Finite Group Databasebeta

← #14960788

Subgroups — #14960788

Order 2816.

2970 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623136C211yesmaximal, characteristic, complemented
2C22×#66939C211yesmaximal, characteristic, complemented
3#13076896C212yesmaximal, complemented
4#13075303C214yesmaximal, complemented
5#13075299C214yesmaximal, complemented
6#13074936C214yesmaximal, complemented
7#13074934C214yesmaximal, complemented
8#13074362C212yesmaximal, complemented
9#13073547C211yesmaximal, characteristic, complemented
10#13073109C211yesmaximal, characteristic, complemented
11#13073108C211yesmaximal, characteristic, complemented
12#13071940C212yesmaximal, complemented
13#13071927C212yesmaximal, complemented
14#13071211C211yesmaximal, characteristic, complemented
15C11×#2539C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic, complemented
18C22×D4×D11C2212yes—
19C2×C11×#123C2212yescomplemented
20C2×C11×#121C2211yescharacteristic
21C2×C11×#120C2212yescomplemented
22C22×C11×C22⋊C4C2211yescharacteristic, complemented
23C2×#67006C2212yescomplemented
24C2×#66992C2212yes—
25C2×#66992C2214yescomplemented
26C2×#66990C2212yescomplemented
27C2×#66990C2214yescomplemented
28C2×#66983C2211yescharacteristic
29C2×#66982C2212yescomplemented
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic, complemented
33C22×C4⋊Dic11C2211yescharacteristic, complemented
34#10623136—28no—
35C2×#66947C2212yescomplemented
36C2×#66939—28no—
37C2×#66939C2214yescomplemented
38C2×#66939C2214yescomplemented
39C2×#66936C2212yescomplemented
40C2×#66935C2212yescomplemented
41C11×#399C2212yescomplemented
42C11×#392C2212yescomplemented
43C11×#390C2214yescomplemented
44C4×C11×C22⋊C4C2211yescharacteristic, complemented
45#10622836C2214yes—
46#10622834C2212yescomplemented
47#10622833C2212yescomplemented
48#10622833C2212yescomplemented
49#10622833C2214yescomplemented
50C4×C22⋊Dic11C2211yescharacteristic, complemented
51#10622607C2214yescomplemented
52#10622604C2214yescomplemented
53#10622602C2214yescomplemented
54#10622597C2214yescomplemented
55#10622590C2212yescomplemented
56#10622574C2214yescomplemented
57#10622573C2214yes—
58#10622573C2212yescomplemented
59#10622572C2214yescomplemented
60#10622571C2212yescomplemented
61#10622571C2212yescomplemented
62#10622571C2214yescomplemented
63#10622570C2214yescomplemented
64#10622569C2214yescomplemented
65#10622568C2212yes—
66#10622568C2214yescomplemented
67#10622566C2214yescomplemented
68#10622562C2212yescomplemented
69#10622561C2214yescomplemented
70#10622555C2214yescomplemented
71#10622555C2212yescomplemented
72#10622553C2214yescomplemented
73#10622552C2212yescomplemented
74#10622549C2212yescomplemented
75#10622287C2214yescomplemented
76#10622282C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2312yes—
80C22×D4×C11C2312yes—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—24no—
86C22×C22⋊D11—44no—
87C22×C22⋊D11C2312yes—
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2312yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11—24no—
93C23×Dic11—44no—
94C23×Dic11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C2×D4×D11—28no—
99C2×D4×D11—44no—
100C2×D4×D11—44no—
101C22×D44C2311yescharacteristic
102C22×D44C2312yes—
103C22×C4×D11C2312yes—
104C11×#123—44no—
105C11×#121—24no—
106C11×#120—44no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C42×C11C2312yes—
