Finite Group Databasebeta

← #14960600

Subgroups — #14960600

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
1C2×#10623148C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3#13076904C211yesmaximal, characteristic, complemented
4#13076895C211yesmaximal, characteristic, complemented
5#13075153C214yesmaximal, complemented
6#13075128C214yesmaximal, complemented
7#13074874C214yesmaximal, complemented
8#13074851C214yesmaximal, complemented
9#13074429C211yesmaximal, characteristic, complemented
10#13073505C212yesmaximal, complemented
11#13072930C212yesmaximal, complemented
12#13072008C212yesmaximal, complemented
13#13071993C212yesmaximal, complemented
14#13071229C211yesmaximal, characteristic, complemented
15C11×#2618C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#123C2212yes—
19C2×C11×#121C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66992C2212yescomplemented
22C2×#66991C2212yescomplemented
23C2×#66990C2212yes—
24C2×#66990C2212yes—
25C2×D4×Dic11C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31#10623148—28no—
32C2×#66951C2212yescomplemented
33C2×#66950C2212yescomplemented
34C2×#66947—28no—
35C2×#66947C2214yes—
36C2×#66947C2214yes—
37C2×#66939C2212yescomplemented
38C2×#66938C2212yescomplemented
39C2×#66937C2214yes—
40C2×C22⋊C4×D11C2212yes—
41C11×#398C2212yescomplemented
42C11×#396C2214yescomplemented
43C11×#394C2212yescomplemented
44C11×#386C2212yes—
45C11×#380C2211yescharacteristic
46#10622833C2212yes—
47#10622825C2211yescharacteristic
48#10622824C2212yes—
49#10622823C2212yes—
50#10622607C2214yescomplemented
51#10622606C2214yescomplemented
52#10622603C2214yescomplemented
53#10622602C2214yescomplemented
54#10622600C2214yescomplemented
55#10622600C2212yescomplemented
56#10622600C2212yescomplemented
57#10622599C2212yescomplemented
58#10622597C2214yescomplemented
59#10622592C2212yescomplemented
60#10622574C2214yescomplemented
61#10622573C2214yes—
62#10622572C2214yescomplemented
63#10622571C2214yescomplemented
64#10622569C2214yescomplemented
65#10622569C2214yescomplemented
66#10622568C2212yes—
67#10622563C2212yes—
68#10622562C2214yescomplemented
69#10622555C2212yes—
70#10622555C2214yescomplemented
71#10622285C2214yes—
72#10622281C2214yescomplemented
73#10622281C2214yescomplemented
74#10622278C2214yes—
75#10622273C2214yescomplemented
76#10622260C2214yescomplemented
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×D4×C11C2312yes—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11C2312yes—
85C22×C22⋊D11C2314yes—
86C22×C22⋊D11C2312yes—
87C23×Dic11C2312yes—
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—
97C22×C4×D11C2314yes—
98C22×Dic22C2311yescharacteristic
99C11×#123—44no—
100C11×#121—24no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2314yes—
115#66992—28no—
116#66991—44no—
117#66990—28no—
118#66990—44no—
119D4×Dic11—28no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4D418yescomplemented
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2312yes—
137#66977—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11C2312yes—
144#66951—28no—
145#66950—44no—
146#66947—216no—
147#66947—216no—
148#66939—28no—
149#66938—28no—
150#66937—48no—
151C22⋊C4×D11—44no—
152C11×#95C2314yes—
153C11×#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161#36709—111nomaximal, Sylow
162C24×C11C2412yes—
163C24×C11C2411yescharacteristic
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—24no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11C2×D414yes—
174C23×D11C2412yes—
175C23×D11C2412yes—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—22no—
180C2×D4×C11—42no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2414yes—
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C2×C22⋊D11—24no—
195C2×C22⋊D11—24no—
196C2×C22⋊D11—28no—
197C2×C22⋊D11—44no—
198C2×C22⋊D11—44no—
199C2×C22⋊D11—44no—
200C2×C22⋊D11—44no—
201C22×Dic11—24no—
202C22×Dic11—22no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11—44no—
206C22×Dic11C2×D414yes—
207C22×Dic11C2414yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C2×D44—28no—
213C2×D44—28no—
214C2×D44—44no—
215C2×D44—416no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11—44no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—416no—
226C2×Dic22—22no—
227C2×Dic22—42no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—42no—
232C11×C4⋊C4—44no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—44no—
236C11×C22⋊C4—44no—
237C22⋊Dic11—24no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11—44no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—28no—
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4C2×D418yes—
