Finite Group Databasebeta

← #14960798

Subgroups — #14960798

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×#10623176C211yesmaximal, characteristic, complemented
2C22×#66982C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075323C214yesmaximal, complemented
5#13075289C214yesmaximal, complemented
6#13074982C214yesmaximal, complemented
7#13074964C214yesmaximal, complemented
8#13074423C211yesmaximal, characteristic, complemented
9#13074353C211yesmaximal, characteristic, complemented
10#13073968C212yesmaximal, complemented
11#13072003C212yesmaximal, complemented
12#13071999C212yesmaximal, complemented
13#13071971C212yesmaximal, complemented
14#13071233C211yesmaximal, characteristic, complemented
15C11×#2848C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2212yescomplemented
20C2×#67006C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#66999C2212yescomplemented
23C2×#66983C2211yescharacteristic
24C2×#66983C2212yescomplemented
25C2×#66982—28no—
26C2×#66982C2214yes—
27C2×#66982C2214yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32#10623176—28no—
33C2×#66951C2212yescomplemented
34C2×#66947C2212yescomplemented
35C2×#66943C2212yescomplemented
36C2×#66939C2212yes—
37C2×#66937C2214yes—
38C2×#66935C2212yes—
39C2×(C22⋊D11)⋊C4C2212yes—
40C2×#66930C2212yes—
41C11×#385C2212yes—
42C11×#385C2214yescomplemented
43C11×#380C2211yescharacteristic
44C11×#380C2212yescomplemented
45C11×#379C2212yes—
46#10622844C2212yescomplemented
47#10622826C2212yes—
48#10622826C2214yescomplemented
49#10622825C2211yescharacteristic
50#10622825C2212yescomplemented
51#10622607C2214yescomplemented
52#10622607C2214yescomplemented
53#10622605C2212yescomplemented
54#10622604C2214yescomplemented
55#10622602C2214yescomplemented
56#10622601C2214yescomplemented
57#10622593C2214yescomplemented
58#10622585C2214yescomplemented
59#10622573C2214yes—
60#10622572C2214yes—
61#10622572C2214yescomplemented
62#10622571C2212yes—
63#10622570C2214yes—
64#10622570C2214yescomplemented
65#10622568C2212yes—
66#10622564C2214yescomplemented
67#10622561C2214yescomplemented
68#10622559C2212yes—
69#10622555C2212yes—
70#10622289C2214yescomplemented
71#10622287C2212yescomplemented
72#10622285C2214yescomplemented
73#10622284C2212yescomplemented
74#10622283C2214yescomplemented
75#10622265C2214yescomplemented
76#10622260C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C23×C4×C11—24no—
81C23×C4×C11—44no—
82C23×C4×C11C2312yes—
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—44no—
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44C2311yescharacteristic
95C22×D44C2314yes—
96C22×C4×D11C2312yes—
97C11×C22⋊Q8—24no—
98C11×C22⋊Q8—44no—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2312yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107#67006—44no—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112#66999—28no—
113#66983—24no—
114#66983—44no—
115#66982—216no—
116#66982—216no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2312yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2312yes—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4D418yescomplemented
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2314yes—
146#66951—28no—
147#66947—28no—
148#66943—28no—
149#66939—28no—
150#66937—48no—
151#66935—44no—
152(C22⋊D11)⋊C4—28no—
153#66930—44no—
154C11×#95C2312yes—
155C11×#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161#36722—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—24no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—42no—
167C24×C11C2412yes—
168C24×C11C2411yescharacteristic
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11C2412yes—
175C23×D11C2412yes—
176C2×Q8×C11—22no—
177C2×Q8×C11—42no—
178C22×C4×C11—22no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—416no—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2414yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—28no—
196C2×C22⋊D11—24no—
197C2×C22⋊D11—24no—
198C2×C22⋊D11—28no—
199C2×C22⋊D11—28no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—416no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—42no—
209C22×Dic11—42no—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2414yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C2×D44—22no—
218C2×D44—44no—
219C2×D44—44no—
220C2×D44—42no—
221C2×D44—44no—
222C2×C4×D11—24no—
223C2×C4×D11—44no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—44no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—44no—
