Finite Group Databasebeta

← #3548×D83 #36312193

Subgroups — #3548×D83 #36312193

Order 21248.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921863C211yesmaximal, characteristic, complemented
2#24921862C214yesmaximal, complemented
3#24921861C212yesmaximal, complemented
4#24921860C214yesmaximal, complemented
5#24921859C214yesmaximal, complemented
6#24921858C218yesmaximal, complemented
7#24921857C214yesmaximal, complemented
8#24921856C214yesmaximal, complemented
9#562×D83C214yesmaximal, complemented
10#554×D83C214yesmaximal, complemented
11#550×D83C214yesmaximal, complemented
12#547×D83C214yesmaximal, complemented
13#540×D83C214yesmaximal, complemented
14#537×D83C218yesmaximal, complemented
15#533×D83C211yesmaximal, characteristic, complemented
16#532×D83C212yesmaximal, complemented
17C83×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D83C2218yes—
19C2×#41×D83C2214yes—
20#19128449C2214yescomplemented
21#19128448C22116yescomplemented
22#19128447C22116yescomplemented
23#19128446C22116yescomplemented
24#19128445C2218yescomplemented
25#19128412C2214yescomplemented
26#19128411C2214yescomplemented
27#19128410C2218yescomplemented
28#19128409C2218yescomplemented
29#19128408C2214yescomplemented
30#19128407C2218yescomplemented
31#19128406C2218yescomplemented
32#19128405C22116yescomplemented
33#19128373C2214yescomplemented
34#19128372C2218yescomplemented
35#19128372C2214yescomplemented
36#19128371C2218yescomplemented
37#19128371C2214yescomplemented
38#19128370C2218yescomplemented
39#19128369C22116yescomplemented
40#19128369C2218yescomplemented
41#19128356C2214yescomplemented
42#19128355C2214yescomplemented
43#19128354C2214yescomplemented
44#19128353C2218yescomplemented
45#19128352C2218yescomplemented
46#19128351C2218yescomplemented
47#19128350C2218yescomplemented
48#19128349C22116yescomplemented
49#19128307C2214yescomplemented
50#19128306C2214yescomplemented
51#19128305C2214yescomplemented
52#19128304C2218yescomplemented
53#19128303C22116yescomplemented
54#19128302C2218yescomplemented
55#19128301C22116yescomplemented
56#19128282C2218yescomplemented
57#19128281C2218yescomplemented
58#19128281C22116yescomplemented
59#19128281C2218yescomplemented
60#19128280C2218yescomplemented
61#19128280C22116yescomplemented
62#19128280C2218yescomplemented
63#19128279C2218yescomplemented
64#19128279C2218yescomplemented
65#19128278C22116yescomplemented
66#19128278C22116yescomplemented
67#19128258C2211yescharacteristic, complemented
68#19128257C2212yescomplemented
69#19128256C2212yescomplemented
70#19128255C2214yescomplemented
71#19128254C2212yescomplemented
72#19128253C2214yescomplemented
73#19128252C2212yescomplemented
74#19128251C2212yescomplemented
75#19128250C2214yescomplemented
76#19128249C2212yescomplemented
77#19128248C2214yescomplemented
78#19128248C2214yescomplemented
79#19128247C2214yescomplemented
80#19128246C2214yescomplemented
81#19128246C2214yescomplemented
82C4⋊Q8×D83C2212yes—
83C4⋊Q8×D83C2212yes—
84#127×D83C2212yes—
85#127×D83C2214yes—
86#125×D83C2214yes—
