Finite Group Databasebeta

← #36312948

Subgroups — #36312948

Order 21248.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128536C212yesmaximal, complemented
2#24921255C216yesmaximal, complemented
3#24921251C212yesmaximal, complemented
4#24921248C211yesmaximal, characteristic, complemented
5#24921243C213yesmaximal, complemented
6#24921239C213yesmaximal, complemented
7#24921228C214yesmaximal, complemented
8#24921219C2112yesmaximal, complemented
9#24920953C214yesmaximal, complemented
10D4×#13050589C2112yesmaximal, complemented
11#24920794C216yesmaximal, complemented
12C2×#19128249C213yesmaximal, complemented
13#532×D83C213yesmaximal, complemented
14C4×#41×D83C211yesmaximal, characteristic, complemented
15C83×#3498C211yesmaximal, characteristic, complemented
16#19128536—232no—
17C2×#14581839C2214yescomplemented
18C2×#14581839C2216yescomplemented
19C2×#14581839C2212yescomplemented
20C2×#14581837C22112yescomplemented
21C2×#14581837C2216yescomplemented
22C22×#13050589C22112yescomplemented
23C22×#13050589C2216yescomplemented
24C2×#41×D83C2211yescharacteristic
25C2×#41×D83C2214yescomplemented
26C2×#41×D83C2216yescomplemented
27#19128371C22112yescomplemented
28Q8×D332C2214yescomplemented
29D4×Dic166C22112yescomplemented
30#19128358C2218yescomplemented
31#19128357C22124yescomplemented
32#19128356C22112yescomplemented
33#19128355C22112yescomplemented
34#19128351C22124yescomplemented
35#19128348C22124yescomplemented
36#19128345C22124yescomplemented
37#19128338C22148yescomplemented
38#19128336C22112yescomplemented
39D4×C22⋊D83C22124yescomplemented
40#19128280C22124yescomplemented
41#19128277C2216yescomplemented
42#19128272C2216yescomplemented
43#19128271C22112yescomplemented
44#19128268C2216yescomplemented
45#19128264C22112yescomplemented
46#19128261C22124yescomplemented
47#19128252C2211yescharacteristic, complemented
48#19128251C2213yescomplemented
49#19128250C2216yescomplemented
50#19128249C22112yescomplemented
51#19128249C22112yescomplemented
52#19128249C2216yescomplemented
53#19128249C2213yescomplemented
54#19128249C2216yescomplemented
55#19128249C2216yescomplemented
56#19128248C22112yescomplemented
57#19128247C2216yescomplemented
58#19128246C22112yescomplemented
59C2×#14581792C2213yescomplemented
60C4⋊Q8×D83C2213yescomplemented
61#127×D83C2213yescomplemented
62C2×#14581779C2216yescomplemented
63#124×D83C2216yescomplemented
64#19128211C22124yescomplemented
65#19128207C22124yescomplemented
66C2×#14581763C22112yescomplemented
67#121×D83C22112yescomplemented
68#41×Dic83C2211yescharacteristic, complemented
69C4×#13050591C2212yescomplemented
70C4×#13050590C2213yescomplemented
71#19128169C2213yescomplemented
72C4×#13050589C2216yescomplemented
