Finite Group Databasebeta

← #14927216

Subgroups — #14927216

Order 2816.

2966 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2#13076955C211yesmaximal, characteristic, complemented
3#13076947C211yesmaximal, characteristic, complemented
4#13076903C211yesmaximal, characteristic, complemented
5#13076898C211yesmaximal, characteristic, complemented
6#13074389C212yesmaximal, complemented
7#13074328C212yesmaximal, complemented
8#13074228C214yesmaximal, complemented
9#13074198C214yesmaximal, complemented
10#13072913C212yesmaximal, complemented
11#13072045C212yesmaximal, complemented
12#13072034C212yesmaximal, complemented
13#13071961C212yesmaximal, complemented
14#13071285C212yesmaximal, complemented
15#13071274C212yesmaximal, complemented
16#13070999C211yesmaximal, characteristic, complemented
17C22×C4×D4×C11C211yesmaximal, characteristic, complemented
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C22×#4339C2211yescharacteristic, complemented
22C2×C4×D4×C11—28no—
23C2×C4×D4×C11C2212yes—
24C2×C4×D4×C11C2212yes—
25C2×C4×D4×C11C2212yes—
26C2×C4×D4×C11C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C2×#67006C2212yes—
32C2×#67006C2212yes—
33#10623322—28no—
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic, complemented
36C2×#66983C2212yescomplemented
37C2×#66982C2212yes—
38C2×#66982C2212yescomplemented
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yescomplemented
41C2×#66979C2211yescharacteristic, complemented
42C2×#66979C2212yescomplemented
43C2×#66977C2211yescharacteristic
44C2×#66977C2211yescharacteristic, complemented
45C2×#66977C2212yescomplemented
46#10622860C2212yes—
47#10622860C2212yes—
48#10622836C2214yes—
49#10622836C2214yes—
50#10622835C2214yes—
51#10622835C2214yes—
52#10622826C2212yes—
53#10622826C2212yes—
54#10622826C2214yescomplemented
55#10622825C2211yescharacteristic
56#10622825C2211yescharacteristic
57#10622825C2212yescomplemented
58#10622825C2212yescomplemented
59#10622825C2212yescomplemented
60#10622824C2212yes—
61#10622824C2212yescomplemented
62#10622823C2212yes—
63#10622823C2212yes—
64#10622823C2214yescomplemented
65C4×C22⋊Dic11C2212yes—
66C4×C22⋊Dic11C2212yescomplemented
67#10622603C2214yescomplemented
68#10622602C2214yescomplemented
69#10622591C2214yescomplemented
70#10622585C2214yescomplemented
71#10622572C2214yescomplemented
72#10622572C2214yescomplemented
73#10622570C2214yescomplemented
74#10622569C2214yescomplemented
75#10622565C2214yescomplemented
76#10622565C2214yescomplemented
77#10622558C2214yescomplemented
78#10622557C2214yescomplemented
79#10622553C2214yescomplemented
80#10622552C2212yescomplemented
81#10622546C2214yescomplemented
82#10622542C2212yescomplemented
83#10622541C2212yescomplemented
84#10622541C2212yescomplemented
85C25×C11C2311yescharacteristic
86C25×C11C2311yescharacteristic
87C22×D4×C11—24no—
88C22×D4×C11—24no—
89C22×D4×C11—24no—
90C22×D4×C11C2312yes—
91C22×D4×C11C2312yes—
92C23×C4×C11—24no—
93C23×C4×C11—44no—
94C23×C4×C11—44no—
95C23×C4×C11D418yescomplemented
96C23×C4×C11C2312yes—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2312yes—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C22×C22⋊D11C2312yes—
108C22×C22⋊D11C2312yes—
109C22×C22⋊D11C2312yes—
110C22×C22⋊D11C2314yes—
111C2×#4339—24no—
112C2×#4339—44no—
113C22×D44C2311yescharacteristic
114C22×C4×D11C2312yes—
115C22×Dic22C2311yescharacteristic
116C4×D4×C11—28no—
117C4×D4×C11—28no—
118C4×D4×C11—28no—
