Finite Group Databasebeta

← #14960802

Subgroups — #14960802

Order 2816.

2602 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C211yesmaximal, characteristic, complemented
2#13076903C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075315C214yesmaximal, complemented
5#13075285C214yesmaximal, complemented
6#13074981C214yesmaximal, complemented
7#13074968C214yesmaximal, complemented
8#13074421C211yesmaximal, characteristic, complemented
9#13074350C211yesmaximal, characteristic, complemented
10#13073963C212yesmaximal, complemented
11#13072001C212yesmaximal, complemented
12#13072001C212yesmaximal, complemented
13#13071966C212yesmaximal, complemented
14#13071234C211yesmaximal, characteristic, complemented
15C22×C11×#123C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C2×C11×#123—28no—
19C2×C11×#123C2214yes—
20C2×C11×#123C2214yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C2×#66991C2214yes—
29C2×#66983C2211yescharacteristic
30C2×#66983C2212yescomplemented
31C2×#66982C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C2×#66979C2212yes—
34C2×#66977C2211yescharacteristic
35C2×#66977C2212yescomplemented
36#10623046—28no—
37C2×#66951C2212yescomplemented
38C2×#66949C2212yescomplemented
39C2×#66947C2212yescomplemented
40C2×#66942C2212yescomplemented
41#10622860C2212yes—
42#10622860C2212yes—
43#10622836C2214yes—
44#10622835C2214yes—
45#10622834C2214yes—
46#10622826C2212yes—
47#10622826C2212yes—
48#10622826C2214yescomplemented
49#10622825C2212yes—
50#10622825C2211yescharacteristic
51#10622825C2211yescharacteristic
52#10622825C2212yescomplemented
53#10622825C2212yescomplemented
54#10622823C2212yes—
55#10622823C2212yes—
56#10622823C2214yescomplemented
57#10622607C2214yescomplemented
58#10622602C2214yescomplemented
59#10622598C2214yescomplemented
60#10622598C2214yescomplemented
61#10622597C2214yescomplemented
62#10622591C2214yescomplemented
63#10622574C2214yescomplemented
64#10622574C2214yescomplemented
65#10622574C2214yescomplemented
66#10622573C2212yescomplemented
67#10622570C2214yescomplemented
68#10622570C2214yescomplemented
69#10622566C2212yescomplemented
70#10622562C2212yescomplemented
71#10622561C2214yescomplemented
72#10622561C2214yescomplemented
73#10622561C2214yescomplemented
74#10622560C2212yescomplemented
75#10622558C2214yescomplemented
76#10622558C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C22×D4×C11—24no—
80C22×D4×C11—44no—
81C22×D4×C11C2314yes—
82C23×C4×C11—24no—
83C23×C4×C11—44no—
84C23×C4×C11C2312yes—
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C22×D44C2311yescharacteristic
95C22×C4×D11C2312yes—
96C22×Dic22C2311yescharacteristic
97C11×#123—216no—
98C11×#123—216no—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4D418yescomplemented
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111#67006—44no—
112#67006—44no—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122#66991—48no—
123#66983—24no—
124#66983—44no—
125#66982—28no—
126C4×C22⋊D11—28no—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133#66979—44no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2312yes—
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2314yes—
140#66977—24no—
141#66977—44no—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2314yes—
150#66951—28no—
151#66949—28no—
152#66947—28no—
153#66942—28no—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161#36722—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—24no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11C2412yes—
173C24×C11C2412yes—
174C24×C11C2411yescharacteristic
175C23×D11C2412yes—
176C2×D4×C11—28no—
177C2×D4×C11—28no—
178C2×D4×C11—44no—
179C2×D4×C11—416no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—24no—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—24no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—416no—
195C22×C4×C11C2×D414yes—
196C22×C4×C11C2×D414yes—
197C22×C4×C11C2×D414yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C22×C4×C11C2412yes—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—28no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—44no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C22×Dic11C2412yes—
214C22×Dic11C2414yes—
215C22×Dic11C2414yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C2×D44—22no—
219C2×D44—42no—
220C2×C4×D11—24no—
221C2×C4×D11—44no—
222C2×Dic22—22no—
223C2×Dic22—42no—
224C11×C4⋊C4—28no—
225C11×C4⋊C4C2×D418yes—
226C11×C4⋊C4C2×D418yes—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—28no—
231C22⋊Dic11—24no—
232C22⋊Dic11—28no—
233C22⋊Dic11—24no—
234C22⋊Dic11—24no—
235C22⋊Dic11—44no—
236C22⋊Dic11—44no—
