Finite Group Databasebeta

← #15638507

Subgroups — #15638507

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic, complemented
2#13080512C214yesmaximal, complemented
3#13080497C214yesmaximal, complemented
4#13080353C214yesmaximal, complemented
5#13080319C214yesmaximal, complemented
6#13079577C212yesmaximal, complemented
7#13079393C212yesmaximal, complemented
8#13079369C211yesmaximal, characteristic, complemented
9#13079364C211yesmaximal, characteristic, complemented
10#13078692C212yesmaximal, complemented
11#13077832C212yesmaximal, complemented
12C2×#10622663C211yesmaximal, characteristic, complemented
13C2×#10622653C211yesmaximal, characteristic, complemented
14#13077640C211yesmaximal, characteristic, complemented
15C11×#3505C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic, complemented
17C23×Dic22C2211yescharacteristic
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
34C22×#4326C2212yescomplemented
35C2×#66992—21no—
36C22×#4324C2212yescomplemented
37C2×#66983C2211yescharacteristic
38C2×#66977C2211yescharacteristic, complemented
39#10623083—22no—
40#10623083—22no—
41#10623083C2214yes—
42#10623083C2214yescomplemented
43C2×#66949—21no—
44C2×#66938—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66928C2211yescharacteristic, complemented
47C2×C4×Dic22C2211yescharacteristic, complemented
48#10622852C2214yescomplemented
49#10622840C2212yescomplemented
50#10622830C2212yescomplemented
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2212yescomplemented
54#10622681C2214yescomplemented
55#10622676C2214yescomplemented
56#10622672C2214yescomplemented
57#10622667C2214yescomplemented
58#10622664C2214yescomplemented
59#10622663C2212yescomplemented
60#10622663C2212yescomplemented
61#10622663C2214yescomplemented
62#10622661C2214yescomplemented
63#10622660C2214yescomplemented
64#10622659C2212yescomplemented
65#10622656C2212yescomplemented
66#10622654C2214yescomplemented
67#10622653C2212yes—
68#10622653C2212yes—
69#10622653C2214yescomplemented
70#10622651C2214yescomplemented
71#10622650C2214yescomplemented
72#10622649C2212yes—
73#10622646C2212yes—
74C4×#4326C2214yescomplemented
75#10622641C2214yescomplemented
76C4×#4324C2214yescomplemented
77#10622629C2214yescomplemented
78D4×C11⋊C8C2214yescomplemented
79D4×C11⋊C8C2214yescomplemented
80#10622615C2214yescomplemented
81#10622609C2214yescomplemented
82C2×#66874C2212yescomplemented
83C2×#66874C2212yescomplemented
84#10622581C2212yescomplemented
85#10622580C2212yescomplemented
86#10622538C2212yescomplemented
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—
96C23×Dic11—21no—
97C2×#4339—22no—
98C2×#4339—44no—
99C2×#4339C2314yes—
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×Dic22—21no—
103C22×Dic22—21no—
104C22×Dic22—21no—
105C22×Dic22—44no—
106C22×Dic22C2311yescharacteristic
107C22×Dic22C2312yes—
108C22×Dic22C2312yes—
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—
163#67003—48no—
164C2×#4326—44no—
165C2×#4326C2314yes—
166C2×#4326C2314yes—
167C2×#4325C2314yes—
168#66992—24no—
169#66992—24no—
170C2×#4324—44no—
171C2×#4324C2314yes—
172C2×#4324C2314yes—
173C2×#4323C2314yes—
174#66983—21no—
175#66983—21no—
176#66983C2312yes—
177#66983C2312yes—
178C2×(C2×D11)⋊C4—21no—
179C2×(C2×D11)⋊C4—21no—
180C2×(C2×D11)⋊C4—21no—
181C2×C4⋊Dic11C2311yescharacteristic
182#66977—22no—
183#66977C2314yes—
184C2×Dic11⋊C4—21no—
185C2×Dic11⋊C4—21no—
186C2×C4×Dic11—21no—
