Finite Group Databasebeta

← #14926370

Subgroups — #14926370

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
2#13076950C211yesmaximal, characteristic, complemented
3#13076942C211yesmaximal, characteristic, complemented
4#13076906C212yesmaximal, complemented
5#13074423C211yesmaximal, characteristic, complemented
6#13074352C211yesmaximal, characteristic, complemented
7#13074330C212yesmaximal, complemented
8#13072648C214yesmaximal, complemented
9#13072549C214yesmaximal, complemented
10#13072513C214yesmaximal, complemented
11#13072495C214yesmaximal, complemented
12#13071281C212yesmaximal, complemented
13#13071214C211yesmaximal, characteristic, complemented
14C4×#66990C212yesmaximal, complemented
15C2×C11×#538C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C11×#538—28no—
20C2×C11×#126C2212yescomplemented
21C2×C11×#124C2212yescomplemented
22C2×C11×#123C2212yescomplemented
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2212yescomplemented
26C2×C11×#120C2212yes—
27C2×C4×D4×C11C2212yes—
28C22×C11×C22⋊C4C2211yescharacteristic
29C2×#66990C2212yes—
30C2×#66988C2212yes—
31C2×#66988C2214yescomplemented
32C2×C4×C22⋊D11C2214yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C2×(C22⋊D11)⋊C4—28no—
37C2×(C22⋊D11)⋊C4C2214yes—
38C2×(C22⋊D11)⋊C4C2214yes—
39#10622860C2212yes—
40#10622844C2212yescomplemented
41#10622843C2212yescomplemented
42#10622836C2214yes—
43#10622836C2214yes—
44#10622836C2212yescomplemented
45#10622834C2212yescomplemented
46#10622833C2212yes—
47#10622833C2212yes—
48#10622833C2214yescomplemented
49#10622825C2211yescharacteristic
50#10622825C2211yescharacteristic
51#10622823C2214yescomplemented
52C4×C22⋊Dic11C2212yes—
53#10622607C2214yescomplemented
54#10622606C2212yescomplemented
55#10622605C2212yescomplemented
56#10622602C2214yescomplemented
57#10622591C2214yescomplemented
58#10622586C2212yescomplemented
59#10622586C2212yescomplemented
60#10622585C2214yescomplemented
61#10622574C2214yescomplemented
62#10622572C2214yes—
63#10622572C2214yes—
64#10622569C2214yescomplemented
65#10622568C2212yes—
66#10622564C2214yescomplemented
67#10622564C2214yescomplemented
68#10622559C2212yes—
69#10622559C2212yes—
70#10622559C2214yescomplemented
71#10622558C2214yescomplemented
72#10622557C2214yescomplemented
73#10622556C2212yes—
74#10622556C2214yescomplemented
75C4×(C2×D11)⋊C4C2214yescomplemented
76#10622546C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2312yes—
81C22×D4×C11C2312yes—
82C22×D4×C11C2312yes—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11—24no—
93C23×Dic11—44no—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×C4×D11—24no—
99C22×C4×D11—44no—
100C22×C4×D11C2314yes—
101C11×#126—28no—
102C11×#124—28no—
103C11×#123—28no—
104C11×C22⋊Q8—24no—
105C11×#121—24no—
106C11×#121—28no—
107C11×#120—28no—
108C4×D4×C11—28no—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C22⋊C4D418yescomplemented
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C42×C11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129#66990—28no—
130#66988—28no—
131#66988—48no—
132C4×C22⋊D11—48no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×C4⋊Dic11C2312yes—
140C2×C4⋊Dic11C2312yes—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—24no—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2314yes—
150(C22⋊D11)⋊C4—216no—
151(C22⋊D11)⋊C4—216no—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161#34986—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11C2×D414yes—
167C24×C11C2412yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11#4114yes—
175C23×D11C2412yes—
176C2×Q8×C11—22no—
177C2×Q8×C11—42no—
178C2×D4×C11—24no—
179C2×D4×C11—24no—
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—22no—
