Finite Group Databasebeta

← C2×D11×#563 #15660653

Subgroups — C2×D11×#563 #15660653

Order 2816.

7238 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623230C212yesmaximal, complemented
2C2×#10623182C212yesmaximal, complemented
3C2×#10623243C214yesmaximal, complemented
4C2×#10623177C214yesmaximal, complemented
5C2×#10623203C211yesmaximal, characteristic, complemented
6C2×#10623266C212yesmaximal, complemented
7D11×#563C2132yesmaximal, direct product factor
8C2×D11×C4⋊Q8C212yesmaximal, complemented
9C2×D11×#126C214yesmaximal, complemented
10C2×D11×#125C212yesmaximal, complemented
11C2×D11×#124C211yesmaximal, characteristic
12C2×D11×#123C212yesmaximal
13C2×D11×C22⋊Q8C214yesmaximal, complemented
14C2×C11×#563C211yesmaximal, characteristic, complemented
15C22×Q8×D11C2211yescharacteristic
16C22×Q8×D11C2212yes—
17C22×D4×D11C2211yescharacteristic
18C23×C4×D11C2212yes—
19C11×#563C22116yescomplemented
20C2×C11×C4⋊Q8C2212yescomplemented
21C2×C11×#126C2214yescomplemented
22C2×C11×#125C2212yescomplemented
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123C2212yes—
25C2×C11×C22⋊Q8C2214yescomplemented
26C2×#67000C2211yescharacteristic
27C2×#66999C2214yescomplemented
28C2×#66997C2212yescomplemented
29C2×#66997C2212yescomplemented
30C2×#66989C2211yescharacteristic
31C2×#66988C2212yes—
32C2×#66982C2212yes—
33C2×#66977C2214yescomplemented
34#10623266C22132yescomplemented
35D11×C4⋊Q8C22132yescomplemented
36#10623243C22164yescomplemented
37D11×#126C22164yescomplemented
38#10623230C22132yescomplemented
39D11×#125C22132yescomplemented
40D11×#124C22116yes—
41#10623203C22116yescomplemented
42D11×#123C22132yes—
43#10623182C22132yescomplemented
44#10623177C22164yescomplemented
45D11×C22⋊Q8C22164yescomplemented
46C2×#66951C2214yescomplemented
47C2×#66951C2214yescomplemented
48C2×#66951C2214yescomplemented
49C2×#66950C2214yescomplemented
50C2×#66949C2214yescomplemented
51C2×#66949C2214yescomplemented
52C2×#66947C2214yes—
53C2×C4⋊C4×D11C2212yes—
54C2×C4⋊C4×D11C2214yes—
55C2×C4⋊C4×D11C2214yes—
56C2×C4⋊C4×D11C2212yes—
57C2×C4⋊C4×D11C2214yes—
58C2×#66943C2212yescomplemented
59C2×#66943C2212yescomplemented
60C2×#66942C2214yescomplemented
61C2×#66942C2214yescomplemented
62C2×#66941C2214yescomplemented
63C2×#66941C2214yescomplemented
64C2×#66939C2212yes—
65C2×#66938C2214yes—
66C2×#66936C2214yes—
67C2×C22⋊C4×D11C2214yes—
68C2×C22⋊C4×D11C2212yes—
69C2×C22⋊C4×D11C2214yes—
70C2×#66932C2214yescomplemented
71C2×#66932C2214yescomplemented
72C2×#66932C2214yescomplemented
73C2×#66931C2214yescomplemented
74C2×#66931C2214yescomplemented
75C2×#66929C2214yescomplemented
