Finite Group Databasebeta

← #14926377

Subgroups — #14926377

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C211yesmaximal, characteristic, complemented
2#13076955C211yesmaximal, characteristic, complemented
3#13076947C211yesmaximal, characteristic, complemented
4#13076908C212yesmaximal, complemented
5#13074421C211yesmaximal, characteristic, complemented
6#13074350C211yesmaximal, characteristic, complemented
7#13074328C212yesmaximal, complemented
8#13072646C214yesmaximal, complemented
9#13072547C214yesmaximal, complemented
10#13072508C214yesmaximal, complemented
11#13072493C214yesmaximal, complemented
12#13071285C212yesmaximal, complemented
13#13071214C211yesmaximal, characteristic, complemented
14C4×#67006C212yesmaximal, complemented
15C22×C4×D4×C11C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C2×C4×D4×C11—28no—
20C2×C4×D4×C11C2214yes—
21C2×C4×D4×C11C2214yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C2×#66983C2211yescharacteristic
29C2×#66982C2212yes—
30C2×#66982C2214yescomplemented
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2214yescomplemented
33C2×#66977C2211yescharacteristic
34#10623025—28no—
35C2×#66938C2212yescomplemented
36C2×#66937C2212yescomplemented
37C2×#66936C2212yescomplemented
38C2×#66932C2212yescomplemented
39#10622860C2212yes—
40#10622860C2212yes—
41#10622836C2214yes—
42#10622836C2214yes—
43#10622835C2214yes—
44#10622835C2214yes—
45#10622826C2212yes—
46#10622826C2212yes—
47#10622826C2214yescomplemented
48#10622826C2214yescomplemented
49#10622825C2211yescharacteristic
50#10622825C2211yescharacteristic
51#10622824C2212yes—
52#10622824C2214yescomplemented
53#10622823C2212yes—
54#10622823C2212yes—
55#10622823C2214yescomplemented
56#10622823C2214yescomplemented
57C4×C22⋊Dic11C2212yes—
58C4×C22⋊Dic11C2214yescomplemented
59#10622603C2214yescomplemented
60#10622602C2214yescomplemented
61#10622591C2214yescomplemented
62#10622585C2214yescomplemented
63#10622574C2214yescomplemented
64#10622573C2212yescomplemented
65#10622566C2212yescomplemented
66#10622564C2214yescomplemented
67#10622564C2214yescomplemented
68#10622562C2212yescomplemented
69#10622561C2214yescomplemented
70#10622560C2212yescomplemented
71#10622553C2214yescomplemented
72#10622552C2212yescomplemented
73#10622546C2214yescomplemented
74#10622542C2212yescomplemented
75#10622541C2212yescomplemented
76#10622541C2212yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11C2314yes—
83C23×C4×C11—24no—
84C23×C4×C11—24no—
85C23×C4×C11—44no—
86C23×C4×C11—44no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2314yes—
89C23×C4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11C2312yes—
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2314yes—
98C22×D44C2311yescharacteristic
99C22×C4×D11C2312yes—
100C22×Dic22C2311yescharacteristic
101C4×D4×C11—216no—
102C4×D4×C11—216no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4D418yescomplemented
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C42×C11—24no—
112C2×C42×C11C2312yes—
113C2×C42×C11C2312yes—
114#67006—28no—
115#67006—28no—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126#66983—24no—
127#66982—28no—
128#66982—48no—
129C4×C22⋊D11—28no—
130C4×C22⋊D11—48no—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2312yes—
140#66977—24no—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2314yes—
148#66938—28no—
149#66937—28no—
150#66936—28no—
151#66932—28no—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161#34986—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11C2×D414yes—
171C24×C11#4114yes—
172C24×C11C2412yes—
173C24×C11C2412yes—
174C24×C11C2411yescharacteristic
175C23×D11C2412yes—
