Finite Group Databasebeta

← #14926407

Subgroups — #14926407

Order 2816.

4082 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C211yesmaximal, characteristic, complemented
2#13076903C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13076893C212yesmaximal, complemented
5#13074421C211yesmaximal, characteristic, complemented
6#13074389C212yesmaximal, complemented
7#13074350C211yesmaximal, characteristic, complemented
8#13072856C214yesmaximal, complemented
9#13072736C214yesmaximal, complemented
10#13072152C214yesmaximal, complemented
11#13072078C214yesmaximal, complemented
12#13071274C212yesmaximal, complemented
13#13071214C211yesmaximal, characteristic, complemented
14C4×#67006C212yesmaximal, complemented
15C23×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C26×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—28no—
20C22×C11×C22⋊C4C2214yes—
21C22×C11×C22⋊C4C2214yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C2×#67006C2212yes—
29C2×#67006C2214yes—
30C2×#67006C2214yes—
31C2×#66983C2211yescharacteristic, complemented
32C2×#66983C2212yescomplemented
33C2×C4×C22⋊D11C2212yescomplemented
34C2×C4×C22⋊D11C2214yescomplemented
35C2×#66977C2211yescharacteristic, complemented
36C2×#66977C2212yescomplemented
37#10623025—28no—
38C2×#66938C2212yescomplemented
39C2×#66937C2212yescomplemented
40C2×#66936C2212yescomplemented
41C2×#66932C2212yescomplemented
42#10622860C2212yes—
43#10622860C2214yes—
44#10622860C2212yes—
45#10622860C2212yes—
46#10622860C2214yes—
47#10622826C2214yescomplemented
48#10622826C2212yescomplemented
49#10622826C2214yescomplemented
50#10622826C2212yescomplemented
51#10622825C2211yescharacteristic, complemented
52#10622825C2211yescharacteristic, complemented
53#10622825C2212yescomplemented
54#10622825C2212yescomplemented
55#10622823C2214yescomplemented
56#10622823C2212yescomplemented
57#10622823C2214yescomplemented
58#10622823C2212yescomplemented
59C4×C22⋊Dic11C2214yescomplemented
60C4×C22⋊Dic11C2212yescomplemented
61#10622574C2214yescomplemented
62#10622573C2212yescomplemented
63#10622572C2214yescomplemented
64#10622572C2214yescomplemented
65#10622570C2214yescomplemented
66#10622569C2214yescomplemented
67#10622566C2212yescomplemented
68#10622565C2214yescomplemented
69#10622565C2214yescomplemented
70#10622564C2214yescomplemented
71#10622564C2214yescomplemented
72#10622562C2212yescomplemented
73#10622561C2214yescomplemented
74#10622560C2212yescomplemented
75#10622558C2214yescomplemented
76#10622557C2214yescomplemented
77C25×C11—24no—
78C25×C11—24no—
79C25×C11—24no—
80C25×C11—44no—
81C25×C11—44no—
82C25×C11C2311yescharacteristic
83C25×C11C2314yes—
84C25×C11C2311yescharacteristic
85C25×C11C2311yescharacteristic
86C23×C4×C11—24no—
87C23×C4×C11—24no—
88C23×C4×C11—44no—
89C23×C4×C11—44no—
90C23×C4×C11C2312yes—
91C23×C4×C11C2314yes—
92C23×C4×C11C2312yes—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2312yes—
100C22×C22⋊D11C2312yes—
101C22×C22⋊D11C2314yes—
102C22×D44C2311yescharacteristic, complemented
103C22×C4×D11C2312yescomplemented
104C22×Dic22C2311yescharacteristic, complemented
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—216no—
109C2×C11×C22⋊C4—216no—
110C2×C11×C22⋊C4D418yescomplemented
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117#67006—28no—
118#67006—28no—
119#67006—28no—
120#67006—48no—
121#67006—48no—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135#66983—24no—
136#66983—44no—
137C4×C22⋊D11—28no—
138C4×C22⋊D11—48no—
139C2×(C2×D11)⋊C4C2312yescomplemented
140C2×(C2×D11)⋊C4C2312yescomplemented
141C2×(C2×D11)⋊C4C2314yescomplemented
