Finite Group Databasebeta

← C2×#13082864 #15661023

Subgroups — C2×#13082864 #15661023

Order 2816.

7162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082864C2132yesmaximal, direct product factor
2C2×#10623243C214yesmaximal, complemented
3C2×#10623112C212yesmaximal, complemented
4C2×#10623225C212yesmaximal, complemented
5C2×#10623236C214yesmaximal, complemented
6C2×Q8×D44C212yesmaximal, complemented
7C2×#10623258C212yesmaximal, complemented
8C2×#10623220C214yesmaximal, complemented
9C2×#10623049C211yesmaximal, characteristic, complemented
10C2×#10623223C214yesmaximal, complemented
11C2×#10623159C212yesmaximal, complemented
12C2×#10623055C211yesmaximal, characteristic
13C2×D11×C22⋊Q8C212yesmaximal, complemented
14C2×C11×#541C211yesmaximal, characteristic, complemented
15C22×Q8×D11C2212yes—
16C22×Q8×D11C2212yescomplemented
17C22×#4339C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C11×#541C22116yescomplemented
20C2×C11×C4⋊Q8C2211yescharacteristic, complemented
21C2×C11×#126C2214yes—
22C2×C11×#125C2211yescharacteristic, complemented
23C2×C11×#125C2214yescomplemented
24C2×C11×C22⋊Q8C2212yes—
25C2×C4×Q8×C11C2212yescomplemented
26C2×C11×#117C2211yescharacteristic
27C2×#66999C2212yes—
28C2×#66999C2212yescomplemented
29C2×#66977C2212yes—
30#10623258C22132yescomplemented
31#10623243C22164yescomplemented
32#10623236C22164yescomplemented
33#10623225C22132yescomplemented
34#10623223C22164yescomplemented
35#10623220C22164yescomplemented
36#10623159C22132yescomplemented
37D11×C22⋊Q8C22132yescomplemented
38#10623112C22132yescomplemented
39Q8×D44C22132yescomplemented
40#10623055C22116yes—
41#10623049C22116yescomplemented
42C2×#66951C2214yescomplemented
43C2×#66950C2214yes—
44C2×#66950C2212yes—
45C2×#66950C2212yes—
46C2×#66950C2212yescomplemented
47C2×#66950C2214yescomplemented
48C2×#66949C2214yes—
49C2×#66949C2214yes—
50C2×#66949C2214yescomplemented
51C2×#66948C2212yes—
52C2×#66947C2214yes—
53C2×#66947C2214yes—
54C2×#66947C2214yescomplemented
55C2×#66946C2214yes—
56C2×#66945C2214yes—
57C2×#66945C2212yescomplemented
58C2×C4⋊C4×D11C2212yes—
59C2×C4⋊C4×D11C2214yes—
60C2×#66943C2214yescomplemented
61C2×#66942C2214yescomplemented
62C2×#66942C2214yescomplemented
63C2×#66941C2214yescomplemented
64C2×#66941C2214yescomplemented
65C2×#66939C2212yes—
66C2×#66938C2214yes—
67C2×#66936C2214yes—
68C2×#66935C2212yes—
69C2×C22⋊C4×D11C2214yes—
70C2×#66932C2214yes—
71C2×#66931C2214yes—
72C2×#66929C2214yescomplemented
73C2×C4×D44C2214yes—
74C2×C4×D44C2212yes—
75C2×C4×D44C2212yes—
76C2×#66925C2214yes—
77C2×#66923C2211yescharacteristic, complemented
78C2×#66922C2214yescomplemented
79C2×#66922C2211yescharacteristic, complemented
80C2×C4×Dic22C2212yescomplemented
81C24×D11C2311yescharacteristic
82C22×Q8×C11C2312yes—
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11C2312yes—
85C23×Dic11C2311yescharacteristic
86C2×Q8×D11—48no—
87C2×Q8×D11—48no—
88C2×Q8×D11C23116yes—
89C2×Q8×D11C23116yescomplemented