237C22⋊Dic11—44no—
238C22⋊Dic11—44no—
239C22⋊Dic11—44no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4—44no—
246C4⋊Dic11—22no—
247C4⋊Dic11—22no—
248C4⋊Dic11—42no—
249C4⋊Dic11—44no—
250C4⋊Dic11—42no—
251C4⋊Dic11—44no—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—44no—
257Dic11⋊C4—44no—
258C4×Dic11—24no—
259C4×Dic11—44no—
260C2×#539—111no—
261C22×#123D1111yescharacteristic, complemented
262#2848—111no—
263#2847—111no—
264#2707—114no—
265#2705—114no—
266#2682—114no—
267#2681—114no—
268#2626—111no—
269#2617—111no—
270#2579—112no—
271#2411—112no—
272#2411—112no—
273#2408—112no—
274#2316—111no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—28no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—24no—
287C23×C11—22no—
288C23×C11—24no—
289C23×C11—48no—
290C23×C11—48no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—84no—
297C23×C11—84no—
298C23×C11C22×D412yes—
299C23×C11H(5,𝔽2)14yes—
300C23×C11H(5,𝔽2)12yes—
301C23×C112−1+412yes—
302C23×C11C2511yescharacteristic
303C22×D11—22no—
304C22×D11—24no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—24no—
308D4×C11—416no—
309C2×C4×C11—28no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—48no—
323C2×C4×C11—48no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11C22×D414yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D414yes—
329C2×C4×C11C22×D412yes—
330C22⋊D11—48no—
331C22⋊D11—88no—
332C22⋊D11—88no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346D44—82no—
347C4×D11—84no—
348Dic22—82no—
349C23×D4C2×D1111yescharacteristic
350C24×C4C2×D1111yescharacteristic
351#539—228no—
352C2×#126—112no—
353C2×#125—112no—
354C2×#123—28no—
355C2×#123—112no—
356C2×#123—112no—
357C2×#123C2×D1114yes—
358C2×#123C2×D1114yes—
359C2×C22⋊Q8—111no—
360C2×C22⋊Q8—112no—
361C2×C22⋊Q8—112no—
362C2×#121—111no—
363C2×#121—114no—
364C2×#121—112no—
365C2×#120—112no—
366C2×#120—112no—
367C2×C4×D4—112no—
368C2×#117—112no—
369C22×C4⋊C4C2×D1111yescharacteristic
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4C2×D1111yescharacteristic
372C22×C22⋊C4C2×D1111yescharacteristic
373C22×C22⋊C4C2×D1111yescharacteristic
374#399—112no—
375#398—114no—
376#397—112no—
377#396—114no—
378#396—114no—
379#396—114no—
380#396—114no—
381#394—114no—
382#394—114no—
383#394—114no—
384#394—114no—
385#393—112no—
386#392—114no—
387#392—112no—
388#390—114no—
389#390—114no—
390#390—114no—
391#389—114no—
392#389—114no—
393#388—114no—
394#388—114no—
395#387—114no—
396#386—112no—
397#386—112no—
398#386—114no—
399#385—112no—
400#385—112no—
401#385—114no—
402#385—114no—
403#380—112no—
404#380—111no—
405#380—111no—
406#380—112no—
407#380—112no—
408#379—112no—
409#379—112no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—416no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—44no—
426C22×C11—44no—
427C22×C11—88no—
428C22×C11#53714yes—
429C22×C11C23×D411yescharacteristic
430C22×C11C2×H(5,𝔽2)12yes—
431C22×C11C2×H(5,𝔽2)11yescharacteristic
432C22×C11C2×2−1+411yescharacteristic
433C22×C11#58512yes—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—44no—
438C2×D11—44no—
439C4×C11—24no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—24no—
443C4×C11—42no—
444C4×C11—42no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448Dic11—44no—
449Dic11—44no—
450C25C22×D1111yescharacteristic
451C25C22×D1111yescharacteristic
452C22×Q8—111no—
453C22×D4—24no—
454C22×D4—44no—
455C22×D4—112no—
456C22×D4—114no—
457C22×D4—114no—
458C22×D4—111no—
459C22×D4C22×D1114yes—
460C23×C4—24no—
461C23×C4—44no—
462C23×C4—112no—
463C23×C4C22×D1112yes—
464C23×C4C22×D1112yes—
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470#126—228no—
471#125—228no—
472#123—216no—
473#123—216no—
474#123—228no—
475#123—228no—
476C22⋊Q8—224no—
477C22⋊Q8—228no—
478C22⋊Q8—444no—
479#121—224no—
480#121—448no—
481#121—444no—
482#120—444no—
483#120—444no—
484C4×D4—228no—
485#117—444no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—112no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—112no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4C22⋊D1118yescomplemented
500C2×C4⋊C4C22×D1114yes—
501C2×C4⋊C4C22×D1112yes—
502C2×C4⋊C4C22×D1112yes—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—112no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—114no—
521C2×C22⋊C4C22×D1114yes—
522C2×C22⋊C4C22×D1114yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1112yes—
525C2×C42—112no—
526C2×C42—114no—
527#95—114no—
528#95—112no—
529#95—114no—
530#95—114no—
531#95—112no—
532#95—114no—
533#95—114no—
534C2×C11—24no—
535C2×C11—44no—
536C2×C11—82no—
537C2×C11C2×#53711yescharacteristic
538C2×C11#348411yescharacteristic
