Finite Group Databasebeta

← #14960528

Subgroups — #14960528

Order 2816.

3018 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic, complemented
2#13076906C212yesmaximal, complemented
3#13075046C214yesmaximal, complemented
4#13075016C214yesmaximal, complemented
5#13074876C214yesmaximal, complemented
6#13074846C214yesmaximal, complemented
7#13074330C212yesmaximal, complemented
8#13072899C211yesmaximal, characteristic, complemented
9#13072886C211yesmaximal, characteristic, complemented
10#13072013C212yesmaximal, complemented
11#13071991C212yesmaximal, complemented
12#13071947C211yesmaximal, characteristic, complemented
13#13071931C211yesmaximal, characteristic, complemented
14#13071194C211yesmaximal, characteristic, complemented
15C2×C11×#535C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C11×#535—28no—
22C2×C11×#127C2212yescomplemented
23C2×C11×#124C2212yescomplemented
24C2×C11×#121C2212yescomplemented
25C2×C11×#121C2212yescomplemented
26C2×C11×#120C2212yes—
27C2×C11×#120C2212yes—
28C2×C11×#117C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2212yes—
31C2×#66992—28no—
32C2×#66992C2214yes—
33C2×#66992C2214yes—
34C2×#66992C2214yescomplemented
35C2×#66990C2212yes—
36C2×#66988C2212yes—
37C2×#66988C2214yescomplemented
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40#10622860C2212yes—
41#10622844C2212yescomplemented
42#10622842C2212yescomplemented
43#10622836C2212yescomplemented
44#10622836C2214yescomplemented
45#10622836C2214yescomplemented
46#10622836C2214yescomplemented
47#10622835C2212yescomplemented
48#10622835C2214yescomplemented
49#10622833C2212yes—
50#10622833C2212yes—
51#10622833C2214yescomplemented
52#10622833C2214yescomplemented
53#10622833C2214yescomplemented
54#10622833C2214yescomplemented
55#10622826C2214yescomplemented
56#10622824C2211yescharacteristic
57#10622824C2211yescharacteristic
58#10622823C2214yescomplemented
59#10622606C2212yescomplemented
60#10622605C2212yescomplemented
61#10622595C2212yescomplemented
62#10622593C2212yescomplemented
63#10622572C2214yescomplemented
64#10622572C2214yescomplemented
65#10622572C2214yescomplemented
66#10622571C2214yescomplemented
67#10622568C2212yes—
68#10622565C2214yescomplemented
69#10622559C2212yes—
70#10622559C2212yes—
71#10622559C2214yescomplemented
72#10622556C2212yes—
73#10622556C2214yescomplemented
74#10622555C2214yescomplemented
75#10622553C2214yescomplemented
76#10622546C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C2×C11×#41—24no—
81C2×C11×#41—44no—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—44no—
84C22×D4×C11D418yescomplemented
85C22×D4×C11C2312yes—
86C22×D4×C11C2312yes—
87C22×D4×C11C2312yes—
88C22×D4×C11C2312yes—
89C22×D4×C11C2312yes—
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2312yes—
92C22×D4×C11C2312yes—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2312yes—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—44no—
98C22×C22⋊D11—44no—
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C23×Dic11—24no—
103C23×Dic11—44no—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2314yes—
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2314yes—
109C11×#127—28no—
110C11×#124—28no—
111C11×#121—28no—
112C11×#121—28no—
113C11×#120—28no—
114C11×#120—28no—
115C11×#117—24no—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2312yes—
123C2×C42×C11C2312yes—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—44no—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135#66992—216no—
136#66992—216no—
137#66992—48no—
138#66990—44no—
139#66988—48no—
140#66988—44no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C11⋊#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163#36704—111nomaximal, Sylow
164C24×C11—24no—
165C24×C11—24no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11C2×D414yes—