90C2×#4339—44no—
91C2×#4339C2318yes—
92C22×D44C2312yes—
93C22×D44C2312yes—
94C22×D44C2311yescharacteristic
95C22×C4×D11—44no—
96C22×C4×D11C2314yes—
97C22×C4×D11C2312yes—
98C22×C4×D11C2312yes—
99C22×C4×D11C2314yes—
100C22×C4×D11C2314yes—
101C22×C4×D11C2312yes—
102C22×C4×D11C2318yes—
103C22×Dic22C2312yes—
104C22×Dic22C2314yes—
105C22×Dic22C2314yes—
106C22×Dic22C2311yescharacteristic
107C11×C4⋊Q8C2318yescomplemented
108C11×#126C23132yes—
109C11×#125C23132yescomplemented
110C11×#125C2318yescomplemented
111C11×C22⋊Q8C23116yes—
112C4×Q8×C11C23116yescomplemented
113C11×#117C2318yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2314yes—
125C2×C22⋊Dic11C2314yes—
126#66999C23116yes—
127#66999C23116yescomplemented
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2314yes—
139C2×C4⋊Dic11C2312yes—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×C4⋊Dic11C2312yes—
143#66977C23116yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2314yes—
152#66951C23132yescomplemented
153#66950C23132yes—
154#66950C23116yes—
155#66950C23116yes—
156#66950C23132yescomplemented
157#66950C23116yescomplemented
158#66949C23132yes—
159#66949C23132yes—
160#66949C23132yescomplemented
161#66948C23116yes—
162#66947C23132yes—
163#66947C23132yes—
164#66947C23132yescomplemented
165#66946C23132yes—
166#66945C23132yes—
167#66945C23116yescomplemented
168C4⋊C4×D11C23116yes—
169C4⋊C4×D11C23132yes—
170#66943C23132yescomplemented
171#66942C23132yescomplemented
172#66942C23132yescomplemented
173#66941C23132yescomplemented
174#66941C23132yescomplemented
175#66939C23116yes—
176#66938C23132yes—
177#66936C23132yes—
178#66935C23116yes—
179C22⋊C4×D11C23132yes—
180#66932C23132yes—
181#66931C23132yes—
182#66929C23132yescomplemented
183C4×D44C23132yes—
184C4×D44C23116yes—
185C4×D44C23116yes—
186#66925C23132yes—
187#66923C2318yescomplemented
188#66922C23132yescomplemented
189#66922C2318yescomplemented
190C4×Dic22C23116yescomplemented
191C2×#3538—111nomaximal, Sylow
192C24×C11C2411yescharacteristic
193C23×D11—28no—
194C23×D11—42no—
195C23×D11C2412yes—
196C23×D11C2414yes—
197C23×D11C2412yes—
198C2×Q8×C11—28no—
199C2×Q8×C11C2418yes—
200C22×C4×C11—24no—
201C22×C4×C11C2412yes—
202C22×C4×C11C2414yes—
203C22×C4×C11C2411yescharacteristic
204C22×C4×C11C2412yes—
205C22×C4×C11C2414yes—
206C22×C4×C11C2414yes—
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—44no—
209C2×C22⋊D11C2418yes—
210C22×Dic11—42no—
211C22×Dic11C2414yes—
212C22×Dic11C2412yes—
213C22×Dic11C2414yes—
214C22×Dic11C2412yes—
215C22×Dic11C2414yes—
216Q8×D11—432no—
217Q8×D11—432no—
218#4339—416no—
219C2×D44—28no—
220C2×D44—28no—
221C2×D44—42no—
222C2×D44C2418yes—
223C2×D44C2418yes—
224C2×D44C2414yes—
225C2×C4×D11—216no—
226C2×C4×D11—28no—
227C2×C4×D11—28no—
228C2×C4×D11—44no—
229C2×C4×D11—48no—
230C2×C4×D11—48no—
231C2×C4×D11—416no—
232C2×C4×D11C24116yes—
233C2×C4×D11C2418yes—
234C2×C4×D11C2418yes—
235C2×C4×D11C24116yes—
236C2×C4×D11C24116yes—
237C2×C4×D11C2418yes—
