Finite Group Databasebeta

← #15629677

Subgroups — #15629677

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623293C212yesmaximal, complemented
2#13082387C211yesmaximal, characteristic, complemented
3#13082380C211yesmaximal, characteristic, complemented
4#13080173C214yesmaximal, complemented
5#13080158C214yesmaximal, complemented
6#13080128C214yesmaximal, complemented
7#13080113C214yesmaximal, complemented
8#13079062C211yesmaximal, characteristic, complemented
9#13078288C212yesmaximal, complemented
10#13078088C211yesmaximal, characteristic, complemented
11#13078080C211yesmaximal, characteristic, complemented
12#13077936C212yesmaximal, complemented
13#13077925C212yesmaximal, complemented
14#13077335C211yesmaximal, characteristic, complemented
15C2×C11×#440C211yesmaximal, characteristic, complemented
16C2×#67040C2212yescomplemented
17C2×#67037C2212yes—
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66995C2212yescomplemented
22C2×#66985C2212yes—
23C2×#66983—22no—
24#10623293—216no—
25C2×#66969C2214yescomplemented
26C2×#66968C2214yescomplemented
27C2×#66967C2214yescomplemented
28C2×SD16×D11C2214yescomplemented
29C2×#66957C2212yescomplemented
30C2×#66957C2212yescomplemented
31C2×#66954C2212yescomplemented
32#10623108—21no—
33#10623108C2212yescomplemented
34#10623107—22no—
35#10623107C2214yescomplemented
36Q8×D44—21no—
37Q8×D44C2212yescomplemented
38#10623086—21no—
39#10623086C2212yes—
40#10623085—22no—
41#10623085C2214yes—
42D4×D44—21no—
43D4×D44C2212yes—
44#10623041—22no—
45#10623041C2212yes—
46#10623041C2212yescomplemented
47#10623024—22no—
48#10623008—22no—
49#10623008C2211yescharacteristic
50#10623008C2211yescharacteristic
51#10623008C2211yescharacteristic, complemented
52C11×#440C2214yescomplemented
53C11×#440C2214yescomplemented
54C2×C11×#107C2211yescharacteristic, complemented
55C2×C11×#103C2211yescharacteristic, complemented
56C2×C11×#102C2211yescharacteristic
57C2×C11×#97C2211yescharacteristic, complemented
58#10622723C2212yescomplemented
59#10622644C2212yescomplemented
60#10622641C2214yescomplemented
61#10622640C2212yescomplemented
62#10622632C2212yescomplemented
63#10622629C2214yescomplemented
64#10622628C2212yescomplemented
65#10622579C2212yescomplemented
66#10622579C2212yescomplemented
67#10622537C2211yescharacteristic, complemented
68#10622500C2214yescomplemented
69#10622499C2214yescomplemented
70#10622499C2214yescomplemented
71#10622496C2214yescomplemented
72#10622424C2214yescomplemented
73#10622423C2214yescomplemented
74#10622421C2214yescomplemented
75#10622419C2214yescomplemented
76#10622396C2214yescomplemented
77#10622394C2214yescomplemented
78#10622389C2214yescomplemented
79#10622386C2214yescomplemented
80#10622328C2212yescomplemented
81#10622328C2212yescomplemented
82#10622325C2212yescomplemented
83#10622325C2212yescomplemented
84#10622319C2214yescomplemented
85#10622319C2214yescomplemented
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C22×C22⋊D11—24no—
90#67040—28no—
91#67040—44no—
92C2×#4343—22no—
93C2×#4343C2314yes—
94C2×Q8×D11—22no—
95C2×Q8×D11C2314yes—
96#67037—28no—
97#67037—44no—
98C2×#4341—22no—
99C2×#4341C2314yes—
100C2×D4×D11—22no—
101C2×D4×D11C2314yes—
102C2×#4339—24no—
103C2×#4339C2312yes—
104C2×#4339C2312yes—
105C2×#4339C2312yes—