117#67006—44no—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123#66992—28no—
124#66992—48no—
125#66990—28no—
126#66990—48no—
127#66983—24no—
128#66982—44no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4D418yescomplemented
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11—24no—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11C2312yes—
151#66947—28no—
152#66939—216no—
153#66939—216no—
154#66936—28no—
155#66935—28no—
156C11×#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163#36721—111nomaximal, Sylow
164C24×C11—22no—
165C24×C11—24no—
166C24×C11—24no—
167C24×C11—42no—
168C24×C11C2412yes—
169C24×C11C2412yes—
170C24×C11C2411yescharacteristic
171C23×D11—24no—
172C23×D11—24no—
173C23×D11—42no—
174C23×D11—42no—
175C23×D11—42no—
176C23×D11—42no—
177C23×D11—44no—
178C23×D11—44no—
179C23×D11C2×D414yes—
180C23×D11C2412yes—
181C23×D11C2412yes—
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—28no—
186C2×D4×C11—22no—
187C2×D4×C11—44no—
188C2×D4×C11—42no—
189C2×D4×C11—44no—
190C22×C4×C11—22no—
191C22×C4×C11—24no—
192C22×C4×C11—42no—
193C22×C4×C11C2×D414yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2414yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—28no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—28no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—416no—
214C22×Dic11—28no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—28no—
218C22×Dic11—42no—
219C22×Dic11—42no—
220C22×Dic11—44no—
221C22×Dic11—42no—
222C22×Dic11—416no—
223C22×Dic11C2×D414yes—
224C22×Dic11C2414yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229D4×D11—432no—
230C2×D44—24no—
231C2×D44—22no—
232C2×D44—42no—
233C2×D44—42no—
234C2×D44—42no—
235C2×C4×D11—24no—
236C2×C4×D11—42no—
237C2×C4×D11—42no—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—44no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—44no—
245C11×C22⋊C4—44no—
246C42×C11—42no—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249C22⋊Dic11—44no—
250C22⋊Dic11—44no—
251C22⋊Dic11—44no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257(C2×D11)⋊C4—44no—
258(C2×D11)⋊C4—44no—
259(C2×D11)⋊C4—44no—
260(C2×D11)⋊C4C2×D418yes—
261(C2×D11)⋊C4C2×D418yes—
262C4⋊Dic11—28no—
263C4⋊Dic11—22no—
264C4⋊Dic11—24no—
265C4⋊Dic11—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—44no—
268Dic11⋊C4—44no—
269C4×Dic11—42no—
270C2×#534—111no—
271C22×#123—111no—
272#2847—112no—
273#2706—114no—
274#2706—114no—
275#2678—114no—
276#2678—114no—
277#2618—112no—
278#2539—111no—
279#2539D1111yescharacteristic, complemented
280#2504—111no—
281#2504—111no—
282#2405—112no—
283#2403—112no—
284#2312—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—24no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—24no—
297C23×C11—416no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11C22×D412yes—
301C23×C11H(5,𝔽2)14yes—
302C23×C11H(5,𝔽2)14yes—
303C23×C11C2511yescharacteristic
304C22×D11—24no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—24no—
308C22×D11—28no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—24no—
312C22×D11—22no—
313C22×D11—24no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—48no—
317C22×D11—84no—
318C22×D11—84no—
319C22×D11—88no—
320C22×D11—88no—
321C22×D11—88no—
322C22×D11C22×D414yes—
323D4×C11—48no—
324D4×C11—82no—
