Finite Group Databasebeta

← #15638668

Subgroups — #15638668

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic, complemented
2#13080706C214yesmaximal, complemented
3#13080586C214yesmaximal, complemented
4#13080172C214yesmaximal, complemented
5#13080137C214yesmaximal, complemented
6#13079640C212yesmaximal, complemented
7#13079437C211yesmaximal, characteristic, complemented
8#13079422C211yesmaximal, characteristic, complemented
9#13079393C212yesmaximal, complemented
10#13078750C212yesmaximal, complemented
11#13077874C211yesmaximal, characteristic, complemented
12#13077866C211yesmaximal, characteristic, complemented
13#13077832C212yesmaximal, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C11×#3505C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×#4339C2211yescharacteristic, complemented
18C11×#553—22no—
19C11×#553C2212yescomplemented
20C11×#552C2212yescomplemented
21C11×#551—22no—
22C11×#548C2212yescomplemented
23C11×#546C2212yescomplemented
24C11×#539—21no—
25C11×#538—21no—
26C11×#534—21no—
27C11×#529C2212yes—
28C11×#525C2212yes—
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C11×#518—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67003C2214yescomplemented
34C2×#66995C2212yescomplemented
35C2×#66991—21no—
36C2×#66985C2212yescomplemented
37C2×#66977C2211yescharacteristic
38C2×#66977C2211yescharacteristic, complemented
39#10623082—22no—
40#10623082—22no—
41#10623082C2214yes—
42#10623082C2214yescomplemented
43C2×C4⋊C4×D11—21no—
44C2×#66936—21no—
45C2×#66936—21no—
46C2×C4×D44C2211yescharacteristic, complemented
47C2×#66922C2211yescharacteristic, complemented
48#10622852C2214yescomplemented
49#10622841C2212yescomplemented
50#10622831C2212yescomplemented
51#10622820C2211yescharacteristic
52#10622820C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2212yescomplemented
54#10622682C2214yescomplemented
55#10622679C2214yescomplemented
56#10622673C2214yescomplemented
57#10622670C2214yescomplemented
58#10622665C2214yescomplemented
59#10622664C2214yescomplemented
60#10622663C2212yescomplemented
61#10622663C2212yescomplemented
62#10622660C2214yescomplemented
63#10622660C2214yescomplemented
64#10622659C2212yescomplemented
65#10622656C2212yescomplemented
66#10622655C2214yescomplemented
67#10622654C2214yescomplemented
68#10622653C2212yes—
69#10622653C2212yes—
70#10622650C2214yescomplemented
71#10622650C2214yescomplemented
72#10622649C2212yes—
73#10622646C2212yes—
74#10622644C2214yescomplemented
75#10622639C2214yescomplemented
76#10622632C2214yescomplemented
77#10622627C2214yescomplemented
78#10622624C2214yescomplemented
79#10622624C2214yescomplemented
80#10622615C2214yescomplemented
81#10622609C2214yescomplemented
82#10622584C2212yescomplemented
83#10622583C2212yescomplemented
84#10622579C2212yescomplemented
85#10622579C2212yescomplemented
86#10622539C2212yescomplemented
87C2×C11×#41C2312yes—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11D411yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C2×#4339—21no—
97C2×#4339—21no—
98C2×#4339—22no—
99C2×#4339—44no—
100C2×#4339—44no—
101C2×#4339C2312yes—
102C2×#4339C2314yes—
103C2×#4339C2312yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C11×#126—22no—
111C11×#126—22no—
112C11×#126—22no—
113C11×#125—22no—
114C11×#125C2312yes—
115C11×#124—22no—
116C11×#124C2312yes—
117C11×#123—22no—
118C11×#123—22no—
119C11×#123—22no—
120C11×#123—22no—
121C11×#123—22no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8C2312yes—
126C11×C22⋊Q8C2312yes—
127C11×C22⋊Q8C2312yes—
128C11×#121—22no—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121—21no—
132C11×#121—22no—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C11×#121C2312yes—
136C11×#120—22no—
