Finite Group Databasebeta

← C2×#13082875 #15661056

Subgroups — C2×#13082875 #15661056

Order 2816.

7354 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082875C2132yesmaximal, direct product factor
2C2×#10623151C214yesmaximal, complemented
3C2×#10623149C214yesmaximal, complemented
4C2×#10623089C212yesmaximal, complemented
5C2×#10623225C212yesmaximal, complemented
6C2×#10623249C212yesmaximal, complemented
7C2×#10623086C212yesmaximal, complemented
8C2×#10623049C211yesmaximal, characteristic, complemented
9C2×#10623194C214yesmaximal, complemented
10C2×#10623196C214yesmaximal, complemented
11C2×#10623139C212yesmaximal, complemented
12C2×#10623055C211yesmaximal, characteristic, complemented
13C2×#10623137C212yesmaximal, complemented
14C2×C11×#540C211yesmaximal, characteristic, complemented
15C22×#4341C2212yes—
16C22×#4341C2212yescomplemented
17C22×#4339C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C11×#540C22116yescomplemented
20C2×C11×#127C2211yescharacteristic, complemented
21C2×C11×#125C2211yescharacteristic, complemented
22C2×C11×#123C2214yescomplemented
23C2×C11×#121C2212yes—
24C2×C11×#121C2214yes—
25C2×C4×D4×C11C2212yescomplemented
26C2×C11×#117C2211yescharacteristic
27C2×#66993C2214yes—
28C2×#66992C2214yes—
29C2×#66992C2214yes—
30C2×#66992C2214yescomplemented
31C2×#66991C2212yes—
32C2×#66991C2214yes—
33C2×#66991C2212yescomplemented
34C2×#66990C2214yes—
35C2×D4×Dic11C2214yes—
36C2×D4×Dic11C2214yescomplemented
37C2×#66983C2214yes—
38C2×#66982C2214yes—
39C2×C4×C22⋊D11C2214yescomplemented
40C22×C4⋊Dic11C2214yescomplemented
41C2×#66977C2212yes—
42#10623249C22132yescomplemented
43#10623225C22132yescomplemented
44#10623196C22164yescomplemented
45#10623194C22164yescomplemented
46#10623151C22164yescomplemented
47#10623149C22164yescomplemented
48#10623139C22132yescomplemented
49#10623137C22132yescomplemented
50#10623089C22132yescomplemented
51#10623086C22132yescomplemented
52#10623055C22116yescomplemented
53#10623049C22116yescomplemented
54C2×#66951C2214yes—
55C2×#66950C2212yes—
56C2×#66950C2212yes—
57C2×#66950C2212yescomplemented
58C2×#66948C2212yes—
59C2×#66947C2214yes—
60C2×#66945C2212yes—
61C2×#66945C2214yescomplemented
62C2×C4⋊C4×D11C2212yescomplemented
63C2×#66943C2214yescomplemented
64C2×#66942C2214yescomplemented
65C2×#66939C2212yes—
66C2×#66939C2214yes—
67C2×#66939C2214yescomplemented
68C2×#66937C2214yes—
69C2×#66937C2214yescomplemented
70C2×#66936C2214yes—
71C2×#66935C2212yes—
72C2×(C22⋊D11)⋊C4C2214yes—
73C2×#66932C2214yes—
74C2×#66932C2214yescomplemented
75C2×#66931C2214yescomplemented
76C2×C4×D44C2212yes—
77C2×C4×D44C2212yes—
78C2×#66923C2211yescharacteristic, complemented
79C2×#66922C2211yescharacteristic, complemented
80C2×C4×Dic22C2212yescomplemented
81C24×D11C2311yescharacteristic
82C22×D4×C11C2312yes—
83C22×D4×C11C2314yes—
84C22×D4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2314yes—
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11C2314yes—
93C23×Dic11C2314yes—
94C23×Dic11C2311yescharacteristic
95C2×#4341—48no—
96C2×#4341—48no—
97C2×#4341C23116yes—
98C2×#4341C23116yescomplemented
