Finite Group Databasebeta

← #14926656

Subgroups — #14926656

Order 2816.

2522 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623165C212yesmaximal
2#13076968C211yesmaximal, characteristic, complemented
3#13076966C212yesmaximal, complemented
4#13074733C212yesmaximal, complemented
5#13074732C212yesmaximal, complemented
6#13073626C214yesmaximal, complemented
7#13073625C214yesmaximal, complemented
8#13072321C212yesmaximal, complemented
9#13072320C212yesmaximal, complemented
10#13072316C212yesmaximal, complemented
11#13072314C212yesmaximal, complemented
12#13071229C212yesmaximal
13D11×#380C212yesmaximal
14C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
15C11×#2857C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×C22⋊Q8C2212yes—
19C22×C42×C11C2211yescharacteristic
20C2×#66999C2214yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C2×#66977C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25#10623165—216no—
26C2×#66950C2214yes—
27C2×#66949C2214yes—
28C2×#66949C2214yes—
29C2×C4⋊C4×D11C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×#66941C2212yescomplemented
32C2×C22⋊C4×D11C2214yes—
33C2×#66931C2214yes—
34C2×#66922C2211yescharacteristic, complemented
35C11×#391C2212yescomplemented
36C11×#389C2212yescomplemented
37C11×#389C2212yescomplemented
38C11×#384C2211yescharacteristic, complemented
39C11×#380C2212yes—
40C11×#380C2212yes—
41#10622842C2214yescomplemented
42#10622825C2212yes—
43#10622825C2212yes—
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46#10622602C2214yes—
47#10622602C2214yes—
48#10622600C2212yes—
49#10622600C2212yes—
50#10622598C2212yescomplemented
51#10622597C2214yescomplemented
52#10622596C2214yescomplemented
53#10622593C2214yescomplemented
54#10622592C2214yescomplemented
55#10622592C2214yescomplemented
56#10622589C2212yescomplemented
57#10622586C2212yescomplemented
58#10622555C2214yes—
59#10622555C2214yes—
60C4×(C2×D11)⋊C4C2212yes—
61C4×(C2×D11)⋊C4C2212yes—
62C4×(C2×D11)⋊C4C2212yes—
63C4×(C2×D11)⋊C4C2212yes—
64#10622548C2211yescharacteristic, complemented
65#10622542C2212yescomplemented
66#10622541C2212yescomplemented
67#10622541C2212yescomplemented
68#10622281C2214yes—
69#10622281C2214yes—
70#10622280C2214yes—
71D11×#95C2214yes—
72#10622270C2214yescomplemented
73#10622269C2214yescomplemented
74#10622260C2214yescomplemented
75#10622259C2214yescomplemented
76C24×D11C2311yescharacteristic
77C22×Q8×C11C2312yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×C4×D11—42no—
85C22×C4×D11—42no—
86C22×C4×D11Q818yescomplemented
87C22×C4×D11C2312yes—
88C22×C4×D11C2314yes—
89C22×C4×D11C2314yes—
90C22×C4×D11C2312yes—
91C22×Dic22C2312yes—
92C22×Dic22C2314yes—
93C11×C4⋊Q8—42no—
94C11×C22⋊Q8—28no—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C42×C11—42no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11C2314yes—
108#66999—216no—
109C2×(C2×D11)⋊C4D418yes—
110C2×(C2×D11)⋊C4Q818yescomplemented
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2314yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2312yes—