76C2×#66928C2211yescharacteristic
77C2×C42×D11C2211yescharacteristic
78C2×C42×D11C2212yes—
79C2×#66923C2212yescomplemented
80C2×#66922C2212yescomplemented
81C24×D11C2312yes—
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2312yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C22×C22⋊D11C2312yes—
87C23×Dic11C2312yes—
88C2×Q8×D11—48no—
89C2×Q8×D11—44no—
90C2×Q8×D11C2318yes—
91C2×Q8×D11C23116yes—
92C2×D4×D11—44no—
93C2×D4×D11C2318yes—
94C22×D44C2311yescharacteristic
95C22×C4×D11—48no—
96C22×C4×D11C2312yes—
97C22×C4×D11C2314yes—
98C22×C4×D11C2312yes—
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2314yes—
101C22×C4×D11C2314yes—
102C22×C4×D11C23116yes—
103C22×Dic22C2312yes—
104C22×Dic22C2312yes—
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2314yes—
107C11×C4⋊Q8C23116yescomplemented
108C11×#126C23132yescomplemented
109C11×#125C23116yescomplemented
110C11×#124C2318yes—
111C11×#123C23116yes—
112C11×C22⋊Q8C23132yescomplemented
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C42×C11C2312yes—
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2312yes—
126#67000C2318yes—
127#66999C23132yescomplemented
128#66997C23116yescomplemented
129#66997C23116yescomplemented
130#66989C2318yes—
131#66988C23116yes—
132#66982C23116yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11C2314yes—
139C2×C4⋊Dic11C2314yes—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2314yes—
143#66977C23132yescomplemented
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2311yescharacteristic
156#66951C23132yescomplemented
157#66951C23132yescomplemented
158#66951C23132yescomplemented
159#66950C23132yescomplemented
160#66949C23132yescomplemented
161#66949C23132yescomplemented
162#66947C23132yes—
163C4⋊C4×D11C23116yes—
164C4⋊C4×D11C23132yes—
165C4⋊C4×D11C23132yes—
166C4⋊C4×D11C23132yes—
167C4⋊C4×D11C23116yes—
168#66943C23116yescomplemented
169#66943C23116yescomplemented
170#66942C23132yescomplemented
171#66942C23132yescomplemented
172#66941C23132yescomplemented
173#66941C23132yescomplemented
174#66939C23116yes—
175#66938C23132yes—
176#66936C23132yes—
177C22⋊C4×D11C23116yes—
178C22⋊C4×D11C23132yes—
179C22⋊C4×D11C23132yes—
180#66932C23132yescomplemented
181#66932C23132yescomplemented
182#66932C23132yescomplemented
183#66931C23132yescomplemented
184#66931C23132yescomplemented
185#66929C23132yescomplemented
186#66928C2318yes—
187C42×D11C23116yes—
188C42×D11C2318yes—
189#66923C23116yescomplemented
190#66922C23116yescomplemented
191C22×#563—111nomaximal, Sylow
192C24×C11C2412yes—
193C23×D11—28no—
194C23×D11—216no—
195C23×D11C2418yes—
196C23×D11C2412yes—