99C2×#4339—44no—
100C2×#4339C2318yes—
101C22×D44C2312yes—
102C22×D44C2312yes—
103C22×D44C2311yescharacteristic
104C22×C4×D11—44no—
105C22×C4×D11C2312yes—
106C22×C4×D11C2312yes—
107C22×C4×D11C2312yes—
108C22×C4×D11C2314yes—
109C22×C4×D11C2318yes—
110C22×Dic22C2312yes—
111C22×Dic22C2311yescharacteristic
112C11×#127C2318yescomplemented
113C11×#125C2318yescomplemented
114C11×#123C23132yescomplemented
115C11×#121C23116yes—
116C11×#121C23132yes—
117C4×D4×C11C23116yescomplemented
118C11×#117C2318yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2314yes—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2312yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130#66993C23132yes—
131#66992C23132yes—
132#66992C23132yes—
133#66992C23132yescomplemented
134#66991C23116yes—
135#66991C23132yes—
136#66991C23116yescomplemented
137#66990C23132yes—
138D4×Dic11C23132yes—
139D4×Dic11C23132yescomplemented
140#66983C23132yes—
141#66982C23132yes—
142C4×C22⋊D11C23132yescomplemented
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145C2×(C2×D11)⋊C4C2312yes—
146C2×(C2×D11)⋊C4C2312yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×C4⋊Dic11C2312yes—
151C2×C4⋊Dic11C2314yes—
152C2×C4⋊Dic11C2312yes—
153C2×C4⋊Dic11C2312yes—
154C2×C4⋊Dic11C2314yes—
155C2×C4⋊Dic11C2314yes—
156C2×C4⋊Dic11C23132yescomplemented
157#66977C23116yes—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2314yes—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164#66951C23132yes—
165#66950C23116yes—
166#66950C23116yes—
167#66950C23116yescomplemented
168#66948C23116yes—
169#66947C23132yes—
170#66945C23116yes—
171#66945C23132yescomplemented
172C4⋊C4×D11C23116yescomplemented
173#66943C23132yescomplemented
174#66942C23132yescomplemented
175#66939C23116yes—
176#66939C23132yes—
177#66939C23132yescomplemented
178#66937C23132yes—
179#66937C23132yescomplemented
180#66936C23132yes—
181#66935C23116yes—
182(C22⋊D11)⋊C4C23132yes—
183#66932C23132yes—
184#66932C23132yescomplemented
185#66931C23132yescomplemented
186C4×D44C23116yes—
187C4×D44C23116yes—
188#66923C2318yescomplemented
189#66922C2318yescomplemented
190C4×Dic22C23116yescomplemented
191C2×#3539—111nomaximal, Sylow
192C24×C11C2411yescharacteristic
193C24×C11C2414yes—
194C23×D11—42no—
195C23×D11—44no—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C23×D11C2414yes—
199C2×D4×C11—28no—
200C2×D4×C11—48no—
201C2×D4×C11—48no—
202C2×D4×C11C2418yes—
203C2×D4×C11C24116yes—
204C2×D4×C11C24116yes—
205C22×C4×C11—24no—
206C22×C4×C11—48no—
207C22×C4×C11C2412yes—
208C22×C4×C11C2414yes—
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2412yes—
211C22×C4×C11C2414yes—
212C22×C4×C11C24116yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—44no—
215C2×C22⋊D11—48no—
216C2×C22⋊D11—48no—
217C2×C22⋊D11—48no—
218C2×C22⋊D11—48no—
219C2×C22⋊D11C24116yes—
220C2×C22⋊D11C2418yes—
221C2×C22⋊D11C24116yes—
222C2×C22⋊D11C24116yes—
223C2×C22⋊D11C24116yes—
224C22×Dic11—42no—
225C22×Dic11—48no—
226C22×Dic11—48no—
227C22×Dic11C2414yes—
228C22×Dic11C2412yes—
229C22×Dic11C2414yes—
230C22×Dic11C2412yes—
231C22×Dic11C24116yes—
232C22×Dic11C24116yes—
