Finite Group Databasebeta

← #14960606

Subgroups — #14960606

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×#10623175C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3#13076900C211yesmaximal, characteristic, complemented
4#13076899C211yesmaximal, characteristic, complemented
5#13075157C214yesmaximal, complemented
6#13075126C214yesmaximal, complemented
7#13074866C214yesmaximal, complemented
8#13074859C214yesmaximal, complemented
9#13074358C211yesmaximal, characteristic, complemented
10#13073511C212yesmaximal, complemented
11#13072932C212yesmaximal, complemented
12#13072014C212yesmaximal, complemented
13#13071988C212yesmaximal, complemented
14#13071229C211yesmaximal, characteristic, complemented
15C11×#2627C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#67000C2212yescomplemented
21C2×#66999C2212yescomplemented
22C2×#66983C2211yescharacteristic
23C2×#66982C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28#10623175—28no—
29C2×#66951C2212yescomplemented
30C2×#66948C2214yes—
31C2×#66948C2212yescomplemented
32C2×#66948C2212yescomplemented
33C2×#66947—28no—
34C2×#66947C2214yes—
35C2×#66947C2214yes—
36C2×#66947C2212yescomplemented
37C2×#66935C2212yes—
38C2×#66935C2212yes—
39C2×(C22⋊D11)⋊C4C2212yes—
40C2×C22⋊C4×D11C2212yes—
41C11×#400C2212yescomplemented
42C11×#398C2214yescomplemented
43C11×#395C2212yescomplemented
44C11×#385C2212yes—
45C11×#381C2212yes—
46C11×#380C2211yescharacteristic
47#10622826C2212yes—
48#10622825C2211yescharacteristic
49#10622607C2214yescomplemented
50#10622605C2214yescomplemented
51#10622604C2214yes—
52#10622604C2212yescomplemented
53#10622602C2214yescomplemented
54#10622602C2214yescomplemented
55#10622600C2212yescomplemented
56#10622600C2212yescomplemented
57#10622596C2212yescomplemented
58#10622585C2214yescomplemented
59#10622571C2212yes—
60#10622568C2212yes—
61#10622559C2212yes—
62#10622555C2212yes—
63#10622289C2214yescomplemented
64#10622288C2214yescomplemented
65#10622285C2214yescomplemented
66#10622285C2214yescomplemented
67#10622284C2214yes—
68#10622282C2214yescomplemented
69#10622281C2214yescomplemented
70#10622280C2214yescomplemented
71#10622280C2214yescomplemented
72#10622278C2214yes—
73#10622278C2214yescomplemented
74#10622278C2214yescomplemented
75#10622278C2214yescomplemented
76#10622271C2214yescomplemented
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11C2312yes—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C22×D44—24no—
87C22×D44—44no—
88C22×D44C2314yes—
89C22×D44C2312yes—
90C22×D44C2312yes—
91C22×D44C2314yes—
92C22×D44C2311yescharacteristic
93C22×C4×D11—24no—
94C22×C4×D11—44no—
95C22×C4×D11C2312yes—
96C22×C4×D11C2312yes—
97C22×C4×D11C2312yes—
98C22×C4×D11C2314yes—
99C11×C22⋊Q8—24no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C22⋊Dic11C2312yes—
110#67000—28no—
111#66999—44no—
112#66983—24no—
113#66982—44no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4D418yescomplemented
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2312yes—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×C4×Dic11C2312yes—
141#66951—28no—
142#66948—28no—
143#66948—48no—
144#66948—44no—
145#66947—216no—
146#66947—216no—
147#66947—28no—
148#66935—28no—
149#66935—44no—
150(C22⋊D11)⋊C4—28no—
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×C11C2411yescharacteristic
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—24no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11C2×D414yes—
173C23×D11C2412yes—
174C23×D11C2412yes—
175C23×D11C2412yes—
176C2×Q8×C11—22no—
177C2×Q8×C11—42no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11C2×D414yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2414yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—24no—
193C2×C22⋊D11—24no—
194C2×C22⋊D11—24no—
195C22×Dic11—22no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11C2×D414yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2414yes—
202C22×Dic11C2412yes—
203C2×D44—28no—
204C2×D44—24no—
205C2×D44—24no—
206C2×D44—28no—
207C2×D44—28no—
208C2×D44—22no—
209C2×D44—44no—
210C2×D44—44no—
211C2×D44—42no—
212C2×D44—44no—
213C2×D44—44no—
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—24no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×C4×D11—416no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—42no—
233C11×C4⋊C4—44no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C22⋊Dic11—24no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—28no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4C2×D418yes—
251(C2×D11)⋊C4C2×D418yes—
252C4⋊Dic11—22no—
253C4⋊Dic11—42no—
254Dic11⋊C4—24no—
255Dic11⋊C4—28no—
256Dic11⋊C4—44no—
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#2627D1111yescharacteristic, complemented
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×C11C22×D412yes—
278C23×C11H(5,𝔽2)12yes—
279C23×C112−1+412yes—
280C23×C11C2511yescharacteristic
281C22×D11—28no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—24no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—24no—
291C22×D11—22no—
292C22×D11—28no—
293C22×D11—22no—
294C22×D11—24no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—24no—
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—
308Q8×C11—82no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
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—48no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—44no—
340C2×Dic11—44no—
341C2×Dic11C22×D414yes—
342D44—416no—
343D44—82no—
344D44—84no—
345D44—84no—
346D44—88no—
347C4×D11—48no—
348C4×D11—48no—
349C4×D11—84no—
350C4×D11—88no—
351C23×D4—111no—
352C24×C4—111no—
353#538—228no—
354C2×#126—112no—
355C2×#124—112no—
356C2×#123—112no—
357C2×#123—114no—
358C2×#123—114no—
359C2×#123—112no—
360C2×#123—228no—
