Finite Group Databasebeta

← #15624584

Subgroups — #15624584

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081945C211yesmaximal, characteristic, complemented
2#13079522C214yesmaximal, complemented
3#13079513C214yesmaximal, complemented
4#13079492C214yesmaximal, complemented
5#13079462C214yesmaximal, complemented
6#13078560C211yesmaximal, characteristic, complemented
7#13078552C211yesmaximal, characteristic, complemented
8#13078539C212yesmaximal, complemented
9#13078242C212yesmaximal, complemented
10#13078231C212yesmaximal, complemented
11#13077874C211yesmaximal, characteristic, complemented
12#13077866C211yesmaximal, characteristic, complemented
13#13077858C212yesmaximal, complemented
14#13077061C211yesmaximal, characteristic, complemented
15C2×C11×#537C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic, complemented
18C22×#4339C2211yescharacteristic
19C11×#537—22no—
20C11×#537—22no—
21C11×#537C2214yes—
22C11×#537C2214yescomplemented
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic, complemented
26C2×C11×#121—21no—
27C2×C11×#121—21no—
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic, complemented
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32#10623364C2212yescomplemented
33#10623364C2212yescomplemented
34#10623363—22no—
35#10623361C2212yescomplemented
36#10623359—22no—
37#10623356C2212yescomplemented
38#10623347—21no—
39C2×#66995C2212yes—
40#10623336—21no—
41#10623335—21no—
42#10623335—21no—
43C2×#66985C2212yes—
44#10623322C2212yes—
45#10623322C2212yes—
46C2×#66979C2211yescharacteristic
47C22×#4318C2212yescomplemented
48#10622852C2214yescomplemented
49#10622852C2214yescomplemented
50#10622851C2214yescomplemented
51#10622851C2214yescomplemented
52#10622847C2214yescomplemented
53#10622847C2214yescomplemented
54#10622838C2212yescomplemented
55#10622828C2212yescomplemented
56#10622820C2211yescharacteristic
57#10622820C2211yescharacteristic
58#10622820C2212yescomplemented
59#10622665C2214yescomplemented
60#10622664C2214yescomplemented
61#10622663C2212yescomplemented
62#10622662C2214yescomplemented
63#10622661C2214yescomplemented
64#10622660C2214yescomplemented
65#10622659C2212yescomplemented
66#10622658C2214yescomplemented
67#10622657C2212yescomplemented
68#10622656C2212yescomplemented
69#10622655C2214yescomplemented
70#10622654C2214yescomplemented
71#10622653C2212yescomplemented
72#10622652C2214yescomplemented
73#10622651C2214yescomplemented
74#10622650C2214yescomplemented
75#10622649C2212yescomplemented
76#10622648C2214yescomplemented
77#10622647C2212yescomplemented
78#10622646C2212yescomplemented
79#10622584C2214yescomplemented
80#10622583C2214yescomplemented
81#10622581C2214yescomplemented
82#10622580C2214yescomplemented
83#10622579C2212yes—
84#10622579C2212yes—
85#10622577C2212yescomplemented
86#10622577C2212yescomplemented
87C2×C11×#41—22no—
88C2×C11×#41—44no—
89C2×C11×#41—44no—
90C2×C11×#41D412yes—
91C2×C11×#41D412yes—
92C2×C11×#41C2314yes—
93C2×C11×#41C2312yes—
94C2×C11×#41C2312yes—
95C22×Q8×C11D411yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11D411yescharacteristic
101C22×D4×C11D411yescharacteristic
102C22×D4×C11D411yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11—21no—
105C23×C4×C11—21no—
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C22×C22⋊D11—21no—
110C2×#4339—21no—
111C2×#4339—21no—
112C2×#4339—44no—
113C2×#4339C2312yes—