87#125×D83C2212yes—
88#124×D83C2214yes—
89#123×D83C22116yes—
90C22⋊Q8×D83C2218yes—
91C22⋊Q8×D83C22116yes—
92C22⋊Q8×D83C2214yes—
93#121×D83C2218yes—
94#121×D83C22116yes—
95#121×D83C2214yes—
96#121×D83C2214yes—
97#121×D83C22116yes—
98C4×Q8×D83C2214yes—
99C4×D4×D83C2214yes—
100C4×D4×D83C2214yes—
101C4×D4×D83C2218yes—
102#117×D83C2212yes—
103C2×C4⋊C4×D83C2218yes—
104C2×C42×D83C2211yescharacteristic
105#562×C83C2214yescomplemented
106#554×C83C2214yescomplemented
107#550×C83C2214yescomplemented
108#547×C83C2214yescomplemented
109#540×C83C2214yescomplemented
110#537×C83C2218yescomplemented
111#533×C83C2211yescharacteristic, complemented
112#532×C83C2212yescomplemented
113C2×#13050591C2318yes—
114C2×#13050591C2314yes—
115C2×#13050590C23116yes—
116C2×#13050590C2318yes—
117C2×#13050590C2314yes—
118C2×#13050590C2318yes—
119C2×#13050589C23116yes—
120C2×#13050589C2318yes—
121C2×#13050589C2318yes—
122C2×#13050589C2314yes—
123#41×D83—416no—
124#41×D83—432no—
125C2×Q8×D83C2314yes—
126C2×Q8×D83C2314yes—
127C2×D4×D83C2314yes—
128C2×D4×D83C2314yes—
129C2×D4×D83C2318yes—
130C2×D4×D83C23116yes—
131C2×D4×D83C2314yes—
132C22×C4×D83C2311yescharacteristic
133C22×C4×D83C2312yes—
134C22×C4×D83C2318yes—
135C22×C4×D83C23116yes—
136#14581792C2312yes—
137#14581792C2312yes—
138#14581791C2314yes—
139#14581791C2314yes—
140#14581791C2314yes—
141#14581791C2314yes—
142#14581790C2314yes—
143#14581790C2314yes—
144#14581789C2312yes—
145#14581789C2314yes—
146#14581788C2314yes—
147#14581788C23116yes—
148#14581788C2314yes—
149#14581788C2314yes—
150#14581788C2318yes—
151#14581784C2314yes—
152#14581784C2312yes—
153#14581783C2318yes—
154#14581783C2314yes—
155#14581782C23116yes—
156#14581782C2318yes—
157#14581781C2314yes—
158#14581780C2314yes—
159#14581779C2314yes—
160#14581778C2318yes—
161#14581778C2318yes—
162#14581777C23116yes—
163#14581777C23116yes—
164#14581776C23116yes—
165#14581775C23116yes—
166#14581774C23116yes—
167#14581774C23116yes—
168#14581773C23116yes—
169#14581772C2318yes—
170#14581772C23116yes—
171#14581772C2314yes—
172#14581771C2318yes—
173#14581771C23116yes—
174#14581771C2314yes—
175#14581770C23116yes—
176#14581770C23116yes—
177#14581770C23116yes—
178#14581770C2318yes—
179#14581769C23116yes—
180#14581769C23116yes—
181#14581769C23116yes—
182#14581769C2318yes—
183#14581768C2318yes—
184#14581768C23116yes—
185#14581768C2314yes—
186#14581767C2318yes—
187#14581767C23116yes—
188#14581767C2314yes—
189#14581767C2314yes—
190#14581767C23116yes—
191#14581766C2318yes—
192#14581766C23116yes—
193#14581766C2314yes—
194#14581766C2314yes—
195#14581766C23116yes—
196#14581765C23116yes—
197#14581765C23116yes—
198#14581765C23116yes—
199#14581765C2318yes—
200#14581765C2318yes—
201#14581765C23116yes—
202#14581765C23116yes—
203#14581764C23116yes—
204#14581764C23116yes—
205#14581764C23116yes—
206#14581764C2318yes—
207#14581764C2318yes—
208#14581764C23116yes—
209#14581764C23116yes—
210#14581763C2318yes—
211#14581763C23116yes—
212#14581763C2314yes—
213#14581763C2314yes—
214#14581763C23116yes—
215Q8×Dic83C2314yes—
