD16—44no—
331C11×SD16C2×D418yescomplemented
332C11×D8—28no—
333C11×D8C2×D418yescomplemented
334C11×M16—28no—
335C11×M16—24no—
336C11×M16—22no—
337C11×M16C2×D414yescomplemented
338C2×C8×C11—28no—
339C2×C8×C11C2412yes—
340C2×C8×C11C2414yes—
341C2×C8×C11C2412yes—
342C11×C4⋊C4—22no—
343C11×C4⋊C4—22no—
344C11×C4⋊C4—24no—
345C11×C4⋊C4—24no—
346C11×C4⋊C4—21no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—21no—
351C11×C4⋊C4—21no—
352C11×C4⋊C4—21no—
353C11×C4⋊C4—21no—
354C11×C4⋊C4—22no—
355C11×C4⋊C4C2×D411yescharacteristic
356C11×C4⋊C4C2×D411yescharacteristic
357C11×C4⋊C4C2×D412yes—
358C11×C4⋊C4C2412yes—
359C11×C4⋊C4C2411yescharacteristic
360C11×C4⋊C4C2411yescharacteristic
361C11×C22⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—21no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—22no—
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×C11C2×D411yescharacteristic
382C42×C11C2×D411yescharacteristic
383C42×C11C2411yescharacteristic
384C42×C11C2411yescharacteristic
385C2×#575C2×C1112yescomplemented
386D4×#41C2×C1111yescharacteristic, complemented
387C2×#547C2×C1111yescharacteristic, complemented
388#3284C2×C1112yescomplemented
389#3283C2×C1112yescomplemented
390#3276C2×C1112yescomplemented
391#3272C2×C1112yescomplemented
392#3269C2×C1114yescomplemented
393#3267C2×C1114yescomplemented
394#3152C2×C1111yescharacteristic, complemented
395#3056C2×C1112yescomplemented
396#3039C2×C1111yescharacteristic, complemented
397#3036C2×C1111yescharacteristic, complemented
398#3007C2×C1112yescomplemented
399#3005C2×C1112yescomplemented
400C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
401D4×M16C2×C1111yescharacteristic, complemented
402C23×C11—24no—
403C23×C11—22no—
404C23×C11—21no—
405C23×C11—24no—
406C23×C11—22no—
407C23×C11—42no—
408C23×C11—42no—
409C23×C11—44no—
410C23×C11—42no—
411C23×C11—42no—
412C23×C11—44no—
413C23×C11—82no—
414C23×C11C22×D412yes—
415C23×C11C22×D412yes—
416C23×C11C22×D411yescharacteristic
417Q8×C11—21no—
418Q8×C11—24no—
419Q8×C11—22no—
420Q8×C11—24no—
421Q8×C11—22no—
422Q8×C11—44no—
423Q8×C11—44no—
424Q8×C11C22×D412yes—
425D4×C11—24no—
426D4×C11—24no—
427D4×C11—22no—
428D4×C11—22no—
429D4×C11—22no—
430D4×C11—22no—
431D4×C11—21no—
432D4×C11—22no—
433D4×C11—42no—
434D4×C11—44no—
435D4×C11—44no—
436D4×C11—48no—
437D4×C11—44no—
438D4×C11—48no—
439D4×C11—44no—
440D4×C11—44no—
441D4×C11—42no—
442D4×C11—81no—
443D4×C11—82no—
444D4×C11C22×D414yes—
445D4×C11C22×D412yes—
446C2×C4×C11—24no—
447C2×C4×C11—21no—
448C2×C4×C11—24no—
449C2×C4×C11—24no—
450C2×C4×C11—24no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—24no—
461C2×C4×C11—41no—
462C2×C4×C11—44no—
463C2×C4×C11—44no—
464C2×C4×C11—44no—
465C2×C4×C11—48no—
466C2×C4×C11—48no—
467C2×C4×C11—44no—
468C2×C4×C11—42no—
469C2×C4×C11—44no—
470C2×C4×C11—44no—
471C2×C4×C11—44no—
472C2×C4×C11—42no—
473C2×C4×C11—81no—
474C2×C4×C11C22×D411yescharacteristic
475C2×C4×C11C22×D411yescharacteristic
476C2×C4×C11C22×D411yescharacteristic
477C2×C4×C11C22×D412yes—
478C2×C4×C11C22×D412yes—
479C2×C4×C11C22×D411yescharacteristic