176C2×D4×C11—232no—
177C2×D4×C11—28no—
178C2×D4×C11—28no—
179C2×D4×C11—28no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—24no—
184C22×C4×C11—22no—
185C22×C4×C11—28no—
186C22×C4×C11—28no—
187C22×C4×C11—28no—
188C22×C4×C11—28no—
189C22×C4×C11—42no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—416no—
195C22×C4×C11—416no—
196C22×C4×C11C2×D414yes—
197C22×C4×C11C2×D414yes—
198C22×C4×C11#4114yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C22×Dic11C2414yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2414yes—
219C22×Dic11C2412yes—
220C2×D44—22no—
221C2×D44—42no—
222C2×C4×D11—24no—
223C2×C4×D11—44no—
224C2×Dic22—22no—
225C2×Dic22—42no—
226C11×C4⋊C4—28no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4C2×D418yes—
230C11×C22⋊C4C2×D418yes—
231C42×C11—24no—
232C42×C11—24no—
233C22⋊Dic11—24no—
234C22⋊Dic11—24no—
235C22⋊Dic11—24no—
236C22⋊Dic11—24no—
237C22⋊Dic11—28no—
238C22⋊Dic11—24no—
239C22⋊Dic11—44no—
240C22⋊Dic11—44no—
241C22⋊Dic11—44no—
242C22⋊Dic11—44no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—28no—
247(C2×D11)⋊C4—44no—
248C4⋊Dic11—22no—
249C4⋊Dic11—22no—
250C4⋊Dic11—42no—
251C4⋊Dic11—42no—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254Dic11⋊C4—28no—
255Dic11⋊C4—28no—
256Dic11⋊C4—44no—
257C4×Dic11—24no—
258C4×Dic11—44no—
259C2×#538—111no—
260C22×C4×D4D1111yescharacteristic, complemented
261#2855—111no—
262#2854—111no—
263#2849—112no—
264#2626—111no—
265#2617—111no—
266#2613—112no—
267#2466—114no—
268#2459—114no—
269#2456—114no—
270#2455—114no—
271#2322—112no—
272#2312—111no—
273C4×#120—112no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—28no—
277C23×C11—28no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—24no—
285C23×C11—24no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11—48no—
289C23×C11—44no—
290C23×C11—48no—
291C23×C11—44no—
292C23×C11—48no—
293C23×C11—48no—
294C23×C11C22×D414yes—
295C23×C11C22×D412yes—
296C23×C11C2×#4114yes—
297C23×C11C2×#4112yes—
298C23×C11C2×#4112yes—
299C23×C11C2511yescharacteristic
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—24no—
305D4×C11—232no—
306C2×C4×C11—28no—
307C2×C4×C11—28no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—44no—
318C2×C4×C11—44no—
319C2×C4×C11—416no—
320C2×C4×C11—416no—
321C2×C4×C11—44no—
322C2×C4×C11C22×D414yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C2×#4114yes—
326C2×C4×C11H(5,𝔽2)14yes—
327C22⋊D11—416no—
328C22⋊D11—48no—
329C22⋊D11—84no—
330C22⋊D11—84no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344D44—82no—
345C4×D11—84no—
346Dic22—82no—
347C23×D4C2×D1111yescharacteristic
348C24×C4C2×D1111yescharacteristic
349C24×C4C2×D1111yescharacteristic
350#538—228no—
351C2×#126—112no—
352C2×#124—112no—
353C2×#123—112no—
354C2×#123—114no—
355C2×#123—112no—
356C2×C22⋊Q8—111no—
357C2×#121—111no—
358C2×#121—112no—
359C2×#120—112no—
360C2×#120—112no—
361C2×C4×D4—28no—
362C2×C4×D4—112no—
363C2×C4×D4—114no—
364C2×C4×D4C2×D1114yes—
365C2×C4×D4C2×D1114yes—
366C22×C4⋊C4C2×D1111yescharacteristic
367C22×C22⋊C4C2×D1111yescharacteristic
368C22×C22⋊C4C2×D1111yescharacteristic
369C22×C42C2×D1111yescharacteristic
370#399—112no—
371#397—112no—
372#396—114no—
373#394—114no—
374#394—114no—
375#394—114no—
376#393—112no—
377#392—114no—
378#392—114no—
379#392—112no—
380#391—112no—
381#390—112no—
382#389—114no—
383#389—112no—
384#389—112no—
385#388—114no—
386#388—114no—
387#388—114no—
388#388—114no—
389#387—114no—
390#387—114no—
391#386—112no—
392#386—112no—
393#386—114no—
394#386—114no—
395#385—112no—
396#385—112no—
397#385—114no—
398#385—114no—
399#385—114no—
400#381—112no—
401#381—114no—
402#380—111no—
403#380—111no—
404#379—112no—