216C4×Dic166C2318yes—
217C4×Dic166C2314yes—
218#14581757C2318yes—
219#14581757C2314yes—
220C4×D332C2314yes—
221C4×D332C2318yes—
222C4×D332C2314yes—
223D4×Dic83C2314yes—
224D4×Dic83C2318yes—
225D4×Dic83C2314yes—
226#14581754C2314yes—
227#14581754C2314yes—
228#14581754C2318yes—
229C4×C22⋊D83C2318yes—
230C4×C22⋊D83C23116yes—
231C4×C22⋊D83C2318yes—
232(C22⋊D83)⋊C4C2318yes—
233(C22⋊D83)⋊C4C2318yes—
234(C22⋊D83)⋊C4C23116yes—
235#14581751C2312yes—
236#14581750C2314yes—
237#14581749C2314yes—
238#14581748C2314yes—
239C2×C4⋊Dic83C2318yes—
240C2×Dic83⋊C4C23116yes—
241C4⋊C4×D83C23116yes—
242C4⋊C4×D83C2318yes—
243C4⋊C4×D83C2318yes—
244C4⋊C4×D83C2314yes—
245C4⋊C4×D83C2314yes—
246C4⋊C4×D83C23116yes—
247C4⋊C4×D83C2314yes—
248C4⋊C4×D83C2314yes—
249C4⋊C4×D83C2318yes—
250C22⋊C4×D83C2314yes—
251C22⋊C4×D83C23116yes—
252C22⋊C4×D83C2318yes—
253C22⋊C4×D83C2318yes—
254C2×C4×Dic83C2311yescharacteristic
255C2×C4×Dic83C2312yes—
256C42×D83C2311yescharacteristic
257C42×D83C2312yes—
258C42×D83C2311yescharacteristic
259C42×D83C2311yescharacteristic
260C42×D83C2312yes—
261C42×D83C2311yescharacteristic
262C42×D83C2314yes—
263C2×#41×C83C2318yes—
264C2×#41×C83C2314yes—
265C4⋊Q8×C83C2312yes—
266C4⋊Q8×C83C2312yes—
267#127×C83C2312yes—
268#127×C83C2314yes—
269#125×C83C2312yes—
270#125×C83C2314yes—
271#124×C83C2314yes—
272#123×C83C23116yes—
273C22⋊Q8×C83C2318yes—
274C22⋊Q8×C83C2314yes—
275C22⋊Q8×C83C23116yes—
276#121×C83C2318yes—
277#121×C83C23116yes—
278#121×C83C2314yes—
279#121×C83C2314yes—
280#121×C83C23116yes—
281C4×Q8×C83C2314yes—
282C4×D4×C83C2314yes—
283C4×D4×C83C2314yes—
284C4×D4×C83C2318yes—
285#117×C83C2312yes—
286C2×C4⋊C4×C83C2318yes—
287C2×C42×C83C2311yescharacteristic
288C23×D83C2411yescharacteristic
289C23×D83C2418yes—
290#13050591—48no—
291#13050591—416no—
292#13050590—432no—
293#13050590—416no—
294#13050590—48no—
295#13050590—416no—
296#13050589—416no—
297#13050589—432no—
298#13050589—48no—
299#13050589—416no—
300C2×Dic166C2418yes—
301C2×Dic166C2414yes—
302C2×Dic166C2414yes—
303C2×Dic166C2418yes—
304Q8×D83—216no—
305Q8×D83—48no—
306C2×D332C2414yes—
307C2×D332C2414yes—
308C2×D332C2418yes—
309C2×D332C2414yes—
310C2×D332C24116yes—
311C2×C22⋊D83C2418yes—
312C2×C22⋊D83C2418yes—
313C2×C22⋊D83C2418yes—
314C2×C22⋊D83C2418yes—
315C2×C22⋊D83C24116yes—
316C2×C22⋊D83C2418yes—
317C2×C22⋊D83C24116yes—
318D4×D83—216no—
319D4×D83—216no—
320D4×D83—416no—
321D4×D83—48no—
322D4×D83—432no—
323C22×Dic83C2411yescharacteristic
324C22×Dic83C2412yes—
325C22×Dic83C2418yes—
326C22×Dic83C24116yes—
327C2×C4×D83—232no—
328C2×C4×D83—28no—
329C2×C4×D83—24no—
330C2×C4×D83—432no—
331C2×C4×D83C2411yescharacteristic
332C2×C4×D83C2412yes—
333C2×C4×D83C2418yes—
334C2×C4×D83C2411yescharacteristic
335C2×C4×D83C2412yes—
336C2×C4×D83C2418yes—
337C2×C4×D83C2418yes—
338C2×C4×D83C2418yes—
339C2×C4×D83C2412yes—
340C2×C4×D83C2411yescharacteristic
341C2×C4×D83C24116yes—
342C2×C4×D83C24116yes—
343C2×C4×D83C2412yes—
344C2×C4×D83C2411yescharacteristic
345C4⋊Dic83C2414yes—
346C4⋊Dic83C2418yes—
347C4⋊Dic83C2414yes—
348C4⋊Dic83C24116yes—
