Finite Group Databasebeta

← #14960595

Subgroups — #14960595

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2#13076900C211yesmaximal, characteristic, complemented
3#13076895C211yesmaximal, characteristic, complemented
4#13075145C214yesmaximal, complemented
5#13075121C214yesmaximal, complemented
6#13074862C214yesmaximal, complemented
7#13074847C214yesmaximal, complemented
8#13074431C211yesmaximal, characteristic, complemented
9#13074360C211yesmaximal, characteristic, complemented
10#13073502C212yesmaximal, complemented
11#13072933C212yesmaximal, complemented
12#13072013C212yesmaximal, complemented
13#13071991C212yesmaximal, complemented
14#13071230C211yesmaximal, characteristic, complemented
15C2×C11×#538C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C11×#538—28no—
19C2×C11×#126C2212yescomplemented
20C2×C11×#124C2212yescomplemented
21C2×C11×#123C2212yescomplemented
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2212yescomplemented
25C2×C11×#120C2212yes—
26C2×C4×D4×C11C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2212yes—
30C2×#66999C2212yescomplemented
31C2×#66992C2214yes—
32C2×#66991C2212yescomplemented
33C2×#66990C2212yes—
34C2×#66988C2212yes—
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C2×#66936—28no—
39C2×#66936C2214yes—
40C2×#66936C2214yes—
41#10622842C2212yescomplemented
42#10622836C2214yes—
43#10622835C2214yescomplemented
44#10622835C2212yescomplemented
45#10622833C2212yes—
46#10622833C2212yes—
47#10622833C2214yescomplemented
48#10622826C2214yescomplemented
49#10622825C2212yes—
50#10622825C2211yescharacteristic
51#10622825C2211yescharacteristic
52#10622825C2214yescomplemented
53#10622607C2214yescomplemented
54#10622602C2214yescomplemented
55#10622600C2212yescomplemented
56#10622600C2212yescomplemented
57#10622599C2214yescomplemented
58#10622597C2214yescomplemented
59#10622595C2212yescomplemented
60#10622593C2212yescomplemented
61#10622574C2214yescomplemented
62#10622572C2214yes—
63#10622571C2214yes—
64#10622569C2214yescomplemented
65#10622568C2212yes—
66#10622565C2214yescomplemented
67#10622563C2214yescomplemented
68#10622563C2214yescomplemented
69#10622562C2214yescomplemented
70#10622561C2214yescomplemented
71#10622559C2212yes—
72#10622559C2212yes—
73#10622556C2212yes—
74#10622555C2214yescomplemented
75#10622553C2214yescomplemented
76#10622541C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2312yes—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2312yes—
83C22×D4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—44no—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2314yes—
95C22×C4×D11—24no—
96C22×C4×D11—44no—
97C22×C4×D11C2312yes—
98C22×C4×D11C2312yes—
99C11×#126—28no—
100C11×#124—28no—
101C11×#123—28no—
102C11×C22⋊Q8—24no—
103C11×#121—24no—
104C11×#121—28no—
105C11×#120—28no—
106C4×D4×C11—28no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C22⋊C4D418yescomplemented
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊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⋊Dic11—24no—
121C2×C22⋊Dic11—44no—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129#66999—44no—
130#66992—48no—
131#66991—44no—
132#66990—44no—
133#66988—44no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×C4⋊Dic11—24no—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×C4⋊Dic11C2312yes—
143C2×C4⋊Dic11C2312yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150#66936—216no—
151#66936—216no—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161#36709—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—24no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—42no—
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—42no—
185C2×D4×C11—44no—
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×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2412yes—
199C2×C22⋊D11—28no—
200C2×C22⋊D11—28no—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—416no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—42no—
212C22×Dic11—42no—
213C22×Dic11—44no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11C2414yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2414yes—
220C22×Dic11C2412yes—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×C4×D11—416no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—22no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4C2×D418yes—
238C11×C22⋊C4C2×D418yes—
239C42×C11—24no—
240C22⋊Dic11—28no—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11—44no—
244C22⋊Dic11—44no—
245C22⋊Dic11—44no—
246C22⋊Dic11—44no—
247(C2×D11)⋊C4—28no—
248(C2×D11)⋊C4—28no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251C4⋊Dic11—28no—
252C4⋊Dic11—44no—
253C4⋊Dic11—42no—
254C4⋊Dic11—42no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259Dic11⋊C4—44no—
260C2×#538D1111yescharacteristic, complemented