114C2×#4339C2312yes—
115C22×D44C2311yescharacteristic
116C22×C4×D11—21no—
117C22×Dic22C2311yescharacteristic
118C11×C22⋊Q8—24no—
119C11×C22⋊Q8—24no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8C2312yes—
124C11×C22⋊Q8C2312yes—
125C11×C22⋊Q8C2314yes—
126C11×#121—24no—
127C11×#121—24no—
128C11×#121—24no—
129C11×#121—24no—
130C11×#121—24no—
131C11×#121—24no—
132C11×#121—21no—
133C11×#121—21no—
134C11×#121—22no—
135C11×#121C2312yes—
136C11×#121C2312yes—
137C11×#121C2314yes—
138C2×C11×C4⋊C4—21no—
139C2×C11×C4⋊C4—22no—
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4—21no—
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2314yes—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4—21no—
149#67006—22no—
150#67006—22no—
151C2×C22⋊Dic11—21no—
152#67000—22no—
153#66999—22no—
154#66999—22no—
155#66997—22no—
156C2×#4326C2314yes—
157#66995—44no—
158C2×#4325C2314yes—
159#66993—22no—
160#66992—22no—
161#66992—22no—
162#66992—22no—
163#66992—22no—
164#66991—22no—
165#66991—22no—
166#66990—22no—
167#66990—22no—
168#66989—22no—
169#66988—22no—
170#66988—22no—
171C2×#4324C2314yes—
172#66985—44no—
173C2×#4323C2314yes—
174#66983C2312yes—
175#66983C2312yes—
176#66983C2312yes—
177#66983C2312yes—
178#66982—22no—
179#66982—22no—
180C4×C22⋊D11—22no—
181C4×C22⋊D11—22no—
182C4×C22⋊D11—22no—
183C4×C22⋊D11—22no—
184#66979—21no—
185#66979—21no—
186#66979C2312yes—
187#66979C2312yes—
188C2×C4⋊Dic11C2311yescharacteristic
189C2×C4⋊Dic11C2311yescharacteristic
190#66977C2312yes—
191#66977C2312yes—
192#66977C2312yes—
193#66977C2312yes—
194C2×C4×Dic11—21no—
195C2×#4318—44no—
196C2×#4318C2312yes—
197C2×#4318C2312yes—
198C2×#4318C2314yes—
199C22×C11⋊C8C2314yes—
200#66899C2314yes—
201#66899C2314yes—
202#66896C2314yes—
203#66896C2314yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2314yes—
209C22⋊(C11⋊C8)C2314yes—
210#66874C2314yes—
211#66874C2314yes—
212#66873C2314yes—
213#66873C2314yes—
214#66872C2314yes—
215#66872C2314yes—
216#66871C2314yes—
217#66871C2314yes—
218#60755—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C24×C11C2×D411yescharacteristic
223C23×D11—21no—
224C11×#41—44no—
225C11×#41—44no—
226C11×#41—42no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41—44no—
231C11×#41—44no—
232C11×#41—48no—
233C2×Q8×C11—21no—
234C2×Q8×C11—24no—
235C2×Q8×C11—42no—
236C2×Q8×C11C2×D412yes—
237C2×Q8×C11C2×D412yes—
238C2×Q8×C11C2412yes—
239C2×D4×C11—24no—
240C2×D4×C11—22no—
241C2×D4×C11—24no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—24no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11—42no—
248C2×D4×C11—44no—
249C2×D4×C11—82no—
250C2×D4×C11—82no—
251C2×D4×C11C2×D412yes—
252C2×D4×C11C2×D412yes—
253C2×D4×C11C2×D412yes—
254C2×D4×C11C2×D412yes—
255C2×D4×C11C2×D412yes—
256C2×D4×C11C2×D412yes—
257C2×D4×C11C2412yes—
258C22×C4×C11—24no—
259C22×C4×C11—24no—
260C22×C4×C11—24no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—24no—
265C22×C4×C11—24no—
266C22×C4×C11—44no—
267C22×C4×C11—82no—
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D412yes—
272C22×C4×C11C2×D412yes—
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C2×C22⋊D11—22no—
281C2×C22⋊D11—22no—
282C2×C22⋊D11—22no—
283C2×C22⋊D11—22no—
284C2×C22⋊D11—22no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—44no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290#4339—24no—
291#4339—24no—
292#4339—42no—
293#4339—42no—
294#4339—44no—
295#4339—44no—