349C4⋊Dic83C2414yes—
350C4⋊Dic83C2414yes—
351Dic83⋊C4C2418yes—
352Dic83⋊C4C2418yes—
353Dic83⋊C4C2418yes—
354Dic83⋊C4C24116yes—
355Dic83⋊C4C24116yes—
356Dic83⋊C4C2418yes—
357Dic83⋊C4C2418yes—
358Dic83⋊C4C2418yes—
359C22⋊Dic83C2414yes—
360C22⋊Dic83C24116yes—
361C22⋊Dic83C2418yes—
362C22⋊Dic83C2418yes—
363(C2×D83)⋊C4C2418yes—
364(C2×D83)⋊C4C2418yes—
365(C2×D83)⋊C4C24116yes—
366(C2×D83)⋊C4C24116yes—
367(C2×D83)⋊C4C2418yes—
368(C2×D83)⋊C4C2418yes—
369(C2×D83)⋊C4C2418yes—
370C4×Dic83C2411yescharacteristic
371C4×Dic83C2412yes—
372C4×Dic83C2418yes—
373C4×Dic83C2414yes—
374C4×Dic83C2412yes—
375C4×Dic83C2412yes—
376C4×Dic83C2412yes—
377C4×Dic83C2412yes—
378C4×Dic83C2411yescharacteristic
379#41×C83—48no—
380#41×C83—416no—
381C2×Q8×C83C2414yes—
382C2×Q8×C83C2414yes—
383C2×D4×C83C2414yes—
384C2×D4×C83C2414yes—
385C2×D4×C83C2418yes—
386C2×D4×C83C24116yes—
387C2×D4×C83C2414yes—
388C22×C4×C83C2411yescharacteristic
389C22×C4×C83C2412yes—
390C22×C4×C83C2418yes—
391C22×C4×C83C24116yes—
392C4⋊C4×C83C2418yes—
393C4⋊C4×C83C2414yes—
394C4⋊C4×C83C24116yes—
395C4⋊C4×C83C2414yes—
396C4⋊C4×C83C2414yes—
397C4⋊C4×C83C2414yes—
398C22⋊C4×C83C2414yes—
399C22⋊C4×C83C24116yes—
400C22⋊C4×C83C2418yes—
401C22⋊C4×C83C2418yes—
402C42×C83C2411yescharacteristic
403C42×C83C2414yes—
404C42×C83C2412yes—
405C42×C83C2411yescharacteristic
406C23×C83C2511yescharacteristic
407C23×C83C2518yes—
408C22×D83—216no—
409C22×D83—24no—
410C22×D83—216no—
411C22×D83—22no—
412C22×D83—216no—
413C22×D83C2511yescharacteristic
414C22×D83C2518yes—
415C22×D83C2511yescharacteristic
416Q8×C83—28no—
417Q8×C83—44no—
418D4×C83—28no—
419D4×C83—28no—
420D4×C83—416no—
421D4×C83—44no—
422D4×C83—48no—
423C2×C4×C83—24no—
424C2×C4×C83—216no—
425C2×C4×C83—22no—
426C2×C4×C83—416no—
427C2×C4×C83C2511yescharacteristic
428C2×C4×C83C2512yes—
429C2×C4×C83C2518yes—
430C2×C4×C83C2518yes—
431C2×C4×C83C2512yes—
432C2×C4×C83C2511yescharacteristic
433C22⋊D83—216no—
434C22⋊D83—216no—
435C22⋊D83—416no—
436C22⋊D83—416no—
437C22⋊D83—48no—
438C22⋊D83—48no—
439C22⋊D83—48no—
440C2×Dic83—24no—
441C2×Dic83—216no—
442C2×Dic83—22no—
443C2×Dic83—416no—
444C2×Dic83C2511yescharacteristic
445C2×Dic83C2512yes—
446C2×Dic83C2518yes—
447C2×Dic83C2518yes—
448C2×Dic83C2512yes—
449C2×Dic83C2511yescharacteristic
450D332—28no—
451D332—28no—
452D332—416no—
453D332—44no—
454D332—48no—
455C4×D83—216no—
456C4×D83—24no—
457C4×D83—216no—
458C4×D83—22no—
459C4×D83—216no—
460C4×D83—24no—
461C4×D83—22no—
462C4×D83—24no—
463C4×D83—216no—
464C4×D83—22no—
465C4×D83—416no—
466C4×D83—416no—
467C4×D83H(5,𝔽2)18yes—
468C4×D832−1+414yes—
469Dic166—28no—
470Dic166—216no—
471Dic166—48no—
472Dic166—44no—
473C22×C83—22no—
474C22×C83—28no—
475C22×C83—28no—
476C22×C83—21no—
477C22×C83—28no—
478C22×C83C2611yescharacteristic
479C2×D83—28no—
480C2×D83—22no—
481C2×D83—28no—
482C2×D83—21no—
483C2×D83—28no—
484C2×D83—44no—
485C2×D83—432no—
486C2×D83C2×H(5,𝔽2)14yes—
487C2×D83C2×2−1+412yes—
488C4×C83—28no—
489C4×C83—22no—
490C4×C83—28no—
491C4×C83—21no—
492C4×C83C2×H(5,𝔽2)14yes—
493C4×C83C2×2−1+412yes—
494Dic83—28no—