119C4×D4×C11—28no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C42×C11—24no—
130C2×C42×C11C2312yes—
131C2×C42×C11C2312yes—
132#67006—28no—
133#67006—28no—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144#66983—24no—
145#66983—24no—
146#66983—44no—
147#66982—28no—
148#66982—28no—
149C4×C22⋊D11—28no—
150C4×C22⋊D11—28no—
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156#66979—24no—
157#66979—44no—
158C2×C4⋊Dic11C2311yescharacteristic
159C2×C4⋊Dic11C2311yescharacteristic
160C2×C4⋊Dic11C2312yes—
161C2×C4⋊Dic11C2312yes—
162#66977—24no—
163#66977—24no—
164#66977—44no—
165C2×Dic11⋊C4C2314yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×Dic11⋊C4C2314yes—
169C2×Dic11⋊C4C2314yes—
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2312yes—
177C11⋊#95C2312yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181#35031—111nomaximal, Sylow
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—42no—
187C24×C11—42no—
188C24×C11—42no—
189C24×C11—42no—
190C24×C11C2×D414yes—
191C24×C11#4114yescomplemented
192C24×C11C2411yescharacteristic
193C24×C11C2411yescharacteristic
194C24×C11C2412yes—
195C24×C11C2411yescharacteristic
196C23×D11C2412yes—
197C2×D4×C11—232no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—24no—
202C2×D4×C11—24no—
203C2×D4×C11—24no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—24no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—24no—
212C22×C4×C11—24no—
213C22×C4×C11—24no—
214C22×C4×C11—24no—
215C22×C4×C11—416no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—416no—
224C22×C4×C11C2×D414yes—
225C22×C4×C11C2×D414yes—
226C22×C4×C11C2×D414yes—
227C22×C4×C11C2×D414yes—
228C22×C4×C11C2×D414yes—
229C22×C4×C11C2×D414yes—
230C22×C4×C11#4114yescomplemented
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C22×C4×C11C2411yescharacteristic
236C22×C4×C11C2412yes—
237C22×C4×C11C2411yescharacteristic
238C2×C22⋊D11—24no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—24no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C22×Dic11C2414yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2414yes—
252C22×Dic11C2412yes—
253#4339—416no—
254C2×D44—22no—
255C2×D44—24no—
256C2×C4×D11—24no—
257C2×C4×D11—44no—
258C2×Dic22—22no—
259C2×Dic22—24no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C42×C11—24no—
267C42×C11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272C22⋊Dic11—28no—
273C22⋊Dic11—24no—
274C22⋊Dic11—44no—
275C22⋊Dic11—44no—
276C22⋊Dic11—44no—
277C22⋊Dic11—44no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—28no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283C4⋊Dic11—22no—
284C4⋊Dic11—22no—
285C4⋊Dic11—24no—
286C4⋊Dic11—24no—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—28no—
290Dic11⋊C4—44no—
291Dic11⋊C4—44no—
292C4×Dic11—24no—
293C4×Dic11—44no—
294C2×#525—111no—
295C22×C4×D4D1111yescharacteristic, complemented
296#2855—111no—
297#2854—111no—
298#2848—111no—
299#2847—111no—
300#2622—112no—
301#2613—112no—
302#2602—114no—
303#2600—114no—
304#2485—112no—
305#2415—112no—
306#2414—112no—
307#2407—112no—
308#2322—112no—
309#2321—112no—
310#2280—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—28no—
314C23×C11—28no—
315C23×C11—22no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—48no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—48no—
335C23×C11—48no—
336C23×C11—48no—
337C23×C11C22×D412yes—
338C23×C11C22×D412yes—
339C23×C11C22×D412yes—