184C2×D4×C11—44no—
185C2×D4×C11—42no—
186C2×D4×C11—44no—
187C22×C4×C11—24no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—44no—
191C22×C4×C11C2×D414yes—
192C22×C4×C11C2×D414yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—232no—
200C2×C22⋊D11—28no—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—28no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—44no—
206C22×Dic11—24no—
207C22×Dic11—28no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—28no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—42no—
214C22×Dic11—44no—
215C22×Dic11—416no—
216C22×Dic11#4114yes—
217C22×Dic11C2414yes—
218C22×Dic11C2414yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C2×C4×D11—28no—
223C2×C4×D11—28no—
224C2×C4×D11—44no—
225C2×C4×D11—416no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4C2×D418yes—
236C11×C22⋊C4C2×D418yes—
237C42×C11—24no—
238C22⋊Dic11—28no—
239C22⋊Dic11—28no—
240C22⋊Dic11—24no—
241C22⋊Dic11—24no—
242C22⋊Dic11—44no—
243C22⋊Dic11—44no—
244C22⋊Dic11—44no—
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250C4⋊Dic11—42no—
251C4⋊Dic11—42no—
252Dic11⋊C4—28no—
253Dic11⋊C4—28no—
254Dic11⋊C4—28no—
255Dic11⋊C4—44no—
256C4×Dic11—24no—
257C4×Dic11—24no—
258C4×Dic11—44no—
259C2×#538D1111yescharacteristic, complemented
260C22×C4×D4—111no—
261#2855—111no—
262#2854—111no—
263#2849—112no—
264#2626—111no—
265#2617—111no—
266#2613—112no—
267#2466—114no—
268#2459—114no—
269#2456—114no—
270#2455—114no—
271#2322—112no—
272#2312—111no—
273C4×#120—112no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—28no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—24no—
285C23×C11—24no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11—48no—
289C23×C11—48no—
290C23×C11C22×D414yes—
291C23×C11C22×D412yes—
292C23×C11C2×#4112yes—
293C23×C11C2×#4112yes—
294C23×C11C2511yescharacteristic
295C22×D11—28no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—48no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11—48no—
304C22×D11C2×#4114yes—
305Q8×C11—82no—
306D4×C11—48no—
307D4×C11—82no—
308D4×C11—84no—
309D4×C11—84no—
310C2×C4×C11—24no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—84no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D414yes—
326C22⋊D11—232no—
327C22⋊D11—416no—
328C2×Dic11—28no—
329C2×Dic11—28no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—416no—
343C2×Dic11—44no—
344C2×Dic11C2×#4114yes—
345C2×Dic11H(5,𝔽2)14yes—
346C4×D11—416no—
347C23×D4—111no—
348C24×C4—111no—
349C24×C4—111no—
350#538—28no—
351C2×#126C2×D1112yescomplemented
352C2×#124C2×D1112yescomplemented
353C2×#123—112no—
354C2×#123—114no—
355C2×#123C2×D1112yescomplemented
356C2×C22⋊Q8C2×D1111yescharacteristic
357C2×#121C2×D1111yescharacteristic
358C2×#121C2×D1112yescomplemented
359C2×#120—112no—
360C2×#120C2×D1112yes—
361C2×C4×D4—114no—
362C2×C4×D4—114no—
363C2×C4×D4—114no—
364C2×C4×D4—228no—
365C2×C4×D4C2×D1112yes—
366C22×C4⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4C2×D1111yescharacteristic
369C22×C42—111no—
370#399—112no—
371#397—112no—
372#396—114no—
373#394—114no—
374#394—114no—
375#394—114no—
376#393—112no—
377#392—114no—
378#392—114no—
379#392—112no—
380#391—112no—
381#390—112no—
382#389—114no—
383#389—112no—
384#389—112no—
385#388—114no—
386#388—114no—
387#388—114no—
388#388—114no—
389#387—114no—
390#387—114no—
391#386—112no—
392#386—112no—
393#386—114no—
394#386—114no—
395#385—114no—
396#385—114no—
397#385—112no—
398#385—112no—
399#385—114no—
400#381—112no—
401#381—114no—
402#380—111no—
403#380—111no—
404#379—112no—
405#379—112no—
406C4×C22⋊C4—112no—
407C4×C22⋊C4—114no—
408C22×C11—24no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—24no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—416no—