187C22×C11⋊C8C2312yes—
188C22×C11⋊C8C2312yes—
189C22×C11⋊C8C2314yes—
190#66949—24no—
191#66949—24no—
192#66938—24no—
193#66938—24no—
194(C22⋊D11)⋊C4—24no—
195(C22⋊D11)⋊C4—24no—
196#66928—22no—
197#66928C2314yes—
198C4×Dic22—22no—
199C4×Dic22C2314yes—
200#66899C2314yes—
201#66896C2314yes—
202C22⋊(C11⋊C8)C2312yes—
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2314yes—
207#66874C2314yes—
208#66874C2314yes—
209#66874C2314yes—
210#66874C2314yes—
211#66873C2314yes—
212#66873C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215C4⋊(C11⋊C8)C2314yes—
216C4×C11⋊C8C2314yes—
217#61564—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—24no—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—21no—
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×D412yes—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2412yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C22×Dic11—21no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—44no—
266#4339—28no—
267#4339—44no—
268#4339—48no—
269C2×D44—21no—
270C2×D44—42no—
271C2×D44C2412yes—
272C2×C4×D11—24no—
273C2×C4×D11—44no—
274C2×Dic22—24no—
275C2×Dic22—24no—
276C2×Dic22—24no—
277C2×Dic22—21no—
278C2×Dic22—21no—
279C2×Dic22—22no—
280C2×Dic22—22no—
281C2×Dic22—42no—
282C2×Dic22—42no—
283C2×Dic22—42no—
284C2×Dic22—44no—
285C2×Dic22—44no—
286C2×Dic22—44no—
287C2×Dic22C2412yes—
288C2×Dic22C2412yes—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4C2×D412yes—
298C11×C4⋊C4C2×D412yes—
299C11×C4⋊C4C2412yes—
300C11×C4⋊C4C2412yes—
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⋊C4—22no—
311C11×C22⋊C4C2×D412yes—
312C11×C22⋊C4C2×D412yes—
313C11×C22⋊C4C2×D412yes—
314C11×C22⋊C4C2×D412yes—
315C42×C11—22no—
316C42×C11—22no—
317C42×C11C2×D412yes—
318C42×C11C2412yes—
319C22⋊Dic11—24no—
320#4326—28no—
321#4326—44no—
322#4325—44no—
323#4324—28no—
324#4324—44no—
325#4323—44no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330C4⋊Dic11—21no—
331C4⋊Dic11C2412yes—
332Dic11⋊C4—24no—
333Dic11⋊C4—24no—
334C4×Dic11—24no—
335C2×C11⋊C8—42no—
336C2×C11⋊C8—42no—
337C2×C11⋊C8—44no—
338C2×C11⋊C8C2414yes—
339C2×C11⋊C8C2414yes—
340#3505D1111yescharacteristic, complemented
341C2×#548—111no—
342#3301—114no—
343#3300—114no—
344#3285—114no—
345#3282—114no—
346#3211—112no—
347#3190—112no—
348#3187—111no—
349#3186—111no—
350#3108—112no—
351#3002—112no—
352C2×#451—111no—
353C2×#448—111no—
354#2972—111no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—42no—
362C23×C11—81no—
363C23×C11—81no—
364C23×C11#13514yescomplemented
365C23×C11C22×D412yes—
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C22×D11—22no—
370C22×D11—42no—
371C22×D11—42no—
372C22×D11—42no—
373Q8×C11—24no—
374Q8×C11—81no—
375D4×C11—24no—
376D4×C11—24no—
377D4×C11—24no—
378D4×C11—44no—
379D4×C11—44no—
380D4×C11—81no—
381D4×C11—82no—
382D4×C11—82no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—24no—
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—41no—
394C2×C4×C11—41no—
395C2×C4×C11—42no—
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×D412yes—
404C2×C4×C11C22×D412yes—
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2511yescharacteristic
409C22⋊D11—48no—
410C22⋊D11—44no—
411C22⋊D11—44no—
412C2×Dic11—24no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—44no—
417C2×Dic11—44no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420D44—24no—
421D44—42no—
422C4×D11—48no—
423Dic22—24no—
424Dic22—22no—
425Dic22—22no—
