Finite Group Databasebeta

← #14960803

Subgroups — #14960803

Order 2816.

2602 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2#13076900C211yesmaximal, characteristic, complemented
3#13076895C211yesmaximal, characteristic, complemented
4#13075313C214yesmaximal, complemented
5#13075283C214yesmaximal, complemented
6#13074981C214yesmaximal, complemented
7#13074971C214yesmaximal, complemented
8#13074423C211yesmaximal, characteristic, complemented
9#13074352C211yesmaximal, characteristic, complemented
10#13073959C212yesmaximal, complemented
11#13072002C212yesmaximal, complemented
12#13072002C212yesmaximal, complemented
13#13071972C212yesmaximal, complemented
14#13071234C211yesmaximal, characteristic, complemented
15C2×C11×#539C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C11×#539—28no—
19C2×C11×#126C2212yescomplemented
20C2×C11×#125C2212yescomplemented
21C2×C11×#123C2212yes—
22C2×C11×#123C2212yescomplemented
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2212yescomplemented
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28C2×#66999C2212yescomplemented
29C2×#66991C2212yescomplemented
30C2×#66990C2212yes—
31C2×#66990C2212yes—
32C2×#66983C2214yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C2×#66979C2212yes—
37C22×Dic11⋊C4C2211yescharacteristic
38C2×#66947—28no—
39C2×#66947C2214yes—
40C2×#66947C2214yes—
41#10622844C2212yescomplemented
42#10622836C2212yescomplemented
43#10622833C2212yes—
44#10622833C2212yes—
45#10622825C2212yes—
46#10622825C2211yescharacteristic
47#10622825C2211yescharacteristic
48#10622823C2214yescomplemented
49#10622607C2214yescomplemented
50#10622607C2214yescomplemented
51#10622607C2214yescomplemented
52#10622606C2212yescomplemented
53#10622605C2212yescomplemented
54#10622604C2214yes—
55#10622603C2214yescomplemented
56#10622603C2214yescomplemented
57#10622602C2214yescomplemented
58#10622600C2212yescomplemented
59#10622600C2212yescomplemented
60#10622598C2214yescomplemented
61#10622598C2214yescomplemented
62#10622597C2214yescomplemented
63#10622574C2214yescomplemented
64#10622574C2214yescomplemented
65#10622574C2214yescomplemented
66#10622573C2214yes—
67#10622570C2214yescomplemented
68#10622570C2214yescomplemented
69#10622569C2214yescomplemented
70#10622568C2212yes—
71#10622568C2212yes—
72#10622561C2214yescomplemented
73#10622559C2212yes—
74#10622559C2212yes—
75#10622552C2214yes—
76#10622546C2214yescomplemented
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2312yes—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×D44—24no—
91C22×D44—44no—
92C22×D44C2314yes—
93C22×C4×D11—24no—
94C22×C4×D11—44no—
95C22×C4×D11C2312yes—
96C22×C4×D11C2312yes—
97C11×#126—28no—
98C11×#125—28no—
99C11×#123—28no—
100C11×#123—28no—
101C11×C22⋊Q8—24no—
102C11×C22⋊Q8—28no—
103C11×#121—24no—
104C4×D4×C11—28no—
105C2×C11×C4⋊C4D418yescomplemented
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C42×C11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124#66999—44no—
125#66991—44no—
126#66990—44no—
127#66990—44no—
128#66983—48no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142#66979—44no—
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2312yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×C4×Dic11C2314yes—
152#66947—216no—
153#66947—216no—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161#36722—111nomaximal, Sylow
162C24×C11C2412yes—
163C24×C11C2411yescharacteristic
164C23×D11—22no—
165C23×D11—24no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11C2412yes—
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—22no—
182C2×D4×C11—42no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—24no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—44no—
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2×D414yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2412yes—
199C2×C22⋊D11—28no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—42no—
208C22×Dic11—42no—
209C22×Dic11C2414yes—
210C22×Dic11C2414yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C2×D44—28no—
214C2×D44—28no—
215C2×D44—44no—
216C2×D44—416no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—416no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4C2×D418yes—
231C11×C4⋊C4C2×D418yes—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C42×C11—24no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11—44no—
241C22⋊Dic11—44no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252C4⋊Dic11—44no—
253C4⋊Dic11—44no—
254C4⋊Dic11—42no—
255C4⋊Dic11—42no—
256Dic11⋊C4—28no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—44no—