137C11×#120—22no—
138C4×Q8×C11C2312yes—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11D412yes—
145C4×D4×C11D412yes—
146C4×D4×C11C2312yes—
147C4×D4×C11C2312yes—
148C4×D4×C11C2312yes—
149C11×#117—22no—
150C11×#117—22no—
151C11×#117C2312yes—
152C2×C11×C4⋊C4—21no—
153C2×C11×C4⋊C4D411yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—22no—
159C2×C11×C22⋊C4D411yescharacteristic
160C2×C11×C22⋊C4D411yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C22⋊Dic11—21no—
163C2×C22⋊Dic11—21no—
164#67003—48no—
165C2×#4326C2314yes—
166C2×#4326C2314yes—
167#66995—44no—
168C2×#4325C2314yes—
169#66991—24no—
170#66991—24no—
171C2×#4324C2314yes—
172C2×#4324C2314yes—
173#66985—44no—
174C2×#4323C2314yes—
175C2×(C2×D11)⋊C4—21no—
176C2×C4⋊Dic11—21no—
177C2×C4⋊Dic11—21no—
178C2×C4⋊Dic11C2311yescharacteristic
179#66977—21no—
180#66977—21no—
181#66977—22no—
182#66977C2312yes—
183#66977C2312yes—
184#66977C2314yes—
185C2×Dic11⋊C4—21no—
186C2×Dic11⋊C4—21no—
187C2×#4318C2312yes—
188C2×#4318C2312yes—
189C22×C11⋊C8C2314yes—
190C4⋊C4×D11—24no—
191C4⋊C4×D11—24no—
192#66936—24no—
193#66936—24no—
194#66936—24no—
195#66936—24no—
196C4×D44—22no—
197C4×D44C2314yes—
198#66922—22no—
199#66922C2314yes—
200#66899C2314yes—
201#66896C2314yes—
202C22⋊(C11⋊C8)C2312yes—
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2314yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2312yes—
207#66874C2314yes—
208#66874C2314yes—
209#66874C2314yes—
210#66874C2314yes—
211#66873C2314yes—
212#66873C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215C4⋊(C11⋊C8)C2314yes—
216#66867C2314yes—
217#61575—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C11×#41—44no—
223C2×Q8×C11—21no—
224C2×Q8×C11—42no—
225C2×Q8×C11C2412yes—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—22no—
230C2×D4×C11—21no—
231C2×D4×C11—42no—
232C2×D4×C11—42no—
233C2×D4×C11—44no—
234C2×D4×C11C2×D412yes—
235C2×D4×C11C2×D412yes—
236C2×D4×C11C2412yes—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2412yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—22no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263#4339—24no—
264#4339—24no—
265#4339—28no—
266#4339—44no—
267#4339—42no—
268#4339—42no—
269#4339—44no—
270#4339—44no—
271#4339—48no—
272C2×D44—24no—
273C2×D44—21no—
274C2×D44C2412yes—
275C2×C4×D11—24no—
276C2×C4×D11—24no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×Dic22—21no—
283C2×Dic22—21no—
284C2×Dic22—42no—
285C2×Dic22—42no—
286C2×Dic22C2412yes—
287C2×Dic22C2412yes—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4C2×D412yes—
297C11×C4⋊C4C2×D412yes—
298C11×C4⋊C4C2412yes—
299C11×C4⋊C4C2412yes—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4C2×D412yes—
311C11×C22⋊C4C2×D412yes—
312C11×C22⋊C4C2×D412yes—
313C11×C22⋊C4C2×D412yes—
314C42×C11—22no—
315C42×C11—22no—
316C42×C11C2×D412yes—
317C42×C11C2412yes—
318C22⋊Dic11—22no—
319C22⋊Dic11—24no—
320C22⋊Dic11—22no—
321#4326—44no—
322#4326—44no—
323#4325—28no—
324#4324—44no—
325#4324—44no—
326#4323—28no—
327(C2×D11)⋊C4—24no—
328C4⋊Dic11—24no—
329C4⋊Dic11—24no—
330C4⋊Dic11—21no—
331C4⋊Dic11C2412yes—
332Dic11⋊C4—24no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335#4318—42no—
336#4318—42no—
337C2×C11⋊C8—44no—
338C2×C11⋊C8C2414yes—
339C2×C11⋊C8C2414yes—
340#3505D1111yescharacteristic, complemented
341C2×#547—111no—
342#3315—114no—
343#3307—114no—
344#3269—114no—
345#3267—114no—
346#3218—112no—
347#3195—111no—
348#3193—111no—
349#3190—112no—
350#3114—112no—
351#3007—111no—
352#3006—111no—
353#3002—112no—
354#2973—111no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—42no—
363C23×C11—81no—
364C23×C11—81no—
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D412yes—
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C22×D11—24no—