325D4×C11—88no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—24no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—44no—
337C2×C4×C11—44no—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C22⋊D11—416no—
341C22⋊D11—48no—
342C22⋊D11—48no—
343C22⋊D11—84no—
344C22⋊D11—88no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—22no—
355C2×Dic11—24no—
356C2×Dic11—44no—
357C2×Dic11—416no—
358C2×Dic11—44no—
359C2×Dic11—44no—
360C2×Dic11C22×D414yes—
361D44—48no—
362D44—82no—
363C4×D11—48no—
364C23×D4—111no—
365C23×D4—112no—
366C24×C4—111no—
367#534—228no—
368C2×#123—112no—
369C2×#123—112no—
370C2×#123—112no—
371C2×#123—114no—
372C2×#123—114no—
373C2×#123—228no—
374C2×#123C2×D1112yescomplemented
375C2×#121—112no—
376C2×#121—111no—
377C2×#121—114no—
378C2×#121C2×D1111yescharacteristic
379C2×#120—112no—
380C2×#120—112no—
381C2×#120—114no—
382C2×#120—112no—
383C2×#120C2×D1112yescomplemented
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4C2×D1111yescharacteristic, complemented
389#399—112no—
390#399C2×D1112yescomplemented
391#398—114no—
392#397—114no—
393#397—114no—
394#396—114no—
395#396—114no—
396#394—114no—
397#394—114no—
398#394—114no—
399#392—114no—
400#392—114no—
401#392—112no—
402#392C2×D1112yescomplemented
403#390—112no—
404#390—114no—
405#390—112no—
406#390C2×D1114yescomplemented
407#388—114no—
408#388—114no—
409#386—112no—
410#386—114no—
411#386—112no—
412#386—112no—
413#386—114no—
414#386—112no—
415#386—114no—
416#385—114no—
417#382—112no—
418#382—112no—
419#380—112no—
420#380—114no—
421#379—112no—
422#379—114no—
423C4×C22⋊C4—111no—
424C4×C22⋊C4C2×D1111yescharacteristic, complemented
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—28no—
428C22×C11—24no—
429C22×C11—28no—
430C22×C11—416no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—44no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—44no—
438C22×C11—44no—
439C22×C11#53514yes—
440C22×C11C23×D411yescharacteristic
441C22×C11C2×H(5,𝔽2)12yes—
442C22×C11C2×H(5,𝔽2)12yes—
443C22×C11#58512yes—
444C2×D11—24no—
445C2×D11—24no—
446C2×D11—24no—
447C2×D11—44no—
448C2×D11—44no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—44no—
453C2×D11—44no—
454C2×D11—88no—
455C2×D11—816no—
456C4×C11—22no—
457C4×C11—22no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11—44no—
461Dic11—24no—
462Dic11—42no—
463Dic11—42no—
464Dic11—42no—
465Dic11—44no—
466C25—111no—
467C25—112no—
468C25C22×D1111yescharacteristic
469C22×D4—112no—
470C22×D4—114no—
471C22×D4—112no—
472C22×D4—114no—
473C22×D4—112no—
474C22×D4—111no—
475C22×D4—112no—
476C22×D4—228no—
477C22×D4—224no—
478C22×D4—444no—
479C22×D4—444no—
480C22×D4—444no—
481C22×D4C22×D1112yes—
482C22×D4C22×D1111yescharacteristic
483C22×D4C22×D1114yes—
484C23×C4—111no—
485C23×C4—114no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—112no—
489C23×C4—224no—
490C23×C4—444no—
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493#123—44no—
494#123—2216no—
495#123—2216no—
496#123—228no—
497#123—228no—
498#123—444no—
499#121—24no—
500#121—228no—
501#121—224no—
502#121—448no—
503#120—44no—
504#120—228no—
505#120—228no—
506#120—444no—
507#120—448no—
508C2×C4⋊C4—112no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—112no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—224no—
516C2×C4⋊C4—224no—