232C22⋊Dic11—28no—
233C22⋊Dic11—24no—
234C22⋊Dic11—44no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4—24no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—28no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—44no—
243(C2×D11)⋊C4—44no—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—44no—
247C4⋊Dic11—24no—
248C4⋊Dic11—24no—
249C4⋊Dic11—22no—
250C4⋊Dic11—42no—
251Dic11⋊C4—24no—
252Dic11⋊C4—28no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256Dic11⋊C4C2×D418yes—
257Dic11⋊C4C2×D418yes—
258C4×Dic11—24no—
259C4×Dic11—44no—
260C2×#539—111no—
261C22×#123—111no—
262#2848D1111yescharacteristic, complemented
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—48no—
285C23×C11—48no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11C22×D412yes—
289C23×C11H(5,𝔽2)14yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C112−1+412yes—
292C23×C11C2511yescharacteristic
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—84no—
307C22×D11—84no—
308Q8×C11—82no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—44no—
322C2×C4×C11—48no—
323C2×C4×C11—48no—
324C2×C4×C11—44no—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C22⋊D11—416no—
328C22⋊D11—48no—
329C22⋊D11—88no—
330C2×Dic11—28no—
331C2×Dic11—22no—
332C2×Dic11—24no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—44no—
343C2×Dic11—44no—
344C2×Dic11C22×D414yes—
345C2×Dic11C22×D414yes—
346D44—82no—
347D44—88no—
348C4×D11—84no—
349C23×D4—111no—
350C24×C4C2×D1111yescharacteristic
351#539—228no—
352C2×#126—112no—
353C2×#125—112no—
354C2×#123—114no—
355C2×#123—114no—
356C2×#123—112no—
357C2×#123—112no—
358C2×#123—228no—
359C2×C22⋊Q8—112no—
360C2×C22⋊Q8C2×D1111yescharacteristic
361C2×C22⋊Q8C2×D1112yescomplemented
362C2×#121—111no—
363C2×#121—112no—
364C2×#121—114no—
365C2×#120—112no—
366C2×#120—112no—
367C2×C4×D4—112no—
368C2×#117—112no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
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—114no—
398#386—112no—
399#385—114no—
400#385—112no—
401#385C2×D1112yes—
402#385C2×D1114yescomplemented
403#380—111no—
404#380—112no—
405#380—112no—
406#380C2×D1111yescharacteristic
407#380C2×D1112yescomplemented
408#379—112no—
409#379C2×D1112yes—
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#53714yes—
423C22×C11C23×D411yescharacteristic
424C22×C11C2×H(5,𝔽2)12yes—
425C22×C11C2×H(5,𝔽2)11yescharacteristic
426C22×C11C2×2−1+411yescharacteristic
427C22×C11#58512yes—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—44no—
435C2×D11—44no—
436C2×D11—44no—
437C2×D11—44no—
438C2×D11—88no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11—44no—
445Dic11—24no—
446Dic11—24no—
447Dic11—42no—
448Dic11—42no—
449Dic11—44no—
450C25—111no—
451C25C22×D1111yescharacteristic
452C22×Q8C22×D1111yescharacteristic
453C22×D4—112no—
454C22×D4—114no—
455C22×D4—114no—
456C22×D4—111no—
457C22×D4—114no—
458C22×D4—224no—
459C22×D4—444no—
460C23×C4—24no—
461C23×C4—44no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—112no—
466C23×C4C22×D1112yes—
467C23×C4C22×D1112yes—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470#126—228no—
471#125—228no—
472#123—228no—
473#123—228no—
474#123—2216no—
475#123—2216no—
476C22⋊Q8—24no—
477C22⋊Q8—44no—
478C22⋊Q8—228no—
479#121—224no—
480#121—448no—
481#121—444no—
482#120—444no—
483#120—444no—
484C4×D4—228no—
485#117—444no—
486C2×C4⋊C4—118no—
487C2×C4⋊C4—112no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4C22×D1112yes—
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1112yes—
502C2×C4⋊C4C22×D1114yes—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—112no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4C22×D1112yes—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1114yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C42—112no—
526C2×C42—114no—
527#95—114no—
528#95—114no—
529#95—112no—
530#95—114no—
531#95—114no—
532#95C22×D1112yes—
533#95C22×D1114yes—
534C2×C11—24no—
535C2×C11—44no—
536C2×C11C2×#53711yescharacteristic
537C2×C11#348411yescharacteristic
538C2×C11#348711yescharacteristic
539C2×C11#353412yes—
540C2×C11#353512yes—
541D11—82no—
542D11—82no—
543C24—22no—
544C24—24no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—112no—
549C24—112no—
550C24—222no—
551C24—222no—
552C24—222no—
553C24—442no—
554C24—442no—
555C24C23×D1112yes—
556C24C23×D1111yescharacteristic