480C2×C4×C11C22×D412yes—
481C2×C4×C11C22×D411yescharacteristic
482C2×C4×C11H(5,𝔽2)12yes—
483C2×C4×C11C2511yescharacteristic
484C8×C11—24no—
485C8×C11—22no—
486C8×C11C22×D414yes—
487C22×#41C22×C1112yes—
488C22×#41C22×C1112yescomplemented
489#575—216no—
490C2×#137C22×C1112yes—
491C2×#137C22×C1112yescomplemented
492C2×#137C22×C1114yescomplemented
493C2×#137C22×C1112yescomplemented
494C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
495C2×AGL(1,ℤ/8)C22×C1112yescomplemented
496C2×AGL(1,ℤ/8)C22×C1114yescomplemented
497C2×#135C22×C1114yescomplemented
498C2×#135C22×C1114yescomplemented
499C22×M16C22×C1112yescomplemented
500#550C22×C1111yescharacteristic, complemented
501D4×Q8C22×C1111yescharacteristic, complemented
502#548C22×C1112yescomplemented
503#547—21no—
504#547—21no—
505#547—22no—
506#547—21no—
507#547C22×C1112yes—
508#547C22×C1114yescomplemented
509#547C22×C1112yescomplemented
510#547C22×C1111yescharacteristic, complemented
511#546—22no—
512#546C22×C1112yescomplemented
513D42—21no—
514D42C22×C1111yescharacteristic, complemented
515#532—21no—
516#532C22×C1111yescharacteristic
517C2×C4⋊Q8C22×C1111yescharacteristic, complemented
518#525—22no—
519#525C22×C1112yes—
520C2×#123—22no—
521C2×C22⋊Q8C22×C1112yescomplemented
522C2×#121—21no—
523C4×#41C22×C1111yescharacteristic
524C2×C4×D4—21no—
525C2×C4×D4C22×C1111yescharacteristic
526C2×C4×D4C22×C1111yescharacteristic, complemented
527C22×C4⋊C4—21no—
528#497C22×C1114yescomplemented
529#494C22×C1112yescomplemented
530#492C22×C1112yescomplemented
531#470C22×C1114yescomplemented
532#468C22×C1114yescomplemented
533#467C22×C1114yescomplemented
534#465C22×C1114yescomplemented
535#463C22×C1114yescomplemented
536#462C22×C1112yescomplemented
537#462C22×C1112yescomplemented
538#461C22×C1112yescomplemented
539#461C22×C1112yescomplemented
540#461C22×C1112yescomplemented
541#459C22×C1112yescomplemented
542#452C22×C1114yescomplemented
543#452C22×C1114yescomplemented
544#452C22×C1114yescomplemented
545#452C22×C1114yescomplemented
546#451C22×C1114yescomplemented
547#450C22×C1114yescomplemented
548#449C22×C1114yescomplemented
549#449C22×C1114yescomplemented
550#442C22×C1112yescomplemented
551#440C22×C1112yescomplemented
552C4×SD16C22×C1112yescomplemented
553C4×D8C22×C1112yescomplemented
554#436C22×C1112yescomplemented
555#435C22×C1114yescomplemented
556C8×D4C22×C1112yescomplemented
557#428C22×C1111yescharacteristic, complemented
558#423C22×C1111yescharacteristic, complemented
559#419C22×C1112yescomplemented
560#418C22×C1111yescharacteristic, complemented
561#417C22×C1111yescharacteristic
562#417C22×C1112yescomplemented
563#407C22×C1112yescomplemented
564C4×M16C22×C1111yescharacteristic, complemented
565C22×C11—21no—
566C22×C11—21no—
567C22×C11—22no—
568C22×C11—22no—
569C22×C11—22no—
570C22×C11—22no—
571C22×C11—22no—
572C22×C11—24no—
573C22×C11—22no—
574C22×C11—22no—
575C22×C11—48no—
576C22×C11—41no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—41no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—84no—
584C22×C11—88no—