197C23×D11C2411yescharacteristic
198C2×Q8×C11—42no—
199C2×Q8×C11—44no—
200C2×Q8×C11C2414yes—
201C2×Q8×C11C2418yes—
202C2×D4×C11—42no—
203C2×D4×C11C2414yes—
204C22×C4×C11—44no—
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2414yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2414yes—
210C22×C4×C11C2418yes—
211C2×C22⋊D11—44no—
212C2×C22⋊D11C2418yes—
213C22×Dic11—44no—
214C22×Dic11C2414yes—
215C22×Dic11C2412yes—
216C22×Dic11C2411yescharacteristic
217C22×Dic11C2412yes—
218C22×Dic11C2414yes—
219C22×Dic11C2418yes—
220Q8×D11—432no—
221Q8×D11—416no—
222D4×D11—416no—
223C2×D44—42no—
224C2×D44C2414yes—
225C2×C4×D11—216no—
226C2×C4×D11—24no—
227C2×C4×D11—28no—
228C2×C4×D11—28no—
229C2×C4×D11—216no—
230C2×C4×D11—48no—
231C2×C4×D11—432no—
232C2×C4×D11C24116yes—
233C2×C4×D11C2418yes—
234C2×C4×D11C2418yes—
235C2×C4×D11C2414yes—
236C2×C4×D11C24116yes—
237C2×C4×D11C24116yes—
238C2×Dic22—44no—
239C2×Dic22—44no—
240C2×Dic22—48no—
241C2×Dic22—42no—
242C2×Dic22C2418yes—
243C2×Dic22C2418yes—
244C2×Dic22C2414yes—
245C2×Dic22C24116yes—
246C11×C4⋊C4C24116yes—
247C11×C4⋊C4C24116yes—
248C11×C4⋊C4C24116yes—
249C11×C4⋊C4C2418yes—
250C11×C4⋊C4C2418yes—
251C11×C22⋊C4C24116yes—
252C11×C22⋊C4C24116yes—
253C11×C22⋊C4C2418yes—
254C42×C11C2418yes—
255C42×C11C2414yes—
256C22⋊Dic11C24116yes—
257C22⋊Dic11C24116yes—
258C22⋊Dic11C2418yes—
259(C2×D11)⋊C4C24116yes—
260(C2×D11)⋊C4C24116yes—
261(C2×D11)⋊C4C24116yes—
262(C2×D11)⋊C4C24116yes—
263(C2×D11)⋊C4C24116yes—
264C4⋊Dic11C24116yes—
265C4⋊Dic11C24116yes—
266C4⋊Dic11C2418yes—
267C4⋊Dic11C2418yes—
268C4⋊Dic11C24116yes—
269Dic11⋊C4C24116yes—
270Dic11⋊C4C24116yes—
271Dic11⋊C4C24116yes—
272Dic11⋊C4C24116yes—
273Dic11⋊C4C24116yes—
274Dic11⋊C4C24116yes—
275Dic11⋊C4C24116yes—
276Dic11⋊C4C24116yes—
277C4×Dic11C24116yes—
278C4×Dic11C2418yes—
279C4×Dic11C2418yes—
280C4×Dic11C2414yes—
281C2×#563—1132no—
282C2×#563—112no—
283C2×#563—114no—
284C2×#563—112no—
285C2×#563—111no—
286C2×#563—112no—
287C2×#563—114no—
288C2×#563D1111yescharacteristic, direct product factor
289C22×C4⋊Q8—112no—
290C22×#126—114no—
291C22×#125—112no—
292C22×#124—111no—
293C22×#123—112no—
294C22×C22⋊Q8—114no—
295C23×C11—24no—
296C23×C11—28no—
297C23×C11C2514yes—
298C23×C11C2511yescharacteristic
299C22×D11—24no—
300C22×D11—28no—
301C22×D11—216no—
302C22×D11—232no—
303C22×D11—432no—
304C22×D11H(5,𝔽2)14yes—
305C22×D112−1+418yes—
306C22×D11C2514yes—
307C22×D11C2512yes—
308Q8×C11—48no—
309Q8×C11—44no—
310D4×C11—44no—
311C2×C4×C11—24no—
312C2×C4×C11—28no—
313C2×C4×C11—22no—
314C2×C4×C11—28no—
315C2×C4×C11—24no—
316C2×C4×C11—48no—
317C2×C4×C11C2512yes—
318C2×C4×C11C2518yes—