123#66977—28no—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×C4×Dic11—42no—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134#66950—216no—
135#66949—216no—
136#66949—216no—
137C4⋊C4×D11—44no—
138C4⋊C4×D11—44no—
139#66941—44no—
140C22⋊C4×D11—216no—
141#66931—216no—
142#66922—42no—
143C11×#95C2314yes—
144C11×#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2312yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154C11⋊#95C2312yes—
155#35002—111nomaximal, Sylow
156C24×C11C2411yescharacteristic
157C23×D11—41no—
158C23×D11—41no—
159C23×D11—41no—
160C23×D11—41no—
161C23×D11C2×D414yes—
162C23×D11C2×Q814yes—
163C23×D11C2×Q814yes—
164C23×D11C2412yes—
165C2×Q8×C11—24no—
166C2×Q8×C11—42no—
167C2×Q8×C11—42no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×Q814yes—
176C22×C4×C11C2×Q814yes—
177C22×C4×C11C2414yes—
178C22×C4×C11C2414yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×Dic11—41no—
186C22×Dic11—41no—
187C22×Dic11—41no—
188C22×Dic11—41no—
189C22×Dic11—41no—
190C22×Dic11—41no—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×Q814yes—
193C22×Dic11C2×Q814yes—
194C22×Dic11C2414yes—
195C22×Dic11C2414yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C2×C4×D11—28no—
200C2×C4×D11—28no—
201C2×C4×D11—24no—
202C2×C4×D11—24no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—44no—
206C2×C4×D11—44no—
207C2×C4×D11—44no—
208C2×C4×D11—44no—
209C2×C4×D11—416no—
210C2×C4×D11C2×Q818yes—
211C2×C4×D11C2×Q818yes—
212C2×Dic22—28no—
213C2×Dic22—24no—
214C2×Dic22—42no—
215C2×Dic22—44no—
216C2×Dic22—42no—
217C2×Dic22—44no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—42no—
223C11×C4⋊C4—42no—
224C11×C22⋊C4—28no—
225C42×C11—22no—
226C42×C11—22no—
227C42×C11—41no—
228C42×C11—41no—
229C22⋊Dic11—28no—
230(C2×D11)⋊C4—28no—
231(C2×D11)⋊C4—28no—
232(C2×D11)⋊C4C2×D418yes—
233(C2×D11)⋊C4C2×D418yes—
234(C2×D11)⋊C4C2×Q818yes—
235(C2×D11)⋊C4C2×Q818yes—
236C4⋊Dic11—28no—
237C4⋊Dic11—24no—
238C4⋊Dic11—24no—
239C4⋊Dic11—24no—
240C4⋊Dic11—42no—
241C4⋊Dic11—42no—
242Dic11⋊C4—28no—
243Dic11⋊C4—28no—
244Dic11⋊C4—28no—
245Dic11⋊C4—44no—
246Dic11⋊C4—44no—
247Dic11⋊C4—44no—
248Dic11⋊C4—44no—
249C4×Dic11—24no—
250C4×Dic11—42no—
251C2×#543—112no—
252#2857—111no—
253#2857—112no—
254#2857D1111yescharacteristic, complemented
255#2659—112no—
256#2659—112no—
257#2549—114no—
258#2549—114no—
259#2440—112no—
260#2440—112no—
261#2440—112no—
262#2440—112no—
263#2315—112no—
264C2×#380—112no—
265C2×C4×C22⋊C4—111no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11C22×D412yes—
271C23×C11C22×Q812yes—
272C23×C11C22×Q812yes—
273C23×C11C2511yescharacteristic
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—44no—
279C22×D11—44no—
280C22×D11—44no—
281C22×D11—44no—
282C22×D11—44no—
283C22×D11—44no—
284C22×D11C4⋊Q8116yescomplemented
285C22×D11C22×D414yes—
286C22×D11C22×Q814yes—
287C22×D11C22×Q814yes—
288Q8×C11—84no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—28no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—44no—