340C23×C11C2×#4114yes—
341C23×C11C2×#4112yes—
342C23×C11C2×#4112yes—
343C23×C11C2511yescharacteristic
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—24no—
348C22×D11—24no—
349D4×C11—216no—
350D4×C11—216no—
351C2×C4×C11—28no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—28no—
358C2×C4×C11—28no—
359C2×C4×C11—28no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—44no—
367C2×C4×C11—44no—
368C2×C4×C11—44no—
369C2×C4×C11—48no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11—48no—
373C2×C4×C11C22×D412yes—
374C2×C4×C11C22×D412yes—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D412yes—
377C2×C4×C11C2×#4114yes—
378C2×C4×C11H(5,𝔽2)14yes—
379C22⋊D11—48no—
380C22⋊D11—48no—
381C22⋊D11—48no—
382C22⋊D11—88no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—24no—
388C2×Dic11—22no—
389C2×Dic11—24no—
390C2×Dic11—24no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—24no—
395C2×Dic11—24no—
396D44—44no—
397C4×D11—48no—
398Dic22—44no—
399C22×#41—111no—
400C23×D4C2×D1111yescharacteristic
401C24×C4C2×D1111yescharacteristic
402C24×C4C2×D1111yescharacteristic
403#525—228no—
404C2×#123—112no—
405C2×#123—112no—
406C2×C22⋊Q8—111no—
407C2×C22⋊Q8—111no—
408C2×C22⋊Q8—112no—
409C2×#121—111no—
410C2×#121—111no—
411C2×#121—112no—
412C2×#120—112no—
413C2×#120—112no—
414C2×C4×D4—28no—
415C2×C4×D4—112no—
416C2×C4×D4—112no—
417C2×C4×D4C2×D1112yes—
418C2×C4×D4C2×D1112yes—
419C2×C4×D4C2×D1112yes—
420C2×C4×D4C2×D1112yes—
421C2×#117—111no—
422C2×#117—112no—
423C22×C4⋊C4C2×D1111yescharacteristic
424C22×C22⋊C4C2×D1111yescharacteristic
425C22×C22⋊C4C2×D1111yescharacteristic
426C22×C42C2×D1111yescharacteristic
427#397—114no—
428#397—114no—
429#394—114no—
430#394—114no—
431#394—114no—
432#394—114no—
433#392—114no—
434#392—114no—
435#391—112no—
436#390—114no—
437#390—112no—
438#389—114no—
439#389—112no—
440#389—112no—
441#388—114no—
442#388—114no—
443#388—114no—
444#388—114no—
445#387—114no—
446#387—114no—
447#386—112no—
448#386—112no—
449#386—114no—
450#386—114no—
451#385—112no—
452#385—112no—
453#385—114no—
454#385—114no—
455#381—112no—
456#381—112no—
457#380—111no—
458#380—112no—
459#380—111no—
460#380—112no—
461#380—112no—
462#379—112no—
463#379—112no—
464C4×C22⋊C4—112no—
465C4×C22⋊C4—112no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—24no—
469C22×C11—24no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—24no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—416no—
480C22×C11—416no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11#52514yes—
490C22×C11C23×D411yescharacteristic
491C22×C11C22×#4111yescharacteristic
492C22×C11C22×#4111yescharacteristic
493C22×C11C2×H(5,𝔽2)12yes—
494C22×C11#58512yes—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—44no—
499C2×D11—44no—
500C4×C11—24no—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11#53414yes—
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11—44no—
511Dic11—44no—
512C25C22×D1111yescharacteristic
513C25C22×D1111yescharacteristic
514C2×#41—224no—
515C2×#41—444no—
516C22×Q8—111no—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—112no—
521C22×D4—112no—
522C22×D4—114no—
523C22×D4—112no—
524C22×D4—111no—
525C22×D4C22×D1112yes—
526C22×D4C22×D1112yes—
527C23×C4—24no—
528C23×C4—44no—
529C23×C4—44no—
530C23×C4—112no—
531C23×C4C22⋊D1118yescomplemented
532C23×C4C22×D1112yes—
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1112yes—
