Finite Group Databasebeta

← C11×#60750 #14637943

Subgroups — C11×#60750 #14637943

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic, complemented
2C22×C11×#121C211yesmaximal, characteristic, complemented
3C11×#3194C214yesmaximal, complemented
4C11×#3193C212yesmaximal, complemented
5C11×#3192C212yesmaximal, complemented
6C11×#3188C214yesmaximal, complemented
7C11×#3187C212yesmaximal, complemented
8C11×#3186C212yesmaximal, complemented
9C11×#3094C212yesmaximal, complemented
10C11×#3092C212yesmaximal, complemented
11C11×#3055C214yesmaximal, complemented
12C11×#3006C212yesmaximal, complemented
13C11×#3003C212yesmaximal, complemented
14C2×C11×#407C211yesmaximal, characteristic, complemented
15C22×C11×#41C2211yescharacteristic, complemented
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2214yescomplemented
20C22×C11×M16C2212yescomplemented
21C11×#525—21no—
22C11×#525—21no—
23C11×#525—21no—
24C11×#525—21no—
25C11×#525C2212yes—
26C11×#525C2212yescomplemented
27C11×#525C2212yescomplemented
28C11×#525C2212yescomplemented
29C2×C11×#123—21no—
30C2×C11×C22⋊Q8C2211yescharacteristic, complemented
31C2×C11×C22⋊Q8C2211yescharacteristic, complemented
32C2×C11×#121—21no—
33C2×C11×#121—21no—
34C2×C11×#121—21no—
35C2×C11×#121—21no—
36C2×C11×#121—21no—
37C2×C11×#121—21no—
38C2×C11×#121C2212yes—
39C2×C11×#121C2212yes—
40C2×C11×#121C2212yes—
41C2×C11×#121C2212yescomplemented
42C2×C11×#121C2212yescomplemented
43C2×C11×#121C2212yescomplemented
44C2×C11×#121C2211yescharacteristic, complemented
45C2×C11×#121C2211yescharacteristic, complemented
46C2×C11×#120—21no—
47C2×C4×D4×C11—21no—
48C2×C4×D4×C11—21no—
49C2×C11×#117C2211yescharacteristic, complemented
50C22×C11×C4⋊C4C2211yescharacteristic, complemented
51C22×C11×C22⋊C4—21no—
52C11×#484C2214yescomplemented
53C11×#483C2214yescomplemented
54C11×#482C2218yescomplemented
55C11×#481C2214yescomplemented
56C11×#481C2214yescomplemented
57C11×#480C2214yescomplemented
58C11×#480C2214yescomplemented
59C11×#469C2218yescomplemented
60C11×#468C2218yescomplemented
61C11×#466C2218yescomplemented
62C11×#465C2218yescomplemented
63C11×#450C2214yescomplemented
64C11×#450C2214yescomplemented
65C11×#449C2218yescomplemented
66C11×#448C2214yescomplemented
67C11×#447C2214yescomplemented
68C11×#447C2214yescomplemented
69C11×#447C2214yescomplemented
70C11×#428C2214yescomplemented
71C11×#418C2214yescomplemented
72C11×#417C2214yescomplemented
73C11×#407C2212yescomplemented
74C11×#407C2212yescomplemented
75C11×#407C2212yescomplemented
76C11×#407C2212yescomplemented
77C2×C11×C22⋊C8C2212yescomplemented
78C2×C11×C22⋊C8C2212yescomplemented
79C25×C11—21no—
80C25×C11D411yescharacteristic
81C2×C11×#41—21no—
82C2×C11×#41—21no—
83C2×C11×#41—44no—
84C2×C11×#41C2312yes—
85C2×C11×#41C2312yescomplemented
86C22×Q8×C11C2311yescharacteristic, complemented
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—22no—
91C22×D4×C11—22no—
92C22×D4×C11—22no—
93C22×D4×C11—22no—
94C22×D4×C11—22no—
95C22×D4×C11—22no—
96C22×D4×C11—21no—
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11—44no—
100C22×D4×C11—48no—
101C22×D4×C11C2312yes—
102C22×D4×C11C2312yes—
103C22×D4×C11C2312yes—
