Finite Group Databasebeta

← #14926643

Subgroups — #14926643

Order 2816.

3754 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C212yesmaximal, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13076948C212yesmaximal, complemented
5#13076899C212yesmaximal, complemented
6#13074361C212yesmaximal, complemented
7#13074353C212yesmaximal, complemented
8#13073576C214yesmaximal, complemented
9#13073508C214yesmaximal, complemented
10#13072925C212yesmaximal, complemented
11#13072050C214yesmaximal, complemented
12#13071973C212yesmaximal, complemented
13#13071191C212yesmaximal, complemented
14C2×C11×#380C211yesmaximal, characteristic, complemented
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic, complemented
19C23×C4×D11C2211yescharacteristic, complemented
20C22×C11×C4⋊C4C2212yescomplemented
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66983—28no—
24C2×#66983C2212yes—
25C2×#66983C2212yes—
26C2×#66983C2218yescomplemented
27C2×#66983C2212yescomplemented
28C2×#66983C2212yescomplemented
29C2×C4×C22⋊D11—28no—
30C2×C4×C22⋊D11C2212yes—
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2212yescomplemented
33C2×C4×C22⋊D11C2212yescomplemented
34C22×(C2×D11)⋊C4C2212yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
36C22×C4⋊Dic11C2211yescharacteristic, complemented
37C22×Dic11⋊C4C2211yescharacteristic, complemented
38C22×C4×Dic11C2211yescharacteristic, complemented
39C2×#66948C2214yescomplemented
40#10623024—216no—
41C2×#66939C2214yes—
42C2×#66939C2214yescomplemented
43C2×#66935C2214yes—
44C2×#66935C2214yescomplemented
45C11×#380C2212yescomplemented
46C11×#380C2212yescomplemented
47C11×#380C2212yescomplemented
48C11×#380C2212yescomplemented
49C2×C11×#95C2212yescomplemented
50#10622826C2218yescomplemented
51#10622607C2218yescomplemented
52#10622604C2218yescomplemented
53#10622601C2214yescomplemented
54#10622600C2214yescomplemented
55#10622598C2214yescomplemented
56#10622571C2214yescomplemented
57#10622571C2214yescomplemented
58#10622568C2214yescomplemented
59#10622556C2214yescomplemented
60#10622287C2214yescomplemented
61#10622285C2214yescomplemented
62#10622284C2214yescomplemented
63#10622283C2218yescomplemented
64#10622278C2218yescomplemented
65#10622274C2214yescomplemented
66C25×C11C2311yescharacteristic
67C24×D11C2312yes—
68C24×D11C2311yescharacteristic
69C23×C4×C11—44no—
70C23×C4×C11D418yescomplemented
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2314yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—24no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11—28no—
81C22×C22⋊D11—28no—
82C22×C22⋊D11—28no—
83C22×C22⋊D11D418yescomplemented
84C22×C22⋊D11C2314yes—
85C22×C22⋊D11C2314yes—
86C22×C22⋊D11C2312yes—
87C22×C22⋊D11C2312yes—
88C23×Dic11C2312yes—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×D44—24no—
93C22×D44—44no—
94C22×D44C2312yes—
95C22×D44C2318yes—
96C22×D44C2312yes—
97C22×C4×D11—24no—
98C22×C4×D11—44no—
99C22×C4×D11C2312yes—
100C22×C4×D11C2312yes—
101C2×C11×C4⋊C4—44no—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C22⋊C4—28no—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C22⋊Dic11—24no—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2312yes—
110#66983—28no—
111#66983—28no—
112#66983—28no—
113#66983—28no—
114#66983—232no—
115C4×C22⋊D11—28no—
116C4×C22⋊D11—28no—
117C4×C22⋊D11—28no—