585C22×C11D4212yes—
586C22×C11C23×D411yescharacteristic
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—22no—
590C4×C11—22no—
591C4×C11—22no—
592C4×C11—21no—
593C4×C11—41no—
594C4×C11—42no—
595C4×C11—44no—
596C4×C11—42no—
597C4×C11—41no—
598C4×C11D4212yes—
599C4×C11#57512yescomplemented
600C4×C11C23×D411yescharacteristic
601C4×C11C2×H(5,𝔽2)11yescharacteristic
602C2×#41—22no—
603C2×#41—22no—
604C2×#41—22no—
605C2×#41—22no—
606C2×#41—28no—
607C2×#41—28no—
608C2×#41—44no—
609C2×#41—44no—
610C2×#41C23×C1112yes—
611C2×#41C23×C1112yes—
612C2×#41C23×C1114yes—
613C2×#41C23×C1114yes—
614C2×#41C23×C1112yes—
615C2×#41C23×C1111yescharacteristic
616C22×Q8C23×C1112yes—
617C22×Q8C23×C1112yes—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—21no—
621C22×D4D4×C1111yescharacteristic
622C22×D4C23×C1112yes—
623C22×D4C23×C1111yescharacteristic
624C23×C4—21no—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4C23×C1112yes—
628#137—28no—
629#137—216no—
630#137—28no—
631#137—44no—
632AGL(1,ℤ/8)—28no—
633AGL(1,ℤ/8)—216no—
634AGL(1,ℤ/8)D4×C1118yescomplemented
635#135—216no—
636#135—216no—
637C2×Q16C23×C1114yes—
638C2×Q16C23×C1114yes—
639C2×Q16C23×C1114yes—
640C2×SD16C23×C1114yes—
641C2×SD16C23×C1114yes—
642C2×SD16C23×C1114yes—
643C2×SD16C23×C1114yes—
644C2×SD16C23×C1112yes—
645C2×D8C23×C1114yes—
646C2×D8C23×C1112yes—
647C2×M16—28no—
648C2×M16C23×C1112yes—
649C2×M16C23×C1114yes—
650C2×M16C23×C1111yescharacteristic
651C2×M16C23×C1111yescharacteristic
652C22×C8C23×C1114yes—
653C4⋊Q8—21no—
654C4⋊Q8—21no—
655C4⋊Q8—21no—
656C4⋊Q8C23×C1112yes—
657C4⋊Q8C23×C1112yes—
658C4⋊Q8C23×C1111yescharacteristic
659#127—21no—
660#127C23×C1111yescharacteristic
661#124—22no—
662#124C23×C1112yes—
663#123—22no—
664#123—22no—
665#123—24no—
666#123—24no—
667#123—24no—
668#123—24no—
669#123—22no—
670C22⋊Q8—22no—
671C22⋊Q8—22no—
672C22⋊Q8—22no—
673C22⋊Q8—22no—
674C22⋊Q8C23×C1114yes—
675C22⋊Q8C23×C1114yes—
676C22⋊Q8C23×C1112yes—
677C22⋊Q8C23×C1112yes—
678#121—22no—
679#121—22no—
680#121—24no—
681#121—22no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—21no—
686#121—22no—
687#121—22no—
688#121C23×C1112yes—
689#121C23×C1112yes—
690#120—22no—
691#120—22no—
692#120—22no—
693C4×Q8C23×C1111yescharacteristic
694C4×Q8C23×C1111yescharacteristic
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—22no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4D4×C1111yescharacteristic
707C4×D4D4×C1112yes—
708C4×D4D4×C1111yescharacteristic
709C4×D4C23×C1112yes—
710C4×D4C23×C1112yes—
711C4×D4C23×C1111yescharacteristic
712C4×D4C23×C1111yescharacteristic
713C4×D4C23×C1111yescharacteristic
714C4×D4C23×C1112yes—
715C4×D4C23×C1111yescharacteristic
716#117—21no—
717#117C23×C1111yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—24no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4D4×C1111yescharacteristic
726C2×C4⋊C4C23×C1111yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4D4×C1112yes—
731C2×C42—21no—
732C2×C42C23×C1111yescharacteristic
733#107C23×C1112yes—
734#106C23×C1112yes—
735C4⋊C8C23×C1112yes—
736C4⋊C8C23×C1112yes—