238C2×Dic22—28no—
239C2×Dic22—42no—
240C2×Dic22—48no—
241C2×Dic22—48no—
242C2×Dic22C2418yes—
243C2×Dic22C24116yes—
244C2×Dic22C24116yes—
245C2×Dic22C2414yes—
246C11×C4⋊C4C24116yes—
247C11×C4⋊C4C24116yes—
248C11×C4⋊C4C2418yes—
249C11×C4⋊C4C24116yes—
250C11×C4⋊C4C24116yes—
251C11×C4⋊C4C2418yes—
252C11×C22⋊C4C24116yes—
253C11×C22⋊C4C2418yes—
254C42×C11C2414yes—
255C42×C11C2414yes—
256C42×C11C24116yes—
257C22⋊Dic11C24116yes—
258(C2×D11)⋊C4C2418yes—
259(C2×D11)⋊C4C24116yes—
260(C2×D11)⋊C4C2418yes—
261(C2×D11)⋊C4C24116yes—
262(C2×D11)⋊C4C2418yes—
263(C2×D11)⋊C4C24116yes—
264(C2×D11)⋊C4C2418yes—
265(C2×D11)⋊C4C24116yes—
266(C2×D11)⋊C4C24116yes—
267C4⋊Dic11C2418yes—
268C4⋊Dic11C24116yes—
269C4⋊Dic11C2418yes—
270C4⋊Dic11C24116yes—
271C4⋊Dic11C24116yes—
272C4⋊Dic11C2418yes—
273Dic11⋊C4C24116yes—
274Dic11⋊C4C24116yes—
275Dic11⋊C4C24116yes—
276Dic11⋊C4C24116yes—
277Dic11⋊C4C24116yes—
278Dic11⋊C4C24116yes—
279C4×Dic11C24116yes—
280C4×Dic11C24116yes—
281#3538—1132no—
282C2×#563—114no—
283C2×#552—112no—
284C2×#552—112no—
285C2×#551—114no—
286C2×D4×Q8—112no—
287C2×D4×Q8—112no—
288C2×#544—114no—
289C2×#541—111no—
290C2×#541D1111yescharacteristic, complemented
291C2×#539—114no—
292C2×#536—112no—
293C2×#525—111no—
294C22×C22⋊Q8—112no—
295C23×C11—22no—
296C23×C11—24no—
297C23×C11C2512yes—
298C23×C11C2511yescharacteristic
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—216no—
305C22×D11—44no—
306C22×D11—416no—
307C22×D112−1+418yes—
308C22×D11C2514yes—
309C22×D11C2514yes—
310Q8×C11—216no—
311C2×C4×C11—28no—
312C2×C4×C11—22no—
313C2×C4×C11—28no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—28no—
317C2×C4×C11H(5,𝔽2)14yes—
318C2×C4×C11C2514yes—
319C2×C4×C11C2518yes—
320C2×C4×C11C2512yes—
321C2×C4×C11C2514yes—
322C2×C4×C11C2518yes—
323C2×C4×C11C2512yes—
324C22⋊D11—48no—
325C2×Dic11—28no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—28no—
329C2×Dic11—44no—
330C2×Dic11C2518yes—
331C2×Dic11C2514yes—
332C2×Dic11C2518yes—
333C2×Dic11C2514yes—
334D44—216no—
335D44—216no—
336D44—44no—
337C4×D11—232no—
338C4×D11—216no—
339C4×D11—216no—
340C4×D11—48no—
341C4×D11—416no—
342C4×D11—416no—
343Dic22—216no—
344Dic22—44no—
345Dic22—416no—
346Dic22—416no—
347C22×#41—111no—
348C23×Q8—112no—
349C23×Q8—112no—
350C24×C4—111no—
351#563—1164no—
352#552—1132no—
353#552—1132no—
354#551—1164no—
355D4×Q8—1132no—
356D4×Q8—1132no—
357#544—1164no—
358#541—1116no—
359#541C2×D11116yescomplemented
360#539—1164no—
361#536—1132no—
362C2×C4⋊Q8—114no—
363C2×C4⋊Q8—114no—
364C2×C4⋊Q8—111no—
365C2×C4⋊Q8—114no—
366C2×C4⋊Q8C2×D1111yescharacteristic, complemented
367C2×#126—114no—
368C2×#126—114no—
369C2×#126—114no—
370C2×#126C2×D1114yes—
371C2×#125—114no—
372C2×#125—114no—
373C2×#125—114no—
374C2×#125—111no—
375C2×#125C2×D1114yescomplemented
376C2×#125C2×D1111yescharacteristic, complemented
377C2×#124—114no—
378#525—1116no—
379C2×#123—114no—
380C2×#123—114no—
381C2×#123—114no—
382C2×#123—114no—
383C2×#123—112no—