118C4×C22⋊D11—28no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—28no—
121C2×(C2×D11)⋊C4C2318yes—
122C2×(C2×D11)⋊C4C2318yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2318yes—
128C2×(C2×D11)⋊C4C2318yes—
129C2×C4⋊Dic11—24no—
130C2×C4⋊Dic11C2318yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×C4×Dic11—24no—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2312yes—
139#66948—48no—
140#66939—216no—
141#66939—216no—
142#66935—216no—
143#66935—216no—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11⋊#95C2318yes—
147C11⋊#95C2318yes—
148#35000—111nomaximal, Sylow
149C24×C11—42no—
150C24×C11—42no—
151C24×C11C2×D414yes—
152C24×C11C2×D414yes—
153C24×C11#4114yes—
154C24×C11C2411yescharacteristic
155C24×C11C2411yescharacteristic
156C24×C11C2411yescharacteristic
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—24no—
160C23×D11—24no—
161C23×D11—24no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11—44no—
165C23×D11—44no—
166C23×D11C2×D414yescomplemented
167C23×D11C2414yes—
168C23×D11C2412yes—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—28no—
173C22×C4×C11—416no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—44no—
178C22×C4×C11—44no—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2×D414yes—
182C22×C4×C11C2×D414yes—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×D414yes—
185C22×C4×C11C2418yes—
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—232no—
191C2×C22⋊D11—24no—
192C2×C22⋊D11—24no—
193C2×C22⋊D11—28no—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—28no—
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—28no—
200C2×C22⋊D11—28no—
201C2×C22⋊D11—432no—
202C2×C22⋊D11C2×D418yes—
203C2×C22⋊D11C2×D418yescomplemented
204C22×Dic11—22no—
205C22×Dic11—24no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—24no—
209C22×Dic11—22no—
210C22×Dic11—24no—
211C22×Dic11—42no—
212C22×Dic11—42no—
213C22×Dic11C2×D414yescomplemented
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2414yes—
217C22×Dic11C2412yes—
218C2×D44—216no—
219C2×D44—24no—
220C2×D44—24no—
221C2×D44—28no—
222C2×D44—44no—
223C2×D44—48no—
224C2×D44—48no—
225C2×D44—416no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—28no—
229C2×C4×D11—44no—
230C2×C4×D11—416no—
231C11×C4⋊C4—28no—
232C11×C4⋊C4—44no—
233C11×C22⋊C4—28no—
234C11×C22⋊C4—28no—
235C22⋊Dic11—24no—
236C22⋊Dic11—24no—
237(C2×D11)⋊C4—216no—
238(C2×D11)⋊C4—216no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—48no—
244(C2×D11)⋊C4—48no—
245C4⋊Dic11—216no—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C2×#534—112no—
253C22×#121—111no—
254C22×C4×D4—111no—
255#2854—112no—
256#2847—112no—
257#2618—112no—
258#2617—112no—
259#2543—114no—
260#2534—114no—
261#2486—112no—
262#2416—114no—
263#2408—112no—
264#2308—112no—
265C2×#380D1111yescharacteristic, complemented
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—44no—
273C23×C11—44no—
274C23×C11—48no—
275C23×C11—48no—
276C23×C11#121116yescomplemented
277C23×C11C22×D412yes—
278C23×C11C22×D412yes—
279C23×C11C22×D412yes—
280C23×C11C22×D412yes—
281C23×C11C22×D412yes—
282C23×C11C22×D412yes—
283C23×C11C2×#4112yes—
284C23×C11C2×#4112yes—
285C23×C11C2×#4112yes—
286C23×C11C2511yescharacteristic
287C22×D11—28no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—28no—
296C22×D11—28no—
297C22×D11—48no—