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C4⋊C4C22×D1114yes—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—112no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—112no—
527C2×C22⋊C4—112no—
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—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—224no—
537C2×C22⋊C4C22×D1112yes—
538C2×C22⋊C4C22×D1112yes—
539C2×C22⋊C4C22×D1112yes—
540C2×C22⋊C4C22×D1112yes—
541C2×C22⋊C4C22×D1114yes—
542C2×C22⋊C4C22×D1114yes—
543C2×C42—112no—
544C2×C42C22×D1112yes—
545#95—112no—
546#95—114no—
547#95—114no—
548#95—114no—
549#95—114no—
550#95—114no—
551#95C22×D1112yes—
552C2×C11—24no—
553C2×C11—44no—
554C2×C11—82no—
555C2×C11C2×#53511yescharacteristic
556C2×C11#348411yescharacteristic
557C2×C11#348511yescharacteristic
558C2×C11#353414yes—
559D11—44no—
560D11—82no—
561C24—22no—
562C24—24no—
563C24—24no—
564C24—42no—
565C24—112no—
566C24—114no—
567C24—112no—
568C24—224no—
569C24—224no—
570C24—442no—
571C24—442no—
572C24—442no—
573C24—442no—
574C24—444no—
575C24—444no—
576C24C23×D1112yes—
577C24C23×D1112yes—
578C24C23×D1111yescharacteristic
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—28no—
583C2×D4—22no—
584C2×D4—44no—
585C2×D4—42no—
586C2×D4—44no—
587C2×D4—224no—
588C2×D4—224no—
589C2×D4—224no—
590C2×D4—228no—
591C2×D4—224no—
592C2×D4—224no—
593C2×D4—224no—
594C2×D4—228no—
595C2×D4—228no—
596C2×D4—222no—
597C2×D4—442no—
598C2×D4—442no—
599C2×D4—442no—
600C2×D4—442no—
601C2×D4—442no—
602C2×D4—444no—
603C2×D4—444no—
604C2×D4—444no—
605C2×D4—444no—
606C2×D4—4432no—
607C2×D4—4416no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—42no—
611C22×C4—112no—
612C22×C4—114no—
613C22×C4—114no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—112no—
617C22×C4—224no—
618C22×C4—228no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—228no—
622C22×C4—442no—
623C22×C4—442no—
624C22×C4—442no—
625C22×C4—444no—
626C22×C4—442no—
627C22×C4—442no—
628C22×C4—4416no—
629C22×C4D4×D1114yes—
630C22×C4C23×D1112yes—
631C22×C4C23×D1114yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1111yescharacteristic
634C22×C4C23×D1111yescharacteristic
635C4⋊C4—22no—
636C4⋊C4—44no—
637C4⋊C4—228no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—222no—
642C4⋊C4—444no—
643C4⋊C4—444no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—118no—
651C22⋊C4—118no—
652C22⋊C4—224no—
653C22⋊C4—228no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—444no—
658C22⋊C4—444no—
659C22⋊C4—444no—
660C22⋊C4—444no—
661C22⋊C4—444no—
662C22⋊C4—444no—
663C22⋊C4—444no—
664C22⋊C4—444no—
665C42—42no—
666C42—442no—
667C11#3672111yescharacteristic, complemented, Sylow
668C23—22no—
669C23—22no—
670C23—28no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—416no—
681C23—44no—
682C23—44no—
683C23—114no—
684C23—222no—
685C23—222no—
686C23—224no—
687C23—224no—
688C23—228no—
689C23—222no—
690C23—222no—
691C23—222no—
692C23—224no—
693C23—224no—
694C23—444no—
695C23—444no—
696C23—448no—
697C23—888no—
698C23—884no—
699C23—884no—
700C23—888no—
701C23—888no—
702C23C2×D4×D1112yes—
703C23#6703714yes—
704C23#6704214yes—
705C23C24×D1111yescharacteristic
706D4—48no—
707D4—82no—
708D4—88no—
709D4—448no—
710D4—4416no—
711D4—448no—
712D4—448no—
713D4—882no—
714D4—884no—
715D4—888no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—114no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—448no—