73C4×Q8×D83C2212yescomplemented
74C2×D4×Dic83C22112yescomplemented
75C4×D4×D83C2216yescomplemented
76C4×D4×D83C22112yescomplemented
77#117×D83C2213yescomplemented
78C2×C42×D83C2213yescomplemented
79C2×H(5,𝔽2)×C83C2212yescomplemented
80#550×C83C2214yescomplemented
81D42×C83C22112yescomplemented
82#535×C83C2216yescomplemented
83#532×C83C2213yescomplemented
84C2×#127×C83C2213yescomplemented
85C4×#41×C83C2211yescharacteristic, complemented
86#14581839—248no—
87#14581839—232no—
88#14581839—216no—
89#14581837—248no—
90#14581837—296no—
91C2×#13050591C2312yes—
92C2×#13050591C2311yescharacteristic
93C2×#13050590C23112yes—
94C2×#13050590C2316yes—
95C2×#13050590C23112yes—
96C2×#13050590C2313yes—
97C2×#13050589—296no—
98C2×#13050589—248no—
99C2×#13050589C23124yes—
100C2×#13050589C23112yes—
101C2×#13050589C23112yes—
102C2×#13050589C23112yes—
103C2×#13050589C23112yes—
104C2×#13050589C2316yes—
105C2×#13050589C23112yes—
106C2×#13050589C23112yes—
107C2×#13050589C2313yes—
108#41×D83—232no—
109#41×D83—248no—
110#41×D83D4116yescomplemented
111C22×Dic166C23112yes—
112C22×Dic166C2316yes—
113C2×Q8×D83C2314yes—
114C2×Q8×D83C2316yes—
115C2×Q8×D83C2311yescharacteristic
116C22×C22⋊D83C23124yes—
117C22×C22⋊D83C23112yes—
118C2×D4×D83C23112yes—
119C2×D4×D83C23112yes—
120C2×D4×D83C2316yes—
121C2×D4×D83C23112yes—
122C2×D4×D83C2313yes—
123C23×Dic83C23112yes—
124C22×C4×D83C23112yes—
125C22×C4×D83C2316yes—
126C22×C4×D83C2313yes—
127#14581792C23112yes—
128#14581792C2313yes—
129#14581792C2316yes—
130#14581791C23112yes—
131#14581790C2316yes—
132#14581789C2311yescharacteristic
133#14581788C23112yes—
134#14581788C2316yes—
135#14581781C2312yes—
136#14581780C2316yes—
137#14581779C23124yes—
138#14581779C2316yes—
139#14581779C23112yes—
140#14581778C23124yes—
141#14581776C23124yes—
142#14581774C23148yes—
143#14581773C23124yes—
144#14581772C23124yes—
145#14581771C23124yes—
146#14581769C23148yes—
147#14581767C2314yes—
148#14581766C23112yes—
149#14581765C23124yes—
150#14581764C23148yes—
151#14581764C23124yes—
152#14581763C23124yes—
153#14581763C23124yes—
154#14581763C23124yes—
155#14581763C23112yes—
156#14581763C23124yes—
157#14581761C23124yes—
158#14581760C23148yes—
159Q8×Dic83C2312yes—
160C4×Dic166C2316yes—
161#14581757C2316yes—
162C4×D332C2316yes—
163C4×D332C23112yes—
164D4×Dic83C23124yes—
165D4×Dic83C23124yes—
166D4×Dic83C2316yes—
167D4×Dic83C23112yes—
168D4×Dic83C23124yes—
169#14581754C2316yes—
170#14581754C2314yes—
171C4×C22⋊D83C23112yes—
172C4×C22⋊D83C23124yes—
173(C22⋊D83)⋊C4C23112yes—
174(C22⋊D83)⋊C4C23124yes—
175#14581751C2313yes—
176#14581750C2316yes—
177#14581749C2316yes—
178#14581748C2316yes—
179C2×C4⋊Dic83C23112yes—
180C4⋊C4×D83C23112yes—