370C22×D11—22no—
371C22×D11—42no—
372C22×D11—42no—
373Q8×C11—24no—
374Q8×C11—81no—
375D4×C11—24no—
376D4×C11—42no—
377D4×C11—42no—
378D4×C11—44no—
379D4×C11—44no—
380D4×C11—81no—
381D4×C11—82no—
382D4×C11—82no—
383C2×C4×C11—22no—
384C2×C4×C11—24no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—42no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—42no—
398C2×C4×C11—82no—
399C2×C4×C11—82no—
400C2×C4×C11—81no—
401C2×C4×C11—81no—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2511yescharacteristic
409C22⋊D11—44no—
410C22⋊D11—48no—
411C22⋊D11—44no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418D44—24no—
419D44—22no—
420D44H(5,𝔽2)14yes—
421C4×D11—48no—
422C4×D11—44no—
423C4×D11—44no—
424C4×D11—48no—
425Dic22—22no—
426Dic22—24no—
427Dic22—22no—
428Dic22—42no—
429Dic22—42no—
430C11⋊C8—24no—
431C11⋊C8—24no—
432C22×#41—111no—
433C22×#41—111no—
434C2×#137—112no—
435C2×AGL(1,ℤ/8)—112no—
436C2×#135—114no—
437#553—22no—
438#553C2×D1112yescomplemented
439#552C2×D1112yescomplemented
440#551—22no—
441#548C2×D1112yescomplemented
442#547—114no—
443#547—114no—
444#547—222no—
445#547—222no—
446#546C2×D1112yescomplemented
447#539—21no—
448#538—21no—
449#534—21no—
450C2×C4⋊Q8—111no—
451#529C2×D1112yes—
452#525C2×D1112yes—
453C2×#123—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8C2×D1111yescharacteristic
458C2×#121—221no—
459C2×#121C2×D1111yescharacteristic
460#518—21no—
461C2×C4×D4—111no—
462C2×C4×D4C2×D1111yescharacteristic
463C22×C4⋊C4—221no—
464#497—114no—
465#491—114no—
466#485—114no—
467#484—112no—
468#483—112no—
469#483—112no—
470#480—112no—
471#478—114no—
472#470—114no—
473#468—114no—
474#467—114no—
475#465—114no—
476#463—114no—
477#462—114no—
478#461—114no—
479#452—114no—
480#452—114no—
481#452—114no—
482#451—112no—
483#451—112no—
484#451—112no—
485#450—112no—
486#450—112no—
487#449—114no—
488#449—114no—
489#448—112no—
490#448—112no—
491#447—112no—
492#442—114no—
493#440—114no—
494#435—114no—
495#435—114no—
496#432—112no—
497#417—112no—
498#417—112no—
499#416—114no—
500#407—111no—
501#407—111no—
502C2×C22⋊C8—112no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—22no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—22no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—22no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—82no—
518C22×C11—82no—
519C22×C11—162no—
520C22×C11#57512yes—
521C22×C11C23×D411yescharacteristic
522C2×D11—24no—
523C2×D11—48no—
524C2×D11—42no—
525C2×D11—42no—
526C4×C11—22no—
527C4×C11—21no—
528C4×C11—22no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11C2×H(5,𝔽2)12yes—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
539C2×#41—114no—
540C2×#41—112no—
541C2×#41—112no—
542C2×#41—221no—
543C2×#41—221no—
544C2×#41—222no—
545C2×#41—444no—
546C2×#41—444no—
547C2×#41C22×D1112yes—
548C22×Q8—111no—
549C22×Q8—111no—
550C22×Q8C22×D1111yescharacteristic
551C22×D4—21no—
552C22×D4—111no—
553C22×D4—221no—
554C22×D4—221no—
555C22×D4C22⋊D1111yescharacteristic
556C22×D4C22×D1111yescharacteristic
557C23×C4—221no—
558C23×C4—221no—
559C23×C4—221no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562#137—444no—
563AGL(1,ℤ/8)—444no—
564#135—448no—
565C2×Q16—114no—
566C2×Q16—114no—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—114no—
570C2×D8—114no—
571C2×M16—112no—
572C2×M16—112no—
573C22×C8—114no—
574C4⋊Q8—114no—
575C4⋊Q8—222no—
576#126—22no—
577#126—22no—
578#126—22no—
579#125—22no—
580#125C22×D1112yes—
581#124—22no—
582#124C22×D1112yes—
583#123—22no—
584#123—22no—
585#123—22no—
586#123—22no—
587#123—22no—
588#123—224no—
589#123—224no—
590#123—224no—
591#123—224no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—22no—
595C22⋊Q8—112no—