104C22×D4×C11C2311yescharacteristic, complemented
105C23×C4×C11—21no—
106C23×C4×C11—21no—
107C23×C4×C11—44no—
108C23×C4×C11D411yescharacteristic
109C23×C4×C11D411yescharacteristic
110C23×C4×C11D411yescharacteristic
111C23×C4×C11D411yescharacteristic
112C23×C4×C11D411yescharacteristic
113C23×C4×C11D411yescharacteristic
114C23×C4×C11D411yescharacteristic
115C23×C4×C11C2311yescharacteristic
116C23×C4×C11C2311yescharacteristic
117C23×C4×C11C2311yescharacteristic
118C23×C4×C11C2311yescharacteristic
119C23×C4×C11C2311yescharacteristic
120C23×C4×C11C2311yescharacteristic
121C23×C4×C11C2311yescharacteristic
122C11×AGL(1,ℤ/8)—48no—
123C2×C11×SD16C2318yescomplemented
124C2×C11×D8C2318yescomplemented
125C2×C11×M16—44no—
126C2×C11×M16C2314yes—
127C2×C11×M16C2314yescomplemented
128C22×C8×C11C2314yescomplemented
129C11×#123—22no—
130C11×#123—22no—
131C11×#123—22no—
132C11×#123—22no—
133C11×C22⋊Q8—21no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8—21no—
136C11×C22⋊Q8—21no—
137C11×C22⋊Q8C2312yes—
138C11×C22⋊Q8C2312yes—
139C11×C22⋊Q8C2312yescomplemented
140C11×C22⋊Q8C2312yescomplemented
141C11×#121—22no—
142C11×#121—22no—
143C11×#121—22no—
144C11×#121—22no—
145C11×#121—22no—
146C11×#121—22no—
147C11×#121—22no—
148C11×#121—22no—
149C11×#121—22no—
150C11×#121—22no—
151C11×#121—22no—
152C11×#121—22no—
153C11×#121—21no—
154C11×#121—21no—
155C11×#121—21no—
156C11×#121—21no—
157C11×#121C2314yes—
158C11×#121C2314yes—
159C11×#121C2314yes—
160C11×#121C2314yes—
161C11×#121C2312yes—
162C11×#121C2312yes—
163C11×#121C2312yescomplemented
164C11×#121C2312yescomplemented
165C11×#120—22no—
166C11×#120—22no—
167C11×#120—22no—
168C11×#120—22no—
169C4×D4×C11—22no—
170C4×D4×C11—22no—
171C4×D4×C11—22no—
172C4×D4×C11—22no—
173C4×D4×C11—22no—
174C4×D4×C11—22no—
175C4×D4×C11—22no—
176C4×D4×C11—22no—
177C11×#117—21no—
178C11×#117—21no—
179C11×#117C2312yes—
180C11×#117C2312yescomplemented
181C2×C11×C4⋊C4—21no—
182C2×C11×C4⋊C4—21no—
183C2×C11×C4⋊C4—21no—
184C2×C11×C4⋊C4—21no—
185C2×C11×C4⋊C4—21no—
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C4⋊C4C2312yes—
188C2×C11×C4⋊C4C2312yes—
189C2×C11×C4⋊C4C2311yescharacteristic, complemented
190C2×C11×C4⋊C4C2311yescharacteristic, complemented
191C2×C11×C22⋊C4—21no—
192C2×C11×C22⋊C4—21no—
193C2×C11×C22⋊C4—21no—
194C2×C11×C22⋊C4—22no—
195C2×C11×C22⋊C4—22no—
196C2×C11×C22⋊C4—22no—
197C2×C11×C22⋊C4—22no—
198C2×C11×C22⋊C4—22no—
199C2×C11×C22⋊C4—22no—
200C2×C11×C22⋊C4—21no—
201C2×C11×C22⋊C4—21no—
202C2×C42×C11—21no—
203C11×#107C2318yescomplemented
204C11×#106C2318yescomplemented
205C11×#103C2318yescomplemented
206C11×#102C2318yescomplemented
207C11×#102C2318yescomplemented
208C11×#102C2318yescomplemented
209C11×C22⋊C8C2314yes—
210C11×C22⋊C8C2314yes—
211C11×C22⋊C8C2314yescomplemented
212C11×C22⋊C8C2314yescomplemented
213#60750C1111yesmaximal, characteristic, direct product factor, Sylow
214C24×C11—24no—
215C24×C11—21no—
216C24×C11—22no—
217C24×C11—22no—
218C24×C11—22no—
219C24×C11—42no—
220C24×C11—42no—
221C24×C11—44no—
222C24×C11—44no—
223C24×C11—44no—
224C24×C11C2×D411yescharacteristic
225C24×C11C2×D411yescharacteristic
226C24×C11C2×D411yescharacteristic