142C2×(C2×D11)⋊C4C2314yescomplemented
143C2×C4⋊Dic11C2311yescharacteristic, complemented
144C2×C4⋊Dic11C2311yescharacteristic, complemented
145C2×C4⋊Dic11C2312yescomplemented
146C2×C4⋊Dic11C2312yescomplemented
147#66977—24no—
148#66977—44no—
149C2×Dic11⋊C4C2312yescomplemented
150C2×Dic11⋊C4C2312yescomplemented
151C2×Dic11⋊C4C2314yescomplemented
152C2×Dic11⋊C4C2314yescomplemented
153C2×C4×Dic11C2312yescomplemented
154C2×C4×Dic11C2314yescomplemented
155#66938—28no—
156#66937—28no—
157#66936—28no—
158#66932—28no—
159C11⋊#95C2314yescomplemented
160C11⋊#95C2314yescomplemented
161C11⋊#95C2314yescomplemented
162C11⋊#95C2314yescomplemented
163C11⋊#95C2312yescomplemented
164C11⋊#95C2312yescomplemented
165C11⋊#95C2314yescomplemented
166#34988—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—24no—
170C24×C11—24no—
171C24×C11—232no—
172C24×C11—28no—
173C24×C11—22no—
174C24×C11—28no—
175C24×C11—28no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—28no—
180C24×C11—28no—
181C24×C11—42no—
182C24×C11—42no—
183C24×C11—42no—
184C24×C11—42no—
185C24×C11—44no—
186C24×C11—44no—
187C24×C11—416no—
188C24×C11—416no—
189C24×C11—432no—
190C24×C11—432no—
191C24×C11C2×D414yes—
192C24×C11#4114yes—
193C24×C11#4114yes—
194C24×C11C2412yes—
195C24×C11C2412yes—
196C24×C11C2411yescharacteristic
197C24×C11C2412yes—
198C23×D11C2412yes—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—24no—
202C22×C4×C11—28no—
203C22×C4×C11—24no—
204C22×C4×C11—28no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—42no—
208C22×C4×C11—44no—
209C22×C4×C11—42no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11—42no—
213C22×C4×C11—42no—
214C22×C4×C11—416no—
215C22×C4×C11—416no—
216C22×C4×C11C2×D414yes—
217C22×C4×C11C2×D414yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C22×C4×C11C2411yescharacteristic
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C22×Dic11C2412yes—
237C22×Dic11C2414yes—
238C22×Dic11C2414yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C2×D44—22no—
242C2×D44—42no—
243C2×C4×D11—24no—
244C2×C4×D11—44no—
245C2×Dic22—22no—
246C2×Dic22—42no—
247C11×C22⋊C4—28no—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4C2×D418yes—
252C11×C22⋊C4C2×D418yes—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—28no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—28no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—22no—
271C4⋊Dic11—22no—
272C4⋊Dic11—42no—
273C4⋊Dic11—42no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278C4×Dic11—24no—
279C4×Dic11—44no—
280C2×#538—111no—
281C23×C22⋊C4D1111yescharacteristic, complemented
282#2848—111no—
283#2847—111no—
284#2846—112no—
285#2626—111no—
286#2622—112no—
287#2617—111no—
288#2480—114no—
289#2472—114no—
290#2424—114no—
291#2418—114no—
292#2321—112no—
293#2312—111no—
294C4×#120—112no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—216no—
298C23×C11—28no—
299C23×C11—216no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—232no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—24no—
314C23×C11—24no—
315C23×C11—24no—
316C23×C11—24no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—48no—
320C23×C11—416no—
321C23×C11—416no—
322C23×C11—416no—
323C23×C11—416no—
324C23×C11—4128no—
325C23×C11—48no—
326C23×C11—48no—
327C23×C11—416no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—48no—
331C23×C11—416no—
332C23×C11C22×D414yes—
333C23×C11C22×D412yes—
334C23×C11C2×#4114yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11C2×#4114yes—
338C23×C11H(5,𝔽2)14yes—
339C23×C11H(5,𝔽2)14yes—
340C23×C11C2511yescharacteristic