250(C2×D11)⋊C4C2×D418yes—
251C4⋊Dic11—24no—
252C4⋊Dic11—22no—
253C4⋊Dic11—44no—
254C4⋊Dic11—42no—
255Dic11⋊C4—28no—
256Dic11⋊C4—24no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—24no—
260C2×#538—111no—
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#2618D1111yescharacteristic, complemented
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—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—24no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—24no—
296C22×D11—22no—
297C22×D11—28no—
298C22×D11—44no—
299C22×D11—44no—
300C22×D11—48no—
301C22×D11—48no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—84no—
305C22×D11—84no—
306C22×D11C22×D414yes—
307C22×D11H(5,𝔽2)14yes—
308D4×C11—48no—
309D4×C11—82no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—44no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C22⋊D11—84no—
329C22⋊D11—84no—
330C22⋊D11—88no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—44no—
343C2×Dic11—44no—
344C2×Dic11—84no—
345C2×Dic11C22×D414yes—
346D44—416no—
347C4×D11—48no—
348C4×D11—48no—
349C4×D11—88no—
350Dic22—82no—
351C23×D4—111no—
352C24×C4—111no—
353#538—228no—
354C2×#126—112no—
355C2×#124—112no—
356C2×#123—114no—
357C2×#123—114no—
358C2×#123—112no—
359C2×#123—228no—
360C2×#123C2×D1112yes—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8—112no—
363C2×#121—112no—
364C2×#121—112no—
365C2×#121—114no—
366C2×#121C2×D1111yescharacteristic
367C2×#120—112no—
368C2×#120—112no—
369C2×C4×D4—112no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4C2×D1111yescharacteristic
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—112no—
376#400—112no—
377#400—114no—
378#399—114no—
379#398—114no—
380#398C2×D1112yescomplemented
381#397—114no—
382#396—114no—
383#396C2×D1114yescomplemented
384#395—112no—
385#394—114no—
386#394—114no—
387#394—114no—
388#394C2×D1112yescomplemented
389#392—114no—
390#389—114no—
391#388—114no—
392#386—112no—
393#386—114no—
394#386—114no—
395#386—114no—
396#386—114no—
397#386C2×D1112yes—
398#385—112no—
399#385—114no—
400#385—112no—
401#385—114no—
402#385—114no—
403#381—112no—
404#380—111no—
405#380—112no—
406#380—112no—
407#380—114no—
408#380—112no—
409#380—114no—
410#380C2×D1111yescharacteristic
411#379—112no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—44no—
420C22×C11—44no—
421C22×C11#53714yes—
422C22×C11C23×D411yescharacteristic
423C22×C11C2×H(5,𝔽2)11yescharacteristic
424C22×C11C2×H(5,𝔽2)12yes—
425C22×C11C2×2−1+411yescharacteristic
426C22×C11#58512yes—
427C2×D11—24no—
428C2×D11—24no—
429C2×D11—24no—
430C2×D11—24no—
431C2×D11—24no—
432C2×D11—24no—
433C2×D11—416no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—44no—
438C2×D11—42no—
439C2×D11—44no—
440C2×D11—88no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—44no—
447Dic11—24no—
448Dic11—42no—
449Dic11—42no—
450Dic11—42no—
451Dic11—44no—
452C25—111no—
453C25—111no—
454C22×Q8—111no—
455C22×D4—112no—
456C22×D4—114no—
457C22×D4—112no—
458C22×D4—114no—
459C22×D4—224no—
460C22×D4—444no—
461C22×D4C22×D1112yes—
462C22×D4C22×D1111yescharacteristic
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—112no—
466C23×C4—112no—
467C23×C4—112no—
468C23×C4—114no—
469C23×C4—224no—
470C23×C4—444no—
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474#126—228no—
475#124—228no—
476#123—44no—
477#123—228no—
478#123—2216no—
479#123—2216no—
480C22⋊Q8—224no—
481C22⋊Q8—444no—
482#121—24no—
483#121—228no—
484#121—448no—
485#121—444no—
486#120—228no—
487#120—444no—
488C4×D4—228no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4C22×D1112yes—
500C2×C4⋊C4C22×D1112yes—
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1112yes—
503C2×C4⋊C4C22×D1114yes—
504C2×C22⋊C4—118no—
505C2×C22⋊C4—112no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—112no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—444no—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C22⋊C4C22×D1114yes—
526C2×C42—112no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—112no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95C22×D1112yes—
535#95C22×D1114yes—
536C2×C11—24no—
537C2×C11—82no—
538C2×C11C2×#53711yescharacteristic
539C2×C11#348411yescharacteristic
540C2×C11#348511yescharacteristic
541C2×C11#353412yes—
542C2×C11#353512yes—
543D11—44no—
544D11—44no—
545C24—112no—
546C24—112no—
547C24—114no—
548C24—224no—
549C24—222no—
550C24—222no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—442no—
555C24—442no—
556C24—442no—
557C24C23×D1112yes—
558C24C23×D1111yescharacteristic
559C2×Q8—222no—
560C2×Q8—442no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—22no—