233C22×Dic11C2414yes—
234#4341—432no—
235#4341—432no—
236#4339—416no—
237C2×D44—44no—
238C2×D44—44no—
239C2×D44—42no—
240C2×D44C2418yes—
241C2×D44C2418yes—
242C2×D44C2414yes—
243C2×C4×D11—28no—
244C2×C4×D11—28no—
245C2×C4×D11—44no—
246C2×C4×D11—48no—
247C2×C4×D11—416no—
248C2×C4×D11C2418yes—
249C2×C4×D11C2418yes—
250C2×C4×D11C2418yes—
251C2×C4×D11C24116yes—
252C2×Dic22—28no—
253C2×Dic22—42no—
254C2×Dic22C2418yes—
255C2×Dic22C2414yes—
256C11×C4⋊C4C2418yes—
257C11×C4⋊C4C24116yes—
258C11×C4⋊C4C2418yes—
259C11×C22⋊C4C24116yes—
260C11×C22⋊C4C2418yes—
261C11×C22⋊C4C24116yes—
262C42×C11C2414yes—
263C42×C11C2414yes—
264C22⋊Dic11C24116yes—
265C22⋊Dic11C24116yes—
266C22⋊Dic11C24116yes—
267(C2×D11)⋊C4C2418yes—
268(C2×D11)⋊C4C2418yes—
269(C2×D11)⋊C4C2418yes—
270(C2×D11)⋊C4C2418yes—
271(C2×D11)⋊C4C24116yes—
272(C2×D11)⋊C4C24116yes—
273(C2×D11)⋊C4C24116yes—
274C4⋊Dic11C2418yes—
275C4⋊Dic11C24116yes—
276C4⋊Dic11C2418yes—
277C4⋊Dic11C2418yes—
278C4⋊Dic11C24116yes—
279C4⋊Dic11C24116yes—
280Dic11⋊C4C24116yes—
281Dic11⋊C4C24116yes—
282Dic11⋊C4C24116yes—
283Dic11⋊C4C24116yes—
284C4×Dic11C24116yes—
285C4×Dic11C24116yes—
286#3539—1132no—
287C2×#560—114no—
288C2×#553—114no—
289C2×#553—112no—
290C2×#552—112no—
291C2×#550—112no—
292C2×#547—112no—
293C2×#541—111no—
294C2×#540—114no—
295C2×#540D1111yescharacteristic, complemented
296C2×#539—114no—
297C2×#537—112no—
298C2×#525—112no—
299C2×#525—111no—
300C23×C11—28no—
301C23×C11—22no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—24no—
305C23×C11C2512yes—
306C23×C11C2518yes—
307C23×C11C2511yescharacteristic
308C22×D11—24no—
309C22×D11—24no—
310C22×D11—24no—
311C22×D11—24no—
312C22×D11—24no—
313C22×D11—24no—
314C22×D11—44no—
315C22×D11—48no—
316C22×D11—416no—
317C22×D11C2514yes—
318C22×D11C2514yes—
319D4×C11—216no—
320D4×C11—416no—
321D4×C11—416no—
322C2×C4×C11—22no—
323C2×C4×C11—28no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—28no—
327C2×C4×C11—416no—
328C2×C4×C11H(5,𝔽2)14yes—
329C2×C4×C11C2514yes—
330C2×C4×C11C2518yes—
331C2×C4×C11C2512yes—
332C2×C4×C11C2514yes—
333C2×C4×C11C2512yes—
334C22⋊D11—48no—
335C22⋊D11—416no—
336C22⋊D11—416no—
337C22⋊D11—416no—
338C22⋊D11—416no—
339C2×Dic11—28no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—28no—
343C2×Dic11—44no—
344C2×Dic11—416no—
345C2×Dic11—416no—
346C2×Dic11C2518yes—
347C2×Dic11C2514yes—
348C2×Dic11C2518yes—
349C2×Dic11C2514yes—
350D44—48no—
351D44—48no—
352D44—44no—
353C4×D11—216no—
354C4×D11—216no—
355C4×D11—48no—
356C4×D11—416no—
357Dic22—216no—
358Dic22—44no—
359C22×#41—112no—
360C22×#41—112no—
361C22×#41—111no—
362C24×C4—111no—
363#560—1164no—
364#553—1164no—
365#553—1132no—
366#552—1132no—
367#550—1132no—
368#547—1132no—
369#541—1116no—
370#540—1164no—
371#540C2×D11116yescomplemented
372#539—1164no—
373#537—1132no—
374C2×C4⋊Q8—111no—
375C2×#127—114no—
376C2×#127C2×D1111yescharacteristic, complemented
377C2×#126—114no—
378C2×#126—114no—
379C2×#126—114no—
380C2×#125—114no—
381C2×#125—114no—
382C2×#125—111no—
383C2×#125C2×D1111yescharacteristic, complemented
384#525—1132no—
385#525—1116no—
386C2×#123—114no—
387C2×#123—114no—