361C2×C22⋊Q8—112no—
362C2×C22⋊Q8C2×D1111yescharacteristic
363C2×#121—111no—
364C2×#121—112no—
365C2×#121—112no—
366C2×#121—114no—
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—114no—
377#400C2×D1112yescomplemented
378#399—114no—
379#398—112no—
380#398C2×D1114yescomplemented
381#397—114no—
382#396—114no—
383#396—114no—
384#395C2×D1112yescomplemented
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—112no—
401#385—114no—
402#385C2×D1112yes—
403#381C2×D1112yes—
404#380—111no—
405#380—112no—
406#380—112no—
407#380—112no—
408#380—114no—
409#380—114no—
410#380C2×D1111yescharacteristic
411#379—112no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11#53714yes—
417C22×C11C23×D411yescharacteristic
418C22×C11C2×H(5,𝔽2)11yescharacteristic
419C22×C11C2×H(5,𝔽2)12yes—
420C22×C11C2×2−1+411yescharacteristic
421C22×C11#58512yes—
422C2×D11—24no—
423C2×D11—24no—
424C2×D11—24no—
425C2×D11—24no—
426C2×D11—24no—
427C2×D11—24no—
428C2×D11—416no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—44no—
433C2×D11—42no—
434C2×D11—44no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—44no—
439C2×D11—44no—
440C2×D11—88no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—44no—
448Dic11—24no—
449Dic11—42no—
450Dic11—42no—
451Dic11—44no—
452C25—111no—
453C25—111no—
454C22×Q8C22×D1111yescharacteristic
455C22×D4—112no—
456C22×D4—114no—
457C22×D4—112no—
458C22×D4—114no—
459C22×D4—112no—
460C22×D4—111no—
461C22×D4—224no—
462C22×D4—444no—
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—2216no—
477#123—2216no—
478#123—228no—
479#123—444no—
480C22⋊Q8—24no—
481C22⋊Q8—444no—
482#121—228no—
483#121—224no—
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—111no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4C22×D1112yes—
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—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—112no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—114no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—444no—
524C2×C22⋊C4C22×D1112yes—
525C2×C22⋊C4C22×D1112yes—
526C2×C42—112no—
527#95—114no—
528#95—114no—
529#95—112no—
530#95—114no—
531#95—114no—
532#95C22×D1114yes—
533#95C22×D1114yes—
534#95C22×D1112yes—
535#95C22×D1114yes—
536C2×C11—24no—
537C2×C11C2×#53711yescharacteristic
538C2×C11#348411yescharacteristic
539C2×C11#348511yescharacteristic
540C2×C11#353412yes—
541C2×C11#353512yes—
542D11—44no—
543D11—44no—
544D11—82no—
545C24—112no—
546C24—112no—
547C24—114no—
548C24—112no—
549C24—224no—
550C24—222no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—222no—
555C24—442no—
556C24—442no—
557C24—442no—
558C24C23×D1111yescharacteristic
559C2×Q8—22no—
560C2×Q8—42no—
561C2×D4—228no—
562C2×D4—228no—
563C2×D4—224no—
564C2×D4—224no—
565C2×D4—228no—
566C2×D4—224no—
567C2×D4—224no—
568C2×D4—224no—
569C2×D4—222no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—442no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—4416no—
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—224no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—222no—
592C22×C4—224no—
593C22×C4—224no—
594C22×C4—442no—
595C22×C4—442no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—4416no—
601C22×C4—442no—
602C22×C4—442no—
603C22×C4D4×D1114yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1114yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1112yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1111yescharacteristic
610C22×C4C23×D1111yescharacteristic
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—228no—
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—118no—
627C22⋊C4—118no—
628C22⋊C4—228no—
629C22⋊C4—224no—
630C22⋊C4—228no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—228no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—444no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C42—224no—
643C11#3670911yescharacteristic, complemented, Sylow
644C23—22no—
645C23—22no—
646C23—114no—
647C23—114no—
648C23—228no—
649C23—222no—
650C23—222no—
651C23—222no—
652C23—222no—
653C23—222no—
654C23—222no—
655C23—224no—
656C23—222no—
657C23—224no—
658C23—222no—
659C23—228no—
660C23—222no—
661C23—222no—
662C23—222no—
663C23—224no—
664C23—224no—
665C23—444no—
666C23—444no—
667C23—448no—
668C23—448no—
669C23—444no—
670C23—444no—
671C23—884no—
672C23—884no—
673C23C2×D4×D1112yes—
674C23#6704012yes—
675C23#6704212yes—
676C23C24×D1111yescharacteristic
677Q8—82no—
678D4—4416no—
679D4—448no—
680D4—882no—
681D4—884no—
682D4—884no—
683D4—888no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—114no—
702C2×C4—224no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—448no—
713C2×C4—448no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—884no—
717C2×C4—888no—
718C2×C4C2×D4×D1112yes—
719C2×C4C2×D4×D1112yes—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—24no—
724C22—224no—
725C22—224no—
726C22—224no—
727C22—224no—
728C22—224no—
729C22—224no—
730C22—4416no—
731C22—442no—
732C22—442no—
733C22—444no—
734C22—442no—
735C22—442no—
736C22—444no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—444no—
741C22—444no—
742C22—888no—
743C22#1062316014yes—
744C22C22×D4×D1111yescharacteristic
745C22C2×#6704011yescharacteristic
746C22C2×#6704211yescharacteristic
747C22D11×H(5,𝔽2)12yes—
748C22#1062345712yes—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—44no—
756C4—224no—
757C4—442no—
758C4—442no—
759C4—444no—
760C2—24no—
761C2—444no—
762C2—444no—
763C2—882no—
764C2C2×#1062316011yescharacteristic
765C2#1308224811yescharacteristic
766C2#1308225911yescharacteristic
767C2#1308281112yes—
768C2#1308282612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2627C2
hypercenter#2627D11
hypocenterC11#36709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2627