227C24×C11C2×D411yescharacteristic
228C24×C11C2×D411yescharacteristic
229C24×C11C2×D411yescharacteristic
230C24×C11C2×D411yescharacteristic
231C11×#41—28no—
232C11×#41—44no—
233C11×#41—44no—
234C11×#41—44no—
235C2×Q8×C11—21no—
236C2×Q8×C11—42no—
237C2×Q8×C11C2412yes—
238C2×D4×C11—22no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—24no—
245C2×D4×C11—24no—
246C2×D4×C11—24no—
247C2×D4×C11—24no—
248C2×D4×C11—22no—
249C2×D4×C11—22no—
250C2×D4×C11—22no—
251C2×D4×C11—21no—
252C2×D4×C11—28no—
253C2×D4×C11—44no—
254C2×D4×C11—44no—
255C2×D4×C11—42no—
256C2×D4×C11—44no—
257C2×D4×C11—44no—
258C2×D4×C11—44no—
259C2×D4×C11—44no—
260C2×D4×C11—48no—
261C2×D4×C11—48no—
262C2×D4×C11—48no—
263C2×D4×C11—48no—
264C2×D4×C11—48no—
265C2×D4×C11—44no—
266C2×D4×C11—44no—
267C2×D4×C11—48no—
268C2×D4×C11C2414yes—
269C2×D4×C11C2412yes—
270C22×C4×C11—24no—
271C22×C4×C11—24no—
272C22×C4×C11—24no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11—44no—
293C22×C4×C11—44no—
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2×D411yescharacteristic
305C22×C4×C11C2×D411yescharacteristic
306C22×C4×C11C2×D411yescharacteristic
307C22×C4×C11C2×D411yescharacteristic
308C22×C4×C11C2×D411yescharacteristic
309C22×C4×C11C2×D411yescharacteristic
310C22×C4×C11C2×D411yescharacteristic
311C22×C4×C11C2×D411yescharacteristic
312C22×C4×C11C2×D411yescharacteristic
313C22×C4×C11C2×D411yescharacteristic
314C22×C4×C11C2×D411yescharacteristic
315C22×C4×C11C2411yescharacteristic
316C22×C4×C11C2411yescharacteristic
317C22×C4×C11C2411yescharacteristic
318C22×C4×C11C2411yescharacteristic
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2411yescharacteristic
321C22×C4×C11C2411yescharacteristic
322C11×SD16—48no—
323C11×D8—48no—
324C11×M16—28no—
325C11×M16—44no—
326C2×C8×C11—44no—
327C2×C8×C11C2418yes—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—22no—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—22no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—21no—
336C11×C4⋊C4—21no—
337C11×C4⋊C4C2412yes—
338C11×C4⋊C4C2412yes—
339C11×C4⋊C4C2414yes—
340C11×C22⋊C4—22no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—24no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—22no—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—22no—
354C42×C11—22no—
355C42×C11—22no—
356C2×#525C2×C1111yescharacteristic, complemented
357C22×#121C2×C1111yescharacteristic, complemented
358#3194C2×C1114yescomplemented
359#3193C2×C1112yescomplemented
360#3192C2×C1112yescomplemented
361#3188C2×C1114yescomplemented
362#3187C2×C1112yescomplemented
363#3186C2×C1112yescomplemented
364#3094C2×C1112yescomplemented
365#3092C2×C1112yescomplemented
366#3055C2×C1114yescomplemented
367#3006C2×C1112yescomplemented
368#3003C2×C1112yescomplemented
369C2×#407C2×C1111yescharacteristic, complemented
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—24no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—416no—
393C23×C11—42no—
394C23×C11—44no—
395C23×C11—44no—
396C23×C11—44no—
397C23×C11—44no—
398C23×C11—42no—
399C23×C11—44no—
400C23×C11—44no—
401C23×C11—44no—
402C23×C11—44no—
403C23×C11—42no—
404C23×C11—44no—