405#379—112no—
406C4×C22⋊C4—112no—
407C4×C22⋊C4—114no—
408C22×C11—24no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—24no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—28no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—416no—
418C22×C11—416no—
419C22×C11—44no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—44no—
423C22×C11—44no—
424C22×C11#52514yes—
425C22×C11C23×D411yescharacteristic
426C22×C11C22×#4111yescharacteristic
427C22×C11C22×#4111yescharacteristic
428C22×C11C2×H(5,𝔽2)12yes—
429C22×C11#58512yes—
430C2×D11—42no—
431C2×D11—44no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—44no—
435C4×C11—24no—
436C4×C11—24no—
437C4×C11—24no—
438C4×C11—22no—
439C4×C11—22no—
440C4×C11—42no—
441Dic11—42no—
442Dic11—44no—
443Dic11—42no—
444Dic11—42no—
445Dic11—44no—
446C25C22×D1111yescharacteristic
447C25C22×D1111yescharacteristic
448C22×Q8—111no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—112no—
453C22×D4—114no—
454C22×D4—112no—
455C22×D4—112no—
456C22×D4—111no—
457C22×D4C22×D1114yes—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—44no—
461C23×C4—44no—
462C23×C4—112no—
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1114yes—
465C23×C4C22×D1114yes—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470#126—228no—
471#124—228no—
472#123—228no—
473#123—228no—
474#123—448no—
475C22⋊Q8—224no—
476#121—224no—
477#121—228no—
478#120—228no—
479#120—228no—
480C4×D4—216no—
481C4×D4—216no—
482C4×D4—228no—
483C4×D4—448no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—112no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—112no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4C22×D1114yes—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—112no—
497C2×C22⋊C4—112no—
498C2×C22⋊C4—112no—
499C2×C22⋊C4—112no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—112no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—112no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4C22⋊D1118yescomplemented
512C2×C22⋊C4C22×D1112yes—
513C2×C22⋊C4C22×D1112yes—
514C2×C22⋊C4C22×D1112yes—
515C2×C22⋊C4C22×D1112yes—
516C2×C42—24no—
517C2×C42—112no—
518C2×C42—114no—
519C2×C42C22×D1112yes—
520C2×C42C22×D1112yes—
521#95—114no—
522#95—114no—
523#95—114no—
524#95—112no—
525#95—112no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530C2×C11—24no—
531C2×C11—44no—
532C2×C11—44no—
533C2×C11C2×#52511yescharacteristic
534C2×C11#345912yes—
535C2×C11#348411yescharacteristic
536C2×C11#348511yescharacteristic
537C2×C11#350612yes—
538D11—82no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—42no—
547C24—112no—
548C24#433914yes—
549C24C2×C22⋊D1114yes—
550C24C23×D1112yes—
551C24C23×D1112yes—
552C24C23×D1111yescharacteristic
553C2×Q8—222no—
554C2×Q8—442no—
555C2×D4—232no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—228no—
560C2×D4—224no—
561C2×D4—224no—
562C2×D4—224no—
563C2×D4—224no—
564C2×D4—224no—
565C2×D4—222no—
566C2×D4—442no—
567C2×D4—444no—
568C2×D4—444no—
569C2×D4—444no—
570C2×D4—444no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—114no—
588C22×C4—112no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—224no—
593C22×C4—444no—
594C22×C4#433914yes—
595C22×C4C2×C22⋊D1114yes—
596C22×C4C2×C22⋊D1114yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1111yescharacteristic
602C22×C4C23×D1111yescharacteristic
603C4⋊C4—28no—
604C4⋊C4—228no—
605C4⋊C4—228no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—444no—
611C4⋊C4—442no—
612C4⋊C4—442no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—228no—
616C22⋊C4—224no—
617C22⋊C4—224no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4—224no—
621C22⋊C4—228no—
622C22⋊C4—228no—