181C4⋊C4×D83C2316yes—
182C2×C22⋊Dic83C23124yes—
183C22⋊C4×D83C23124yes—
184C22⋊C4×D83C2316yes—
185C2×C4×Dic83C2316yes—
186C2×C4×Dic83C2313yes—
187C42×D83C2311yescharacteristic
188C42×D83C2313yes—
189C42×D83C2316yes—
190C42×D83C2316yes—
191C42×D83C2313yes—
192C42×D83C2313yes—
193H(5,𝔽2)×C83—216no—
194C2×#41×C83C2314yes—
195C2×#41×C83C2316yes—
196C2×#41×C83C2311yescharacteristic
197C22×D4×C83C23112yes—
198C22×D4×C83C2316yes—
199C22×D4×C83C23112yes—
200C4⋊Q8×C83C2311yescharacteristic
201#127×C83C23112yes—
202#127×C83C2313yes—
203#127×C83C2316yes—
204#124×C83C2316yes—
205#121×C83C23124yes—
206#121×C83C23112yes—
207#120×C83C23124yes—
208C4×Q8×C83C2312yes—
209C4×D4×C83C2316yes—
210C4×D4×C83C23112yes—
211#117×C83C2313yes—
212C2×C42×C83C2313yes—
213C23×D83C24112yes—
214C23×D83C2413yes—
215#13050591—28no—
216#13050591C2×D418yescomplemented
217#13050590—224no—
218#13050590—248no—
219#13050590—248no—
220#13050590C2×D4124yescomplemented
221#13050589—248no—
222#13050589—296no—
223#13050589—248no—
224#13050589—248no—
225#13050589—224no—
226#13050589—248no—
227#13050589—248no—
228#13050589—248no—
229#13050589C2×D4124yescomplemented
230C2×Dic166—224no—
231C2×Dic166—248no—
232C2×Dic166C24112yes—
233C2×Dic166C24112yes—
234C2×Dic166C2416yes—
235C2×Dic166C2413yes—
236Q8×D83—216no—
237Q8×D83—224no—
238Q8×D83C2×D418yescomplemented
239C2×D332C2414yes—
240C2×D332C2414yes—
241C2×D332C2412yes—
242C2×D332C2413yes—
243C2×C22⋊D83—248no—
244C2×C22⋊D83—296no—
245C2×C22⋊D83C24124yes—
246C2×C22⋊D83C24112yes—
247C2×C22⋊D83C24112yes—
248C2×C22⋊D83C24112yes—
249C2×C22⋊D83C24124yes—
250C2×C22⋊D83C2416yes—
251D4×D83—248no—
252D4×D83—248no—
253D4×D83—224no—
254D4×D83—424no—
255D4×D83C2×D4124yescomplemented
256C22×Dic83—248no—
257C22×Dic83C24124yes—
258C22×Dic83C24112yes—
259C22×Dic83C24112yes—
260C22×Dic83C2416yes—
261C22×Dic83C2413yes—
262C2×C4×D83—248no—
263C2×C4×D83—412no—
264C2×C4×D83C2×D4124yescomplemented
265C2×C4×D83C2412yes—
266C2×C4×D83C2416yes—
267C2×C4×D83C24112yes—
268C2×C4×D83C24112yes—
269C2×C4×D83C2414yes—
270C2×C4×D83C2416yes—
271C2×C4×D83C2416yes—
272C2×C4×D83C2413yes—
273C2×C4×D83C2411yescharacteristic
274C2×C4×D83C2413yes—
275C2×C4×D83C2413yes—
276C4⋊Dic83C2416yes—
277C4⋊Dic83C24112yes—
278C4⋊Dic83C24124yes—
279Dic83⋊C4C24112yes—
280Dic83⋊C4C24124yes—
281C22⋊Dic83C24148yes—
282C22⋊Dic83C2416yes—
283C22⋊Dic83C24124yes—
284(C2×D83)⋊C4C24112yes—
285(C2×D83)⋊C4C24124yes—
286(C2×D83)⋊C4C2418yes—
287C4×Dic83C2416yes—
288C4×Dic83C2411yescharacteristic
289C4×Dic83C2413yes—
290C4×Dic83C2416yes—
291C4×Dic83C2416yes—
292C4×Dic83C2412yes—
293C4×Dic83C2416yes—
294C24×C83C24112yes—
295#41×C83—216no—
296#41×C83—224no—
297#41×C83C2×D418yescomplemented