260C2×#539D1111yescharacteristic, complemented
261C22×#123—111no—
262#2848—111no—
263#2847—111no—
264#2707—114no—
265#2705—114no—
266#2682—114no—
267#2681—114no—
268#2626—111no—
269#2617—111no—
270#2579—112no—
271#2411—112no—
272#2411—112no—
273#2408—112no—
274#2316—111no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—24no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—24no—
282C23×C11C22×D412yes—
283C23×C11H(5,𝔽2)12yes—
284C23×C112−1+412yes—
285C23×C11C2511yescharacteristic
286C22×D11—28no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—24no—
296C22×D11—22no—
297C22×D11—24no—
298C22×D11—48no—
299C22×D11—48no—
300C22×D11—44no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—84no—
306C22×D11—84no—
307C22×D11H(5,𝔽2)14yes—
308Q8×C11—82no—
309D4×C11—48no—
310D4×C11—82no—
311C2×C4×C11—28no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11—84no—
327C2×C4×C11C22×D414yes—
328C2×C4×C11C22×D414yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C22⋊D11—88no—
332C22⋊D11—88no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—44no—
345C2×Dic11—44no—
346D44—416no—
347C4×D11—48no—
348C4×D11—48no—
349C23×D4—111no—
350C24×C4—111no—
351#539—28no—
352C2×#126C2×D1112yescomplemented
353C2×#125C2×D1112yescomplemented
354C2×#123—114no—
355C2×#123—114no—
356C2×#123—228no—
357C2×#123C2×D1112yes—
358C2×#123C2×D1112yescomplemented
359C2×C22⋊Q8—112no—
360C2×C22⋊Q8C2×D1111yescharacteristic
361C2×C22⋊Q8C2×D1112yescomplemented
362C2×#121—112no—
363C2×#121—114no—
364C2×#121C2×D1111yescharacteristic
365C2×#120—112no—
366C2×#120—112no—
367C2×C4×D4C2×D1112yes—
368C2×#117—112no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374#399—112no—
375#398—114no—
376#397—112no—
377#396—114no—
378#396—114no—
379#396—114no—
380#396—114no—
381#394—114no—
382#394—114no—
383#394—114no—
384#394—114no—
385#393—112no—
386#392—112no—
387#392—114no—
388#390—114no—
389#390—114no—
390#390—114no—
391#389—114no—
392#389—114no—
393#388—114no—
394#388—114no—
395#387—114no—
396#386—112no—
397#386—112no—
398#386—114no—
399#385—114no—
400#385—114no—
401#385—112no—
402#385—112no—
403#380—112no—
404#380—111no—
405#380—111no—
406#380—112no—
407#380—112no—
408#379—112no—
409#379—112no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—44no—
418C22×C11—44no—
419C22×C11#53714yes—
420C22×C11C23×D411yescharacteristic
421C22×C11C2×H(5,𝔽2)11yescharacteristic
422C22×C11C2×H(5,𝔽2)12yes—
423C22×C11C2×2−1+411yescharacteristic
424C22×C11#58512yes—
425C2×D11—24no—
426C2×D11—24no—
427C2×D11—24no—
428C2×D11—416no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—44no—
437C2×D11—44no—
438C2×D11—88no—
439C4×C11—24no—
440C4×C11—24no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446Dic11—42no—
447Dic11—42no—
448Dic11—44no—
449Dic11—44no—
450C25—111no—
451C25—111no—
452C22×Q8C22×D1111yescharacteristic
453C22×D4—114no—
454C22×D4—114no—
455C22×D4—114no—
456C22×D4—224no—
457C22×D4—444no—
458C22×D4C22×D1112yes—
459C22×D4C22×D1111yescharacteristic
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—112no—
463C23×C4—112no—
464C23×C4—224no—
465C23×C4—444no—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1112yes—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470#126—28no—
471#125—28no—
472#123—28no—
473#123—28no—
474#123—2216no—
475#123—2216no—
476C22⋊Q8—24no—
477C22⋊Q8—28no—
478C22⋊Q8—444no—
479#121—24no—
480#121—448no—
481#121—444no—
482#120—444no—
483#120—444no—
484C4×D4—28no—
485#117—444no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—224no—
494C2×C4⋊C4C22⋊D1118yescomplemented
495C2×C4⋊C4C22×D1112yes—
496C2×C4⋊C4C22×D1111yescharacteristic
497C2×C4⋊C4C22×D1112yes—
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1112yes—
500C2×C4⋊C4C22×D1112yes—
501C2×C4⋊C4C22×D1112yes—
502C2×C4⋊C4C22×D1112yes—
503C2×C22⋊C4—112no—
504C2×C22⋊C4—112no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4C22×D1112yes—
521C2×C22⋊C4C22×D1112yes—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1112yes—
525C2×C42—114no—
526C2×C42C22×D1112yes—
527#95—114no—
528#95—112no—
529#95—114no—
530#95—114no—
531#95—112no—
532#95—114no—
533#95—114no—
534C2×C11—24no—
535C2×C11—82no—
536C2×C11C2×#53711yescharacteristic
537C2×C11#348411yescharacteristic
538C2×C11#348711yescharacteristic
539C2×C11#353412yes—
540C2×C11#353512yes—
541D11—44no—
542D11—82no—
543C24—112no—
544C24—112no—
545C24—224no—
546C24—222no—
547C24—222no—
548C24—222no—
549C24—222no—
550C24—222no—
551C24—222no—
552C24—442no—
553C24—442no—
554C24—442no—
555C24C23×D1112yes—
556C24C23×D1111yescharacteristic
557C2×Q8—22no—