495Dic83—22no—
496Dic83—28no—
497Dic83—21no—
498Dic83C2×H(5,𝔽2)14yes—
499Dic83C2×2−1+412yes—
500C2×#3548—831nomaximal, Sylow
501C2×C83—41no—
502C2×C83—48no—
503C2×C83C22×H(5,𝔽2)12yes—
504C2×C83C22×2−1+411yescharacteristic
505D83—41no—
506D83—48no—
507D83#354814yesdirect product factor
508#3548—834no—
509#3548—834no—
510#3548—834no—
511#3548—834no—
512#3548—834no—
513#3548—838no—
514#3548—831no—
515#3548—832no—
516#3548D8311yescharacteristic, direct product factor
517C2×#562—834no—
518C2×#554—834no—
519C2×#550—834no—
520C2×#547—834no—
521C2×#540—834no—
522C2×#537—838no—
523C2×#533—831no—
524C2×#532—832no—
525C83C2×#354811yescharacteristic, complemented, Sylow
526C22×#41—834no—
527C22×#41—838no—
528#562—834no—
529#562—838no—
530#562—8316no—
531#562—8316no—
532#562—8316no—
533#562C2×D8314yescomplemented
534#554—834no—
535#554—838no—
536#554—8316no—
537#554—838no—
538#554—834no—
539#554—834no—
540#554—838no—
541#554—838no—
542#554C2×D8314yescomplemented
543#550—838no—
544#550—838no—
545#550—834no—
546#550—838no—
547#550—8316no—
548#550—834no—
549#550—838no—
550#550—834no—
551#550C2×D8314yescomplemented
552#547—838no—
553#547—834no—
554#547—8316no—
555#547—838no—
556#547—838no—
557#547—834no—
558#547—834no—
559#547—838no—
560#547C2×D8314yescomplemented
561#540—834no—
562#540—834no—
563#540—8316no—
564#540—8316no—
565#540—838no—
566#540—838no—
567#540—834no—
568#540C2×D8314yescomplemented
569#537—838no—
570#537—838no—
571#537—838no—
572#537—8316no—
573#537—838no—
574#537—8316no—
575#537—8316no—
576#537—838no—
577#537—838no—
578#537—8316no—
579#537—838no—
580#537C2×D8318yescomplemented
581#533—832no—
582#533—832no—
583#533—834no—
584#533—834no—
585#533—832no—
586#533—831no—
587#533C2×D8311yescharacteristic, complemented
588#532—834no—
589#532—832no—
590#532—832no—
591#532—834no—
592#532—834no—
593#532—834no—
594#532—834no—
595#532—834no—
596#532—832no—
597#532C2×D8312yescomplemented
598C2×C4⋊Q8—832no—
599C2×C4⋊Q8—832no—
600C2×#127—832no—
601C2×#127—834no—
602C2×#125—832no—
603C2×#125—834no—
604C2×#124—834no—
605C2×#123—8316no—
606C2×C22⋊Q8—834no—
607C2×C22⋊Q8—838no—
608C2×C22⋊Q8—8316no—
609C2×#121—834no—
610C2×#121—834no—
611C2×#121—8316no—
612C2×#121—838no—
613C2×#121—8316no—
614C2×C4×Q8—834no—
615C2×C4×D4—834no—
616C2×C4×D4—834no—
617C2×C4×D4—838no—
618C2×#117—832no—
619C22×C4⋊C4—838no—
620C22×C42—831no—
621C2×#41—33232no—
622C2×#41—33216no—
623C2×#41—834no—
624C2×#41—838no—
625C2×#41—838no—
626C2×#41—834no—
627C2×#41—838no—
628C2×#41—8316no—
629C2×#41—838no—
630C2×#41—834no—
631C2×#41—838no—
632C2×#41—8316no—
633C2×#41C22×D8314yes—
634C2×#41C22×D8318yes—
635C22×Q8—834no—
636C22×Q8—834no—
637C22×D4—838no—
638C22×D4—8316no—
639C22×D4—834no—
640C22×D4—834no—
641C22×D4—834no—
642C23×C4—8316no—
643C23×C4—838no—
644C23×C4—831no—
645C23×C4—832no—
646C4⋊Q8—834no—
647C4⋊Q8—834no—
648C4⋊Q8—834no—
649C4⋊Q8—834no—
650C4⋊Q8—834no—
651C4⋊Q8—834no—
652C4⋊Q8—832no—
653C4⋊Q8—832no—
654C4⋊Q8C22×D8312yes—
655C4⋊Q8C22×D8312yes—
656#127—834no—
657#127—834no—
658#127—834no—