298C22×D11—44no—
299C22×D11—44no—
300C22×D11—48no—
301C22×D11—48no—
302C22×D11—48no—
303C22×D11—48no—
304C22×D11—88no—
305C22×D11—88no—
306C22×D11C22×D414yes—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—28no—
311C2×C4×C11—28no—
312C2×C4×C11—28no—
313C2×C4×C11—28no—
314C2×C4×C11—28no—
315C2×C4×C11—28no—
316C2×C4×C11—44no—
317C2×C4×C11—44no—
318C2×C4×C11—44no—
319C2×C4×C11—88no—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11H(5,𝔽2)14yes—
325C22⋊D11—216no—
326C22⋊D11—216no—
327C22⋊D11—416no—
328C22⋊D11—416no—
329C2×Dic11—28no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—44no—
340C2×Dic11—44no—
341C2×Dic11—48no—
342C2×Dic11C22×D414yes—
343D44—48no—
344D44—48no—
345D44—816no—
346C4×D11—48no—
347C4×D11—48no—
348C23×D4—111no—
349C23×D4—112no—
350C23×D4—111no—
351C24×C4—111no—
352C24×C4C2×D1111yescharacteristic
353#534—2216no—
354C2×#123—114no—
355C2×#123—114no—
356C2×#121—112no—
357C2×#121—112no—
358C2×#121—112no—
359C2×#121—112no—
360C2×#121—118no—
361C2×#121—114no—
362C2×#121—228no—
363C2×#120—114no—
364C2×#120—114no—
365C2×C4×D4—112no—
366C2×C4×D4—112no—
367C2×C4×D4—112no—
368C2×C4×D4—112no—
369C2×C4×D4—228no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4C2×D1112yescomplemented
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—112no—
376C22×C22⋊C4C2×D1112yes—
377C22×C42—111no—
378#398—114no—
379#397—114no—
380#396—118no—
381#394—118no—
382#394—114no—
383#392—114no—
384#390—114no—
385#389—114no—
386#388—118no—
387#386—118no—
388#386—114no—
389#386—114no—
390#386—118no—
391#381—114no—
392#380—114no—
393#380C2×D1112yescomplemented
394#380C2×D1112yescomplemented
395#380C2×D1112yescomplemented
396#380C2×D1112yescomplemented
397#379—114no—
398C2×#95C2×D1112yescomplemented
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—24no—
406C22×C11—24no—
407C22×C11—24no—
408C22×C11—24no—
409C22×C11—24no—
410C22×C11—24no—
411C22×C11—416no—
412C22×C11C2×#12114yes—
413C22×C11C2×#12114yes—
414C22×C11C2×#12114yes—
415C22×C11C23×D411yescharacteristic
416C22×C11C23×D411yescharacteristic
417C22×C11C22×#4111yescharacteristic
418C22×C11C2×H(5,𝔽2)12yes—
419C22×C11#58512yes—
420C2×D11—24no—
421C2×D11—28no—
422C2×D11—416no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—44no—
426C2×D11—44no—
427C2×D11—44no—
428C2×D11—44no—
429C2×D11—48no—
430C2×D11—48no—
431C2×D11—816no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—48no—
436C4×C11#53414yescomplemented
437Dic11—24no—
438Dic11—44no—
439Dic11—42no—
440Dic11—42no—
441C25—111no—
442C25—112no—
443C25C22×D1111yescharacteristic
444C22×D4—118no—
445C22×D4—112no—
446C22×D4—112no—
447C22×D4—114no—
448C22×D4—114no—
449C22×D4—112no—
450C22×D4—118no—
451C22×D4—112no—
452C22×D4—224no—
453C22×D4—224no—
454C22×D4—228no—
455C22×D4—228no—
456C22×D4—228no—
457C22×D4—224no—
458C22×D4—444no—
459C23×C4—44no—
460C23×C4—111no—
461C23×C4—112no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—112no—
465C23×C4—112no—
466C23×C4—224no—
467C23×C4—444no—
468C23×C4D4418yescomplemented
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1114yes—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476#123—2216no—
477#123—2216no—
478#121—2232no—
479#121—228no—
480#121—228no—
481#121—228no—
482#121—228no—
483#121—448no—
484#120—2216no—
485#120—2216no—
486C4×D4—228no—
487C4×D4—228no—
488C4×D4—228no—