539C2×C11#348711yescharacteristic
540C2×C11#353412yes—
541C2×C11#353512yes—
542D11—82no—
543C24—24no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—112no—
554C24C23×D1112yes—
555C24C23×D1112yes—
556C24C23×D1111yescharacteristic
557C2×Q8—222no—
558C2×Q8—442no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—44no—
562C2×D4—416no—
563C2×D4—224no—
564C2×D4—224no—
565C2×D4—224no—
566C2×D4—228no—
567C2×D4—222no—
568C2×D4—442no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—444no—
573C2×D4—444no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—416no—
589C22×C4—114no—
590C22×C4—114no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—224no—
595C22×C4—444no—
596C22×C4C2×C22⋊D1114yes—
597C22×C4C2×C22⋊D1114yes—
598C22×C4C2×C22⋊D1114yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1111yescharacteristic
603C22×C4C23×D1111yescharacteristic
604C22×C4C23×D1112yes—
605C4⋊C4—28no—
606C4⋊C4—224no—
607C4⋊C4—222no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—222no—
611C4⋊C4—224no—
612C4⋊C4—444no—
613C4⋊C4—442no—
614C4⋊C4—444no—
615C4⋊C4—444no—
616C4⋊C4—442no—
617C4⋊C4—444no—
618C4⋊C4C2×C22⋊D1118yes—
619C4⋊C4C2×C22⋊D1118yes—
620C22⋊C4—28no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—28no—
624C22⋊C4—228no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—444no—
633C22⋊C4—444no—
634C22⋊C4—444no—
635C22⋊C4—444no—
636C22⋊C4—444no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C42—224no—
640C42—444no—
641C11#3672211yescharacteristic, complemented, Sylow
642C23—22no—
643C23—22no—
644C23—28no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—48no—
657C23—48no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—84no—
664C23—84no—
665C23—224no—
666C23—222no—
667C23—222no—
668C23—224no—
669C23—222no—
670C23#6703714yes—
671C23#6704212yes—
672C23#6704312yes—
673C23C22×C22⋊D1112yes—
674C23C24×D1111yescharacteristic
675Q8—882no—
676D4—416no—
677D4—448no—
678D4—882no—
679D4—888no—
680D4—888no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—48no—
695C2×C4—48no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—884no—
712C2×C4C22×C22⋊D1114yes—
713C2×C4C22×C22⋊D1114yes—
714C2×C4C22×C22⋊D1112yes—
715C2×C4C22×C22⋊D1112yes—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—416no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—88no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—444no—
738C22—444no—
739C22#1062336414yes—
740C22C2×#6703712yes—
741C22C2×#6704211yescharacteristic
742C22C2×#6704311yescharacteristic
743C22#1062345312yes—
744C22C23×C22⋊D1111yescharacteristic
745C4—24no—
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—442no—
752C4—442no—
753C4—442no—
754C4—444no—
755C4—444no—
756C2—24no—
757C2—44no—
758C2—82no—
759C2—882no—
760C2C2×#1062336411yescharacteristic
761C2#1308225111yescharacteristic
762C2#1308227411yescharacteristic
763C2#1308281012yes—
764C2#1308282912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#123C2
hypercenterC22×#123D11
hypocenterC11#36722
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10623046C2semidirect
2. #13076903C2semidirect
3. #13076898C2semidirect
4. #13075315C2semidirect
5. #13075285C2semidirect
6. #13074981C2semidirect
7. #13074968C2semidirect
8. #13074421C2semidirect
9. #13074350C2semidirect
10. #13073963C2semidirect
11. #13072001C2semidirect
12. #13072001C2semidirect
13. #13071966C2semidirect
14. #13071234C2semidirect
15. C22×C11×#123C2semidirect
30. C2×#66983C22semidirect
35. C2×#66977C22semidirect
37. C2×#66951C22semidirect
38. C2×#66949C22semidirect
39. C2×#66947C22semidirect
40. C2×#66942C22semidirect
48. #10622826C22semidirect
52. #10622825C22semidirect
53. #10622825C22semidirect
56. #10622823C22semidirect
57. #10622607C22semidirect
58. #10622602C22semidirect
59. #10622598C22semidirect
60. #10622598C22semidirect
61. #10622597C22semidirect
62. #10622591C22semidirect
63. #10622574C22semidirect
64. #10622574C22semidirect
65. #10622574C22semidirect
66. #10622573C22semidirect
67. #10622570C22semidirect
68. #10622570C22semidirect
69. #10622566C22semidirect
70. #10622562C22semidirect
71. #10622561C22semidirect
72. #10622561C22semidirect
73. #10622561C22semidirect
74. #10622560C22semidirect
75. #10622558C22semidirect
76. #10622558C22semidirect
100. C2×C11×C4⋊C4D4semidirect
261. C22×#123D11semidirect
499. C2×C4⋊C4C22⋊D11semidirect
641. C11#36722semidirect

Maximal subgroups

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

subgroupindex
C2×#106230462
#130769032
#130768982
#130753152
#130752852
#130749812
#130749682
#130744212
#130743502
#130739632
#130720012
#130719662
#130712342
C22×C11×#1232
#3672211