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543#123—228no—
544#123—228no—
545C22⋊Q8—224no—
546C22⋊Q8—224no—
547C22⋊Q8—444no—
548#121—224no—
549#121—224no—
550#121—444no—
551#120—228no—
552#120—228no—
553C4×D4—28no—
554C4×D4—28no—
555C4×D4—28no—
556C4×D4—28no—
557C4×D4—228no—
558C4×D4—228no—
559#117—224no—
560#117—444no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—112no—
565C2×C4⋊C4—112no—
566C2×C4⋊C4—112no—
567C2×C4⋊C4—112no—
568C2×C4⋊C4—114no—
569C2×C4⋊C4—114no—
570C2×C4⋊C4—114no—
571C2×C4⋊C4C22×D1112yes—
572C2×C4⋊C4C22×D1112yes—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—112no—
576C2×C22⋊C4—112no—
577C2×C22⋊C4—112no—
578C2×C22⋊C4—112no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—112no—
581C2×C22⋊C4—112no—
582C2×C22⋊C4—112no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—114no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—114no—
590C2×C22⋊C4C22×D1112yes—
591C2×C22⋊C4C22×D1112yes—
592C2×C22⋊C4C22×D1112yes—
593C2×C22⋊C4C22×D1112yes—
594C2×C42—24no—
595C2×C42—112no—
596C2×C42—114no—
597C2×C42C22×D1112yes—
598C2×C42C22×D1112yes—
599#95—112no—
600#95—114no—
601#95—112no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95—114no—
608C2×C11—24no—
609C2×C11—42no—
610C2×C11—42no—
611C2×C11—44no—
612C2×C11C2×#52511yescharacteristic
613C2×C11C2×#53411yescharacteristic
614C2×C11#344911yescharacteristic
615C2×C11#350512yes—
616C2×C11#350612yes—
617D11—82no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—42no—
623C24—42no—
624C24—42no—
625C24—42no—
626C24—112no—
627C24#433914yescomplemented
628C24C2×C22⋊D1114yes—
629C24C23×D1112yes—
630C24C23×D1111yescharacteristic
631C24C23×D1111yescharacteristic
632C24C23×D1111yescharacteristic
633#41—4416no—
634C2×Q8—224no—
635C2×Q8—222no—
636C2×D4—232no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—228no—
649C2×D4—224no—
650C2×D4—222no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—444no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—416no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—416no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—224no—
681C22×C4—444no—
682C22×C4#433914yescomplemented
683C22×C4C2×C22⋊D1114yes—
684C22×C4C2×C22⋊D1114yes—
685C22×C4C2×C22⋊D1114yes—
686C22×C4C2×C22⋊D1114yes—
687C22×C4C2×C22⋊D1114yes—
688C22×C4C2×C22⋊D1114yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1111yescharacteristic
693C22×C4C23×D1111yescharacteristic
694C22×C4C23×D1111yescharacteristic
695C22×C4C23×D1111yescharacteristic
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—228no—
699C4⋊C4—224no—
700C4⋊C4—224no—
701C4⋊C4—222no—
702C4⋊C4—222no—
703C4⋊C4—224no—
704C4⋊C4—224no—
705C4⋊C4—444no—
706C4⋊C4—444no—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—228no—
712C22⋊C4—224no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—228no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—444no—
721C22⋊C4—444no—
722C22⋊C4—444no—
723C22⋊C4—444no—
724C22⋊C4—444no—
725C22⋊C4—444no—
726C42—24no—
727C42—24no—
728C42—224no—
729C42—444no—
730C11#3503111yescharacteristic, complemented, Sylow
731C23—22no—
732C23—22no—
733C23—28no—
734C23—28no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—48no—
751C23—44no—
752C23—44no—
753C23—48no—
754C23—44no—
755C23—48no—
756C23—48no—
757C23—222no—
758C23—222no—
759C23—224no—
760C23—224no—
761C23—222no—
762C23C2×#433914yes—
763C23C2×#433912yes—
764C23C2×#433912yes—
765C23C22×C22⋊D1112yes—
766C23C22×C22⋊D1112yes—