106C22×D44—22no—
107C2×C11×SD16D418yescomplemented
108C2×C11×SD16C2314yes—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C4×Q8×C11—21no—
112C4×Q8×C11—21no—
113C4×Q8×C11C2312yes—
114C4×Q8×C11C2312yes—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11C2312yes—
118C4×D4×C11C2312yes—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C42×C11—21no—
124C2×C42×C11C2311yescharacteristic
125C2×#4326C2314yes—
126#66995—28no—
127C2×#4325C2314yes—
128C2×#4324C2314yes—
129#66985—28no—
130C2×#4323C2314yes—
131#66983—21no—
132#66983—21no—
133#66983—21no—
134#66983—21no—
135#66983—24no—
136#66983—24no—
137#66983—22no—
138#66983—24no—
139#66983—22no—
140#66983D412yes—
141#66983D412yes—
142C2×(C2×D11)⋊C4—24no—
143C2×C4⋊Dic11—22no—
144C2×#4318C2312yes—
145#66969—216no—
146#66968—216no—
147#66967—216no—
148SD16×D11—216no—
149C2×Dic44C2312yes—
150C2×Dic44C2312yes—
151#66957—28no—
152#66957—44no—
153C2×D88C2312yes—
154C2×D88C2312yes—
155C2×#4314C2312yes—
156C2×#4314C2312yes—
157C2×#4314C2312yes—
158C2×#4314C2312yes—
159#66954—28no—
160C2×#4313C2314yes—
161C2×C8×D11C2314yes—
162#66950—22no—
163#66950—22no—
164#66950—24no—
165#66950—24no—
166#66950C2314yes—
167#66950C2314yes—
168#66948—24no—
169#66948—22no—
170#66948—22no—
171#66948—24no—
172#66948C2314yes—
173#66948C2314yes—
174#66939—24no—
175#66939—24no—
176#66935—24no—
177#66935—24no—
178#66928—24no—
179#66928D412yes—
180#66928C2312yes—
181#66928C2312yes—
182#66927—22no—
183#66927D411yescharacteristic
184#66927C2311yescharacteristic
185#66927C2311yescharacteristic
186C4×D44—22no—
187C4×D44—21no—
188C4×D44—21no—
189C4×D44—21no—
190C4×D44—21no—
191C4×D44—24no—
192C4×D44—22no—
193C4×D44C2312yes—
194C4×D44C2312yes—
195#66922—22no—
196#66922D411yescharacteristic
197#66922C2311yescharacteristic
198#66922C2311yescharacteristic
199C11×#107C2314yes—
200C11×#103C2314yes—
201C11×#102C2314yes—
202C11×#97C2312yes—
203C11×#97C2312yes—
204(C2×D11)⋊C8C2314yes—
205(C2×D11)⋊C8C2314yes—
206#66874C2314yes—
207#66874C2314yes—
208#66873C2314yes—
209#66873C2314yes—
210C4⋊(C11⋊C8)C2312yes—
211C4⋊(C11⋊C8)C2312yes—
212#61080—111nomaximal, Sylow
213C24×C11—21no—
214C23×D11—24no—
215C2×Q8×C11—21no—
216C2×Q8×C11—22no—
217C2×Q8×C11C2×D414yescomplemented
218C2×Q8×C11C2412yes—
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11C2×D414yes—
222C2×D4×C11C2412yes—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—82no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C2×C22⋊D11—24no—
233C2×C22⋊D11—22no—
234C2×C22⋊D11—22no—
235C2×C22⋊D11—24no—
236C2×C22⋊D11—416no—
237C2×C22⋊D11C2×D414yes—
238C22×Dic11—24no—
239#4343—28no—
240#4343—44no—
241#4343—48no—
242Q8×D11—28no—
243Q8×D11—44no—
244Q8×D11—48no—
245#4341—28no—
246#4341—44no—
247#4341—48no—
248D4×D11—28no—
249D4×D11—44no—
250D4×D11—48no—
251#4339—24no—
252#4339—24no—
253#4339—24no—
254#4339—24no—
255#4339—24no—
256#4339—24no—
257#4339—416no—
258C2×D44—24no—
259C2×D44—24no—
260C2×D44—24no—
261C2×D44—21no—
262C2×D44—21no—
263C2×D44—21no—
264C2×D44—21no—
265C2×D44—84no—
266C2×D44C2×D412yes—
267C2×D44C2×D412yes—
268C2×D44C2×D412yes—
269C2×D44C2412yes—
270C2×D44C2412yes—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11C2414yes—
276C2×Dic22—24no—
277C2×Dic22C2×D412yes—
278C2×Dic22C2412yes—
279C2×Dic22C2412yes—