596C22⋊Q8—112no—
597C22⋊Q8—114no—
598C22⋊Q8—221no—
599C22⋊Q8—221no—
600C22⋊Q8—222no—
601C22⋊Q8C22×D1112yes—
602C22⋊Q8C22×D1112yes—
603C22⋊Q8C22×D1112yes—
604#121—22no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121—22no—
609#121—224no—
610#121—224no—
611#121C22×D1112yes—
612#121C22×D1112yes—
613#121C22×D1112yes—
614#120—22no—
615#120—22no—
616C4×Q8C22×D1112yes—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—114no—
623C4×D4—222no—
624C4×D4C22⋊D1112yes—
625C4×D4C22⋊D1112yes—
626C4×D4C22×D1112yes—
627C4×D4C22×D1112yes—
628C4×D4C22×D1112yes—
629#117—22no—
630#117—22no—
631#117C22×D1112yes—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—221no—
635C2×C4⋊C4—221no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4—221no—
638C2×C4⋊C4—224no—
639C2×C4⋊C4—224no—
640C2×C4⋊C4C22⋊D1111yescharacteristic
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C4⋊C4C22×D1111yescharacteristic
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—221no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4C22⋊D1111yescharacteristic
650C2×C22⋊C4C22⋊D1111yescharacteristic
651C2×C42C22×D1111yescharacteristic
652#107—114no—
653#106—114no—
654C4⋊C8—114no—
655#103—114no—
656#103—114no—
657#103—114no—
658#103—114no—
659#103—114no—
660#102—114no—
661#102—114no—
662#102—114no—
663C22⋊C8—112no—
664C22⋊C8—112no—
665C22⋊C8—114no—
666C22⋊C8—112no—
667C22⋊C8—112no—
668#97—114no—
669C2×C11—22no—
670C2×C11—41no—
671C2×C11—42no—
672C2×C11—41no—
673C2×C11—82no—
674C2×C11#348411yescharacteristic
675C2×C11C2×#57511yescharacteristic
676C2×C11#358611yescharacteristic
677D11—44no—
678C24—21no—
679C24—221no—
680C24C2×C22⋊D1111yescharacteristic
681C24C2×C22⋊D1111yescharacteristic
682#41—44no—
683#41—228no—
684#41—224no—
685#41—224no—
686#41—444no—
687#41—442no—
688#41—442no—
689#41—448no—
690#41—444no—
691#41—444no—
692C2×Q8—21no—
693C2×Q8—42no—
694C2×Q8—112no—
695C2×Q8—112no—
696C2×Q8—221no—
697C2×Q8—221no—
698C2×Q8—442no—
699C2×Q8—442no—
700C2×Q8C23×D1112yes—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—112no—
710C2×D4—224no—
711C2×D4—222no—
712C2×D4—224no—
713C2×D4—222no—
714C2×D4—221no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4C2×C22⋊D1112yes—
718C2×D4C2×C22⋊D1112yes—
719C2×D4C23×D1112yes—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—224no—
731C22×C4—224no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—444no—
737C22×C4C2×C22⋊D1111yescharacteristic
738C22×C4C2×C22⋊D1111yescharacteristic
739C22×C4C2×C22⋊D1111yescharacteristic
740C22×C4C2×C22⋊D1111yescharacteristic
741C22×C4C2×C22⋊D1111yescharacteristic
742C22×C4C2×C22⋊D1111yescharacteristic
743C22×C4C2×C22⋊D1112yes—
744C22×C4C23×D1111yescharacteristic
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1112yes—
748Q16—444no—
749Q16—444no—
750SD16—228no—
751SD16—444no—
752SD16—444no—
753D8—228no—
754M16—442no—
755M16—442no—
756C2×C8—114no—
757C2×C8—114no—
758C2×C8—444no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—22no—
764C4⋊C4—22no—
765C4⋊C4—22no—
766C4⋊C4—22no—
767C4⋊C4—112no—
768C4⋊C4—221no—
769C4⋊C4—224no—
770C4⋊C4—224no—
771C4⋊C4—222no—
772C4⋊C4—222no—
773C4⋊C4—224no—
774C4⋊C4C2×C22⋊D1112yes—
775C4⋊C4C2×C22⋊D1112yes—
776C4⋊C4C23×D1112yes—
777C4⋊C4C23×D1112yes—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—22no—
782C22⋊C4—22no—
783C22⋊C4—22no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—222no—
789C22⋊C4—224no—
790C22⋊C4—222no—
791C22⋊C4—224no—
792C22⋊C4C2×C22⋊D1112yes—
793C22⋊C4C2×C22⋊D1112yes—
794C22⋊C4C2×C22⋊D1112yes—
795C22⋊C4C2×C22⋊D1112yes—
796C42—22no—
797C42—22no—
798C42C2×C22⋊D1112yes—
799C42C23×D1112yes—
800C11#6157511yescharacteristic, complemented, Sylow
801C23—22no—
802C23—22no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23—224no—