416C22×C11—44no—
417C22×C11—44no—
418C22×C11—42no—
419C22×C11—44no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—44no—
423C22×C11#52514yes—
424C22×C11C23×D411yescharacteristic
425C22×C11C22×#4111yescharacteristic
426C22×C11C22×#4111yescharacteristic
427C22×C11C2×H(5,𝔽2)12yes—
428C22×C11#58512yes—
429C2×D11—24no—
430C2×D11—28no—
431C2×D11—416no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—44no—
435C4×C11—24no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11—42no—
441Dic11—24no—
442Dic11—24no—
443Dic11—44no—
444Dic11—42no—
445Dic11—44no—
446C25—111no—
447C25C22×D1111yescharacteristic
448C22×Q8C22×D1111yescharacteristic
449C22×D4—114no—
450C22×D4—114no—
451C22×D4—224no—
452C22×D4—224no—
453C22×D4—224no—
454C22×D4C22×D1112yes—
455C22×D4C22×D1112yes—
456C22×D4C22×D1112yes—
457C22×D4C22×D1111yescharacteristic
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—114no—
461C23×C4—111no—
462C23×C4—114no—
463C23×C4—224no—
464C23×C4—224no—
465C23×C4—444no—
466C23×C4—444no—
467C23×C4C22×D1112yes—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470#126—28no—
471#124—28no—
472#123—28no—
473#123—228no—
474#123—448no—
475C22⋊Q8—24no—
476#121—24no—
477#121—28no—
478#120—28no—
479#120—228no—
480C4×D4—28no—
481C4×D4—2216no—
482C4×D4—2216no—
483C4×D4—448no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—112no—
490C2×C4⋊C4—224no—
491C2×C4⋊C4C22×D1112yes—
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C4⋊C4C22×D1112yes—
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C22⋊C4—114no—
496C2×C22⋊C4—112no—
497C2×C22⋊C4—112no—
498C2×C22⋊C4—114no—
499C2×C22⋊C4—112no—
500C2×C22⋊C4—112no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—114no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—224no—
508C2×C22⋊C4C22⋊D1118yescomplemented
509C2×C22⋊C4C22×D1112yes—
510C2×C22⋊C4C22×D1112yes—
511C2×C22⋊C4C22×D1112yes—
512C2×C22⋊C4C22×D1112yes—
513C2×C22⋊C4C22×D1112yes—
514C2×C22⋊C4C22×D1112yes—
515C2×C22⋊C4C22×D1112yes—
516C2×C42—112no—
517C2×C42—112no—
518C2×C42—114no—
519C2×C42—224no—
520C2×C42C22×D1112yes—
521#95—114no—
522#95—114no—
523#95—114no—
524#95—112no—
525#95—112no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530C2×C11—24no—
531C2×C11—44no—
532C2×C11—82no—
533C2×C11C2×#52511yescharacteristic
534C2×C11#345912yes—
535C2×C11#348411yescharacteristic
536C2×C11#348511yescharacteristic
537C2×C11#350612yes—
538D11—44no—
539C24—22no—
540C24—22no—
541C24—42no—
542C24—42no—
543C24—112no—
544C24—114no—
545C24—222no—
546C24—222no—
547C24—442no—
548C24—442no—
549C24C2×C22⋊D1114yes—
550C24C23×D1112yes—
551C24C23×D1112yes—
552C24C23×D1111yescharacteristic
553C2×Q8—22no—
554C2×Q8—42no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—44no—
562C2×D4—42no—
563C2×D4—44no—
564C2×D4—228no—
565C2×D4—228no—
566C2×D4—2232no—
567C2×D4—228no—
568C2×D4—228no—
569C2×D4—444no—
570C2×D4—444no—
571C22×C4—24no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—44no—
575C22×C4—114no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—114no—
579C22×C4—114no—
580C22×C4—112no—
581C22×C4—228no—
582C22×C4—224no—
583C22×C4—228no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—228no—
589C22×C4—228no—
590C22×C4—444no—
591C22×C4—4416no—
592C22×C4—444no—
593C22×C4—442no—
594C22×C4—4416no—
595C22×C4C2×C22⋊D1114yes—
596C22×C4C2×C22⋊D1114yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1111yescharacteristic
602C22×C4C23×D1111yescharacteristic
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—228no—
608C4⋊C4—228no—
609C4⋊C4—228no—
610C4⋊C4—444no—
611C4⋊C4—442no—
612C4⋊C4—442no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—228no—