280C11×SD16C2×D4116yescomplemented
281C2×C8×C11—22no—
282C2×C8×C11C2×D414yescomplemented
283C2×C8×C11C2412yes—
284C2×C8×C11C2412yes—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4C2412yes—
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C42×C11—22no—
294C42×C11—22no—
295C42×C11C2×D411yescharacteristic
296C42×C11C2×D411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2411yescharacteristic
299#4326—28no—
300#4325—28no—
301#4324—28no—
302#4323—28no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4C2×D414yes—
312(C2×D11)⋊C4C2×D414yes—
313C4⋊Dic11—24no—
314C4⋊Dic11—24no—
315C4⋊Dic11—21no—
316C4⋊Dic11—21no—
317C4⋊Dic11—21no—
318C4⋊Dic11—21no—
319C4⋊Dic11C2×D412yes—
320C4⋊Dic11C2×D412yes—
321#4318—24no—
322C2×C11⋊C8C2414yes—
323Dic44—24no—
324Dic44—42no—
325D88—24no—
326D88—42no—
327#4314—24no—
328#4314—24no—
329#4314—42no—
330#4314—42no—
331#4313—28no—
332C8×D11—28no—
333C2×#577—112no—
334#3497—111no—
335#3496—111no—
336#3269—114no—
337#3268—114no—
338#3266—114no—
339#3265—114no—
340#3150—111no—
341#3061—112no—
342#3037—111no—
343#3036—111no—
344#3013—112no—
345#3012—112no—
346C2×#440D1111yescharacteristic, complemented
347#2932—111no—
348C23×C11—22no—
349C23×C11—24no—
350C23×C11—81no—
351C23×C11—81no—
352C23×C11C22×D411yescharacteristic
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—48no—
356C22×D11—84no—
357C22×D11—84no—
358C22×D11C22×D414yes—
359Q8×C11—24no—
360Q8×C11—22no—
361Q8×C11C22×D414yes—
362D4×C11—24no—
363D4×C11—22no—
364D4×C11C22×D414yes—
365C2×C4×C11—24no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—44no—
372C2×C4×C11—82no—
373C2×C4×C11—81no—
374C2×C4×C11—81no—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11H(5,𝔽2)12yes—
382C2×C4×C11C2511yescharacteristic
383C22⋊D11—28no—
384C22⋊D11—48no—
385C22⋊D11—48no—
386C22⋊D11—44no—
387C22⋊D11—44no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—48no—
391C2×Dic11C22×D414yes—
392D44—24no—
393D44—22no—
394D44—22no—
395D44—22no—
396D44—22no—
397D44—42no—
398D44—42no—
399D44—48no—
400D44—42no—
401D44—42no—
402D44—81no—
403D44—81no—
404D44—84no—
405D44—84no—
406C4×D11—24no—
407C4×D11—24no—
408C4×D11—48no—
409C4×D11—48no—
410C4×D11—44no—
411C4×D11—44no—
412Dic22—24no—
413Dic22—22no—
414Dic22—22no—
415Dic22—22no—
416Dic22—22no—
417Dic22—48no—
418C8×C11—22no—
419C8×C11C22×D414yes—
420C11⋊C8—24no—
421C2×2−1+4—112no—
422C2×H(5,𝔽2)—112no—
423#577—2216no—
424C2×#137—112no—
425C2×#137—114no—
426C2×AGL(1,ℤ/8)—112no—
427C2×AGL(1,ℤ/8)—114no—
428C2×#135—114no—
429C2×#135—112no—
430C2×#135—112no—
431C22×SD16—114no—
432C22×SD16C2×D1111yescharacteristic
433C2×#131—112no—
434#550—112no—
435#550—221no—
436D4×Q8—112no—
437D4×Q8—221no—
438#548—114no—
439#548—222no—
440#547—112no—
441#547—221no—
442#546—114no—
443#546—222no—
444D42—112no—
445D42—221no—
446#537—112no—
447#537—112no—
448#537—222no—
449#534—222no—
450#532—111no—
451#532—111no—
452#532—111no—
453#532—222no—
454C2×#121—222no—
455C2×C4×Q8C2×D1111yescharacteristic, complemented
456C2×C4×D4C2×D1111yescharacteristic
457#497—112no—
458#497—112no—
459#496—112no—
460#496—112no—
461#468—114no—
462#468—114no—
463#467—114no—
464#466—114no—
465#464—114no—
466#463—114no—
467#462—112no—
468#461—112no—
469#460—112no—
470#459—112no—
471#452—114no—
472#452—114no—