737#103C23×C1112yes—
738#103C23×C1114yes—
739#103C23×C1114yes—
740#103C23×C1114yes—
741#102C23×C1112yes—
742#102C23×C1114yes—
743#102C23×C1112yes—
744#102C23×C1112yes—
745C22⋊C8C23×C1114yes—
746C22⋊C8C23×C1114yes—
747#97C23×C1112yes—
748C4×C8C23×C1112yes—
749C2×C11—22no—
750C2×C11—42no—
751C2×C11—42no—
752C2×C11—44no—
753C2×C11—42no—
754C2×C11—82no—
755C2×C11C2×D4211yescharacteristic
756C2×C11C2×#57511yescharacteristic
757C2×C11#358611yescharacteristic
758C24—21no—
759C24—22no—
760C24C2×D4×C1112yes—
761#41—22no—
762#41—24no—
763#41—28no—
764#41—24no—
765#41—28no—
766#41—24no—
767#41—24no—
768#41—48no—
769#41—44no—
770#41—42no—
771#41—44no—
772#41—42no—
773#41—48no—
774#41—48no—
775#41—48no—
776#41C2×D4×C1114yes—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—42no—
783C2×Q8C24×C1112yes—
784C2×Q8C24×C1114yes—
785C2×Q8C24×C1111yescharacteristic
786C2×D4—21no—
787C2×D4—24no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—22no—
798C2×D4—21no—
799C2×D4—22no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—48no—
803C2×D4—44no—
804C2×D4—48no—
805C2×D4C2×D4×C1111yescharacteristic
806C2×D4C2×D4×C1111yescharacteristic
807C2×D4C2×D4×C1112yes—
808C2×D4C2×D4×C1114yescomplemented
809C2×D4C24×C1112yes—
810C2×D4C24×C1112yes—
811C2×D4C24×C1111yescharacteristic
812C22×C4—21no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—44no—
830C22×C4C2×D4×C1111yescharacteristic
831C22×C4C2×D4×C1112yes—
832C22×C4C2×D4×C1112yes—
833C22×C4C2×D4×C1112yes—
834C22×C4C2×D4×C1111yescharacteristic
835C22×C4C24×C1112yes—
836C22×C4C24×C1112yes—
837C22×C4C24×C1111yescharacteristic
838Q16—28no—
839Q16—28no—
840Q16—44no—
841SD16—28no—
842SD16—28no—
843SD16—28no—
844SD16—44no—
845SD16C2×D4×C1118yescomplemented
846D8—28no—
847D8C2×D4×C1118yescomplemented
848M16—24no—
849M16—22no—
850M16—28no—
851M16C2×D4×C1114yescomplemented
852C2×C8—28no—
853C2×C8C24×C1112yes—
854C2×C8C24×C1114yes—
855C2×C8C24×C1112yes—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—21no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—22no—
869C4⋊C4C2×D4×C1111yescharacteristic
870C4⋊C4C2×D4×C1111yescharacteristic
871C4⋊C4C2×D4×C1112yes—
872C4⋊C4C24×C1112yes—
873C4⋊C4C24×C1111yescharacteristic
874C4⋊C4C24×C1111yescharacteristic
875C22⋊C4—22no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—21no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—21no—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4C2×D4×C1112yes—
889C22⋊C4C2×D4×C1112yes—
890C22⋊C4C2×D4×C1112yes—
891C22⋊C4C2×D4×C1112yes—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C1111yescharacteristic
896C42C2×D4×C1111yescharacteristic
897C42C24×C1111yescharacteristic
898C42C24×C1111yescharacteristic
899C11#6106711yescharacteristic, direct product factor, Sylow
900C23—24no—
901C23—22no—
902C23—21no—
903C23—24no—
904C23—22no—
905C23—42no—
906C23—42no—
907C23—44no—
908C23—42no—
909C23—42no—
910C23—44no—
911C23—82no—
912C23C22×D4×C1112yes—
913C23C22×D4×C1112yes—
914C23C22×D4×C1111yescharacteristic
915Q8—21no—
916Q8—22no—
917Q8—24no—
918Q8—24no—