426Dic22—22no—
427Dic22—44no—
428Dic22—44no—
429Dic22—42no—
430Dic22H(5,𝔽2)14yes—
431C11⋊C8—24no—
432C11⋊C8—24no—
433C22×#41—111no—
434C23×Q8—111no—
435C2×#135—114no—
436C22×Q16—112no—
437C22×SD16—112no—
438#553—22no—
439#553C2×D1112yescomplemented
440#552C2×D1112yescomplemented
441#551—22no—
442#548—114no—
443#548—114no—
444#548—222no—
445#548—222no—
446#548C2×D1112yescomplemented
447#546C2×D1112yescomplemented
448#539—21no—
449#538—21no—
450#534—21no—
451#529C2×D1112yes—
452C2×#124—111no—
453C2×#124—221no—
454#525C2×D1112yes—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—221no—
457C2×C22⋊Q8C2×D1111yescharacteristic
458C2×#121—111no—
459C2×#121—221no—
460C2×#121C2×D1111yescharacteristic
461#518—21no—
462C2×C4×Q8—111no—
463C2×C4×D4—221no—
464C2×C4×D4C2×D1111yescharacteristic
465#495—114no—
466#488—114no—
467#485—114no—
468#483—112no—
469#481—112no—
470#480—112no—
471#480—112no—
472#479—114no—
473#467—114no—
474#466—114no—
475#465—114no—
476#465—114no—
477#464—114no—
478#464—114no—
479#463—114no—
480#452—114no—
481#452—114no—
482#451—112no—
483#451—112no—
484#451—114no—
485#450—112no—
486#449—114no—
487#448—112no—
488#448—112no—
489#448—112no—
490#448—114no—
491#447—112no—
492#447—112no—
493C4×Q16—114no—
494C4×SD16—114no—
495C8×D4—114no—
496C8×D4—114no—
497#431—112no—
498#416—114no—
499C2×#103—112no—
500C2×#103—112no—
501C2×C22⋊C8—111no—
502C2×C22⋊C8—111no—
503C2×C22⋊C8—112no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—44no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—82no—
518C22×C11—162no—
519C22×C11C2×#13512yes—
520C22×C11C2×#13512yes—
521C22×C11C2×#13512yes—
522C22×C11C23×D411yescharacteristic
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—84no—
527C4×C11—22no—
528C4×C11—21no—
529C4×C11—22no—
530C4×C11—21no—
531C4×C11—21no—
532C4×C11—22no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11C2×H(5,𝔽2)12yes—
537Dic11—24no—
538Dic11—42no—
539Dic11—42no—
540C2×#41—114no—
541C2×#41—222no—
542C2×#41—444no—
543C2×#41C22×D1112yes—
544C22×Q8—111no—
545C22×Q8—112no—
546C22×Q8—112no—
547C22×Q8—111no—
548C22×Q8—221no—
549C22×Q8—221no—
550C22×Q8—221no—
551C22×Q8—444no—
552C22×Q8C22×D1111yescharacteristic
553C22×D4—21no—
554C22×D4—111no—
555C22×D4—221no—
556C22×D4—221no—
557C22×D4C22⋊D1111yescharacteristic
558C22×D4C22×D1111yescharacteristic
559C23×C4—221no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563#135—448no—
564C2×Q16—114no—
565C2×Q16—114no—
566C2×Q16—444no—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—114no—
570C2×SD16—444no—
571C2×D8—114no—
572C22×C8—112no—
573C22×C8—112no—
574C22×C8—114no—
575#126—22no—
576#126—22no—
577#126—22no—
578#125—22no—
579#125C22×D1112yes—
580#124—22no—
581#124—114no—
582#124—224no—
583#124—224no—
584#124—222no—
585#124C22×D1112yes—
586#123—22no—
587#123—22no—
588#123—22no—
589#123—22no—
590#123—22no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—22no—
594C22⋊Q8—114no—
595C22⋊Q8—222no—
596C22⋊Q8—224no—
597C22⋊Q8—224no—
598C22⋊Q8C22×D1112yes—
599C22⋊Q8C22×D1112yes—
600C22⋊Q8C22×D1112yes—
601#121—22no—
602#121—22no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—112no—
607#121—112no—
608#121—224no—
609#121—224no—
610#121—221no—
611#121—221no—
612#121C22×D1112yes—
613#121C22×D1112yes—
614#121C22×D1112yes—
615#120—22no—
616#120—22no—
617C4×Q8—114no—
618C4×Q8—222no—
619C4×Q8C22×D1112yes—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—224no—