473#451—114no—
474#450—114no—
475#449—114no—
476#449—114no—
477#448—114no—
478#447—114no—
479#440C2×D1114yescomplemented
480#440C2×D1114yescomplemented
481#435—114no—
482#435—114no—
483C2×#107C2×D1111yescharacteristic, complemented
484#423—111no—
485#417—112no—
486#417—112no—
487C2×#103C2×D1111yescharacteristic, complemented
488C2×#102C2×D1111yescharacteristic
489#408—112no—
490C2×#97C2×D1111yescharacteristic, complemented
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—24no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—84no—
497C22×C11D4212yes—
498C22×C11C23×D411yescharacteristic
499C2×D11—24no—
500C2×D11—24no—
501C2×D11—24no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—168no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—24no—
514C4×C11—42no—
515C4×C11—42no—
516C4×C11D4212yes—
517C4×C11C23×D411yescharacteristic
518C4×C11C2×H(5,𝔽2)11yescharacteristic
519Dic11—24no—
520Dic11—42no—
521Dic11—42no—
5222−1+4—228no—
5232−1+4—444no—
524H(5,𝔽2)—228no—
525H(5,𝔽2)—444no—
526C2×#41—112no—
527C2×#41—114no—
528C2×#41—114no—
529C2×#41—112no—
530C2×#41—112no—
531C2×#41—224no—
532C2×#41—222no—
533C2×#41—222no—
534C22×Q8—114no—
535C22×Q8—222no—
536C22×Q8C22×D1111yescharacteristic
537C22×D4—114no—
538C22×D4—222no—
539C22×D4—222no—
540C22×D4—224no—
541C22×D4C22×D1111yescharacteristic
542C23×C4—21no—
543#137—228no—
544#137—2216no—
545AGL(1,ℤ/8)—228no—
546AGL(1,ℤ/8)—2216no—
547#135—2216no—
548#135—228no—
549#135—444no—
550C2×Q16—114no—
551C2×Q16—112no—
552C2×Q16—112no—
553C2×SD16—114no—
554C2×SD16—114no—
555C2×SD16—112no—
556C2×SD16—112no—
557C2×SD16—112no—
558C2×SD16—112no—
559C2×SD16—2216no—
560C2×SD16D4418yescomplemented
561C2×SD16C22×D1114yes—
562C2×D8—114no—
563C2×D8—112no—
564C2×D8—112no—
565#131—228no—
566C2×M16—112no—
567C2×M16—114no—
568C22×C8—114no—
569C22×C8C22×D1111yescharacteristic
570C22×C8C22×D1111yescharacteristic
571C4⋊Q8—111no—
572C4⋊Q8—111no—
573C4⋊Q8—111no—
574C4⋊Q8—222no—
575#127—111no—
576#127—111no—
577#127—111no—
578#127—222no—
579#124—112no—
580#124—112no—
581#124—112no—
582#124—224no—
583#123—224no—
584#123—224no—
585C22⋊Q8—114no—
586C22⋊Q8—114no—
587C22⋊Q8—224no—
588C22⋊Q8—224no—
589C22⋊Q8—222no—
590C22⋊Q8—222no—
591#121—112no—
592#121—112no—
593#121—114no—
594#121—114no—
595#121—224no—
596#121—224no—
597#121—222no—
598#121—222no—
599#121—224no—
600#121—222no—
601#121—224no—
602#121—222no—
603#121—224no—
604#121—221no—
605#121—221no—
606#121—221no—
607#121—221no—
608#120—224no—
609#120—224no—
610C4×Q8—21no—
611C4×Q8—21no—
612C4×Q8C22×D1112yes—
613C4×Q8C22×D1112yes—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—112no—
617C4×D4—112no—
618C4×D4—224no—
619C4×D4—222no—
620C4×D4—222no—
621C4×D4—221no—
622C4×D4—221no—
623C4×D4—221no—
624C4×D4—221no—
625C4×D4C22×D1112yes—
626C4×D4C22×D1112yes—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4C22×D1111yescharacteristic
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—224no—
633C2×C42—21no—
634C2×C42C22×D1111yescharacteristic
635#107C22×D1114yes—
636C4⋊C8—112no—
637C4⋊C8—112no—
638#103—114no—
639#103—114no—
640#103C22×D1114yes—
641#102—114no—
642#102—114no—
643#102C22×D1114yes—
644C22⋊C8—114no—
645C22⋊C8—114no—
646#97C22×D1112yes—
647#97C22×D1112yes—
648C2×C11—22no—
649C2×C11—44no—