659#127—838no—
660#127—8316no—
661#127—832no—
662#127—834no—
663#127C22×D8312yes—
664#127C22×D8314yes—
665#125—838no—
666#125—834no—
667#125—8316no—
668#125—838no—
669#125—832no—
670#125—834no—
671#125C22×D8312yes—
672#125C22×D8314yes—
673#124—834no—
674#124—834no—
675#124—838no—
676#124—838no—
677#124—834no—
678#124C22×D8314yes—
679#123—8316no—
680#123—8316no—
681#123—8316no—
682#123—8316no—
683#123—8316no—
684#123—8316no—
685#123—8316no—
686#123C22×D83116yes—
687C22⋊Q8—834no—
688C22⋊Q8—838no—
689C22⋊Q8—8316no—
690C22⋊Q8—834no—
691C22⋊Q8—838no—
692C22⋊Q8—8316no—
693C22⋊Q8—838no—
694C22⋊Q8—8316no—
695C22⋊Q8—8316no—
696C22⋊Q8—8316no—
697C22⋊Q8—834no—
698C22⋊Q8—838no—
699C22⋊Q8—8316no—
700C22⋊Q8—838no—
701C22⋊Q8—8316no—
702C22⋊Q8—8316no—
703C22⋊Q8—8316no—
704C22⋊Q8C22×D8314yes—
705C22⋊Q8C22×D8318yes—
706C22⋊Q8C22×D83116yes—
707#121—834no—
708#121—834no—
709#121—8316no—
710#121—838no—
711#121—8316no—
712#121—838no—
713#121—838no—
714#121—8316no—
715#121—8316no—
716#121—8316no—
717#121—8316no—
718#121—8316no—
719#121—834no—
720#121—834no—
721#121—8316no—
722#121—838no—
723#121—8316no—
724#121—834no—
725#121—834no—
726#121—8316no—
727#121—838no—
728#121—8316no—
729#121—838no—
730#121—838no—
731#121—8316no—
732#121—8316no—
733#121—8316no—
734#121—8316no—
735#121—8316no—
736#121C22×D8314yes—
737#121C22×D8314yes—
738#121C22×D83116yes—
739#121C22×D8318yes—
740#121C22×D83116yes—
741C4×Q8—834no—
742C4×Q8—838no—
743C4×Q8—834no—
744C4×Q8—838no—
745C4×Q8—834no—
746C4×Q8C22×D8314yes—
747C4×D4—834no—
748C4×D4—834no—
749C4×D4—838no—
750C4×D4—838no—
751C4×D4—838no—
752C4×D4—8316no—
753C4×D4—834no—
754C4×D4—834no—
755C4×D4—838no—
756C4×D4—838no—
757C4×D4—838no—
758C4×D4—8316no—
759C4×D4—834no—
760C4×D4—834no—
761C4×D4—838no—
762C4×D4C22×D8314yes—
763C4×D4C22×D8314yes—
764C4×D4C22×D8318yes—
765#117—832no—
766#117—834no—
767#117—834no—
768#117—834no—
769#117C22×D8312yes—
770C2×C4⋊C4—8316no—
771C2×C4⋊C4—838no—
772C2×C4⋊C4—834no—
773C2×C4⋊C4—834no—
774C2×C4⋊C4—8316no—
775C2×C4⋊C4—8316no—
776C2×C4⋊C4—838no—
777C2×C4⋊C4—838no—
778C2×C4⋊C4—834no—
779C2×C4⋊C4—834no—
780C2×C4⋊C4—838no—
781C2×C4⋊C4C22×D8318yes—
782C2×C22⋊C4—834no—
783C2×C22⋊C4—8316no—
784C2×C22⋊C4—838no—
785C2×C22⋊C4—838no—
786C2×C42—832no—
787C2×C42—831no—
788C2×C42—834no—
789C2×C42—831no—
790C2×C42—832no—
791C2×C42—831no—
792C2×C42—831no—
793C2×C42—832no—
794C2×C42—831no—
795C2×C42C22×D8311yescharacteristic
796C24—838no—
797C24—831no—
798#41—48no—
799#41—416no—
800#41—33216no—
801#41—33216no—
802#41—3328no—
803#41—33232no—
804#41—33216no—
805#41—33232no—
806#41—33216no—
807#41—33216no—
808#41—3328no—
809#41—3328no—
810C2×Q8—3328no—
811C2×Q8—838no—
812C2×Q8—834no—
813C2×Q8—838no—
814C2×Q8—834no—
815C2×Q8—16616no—
816C2×Q8C23×D8314yes—
817C2×Q8C23×D8314yes—
818C2×D4—33216no—
819C2×D4—33232no—
820C2×D4—3328no—
821C2×D4—838no—
822C2×D4—838no—
823C2×D4—8316no—
824C2×D4—8316no—
825C2×D4—838no—
826C2×D4—838no—
827C2×D4—838no—
828C2×D4—838no—
829C2×D4—8316no—
830C2×D4—834no—
831C2×D4—834no—
832C2×D4—834no—
833C2×D4—16616no—