558C2×Q8—42no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—42no—
564C2×D4—228no—
565C2×D4—228no—
566C2×D4—228no—
567C2×D4—444no—
568C2×D4—4416no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—444no—
573C2×D4—444no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—114no—
581C22×C4—114no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—224no—
589C22×C4—224no—
590C22×C4—442no—
591C22×C4—442no—
592C22×C4—4416no—
593C22×C4—442no—
594C22×C4—442no—
595C22×C4C2×C22⋊D1114yes—
596C22×C4C2×C22⋊D1114yes—
597C22×C4C2×C22⋊D1114yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1111yescharacteristic
603C22×C4C23×D1111yescharacteristic
604C22×C4C23×D1112yes—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—24no—
611C4⋊C4—228no—
612C4⋊C4—444no—
613C4⋊C4—444no—
614C4⋊C4—442no—
615C4⋊C4—444no—
616C4⋊C4—442no—
617C4⋊C4—444no—
618C4⋊C4C2×C22⋊D1118yes—
619C4⋊C4C2×C22⋊D1118yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—228no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—228no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—228no—
632C22⋊C4—444no—
633C22⋊C4—444no—
634C22⋊C4—444no—
635C22⋊C4—444no—
636C22⋊C4—444no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C42—24no—
640C42—444no—
641C11#3672211yescharacteristic, complemented, Sylow
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—114no—
650C23—228no—
651C23—222no—
652C23—222no—
653C23—222no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23—224no—
660C23—224no—
661C23—222no—
662C23—448no—
663C23—448no—
664C23—444no—
665C23—444no—
666C23—444no—
667C23—444no—
668C23—444no—
669C23—884no—
670C23—884no—
671C23#6704212yes—
672C23#6704312yes—
673C23C22×C22⋊D1112yes—
674C23C24×D1111yescharacteristic
675Q8—82no—
676D4—48no—
677D4—82no—
678D4—4416no—
679D4—888no—
680D4—888no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—84no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—448no—
709C2×C4—448no—
710C2×C4—444no—
711C2×C4—444no—
712C2×C4C22×C22⋊D1114yes—
713C2×C4C22×C22⋊D1114yes—
714C2×C4C22×C22⋊D1112yes—
715C2×C4C22×C22⋊D1112yes—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—44no—
724C22—44no—
725C22—224no—
726C22—224no—
727C22—224no—
728C22—4416no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—444no—
737C22—444no—
738C22—888no—
739C22#1062336414yes—
740C22C2×#6704211yescharacteristic
741C22C2×#6704311yescharacteristic
742C22D11×H(5,𝔽2)12yes—
743C22#1062345712yes—
744C22C23×C22⋊D1111yescharacteristic
745C4—24no—
746C4—24no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—442no—
753C4—442no—
754C4—444no—
755C4—444no—
756C2—24no—
757C2—82no—
758C2—444no—
759C2—882no—
760C2C2×#1062336411yescharacteristic
761C2#1308224711yescharacteristic
762C2#1308227111yescharacteristic
763C2#1308281112yes—
764C2#1308282212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#539C2
hypercenterC2×#539D11
hypocenterC11#36722
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. #13076900C2semidirect
3. #13076895C2semidirect
4. #13075313C2semidirect
5. #13075283C2semidirect
6. #13074981C2semidirect
7. #13074971C2semidirect
8. #13074423C2semidirect
9. #13074352C2semidirect
10. #13073959C2semidirect
11. #13072002C2semidirect
12. #13072002C2semidirect
13. #13071972C2semidirect
14. #13071234C2semidirect
15. C2×C11×#539C2semidirect
19. C2×C11×#126C22semidirect
20. C2×C11×#125C22semidirect
22. C2×C11×#123C22semidirect
24. C2×C11×C22⋊Q8C22semidirect
28. C2×#66999C22semidirect
29. C2×#66991C22semidirect
41. #10622844C22semidirect
42. #10622836C22semidirect
48. #10622823C22semidirect
49. #10622607C22semidirect
50. #10622607C22semidirect
51. #10622607C22semidirect
52. #10622606C22semidirect
53. #10622605C22semidirect
55. #10622603C22semidirect
56. #10622603C22semidirect
57. #10622602C22semidirect
58. #10622600C22semidirect
59. #10622600C22semidirect
60. #10622598C22semidirect
61. #10622598C22semidirect
62. #10622597C22semidirect
63. #10622574C22semidirect
64. #10622574C22semidirect
65. #10622574C22semidirect
67. #10622570C22semidirect
68. #10622570C22semidirect
69. #10622569C22semidirect
72. #10622561C22semidirect
76. #10622546C22semidirect
105. C2×C11×C4⋊C4D4semidirect
260. C2×#539D11semidirect
352. C2×#126C2×D11semidirect
353. C2×#125C2×D11semidirect
358. C2×#123C2×D11semidirect
361. C2×C22⋊Q8C2×D11semidirect
494. C2×C4⋊C4C22⋊D11semidirect
641. C11#36722semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
#130769002
#130768952
#130753132
#130752832
#130749812
#130749712
#130744232
#130743522
#130739592
#130720022
#130719722
#130712342
C2×C11×#5392
#3672211