319C2×C4×C11C2514yes—
320C2×C4×C11C2514yes—
321C2×C4×C11C2518yes—
322C22⋊D11—48no—
323C2×Dic11—24no—
324C2×Dic11—28no—
325C2×Dic11—22no—
326C2×Dic11—28no—
327C2×Dic11—24no—
328C2×Dic11—48no—
329C2×Dic11C2518yes—
330C2×Dic11C2514yes—
331C2×Dic11C2512yes—
332C2×Dic11C2514yes—
333C2×Dic11C2518yes—
334D44—44no—
335C4×D11—232no—
336C4×D11—28no—
337C4×D11—216no—
338C4×D11—232no—
339C4×D11—216no—
340C4×D11—416no—
341Dic22—44no—
342Dic22—416no—
343Dic22—48no—
344Dic22—48no—
345C23×Q8—112no—
346C23×Q8—111no—
347C23×D4—111no—
348C24×C4—112no—
349#563—1132no—
350#563—1164no—
351#563—1132no—
352#563—1116no—
353#563—1132no—
354#563—1164no—
355#563C2×D11116yesdirect product factor
356C2×C4⋊Q8—112no—
357C2×C4⋊Q8—112no—
358C2×C4⋊Q8—1132no—
359C2×C4⋊Q8—114no—
360C2×C4⋊Q8—114no—
361C2×C4⋊Q8—112no—
362C2×C4⋊Q8C2×D1112yescomplemented
363C2×#126—1164no—
364C2×#126—114no—
365C2×#126—114no—
366C2×#126—114no—
367C2×#126—114no—
368C2×#126—114no—
369C2×#126—114no—
370C2×#126—114no—
371C2×#126C2×D1114yescomplemented
372C2×#125—1132no—
373C2×#125—114no—
374C2×#125—114no—
375C2×#125—112no—
376C2×#125—112no—
377C2×#125—112no—
378C2×#125C2×D1112yescomplemented
379C2×#124—111no—
380C2×#124—111no—
381C2×#124—1116no—
382C2×#124—114no—
383C2×#124—111no—
384C2×#124C2×D1111yescharacteristic
385C2×#123—112no—
386C2×#123—112no—
387C2×#123—1132no—
388C2×#123—114no—
389C2×#123—114no—
390C2×#123—112no—
391C2×#123C2×D1112yes—
392C2×C22⋊Q8—114no—
393C2×C22⋊Q8—114no—
394C2×C22⋊Q8—1164no—
395C2×C22⋊Q8—114no—
396C2×C22⋊Q8—114no—
397C2×C22⋊Q8—114no—
398C2×C22⋊Q8—114no—
399C2×C22⋊Q8—114no—
400C2×C22⋊Q8C2×D1114yescomplemented
401C22×C4⋊C4—112no—
402C22×C4⋊C4—114no—
403C22×C4⋊C4—114no—
404C22×C4⋊C4—114no—
405C22×C4⋊C4—112no—
406C22×C22⋊C4—114no—
407C22×C22⋊C4—114no—
408C22×C22⋊C4—112no—
409C22×C42—111no—
410C22×C42—112no—
411C22×C11—24no—
412C22×C11—28no—
413C22×C11—48no—
414C22×C11C2×H(5,𝔽2)12yes—
415C22×C11C2×2−1+414yes—
416C22×C11C2611yescharacteristic
417C2×D11—24no—
418C2×D11—28no—
419C2×D11—48no—
420C2×D11—432no—
421C2×D11#563116yesdirect product factor
422C2×D11C2×H(5,𝔽2)14yes—
423C2×D11C2×2−1+418yes—
424C4×C11—28no—
425C4×C11—22no—
426C4×C11—24no—
427C4×C11—28no—
428C4×C11—24no—
429Dic11—24no—
430Dic11—28no—
431Dic11—22no—
432Dic11—28no—
433Dic11—24no—
434C25—112no—
435C22×Q8—1116no—
436C22×Q8—118no—
437C22×Q8—114no—
438C22×Q8—112no—
439C22×Q8—111no—
440C22×Q8—112no—
441C22×Q8—448no—
442C22×Q8—444no—
443C22×Q8C22×D1112yes—
444C22×Q8C22×D1111yescharacteristic
445C22×D4—112no—
446C22×D4—118no—
447C22×D4—111no—
448C22×D4—444no—
449C22×D4C22×D1111yescharacteristic