298C2×Q8×C83C2412yes—
299C2×Q8×C83C2411yescharacteristic
300C2×D4×C83—248no—
301C2×D4×C83—224no—
302C2×D4×C83—424no—
303C2×D4×C83C24112yes—
304C2×D4×C83C24112yes—
305C2×D4×C83C24112yes—
306C2×D4×C83C2416yes—
307C2×D4×C83C24124yes—
308C2×D4×C83C2413yes—
309C22×C4×C83C2416yes—
310C22×C4×C83C24112yes—
311C22×C4×C83C2413yes—
312C4⋊C4×C83C2414yes—
313C4⋊C4×C83C2416yes—
314C22⋊C4×C83C24124yes—
315C22⋊C4×C83C2416yes—
316C42×C83C2413yes—
317C42×C83C2411yescharacteristic
318C42×C83C2416yes—
319C23×C83—224no—
320C23×C83—424no—
321C23×C83C25112yes—
322C23×C83C2513yes—
323C22×D83—224no—
324C22×D83—46no—
325C22×D83—424no—
326C22×D83C22×D4112yes—
327C22×D83C2514yes—
328C22×D83C2513yes—
329C22×D83C2511yescharacteristic
330Q8×C83—24no—
331Q8×C83C22×D414yes—
332D4×C83—224no—
333D4×C83—212no—
334D4×C83—224no—
335D4×C83—224no—
336D4×C83—424no—
337D4×C83C22×D4112yes—
338C2×C4×C83—224no—
339C2×C4×C83—212no—
340C2×C4×C83C22×D4112yes—
341C2×C4×C83C2516yes—
342C2×C4×C83C2514yes—
343C2×C4×C83C2511yescharacteristic
344C2×C4×C83C2513yes—
345C2×C4×C83C2512yes—
346C22⋊D83—224no—
347C22⋊D83—248no—
348C22⋊D83—224no—
349C22⋊D83—224no—
350C22⋊D83—424no—
351C22⋊D83C22×D4124yes—
352C2×Dic83—224no—
353C2×Dic83—224no—
354C2×Dic83—248no—
355C2×Dic83—46no—
356C2×Dic83C22×D4112yes—
357C2×Dic83C2512yes—
358C2×Dic83C2516yes—
359C2×Dic83C25112yes—
360C2×Dic83C2511yescharacteristic
361C2×Dic83C2513yes—
362D332—28no—
363D332—24no—
364D332—28no—
365D332C22×D4112yes—
366C4×D83—224no—
367C4×D83—224no—
368C4×D83—24no—
369C4×D83—212no—
370C4×D83—28no—
371C4×D83—46no—
372C4×D83—46no—
373C4×D83C22×D4112yes—
374C4×D83C22×D414yes—
375C4×D83C22×D4112yes—
376C4×D83C22×D4112yes—
377Dic166—212no—
378Dic166—224no—
379Dic166—224no—
380Dic166C22×D4112yes—
381C22×C83—26no—
382C22×C83—212no—
383C22×C83—224no—
384C22×C83—824no—
385C22×C83C23×D416yes—
386C22×C83C2611yescharacteristic
387C2×D83—22no—
388C2×D83—26no—
389C2×D83—24no—
390C2×D83—28no—
391C2×D83—412no—
392C2×D83—824no—
393C2×D83C23×D416yes—
394C2×D83C23×D412yes—
395C4×C83—24no—
396C4×C83—26no—
397C4×C83C23×D412yes—
398C4×C83C23×D416yes—
399C4×C83#58514yescomplemented
400Dic83—212no—
401Dic83—22no—
402Dic83—26no—
403Dic83C23×D416yes—
404Dic83C23×D412yes—
405#62812—831nomaximal, Sylow
406C2×C83—26no—
407C2×C83—412no—
408C2×C83C24×D411yescharacteristic
409C2×C83C2×#58512yes—
410D83—22no—
411D83—26no—
412D83—44no—
413C2×#585—832no—
414#3500—832no—
415#3500—836no—
416#3499—833no—
417#3499—831no—
418#3498—833no—
419#3498D8311yescharacteristic, complemented
420#3497—834no—
421#3496—8312no—
422D4×#41—834no—
423D4×#41—8312no—
424#3449—836no—
425C2×#532—833no—
426C2×#532—833no—
427C2×C4×#41—831no—
428C83#6281211yescharacteristic, complemented, Sylow