171C24×C11C2×D414yes—
172C24×C11C2412yes—
173C24×C11C2412yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—24no—
178C23×D11—42no—
179C23×D11—42no—
180C23×D11C2412yes—
181C11×#41—416no—
182C2×Q8×C11—22no—
183C2×Q8×C11—42no—
184C2×D4×C11—24no—
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—22no—
192C2×D4×C11—416no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—44no—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11C2×D418yes—
203C2×D4×C11C2×D418yes—
204C22×C4×C11—24no—
205C22×C4×C11—24no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11C2×D414yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—416no—
224C2×C22⋊D11—416no—
225C22×Dic11—24no—
226C22×Dic11—28no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—28no—
231C22×Dic11—24no—
232C22×Dic11—42no—
233C22×Dic11—44no—
234C22×Dic11—44no—
235C22×Dic11—44no—
236C22×Dic11—44no—
237C22×Dic11—416no—
238C22×Dic11C2414yes—
239C22×Dic11C2412yes—
240C22×Dic11C2414yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—22no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C42×C11—24no—
251C22⋊Dic11—28no—
252C22⋊Dic11—28no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—44no—
256C22⋊Dic11—44no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265Dic11⋊C4—28no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—44no—
269Dic11⋊C4—44no—
270C2×#535D1111yescharacteristic, complemented
271C22×#121—111no—
272#2849—112no—
273#2688—114no—
274#2686—114no—
275#2673—114no—
276#2671—114no—
277#2613—112no—
278#2484—111no—
279#2482—111no—
280#2412—112no—
281#2410—112no—
282#2406—111no—
283#2404—111no—
284#2308—111no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—28no—
288C23×C11—22no—
289C23×C11—24no—
290C23×C11—22no—
291C23×C11—24no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—28no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—24no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—416no—
307C23×C11—88no—
308C23×C11C22×D414yes—
309C23×C11C22×D414yes—
310C23×C11C22×D412yes—
311C23×C11H(5,𝔽2)14yes—
312C23×C11C2511yescharacteristic
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—44no—
319C22×D11—44no—
320C22×D11—44no—
321C22×D11—88no—
322Q8×C11—44no—
323D4×C11—48no—
324D4×C11—48no—
325D4×C11—44no—
326D4×C11—48no—
327D4×C11—84no—
328D4×C11—84no—
329D4×C11—84no—
330D4×C11—84no—
331C2×C4×C11—28no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—48no—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D412yes—
344C22⋊D11—416no—
345C22⋊D11—416no—
346C22⋊D11—88no—
347C2×Dic11—28no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—24no—
356C2×Dic11—24no—
357C2×Dic11—24no—
358C2×Dic11—24no—
359C2×Dic11—24no—
360C2×Dic11—416no—
361C2×Dic11—44no—
362C2×Dic11—44no—
363C2×Dic11—88no—
364C2×Dic11H(5,𝔽2)14yes—
365C22×#41C2×D1111yescharacteristic
366C23×D4—111no—
367C23×D4—111no—
368C23×D4C2×D1111yescharacteristic
369C24×C4—111no—
370#535—28no—
371C2×#127C2×D1112yescomplemented
372C2×#124C2×D1112yescomplemented
373C2×#123—114no—
374C2×#123—112no—
375C2×#121—114no—
376C2×#121—114no—
377C2×#121—114no—
378C2×#121—228no—
379C2×#121C2×D1112yescomplemented
380C2×#121C2×D1112yescomplemented
381C2×#120—112no—
382C2×#120C2×D1112yes—
383C2×#120C2×D1112yes—
384C2×#117C2×D1111yescharacteristic
385C22×C4⋊C4—111no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4—112no—
389#400—112no—
390#399—112no—
391#398—112no—
392#397—112no—
393#397—114no—
394#395—112no—
395#394—112no—
396#394—114no—
397#394—114no—
398#394—114no—
399#394—114no—
400#393—112no—
401#392—114no—
402#392—114no—
403#392—112no—
404#392—114no—
405#388—114no—
406#387—114no—
407#386—114no—
408#386—114no—
409#386—112no—
410#386—112no—
411#386—114no—
412#386—114no—
413#386—114no—
414#386—114no—
415#385—114no—
416#385—112no—
417#385—112no—