384C2×C22⋊Q8—112no—
385C2×C22⋊Q8—112no—
386C2×C22⋊Q8—112no—
387C2×C22⋊Q8—1132no—
388C2×C22⋊Q8—114no—
389C2×C22⋊Q8—114no—
390C2×C22⋊Q8—114no—
391C2×C22⋊Q8—112no—
392C2×C22⋊Q8—112no—
393C2×C22⋊Q8—114no—
394C2×C22⋊Q8—112no—
395C2×C22⋊Q8—114no—
396C2×C22⋊Q8—114no—
397C2×C22⋊Q8C2×D1112yes—
398C2×#121—112no—
399C2×#120—112no—
400C2×C4×Q8—112no—
401C2×C4×Q8C2×D1112yescomplemented
402C2×C4×D4—114no—
403C2×C4×D4—112no—
404C2×C4×D4—112no—
405C2×C4×D4—114no—
406C2×#117—114no—
407C2×#117—112no—
408C2×#117—114no—
409C2×#117C2×D1111yescharacteristic
410C22×C4⋊C4—114no—
411C22×C4⋊C4—112no—
412C22×C22⋊C4—114no—
413C22×C11—22no—
414C22×C11—24no—
415C22×C11—44no—
416C22×C11C2×H(5,𝔽2)12yes—
417C22×C11C2×2−1+414yes—
418C22×C11C2611yescharacteristic
419C2×D11—24no—
420C2×D11—24no—
421C2×D11—216no—
422C2×D11—24no—
423C2×D11—24no—
424C2×D11—24no—
425C2×D11—416no—
426C2×D11—48no—
427C2×D11C2×2−1+418yes—
428C4×C11—22no—
429C4×C11—28no—
430C4×C11—28no—
431C4×C11—24no—
432C4×C11—24no—
433C4×C11C2×H(5,𝔽2)14yes—
434Dic11—28no—
435Dic11—24no—
436Dic11—24no—
437Dic11—28no—
438C25—111no—
439C2×#41—118no—
440C2×#41—444no—
441C22×Q8—1116no—
442C22×Q8—1116no—
443C22×Q8—112no—
444C22×Q8—114no—
445C22×Q8—114no—
446C22×Q8—111no—
447C22×Q8—448no—
448C22×Q8—448no—
449C22×Q8C22×D1112yes—
450C22×D4—112no—
451C22×D4—112no—
452C22×D4—112no—
453C22×D4—111no—
454C23×C4—111no—
455C23×C4—114no—
456C23×C4—112no—
457C23×C4—112no—
458C23×C4—114no—
459C23×C4—112no—
460C23×C4—114no—
461C23×C4—118no—
462C23×C4—444no—
463C23×C4C22×D1111yescharacteristic
464C4⋊Q8—1132no—
465C4⋊Q8—1132no—
466C4⋊Q8—118no—
467C4⋊Q8—1132no—
468C4⋊Q8C22×D1118yescomplemented
469#126—1132no—
470#126—1132no—
471#126—1132no—
472#126C22×D11132yes—
473#125—1132no—
474#125—1132no—
475#125—1132no—
476#125—118no—
477#125C22×D11132yescomplemented
478#125C22×D1118yescomplemented
479#124—1132no—
480#123—1132no—
481#123—1132no—
482#123—1132no—
483#123—1116no—
484#123—1132no—
485C22⋊Q8—1116no—
486C22⋊Q8—1116no—
487C22⋊Q8—1116no—
488C22⋊Q8—1132no—
489C22⋊Q8—1116no—
490C22⋊Q8—1116no—
491C22⋊Q8—1116no—
492C22⋊Q8—1132no—
493C22⋊Q8—1132no—
494C22⋊Q8—1132no—
495C22⋊Q8—1132no—
496C22⋊Q8—1132no—
497C22⋊Q8C22×D11116yes—
498#121—1116no—
499#120—1116no—
500C4×Q8—1116no—
501C4×Q8C22×D11116yescomplemented
502C4×D4—1132no—
503C4×D4—1116no—
504C4×D4—1116no—
505C4×D4—1132no—
506#117—1116no—
507#117—1132no—
508#117—1132no—
509#117C22×D1118yes—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—112no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—1132no—
523C2×C4⋊C4—1116no—
524C2×C4⋊C4C22×D1112yes—
525C2×C4⋊C4C22×D1114yes—
526C2×C4⋊C4C22×D1114yes—
527C2×C4⋊C4C22×D1112yes—
528C2×C4⋊C4C22×D1114yes—
529C2×C4⋊C4C22×D1114yes—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—1132no—
541C2×C22⋊C4C22×D1114yes—
542C2×C22⋊C4C22×D1112yes—
543C2×C42—114no—
544C2×C42—114no—
545C2×C42C22×D1114yes—
546C2×C42C22×D1111yescharacteristic
547C2×C42C22×D1111yescharacteristic
548C2×C11—42no—