405C23×C11—816no—
406C23×C11AGL(1,ℤ/8)14yescomplemented
407C23×C11C22×D411yescharacteristic
408C23×C11C22×D411yescharacteristic
409C23×C11C22×D411yescharacteristic
410C23×C11C22×D411yescharacteristic
411C23×C11C22×D411yescharacteristic
412C23×C11C22×D411yescharacteristic
413C23×C11C22×D411yescharacteristic
414Q8×C11—24no—
415Q8×C11—42no—
416D4×C11—24no—
417D4×C11—28no—
418D4×C11—44no—
419D4×C11—44no—
420D4×C11—42no—
421D4×C11—44no—
422D4×C11—48no—
423D4×C11—48no—
424D4×C11—44no—
425D4×C11—44no—
426D4×C11—44no—
427D4×C11—44no—
428D4×C11—48no—
429D4×C11—48no—
430D4×C11—44no—
431D4×C11—44no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—24no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—44no—
464C2×C4×C11—44no—
465C2×C4×C11—44no—
466C2×C4×C11—42no—
467C2×C4×C11—42no—
468C2×C4×C11—44no—
469C2×C4×C11—42no—
470C2×C4×C11—44no—
471C2×C4×C11C22×D411yescharacteristic
472C2×C4×C11C22×D411yescharacteristic
473C2×C4×C11C22×D411yescharacteristic
474C2×C4×C11C22×D411yescharacteristic
475C2×C4×C11C22×D411yescharacteristic
476C2×C4×C11C22×D411yescharacteristic
477C2×C4×C11C22×D411yescharacteristic
478C2×C4×C11H(5,𝔽2)14yes—
479C2×C4×C11C2511yescharacteristic
480C8×C11—28no—
481C22×#41C22×C1111yescharacteristic, complemented
482C23×D4—21no—
483C23×D4C22×C1111yescharacteristic, complemented
484C24×C4C22×C1111yescharacteristic
485C2×AGL(1,ℤ/8)C22×C1114yescomplemented
486C22×M16C22×C1112yescomplemented
487#525—21no—
488#525—21no—
489#525—21no—
490#525—21no—
491#525C22×C1112yes—
492#525C22×C1112yescomplemented
493#525C22×C1112yescomplemented
494#525C22×C1112yescomplemented
495C2×#123—21no—
496C2×C22⋊Q8C22×C1111yescharacteristic, complemented
497C2×C22⋊Q8C22×C1111yescharacteristic, complemented
498C2×#121—21no—
499C2×#121—21no—
500C2×#121—21no—
501C2×#121—21no—
502C2×#121—21no—
503C2×#121—21no—
504C2×#121C22×C1112yes—
505C2×#121C22×C1112yes—
506C2×#121C22×C1112yes—
507C2×#121C22×C1112yescomplemented
508C2×#121C22×C1112yescomplemented
509C2×#121C22×C1112yescomplemented
510C2×#121C22×C1111yescharacteristic, complemented
511C2×#121C22×C1111yescharacteristic, complemented
512C2×#120—21no—
513C2×C4×D4—21no—
514C2×C4×D4—21no—
515C2×#117C22×C1111yescharacteristic, complemented
516C22×C4⋊C4C22×C1111yescharacteristic, complemented
517C22×C22⋊C4—21no—
518#484C22×C1114yescomplemented
519#483C22×C1114yescomplemented
520#482C22×C1118yescomplemented
521#481C22×C1114yescomplemented
522#481C22×C1114yescomplemented
523#480C22×C1114yescomplemented
524#480C22×C1114yescomplemented
525#469C22×C1118yescomplemented
526#468C22×C1118yescomplemented
527#466C22×C1118yescomplemented
528#465C22×C1118yescomplemented
529#450C22×C1114yescomplemented
530#450C22×C1114yescomplemented
531#449C22×C1118yescomplemented
532#448C22×C1114yescomplemented
533#447C22×C1114yescomplemented
534#447C22×C1114yescomplemented
535#447C22×C1114yescomplemented
536#428C22×C1114yescomplemented
537#418C22×C1114yescomplemented
538#417C22×C1114yescomplemented
539#407C22×C1112yescomplemented
540#407C22×C1112yescomplemented
541#407C22×C1112yescomplemented
542#407C22×C1112yescomplemented
543C2×C22⋊C8C22×C1112yescomplemented