261C22×#123—111no—
262#2848—111no—
263#2847—111no—
264#2695—114no—
265#2693—114no—
266#2672—114no—
267#2671—114no—
268#2627—111no—
269#2618—111no—
270#2534—112no—
271#2487—112no—
272#2412—112no—
273#2410—112no—
274#2315—111no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—24no—
279C23×C11—22no—
280C23×C11—24no—
281C23×C11—28no—
282C23×C11—22no—
283C23×C11—24no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—24no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—84no—
290C23×C11—84no—
291C23×C11C22×D414yes—
292C23×C11C22×D412yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C112−1+412yes—
295C23×C11C2511yescharacteristic
296C22×D11—28no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—48no—
304C22×D11—48no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11H(5,𝔽2)14yes—
308Q8×C11—82no—
309D4×C11—48no—
310D4×C11—82no—
311D4×C11—84no—
312D4×C11—84no—
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—24no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—44no—
324C2×C4×C11—44no—
325C2×C4×C11—84no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D414yes—
329C22⋊D11—416no—
330C22⋊D11—88no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—44no—
346C2×Dic11—44no—
347C2×Dic11—44no—
348C2×Dic11—88no—
349C4×D11—48no—
350C4×D11—48no—
351C23×D4—111no—
352C24×C4—111no—
353#538—28no—
354C2×#126C2×D1112yescomplemented
355C2×#124C2×D1112yescomplemented
356C2×#123—112no—
357C2×#123—114no—
358C2×#123—114no—
359C2×#123—228no—
360C2×#123C2×D1112yescomplemented
361C2×C22⋊Q8—112no—
362C2×C22⋊Q8C2×D1111yescharacteristic
363C2×#121—112no—
364C2×#121—114no—
365C2×#121C2×D1111yescharacteristic
366C2×#121C2×D1112yescomplemented
367C2×#120—112no—
368C2×#120C2×D1112yes—
369C2×C4×D4C2×D1112yes—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—112no—
375C22×C22⋊C4C2×D1111yescharacteristic
376#400—112no—
377#400—114no—
378#399—114no—
379#398—112no—
380#398—114no—
381#397—114no—
382#396—114no—
383#396—114no—
384#395—112no—
385#394—112no—
386#394—114no—
387#394—114no—
388#394—114no—
389#392—114no—
390#389—114no—
391#388—114no—
392#386—112no—
393#386—112no—
394#386—114no—
395#386—114no—
396#386—114no—
397#386—114no—
398#385—114no—
399#385—114no—
400#385—114no—
401#385—112no—
402#385—112no—
403#381—112no—
404#380—111no—
405#380—111no—
406#380—112no—
407#380—114no—
408#380—112no—
409#380—112no—
410#380—114no—
411#379—112no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—44no—
420C22×C11—44no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—44no—
425C22×C11—44no—
426C22×C11—88no—
427C22×C11#53714yes—
428C22×C11C23×D411yescharacteristic
429C22×C11C2×H(5,𝔽2)11yescharacteristic
430C22×C11C2×H(5,𝔽2)12yes—
431C22×C11C2×2−1+411yescharacteristic
432C22×C11#58512yes—
433C2×D11—24no—
434C2×D11—24no—
435C2×D11—24no—
436C2×D11—416no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—24no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447Dic11—42no—
448Dic11—42no—
449Dic11—42no—
450Dic11—44no—
451Dic11—44no—
452C25—111no—
453C25C22×D1111yescharacteristic
454C22×Q8C22×D1111yescharacteristic
455C22×D4—114no—
456C22×D4—114no—
457C22×D4—224no—
458C22×D4—444no—
459C22×D4C22×D1112yes—
460C22×D4C22×D1112yes—
461C22×D4C22×D1112yes—
462C22×D4C22×D1111yescharacteristic
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—114no—
467C23×C4—112no—
468C23×C4—112no—
469C23×C4—224no—
470C23×C4—444no—
471C23×C4C22×D1112yes—
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474#126—28no—
475#124—28no—
476#123—28no—
477#123—2216no—
478#123—2216no—
479#123—444no—
480C22⋊Q8—24no—
481C22⋊Q8—444no—
482#121—24no—
483#121—28no—
484#121—448no—
485#121—444no—
486#120—28no—
487#120—444no—
488C4×D4—28no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4C22×D1112yes—
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1112yes—
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C22⋊C4—112no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
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—224no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—444no—
518C2×C22⋊C4C22⋊D1118yescomplemented
519C2×C22⋊C4C22×D1112yes—
520C2×C22⋊C4C22×D1112yes—
521C2×C22⋊C4C22×D1112yes—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1112yes—
525C2×C22⋊C4C22×D1112yes—
526C2×C42C22×D1112yes—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—112no—
531#95—112no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536C2×C11—24no—
537C2×C11—44no—
538C2×C11—82no—
539C2×C11C2×#53711yescharacteristic
540C2×C11#348411yescharacteristic
541C2×C11#348511yescharacteristic
542C2×C11#353412yes—
543C2×C11#353512yes—
544D11—44no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24—112no—
550C24—224no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—442no—