919Q8—22no—
920Q8—44no—
921Q8—44no—
922Q8C22×D4×C1112yes—
923D4—24no—
924D4—24no—
925D4—22no—
926D4—22no—
927D4—22no—
928D4—22no—
929D4—21no—
930D4—22no—
931D4—42no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—44no—
936D4—48no—
937D4—44no—
938D4—44no—
939D4—42no—
940D4—81no—
941D4—82no—
942D4C22×D4×C1114yes—
943D4C22×D4×C1112yes—
944C2×C4—24no—
945C2×C4—21no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—41no—
960C2×C4—44no—
961C2×C4—44no—
962C2×C4—44no—
963C2×C4—48no—
964C2×C4—48no—
965C2×C4—44no—
966C2×C4—42no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—42no—
971C2×C4—81no—
972C2×C4C22×D4×C1111yescharacteristic
973C2×C4C22×D4×C1111yescharacteristic
974C2×C4C22×D4×C1111yescharacteristic
975C2×C4C22×D4×C1112yes—
976C2×C4C22×D4×C1112yes—
977C2×C4C22×D4×C1111yescharacteristic
978C2×C4C22×D4×C1112yes—
979C2×C4C22×D4×C1111yescharacteristic
980C2×C4C11×H(5,𝔽2)12yes—
981C2×C4C25×C1111yescharacteristic
982C8—24no—
983C8—22no—
984C8C22×D4×C1114yes—
985C22—21no—
986C22—21no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—24no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—48no—
996C22—42no—
997C22—41no—
998C22—41no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—84no—
1004C22—88no—
1005C22D42×C1112yes—
1006C22C23×D4×C1111yescharacteristic
1007C4—22no—
1008C4—22no—
1009C4—22no—
1010C4—21no—
1011C4—21no—
1012C4—21no—
1013C4—42no—
1014C4—44no—
1015C4—42no—
1016C4—41no—
1017C4—41no—
1018C4D42×C1112yes—
1019C4C11×#57512yescomplemented
1020C4C23×D4×C1111yescharacteristic
1021C4C2×C11×H(5,𝔽2)11yescharacteristic
1022C2—22no—
1023C2—42no—
1024C2—42no—
1025C2—44no—
1026C2—42no—
1027C2—82no—
1028C2C2×D42×C1111yescharacteristic
1029C2C2×C11×#57511yescharacteristic
1030C2C11×#358611yescharacteristic
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×#547C2semidirect
4. C11×#3284C2semidirect
5. C11×#3283C2semidirect
6. C11×#3276C2semidirect
7. C11×#3272C2semidirect
8. C11×#3269C2semidirect
9. C11×#3267C2semidirect
10. C11×#3152C2semidirect
11. C11×#3056C2semidirect
12. C11×#3039C2semidirect
13. C11×#3036C2semidirect
14. C11×#3007C2semidirect
15. C11×#3005C2semidirect
16. C4×C11×AGL(1,ℤ/8)C2semidirect
17. D4×C11×M16C2semidirect
19. C22×C11×#41C22semidirect
22. C2×C11×#137C22semidirect
23. C2×C11×#137C22semidirect
24. C2×C11×#137C22semidirect
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
31. C11×#550C22semidirect
32. D4×Q8×C11C22semidirect
33. C11×#548C22semidirect
39. C11×#547C22semidirect
40. C11×#547C22semidirect
41. C11×#547C22semidirect
43. C11×#546C22semidirect
45. D42×C11C22semidirect
48. C2×C11×C4⋊Q8C22semidirect
52. C2×C11×C22⋊Q8C22semidirect
57. C2×C4×D4×C11C22semidirect
59. C11×#497C22semidirect
60. C11×#494C22semidirect
61. C11×#492C22semidirect
62. C11×#470C22semidirect
63. C11×#468C22semidirect
64. C11×#467C22semidirect
65. C11×#465C22semidirect
66. C11×#463C22semidirect
67. C11×#462C22semidirect
68. C11×#462C22semidirect
69. C11×#461C22semidirect
70. C11×#461C22semidirect
71. C11×#461C22semidirect
72. C11×#459C22semidirect