623C22⋊C4—224no—
624C22⋊C4—224no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C22⋊C4—444no—
628C22⋊C4—444no—
629C22⋊C4—444no—
630C22⋊C4C2×C22⋊D1118yes—
631C22⋊C4C2×C22⋊D1118yes—
632C42—24no—
633C42—24no—
634C42—224no—
635C42—444no—
636C11#3498611yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—28no—
640C23—28no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—44no—
650C23—48no—
651C23—44no—
652C23—44no—
653C23—48no—
654C23—48no—
655C23—44no—
656C23—48no—
657C23—222no—
658C23—222no—
659C23—224no—
660C23—224no—
661C23—222no—
662C23C2×#433914yes—
663C23C2×#433912yes—
664C23C2×#433912yes—
665C23C22×C22⋊D1114yes—
666C23C22×C22⋊D1112yes—
667C23C24×D1111yescharacteristic
668Q8—882no—
669D4—232no—
670D4—4416no—
671D4—448no—
672D4—882no—
673D4—884no—
674D4—884no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—416no—
689C2×C4—416no—
690C2×C4—44no—
691C2×C4—224no—
692C2×C4—222no—
693C2×C4—224no—
694C2×C4—222no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—884no—
705C2×C4C2×#433914yes—
706C2×C4#6703714yes—
707C2×C4C22×C22⋊D1112yes—
708C2×C4C22×C22⋊D1112yes—
709C2×C4C22×C22⋊D1114yes—
710C22—24no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—24no—
718C22—28no—
719C22—416no—
720C22—416no—
721C22—44no—
722C22—44no—
723C22—42no—
724C22—42no—
725C22—44no—
726C22—442no—
727C22—444no—
728C22—442no—
729C22—442no—
730C22—444no—
731C22#1062332214yes—
732C22C22×#433911yescharacteristic
733C22C22×#433911yescharacteristic
734C22C2×#6703712yes—
735C22#1062345312yes—
736C22C23×C22⋊D1111yescharacteristic
737C4—24no—
738C4—24no—
739C4—24no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—442no—
744C4—444no—
745C4—442no—
746C4—442no—
747C4—444no—
748C2—24no—
749C2—44no—
750C2—44no—
751C2—882no—
752C2C2×#1062332211yescharacteristic
753C2#1308202512yes—
754C2#1308225111yescharacteristic
755C2#1308226011yescharacteristic
756C2#1308246812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C4×D4×C11C2
hypercenterC22×C4×D4D11
hypocenterC11#34986
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623025C2semidirect
2. #13076955C2semidirect
3. #13076947C2semidirect
4. #13076908C2semidirect
5. #13074421C2semidirect
6. #13074350C2semidirect
7. #13074328C2semidirect
8. #13072646C2semidirect
9. #13072547C2semidirect
10. #13072508C2semidirect
11. #13072493C2semidirect
12. #13071285C2semidirect
13. #13071214C2semidirect
14. C4×#67006C2semidirect
15. C22×C4×D4×C11C2semidirect
30. C2×#66982C22semidirect
32. C2×C4×C22⋊D11C22semidirect
35. C2×#66938C22semidirect
36. C2×#66937C22semidirect
37. C2×#66936C22semidirect
38. C2×#66932C22semidirect
47. #10622826C22semidirect
48. #10622826C22semidirect
52. #10622824C22semidirect
55. #10622823C22semidirect
56. #10622823C22semidirect
58. C4×C22⋊Dic11C22semidirect
59. #10622603C22semidirect
60. #10622602C22semidirect
61. #10622591C22semidirect
62. #10622585C22semidirect
63. #10622574C22semidirect
64. #10622573C22semidirect
65. #10622566C22semidirect
66. #10622564C22semidirect
67. #10622564C22semidirect
68. #10622562C22semidirect
69. #10622561C22semidirect
70. #10622560C22semidirect
71. #10622553C22semidirect
72. #10622552C22semidirect
73. #10622546C22semidirect
74. #10622542C22semidirect
75. #10622541C22semidirect
76. #10622541C22semidirect
106. C2×C11×C22⋊C4D4semidirect
260. C22×C4×D4D11semidirect
511. C2×C22⋊C4C22⋊D11semidirect
636. C11#34986semidirect

Maximal subgroups

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

subgroupindex
C2×#106230252
#130769552
#130769472
#130769082
#130744212
#130743502
#130743282
#130726462
#130725472
#130725082
#130724932
#130712852
#130712142
C4×#670062
C22×C4×D4×C112
#3498611