544C2×C22⋊C8C22×C1112yescomplemented
545C22×C11—28no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—21no—
555C22×C11—21no—
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—21no—
561C22×C11—21no—
562C22×C11—44no—
563C22×C11—44no—
564C22×C11—44no—
565C22×C11—44no—
566C22×C11—44no—
567C22×C11—44no—
568C22×C11—42no—
569C22×C11—44no—
570C22×C11—44no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—44no—
574C22×C11—84no—
575C22×C11—88no—
576C22×C11—88no—
577C22×C11—88no—
578C22×C11#53412yes—
579C22×C11C2×AGL(1,ℤ/8)12yes—
580C22×C11C2×AGL(1,ℤ/8)12yes—
581C22×C11C2×AGL(1,ℤ/8)12yes—
582C22×C11#57512yes—
583C22×C11C23×D411yescharacteristic
584C4×C11—21no—
585C4×C11—21no—
586C4×C11—21no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11—42no—
591C4×C11—44no—
592C4×C11—42no—
593C4×C11—42no—
594C4×C11#53412yes—
595C4×C11C2×H(5,𝔽2)12yes—
596C25—21no—
597C25D4×C1111yescharacteristic
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—44no—
601C2×#41C23×C1112yes—
602C2×#41C23×C1112yescomplemented
603C22×Q8C23×C1111yescharacteristic, complemented
604C22×D4—21no—
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—22no—
612C22×D4—22no—
613C22×D4—21no—
614C22×D4—21no—
615C22×D4—21no—
616C22×D4—44no—
617C22×D4—48no—
618C22×D4C23×C1112yes—
619C22×D4C23×C1112yes—
620C22×D4C23×C1112yes—
621C22×D4C23×C1111yescharacteristic, complemented
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—44no—
625C23×C4D4×C1111yescharacteristic
626C23×C4D4×C1111yescharacteristic
627C23×C4D4×C1111yescharacteristic
628C23×C4D4×C1111yescharacteristic
629C23×C4D4×C1111yescharacteristic
630C23×C4D4×C1111yescharacteristic
631C23×C4D4×C1111yescharacteristic
632C23×C4C23×C1111yescharacteristic
633C23×C4C23×C1111yescharacteristic
634C23×C4C23×C1111yescharacteristic
635C23×C4C23×C1111yescharacteristic
636C23×C4C23×C1111yescharacteristic
637C23×C4C23×C1111yescharacteristic
638C23×C4C23×C1111yescharacteristic
639AGL(1,ℤ/8)—48no—
640C2×SD16C23×C1118yescomplemented
641C2×D8C23×C1118yescomplemented
642C2×M16—44no—
643C2×M16C23×C1114yes—
644C2×M16C23×C1114yescomplemented
645C22×C8C23×C1114yescomplemented
646#123—22no—
647#123—22no—
648#123—22no—
649#123—22no—
650C22⋊Q8—21no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8C23×C1112yes—
655C22⋊Q8C23×C1112yes—
656C22⋊Q8C23×C1112yescomplemented
657C22⋊Q8C23×C1112yescomplemented
658#121—22no—
659#121—22no—
660#121—22no—
661#121—22no—
662#121—22no—
663#121—22no—
664#121—22no—
665#121—22no—
666#121—22no—
667#121—22no—
668#121—22no—
669#121—22no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121C23×C1114yes—
675#121C23×C1114yes—
676#121C23×C1114yes—
677#121C23×C1114yes—
678#121C23×C1112yes—
679#121C23×C1112yes—
680#121C23×C1112yescomplemented
681#121C23×C1112yescomplemented
682#120—22no—
683#120—22no—
684#120—22no—
685#120—22no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—22no—
689C4×D4—22no—
690C4×D4—22no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694#117—21no—
695#117—21no—
696#117C23×C1112yes—
697#117C23×C1112yescomplemented
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4C23×C1112yes—
704C2×C4⋊C4C23×C1112yes—