418#385—114no—
419#381—111no—
420#381—111no—
421#381—114no—
422#381—112no—
423#380—114no—
424#379—112no—
425#379—112no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—28no—
429C22×C11—24no—
430C22×C11—24no—
431C22×C11—24no—
432C22×C11—24no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—416no—
436C22×C11—44no—
437C22×C11—44no—
438C22×C11—44no—
439C22×C11—44no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—44no—
444C22×C11—44no—
445C22×C11—88no—
446C22×C11#53414yes—
447C22×C11C23×D411yescharacteristic
448C22×C11C2×H(5,𝔽2)12yes—
449C22×C11C2×H(5,𝔽2)12yes—
450C22×C11#58512yes—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—44no—
455C2×D11—44no—
456C2×D11—88no—
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11—42no—
462Dic11—24no—
463Dic11—42no—
464Dic11—42no—
465Dic11—44no—
466Dic11—44no—
467C25—111no—
468C25C22×D1111yescharacteristic
469C25C22×D1111yescharacteristic
470C2×#41—24no—
471C2×#41—44no—
472C22×Q8C22×D1111yescharacteristic
473C22×D4—44no—
474C22×D4—114no—
475C22×D4—114no—
476C22×D4—114no—
477C22×D4—224no—
478C22×D4—224no—
479C22×D4—444no—
480C22×D4—444no—
481C22×D4C22⋊D1118yescomplemented
482C22×D4C22×D1112yes—
483C22×D4C22×D1112yes—
484C22×D4C22×D1112yes—
485C22×D4C22×D1112yes—
486C22×D4C22×D1112yes—
487C22×D4C22×D1111yescharacteristic
488C22×D4C22×D1112yes—
489C22×D4C22×D1112yes—
490C23×C4—111no—
491C23×C4—111no—
492C23×C4—114no—
493C23×C4—111no—
494C23×C4—114no—
495C23×C4—224no—
496C23×C4—444no—
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1112yes—
499#127—28no—
500#124—28no—
501#123—448no—
502#123—444no—
503#121—28no—
504#121—28no—
505#121—2216no—
506#121—2216no—
507#121—448no—
508#120—28no—
509#120—28no—
510#120—444no—
511#117—24no—
512C2×C4⋊C4—112no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—224no—
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C22⋊C4—112no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—112no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4—444no—
537C2×C22⋊C4C22×D1112yes—
538C2×C22⋊C4C22×D1112yes—
539C2×C22⋊C4C22×D1112yes—
540C2×C22⋊C4C22×D1112yes—
541C2×C22⋊C4C22×D1112yes—
542C2×C42C22×D1112yes—
543#95—114no—
544#95—114no—
545#95—114no—
546#95—112no—
547#95—114no—
548#95—114no—
549#95—112no—
550#95—112no—
551#95—112no—
552#95—114no—
553C2×C11—24no—
554C2×C11—44no—
555C2×C11—44no—
556C2×C11—82no—
557C2×C11C2×#53411yescharacteristic
558C2×C11#348411yescharacteristic
559C2×C11#348511yescharacteristic
560C2×C11#354214yes—
561D11—82no—
562C24—24no—
563C24—24no—
564C24—42no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—112no—
569C24—222no—
570C24—224no—
571C24—442no—
572C24—442no—
573C24C2×C22⋊D1114yes—
574C24C2×C22⋊D1114yes—
575C24C23×D1112yes—
576C24C23×D1112yes—
577C24C23×D1112yes—
578C24C23×D1111yescharacteristic
579#41—416no—
580C2×Q8—22no—
581C2×Q8—42no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—22no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—416no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—228no—
601C2×D4—228no—
602C2×D4—228no—
603C2×D4—444no—
604C2×D4—444no—
605C2×D4—444no—
606C2×D4—4416no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4—4416no—
611C2×D4C2×C22⋊D1118yes—
612C2×D4C2×C22⋊D1118yes—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—112no—
618C22×C4—114no—
619C22×C4—114no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—224no—
623C22×C4—228no—
624C22×C4—222no—
625C22×C4—224no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—228no—
629C22×C4—444no—
630C22×C4—442no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4—4416no—
635C22×C4C2×C22⋊D1114yes—
636C22×C4C23×D1112yes—
637C22×C4C23×D1112yes—
638C22×C4C23×D1112yes—
639C22×C4C23×D1111yescharacteristic
640C22×C4C23×D1111yescharacteristic