388C2×#123—114no—
389C2×#123—112no—
390C2×#123—114no—
391C2×#123—114no—
392C2×#123C2×D1114yescomplemented
393C2×C22⋊Q8—112no—
394C2×C22⋊Q8—112no—
395C2×C22⋊Q8—112no—
396C2×C22⋊Q8—112no—
397C2×C22⋊Q8—114no—
398C2×#121—112no—
399C2×#121—114no—
400C2×#121—112no—
401C2×#121—114no—
402C2×#121—114no—
403C2×#121—114no—
404C2×#121—114no—
405C2×#121—112no—
406C2×#121—114no—
407C2×#121—114no—
408C2×#121C2×D1112yes—
409C2×#121C2×D1114yes—
410C2×#120—114no—
411C2×#120—112no—
412C2×C4×Q8—112no—
413C2×C4×D4—114no—
414C2×C4×D4—114no—
415C2×C4×D4—114no—
416C2×C4×D4—114no—
417C2×C4×D4—112no—
418C2×C4×D4—112no—
419C2×C4×D4C2×D1112yescomplemented
420C2×#117—112no—
421C2×#117—114no—
422C2×#117C2×D1111yescharacteristic
423C22×C4⋊C4—114no—
424C22×C4⋊C4—112no—
425C22×C11—22no—
426C22×C11—28no—
427C22×C11—28no—
428C22×C11—24no—
429C22×C11—28no—
430C22×C11—44no—
431C22×C11—416no—
432C22×C11C2×H(5,𝔽2)12yes—
433C22×C11#58514yes—
434C22×C11C2611yescharacteristic
435C2×D11—24no—
436C2×D11—24no—
437C2×D11—24no—
438C2×D11—24no—
439C2×D11—24no—
440C2×D11—24no—
441C2×D11—416no—
442C2×D11—48no—
443C2×D11—48no—
444C4×C11—22no—
445C4×C11—24no—
446C4×C11—28no—
447C4×C11—24no—
448C4×C11C2×H(5,𝔽2)14yes—
449Dic11—28no—
450Dic11—24no—
451Dic11—24no—
452Dic11—28no—
453C25—111no—
454C2×#41—1116no—
455C2×#41—1116no—
456C2×#41—118no—
457C2×#41—444no—
458C2×#41—448no—
459C2×#41—448no—
460C22×Q8—112no—
461C22×Q8—111no—
462C22×D4—114no—
463C22×D4—114no—
464C22×D4—112no—
465C22×D4—114no—
466C22×D4—114no—
467C22×D4—112no—
468C22×D4—112no—
469C22×D4—111no—
470C22×D4C22×D1112yes—
471C22×D4C22×D1114yes—
472C22×D4C22×D1114yes—
473C23×C4—114no—
474C23×C4—114no—
475C23×C4—111no—
476C23×C4—112no—
477C23×C4—112no—
478C23×C4—114no—
479C23×C4—112no—
480C23×C4—118no—
481C23×C4—444no—
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D1114yes—
484C4⋊Q8—118no—
485#127—1132no—
486#127C22×D1118yescomplemented
487#126—1132no—
488#126—1132no—
489#126—1132no—
490#125—1132no—
491#125—1132no—
492#125—118no—
493#125C22×D1118yescomplemented
494#123—1132no—
495#123—1132no—
496#123—1132no—
497#123—1116no—
498#123—1132no—
499#123—1132no—
500#123C22×D11132yescomplemented
501C22⋊Q8—1116no—
502C22⋊Q8—1116no—
503C22⋊Q8—1116no—
504C22⋊Q8—1116no—
505C22⋊Q8—1132no—
506#121—1116no—
507#121—1116no—
508#121—1132no—
509#121—1132no—
510#121—1132no—
511#121—1132no—
512#121—1132no—
513#121—1116no—
514#121—1132no—
515#121—1132no—
516#121C22×D11116yes—
517#121C22×D11132yes—
518#120—1132no—
519#120—1116no—
520C4×Q8—1116no—
521C4×D4—1132no—
522C4×D4—1132no—
523C4×D4—1132no—
524C4×D4—1132no—
525C4×D4—1116no—
526C4×D4—1116no—
527C4×D4C22×D11116yescomplemented
528#117—1116no—
529#117—1132no—
530#117C22×D1118yes—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—1132no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—1116no—
543C2×C4⋊C4C22×D1112yes—
544C2×C4⋊C4C22×D1114yes—
545C2×C4⋊C4C22×D1112yes—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4C22×D1112yes—
557C2×C22⋊C4C22×D1114yes—
558C2×C22⋊C4C22×D1114yes—
559C2×C42—114no—
560C2×C42—114no—
561C2×C42C22×D1111yescharacteristic
562C2×C42C22×D1111yescharacteristic