429#585—16632no—
430C2×2−1+4—834no—
431C2×2−1+4—836no—
432C2×2−1+4—832no—
433C2×H(5,𝔽2)—8312no—
434C2×H(5,𝔽2)—836no—
435C2×H(5,𝔽2)C2×D8312yescomplemented
436C22×#41—831no—
437C22×#41—836no—
438C22×#41—834no—
439C22×#41—836no—
440C22×#41—8312no—
441#550—8312no—
442#550C2×D8314yescomplemented
443D4×Q8—834no—
444D4×Q8—8312no—
445#548—838no—
446#548—8324no—
447#547—8324no—
448#547—8312no—
449#547—8312no—
450#546—8324no—
451#546—8324no—
452#546—8348no—
453D42—8324no—
454D42—8312no—
455D42C2×D83112yescomplemented
456#537—8324no—
457#536—836no—
458#536—8312no—
459#536—836no—
460#535—836no—
461#535—8312no—
462#535C2×D8316yescomplemented
463#534—8324no—
464#532—836no—
465#532—831no—
466#532—833no—
467#532—836no—
468#532—8312no—
469#532—8312no—
470#532—836no—
471#532—836no—
472#532—836no—
473#532—8312no—
474#532—8312no—
475#532—833no—
476#532C2×D8313yescomplemented
477C2×C4⋊Q8—833no—
478C2×C4⋊Q8—833no—
479C2×#127—833no—
480C2×#127C2×D8313yescomplemented
481C2×#124—836no—
482C2×#124—836no—
483#525—8324no—
484#525—8324no—
485C2×#121—8312no—
486C2×#121—8312no—
487C4×#41—831no—
488C4×#41—832no—
489C4×#41—836no—
490C4×#41—833no—
491C4×#41—833no—
492C4×#41C2×D8311yescharacteristic, complemented
493C2×C4×Q8—832no—
494C2×C4×D4—8312no—
495C2×C4×D4—836no—
496C2×C4×D4—8312no—
497C2×#117—833no—
498C22×C42—833no—
4992−1+4—16632no—
5002−1+4—16648no—
5012−1+4—16616no—
502H(5,𝔽2)—216no—
503H(5,𝔽2)—16696no—
504H(5,𝔽2)—16648no—
505C2×#41—8316no—
506C2×#41—831no—
507C2×#41—832no—
508C2×#41—833no—
509C2×#41—8312no—
510C2×#41—8312no—
511C2×#41—836no—
512C2×#41—8312no—
513C2×#41—8312no—
514C2×#41—8312no—
515C2×#41—8324no—
516C2×#41—8312no—
517C2×#41—833no—
518C2×#41—836no—
519C2×#41—8312no—
520C2×#41—8312no—
521C2×#41—16648no—
522C2×#41—16648no—
523C2×#41—16696no—
524C2×#41—16632no—
525C2×#41C22×D8316yes—
526C2×#41C22×D8314yes—
527C2×#41C22×D8311yescharacteristic
528C22×Q8—831no—
529C22×Q8—836no—
530C22×Q8—834no—
531C22×Q8—836no—
532C22×Q8—8312no—
533C22×D4—8312no—
534C22×D4—833no—
535C22×D4—8312no—
536C22×D4—8324no—
537C22×D4—8312no—
538C22×D4—836no—
539C22×D4—8312no—
540C22×D4C22×D8316yes—
541C22×D4C22×D83112yes—
542C22×D4C22×D83112yes—
543C23×C4—836no—
544C23×C4—833no—
545C23×C4—8312no—
546C23×C4—8312no—
547C4⋊Q8—836no—
548C4⋊Q8—8312no—
549C4⋊Q8—833no—
550C4⋊Q8—836no—
551C4⋊Q8—8312no—
552C4⋊Q8C22×D8311yescharacteristic
553#127—836no—
554#127—8312no—
555#127—831no—
556#127C22×D8313yes—
557#127C22×D8316yes—
558#127C22×D83112yes—
559#124—832no—
560#124—836no—
561#124—8312no—
562#124—8324no—
563#124—8324no—
564#124—836no—
565#124C22×D8316yes—
566#123—8324no—
567#123—8348no—
568#123—8324no—
569C22⋊Q8—8324no—
570C22⋊Q8—8324no—