565C2×D4—42no—
566C2×D4—228no—
567C2×D4—228no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—228no—
571C2×D4—444no—
572C2×D4—4416no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—444no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—112no—
584C22×C4—114no—
585C22×C4—112no—
586C22×C4—114no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—224no—
592C22×C4—222no—
593C22×C4—224no—
594C22×C4—224no—
595C22×C4—442no—
596C22×C4—442no—
597C22×C4—444no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—4416no—
601C22×C4—442no—
602C22×C4—442no—
603C22×C4—444no—
604C22×C4D4×D1114yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1114yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1111yescharacteristic
610C22×C4C23×D1111yescharacteristic
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—42no—
615C4⋊C4—44no—
616C4⋊C4—228no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—222no—
620C4⋊C4—444no—
621C4⋊C4—442no—
622C4⋊C4—444no—
623C4⋊C4—444no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—118no—
629C22⋊C4—118no—
630C22⋊C4—228no—
631C22⋊C4—228no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—228no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C42—224no—
643C11#3670911yescharacteristic, complemented, Sylow
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—114no—
652C23—114no—
653C23—228no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—224no—
661C23—222no—
662C23—224no—
663C23—222no—
664C23—228no—
665C23—444no—
666C23—444no—
667C23—448no—
668C23—448no—
669C23—444no—
670C23—444no—
671C23—884no—
672C23—884no—
673C23C2×D4×D1112yes—
674C23#6703712yes—
675C23#6704312yes—
676C23C24×D1111yescharacteristic
677Q8—882no—
678D4—48no—
679D4—82no—
680D4—4416no—
681D4—884no—
682D4—884no—
683D4—888no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—114no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—448no—
713C2×C4—448no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—888no—
717C2×C4—884no—
718C2×C4C2×D4×D1112yes—
719C2×C4C2×D4×D1112yes—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—44no—
729C22—224no—
730C22—224no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—224no—
735C22—4416no—
736C22—442no—
737C22—442no—
738C22—444no—
739C22—442no—
740C22—442no—
741C22—444no—
742C22—888no—
743C22#1062313914yes—
744C22C22×D4×D1111yescharacteristic
745C22C2×#6703711yescharacteristic
746C22C2×#6704311yescharacteristic
747C22D11×H(5,𝔽2)12yes—
748C22#1062345712yes—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—44no—
755C4—224no—
756C4—442no—
757C4—442no—
758C4—442no—
759C4—444no—
760C2—24no—
761C2—82no—
762C2—444no—
763C2—444no—
764C2C2×#1062313911yescharacteristic
765C2#1308224811yescharacteristic
766C2#1308225911yescharacteristic
767C2#1308279512yes—
768C2#1308282212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2618C2
hypercenter#2618D11
hypocenterC11#36709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. C2×#10623148C2semidirect
2. C22×#66947C2semidirect
3. #13076904C2semidirect
4. #13076895C2semidirect
5. #13075153C2semidirect
6. #13075128C2semidirect
7. #13074874C2semidirect
8. #13074851C2semidirect
9. #13074429C2semidirect
10. #13073505C2semidirect
11. #13072930C2semidirect
12. #13072008C2semidirect
13. #13071993C2semidirect
14. #13071229C2semidirect
15. C11×#2618C2semidirect
21. C2×#66992C22semidirect
22. C2×#66991C22semidirect
32. C2×#66951C22semidirect
33. C2×#66950C22semidirect
37. C2×#66939C22semidirect
38. C2×#66938C22semidirect
41. C11×#398C22semidirect
42. C11×#396C22semidirect
43. C11×#394C22semidirect
50. #10622607C22semidirect
51. #10622606C22semidirect
52. #10622603C22semidirect
53. #10622602C22semidirect
54. #10622600C22semidirect
55. #10622600C22semidirect
56. #10622600C22semidirect
57. #10622599C22semidirect
58. #10622597C22semidirect
59. #10622592C22semidirect
60. #10622574C22semidirect
62. #10622572C22semidirect
63. #10622571C22semidirect
64. #10622569C22semidirect
65. #10622569C22semidirect
68. #10622562C22semidirect
70. #10622555C22semidirect
72. #10622281C22semidirect
73. #10622281C22semidirect
75. #10622273C22semidirect
76. #10622260C22semidirect
122. C2×(C2×D11)⋊C4D4semidirect
269. #2618D11semidirect
380. #398C2×D11semidirect
383. #396C2×D11semidirect
388. #394C2×D11semidirect
643. C11#36709semidirect

Maximal subgroups

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

subgroupindex
C2×#106231482
C22×#669472
#130769042
#130768952
#130751532
#130751282
#130748742
#130748512
#130744292
#130735052
#130729302
#130720082
#130719932
#130712292
C11×#26182
#3670911