563C2×C11—42no—
564C2×C11—48no—
565C2×C11#353914yescomplemented
566C2×C11C22×H(5,𝔽2)11yescharacteristic
567C2×C11C2×#58512yes—
568D11—44no—
569D11—44no—
570C24—112no—
571C24—112no—
572C24—114no—
573C24—442no—
574C24—444no—
575C24C23×D1111yescharacteristic
576C24C23×D1114yes—
577#41—4416no—
578#41—4432no—
579#41—4432no—
580C2×Q8—118no—
581C2×Q8—114no—
582C2×Q8—228no—
583C2×Q8—442no—
584C2×D4—28no—
585C2×D4—48no—
586C2×D4—48no—
587C2×D4—1116no—
588C2×D4—1116no—
589C2×D4—118no—
590C2×D4—1116no—
591C2×D4—1116no—
592C2×D4—118no—
593C2×D4—118no—
594C2×D4—114no—
595C2×D4—442no—
596C2×D4—444no—
597C2×D4—444no—
598C2×D4—444no—
599C2×D4—448no—
600C2×D4—448no—
601C2×D4—448no—
602C2×D4—448no—
603C2×D4C23×D1118yes—
604C2×D4C23×D11116yes—
605C2×D4C23×D11116yes—
606C22×C4—24no—
607C22×C4—48no—
608C22×C4—114no—
609C22×C4—112no—
610C22×C4—114no—
611C22×C4—112no—
612C22×C4—1116no—
613C22×C4—1116no—
614C22×C4—114no—
615C22×C4—118no—
616C22×C4—118no—
617C22×C4—1116no—
618C22×C4—118no—
619C22×C4—228no—
620C22×C4—228no—
621C22×C4—4416no—
622C22×C4—444no—
623C22×C4—448no—
624C22×C4—442no—
625C22×C4—448no—
626C22×C4—448no—
627C22×C4C23×D1114yes—
628C22×C4C23×D1112yes—
629C22×C4C23×D1114yes—
630C22×C4C23×D1112yes—
631C22×C4C23×D1111yescharacteristic
632C22×C4C23×D11116yes—
633C22×C4C23×D1111yescharacteristic
634C4⋊C4—118no—
635C4⋊C4—1116no—
636C4⋊C4—118no—
637C4⋊C4—1116no—
638C4⋊C4—1116no—
639C4⋊C4—1116no—
640C4⋊C4—118no—
641C4⋊C4—1116no—
642C4⋊C4—1116no—
643C4⋊C4—1116no—
644C4⋊C4C23×D1118yes—
645C4⋊C4C23×D11116yes—
646C4⋊C4C23×D1118yes—
647C22⋊C4—1116no—
648C22⋊C4—1116no—
649C22⋊C4—1116no—
650C22⋊C4—118no—
651C22⋊C4—1116no—
652C22⋊C4—1116no—
653C22⋊C4—118no—
654C22⋊C4—118no—
655C22⋊C4—1116no—
656C22⋊C4—118no—
657C22⋊C4C23×D1118yes—
658C22⋊C4C23×D11116yes—
659C22⋊C4C23×D11116yes—
660C42—1116no—
661C42—1116no—
662C42C23×D1114yes—
663C42C23×D1114yes—
664C11C2×#353911yescharacteristic, complemented, Sylow
665C23—22no—
666C23—28no—
667C23—28no—
668C23—28no—
669C23—24no—
670C23—114no—
671C23—114no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—224no—
677C23—224no—
678C23—444no—
679C23—448no—
680C23—4416no—
681C23C24×D1112yes—
682C23C24×D1118yes—
683C23C24×D1111yescharacteristic
684Q8—2216no—
685Q8—444no—
686D4—216no—
687D4—416no—
688D4—416no—
689D4—444no—
690D4—448no—
691D4—448no—
692D4—448no—
693D4—4416no—
694D4—4416no—
695D4—4416no—
696D4—4416no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—118no—
704C2×C4—114no—
705C2×C4—118no—
706C2×C4—114no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—228no—
710C2×C4—228no—
711C2×C4—2216no—
712C2×C4—2216no—
713C2×C4—448no—
714C2×C4—4416no—
715C2×C4—444no—
716C2×C4—4416no—
717C2×C4—4416no—
718C2×C4#6704214yes—
719C2×C4C24×D1114yes—
720C2×C4C24×D1118yes—
721C2×C4C24×D1114yes—
722C2×C4C24×D1112yes—
723C2×C4C24×D1112yes—
724C22—22no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—24no—
729C22—44no—
730C22—416no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—224no—
735C22—224no—
736C22—224no—
737C22—4416no—
738C22—448no—
739C22—448no—
740C22C2×#6704212yes—