450C23×C4—112no—
451C23×C4—114no—
452C23×C4—112no—
453C23×C4—112no—
454C23×C4—114no—
455C23×C4—111no—
456C23×C4—114no—
457C23×C4—1116no—
458C23×C4—448no—
459C23×C4C22×D1112yes—
460C4⋊Q8—1116no—
461C4⋊Q8—1116no—
462C4⋊Q8—1132no—
463C4⋊Q8—1132no—
464C4⋊Q8—1116no—
465C4⋊Q8C22×D11116yescomplemented
466#126—1132no—
467#126—1132no—
468#126—1132no—
469#126—1132no—
470#126—1132no—
471#126—1132no—
472#126—1132no—
473#126C22×D11132yescomplemented
474#125—1132no—
475#125—1132no—
476#125—1116no—
477#125—1116no—
478#125—1116no—
479#125C22×D11116yescomplemented
480#124—118no—
481#124—118no—
482#124—1132no—
483#124—118no—
484#124C22×D1118yes—
485#123—1116no—
486#123—1116no—
487#123—1132no—
488#123—1132no—
489#123—1116no—
490#123C22×D11116yes—
491C22⋊Q8—1132no—
492C22⋊Q8—1132no—
493C22⋊Q8—1132no—
494C22⋊Q8—1132no—
495C22⋊Q8—1132no—
496C22⋊Q8—1132no—
497C22⋊Q8—1132no—
498C22⋊Q8C22×D11132yescomplemented
499C2×C4⋊C4—114no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—114no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—112no—
512C2×C4⋊C4—1116no—
513C2×C4⋊C4—1132no—
514C2×C4⋊C4—1132no—
515C2×C4⋊C4—1132no—
516C2×C4⋊C4—1116no—
517C2×C4⋊C4C22×D1112yes—
518C2×C4⋊C4C22×D1114yes—
519C2×C4⋊C4C22×D1114yes—
520C2×C4⋊C4C22×D1114yes—
521C2×C4⋊C4C22×D1112yes—
522C2×C22⋊C4—114no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—112no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—1132no—
531C2×C22⋊C4—1132no—
532C2×C22⋊C4—1116no—
533C2×C22⋊C4C22×D1114yes—
534C2×C22⋊C4C22×D1114yes—
535C2×C22⋊C4C22×D1112yes—
536C2×C42—111no—
537C2×C42—112no—
538C2×C42—112no—
539C2×C42—114no—
540C2×C42—118no—
541C2×C42—1116no—
542C2×C42C22×D1111yescharacteristic
543C2×C42C22×D1112yes—
544C2×C11—44no—
545C2×C11C2×#56314yescomplemented
546C2×C11C22×H(5,𝔽2)11yescharacteristic
547C2×C11C22×2−1+412yes—
548D11—44no—
549D11C2×#56318yesdirect product factor
550C24—111no—
551C24—118no—
552C24—112no—
553C24—228no—
554C24—2216no—
555C24C23×D1112yes—
556C2×Q8—44no—
557C2×Q8—42no—
558C2×Q8—1116no—
559C2×Q8—118no—
560C2×Q8—114no—
561C2×Q8—118no—
562C2×Q8—448no—
563C2×Q8—442no—
564C2×Q8—444no—
565C2×Q8—444no—
566C2×Q8—4432no—
567C2×Q8—4416no—
568C2×Q8C23×D1118yes—
569C2×Q8C23×D1114yes—
570C2×D4—42no—
571C2×D4—118no—
572C2×D4—114no—
573C2×D4—442no—
574C2×D4—4416no—
575C2×D4—444no—
576C2×D4C23×D1114yes—
577C22×C4—44no—
578C22×C4—112no—
579C22×C4—114no—
580C22×C4—112no—
581C22×C4—111no—
582C22×C4—114no—
583C22×C4—118no—
584C22×C4—118no—
585C22×C4—1116no—
586C22×C4—118no—
587C22×C4—114no—
588C22×C4—1116no—
589C22×C4—1116no—
590C22×C4—2216no—
591C22×C4—224no—
592C22×C4—228no—
593C22×C4—2216no—