812C23—222no—
813C23—442no—
814C23—442no—
815C23C22×C22⋊D1111yescharacteristic
816C23C22×C22⋊D1112yes—
817C23C22×C22⋊D1111yescharacteristic
818C23C22×C22⋊D1111yescharacteristic
819Q8—24no—
820Q8—81no—
821Q8—222no—
822Q8—224no—
823Q8—222no—
824Q8—442no—
825Q8—442no—
826D4—24no—
827D4—42no—
828D4—42no—
829D4—44no—
830D4—44no—
831D4—81no—
832D4—82no—
833D4—82no—
834D4—114no—
835D4—224no—
836D4—222no—
837D4—444no—
838D4—448no—
839D4—444no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—82no—
856C2×C4—82no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—448no—
863C2×C4—444no—
864C2×C4—444no—
865C2×C4—448no—
866C2×C4—442no—
867C2×C4—442no—
868C2×C4—442no—
869C2×C4C22×C22⋊D1112yes—
870C2×C4C22×C22⋊D1112yes—
871C2×C4C22×C22⋊D1111yescharacteristic
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1111yescharacteristic
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C24×D1111yescharacteristic
876C8—224no—
877C8—224no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—22no—
882C22—21no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—82no—
893C22—82no—
894C22—162no—
895C22—224no—
896C22—448no—
897C22—442no—
898C22—442no—
899C22#1062335312yes—
900C22C23×C22⋊D1111yescharacteristic
901C4—22no—
902C4—21no—
903C4—22no—
904C4—21no—
905C4—21no—
906C4—22no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—442no—
911C4—442no—
912C4—442no—
913C4D11×H(5,𝔽2)12yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—82no—
919C2—444no—
920C2#1308224711yescharacteristic
921C2C2×#1062335311yescharacteristic
922C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3505C2
socleC22×C11C23×D4
hypercenter#3505D11
hypocenterC11#61575
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. C2×#10623082C2semidirect
2. #13080706C2semidirect
3. #13080586C2semidirect
4. #13080172C2semidirect
5. #13080137C2semidirect
6. #13079640C2semidirect
7. #13079437C2semidirect
8. #13079422C2semidirect
9. #13079393C2semidirect
10. #13078750C2semidirect
11. #13077874C2semidirect
12. #13077866C2semidirect
13. #13077832C2semidirect
14. #13077645C2semidirect
15. C11×#3505C2semidirect
17. C22×#4339C22semidirect
19. C11×#553C22semidirect
20. C11×#552C22semidirect
22. C11×#548C22semidirect
23. C11×#546C22semidirect
33. C2×#67003C22semidirect
34. C2×#66995C22semidirect
36. C2×#66985C22semidirect
38. C2×#66977C22semidirect
42. #10623082C22semidirect
46. C2×C4×D44C22semidirect
47. C2×#66922C22semidirect
48. #10622852C22semidirect
49. #10622841C22semidirect
50. #10622831C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622682C22semidirect
55. #10622679C22semidirect
56. #10622673C22semidirect
57. #10622670C22semidirect
58. #10622665C22semidirect
59. #10622664C22semidirect
60. #10622663C22semidirect
61. #10622663C22semidirect
62. #10622660C22semidirect
63. #10622660C22semidirect
64. #10622659C22semidirect
65. #10622656C22semidirect
66. #10622655C22semidirect
67. #10622654C22semidirect
70. #10622650C22semidirect
71. #10622650C22semidirect
74. #10622644C22semidirect
75. #10622639C22semidirect
76. #10622632C22semidirect
77. #10622627C22semidirect
78. #10622624C22semidirect
79. #10622624C22semidirect
80. #10622615C22semidirect
81. #10622609C22semidirect
82. #10622584C22semidirect
83. #10622583C22semidirect
84. #10622579C22semidirect
85. #10622579C22semidirect
86. #10622539C22semidirect
340. #3505D11semidirect
438. #553C2×D11semidirect
439. #552C2×D11semidirect
441. #548C2×D11semidirect
446. #546C2×D11semidirect
800. C11#61575semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
#130807062
#130805862
#130801722
#130801372
#130796402
#130794372
#130794222
#130793932
#130787502
#130778742
#130778662
#130778322
#130776452
C11×#35052
#6157511