619C22⋊C4—228no—
620C22⋊C4—228no—
621C22⋊C4—224no—
622C22⋊C4—224no—
623C22⋊C4—224no—
624C22⋊C4—224no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C22⋊C4—444no—
628C22⋊C4—444no—
629C22⋊C4—444no—
630C22⋊C4C2×C22⋊D1118yes—
631C22⋊C4C2×C22⋊D1118yes—
632C42—24no—
633C42—224no—
634C42—224no—
635C42—444no—
636C11#3498611yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—28no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—48no—
653C23—114no—
654C23—228no—
655C23—222no—
656C23—224no—
657C23—224no—
658C23—222no—
659C23—448no—
660C23—444no—
661C23—448no—
662C23—444no—
663C23#41×D1112yes—
664C23#41×D1112yes—
665C23C22×C22⋊D1114yes—
666C23C22×C22⋊D1112yes—
667C23C24×D1111yescharacteristic
668Q8—82no—
669D4—48no—
670D4—82no—
671D4—84no—
672D4—84no—
673D4—2232no—
674D4—4416no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—84no—
688C2×C4—114no—
689C2×C4—114no—
690C2×C4—228no—
691C2×C4—228no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—222no—
704C2×C4—4416no—
705C2×C4—4416no—
706C2×C4—444no—
707C2×C4C22×C22⋊D1114yes—
708C2×C4C22×C22⋊D1112yes—
709C2×C4C22×C22⋊D1112yes—
710C22—24no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—416no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—42no—
722C22—42no—
723C22—44no—
724C22—42no—
725C22—228no—
726C22—224no—
727C22—4416no—
728C22—444no—
729C22—442no—
730C22—442no—
731C22#1062335914yes—
732C22C2×#41×D1111yescharacteristic
733C22C2×#41×D1111yescharacteristic
734C22D11×H(5,𝔽2)12yes—
735C22#1062345512yes—
736C22C23×C22⋊D1111yescharacteristic
737C4—24no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—224no—
744C4—224no—
745C4—444no—
746C4—442no—
747C4—444no—
748C2—24no—
749C2—44no—
750C2—82no—
751C2—444no—
752C2C2×#1062335911yescharacteristic
753C2#1308202712yes—
754C2#1308224711yescharacteristic
755C2#1308225611yescharacteristic
756C2#1308246312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#538C2
hypercenterC2×#538D11
hypocenterC11#34986
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. C22×(C22⋊D11)⋊C4C2semidirect
2. #13076950C2semidirect
3. #13076942C2semidirect
4. #13076906C2semidirect
5. #13074423C2semidirect
6. #13074352C2semidirect
7. #13074330C2semidirect
8. #13072648C2semidirect
9. #13072549C2semidirect
10. #13072513C2semidirect
11. #13072495C2semidirect
12. #13071281C2semidirect
13. #13071214C2semidirect
14. C4×#66990C2semidirect
15. C2×C11×#538C2semidirect
20. C2×C11×#126C22semidirect
21. C2×C11×#124C22semidirect
22. C2×C11×#123C22semidirect
25. C2×C11×#121C22semidirect
31. C2×#66988C22semidirect
32. C2×C4×C22⋊D11C22semidirect
40. #10622844C22semidirect
41. #10622843C22semidirect
44. #10622836C22semidirect
45. #10622834C22semidirect
48. #10622833C22semidirect
51. #10622823C22semidirect
53. #10622607C22semidirect
54. #10622606C22semidirect
55. #10622605C22semidirect
56. #10622602C22semidirect
57. #10622591C22semidirect
58. #10622586C22semidirect
59. #10622586C22semidirect
60. #10622585C22semidirect
61. #10622574C22semidirect
64. #10622569C22semidirect
66. #10622564C22semidirect
67. #10622564C22semidirect
70. #10622559C22semidirect
71. #10622558C22semidirect
72. #10622557C22semidirect
74. #10622556C22semidirect
75. C4×(C2×D11)⋊C4C22semidirect
76. #10622546C22semidirect
113. C2×C11×C22⋊C4D4semidirect
259. C2×#538D11semidirect
351. C2×#126C2×D11semidirect
352. C2×#124C2×D11semidirect
355. C2×#123C2×D11semidirect
358. C2×#121C2×D11semidirect
508. C2×C22⋊C4C22⋊D11semidirect
636. C11#34986semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
#130769502
#130769422
#130769062
#130744232
#130743522
#130743302
#130726482
#130725492
#130725132
#130724952
#130712812
#130712142
C4×#669902
C2×C11×#5382
#3498611