555C24C2×C22⋊D1114yes—
556C24C23×D1112yes—
557C24C23×D1112yes—
558C24C23×D1111yescharacteristic
559C2×Q8—22no—
560C2×Q8—42no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—228no—
571C2×D4—228no—
572C2×D4—228no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—4416no—
577C22×C4—24no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—114no—
582C22×C4—114no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—112no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—224no—
594C22×C4—224no—
595C22×C4—442no—
596C22×C4—442no—
597C22×C4—4416no—
598C22×C4—442no—
599C22×C4—442no—
600C22×C4—444no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4C2×C22⋊D1114yes—
604C22×C4C2×C22⋊D1114yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1112yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1111yescharacteristic
610C22×C4C23×D1111yescharacteristic
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—228no—
618C4⋊C4—444no—
619C4⋊C4—442no—
620C4⋊C4—444no—
621C4⋊C4—442no—
622C4⋊C4—444no—
623C4⋊C4—444no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—228no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—228no—
633C22⋊C4—228no—
634C22⋊C4—444no—
635C22⋊C4—444no—
636C22⋊C4—444no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C22⋊C4C2×C22⋊D1118yes—
641C22⋊C4C2×C22⋊D1118yes—
642C42—24no—
643C11#3670911yescharacteristic, complemented, Sylow
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—28no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—84no—
659C23—84no—
660C23—114no—
661C23—228no—
662C23—222no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—448no—
669C23—448no—
670C23—444no—
671C23—444no—
672C23#6704212yes—
673C23#6704312yes—
674C23C22×C22⋊D1114yes—
675C23C22×C22⋊D1112yes—
676C23C24×D1111yescharacteristic
677Q8—82no—
678D4—48no—
679D4—82no—
680D4—84no—
681D4—84no—
682D4—4416no—
683D4—888no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
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—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—448no—
712C2×C4—448no—
713C2×C4—444no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—888no—
717C2×C4C22×C22⋊D1114yes—
718C2×C4C22×C22⋊D1112yes—
719C2×C4C22×C22⋊D1112yes—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—44no—
728C22—44no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—44no—
733C22—44no—
734C22—88no—
735C22—224no—
736C22—224no—
737C22—224no—
738C22—4416no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22#1062336414yes—
744C22C2×#6704211yescharacteristic
745C22C2×#6704311yescharacteristic
746C22D11×H(5,𝔽2)12yes—
747C22#1062345512yes—
748C22C23×C22⋊D1111yescharacteristic
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—442no—
756C4—442no—
757C4—442no—
758C4—444no—
759C4—444no—
760C2—24no—
761C2—44no—
762C2—82no—
763C2—444no—
764C2C2×#1062336411yescharacteristic
765C2#1308224711yescharacteristic
766C2#1308225611yescharacteristic
767C2#1308280712yes—
768C2#1308281412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#538C2
hypercenterC2×#538D11
hypocenterC11#36709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. #13076900C2semidirect
3. #13076895C2semidirect
4. #13075145C2semidirect
5. #13075121C2semidirect
6. #13074862C2semidirect
7. #13074847C2semidirect
8. #13074431C2semidirect
9. #13074360C2semidirect
10. #13073502C2semidirect
11. #13072933C2semidirect
12. #13072013C2semidirect
13. #13071991C2semidirect
14. #13071230C2semidirect
15. C2×C11×#538C2semidirect
19. C2×C11×#126C22semidirect
20. C2×C11×#124C22semidirect
21. C2×C11×#123C22semidirect
24. C2×C11×#121C22semidirect
30. C2×#66999C22semidirect
32. C2×#66991C22semidirect
41. #10622842C22semidirect
43. #10622835C22semidirect
44. #10622835C22semidirect
47. #10622833C22semidirect
48. #10622826C22semidirect
52. #10622825C22semidirect
53. #10622607C22semidirect
54. #10622602C22semidirect
55. #10622600C22semidirect
56. #10622600C22semidirect
57. #10622599C22semidirect
58. #10622597C22semidirect
59. #10622595C22semidirect
60. #10622593C22semidirect
61. #10622574C22semidirect
64. #10622569C22semidirect
66. #10622565C22semidirect
67. #10622563C22semidirect
68. #10622563C22semidirect
69. #10622562C22semidirect
70. #10622561C22semidirect
74. #10622555C22semidirect
75. #10622553C22semidirect
76. #10622541C22semidirect
111. C2×C11×C22⋊C4D4semidirect
260. C2×#538D11semidirect
354. C2×#126C2×D11semidirect
355. C2×#124C2×D11semidirect
360. C2×#123C2×D11semidirect
366. C2×#121C2×D11semidirect
518. C2×C22⋊C4C22⋊D11semidirect
643. C11#36709semidirect

Maximal subgroups

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

subgroupindex
C22×#669362
#130769002
#130768952
#130751452
#130751212
#130748622
#130748472
#130744312
#130743602
#130735022
#130729332
#130720132
#130719912
#130712302
C2×C11×#5382
#3670911