Complements

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

NH ≅ G/Ntype
1. C2×#10623175C2semidirect
2. C22×#66947C2semidirect
3. #13076900C2semidirect
4. #13076899C2semidirect
5. #13075157C2semidirect
6. #13075126C2semidirect
7. #13074866C2semidirect
8. #13074859C2semidirect
9. #13074358C2semidirect
10. #13073511C2semidirect
11. #13072932C2semidirect
12. #13072014C2semidirect
13. #13071988C2semidirect
14. #13071229C2semidirect
15. C11×#2627C2semidirect
20. C2×#67000C22semidirect
21. C2×#66999C22semidirect
29. C2×#66951C22semidirect
31. C2×#66948C22semidirect
32. C2×#66948C22semidirect
36. C2×#66947C22semidirect
41. C11×#400C22semidirect
42. C11×#398C22semidirect
43. C11×#395C22semidirect
49. #10622607C22semidirect
50. #10622605C22semidirect
52. #10622604C22semidirect
53. #10622602C22semidirect
54. #10622602C22semidirect
55. #10622600C22semidirect
56. #10622600C22semidirect
57. #10622596C22semidirect
58. #10622585C22semidirect
63. #10622289C22semidirect
64. #10622288C22semidirect
65. #10622285C22semidirect
66. #10622285C22semidirect
68. #10622282C22semidirect
69. #10622281C22semidirect
70. #10622280C22semidirect
71. #10622280C22semidirect
73. #10622278C22semidirect
74. #10622278C22semidirect
75. #10622278C22semidirect
76. #10622271C22semidirect
116. C2×(C2×D11)⋊C4D4semidirect
268. #2627D11semidirect
377. #400C2×D11semidirect
380. #398C2×D11semidirect
384. #395C2×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×#106231752
C22×#669472
#130769002
#130768992
#130751572
#130751262
#130748662
#130748592
#130743582
#130735112
#130729322
#130720142
#130719882
#130712292
C11×#26272
#3670911