834C2×D4—16616no—
835C2×D4C23×D8314yes—
836C2×D4C23×D8314yes—
837C2×D4C23×D8318yes—
838C2×D4C23×D83116yes—
839C2×D4C23×D8314yes—
840C22×C4—33232no—
841C22×C4—8316no—
842C22×C4—8316no—
843C22×C4—8316no—
844C22×C4—831no—
845C22×C4—832no—
846C22×C4—831no—
847C22×C4—832no—
848C22×C4—838no—
849C22×C4—831no—
850C22×C4—832no—
851C22×C4—831no—
852C22×C4—831no—
853C22×C4—832no—
854C22×C4—832no—
855C22×C4—838no—
856C22×C4—838no—
857C22×C4—838no—
858C22×C4—838no—
859C22×C4—16632no—
860C22×C4—1668no—
861C22×C4—1664no—
862C22×C4C23×D8311yescharacteristic
863C22×C4C23×D8312yes—
864C22×C4C23×D8318yes—
865C22×C4C23×D83116yes—
866C4⋊C4—838no—
867C4⋊C4—834no—
868C4⋊C4—838no—
869C4⋊C4—834no—
870C4⋊C4—8316no—
871C4⋊C4—8316no—
872C4⋊C4—8316no—
873C4⋊C4—838no—
874C4⋊C4—834no—
875C4⋊C4—838no—
876C4⋊C4—834no—
877C4⋊C4—838no—
878C4⋊C4—838no—
879C4⋊C4—838no—
880C4⋊C4C23×D8314yes—
881C4⋊C4C23×D8314yes—
882C4⋊C4C23×D83116yes—
883C4⋊C4C23×D8314yes—
884C4⋊C4C23×D8314yes—
885C4⋊C4C23×D8318yes—
886C22⋊C4—834no—
887C22⋊C4—8316no—
888C22⋊C4—838no—
889C22⋊C4—838no—
890C22⋊C4—838no—
891C22⋊C4—8316no—
892C22⋊C4—8316no—
893C22⋊C4—838no—
894C22⋊C4—838no—
895C22⋊C4—838no—
896C22⋊C4—838no—
897C22⋊C4C23×D8314yes—
898C22⋊C4C23×D83116yes—
899C22⋊C4C23×D8318yes—
900C22⋊C4C23×D8318yes—
901C42—831no—
902C42—832no—
903C42—832no—
904C42—832no—
905C42—832no—
906C42—832no—
907C42—831no—
908C42—838no—
909C42—834no—
910C42C23×D8311yescharacteristic
911C42C23×D8312yes—
912C42C23×D8311yescharacteristic
913C42C23×D8314yes—
914C23—831no—
915C23—838no—
916C23—831no—
917C23—16616no—
918C23—16616no—
919C23—1664no—
920C23—1662no—
921C23—16616no—
922C23C24×D8311yescharacteristic
923C23C24×D8318yes—
924Q8—28no—
925Q8—44no—
926Q8—3328no—
927Q8—3324no—
928Q8—16616no—
929Q8—1668no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—3328no—
936D4—3324no—
937D4—33216no—
938D4—3328no—
939D4—3328no—
940D4—33216no—
941D4—33216no—
942D4—3328no—
943D4—16616no—
944D4—16616no—
945D4—1668no—
946D4—1668no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—33216no—
952C2×C4—33216no—
953C2×C4—33216no—
954C2×C4—831no—
955C2×C4—832no—
956C2×C4—838no—
957C2×C4—834no—
958C2×C4—831no—
959C2×C4—832no—
960C2×C4—838no—
961C2×C4—838no—
962C2×C4—16616no—
963C2×C4—1664no—
964C2×C4—1662no—
965C2×C4—16616no—
966C2×C4—16616no—
967C2×C4—1664no—
968C2×C4—1662no—
969C2×C4—16616no—
970C2×C4—1664no—
971C2×C4—1662no—
972C2×C4—16616no—
973C2×C4—1664no—
974C2×C4—1662no—
975C2×C4C24×D8311yescharacteristic
976C2×C4C24×D8312yes—
977C2×C4C24×D8318yes—
978C2×C4C24×D8318yes—
979C2×C4C24×D8312yes—
980C2×C4C24×D8311yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—33232no—
987C22—3324no—
988C22—834no—
989C22—832no—
990C22—1668no—
991C22—1668no—
992C22—1662no—
993C22—1661no—
994C22—1668no—
995C22C25×D8311yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—834no—
1001C4—832no—
1002C4—1668no—
1003C4—1668no—
1004C4—1662no—
1005C4—1661no—
1006C4H(5,𝔽2)×D8314yes—
1007C42−1+4×D8312yes—
1008C2—41no—
1009C2—48no—
1010C2—3328no—
1011C2—3321no—
1012C2—834no—
1013C2C2×H(5,𝔽2)×D8312yes—