741C2×C4—444no—
742C2×C4—4416no—
743C2×C4—444no—
744C2×C4—444no—
745C2×C4C2×D4×D1112yes—
746C2×C4C2×D4×D1112yes—
747C22—22no—
748C22—22no—
749C22—28no—
750C22—24no—
751C22—28no—
752C22—416no—
753C22—42no—
754C22—42no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—44no—
760C22—44no—
761C22—224no—
762C22—224no—
763C22—224no—
764C22—444no—
765C22—444no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—444no—
770C22—444no—
771C22—888no—
772C22—8816no—
773C22#1062324614yes—
774C22C22×D4×D1111yescharacteristic
775C22C2×#6703712yes—
776C22C2×#6704212yes—
777C22#1062345512yes—
778C4—22no—
779C4—22no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—224no—
784C4—442no—
785C4—442no—
786C4—442no—
787C4—444no—
788C2—24no—
789C2—44no—
790C2—82no—
791C2—444no—
792C2—882no—
793C2C2×#1062324611yescharacteristic
794C2#1308224911yescharacteristic
795C2#1308225711yescharacteristic
796C2#1308280214yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2539C2
hypercenter#2539D11
hypocenterC11#36721
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#10623136C2semidirect
2. C22×#66939C2semidirect
3. #13076896C2semidirect
4. #13075303C2semidirect
5. #13075299C2semidirect
6. #13074936C2semidirect
7. #13074934C2semidirect
8. #13074362C2semidirect
9. #13073547C2semidirect
10. #13073109C2semidirect
11. #13073108C2semidirect
12. #13071940C2semidirect
13. #13071927C2semidirect
14. #13071211C2semidirect
15. C11×#2539C2semidirect
17. C24×Dic11C22semidirect
19. C2×C11×#123C22semidirect
21. C2×C11×#120C22semidirect
22. C22×C11×C22⋊C4C22semidirect
23. C2×#67006C22semidirect
25. C2×#66992C22semidirect
26. C2×#66990C22semidirect
27. C2×#66990C22semidirect
29. C2×#66982C22semidirect
32. C22×C4⋊Dic11C22semidirect
33. C22×C4⋊Dic11C22semidirect
35. C2×#66947C22semidirect
37. C2×#66939C22semidirect
38. C2×#66939C22semidirect
39. C2×#66936C22semidirect
40. C2×#66935C22semidirect
41. C11×#399C22semidirect
42. C11×#392C22semidirect
43. C11×#390C22semidirect
44. C4×C11×C22⋊C4C22semidirect
46. #10622834C22semidirect
47. #10622833C22semidirect
48. #10622833C22semidirect
49. #10622833C22semidirect
50. C4×C22⋊Dic11C22semidirect
51. #10622607C22semidirect
52. #10622604C22semidirect
53. #10622602C22semidirect
54. #10622597C22semidirect
55. #10622590C22semidirect
56. #10622574C22semidirect
58. #10622573C22semidirect
59. #10622572C22semidirect
60. #10622571C22semidirect
61. #10622571C22semidirect
62. #10622571C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
66. #10622568C22semidirect
67. #10622566C22semidirect
68. #10622562C22semidirect
69. #10622561C22semidirect
70. #10622555C22semidirect
71. #10622555C22semidirect
72. #10622553C22semidirect
73. #10622552C22semidirect
74. #10622549C22semidirect
75. #10622287C22semidirect
76. #10622282C22semidirect
130. C2×(C2×D11)⋊C4D4semidirect
279. #2539D11semidirect
374. C2×#123C2×D11semidirect
383. C2×#120C2×D11semidirect
388. C22×C22⋊C4C2×D11semidirect
390. #399C2×D11semidirect
402. #392C2×D11semidirect
406. #390C2×D11semidirect
424. C4×C22⋊C4C2×D11semidirect
667. C11#36721semidirect

Maximal subgroups

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

subgroupindex
C2×#106231362
C22×#669392
#130768962
#130753032
#130752992
#130749362
#130749342
#130743622
#130735472
#130731092
#130731082
#130719402
#130719272
#130712112
C11×#25392
#3672111