307C2×C4×C11—44no—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×Q812yes—
311C2×C4×C11C22×Q812yes—
312C2×C4×C11C22×Q812yes—
313C2×C4×C11C22×Q812yes—
314C2×C4×C11H(5,𝔽2)12yes—
315C2×C4×C11H(5,𝔽2)12yes—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—44no—
329C2×Dic11—44no—
330C2×Dic11—44no—
331C2×Dic11C22×D414yes—
332C2×Dic11C22×Q814yes—
333C2×Dic11C22×Q814yes—
334C4×D11—216no—
335C4×D11—48no—
336C4×D11—88no—
337C4×D11—88no—
338Dic22—88no—
339Dic22—84no—
340C24×C4—111no—
341#543—2216no—
342C2×C4⋊Q8—112no—
343C2×C4⋊Q8—111no—
344C2×C4⋊Q8C2×D1111yescharacteristic, complemented
345C2×C22⋊Q8—114no—
346C2×C22⋊Q8—112no—
347C2×C22⋊Q8—114no—
348C2×C22⋊Q8—114no—
349C2×C22⋊Q8—114no—
350C2×C22⋊Q8—114no—
351C2×C22⋊Q8C2×D1112yes—
352C22×C4⋊C4—112no—
353C22×C4⋊C4—112no—
354C22×C22⋊C4—111no—
355C22×C22⋊C4—111no—
356C22×C22⋊C4—114no—
357C22×C42—111no—
358C22×C42C2×D1111yescharacteristic
359#398—114no—
360#398—114no—
361#398—114no—
362#398—114no—
363#395—114no—
364#395—114no—
365#395—114no—
366#395—114no—
367#391—112no—
368#391—114no—
369#391C2×D1112yescomplemented
370#389—112no—
371#389—112no—
372#389—112no—
373#389—112no—
374#389—114no—
375#389C2×D1112yescomplemented
376#389C2×D1112yescomplemented
377#385—114no—
378#385—114no—
379#385—114no—
380#385—114no—
381#384—112no—
382#384—111no—
383#384C2×D1111yescharacteristic, complemented
384#380—112no—
385#380—112no—
386#380—112no—
387#380—112no—
388#380—114no—
389#380—114no—
390#380—114no—
391#380C2×D1112yes—
392#380C2×D1112yes—
393C4×C22⋊C4—112no—
394C4×C22⋊C4—112no—
395C4×C22⋊C4—112no—
396C4×C22⋊C4—112no—
397C2×#95—111no—
398C2×#95—111no—
399C2×#95—114no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11C2×C4⋊Q814yes—
407C22×C11C23×D411yescharacteristic
408C22×C11C23×Q811yescharacteristic
409C22×C11C23×Q811yescharacteristic
410C22×C11C2×H(5,𝔽2)11yescharacteristic
411C22×C11C2×H(5,𝔽2)11yescharacteristic
412C22×C11#58511yescharacteristic
413C22×C11#58511yescharacteristic
414C2×D11—24no—
415C2×D11—24no—
416C2×D11—24no—
417C2×D11—24no—
418C2×D11—24no—
419C2×D11—24no—
420C2×D11—416no—
421C2×D11C2×C4⋊Q818yes—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—44no—
428C4×C11—44no—
429C4×C11#54314yescomplemented
430Dic11—24no—
431Dic11—24no—
432Dic11—24no—
433Dic11—44no—
434Dic11—44no—
435C25—111no—
436C22×Q8—114no—
437C22×Q8—112no—
438C22×Q8C22×D1112yes—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—112no—
443C23×C4—118no—
444C23×C4—112no—
445C23×C4—114no—
446C23×C4—114no—
447C23×C4—442no—
448C23×C4—442no—
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1111yescharacteristic
452C4⋊Q8—42no—
453C4⋊Q8—442no—
454C4⋊Q8—444no—
455C22⋊Q8—28no—
456C22⋊Q8—2216no—
457C22⋊Q8—2216no—
458C22⋊Q8—2216no—
459C22⋊Q8—2216no—
460C22⋊Q8—2216no—
461C22⋊Q8—228no—
462C2×C4⋊C4—112no—
463C2×C4⋊C4—112no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—444no—
476C2×C4⋊C4—444no—
477C2×C4⋊C4C22×D1112yes—
478C2×C4⋊C4C22×D1112yes—
479C2×C4⋊C4C22×D1112yes—
480C2×C4⋊C4C22×D1114yes—
481C2×C4⋊C4C22×D1112yes—
482C2×C4⋊C4C22×D1112yes—