489C4×D4—228no—
490C2×C4⋊C4—44no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—118no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4C22×D1114yes—
499C2×C4⋊C4C22×D1114yes—
500C2×C22⋊C4—28no—
501C2×C22⋊C4—112no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4—112no—
504C2×C22⋊C4—112no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—118no—
509C2×C22⋊C4—118no—
510C2×C22⋊C4—118no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—228no—
514C2×C22⋊C4C22×D1114yes—
515C2×C22⋊C4C22×D1114yes—
516C2×C42—112no—
517C2×C42—112no—
518C2×C42—224no—
519#95—118no—
520#95—118no—
521#95C22×D1114yes—
522#95C22×D1114yes—
523C2×C11—24no—
524C2×C11—24no—
525C2×C11—24no—
526C2×C11C22×#12111yescharacteristic
527C2×C11C2×#53411yescharacteristic
528C2×C11#344911yescharacteristic
529C2×C11#349612yes—
530C2×C11#350512yes—
531D11—44no—
532D11—84no—
533C24—42no—
534C24—42no—
535C24—112no—
536C24—114no—
537C24—114no—
538C24—222no—
539C24—222no—
540C24—224no—
541C24—224no—
542C24—224no—
543C24—442no—
544C24—442no—
545C24—444no—
546C24—444no—
547C24C2×D4414yes—
548C24D4×D1114yes—
549C24#434314yes—
550C24C23×D1111yescharacteristic
551C24C23×D1111yescharacteristic
552C24C23×D1111yescharacteristic
553C2×D4—118no—
554C2×D4—118no—
555C2×D4—2216no—
556C2×D4—2232no—
557C2×D4—224no—
558C2×D4—224no—
559C2×D4—224no—
560C2×D4—224no—
561C2×D4—228no—
562C2×D4—228no—
563C2×D4—228no—
564C2×D4—228no—
565C2×D4—228no—
566C2×D4—228no—
567C2×D4—224no—
568C2×D4—224no—
569C2×D4—228no—
570C2×D4—444no—
571C2×D4—4416no—
572C2×D4—448no—
573C2×D4—448no—
574C2×D4—4432no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—28no—
579C22×C4—416no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—114no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—114no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—224no—
595C22×C4—224no—
596C22×C4—224no—
597C22×C4—224no—
598C22×C4—224no—
599C22×C4—228no—
600C22×C4—444no—
601C22×C4—4416no—
602C22×C4—442no—
603C22×C4—442no—
604C22×C4C2×D4414yes—
605C22×C4C2×D4414yes—
606C22×C4C2×D4414yes—
607C22×C4C2×D4414yes—
608C22×C4C2×D4414yes—
609C22×C4C2×D4414yes—
610C22×C4C23×D1118yes—
611C22×C4C23×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613C22×C4C23×D1111yescharacteristic
614C22×C4C23×D1111yescharacteristic
615C4⋊C4—28no—
616C4⋊C4—44no—
617C4⋊C4—2216no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—2216no—
625C22⋊C4—2216no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—228no—
631C22⋊C4—228no—
632C22⋊C4—448no—
633C22⋊C4—448no—
634C42—224no—
635C42—224no—
636C11#3500011yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—48no—
646C23—48no—
647C23—114no—
648C23—228no—
649C23—222no—
650C23—224no—
651C23—222no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—228no—
656C23—224no—
657C23—228no—
658C23—448no—
659C23—444no—
660C23—448no—
661C23—444no—
662C23—448no—
663C23—448no—
664C23—448no—
665C23—888no—
666C23—888no—
667C23#66948116yescomplemented
668C23C22×D4412yes—
669C23C22×D4412yes—
670C23C22×D4412yes—
671C23C2×D4×D1112yes—
672C23C2×D4×D1112yes—
673C23C2×D4×D1112yes—
674C23C2×#434312yes—
675C23C2×#434312yes—
676C23C2×#434312yes—
677C23C24×D1111yescharacteristic
678D4—2216no—
679D4—2216no—
680D4—448no—
681D4—4416no—
682D4—4416no—
683D4—448no—
684D4—8816no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—88no—