296C2×D44—21no—
297C2×D44—42no—
298C2×D44C2412yes—
299C2×C4×D11—22no—
300C2×C4×D11—22no—
301C2×C4×D11—44no—
302C2×Dic22—21no—
303C2×Dic22—42no—
304C2×Dic22C2412yes—
305C11×C4⋊C4—24no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—24no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4C2412yes—
312C11×C4⋊C4C2412yes—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—24no—
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—24no—
318C11×C22⋊C4—22no—
319C22⋊Dic11—22no—
320C22⋊Dic11—22no—
321C22⋊Dic11—22no—
322C22⋊Dic11—22no—
323C22⋊Dic11—22no—
324C22⋊Dic11—22no—
325#4326—44no—
326#4325—44no—
327#4324—44no—
328#4323—44no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—22no—
333C4⋊Dic11—21no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2412yes—
336C4⋊Dic11C2412yes—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343#4318—24no—
344#4318—24no—
345#4318—44no—
346C2×C11⋊C8—44no—
347C2×C11⋊C8C2414yes—
348C2×C11⋊C8C2414yes—
349#3449—111no—
350C2×#537D1111yescharacteristic, complemented
351#3204—114no—
352#3203—114no—
353#3201—114no—
354#3198—114no—
355#3095—111no—
356#3094—111no—
357#3092—112no—
358#3056—112no—
359#3055—112no—
360#3007—111no—
361#3006—111no—
362#3005—112no—
363#2879—111no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—42no—
375C23×C11—42no—
376C23×C11—42no—
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D412yes—
379C23×C11C22×D412yes—
380C23×C11C22×D411yescharacteristic
381C23×C11C22×D411yescharacteristic
382C22×D11—22no—
383C22×D11—42no—
384C22×D11—81no—
385C22×D11—81no—
386Q8×C11—24no—
387Q8×C11—42no—
388Q8×C11—42no—
389Q8×C11—42no—
390D4×C11—24no—
391D4×C11—42no—
392D4×C11—42no—
393D4×C11—42no—
394D4×C11—42no—
395D4×C11—42no—
396D4×C11—42no—
397D4×C11—48no—
398D4×C11—42no—
399D4×C11—82no—
400D4×C11—82no—
401D4×C11—84no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—24no—
408C2×C4×C11—24no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—48no—
419C2×C4×C11—42no—
420C2×C4×C11—42no—
421C2×C4×C11—42no—
422C2×C4×C11—84no—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D412yes—
425C2×C4×C11C22×D412yes—
426C2×C4×C11C22×D411yescharacteristic
427C2×C4×C11C22×D411yescharacteristic
428C2×C4×C11H(5,𝔽2)14yes—
429C2×C4×C11C2511yescharacteristic
430C22⋊D11—44no—
431C22⋊D11—44no—
432C22⋊D11—82no—
433C22⋊D11—82no—
434C22⋊D11—82no—
435C22⋊D11—82no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—42no—
440C2×Dic11—81no—
441C2×Dic11—81no—
442D44—22no—
443D44—22no—
444D44—42no—
445C4×D11—44no—
446C4×D11—44no—
447Dic22—22no—
448Dic22—22no—
449Dic22—42no—
450C11⋊C8—24no—
451C11⋊C8—24no—
452C22×#41—111no—
453C22×#41C2×D1111yescharacteristic
454C22×#41C2×D1111yescharacteristic, complemented
455C2×#137—112no—
456C2×AGL(1,ℤ/8)—112no—
457C22×M16—112no—
458#537—22no—
459#537—22no—
460#537—112no—
461#537—112no—
462#537C2×D1114yes—
463#537C2×D1114yescomplemented
464#536—112no—
465#536—221no—
466#535—112no—
467#535—221no—
468#534—221no—
469#534—221no—
470#532—222no—
471#525—112no—
472#525—112no—
473#525—222no—
474C2×C22⋊Q8—21no—
475C2×C22⋊Q8C2×D1111yescharacteristic
476C2×C22⋊Q8C2×D1111yescharacteristic, complemented
477C2×#121—21no—
478C2×#121—21no—
479C2×#121—21no—
480C2×#121C2×D1111yescharacteristic
481C2×#121C2×D1111yescharacteristic, complemented
482C2×#117—111no—
483C22×C4⋊C4C2×D1111yescharacteristic, complemented
484#485—114no—
485#484—112no—
486#484—114no—