73. C11×#452C22semidirect
74. C11×#452C22semidirect
75. C11×#452C22semidirect
76. C11×#452C22semidirect
77. C11×#451C22semidirect
78. C11×#450C22semidirect
79. C11×#449C22semidirect
80. C11×#449C22semidirect
81. C11×#442C22semidirect
82. C11×#440C22semidirect
83. C4×C11×SD16C22semidirect
84. C4×C11×D8C22semidirect
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
128. C11×AGL(1,ℤ/8)D4semidirect
243. #61067C11direct (N × H)
294. C2×D4×C11C2×D4semidirect
331. C11×SD16C2×D4semidirect
333. C11×D8C2×D4semidirect
337. C11×M16C2×D4semidirect
385. C2×#575C2×C11semidirect
386. D4×#41C2×C11semidirect
387. C2×#547C2×C11semidirect
388. #3284C2×C11semidirect
389. #3283C2×C11semidirect
390. #3276C2×C11semidirect
391. #3272C2×C11semidirect
392. #3269C2×C11semidirect
393. #3267C2×C11semidirect
394. #3152C2×C11semidirect
395. #3056C2×C11semidirect
396. #3039C2×C11semidirect
397. #3036C2×C11semidirect
398. #3007C2×C11semidirect
399. #3005C2×C11semidirect
400. C4×AGL(1,ℤ/8)C2×C11semidirect
401. D4×M16C2×C11semidirect
488. C22×#41C22×C11semidirect
491. C2×#137C22×C11semidirect
492. C2×#137C22×C11semidirect
493. C2×#137C22×C11semidirect
495. C2×AGL(1,ℤ/8)C22×C11semidirect
496. C2×AGL(1,ℤ/8)C22×C11semidirect
497. C2×#135C22×C11semidirect
498. C2×#135C22×C11semidirect
499. C22×M16C22×C11semidirect
500. #550C22×C11semidirect
501. D4×Q8C22×C11semidirect
502. #548C22×C11semidirect
508. #547C22×C11semidirect
509. #547C22×C11semidirect
510. #547C22×C11semidirect
512. #546C22×C11semidirect
514. D42C22×C11semidirect
517. C2×C4⋊Q8C22×C11semidirect
521. C2×C22⋊Q8C22×C11semidirect
526. C2×C4×D4C22×C11semidirect
528. #497C22×C11semidirect
529. #494C22×C11semidirect
530. #492C22×C11semidirect
531. #470C22×C11semidirect
532. #468C22×C11semidirect
533. #467C22×C11semidirect
534. #465C22×C11semidirect
535. #463C22×C11semidirect
536. #462C22×C11semidirect
537. #462C22×C11semidirect
538. #461C22×C11semidirect
539. #461C22×C11semidirect
540. #461C22×C11semidirect
541. #459C22×C11semidirect
542. #452C22×C11semidirect
543. #452C22×C11semidirect
544. #452C22×C11semidirect
545. #452C22×C11semidirect
546. #451C22×C11semidirect
547. #450C22×C11semidirect
548. #449C22×C11semidirect
549. #449C22×C11semidirect
550. #442C22×C11semidirect
551. #440C22×C11semidirect
552. C4×SD16C22×C11semidirect
553. C4×D8C22×C11semidirect
554. #436C22×C11semidirect
555. #435C22×C11semidirect
556. C8×D4C22×C11semidirect
557. #428C22×C11semidirect
558. #423C22×C11semidirect
559. #419C22×C11semidirect
560. #418C22×C11semidirect
562. #417C22×C11semidirect
563. #407C22×C11semidirect
564. C4×M16C22×C11semidirect
599. C4×C11#575semidirect
634. AGL(1,ℤ/8)D4×C11semidirect
808. C2×D4C2×D4×C11semidirect
845. SD16C2×D4×C11semidirect
847. D8C2×D4×C11semidirect
851. M16C2×D4×C11semidirect
899. C11#61067direct (N × H)
1019. 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×#5472
C11×#32842
C11×#32832
C11×#32762
C11×#32722
C11×#32692
C11×#32672
C11×#31522
C11×#30562
C11×#30392
C11×#30362
C11×#30072
C11×#30052
C4×C11×AGL(1,ℤ/8)2
D4×C11×M162
#6106711