1014C2C2×2−1+4×D8311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3548C2
hypercenter#3548D83
hypocenterC83C2×#3548
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #24921863C2semidirect
2. #24921862C2semidirect
3. #24921861C2semidirect
4. #24921860C2semidirect
5. #24921859C2semidirect
6. #24921858C2semidirect
7. #24921857C2semidirect
8. #24921856C2semidirect
9. #562×D83C2semidirect
10. #554×D83C2semidirect
11. #550×D83C2semidirect
12. #547×D83C2semidirect
13. #540×D83C2semidirect
14. #537×D83C2semidirect
15. #533×D83C2semidirect
16. #532×D83C2semidirect
17. C83×#3548C2semidirect
20. #19128449C22semidirect
21. #19128448C22semidirect
22. #19128447C22semidirect
23. #19128446C22semidirect
24. #19128445C22semidirect
25. #19128412C22semidirect
26. #19128411C22semidirect
27. #19128410C22semidirect
28. #19128409C22semidirect
29. #19128408C22semidirect
30. #19128407C22semidirect
31. #19128406C22semidirect
32. #19128405C22semidirect
33. #19128373C22semidirect
34. #19128372C22semidirect
35. #19128372C22semidirect
36. #19128371C22semidirect
37. #19128371C22semidirect
38. #19128370C22semidirect
39. #19128369C22semidirect
40. #19128369C22semidirect
41. #19128356C22semidirect
42. #19128355C22semidirect
43. #19128354C22semidirect
44. #19128353C22semidirect
45. #19128352C22semidirect
46. #19128351C22semidirect
47. #19128350C22semidirect
48. #19128349C22semidirect
49. #19128307C22semidirect
50. #19128306C22semidirect
51. #19128305C22semidirect
52. #19128304C22semidirect
53. #19128303C22semidirect
54. #19128302C22semidirect
55. #19128301C22semidirect
56. #19128282C22semidirect
57. #19128281C22semidirect
58. #19128281C22semidirect
59. #19128281C22semidirect
60. #19128280C22semidirect
61. #19128280C22semidirect
62. #19128280C22semidirect
63. #19128279C22semidirect
64. #19128279C22semidirect
65. #19128278C22semidirect
66. #19128278C22semidirect
67. #19128258C22semidirect
68. #19128257C22semidirect
69. #19128256C22semidirect
70. #19128255C22semidirect
71. #19128254C22semidirect
72. #19128253C22semidirect
73. #19128252C22semidirect
74. #19128251C22semidirect
75. #19128250C22semidirect
76. #19128249C22semidirect
77. #19128248C22semidirect
78. #19128248C22semidirect
79. #19128247C22semidirect
80. #19128246C22semidirect
81. #19128246C22semidirect
105. #562×C83C22semidirect
106. #554×C83C22semidirect
107. #550×C83C22semidirect
108. #547×C83C22semidirect
109. #540×C83C22semidirect
110. #537×C83C22semidirect
111. #533×C83C22semidirect
112. #532×C83C22semidirect
507. D83#3548direct (N × H)
516. #3548D83direct (N × H)
525. C83C2×#3548semidirect
533. #562C2×D83semidirect
542. #554C2×D83semidirect
551. #550C2×D83semidirect
560. #547C2×D83semidirect
568. #540C2×D83semidirect
580. #537C2×D83semidirect
587. #533C2×D83semidirect
597. #532C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249218632
#249218622
#249218612
#249218602
#249218592
#249218582
#249218572
#249218562
#562×D832
#554×D832
#550×D832
#547×D832
#540×D832
#537×D832
#533×D832
#532×D832
C83×#35482
C2×#354883