594C22×C4—228no—
595C22×C4—448no—
596C22×C4—4432no—
597C22×C4—444no—
598C22×C4C23×D1112yes—
599C22×C4C23×D1114yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1111yescharacteristic
602C22×C4C23×D1114yes—
603C22×C4C23×D1118yes—
604C4⋊C4—1116no—
605C4⋊C4—118no—
606C4⋊C4—1116no—
607C4⋊C4—1116no—
608C4⋊C4—1116no—
609C4⋊C4—1116no—
610C4⋊C4—1116no—
611C4⋊C4—1116no—
612C4⋊C4—1116no—
613C4⋊C4—1116no—
614C4⋊C4—1116no—
615C4⋊C4—1116no—
616C4⋊C4—118no—
617C4⋊C4C23×D1118yes—
618C4⋊C4C23×D11116yes—
619C4⋊C4C23×D11116yes—
620C4⋊C4C23×D11116yes—
621C4⋊C4C23×D1118yes—
622C22⋊C4—1116no—
623C22⋊C4—1116no—
624C22⋊C4—118no—
625C22⋊C4—1116no—
626C22⋊C4—1116no—
627C22⋊C4—1116no—
628C22⋊C4—1116no—
629C22⋊C4—1116no—
630C22⋊C4C23×D11116yes—
631C22⋊C4C23×D11116yes—
632C22⋊C4C23×D1118yes—
633C42—114no—
634C42—118no—
635C42—118no—
636C42—1116no—
637C42C23×D1114yes—
638C42C23×D1118yes—
639C11C22×#56311yescharacteristic, complemented, Sylow
640C23—24no—
641C23—28no—
642C23—114no—
643C23—118no—
644C23—112no—
645C23—114no—
646C23—2216no—
647C23—2232no—
648C23—224no—
649C23—228no—
650C23—4432no—
651C23C24×D1114yes—
652C23C24×D1111yescharacteristic
653Q8—48no—
654Q8—44no—
655Q8—4416no—
656Q8—444no—
657Q8—448no—
658Q8—448no—
659D4—44no—
660D4—444no—
661D4—448no—
662C2×C4—28no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—28no—
667C2×C4—48no—
668C2×C4—114no—
669C2×C4—118no—
670C2×C4—114no—
671C2×C4—112no—
672C2×C4—118no—
673C2×C4—2232no—
674C2×C4—228no—
675C2×C4—2216no—
676C2×C4—2216no—
677C2×C4—2232no—
678C2×C4—228no—
679C2×C4—222no—
680C2×C4—224no—
681C2×C4—224no—
682C2×C4—228no—
683C2×C4—4416no—
684C2×C4—448no—
685C2×C4C24×D1114yes—
686C2×C4C24×D1118yes—
687C2×C4C24×D1114yes—
688C2×C4C24×D1112yes—
689C2×C4C24×D1118yes—
690C22—24no—
691C22—28no—
692C22—48no—
693C22—114no—
694C22—118no—
695C22—1116no—
696C22—224no—
697C22—228no—
698C22—4432no—
699C22—448no—
700C22D11×H(5,𝔽2)12yes—
701C22D11×2−1+414yes—
702C22C25×D1111yescharacteristic
703C4—28no—
704C4—22no—
705C4—24no—
706C4—24no—
707C4—28no—
708C4—228no—
709C4—222no—
710C4—224no—
711C4—224no—
712C4—228no—
713C2—44no—
714C2—118no—
715C2—444no—
716C2D11×#56314yesdirect product factor
717C2C2×D11×H(5,𝔽2)11yescharacteristic
718C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#563C2
socleC23×C11C25
prime radicalC22×D4×D11C22
hypercenterC2×#563D11
hypocenterC11C22×#563
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. C2×#10623230C2semidirect
2. C2×#10623182C2semidirect
3. C2×#10623243C2semidirect
4. C2×#10623177C2semidirect
5. C2×#10623203C2semidirect
6. C2×#10623266C2semidirect
7. D11×#563C2direct (N × H)