705C2×C4⋊C4C23×C1112yes—
706C2×C4⋊C4C23×C1111yescharacteristic, complemented
707C2×C4⋊C4C23×C1111yescharacteristic, complemented
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C42—21no—
720#107C23×C1118yescomplemented
721#106C23×C1118yescomplemented
722#103C23×C1118yescomplemented
723#102C23×C1118yescomplemented
724#102C23×C1118yescomplemented
725#102C23×C1118yescomplemented
726C22⋊C8C23×C1114yes—
727C22⋊C8C23×C1114yes—
728C22⋊C8C23×C1114yescomplemented
729C22⋊C8C23×C1114yescomplemented
730C2×C11—22no—
731C2×C11—22no—
732C2×C11—22no—
733C2×C11—22no—
734C2×C11—22no—
735C2×C11—41no—
736C2×C11—41no—
737C2×C11—82no—
738C2×C11—84no—
739C2×C11C2×#53411yescharacteristic
740C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
741C2×C11C2×#57511yescharacteristic
742C24—24no—
743C24—21no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24C2×D4×C1111yescharacteristic
753C24C2×D4×C1111yescharacteristic
754C24C2×D4×C1111yescharacteristic
755C24C2×D4×C1111yescharacteristic
756C24C2×D4×C1111yescharacteristic
757C24C2×D4×C1111yescharacteristic
758C24C2×D4×C1111yescharacteristic
759#41—28no—
760#41—44no—
761#41—44no—
762#41—44no—
763C2×Q8—21no—
764C2×Q8—42no—
765C2×Q8C24×C1112yes—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—42no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—48no—
795C2×D4—44no—
796C2×D4C24×C1114yes—
797C2×D4C24×C1112yes—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4C2×D4×C1111yescharacteristic
823C22×C4C2×D4×C1111yescharacteristic
824C22×C4C2×D4×C1111yescharacteristic
825C22×C4C2×D4×C1111yescharacteristic
826C22×C4C2×D4×C1111yescharacteristic
827C22×C4C2×D4×C1111yescharacteristic
828C22×C4C2×D4×C1111yescharacteristic
829C22×C4C2×D4×C1111yescharacteristic
830C22×C4C2×D4×C1111yescharacteristic
831C22×C4C2×D4×C1111yescharacteristic
832C22×C4C2×D4×C1111yescharacteristic
833C22×C4C2×D4×C1111yescharacteristic
834C22×C4C2×D4×C1111yescharacteristic
835C22×C4C2×D4×C1111yescharacteristic
836C22×C4C2×D4×C1111yescharacteristic
837C22×C4C2×D4×C1111yescharacteristic
838C22×C4C2×D4×C1111yescharacteristic
839C22×C4C2×D4×C1111yescharacteristic
840C22×C4C2×D4×C1111yescharacteristic
841C22×C4C2×D4×C1111yescharacteristic
842C22×C4C2×D4×C1111yescharacteristic
843C22×C4C24×C1111yescharacteristic
844C22×C4C24×C1111yescharacteristic
845C22×C4C24×C1111yescharacteristic
846C22×C4C24×C1111yescharacteristic
847C22×C4C24×C1111yescharacteristic
848C22×C4C24×C1111yescharacteristic
849C22×C4C24×C1111yescharacteristic
850SD16—48no—
851D8—48no—
852M16—28no—
853M16—44no—
854C2×C8—44no—
855C2×C8C24×C1118yes—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4C24×C1112yes—
866C4⋊C4C24×C1112yes—
867C4⋊C4C24×C1114yes—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C42—22no—
883C42—22no—
884C11#6075011yescharacteristic, direct product factor, Sylow
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—24no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—416no—
908C23—42no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—42no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—42no—
919C23—44no—
920C23—816no—
921C23C11×AGL(1,ℤ/8)14yescomplemented