698C2×C4—114no—
699C2×C4—228no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—448no—
710C2×C4—444no—
711C2×C4—444no—
712C2×C4—448no—
713C2×C4—448no—
714C2×C4C22×D4412yes—
715C2×C4C22×D4412yes—
716C2×C4C22×D4412yes—
717C2×C4C22×D4412yes—
718C2×C4#6703714yes—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—228no—
733C22—224no—
734C22—4416no—
735C22—442no—
736C22—444no—
737C22—442no—
738C22—448no—
739C22—444no—
740C22—448no—
741C22—444no—
742C22—444no—
743C22—8816no—
744C22C2×#6694814yes—
745C22C2×#6694814yes—
746C22C2×#6694814yes—
747C22C23×D4411yescharacteristic
748C22C22×D4×D1111yescharacteristic
749C22C2×#6703712yes—
750C22C22×#434311yescharacteristic
751C22#1062345312yes—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—48no—
756C4—224no—
757C4—442no—
758C4—442no—
759C4—444no—
760C4#1062302414yescomplemented
761C2—24no—
762C2—24no—
763C2—24no—
764C2—444no—
765C2—884no—
766C2C22×#6694811yescharacteristic
767C2C2×#1062302411yescharacteristic
768C2#1308194911yescharacteristic
769C2#1308237312yes—
770C2#1308245712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#380C2
hypercenterC2×#380D11
hypocenterC11#35000
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C22×#66983C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13076948C2semidirect
5. #13076899C2semidirect
6. #13074361C2semidirect
7. #13074353C2semidirect
8. #13073576C2semidirect
9. #13073508C2semidirect
10. #13072925C2semidirect
11. #13072050C2semidirect
12. #13071973C2semidirect
13. #13071191C2semidirect
14. C2×C11×#380C2semidirect
18. C23×D44C22semidirect
19. C23×C4×D11C22semidirect
20. C22×C11×C4⋊C4C22semidirect
26. C2×#66983C22semidirect
27. C2×#66983C22semidirect
28. C2×#66983C22semidirect
32. C2×C4×C22⋊D11C22semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C22×(C2×D11)⋊C4C22semidirect
35. C22×(C2×D11)⋊C4C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. C22×Dic11⋊C4C22semidirect
38. C22×C4×Dic11C22semidirect
39. C2×#66948C22semidirect
42. C2×#66939C22semidirect
44. C2×#66935C22semidirect
45. C11×#380C22semidirect
46. C11×#380C22semidirect
47. C11×#380C22semidirect
48. C11×#380C22semidirect
49. C2×C11×#95C22semidirect
50. #10622826C22semidirect
51. #10622607C22semidirect
52. #10622604C22semidirect
53. #10622601C22semidirect
54. #10622600C22semidirect
55. #10622598C22semidirect
56. #10622571C22semidirect
57. #10622571C22semidirect
58. #10622568C22semidirect
59. #10622556C22semidirect
60. #10622287C22semidirect
61. #10622285C22semidirect
62. #10622284C22semidirect
63. #10622283C22semidirect
64. #10622278C22semidirect
65. #10622274C22semidirect
70. C23×C4×C11D4semidirect
83. C22×C22⋊D11D4semidirect
166. C23×D11C2×D4semidirect
203. C2×C22⋊D11C2×D4semidirect
213. C22×Dic11C2×D4semidirect
265. C2×#380D11semidirect
276. C23×C11#121semidirect
372. C22×C4⋊C4C2×D11semidirect
393. #380C2×D11semidirect
394. #380C2×D11semidirect
395. #380C2×D11semidirect
396. #380C2×D11semidirect
398. C2×#95C2×D11semidirect
436. C4×C11#534semidirect
468. C23×C4D44semidirect
636. C11#35000semidirect
667. C23#66948semidirect
760. C4#10623024semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C22×#669832
C22×C4×C22⋊D112
#130769482
#130768992
#130743612
#130743532
#130735762
#130735082
#130729252
#130720502
#130719732
#130711912
C2×C11×#3802
#3500011