487#483—112no—
488#483—114no—
489#482—114no—
490#481—112no—
491#481—114no—
492#480—112no—
493#480—114no—
494#470—114no—
495#469—114no—
496#468—114no—
497#468—114no—
498#467—114no—
499#466—114no—
500#465—114no—
501#465—114no—
502#452—114no—
503#452—114no—
504#452—114no—
505#451—112no—
506#450—112no—
507#449—114no—
508#449—114no—
509#449—114no—
510#448—112no—
511#447—112no—
512#428—112no—
513#428—112no—
514#419—112no—
515#418—112no—
516#417—112no—
517#417—112no—
518#408—114no—
519#408—114no—
520#407—112no—
521#407—111no—
522#407—111no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—22no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—22no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—22no—
532C22×C11—22no—
533C22×C11—22no—
534C22×C11—21no—
535C22×C11—22no—
536C22×C11—21no—
537C22×C11—44no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—82no—
542C22×C11—82no—
543C22×C11—84no—
544C22×C11#53412yes—
545C22×C11C23×D411yescharacteristic
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—84no—
550C4×C11—22no—
551C4×C11—22no—
552C4×C11—21no—
553C4×C11—21no—
554C4×C11—42no—
555C4×C11—42no—
556C4×C11—42no—
557C4×C11#53412yes—
558C4×C11C2×H(5,𝔽2)12yes—
559Dic11—42no—
560Dic11—42no—
561Dic11—42no—
562C2×#41—22no—
563C2×#41—44no—
564C2×#41—44no—
565C2×#41—112no—
566C2×#41—112no—
567C2×#41—221no—
568C2×#41—221no—
569C2×#41—444no—
570C2×#41C22⋊D1112yes—
571C2×#41C22⋊D1112yes—
572C2×#41C22×D1114yes—
573C2×#41C22×D1112yes—
574C2×#41C22×D1112yes—
575C22×Q8—111no—
576C22×Q8C22⋊D1111yescharacteristic
577C22×Q8C22×D1111yescharacteristic
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—111no—
582C22×D4—221no—
583C22×D4C22⋊D1111yescharacteristic
584C22×D4C22⋊D1111yescharacteristic
585C22×D4C22⋊D1111yescharacteristic
586C22×D4C22×D1111yescharacteristic
587C23×C4—21no—
588C23×C4—21no—
589C23×C4—221no—
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593#137—444no—
594AGL(1,ℤ/8)—444no—
595C2×Q16—114no—
596C2×SD16—114no—
597C2×SD16—114no—
598C2×D8—114no—
599C2×M16—112no—
600C2×M16—112no—
601C2×M16—114no—
602C2×M16—444no—
603C22×C8—114no—
604C4⋊Q8—222no—
605#127—222no—
606#124—222no—
607#124—222no—
608#123—222no—
609#123—222no—
610#123—222no—
611#123—222no—
612C22⋊Q8—24no—
613C22⋊Q8—24no—
614C22⋊Q8—21no—
615C22⋊Q8—21no—
616C22⋊Q8—22no—
617C22⋊Q8—112no—
618C22⋊Q8—112no—
619C22⋊Q8—112no—
620C22⋊Q8—112no—
621C22⋊Q8—222no—
622C22⋊Q8—222no—
623C22⋊Q8C22×D1112yes—
624C22⋊Q8C22×D1112yes—
625C22⋊Q8C22×D1114yes—
626#121—24no—
627#121—24no—
628#121—24no—
629#121—24no—
630#121—24no—
631#121—24no—
632#121—21no—
633#121—21no—
634#121—22no—
635#121—112no—
636#121—112no—
637#121—112no—
638#121—112no—
639#121—222no—
640#121—222no—
641#121—222no—
642#121—222no—
643#121—222no—
644#121—222no—
645#121C22×D1112yes—
646#121C22×D1112yes—
647#121C22×D1114yes—
648#120—222no—
649#120—222no—
650#120—222no—
651#120—222no—
652C4×D4—222no—
653C4×D4—222no—
654C4×D4—222no—
655C4×D4—222no—
656#117—112no—
657#117—112no—
658#117—221no—
659#117—221no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—111no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1114yes—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—221no—
674C2×C42—221no—
675#107—114no—
676#107—114no—
677#106—114no—
678#106—114no—
679#103—114no—
680#103—114no—
681#103—114no—
682#103—114no—
683#102—114no—
684#102—114no—
685#102—114no—
686#102—114no—