650C2×C11C2×D4211yescharacteristic
651C2×C11#358511yescharacteristic
652C2×C11#358611yescharacteristic
653D11—44no—
654D11—82no—
655D11—82no—
656C24—21no—
657C24—224no—
658#41—224no—
659#41—224no—
660#41—228no—
661#41—228no—
662#41—224no—
663#41—224no—
664#41—224no—
665#41—224no—
666#41—4416no—
667#41—444no—
668#41—444no—
669#41—448no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—112no—
674C2×Q8—112no—
675C2×Q8—112no—
676C2×Q8—224no—
677C2×Q8—228no—
678C2×Q8—444no—
679C2×Q8—448no—
680C2×Q8C2×D4414yescomplemented
681C2×Q8C23×D1112yes—
682C2×D4—21no—
683C2×D4—22no—
684C2×D4—114no—
685C2×D4—112no—
686C2×D4—112no—
687C2×D4—112no—
688C2×D4—112no—
689C2×D4—112no—
690C2×D4—224no—
691C2×D4—224no—
692C2×D4—224no—
693C2×D4—224no—
694C2×D4—228no—
695C2×D4—224no—
696C2×D4—222no—
697C2×D4—222no—
698C2×D4—221no—
699C2×D4—221no—
700C2×D4—221no—
701C2×D4—221no—
702C2×D4—444no—
703C2×D4—448no—
704C2×D4—4416no—
705C2×D4—884no—
706C2×D4C2×D4414yes—
707C2×D4C23×D1112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—82no—
714C22×C4—114no—
715C22×C4—224no—
716C22×C4—224no—
717C22×C4—224no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4D4×D1111yescharacteristic
721C22×C4D4×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723Q16—228no—
724Q16—224no—
725Q16—442no—
726SD16—228no—
727SD16—228no—
728SD16—224no—
729SD16—224no—
730SD16—442no—
731SD16—442no—
732SD16C2×D44116yescomplemented
733D8—228no—
734D8—224no—
735D8—442no—
736M16—224no—
737M16—228no—
738C2×C8—22no—
739C2×C8—114no—
740C2×C8—228no—
741C2×C8C2×D4414yescomplemented
742C2×C8C23×D1112yes—
743C2×C8C23×D1112yes—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—112no—
749C4⋊C4—112no—
750C4⋊C4—224no—
751C4⋊C4—224no—
752C4⋊C4—221no—
753C4⋊C4—221no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4C23×D1112yes—
757C4⋊C4C23×D1112yes—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—114no—
761C22⋊C4—114no—
762C22⋊C4—224no—
763C22⋊C4—224no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—222no—
767C22⋊C4—222no—
768C22⋊C4—222no—
769C22⋊C4—222no—
770C42—22no—
771C42—22no—
772C42D4×D1111yescharacteristic
773C42D4×D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C11#6108011yescharacteristic, complemented, Sylow
777C23—22no—
778C23—24no—
779C23—81no—
780C23—81no—
781C23—114no—
782C23—222no—
783C23—222no—
784C23—448no—
785C23—884no—
786C23—884no—
787C23C2×D4×D1111yescharacteristic
788Q8—24no—
789Q8—22no—
790Q8—224no—
791Q8—222no—
792Q8—222no—
793Q8—222no—
794Q8—222no—
795Q8—448no—
796Q8C22×D4414yes—
797D4—24no—
798D4—22no—
799D4—228no—
800D4—224no—
801D4—222no—
802D4—222no—
803D4—222no—
804D4—222no—
805D4—442no—
806D4—442no—
807D4—448no—
808D4—442no—
809D4—442no—
810D4—448no—
811D4—448no—
812D4—444no—
813D4—444no—
814D4—881no—
815D4—881no—
816D4—884no—
817D4—884no—
818D4C22×D4414yes—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—44no—
826C2×C4—82no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—114no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—448no—
835C2×C4—448no—
836C2×C4—448no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4C22×D4412yes—
840C2×C4C2×D4×D1111yescharacteristic
841C2×C4C2×D4×D1111yescharacteristic
842C2×C4C2×D4×D1111yescharacteristic
843C2×C4C2×D4×D1111yescharacteristic