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—228no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4—444no—
647C4⋊C4—444no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—228no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—228no—
657C22⋊C4—224no—
658C22⋊C4—224no—
659C22⋊C4—444no—
660C22⋊C4—444no—
661C22⋊C4—444no—
662C22⋊C4—444no—
663C22⋊C4—444no—
664C22⋊C4—444no—
665C22⋊C4—444no—
666C22⋊C4—444no—
667C42—24no—
668C11#3670411yescharacteristic, complemented, Sylow
669C23—22no—
670C23—22no—
671C23—28no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—416no—
691C23—88no—
692C23—224no—
693C23—224no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—444no—
698C23—444no—
699C23—444no—
700C23—888no—
701C23#6703714yes—
702C23C22×C22⋊D1114yes—
703C23C22×C22⋊D1114yes—
704C23C22×C22⋊D1112yes—
705C23C24×D1111yescharacteristic
706Q8—44no—
707D4—48no—
708D4—48no—
709D4—44no—
710D4—48no—
711D4—84no—
712D4—84no—
713D4—84no—
714D4—84no—
715D4—4416no—
716D4—4416no—
717D4—888no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—48no—
729C2×C4—114no—
730C2×C4—228no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—4416no—
744C2×C4—444no—
745C2×C4—444no—
746C2×C4—888no—
747C2×C4C22×C22⋊D1112yes—
748C2×C4C22×C22⋊D1112yes—
749C22—28no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—416no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—88no—
769C22—444no—
770C22—444no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—888no—
775C22#1062333514yes—
776C22C2×#6703712yes—
777C22D11×H(5,𝔽2)12yes—
778C22#1062345512yes—
779C22C23×C22⋊D1111yescharacteristic
780C4—22no—
781C4—22no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—224no—
786C4—444no—
787C4—444no—
788C4—442no—
789C4—442no—
790C2—24no—
791C2—44no—
792C2—44no—
793C2—82no—
794C2—882no—
795C2C2×#1062333511yescharacteristic
796C2#1308224711yescharacteristic
797C2#1308225611yescharacteristic
798C2#1308291914yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#535C2
hypercenterC2×#535D11
hypocenterC11#36704
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. #13076906C2semidirect
3. #13075046C2semidirect
4. #13075016C2semidirect
5. #13074876C2semidirect
6. #13074846C2semidirect
7. #13074330C2semidirect
8. #13072899C2semidirect
9. #13072886C2semidirect
10. #13072013C2semidirect
11. #13071991C2semidirect
12. #13071947C2semidirect
13. #13071931C2semidirect
14. #13071194C2semidirect
15. C2×C11×#535C2semidirect
22. C2×C11×#127C22semidirect
23. C2×C11×#124C22semidirect
24. C2×C11×#121C22semidirect
25. C2×C11×#121C22semidirect
34. C2×#66992C22semidirect
37. C2×#66988C22semidirect
41. #10622844C22semidirect
42. #10622842C22semidirect
43. #10622836C22semidirect
44. #10622836C22semidirect
45. #10622836C22semidirect
46. #10622836C22semidirect
47. #10622835C22semidirect
48. #10622835C22semidirect
51. #10622833C22semidirect
52. #10622833C22semidirect
53. #10622833C22semidirect
54. #10622833C22semidirect
55. #10622826C22semidirect
58. #10622823C22semidirect
59. #10622606C22semidirect
60. #10622605C22semidirect
61. #10622595C22semidirect
62. #10622593C22semidirect
63. #10622572C22semidirect
64. #10622572C22semidirect
65. #10622572C22semidirect
66. #10622571C22semidirect
68. #10622565C22semidirect
71. #10622559C22semidirect
73. #10622556C22semidirect
74. #10622555C22semidirect
75. #10622553C22semidirect
76. #10622546C22semidirect
84. C22×D4×C11D4semidirect
270. C2×#535D11semidirect
371. C2×#127C2×D11semidirect
372. C2×#124C2×D11semidirect
379. C2×#121C2×D11semidirect
380. C2×#121C2×D11semidirect
481. C22×D4C22⋊D11semidirect
668. C11#36704semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
#130769062
#130750462
#130750162
#130748762
#130748462
#130743302
#130728992
#130728862
#130720132
#130719912
#130719472
#130719312
#130711942
C2×C11×#5352
#3670411