922C23C22×D4×C1111yescharacteristic
923C23C22×D4×C1111yescharacteristic
924C23C22×D4×C1111yescharacteristic
925C23C22×D4×C1111yescharacteristic
926C23C22×D4×C1111yescharacteristic
927C23C22×D4×C1111yescharacteristic
928C23C22×D4×C1111yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—28no—
933D4—44no—
934D4—44no—
935D4—42no—
936D4—44no—
937D4—48no—
938D4—48no—
939D4—44no—
940D4—44no—
941D4—44no—
942D4—44no—
943D4—48no—
944D4—48no—
945D4—44no—
946D4—44no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—44no—
984C2×C4—42no—
985C2×C4—44no—
986C2×C4C22×D4×C1111yescharacteristic
987C2×C4C22×D4×C1111yescharacteristic
988C2×C4C22×D4×C1111yescharacteristic
989C2×C4C22×D4×C1111yescharacteristic
990C2×C4C22×D4×C1111yescharacteristic
991C2×C4C22×D4×C1111yescharacteristic
992C2×C4C22×D4×C1111yescharacteristic
993C2×C4C11×H(5,𝔽2)14yes—
994C2×C4C25×C1111yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—44no—
1021C22—44no—
1022C22—42no—
1023C22—42no—
1024C22—44no—
1025C22—88no—
1026C22—88no—
1027C22—88no—
1028C22—84no—
1029C22C11×#53412yes—
1030C22C2×C11×AGL(1,ℤ/8)12yes—
1031C22C2×C11×AGL(1,ℤ/8)12yes—
1032C22C2×C11×AGL(1,ℤ/8)12yes—
1033C22C11×#57512yes—
1034C22C23×D4×C1111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—44no—
1043C4—42no—
1044C4—42no—
1045C4C11×#53412yes—
1046C4C2×C11×H(5,𝔽2)12yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—82no—
1056C2C2×C11×#53411yescharacteristic
1057C2C22×C11×AGL(1,ℤ/8)11yescharacteristic
1058C2C2×C11×#57511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#525C2semidirect
2. C22×C11×#121C2semidirect
3. C11×#3194C2semidirect
4. C11×#3193C2semidirect
5. C11×#3192C2semidirect
6. C11×#3188C2semidirect
7. C11×#3187C2semidirect
8. C11×#3186C2semidirect
9. C11×#3094C2semidirect
10. C11×#3092C2semidirect
11. C11×#3055C2semidirect
12. C11×#3006C2semidirect
13. C11×#3003C2semidirect
14. C2×C11×#407C2semidirect
15. C22×C11×#41C22semidirect
17. C23×D4×C11C22semidirect
19. C2×C11×AGL(1,ℤ/8)C22semidirect
20. C22×C11×M16C22semidirect
26. C11×#525C22semidirect
27. C11×#525C22semidirect
28. C11×#525C22semidirect
30. C2×C11×C22⋊Q8C22semidirect
31. C2×C11×C22⋊Q8C22semidirect
41. C2×C11×#121C22semidirect
42. C2×C11×#121C22semidirect
43. C2×C11×#121C22semidirect
44. C2×C11×#121C22semidirect
45. C2×C11×#121C22semidirect
49. C2×C11×#117C22semidirect
50. C22×C11×C4⋊C4C22semidirect
52. C11×#484C22semidirect
53. C11×#483C22semidirect
54. C11×#482C22semidirect
55. C11×#481C22semidirect
56. C11×#481C22semidirect
57. C11×#480C22semidirect
58. C11×#480C22semidirect
59. C11×#469C22semidirect
60. C11×#468C22semidirect
61. C11×#466C22semidirect
62. C11×#465C22semidirect
63. C11×#450C22semidirect
64. C11×#450C22semidirect
65. C11×#449C22semidirect
66. C11×#448C22semidirect
67. C11×#447C22semidirect
68. C11×#447C22semidirect
69. C11×#447C22semidirect
70. C11×#428C22semidirect
71. C11×#418C22semidirect
72. C11×#417C22semidirect
73. C11×#407C22semidirect
74. C11×#407C22semidirect
75. C11×#407C22semidirect
76. C11×#407C22semidirect
77. C2×C11×C22⋊C8C22semidirect
78. C2×C11×C22⋊C8C22semidirect
85. C2×C11×#41C23semidirect
86. C22×Q8×C11C23semidirect