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—24no—
345C22×D11—24no—
346C2×C4×C11—24no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—24no—
353C2×C4×C11—22no—
354C2×C4×C11—44no—
355C2×C4×C11—44no—
356C2×C4×C11—48no—
357C2×C4×C11—416no—
358C2×C4×C11—48no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D412yes—
364C22⋊D11—48no—
365C22⋊D11—416no—
366C22⋊D11—84no—
367C22⋊D11—84no—
368C22⋊D11—88no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—24no—
377C2×Dic11—24no—
378C2×Dic11—24no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—24no—
382D44—82no—
383C4×D11—84no—
384Dic22—82no—
385C26C2×D1111yescharacteristic
386C24×C4C2×D1111yescharacteristic
387C24×C4C2×D1111yescharacteristic
388#538—228no—
389C2×#126—112no—
390C2×#124—112no—
391C2×#123—112no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—112no—
394C2×#121—111no—
395C2×#121—112no—
396C2×#121—112no—
397C2×#120—112no—
398C2×#120—112no—
399C2×#120—112no—
400C2×#120—114no—
401C2×#120—114no—
402C2×C4×D4—112no—
403C2×C4×D4—114no—
404C22×C22⋊C4—28no—
405C22×C22⋊C4C2×D1111yescharacteristic
406C22×C22⋊C4C2×D1111yescharacteristic
407C22×C22⋊C4C2×D1111yescharacteristic
408C22×C22⋊C4C2×D1114yes—
409C22×C22⋊C4C2×D1114yes—
410C22×C22⋊C4C2×D1111yescharacteristic
411#399—112no—
412#397—112no—
413#397—114no—
414#397—114no—
415#396—114no—
416#394—114no—
417#394—114no—
418#394—114no—
419#393—112no—
420#392—112no—
421#390—114no—
422#388—114no—
423#388—114no—
424#388—114no—
425#388—114no—
426#386—112no—
427#386—114no—
428#386—112no—
429#386—114no—
430#386—114no—
431#385—112no—
432#385—114no—
433#385—112no—
434#385—114no—
435#380—111no—
436#380—111no—
437#380—112no—
438#380—112no—
439#379—112no—
440#379—112no—
441#379—112no—
442#379—114no—
443#379—114no—
444C4×C22⋊C4—112no—
445C4×C22⋊C4—114no—
446C22×C11—232no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—24no—
453C22×C11—24no—
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—28no—
462C22×C11—416no—
463C22×C11—416no—
464C22×C11—464no—
465C22×C11—44no—
466C22×C11—44no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—44no—
470C22×C11#52514yes—
471C22×C11#53818yescomplemented
472C22×C11C23×D411yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C22×#4111yescharacteristic
475C22×C11C2×H(5,𝔽2)12yes—
476C22×C11C2×H(5,𝔽2)12yes—
477C2×D11—42no—
478C2×D11—44no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—44no—
482C4×C11—22no—
483C4×C11—24no—
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—42no—
487Dic11—42no—
488Dic11—44no—
489Dic11—42no—
490Dic11—42no—
491Dic11—44no—
492C25—24no—
493C25—24no—
494C25—24no—
495C25—44no—
496C25—44no—
497C25C22×D1111yescharacteristic
498C25C22×D1114yes—
499C25C22×D1111yescharacteristic
500C25C22×D1111yescharacteristic
501C22×Q8—111no—
502C22×D4—112no—
503C22×D4—114no—
504C22×D4—112no—
505C22×D4—112no—
506C22×D4—114no—
507C22×D4—111no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—44no—
511C23×C4—44no—
512C23×C4—112no—
513C23×C4C22×D1114yes—
514C23×C4C22×D1112yes—
515C23×C4C22×D1112yes—
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520#126—228no—
521#124—228no—
522#123—228no—
523C22⋊Q8—224no—
524C22⋊Q8—444no—
525#121—224no—
526#121—228no—
527#121—444no—
528#120—228no—
529#120—228no—
530#120—228no—
531#120—448no—
532#120—448no—
533C4×D4—228no—
534C4×D4—448no—
535C2×C4⋊C4—112no—
536C2×C4⋊C4—112no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—114no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—216no—
547C2×C22⋊C4—216no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4C22⋊D1118yescomplemented