741C22#1062345514yes—
742C22C25×D1111yescharacteristic
743C4—22no—
744C4—24no—
745C4—28no—
746C4—24no—
747C4—224no—
748C4—224no—
749C4—228no—
750C4—228no—
751C4C2×#6704214yes—
752C2—42no—
753C2—48no—
754C2—444no—
755C2—444no—
756C2#1308287514yesdirect product factor
757C2C22×#6704211yescharacteristic
758C2C2×#1062345512yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#540C2
socleC23×C11C25
hypercenterC2×#540D11
hypocenterC11C2×#3539
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #13082875C2direct (N × H)
2. C2×#10623151C2semidirect
3. C2×#10623149C2semidirect
4. C2×#10623089C2semidirect
5. C2×#10623225C2semidirect
6. C2×#10623249C2semidirect
7. C2×#10623086C2semidirect
8. C2×#10623049C2semidirect
9. C2×#10623194C2semidirect
10. C2×#10623196C2semidirect
11. C2×#10623139C2semidirect
12. C2×#10623055C2semidirect
13. C2×#10623137C2semidirect
14. C2×C11×#540C2semidirect
16. C22×#4341C22semidirect
19. C11×#540C22semidirect
20. C2×C11×#127C22semidirect
21. C2×C11×#125C22semidirect
22. C2×C11×#123C22semidirect
25. C2×C4×D4×C11C22semidirect
30. C2×#66992C22semidirect
33. C2×#66991C22semidirect
36. C2×D4×Dic11C22semidirect
39. C2×C4×C22⋊D11C22semidirect
40. C22×C4⋊Dic11C22semidirect
42. #10623249C22semidirect
43. #10623225C22semidirect
44. #10623196C22semidirect
45. #10623194C22semidirect
46. #10623151C22semidirect
47. #10623149C22semidirect
48. #10623139C22semidirect
49. #10623137C22semidirect
50. #10623089C22semidirect
51. #10623086C22semidirect
52. #10623055C22semidirect
53. #10623049C22semidirect
57. C2×#66950C22semidirect
61. C2×#66945C22semidirect
62. C2×C4⋊C4×D11C22semidirect
63. C2×#66943C22semidirect
64. C2×#66942C22semidirect
67. C2×#66939C22semidirect
69. C2×#66937C22semidirect
74. C2×#66932C22semidirect
75. C2×#66931C22semidirect
78. C2×#66923C22semidirect
79. C2×#66922C22semidirect
80. C2×C4×Dic22C22semidirect
98. C2×#4341C23semidirect
112. C11×#127C23semidirect
113. C11×#125C23semidirect
114. C11×#123C23semidirect
117. C4×D4×C11C23semidirect
133. #66992C23semidirect
136. #66991C23semidirect
139. D4×Dic11C23semidirect
142. C4×C22⋊D11C23semidirect
156. C2×C4⋊Dic11C23semidirect
167. #66950C23semidirect
171. #66945C23semidirect
172. C4⋊C4×D11C23semidirect
173. #66943C23semidirect
174. #66942C23semidirect
177. #66939C23semidirect
179. #66937C23semidirect
184. #66932C23semidirect
185. #66931C23semidirect
188. #66923C23semidirect
189. #66922C23semidirect
190. C4×Dic22C23semidirect
295. C2×#540D11semidirect
371. #540C2×D11semidirect
376. C2×#127C2×D11semidirect
383. C2×#125C2×D11semidirect
392. C2×#123C2×D11semidirect
419. C2×C4×D4C2×D11semidirect
486. #127C22×D11semidirect
493. #125C22×D11semidirect
500. #123C22×D11semidirect
527. C4×D4C22×D11semidirect
565. C2×C11#3539semidirect
664. C11C2×#3539semidirect
756. C2#13082875direct (N × H)

Maximal subgroups

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

subgroupindex
#130828752
C2×#106231512
C2×#106231492
C2×#106230892
C2×#106232252
C2×#106232492
C2×#106230862
C2×#106230492
C2×#106231942
C2×#106231962
C2×#106231392
C2×#106230552
C2×#106231372
C2×C11×#5402
C2×#353911