104. C22×D4×C11C23semidirect
123. C2×C11×SD16C23semidirect
124. C2×C11×D8C23semidirect
127. C2×C11×M16C23semidirect
128. C22×C8×C11C23semidirect
139. C11×C22⋊Q8C23semidirect
140. C11×C22⋊Q8C23semidirect
163. C11×#121C23semidirect
164. C11×#121C23semidirect
180. C11×#117C23semidirect
189. C2×C11×C4⋊C4C23semidirect
190. C2×C11×C4⋊C4C23semidirect
203. C11×#107C23semidirect
204. C11×#106C23semidirect
205. C11×#103C23semidirect
206. C11×#102C23semidirect
207. C11×#102C23semidirect
208. C11×#102C23semidirect
211. C11×C22⋊C8C23semidirect
212. C11×C22⋊C8C23semidirect
213. #60750C11direct (N × H)
356. C2×#525C2×C11semidirect
357. C22×#121C2×C11semidirect
358. #3194C2×C11semidirect
359. #3193C2×C11semidirect
360. #3192C2×C11semidirect
361. #3188C2×C11semidirect
362. #3187C2×C11semidirect
363. #3186C2×C11semidirect
364. #3094C2×C11semidirect
365. #3092C2×C11semidirect
366. #3055C2×C11semidirect
367. #3006C2×C11semidirect
368. #3003C2×C11semidirect
369. C2×#407C2×C11semidirect
406. C23×C11AGL(1,ℤ/8)semidirect
481. C22×#41C22×C11semidirect
483. C23×D4C22×C11semidirect
485. C2×AGL(1,ℤ/8)C22×C11semidirect
486. C22×M16C22×C11semidirect
492. #525C22×C11semidirect
493. #525C22×C11semidirect
494. #525C22×C11semidirect
496. C2×C22⋊Q8C22×C11semidirect
497. C2×C22⋊Q8C22×C11semidirect
507. C2×#121C22×C11semidirect
508. C2×#121C22×C11semidirect
509. C2×#121C22×C11semidirect
510. C2×#121C22×C11semidirect
511. C2×#121C22×C11semidirect
515. C2×#117C22×C11semidirect
516. C22×C4⋊C4C22×C11semidirect
518. #484C22×C11semidirect
519. #483C22×C11semidirect
520. #482C22×C11semidirect
521. #481C22×C11semidirect
522. #481C22×C11semidirect
523. #480C22×C11semidirect
524. #480C22×C11semidirect
525. #469C22×C11semidirect
526. #468C22×C11semidirect
527. #466C22×C11semidirect
528. #465C22×C11semidirect
529. #450C22×C11semidirect
530. #450C22×C11semidirect
531. #449C22×C11semidirect
532. #448C22×C11semidirect
533. #447C22×C11semidirect
534. #447C22×C11semidirect
535. #447C22×C11semidirect
536. #428C22×C11semidirect
537. #418C22×C11semidirect
538. #417C22×C11semidirect
539. #407C22×C11semidirect
540. #407C22×C11semidirect
541. #407C22×C11semidirect
542. #407C22×C11semidirect
543. C2×C22⋊C8C22×C11semidirect
544. C2×C22⋊C8C22×C11semidirect
602. C2×#41C23×C11semidirect
603. C22×Q8C23×C11semidirect
621. C22×D4C23×C11semidirect
640. C2×SD16C23×C11semidirect
641. C2×D8C23×C11semidirect
644. C2×M16C23×C11semidirect
645. C22×C8C23×C11semidirect
656. C22⋊Q8C23×C11semidirect
657. C22⋊Q8C23×C11semidirect
680. #121C23×C11semidirect
681. #121C23×C11semidirect
697. #117C23×C11semidirect
706. C2×C4⋊C4C23×C11semidirect
707. C2×C4⋊C4C23×C11semidirect
720. #107C23×C11semidirect
721. #106C23×C11semidirect
722. #103C23×C11semidirect
723. #102C23×C11semidirect
724. #102C23×C11semidirect
725. #102C23×C11semidirect
728. C22⋊C8C23×C11semidirect
729. C22⋊C8C23×C11semidirect
884. C11#60750direct (N × H)
921. C23C11×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C22×C11×#1212
C11×#31942
C11×#31932
C11×#31922
C11×#31882
C11×#31872
C11×#31862
C11×#30942
C11×#30922
C11×#30552
C11×#30062
C11×#30032
C2×C11×#4072
#6075011