844C2×C4C2×D4×D1111yescharacteristic
845C2×C4#6704212yes—
846C2×C4C24×D1111yescharacteristic
847C8—22no—
848C8—224no—
849C8C22×D4414yes—
850C22—21no—
851C22—21no—
852C22—24no—
853C22—42no—
854C22—42no—
855C22—84no—
856C22—224no—
857C22—224no—
858C22—224no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—1768no—
866C22D4×D4412yes—
867C22C22×D4×D1111yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—24no—
873C4—42no—
874C4—42no—
875C4—224no—
876C4—442no—
877C4—442no—
878C4D4×D4412yes—
879C4C23×D4411yescharacteristic
880C4C2×#6704211yescharacteristic
881C2—22no—
882C2—44no—
883C2—444no—
884C2—882no—
885C2—882no—
886C2C2×D4×D4411yescharacteristic
887C2#1308339211yescharacteristic
888C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC22×C11C23×D4
hypercenterC2×#440D11
hypocenterC11#61080
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623293C2semidirect
2. #13082387C2semidirect
3. #13082380C2semidirect
4. #13080173C2semidirect
5. #13080158C2semidirect
6. #13080128C2semidirect
7. #13080113C2semidirect
8. #13079062C2semidirect
9. #13078288C2semidirect
10. #13078088C2semidirect
11. #13078080C2semidirect
12. #13077936C2semidirect
13. #13077925C2semidirect
14. #13077335C2semidirect
15. C2×C11×#440C2semidirect
16. C2×#67040C22semidirect
19. C2×C4×Q8×C11C22semidirect
21. C2×#66995C22semidirect
25. C2×#66969C22semidirect
26. C2×#66968C22semidirect
27. C2×#66967C22semidirect
28. C2×SD16×D11C22semidirect
29. C2×#66957C22semidirect
30. C2×#66957C22semidirect
31. C2×#66954C22semidirect
33. #10623108C22semidirect
35. #10623107C22semidirect
37. Q8×D44C22semidirect
46. #10623041C22semidirect
51. #10623008C22semidirect
52. C11×#440C22semidirect
53. C11×#440C22semidirect
54. C2×C11×#107C22semidirect
55. C2×C11×#103C22semidirect
57. C2×C11×#97C22semidirect
58. #10622723C22semidirect
59. #10622644C22semidirect
60. #10622641C22semidirect
61. #10622640C22semidirect
62. #10622632C22semidirect
63. #10622629C22semidirect
64. #10622628C22semidirect
65. #10622579C22semidirect
66. #10622579C22semidirect
67. #10622537C22semidirect
68. #10622500C22semidirect
69. #10622499C22semidirect
70. #10622499C22semidirect
71. #10622496C22semidirect
72. #10622424C22semidirect
73. #10622423C22semidirect
74. #10622421C22semidirect
75. #10622419C22semidirect
76. #10622396C22semidirect
77. #10622394C22semidirect
78. #10622389C22semidirect
79. #10622386C22semidirect
80. #10622328C22semidirect
81. #10622328C22semidirect
82. #10622325C22semidirect
83. #10622325C22semidirect
84. #10622319C22semidirect
85. #10622319C22semidirect
107. C2×C11×SD16D4semidirect
217. C2×Q8×C11C2×D4semidirect
280. C11×SD16C2×D4semidirect
282. C2×C8×C11C2×D4semidirect
346. C2×#440D11semidirect
455. C2×C4×Q8C2×D11semidirect
479. #440C2×D11semidirect
480. #440C2×D11semidirect
483. C2×#107C2×D11semidirect
487. C2×#103C2×D11semidirect
490. C2×#97C2×D11semidirect
560. C2×SD16D44semidirect
680. C2×Q8C2×D44semidirect
732. SD16C2×D44semidirect
741. C2×C8C2×D44semidirect
776. C11#61080semidirect

Maximal subgroups

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

subgroupindex
C2×#106232932
#130823872
#130823802
#130801732
#130801582
#130801282
#130801132
#130790622
#130782882
#130780882
#130780802
#130779362
#130779252
#130773352
C2×C11×#4402
#6108011