767C23C22×C22⋊D1112yes—
768C23C24×D1111yescharacteristic
769Q8—444no—
770D4—216no—
771D4—216no—
772D4—448no—
773D4—448no—
774D4—448no—
775D4—444no—
776D4—888no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—48no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—48no—
799C2×C4—224no—
800C2×C4—222no—
801C2×C4—224no—
802C2×C4—222no—
803C2×C4—224no—
804C2×C4—224no—
805C2×C4—224no—
806C2×C4—224no—
807C2×C4—224no—
808C2×C4—224no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—448no—
813C2×C4C2×#433914yes—
814C2×C4#6703714yes—
815C2×C4C22×C22⋊D1112yes—
816C2×C4C22×C22⋊D1112yes—
817C2×C4C22×C22⋊D1112yes—
818C2×C4C22×C22⋊D1112yes—
819C22—22no—
820C22—24no—
821C22—22no—
822C22—24no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—416no—
833C22—416no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—442no—
843C22—442no—
844C22—444no—
845C22—442no—
846C22—444no—
847C22#1062332214yes—
848C22C22×#433911yescharacteristic
849C22C22×#433911yescharacteristic
850C22C2×#6703712yes—
851C22#1062345312yes—
852C22C23×C22⋊D1111yescharacteristic
853C4—24no—
854C4—22no—
855C4—22no—
856C4—22no—
857C4—42no—
858C4—42no—
859C4—442no—
860C4—442no—
861C4—444no—
862C4—442no—
863C4—444no—
864C4#1062333514yes—
865C2—24no—
866C2—44no—
867C2—42no—
868C2—42no—
869C2—882no—
870C2C2×#1062332211yescharacteristic
871C2C2×#1062333511yescharacteristic
872C2#1308194511yescharacteristic
873C2#1308245512yes—
874C2#1308246812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C4×D4×C11C2
hypercenterC22×C4×D4D11
hypocenterC11#35031
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×#10623322C2semidirect
2. #13076955C2semidirect
3. #13076947C2semidirect
4. #13076903C2semidirect
5. #13076898C2semidirect
6. #13074389C2semidirect
7. #13074328C2semidirect
8. #13074228C2semidirect
9. #13074198C2semidirect
10. #13072913C2semidirect
11. #13072045C2semidirect
12. #13072034C2semidirect
13. #13071961C2semidirect
14. #13071285C2semidirect
15. #13071274C2semidirect
16. #13070999C2semidirect
17. C22×C4×D4×C11C2semidirect
21. C22×#4339C22semidirect
35. C2×#66983C22semidirect
36. C2×#66983C22semidirect
38. C2×#66982C22semidirect
40. C2×C4×C22⋊D11C22semidirect
41. C2×#66979C22semidirect
42. C2×#66979C22semidirect
44. C2×#66977C22semidirect
45. C2×#66977C22semidirect
54. #10622826C22semidirect
57. #10622825C22semidirect
58. #10622825C22semidirect
59. #10622825C22semidirect
61. #10622824C22semidirect
64. #10622823C22semidirect
66. C4×C22⋊Dic11C22semidirect
67. #10622603C22semidirect
68. #10622602C22semidirect
69. #10622591C22semidirect
70. #10622585C22semidirect
71. #10622572C22semidirect
72. #10622572C22semidirect
73. #10622570C22semidirect
74. #10622569C22semidirect
75. #10622565C22semidirect
76. #10622565C22semidirect
77. #10622558C22semidirect
78. #10622557C22semidirect
79. #10622553C22semidirect
80. #10622552C22semidirect
81. #10622546C22semidirect
82. #10622542C22semidirect
83. #10622541C22semidirect
84. #10622541C22semidirect
95. C23×C4×C11D4semidirect
191. C24×C11#41semidirect
230. C22×C4×C11#41semidirect
295. C22×C4×D4D11semidirect
531. C23×C4C22⋊D11semidirect
627. C24#4339semidirect
682. C22×C4#4339semidirect
730. C11#35031semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130769552
#130769472
#130769032
#130768982
#130743892
#130743282
#130742282
#130741982
#130729132
#130720452
#130720342
#130719612
#130712852
#130712742
#130709992
C22×C4×D4×C112
#3503111