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1112yes—
568C2×C22⋊C4C22×D1112yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C22⋊C4C22×D1112yes—
571C2×C22⋊C4C22×D1112yes—
572C2×C42—112no—
573C2×C42—114no—
574#95—114no—
575#95—114no—
576#95—114no—
577#95—114no—
578#95—112no—
579#95—112no—
580#95—114no—
581C2×C11—24no—
582C2×C11—28no—
583C2×C11—44no—
584C2×C11—44no—
585C2×C11C2×#52511yescharacteristic
586C2×C11C2×#53812yes—
587C2×C11#348411yescharacteristic
588C2×C11#348411yescharacteristic
589C2×C11#349012yes—
590D11—82no—
591C24—22no—
592C24—24no—
593C24—24no—
594C24—22no—
595C24—232no—
596C24—28no—
597C24—28no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—28no—
602C24—22no—
603C24—28no—
604C24—28no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—44no—
610C24—44no—
611C24—416no—
612C24—416no—
613C24—432no—
614C24—432no—
615C24—112no—
616C24#433914yes—
617C24#433914yes—
618C24C2×C22⋊D1114yes—
619C24C23×D1112yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C24C23×D1112yes—
623C2×Q8—222no—
624C2×Q8—442no—
625C2×D4—228no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—224no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—222no—
635C2×D4—442no—
636C2×D4—444no—
637C2×D4—444no—
638C2×D4—444no—
639C2×D4—444no—
640C22×C4—28no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—28no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—42no—
649C22×C4—44no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—416no—
656C22×C4—416no—
657C22×C4—112no—
658C22×C4—114no—
659C22×C4—114no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—224no—
663C22×C4—444no—
664C22×C4C2×C22⋊D1114yes—
665C22×C4C2×C22⋊D1114yes—
666C22×C4C23×D1112yes—
667C22×C4C23×D1112yes—
668C22×C4C23×D1112yes—
669C22×C4C23×D1111yescharacteristic
670C22×C4C23×D1111yescharacteristic
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—222no—
674C4⋊C4—222no—
675C4⋊C4—444no—
676C4⋊C4—442no—
677C4⋊C4—444no—
678C4⋊C4—442no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—228no—
684C22⋊C4—228no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—228no—
688C22⋊C4—228no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—444no—
695C22⋊C4—444no—
696C22⋊C4—444no—
697C22⋊C4—444no—
698C22⋊C4—444no—
699C22⋊C4—444no—
700C22⋊C4C2×C22⋊D1118yes—
701C22⋊C4C2×C22⋊D1118yes—
702C42—224no—
703C42—444no—
704C11#3498811yescharacteristic, complemented, Sylow
705C23—28no—
706C23—28no—
707C23—216no—
708C23—216no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—232no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—48no—
728C23—44no—
729C23—44no—
730C23—416no—
731C23—416no—
732C23—416no—
733C23—416no—
734C23—4128no—
735C23—416no—
736C23—48no—
737C23—48no—
738C23—44no—
739C23—44no—
740C23—48no—
741C23—416no—
742C23—222no—
743C23—222no—
744C23—224no—
745C23—224no—
746C23—222no—
747C23C2×#433914yes—
748C23C2×#433914yes—
749C23C2×#433912yes—
750C23C2×#433912yes—
751C23#6703714yes—
752C23#6703714yes—
753C23C22×C22⋊D1114yes—
754C23C22×C22⋊D1112yes—
755C23C24×D1111yescharacteristic
756Q8—882no—
757D4—4416no—
758D4—448no—
759D4—882no—
760D4—884no—
761D4—884no—
762D4—888no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—416no—
774C2×C4—48no—
775C2×C4—48no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—224no—
781C2×C4—224no—
782C2×C4—224no—
783C2×C4—224no—
784C2×C4—224no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—224no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—884no—
792C2×C4C22×C22⋊D1114yes—
793C2×C4C22×C22⋊D1112yes—
794C2×C4C22×C22⋊D1112yes—
795C22—232no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—22no—