626C4×D4—224no—
627C4×D4C22⋊D1112yes—
628C4×D4C22⋊D1112yes—
629C4×D4C22×D1112yes—
630C4×D4C22×D1112yes—
631C4×D4C22×D1112yes—
632#117—22no—
633#117—22no—
634#117C22×D1112yes—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—221no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4C22⋊D1111yescharacteristic
640C2×C4⋊C4C22×D1111yescharacteristic
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—221no—
646C2×C22⋊C4—221no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4C22⋊D1111yescharacteristic
650C2×C22⋊C4C22⋊D1111yescharacteristic
651C2×C42—221no—
652C2×C42C22×D1111yescharacteristic
653#107—114no—
654#106—114no—
655C4⋊C8—114no—
656#103—114no—
657#103—114no—
658#103—114no—
659#103—114no—
660#103—114no—
661#102—114no—
662#102—114no—
663#102—114no—
664C22⋊C8—112no—
665C22⋊C8—112no—
666C22⋊C8—112no—
667C22⋊C8—112no—
668C22⋊C8—114no—
669C4×C8—114no—
670C2×C11—22no—
671C2×C11—22no—
672C2×C11—22no—
673C2×C11—42no—
674C2×C11—82no—
675C2×C11#348411yescharacteristic
676C2×C11C22×#13511yescharacteristic
677C2×C11#358611yescharacteristic
678D11—82no—
679C24—21no—
680C24—221no—
681C24C2×C22⋊D1111yescharacteristic
682C24C2×C22⋊D1111yescharacteristic
683#41—44no—
684#41—228no—
685#41—444no—
686#41—448no—
687C2×Q8—21no—
688C2×Q8—42no—
689C2×Q8—112no—
690C2×Q8—112no—
691C2×Q8—224no—
692C2×Q8—224no—
693C2×Q8—224no—
694C2×Q8—221no—
695C2×Q8—222no—
696C2×Q8—222no—
697C2×Q8—221no—
698C2×Q8—442no—
699C2×Q8—442no—
700C2×Q8—442no—
701C2×Q8—444no—
702C2×Q8—444no—
703C2×Q8—444no—
704C2×Q8C23×D1112yes—
705C2×D4—24no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—42no—
712C2×D4—44no—
713C2×D4—112no—
714C2×D4—222no—
715C2×D4—222no—
716C2×D4—224no—
717C2×D4—221no—
718C2×D4—442no—
719C2×D4—444no—
720C2×D4—444no—
721C2×D4C2×C22⋊D1112yes—
722C2×D4C2×C22⋊D1112yes—
723C2×D4C23×D1112yes—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—224no—
737C22×C4—444no—
738C22×C4—444no—
739C22×C4C2×C22⋊D1111yescharacteristic
740C22×C4C2×C22⋊D1111yescharacteristic
741C22×C4C2×C22⋊D1111yescharacteristic
742C22×C4C2×C22⋊D1111yescharacteristic
743C22×C4C2×C22⋊D1111yescharacteristic
744C22×C4C2×C22⋊D1111yescharacteristic
745C22×C4C2×C22⋊D1112yes—
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1112yes—
750Q16—228no—
751Q16—444no—
752SD16—228no—
753SD16—444no—
754SD16—444no—
755D8—444no—
756C2×C8—114no—
757C2×C8—114no—
758C2×C8—442no—
759C2×C8—442no—
760C2×C8—444no—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—22no—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—112no—
770C4⋊C4—221no—
771C4⋊C4—224no—
772C4⋊C4—224no—
773C4⋊C4C2×C22⋊D1112yes—
774C4⋊C4C2×C22⋊D1112yes—
775C4⋊C4C23×D1112yes—
776C4⋊C4C23×D1112yes—
777C22⋊C4—22no—
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—224no—
788C22⋊C4—224no—
789C22⋊C4—222no—
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—
798C42—224no—
799C42C2×C22⋊D1112yes—
800C42C23×D1112yes—
801C11#6156411yescharacteristic, complemented, Sylow
802C23—22no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23—222no—
812C23—442no—
813C23—442no—
814C23—442no—
815C23#6700314yescomplemented
816C23C22×C22⋊D1112yes—
817C23C22×C22⋊D1111yescharacteristic
818C23C22×C22⋊D1111yescharacteristic
819C23C22×C22⋊D1111yescharacteristic
820Q8—24no—
821Q8—81no—
822Q8—114no—
823Q8—224no—
824Q8—222no—
825Q8—222no—
826Q8—222no—
827Q8—444no—
828Q8—444no—
829Q8—442no—
830D4—24no—
831D4—24no—
832D4—24no—
833D4—44no—
834D4—44no—