549C2×C11#353814yescomplemented
550C2×C11C22×H(5,𝔽2)11yescharacteristic
551C2×C11C22×2−1+412yes—
552D11—28no—
553D11—44no—
554C24—112no—
555C24—112no—
556C24—114no—
557C24—228no—
558C24—442no—
559C24C23×D1111yescharacteristic
560#41—4416no—
561C2×Q8—28no—
562C2×Q8—118no—
563C2×Q8—1116no—
564C2×Q8—1116no—
565C2×Q8—114no—
566C2×Q8—228no—
567C2×Q8—448no—
568C2×Q8—448no—
569C2×Q8—442no—
570C2×Q8—4432no—
571C2×Q8—4432no—
572C2×Q8C23×D1118yes—
573C2×D4—118no—
574C2×D4—118no—
575C2×D4—118no—
576C2×D4—114no—
577C2×D4—228no—
578C2×D4—228no—
579C2×D4—442no—
580C2×D4—444no—
581C22×C4—24no—
582C22×C4—114no—
583C22×C4—112no—
584C22×C4—114no—
585C22×C4—112no—
586C22×C4—114no—
587C22×C4—1116no—
588C22×C4—118no—
589C22×C4—118no—
590C22×C4—1116no—
591C22×C4—118no—
592C22×C4—1116no—
593C22×C4—2216no—
594C22×C4—228no—
595C22×C4—228no—
596C22×C4—4416no—
597C22×C4—444no—
598C22×C4—448no—
599C22×C4—448no—
600C22×C4—442no—
601C22×C4C23×D1114yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1114yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1114yes—
606C22×C4C23×D1111yescharacteristic
607C22×C4C23×D1111yescharacteristic
608C4⋊C4—118no—
609C4⋊C4—1116no—
610C4⋊C4—1116no—
611C4⋊C4—1116no—
612C4⋊C4—1116no—
613C4⋊C4—1116no—
614C4⋊C4—1116no—
615C4⋊C4—1116no—
616C4⋊C4—1116no—
617C4⋊C4—118no—
618C4⋊C4—118no—
619C4⋊C4—1116no—
620C4⋊C4C23×D1118yes—
621C4⋊C4C23×D11116yes—
622C4⋊C4C23×D11116yes—
623C4⋊C4C23×D1118yes—
624C4⋊C4C23×D11116yes—
625C4⋊C4C23×D11116yes—
626C22⋊C4—1116no—
627C22⋊C4—1116no—
628C22⋊C4—1116no—
629C22⋊C4—118no—
630C22⋊C4—118no—
631C22⋊C4—1116no—
632C22⋊C4—118no—
633C22⋊C4—118no—
634C22⋊C4—1116no—
635C22⋊C4—1116no—
636C22⋊C4C23×D11116yes—
637C22⋊C4C23×D1118yes—
638C42—1116no—
639C42—1116no—
640C42C23×D11116yes—
641C42C23×D1114yes—
642C42C23×D1114yes—
643C11C2×#353811yescharacteristic, complemented, Sylow
644C23—22no—
645C23—24no—
646C23—118no—
647C23—114no—
648C23—114no—
649C23—2216no—
650C23—224no—
651C23—224no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—444no—
656C23—4416no—
657C23C24×D1112yes—
658C23C24×D1111yescharacteristic
659Q8—216no—
660Q8—2216no—
661Q8—4416no—
662Q8—4416no—
663Q8—444no—
664D4—2216no—
665D4—2216no—
666D4—444no—
667D4—448no—
668C2×C4—22no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—118no—
675C2×C4—114no—
676C2×C4—118no—
677C2×C4—114no—
678C2×C4—2232no—
679C2×C4—224no—
680C2×C4—224no—
681C2×C4—228no—
682C2×C4—228no—
683C2×C4—2216no—
684C2×C4—2216no—
685C2×C4—448no—
686C2×C4—4416no—
687C2×C4—4416no—
688C2×C4—444no—
689C2×C4#6704214yes—
690C2×C4C24×D1114yes—
691C2×C4C24×D1118yes—
692C2×C4C24×D1114yes—
693C2×C4C24×D1118yes—
694C2×C4C24×D1112yes—
695C2×C4C24×D1112yes—
696C22—22no—
697C22—24no—
698C22—44no—
699C22—118no—
700C22—224no—
701C22—224no—
702C22—2216no—
703C22—224no—
704C22—224no—
705C22—224no—
706C22—4416no—
707C22—448no—
708C22C2×#6704212yes—
709C22D11×2−1+414yes—
710C22C25×D1111yescharacteristic
711C4—22no—
712C4—28no—
713C4—28no—