483C2×C22⋊C4—118no—
484C2×C22⋊C4—118no—
485C2×C22⋊C4—112no—
486C2×C22⋊C4—112no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—112no—
489C2×C22⋊C4—114no—
490C2×C22⋊C4—114no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—2216no—
493C2×C22⋊C4C22×D1114yes—
494C2×C42—42no—
495C2×C42—112no—
496C2×C42—112no—
497C2×C42—442no—
498C2×C42C22×D1111yescharacteristic
499C2×C42C22×D1111yescharacteristic
500C2×C42C22×D1111yescharacteristic
501C2×C42C22×D1111yescharacteristic
502#95—112no—
503#95—112no—
504#95—112no—
505#95—112no—
506#95—114no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95C22×D1114yes—
513#95C22×D1114yes—
514C2×C11—24no—
515C2×C11C22×C4⋊Q811yescharacteristic
516C2×C11C2×#54311yescharacteristic
517C2×C11#345811yescharacteristic
518C2×C11#349611yescharacteristic
519C2×C11#349611yescharacteristic
520C2×C11#350111yescharacteristic
521C2×C11#350111yescharacteristic
522D11—28no—
523C24—112no—
524C24—114no—
525C24—114no—
526C24—114no—
527C24—441no—
528C24—441no—
529C24—441no—
530C24—441no—
531C24C23×D1111yescharacteristic
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—228no—
536C2×Q8—224no—
537C2×Q8—442no—
538C2×Q8—444no—
539C2×Q8—442no—
540C2×Q8—444no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—114no—
551C22×C4—114no—
552C22×C4—114no—
553C22×C4—118no—
554C22×C4—118no—
555C22×C4—114no—
556C22×C4—114no—
557C22×C4—228no—
558C22×C4—228no—
559C22×C4—224no—
560C22×C4—224no—
561C22×C4—4416no—
562C22×C4—442no—
563C22×C4—442no—
564C22×C4—444no—
565C22×C4—444no—
566C22×C4—444no—
567C22×C4—444no—
568C22×C4—441no—
569C22×C4—441no—
570C22×C4—441no—
571C22×C4—441no—
572C22×C4—441no—
573C22×C4—441no—
574C22×C4D4×D1114yes—
575C22×C4Q8×D1114yes—
576C22×C4Q8×D1114yes—
577C22×C4C23×D1114yes—
578C22×C4C23×D1114yes—
579C22×C4C23×D1111yescharacteristic
580C22×C4C23×D1111yescharacteristic
581C22×C4C23×D1111yescharacteristic
582C22×C4C23×D1111yescharacteristic
583C22×C4C23×D1111yescharacteristic
584C22×C4C23×D1111yescharacteristic
585C4⋊C4—24no—
586C4⋊C4—28no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—228no—
592C4⋊C4—228no—
593C4⋊C4—228no—
594C4⋊C4—228no—
595C4⋊C4—224no—
596C4⋊C4—224no—
597C4⋊C4—224no—
598C4⋊C4—444no—
599C4⋊C4—444no—
600C4⋊C4—444no—
601C4⋊C4—442no—
602C4⋊C4—444no—
603C4⋊C4—442no—
604C22⋊C4—28no—
605C22⋊C4—118no—
606C22⋊C4—118no—
607C22⋊C4—118no—
608C22⋊C4—118no—
609C22⋊C4—228no—
610C22⋊C4—228no—
611C22⋊C4—228no—
612C42—22no—
613C42—22no—
614C42—41no—
615C42—41no—
616C42—224no—
617C42—442no—
618C11#3500211yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—114no—
624C23—114no—
625C23—114no—
626C23—1116no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—444no—
632C23—444no—
633C23—444no—
634C23—444no—
635C23—444no—
636C23—444no—
637C23C2×D4×D1112yes—
638C23C2×Q8×D1112yes—
639C23C2×Q8×D1112yes—
640C23C24×D1111yescharacteristic
641Q8—84no—
642Q8—884no—
643Q8—888no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—28no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—114no—
664C2×C4—114no—