835D4—81no—
836D4—82no—
837D4—82no—
838D4—224no—
839D4—442no—
840D4—448no—
841D4—444no—
842D4—444no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—224no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—448no—
867C2×C4—444no—
868C2×C4—444no—
869C2×C4—442no—
870C2×C4—442no—
871C2×C4C22×C22⋊D1112yes—
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1111yescharacteristic
874C2×C4C22×C22⋊D1112yes—
875C2×C4C22×C22⋊D1111yescharacteristic
876C2×C4C22×C22⋊D1111yescharacteristic
877C2×C4C24×D1111yescharacteristic
878C8—224no—
879C8—224no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—44no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—162no—
895C22—442no—
896C22—442no—
897C22—442no—
898C22—884no—
899C22C2×#6700312yes—
900C22C2×#6700312yes—
901C22C2×#6700312yes—
902C22C23×C22⋊D1111yescharacteristic
903C4—22no—
904C4—21no—
905C4—22no—
906C4—21no—
907C4—21no—
908C4—22no—
909C4—42no—
910C4—42no—
911C4—42no—
912C4—224no—
913C4—442no—
914C4—442no—
915C4D11×H(5,𝔽2)12yes—
916C2—22no—
917C2—22no—
918C2—22no—
919C2—42no—
920C2—82no—
921C2—882no—
922C2#1308224711yescharacteristic
923C2C22×#6700311yescharacteristic
924C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3505C2
socleC22×C11C23×D4
hypercenter#3505D11
hypocenterC11#61564
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×#10623083C2semidirect
2. #13080512C2semidirect
3. #13080497C2semidirect
4. #13080353C2semidirect
5. #13080319C2semidirect
6. #13079577C2semidirect
7. #13079393C2semidirect
8. #13079369C2semidirect
9. #13079364C2semidirect
10. #13078692C2semidirect
11. #13077832C2semidirect
12. C2×#10622663C2semidirect
13. C2×#10622653C2semidirect
14. #13077640C2semidirect
15. C11×#3505C2semidirect
16. C22×#4339C22semidirect
19. C11×#553C22semidirect
20. C11×#552C22semidirect
22. C11×#548C22semidirect
23. C11×#546C22semidirect
33. C2×#67003C22semidirect
34. C22×#4326C22semidirect
36. C22×#4324C22semidirect
38. C2×#66977C22semidirect
42. #10623083C22semidirect
46. C2×#66928C22semidirect
47. C2×C4×Dic22C22semidirect
48. #10622852C22semidirect
49. #10622840C22semidirect
50. #10622830C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622681C22semidirect
55. #10622676C22semidirect
56. #10622672C22semidirect
57. #10622667C22semidirect
58. #10622664C22semidirect
59. #10622663C22semidirect
60. #10622663C22semidirect
61. #10622663C22semidirect
62. #10622661C22semidirect
63. #10622660C22semidirect
64. #10622659C22semidirect
65. #10622656C22semidirect
66. #10622654C22semidirect
69. #10622653C22semidirect
70. #10622651C22semidirect
71. #10622650C22semidirect
74. C4×#4326C22semidirect
75. #10622641C22semidirect
76. C4×#4324C22semidirect
77. #10622629C22semidirect
78. D4×C11⋊C8C22semidirect
79. D4×C11⋊C8C22semidirect
80. #10622615C22semidirect
81. #10622609C22semidirect
82. C2×#66874C22semidirect
83. C2×#66874C22semidirect
84. #10622581C22semidirect
85. #10622580C22semidirect
86. #10622538C22semidirect
340. #3505D11semidirect
364. C23×C11#135semidirect
439. #553C2×D11semidirect
440. #552C2×D11semidirect
446. #548C2×D11semidirect
447. #546C2×D11semidirect
801. C11#61564semidirect
815. C23#67003semidirect

Maximal subgroups

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

subgroupindex
C2×#106230832
#130805122
#130804972
#130803532
#130803192
#130795772
#130793932
#130793692
#130793642
#130786922
#130778322
C2×#106226632
C2×#106226532
#130776402
C11×#35052
#6156411