714C4—24no—
715C4—24no—
716C4—224no—
717C4—224no—
718C4—228no—
719C4—228no—
720C4C2×#6704214yes—
721C2—42no—
722C2—228no—
723C2—444no—
724C2#1308286414yesdirect product factor
725C2C22×#6704211yescharacteristic
726C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#541C2
socleC23×C11C25
prime radicalC2×#10623055C2
hypercenterC2×#541D11
hypocenterC11C2×#3538
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #13082864C2direct (N × H)
2. C2×#10623243C2semidirect
3. C2×#10623112C2semidirect
4. C2×#10623225C2semidirect
5. C2×#10623236C2semidirect
6. C2×Q8×D44C2semidirect
7. C2×#10623258C2semidirect
8. C2×#10623220C2semidirect
9. C2×#10623049C2semidirect
10. C2×#10623223C2semidirect
11. C2×#10623159C2semidirect
13. C2×D11×C22⋊Q8C2semidirect
14. C2×C11×#541C2semidirect
16. C22×Q8×D11C22semidirect
19. C11×#541C22semidirect
20. C2×C11×C4⋊Q8C22semidirect
22. C2×C11×#125C22semidirect
23. C2×C11×#125C22semidirect
25. C2×C4×Q8×C11C22semidirect
28. C2×#66999C22semidirect
30. #10623258C22semidirect
31. #10623243C22semidirect
32. #10623236C22semidirect
33. #10623225C22semidirect
34. #10623223C22semidirect
35. #10623220C22semidirect
36. #10623159C22semidirect
37. D11×C22⋊Q8C22semidirect
38. #10623112C22semidirect
39. Q8×D44C22semidirect
41. #10623049C22semidirect
42. C2×#66951C22semidirect
46. C2×#66950C22semidirect
47. C2×#66950C22semidirect
50. C2×#66949C22semidirect
54. C2×#66947C22semidirect
57. C2×#66945C22semidirect
60. C2×#66943C22semidirect
61. C2×#66942C22semidirect
62. C2×#66942C22semidirect
63. C2×#66941C22semidirect
64. C2×#66941C22semidirect
72. C2×#66929C22semidirect
77. C2×#66923C22semidirect
78. C2×#66922C22semidirect
79. C2×#66922C22semidirect
80. C2×C4×Dic22C22semidirect
89. C2×Q8×D11C23semidirect
107. C11×C4⋊Q8C23semidirect
109. C11×#125C23semidirect
110. C11×#125C23semidirect
112. C4×Q8×C11C23semidirect
127. #66999C23semidirect
152. #66951C23semidirect
156. #66950C23semidirect
157. #66950C23semidirect
160. #66949C23semidirect
164. #66947C23semidirect
167. #66945C23semidirect
170. #66943C23semidirect
171. #66942C23semidirect
172. #66942C23semidirect
173. #66941C23semidirect
174. #66941C23semidirect
182. #66929C23semidirect
187. #66923C23semidirect
188. #66922C23semidirect
189. #66922C23semidirect
190. C4×Dic22C23semidirect
290. C2×#541D11semidirect
359. #541C2×D11semidirect
366. C2×C4⋊Q8C2×D11semidirect
375. C2×#125C2×D11semidirect
376. C2×#125C2×D11semidirect
401. C2×C4×Q8C2×D11semidirect
468. C4⋊Q8C22×D11semidirect
477. #125C22×D11semidirect
478. #125C22×D11semidirect
501. C4×Q8C22×D11semidirect
549. C2×C11#3538semidirect
643. C11C2×#3538semidirect
724. C2#13082864direct (N × H)

Maximal subgroups

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

subgroupindex
#130828642
C2×#106232432
C2×#106231122
C2×#106232252
C2×#106232362
C2×Q8×D442
C2×#106232582
C2×#106232202
C2×#106230492
C2×#106232232
C2×#106231592
C2×#106230552
C2×D11×C22⋊Q82
C2×C11×#5412
C2×#353811