557C2×Q8—22no—
558C2×Q8—42no—
559C2×D4—228no—
560C2×D4—224no—
561C2×D4—228no—
562C2×D4—224no—
563C2×D4—224no—
564C2×D4—228no—
565C2×D4—222no—
566C2×D4—444no—
567C2×D4—442no—
568C2×D4—444no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—444no—
573C2×D4—4416no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—416no—
584C22×C4—114no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—114no—
588C22×C4—112no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—224no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—444no—
596C22×C4—442no—
597C22×C4—442no—
598C22×C4D4×D1114yes—
599C22×C4C23×D1114yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1111yescharacteristic
604C22×C4C23×D1111yescharacteristic
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4—118no—
610C4⋊C4—118no—
611C4⋊C4—228no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—222no—
616C4⋊C4—444no—
617C4⋊C4—444no—
618C4⋊C4—442no—
619C4⋊C4—444no—
620C22⋊C4—24no—
621C22⋊C4—28no—
622C22⋊C4—24no—
623C22⋊C4—44no—
624C22⋊C4—228no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—228no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
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—48no—
652C23—48no—
653C23—44no—
654C23—44no—
655C23—222no—
656C23—222no—
657C23—224no—
658C23—224no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—222no—
663C23—224no—
664C23—224no—
665C23—444no—
666C23—444no—
667C23—444no—
668C23—884no—
669C23—884no—
670C23C2×D4×D1112yes—
671C23#6703714yes—
672C23#6704012yes—
673C23#6704212yes—
674C23C24×D1111yescharacteristic
675Q8—82no—
676D4—4416no—
677D4—448no—
678D4—882no—
679D4—888no—
680D4—888no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—44no—
694C2×C4—48no—
695C2×C4—48no—
696C2×C4—44no—
697C2×C4—114no—
698C2×C4—114no—
699C2×C4—228no—
700C2×C4—224no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—222no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—444no—
712C2×C4—444no—
713C2×C4—884no—
714C2×C4C2×D4×D1112yes—
715C2×C4C2×D4×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—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—444no—
735C22—444no—
736C22—444no—
737C22—444no—
738C22—888no—
739C22#1062316014yes—
740C22C22×D4×D1111yescharacteristic
741C22C2×#6703712yes—
742C22C2×#6704011yescharacteristic
743C22C2×#6704211yescharacteristic
744C22#1062345312yes—
745C4—22no—
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—44no—
751C4—224no—
752C4—224no—
753C4—442no—
754C4—442no—
755C4—444no—
756C2—24no—
757C2—44no—
758C2—882no—
759C2—882no—
760C2C2×#1062316011yescharacteristic
761C2#1308224511yescharacteristic
762C2#1308227011yescharacteristic
763C2#1308280012yes—
764C2#1308282512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
hypercenter#2848D11
hypocenterC11#36722
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623176C2semidirect
2. C22×#66982C2semidirect
3. #13076898C2semidirect
4. #13075323C2semidirect
5. #13075289C2semidirect
6. #13074982C2semidirect
7. #13074964C2semidirect
8. #13074423C2semidirect
9. #13074353C2semidirect
10. #13073968C2semidirect
11. #13072003C2semidirect
12. #13071999C2semidirect
13. #13071971C2semidirect
14. #13071233C2semidirect
15. C11×#2848C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
22. C2×#66999C22semidirect
24. C2×#66983C22semidirect
33. C2×#66951C22semidirect
34. C2×#66947C22semidirect
35. C2×#66943C22semidirect
42. C11×#385C22semidirect
44. C11×#380C22semidirect
46. #10622844C22semidirect
48. #10622826C22semidirect
50. #10622825C22semidirect
51. #10622607C22semidirect
52. #10622607C22semidirect
53. #10622605C22semidirect
54. #10622604C22semidirect
55. #10622602C22semidirect
56. #10622601C22semidirect
57. #10622593C22semidirect
58. #10622585C22semidirect
61. #10622572C22semidirect
64. #10622570C22semidirect
66. #10622564C22semidirect
67. #10622561C22semidirect
70. #10622289C22semidirect
71. #10622287C22semidirect
72. #10622285C22semidirect
73. #10622284C22semidirect
74. #10622283C22semidirect
75. #10622265C22semidirect
76. #10622260C22semidirect
136. C2×Dic11⋊C4D4semidirect
262. #2848D11semidirect
361. C2×C22⋊Q8C2×D11semidirect
402. #385C2×D11semidirect
407. #380C2×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×#106231762
C22×#669822
#130768982
#130753232
#130752892
#130749822
#130749642
#130744232
#130743532
#130739682
#130720032
#130719992
#130719712
#130712332
C11×#28482
#3672211