687C22⋊C8—112no—
688C22⋊C8—112no—
689C22⋊C8—114no—
690C22⋊C8—114no—
691C22⋊C8—112no—
692C22⋊C8—112no—
693C2×C11—22no—
694C2×C11—41no—
695C2×C11—42no—
696C2×C11—41no—
697C2×C11—42no—
698C2×C11—82no—
699C2×C11C2×#53411yescharacteristic
700C2×C11#358511yescharacteristic
701C2×C11#358611yescharacteristic
702D11—82no—
703C24—21no—
704C24—221no—
705C24C2×C22⋊D1111yescharacteristic
706C24C2×C22⋊D1111yescharacteristic
707C24C2×C22⋊D1111yescharacteristic
708#41—42no—
709#41—42no—
710#41—42no—
711#41—42no—
712#41—44no—
713#41—44no—
714#41—44no—
715#41—44no—
716#41—48no—
717#41—224no—
718#41—224no—
719#41—442no—
720#41—442no—
721#41—444no—
722#41—444no—
723C2×Q8—21no—
724C2×Q8—24no—
725C2×Q8—42no—
726C2×Q8—112no—
727C2×Q8—221no—
728C2×Q8—442no—
729C2×Q8C2×C22⋊D1112yes—
730C2×Q8C2×C22⋊D1112yes—
731C2×Q8C23×D1112yes—
732C2×D4—24no—
733C2×D4—22no—
734C2×D4—24no—
735C2×D4—22no—
736C2×D4—24no—
737C2×D4—21no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—82no—
743C2×D4—82no—
744C2×D4—112no—
745C2×D4—222no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—222no—
749C2×D4—222no—
750C2×D4—222no—
751C2×D4—221no—
752C2×D4—442no—
753C2×D4—444no—
754C2×D4C2×C22⋊D1112yes—
755C2×D4C2×C22⋊D1112yes—
756C2×D4C2×C22⋊D1112yes—
757C2×D4C2×C22⋊D1112yes—
758C2×D4C2×C22⋊D1112yes—
759C2×D4C2×C22⋊D1112yes—
760C2×D4C23×D1112yes—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—44no—
770C22×C4—82no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—444no—
777C22×C4C2×C22⋊D1111yescharacteristic
778C22×C4C2×C22⋊D1111yescharacteristic
779C22×C4C2×C22⋊D1111yescharacteristic
780C22×C4C2×C22⋊D1112yes—
781C22×C4C2×C22⋊D1111yescharacteristic
782C22×C4C2×C22⋊D1111yescharacteristic
783C22×C4C2×C22⋊D1112yes—
784C22×C4C23×D1111yescharacteristic
785C22×C4C23×D1112yes—
786C22×C4C23×D1111yescharacteristic
787C22×C4C23×D1112yes—
788C22×C4C23×D1111yescharacteristic
789Q16—444no—
790SD16—444no—
791SD16—444no—
792D8—444no—
793M16—224no—
794M16—224no—
795M16—444no—
796C2×C8—114no—
797C2×C8—114no—
798C2×C8—444no—
799C4⋊C4—24no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—22no—
803C4⋊C4—24no—
804C4⋊C4—22no—
805C4⋊C4—112no—
806C4⋊C4—112no—
807C4⋊C4—221no—
808C4⋊C4—221no—
809C4⋊C4—222no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4—222no—
813C4⋊C4C23×D1112yes—
814C4⋊C4C23×D1112yes—
815C22⋊C4—22no—
816C22⋊C4—24no—
817C22⋊C4—22no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—222no—
822C22⋊C4—222no—
823C22⋊C4—222no—
824C22⋊C4—222no—
825C22⋊C4—222no—
826C22⋊C4—222no—
827C22⋊C4—222no—
828C22⋊C4—222no—
829C22⋊C4—222no—
830C22⋊C4—222no—
831C42—222no—
832C42—222no—
833C11#6075511yescharacteristic, complemented, Sylow
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—222no—
848C23—442no—
849C23—881no—
850C23—881no—
851C23C22×C22⋊D1111yescharacteristic
852C23C22×C22⋊D1112yes—
853C23C22×C22⋊D1111yescharacteristic
854C23C22×C22⋊D1112yes—
855C23C22×C22⋊D1111yescharacteristic
856Q8—24no—
857Q8—42no—
858Q8—42no—
859Q8—42no—
860Q8—222no—
861Q8—222no—
862Q8—442no—
863D4—24no—
864D4—42no—
865D4—42no—
866D4—42no—
867D4—42no—
868D4—42no—
869D4—42no—
870D4—48no—
871D4—42no—
872D4—82no—
873D4—84no—
874D4—82no—
875D4—222no—
876D4—222no—
877D4—442no—
878D4—444no—
879D4—444no—
880D4—882no—
881D4—882no—
882D4—882no—
883D4—882no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—48no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—84no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—444no—