802C22—22no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—28no—
811C22—464no—
812C22—416no—
813C22—416no—
814C22—44no—
815C22—44no—
816C22—42no—
817C22—42no—
818C22—44no—
819C22—442no—
820C22—444no—
821C22—442no—
822C22—442no—
823C22—444no—
824C22#1062302518yescomplemented
825C22#1062332214yes—
826C22C22×#433911yescharacteristic
827C22C22×#433911yescharacteristic
828C22C2×#6703712yes—
829C22C2×#6703712yes—
830C22C23×C22⋊D1111yescharacteristic
831C4—24no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—442no—
837C4—444no—
838C4—442no—
839C4—442no—
840C4—444no—
841C2—28no—
842C2—24no—
843C2—44no—
844C2—44no—
845C2—882no—
846C2C2×#1062332211yescharacteristic
847C2C2×#1062302512yes—
848C2#1308225111yescharacteristic
849C2#1308225111yescharacteristic
850C2#1308230512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC23×C11×C22⋊C4C2
hypercenterC23×C22⋊C4D11
hypocenterC11#34988
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10623025C2semidirect
2. #13076903C2semidirect
3. #13076898C2semidirect
4. #13076893C2semidirect
5. #13074421C2semidirect
6. #13074389C2semidirect
7. #13074350C2semidirect
8. #13072856C2semidirect
9. #13072736C2semidirect
10. #13072152C2semidirect
11. #13072078C2semidirect
12. #13071274C2semidirect
13. #13071214C2semidirect
14. C4×#67006C2semidirect
15. C23×C11×C22⋊C4C2semidirect
31. C2×#66983C22semidirect
32. C2×#66983C22semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
35. C2×#66977C22semidirect
36. C2×#66977C22semidirect
38. C2×#66938C22semidirect
39. C2×#66937C22semidirect
40. C2×#66936C22semidirect
41. C2×#66932C22semidirect
47. #10622826C22semidirect
48. #10622826C22semidirect
49. #10622826C22semidirect
50. #10622826C22semidirect
51. #10622825C22semidirect
52. #10622825C22semidirect
53. #10622825C22semidirect
54. #10622825C22semidirect
55. #10622823C22semidirect
56. #10622823C22semidirect
57. #10622823C22semidirect
58. #10622823C22semidirect
59. C4×C22⋊Dic11C22semidirect
60. C4×C22⋊Dic11C22semidirect
61. #10622574C22semidirect
62. #10622573C22semidirect
63. #10622572C22semidirect
64. #10622572C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622566C22semidirect
68. #10622565C22semidirect
69. #10622565C22semidirect
70. #10622564C22semidirect
71. #10622564C22semidirect
72. #10622562C22semidirect
73. #10622561C22semidirect
74. #10622560C22semidirect
75. #10622558C22semidirect
76. #10622557C22semidirect
102. C22×D44C23semidirect
103. C22×C4×D11C23semidirect
104. C22×Dic22C23semidirect
110. C2×C11×C22⋊C4D4semidirect
139. C2×(C2×D11)⋊C4C23semidirect
140. C2×(C2×D11)⋊C4C23semidirect
141. C2×(C2×D11)⋊C4C23semidirect
142. C2×(C2×D11)⋊C4C23semidirect
143. C2×C4⋊Dic11C23semidirect
144. C2×C4⋊Dic11C23semidirect
145. C2×C4⋊Dic11C23semidirect
146. C2×C4⋊Dic11C23semidirect
149. C2×Dic11⋊C4C23semidirect
150. C2×Dic11⋊C4C23semidirect
151. C2×Dic11⋊C4C23semidirect
152. C2×Dic11⋊C4C23semidirect
153. C2×C4×Dic11C23semidirect
154. C2×C4×Dic11C23semidirect
159. C11⋊#95C23semidirect
160. C11⋊#95C23semidirect
161. C11⋊#95C23semidirect
162. C11⋊#95C23semidirect
163. C11⋊#95C23semidirect
164. C11⋊#95C23semidirect
165. C11⋊#95C23semidirect
281. C23×C22⋊C4D11semidirect
471. C22×C11#538semidirect
565. C2×C22⋊C4C22⋊D11semidirect
704. C11#34988semidirect
824. C22#10623025semidirect

Maximal subgroups

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

subgroupindex
C2×#106230252
#130769032
#130768982
#130768932
#130744212
#130743892
#130743502
#130728562
#130727362
#130721522
#130720782
#130712742
#130712142
C4×#670062
C23×C11×C22⋊C42
#3498811