665C2×C4—114no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—2216no—
673C2×C4—224no—
674C2×C4—224no—
675C2×C4—224no—
676C2×C4—224no—
677C2×C4—224no—
678C2×C4—224no—
679C2×C4—448no—
680C2×C4—444no—
681C2×C4—444no—
682C2×C4—444no—
683C2×C4—888no—
684C2×C4—888no—
685C2×C4C2×D4×D1112yes—
686C2×C4C2×D4×D1112yes—
687C2×C4#6703712yes—
688C2×C4C2×Q8×D1112yes—
689C2×C4C2×Q8×D1112yes—
690C2×C4C2×Q8×D1112yes—
691C2×C4C2×Q8×D1112yes—
692C2×C4#6704212yes—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—118no—
700C22—224no—
701C22—224no—
702C22—224no—
703C22—224no—
704C22—224no—
705C22—224no—
706C22—4416no—
707C22D11×C4⋊Q814yes—
708C22C22×D4×D1111yescharacteristic
709C22C2×#6703711yescharacteristic
710C22C22×Q8×D1111yescharacteristic
711C22C22×Q8×D1111yescharacteristic
712C22C2×#6704211yescharacteristic
713C22#1062345311yescharacteristic
714C22#1062345311yescharacteristic
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—44no—
721C4—44no—
722C4—224no—
723C4—224no—
724C4—224no—
725C4—444no—
726C4—444no—
727C4#1062316514yescomplemented
728C2—24no—
729C2—228no—
730C2C2×D11×C4⋊Q811yescharacteristic
731C2C2×#1062316511yescharacteristic
732C2#1308201911yescharacteristic
733C2#1308237311yescharacteristic
734C2#1308237811yescharacteristic
735C2#1308241211yescharacteristic
736C2#1308241711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2857C2
prime radicalC24×D11C23
hypercenter#2857D11
hypocenterC11#35002
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
2. #13076968C2semidirect
3. #13076966C2semidirect
4. #13074733C2semidirect
5. #13074732C2semidirect
6. #13073626C2semidirect
7. #13073625C2semidirect
8. #13072321C2semidirect
9. #13072320C2semidirect
10. #13072316C2semidirect
11. #13072314C2semidirect
15. C11×#2857C2semidirect
17. C2×C11×C4⋊Q8C22semidirect
31. C2×#66941C22semidirect
34. C2×#66922C22semidirect
35. C11×#391C22semidirect
36. C11×#389C22semidirect
37. C11×#389C22semidirect
38. C11×#384C22semidirect
41. #10622842C22semidirect
50. #10622598C22semidirect
51. #10622597C22semidirect
52. #10622596C22semidirect
53. #10622593C22semidirect
54. #10622592C22semidirect
55. #10622592C22semidirect
56. #10622589C22semidirect
57. #10622586C22semidirect
64. #10622548C22semidirect
65. #10622542C22semidirect
66. #10622541C22semidirect
67. #10622541C22semidirect
72. #10622270C22semidirect
73. #10622269C22semidirect
74. #10622260C22semidirect
75. #10622259C22semidirect
86. C22×C4×D11Q8semidirect
110. C2×(C2×D11)⋊C4Q8semidirect
254. #2857D11semidirect
284. C22×D11C4⋊Q8semidirect
344. C2×C4⋊Q8C2×D11semidirect
369. #391C2×D11semidirect
375. #389C2×D11semidirect
376. #389C2×D11semidirect
383. #384C2×D11semidirect
429. C4×C11#543semidirect
618. C11#35002semidirect
727. C4#10623165semidirect

Maximal subgroups

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

subgroupindex
C2×#106231652
#130769682
#130769662
#130747332
#130747322
#130736262
#130736252
#130723212
#130723202
#130723162
#130723142
#130712292
D11×#3802
C2×C4×(C2×D11)⋊C42
C11×#28572
#3500211