909C2×C4—442no—
910C2×C4—444no—
911C2×C4—881no—
912C2×C4—881no—
913C2×C4#6703714yes—
914C2×C4C22×C22⋊D1111yescharacteristic
915C2×C4C22×C22⋊D1112yes—
916C2×C4C22×C22⋊D1111yescharacteristic
917C2×C4C22×C22⋊D1112yes—
918C2×C4C22×C22⋊D1111yescharacteristic
919C2×C4C24×D1111yescharacteristic
920C8—224no—
921C8—224no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—21no—
926C22—22no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—22no—
931C22—21no—
932C22—21no—
933C22—22no—
934C22—21no—
935C22—22no—
936C22—44no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—82no—
941C22—82no—
942C22—84no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—884no—
947C22#1062333512yes—
948C22C23×C22⋊D1111yescharacteristic
949C4—22no—
950C4—21no—
951C4—21no—
952C4—22no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—442no—
957C4—442no—
958C4—442no—
959C4#1062333512yes—
960C4C2×#6703712yes—
961C2—22no—
962C2—42no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—82no—
967C2—882no—
968C2C2×#1062333511yescharacteristic
969C2#1308339611yescharacteristic
970C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#537C2
socleC22×C11C23×D4
hypercenterC2×#537D11
hypocenterC11#60755
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13081945C2semidirect
2. #13079522C2semidirect
3. #13079513C2semidirect
4. #13079492C2semidirect
5. #13079462C2semidirect
6. #13078560C2semidirect
7. #13078552C2semidirect
8. #13078539C2semidirect
9. #13078242C2semidirect
10. #13078231C2semidirect
11. #13077874C2semidirect
12. #13077866C2semidirect
13. #13077858C2semidirect
14. #13077061C2semidirect
15. C2×C11×#537C2semidirect
17. C22×C11×#41C22semidirect
22. C11×#537C22semidirect
25. C2×C11×C22⋊Q8C22semidirect
30. C2×C11×#121C22semidirect
31. C22×C11×C4⋊C4C22semidirect
32. #10623364C22semidirect
33. #10623364C22semidirect
35. #10623361C22semidirect
37. #10623356C22semidirect
47. C22×#4318C22semidirect
48. #10622852C22semidirect
49. #10622852C22semidirect
50. #10622851C22semidirect
51. #10622851C22semidirect
52. #10622847C22semidirect
53. #10622847C22semidirect
54. #10622838C22semidirect
55. #10622828C22semidirect
58. #10622820C22semidirect
59. #10622665C22semidirect
60. #10622664C22semidirect
61. #10622663C22semidirect
62. #10622662C22semidirect
63. #10622661C22semidirect
64. #10622660C22semidirect
65. #10622659C22semidirect
66. #10622658C22semidirect
67. #10622657C22semidirect
68. #10622656C22semidirect
69. #10622655C22semidirect
70. #10622654C22semidirect
71. #10622653C22semidirect
72. #10622652C22semidirect
73. #10622651C22semidirect
74. #10622650C22semidirect
75. #10622649C22semidirect
76. #10622648C22semidirect
77. #10622647C22semidirect
78. #10622646C22semidirect
79. #10622584C22semidirect
80. #10622583C22semidirect
81. #10622581C22semidirect
82. #10622580C22semidirect
85. #10622577C22semidirect
86. #10622577C22semidirect
350. C2×#537D11semidirect
454. C22×#41C2×D11semidirect
463. #537C2×D11semidirect
476. C2×C22⋊Q8C2×D11semidirect
481. C2×#121C2×D11semidirect
483. C22×C4⋊C4C2×D11semidirect
833. C11#60755semidirect

Maximal subgroups

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

subgroupindex
#130819452
#130795222
#130795132
#130794922
#130794622
#130785602
#130785522
#130785392
#130782422
#130782312
#130778742
#130778662
#130778582
#130770612
C2×C11×#5372
#6075511