8. C2×D11×C4⋊Q8C2semidirect
9. C2×D11×#126C2semidirect
10. C2×D11×#125C2semidirect
13. C2×D11×C22⋊Q8C2semidirect
14. C2×C11×#563C2semidirect
19. C11×#563C22semidirect
20. C2×C11×C4⋊Q8C22semidirect
21. C2×C11×#126C22semidirect
22. C2×C11×#125C22semidirect
25. C2×C11×C22⋊Q8C22semidirect
27. C2×#66999C22semidirect
28. C2×#66997C22semidirect
29. C2×#66997C22semidirect
33. C2×#66977C22semidirect
34. #10623266C22semidirect
35. D11×C4⋊Q8C22semidirect
36. #10623243C22semidirect
37. D11×#126C22semidirect
38. #10623230C22semidirect
39. D11×#125C22semidirect
41. #10623203C22semidirect
43. #10623182C22semidirect
44. #10623177C22semidirect
45. D11×C22⋊Q8C22semidirect
46. C2×#66951C22semidirect
47. C2×#66951C22semidirect
48. C2×#66951C22semidirect
49. C2×#66950C22semidirect
50. C2×#66949C22semidirect
51. C2×#66949C22semidirect
58. C2×#66943C22semidirect
59. C2×#66943C22semidirect
60. C2×#66942C22semidirect
61. C2×#66942C22semidirect
62. C2×#66941C22semidirect
63. C2×#66941C22semidirect
70. C2×#66932C22semidirect
71. C2×#66932C22semidirect
72. C2×#66932C22semidirect
73. C2×#66931C22semidirect
74. C2×#66931C22semidirect
75. C2×#66929C22semidirect
79. C2×#66923C22semidirect
80. C2×#66922C22semidirect
107. C11×C4⋊Q8C23semidirect
108. C11×#126C23semidirect
109. C11×#125C23semidirect
112. C11×C22⋊Q8C23semidirect
127. #66999C23semidirect
128. #66997C23semidirect
129. #66997C23semidirect
143. #66977C23semidirect
156. #66951C23semidirect
157. #66951C23semidirect
158. #66951C23semidirect
159. #66950C23semidirect
160. #66949C23semidirect
161. #66949C23semidirect
168. #66943C23semidirect
169. #66943C23semidirect
170. #66942C23semidirect
171. #66942C23semidirect
172. #66941C23semidirect
173. #66941C23semidirect
180. #66932C23semidirect
181. #66932C23semidirect
182. #66932C23semidirect
183. #66931C23semidirect
184. #66931C23semidirect
185. #66929C23semidirect
189. #66923C23semidirect
190. #66922C23semidirect
288. C2×#563D11direct (N × H)
355. #563C2×D11direct (N × H)
362. C2×C4⋊Q8C2×D11semidirect
371. C2×#126C2×D11semidirect
378. C2×#125C2×D11semidirect
400. C2×C22⋊Q8C2×D11semidirect
421. C2×D11#563direct (N × H)
465. C4⋊Q8C22×D11semidirect
473. #126C22×D11semidirect
479. #125C22×D11semidirect
498. C22⋊Q8C22×D11semidirect
545. C2×C11C2×#563semidirect
549. D11C2×#563direct (N × H)
639. C11C22×#563semidirect
716. C2D11×#563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232302
C2×#106231822
C2×#106232432
C2×#106231772
C2×#106232032
C2×#106232662
D11×#5632
C2×D11×C4⋊Q82
C2×D11×#1262
C2×D11×#1252
C2×D11×#1242
C2×D11×#1232
C2×D11×C22⋊Q82
C2×C11×#5632
C22×#56311