571C22⋊Q8—8348no—
572#121—8312no—
573#121—8324no—
574#121—8324no—
575#121—8324no—
576#121—8324no—
577#121—8324no—
578#121—8348no—
579#121—8312no—
580#121—834no—
581#121—8324no—
582#121C22×D83112yes—
583#121C22×D83124yes—
584#120—8324no—
585#120—8348no—
586#120C22×D83124yes—
587C4×Q8—832no—
588C4×Q8—836no—
589C4×Q8—836no—
590C4×Q8C22×D8312yes—
591C4×D4—8312no—
592C4×D4—836no—
593C4×D4—8324no—
594C4×D4—8324no—
595C4×D4—8324no—
596C4×D4—8312no—
597C4×D4—8324no—
598C4×D4—834no—
599C4×D4—836no—
600C4×D4—8312no—
601C4×D4—8324no—
602C4×D4—836no—
603C4×D4—8312no—
604C4×D4C22×D8316yes—
605C4×D4C22×D83112yes—
606#117—833no—
607#117—836no—
608#117—836no—
609#117—836no—
610#117C22×D8313yes—
611C2×C4⋊C4—8312no—
612C2×C4⋊C4—836no—
613C2×C4⋊C4—8312no—
614C2×C22⋊C4—8324no—
615C2×C22⋊C4—836no—
616C2×C22⋊C4—8324no—
617C2×C42—836no—
618C2×C42—833no—
619C2×C42—833no—
620C2×C42—836no—
621C2×C42—836no—
622C2×C42—833no—
623C2×C42—833no—
624C2×C42—831no—
625C2×C42C22×D8313yes—
626C24—833no—
627C24—8312no—
628C24C23×D83112yes—
629#41—216no—
630#41—224no—
631#41—838no—
632#41—8324no—
633#41—8324no—
634#41—16648no—
635#41—16648no—
636#41—16648no—
637#41—16624no—
638#41—16648no—
639#41—16648no—
640#41—16648no—
641#41—1668no—
642#41—16696no—
643#41—16648no—
644#41—16648no—
645#41—16624no—
646#41D4×D8318yescomplemented
647C2×Q8—838no—
648C2×Q8—833no—
649C2×Q8—8312no—
650C2×Q8—8312no—
651C2×Q8—836no—
652C2×Q8—16648no—
653C2×Q8—16624no—
654C2×Q8—16616no—
655C2×Q8—16624no—
656C2×Q8C23×D8312yes—
657C2×Q8C23×D8311yescharacteristic
658C2×D4—248no—
659C2×D4—224no—
660C2×D4—424no—
661C2×D4—33224no—
662C2×D4—8324no—
663C2×D4—836no—
664C2×D4—8324no—
665C2×D4—8324no—
666C2×D4—8312no—
667C2×D4—8312no—
668C2×D4—8312no—
669C2×D4—833no—
670C2×D4—834no—
671C2×D4—834no—
672C2×D4—832no—
673C2×D4—16624no—
674C2×D4—16648no—
675C2×D4—16648no—
676C2×D4—16696no—
677C2×D4—16648no—
678C2×D4C23×D83112yes—
679C2×D4C23×D83112yes—
680C2×D4C23×D83112yes—
681C2×D4C23×D8316yes—
682C2×D4C23×D83124yes—
683C2×D4C23×D8313yes—
684C22×C4—33212no—
685C22×C4—836no—
686C22×C4—836no—
687C22×C4—836no—
688C22×C4—833no—
689C22×C4—8324no—
690C22×C4—831no—
691C22×C4—833no—
692C22×C4—833no—
693C22×C4—833no—
694C22×C4—8312no—
695C22×C4—8312no—
696C22×C4—8324no—
697C22×C4—832no—
698C22×C4—836no—
699C22×C4—8312no—
700C22×C4—834no—
701C22×C4—8312no—
702C22×C4—16648no—
703C22×C4—16648no—
704C22×C4C23×D8316yes—
705C22×C4C23×D83112yes—
706C22×C4C23×D8313yes—
707C4⋊C4—8312no—
708C4⋊C4—8312no—
709C4⋊C4—836no—
710C4⋊C4—8324no—
711C4⋊C4—8324no—
712C4⋊C4C23×D8314yes—
713C4⋊C4C23×D8316yes—
714C22⋊C4—8324no—
715C22⋊C4—836no—
716C22⋊C4—8348no—
717C22⋊C4—838no—
718C22⋊C4—8312no—
719C22⋊C4—8324no—
720C22⋊C4C23×D8316yes—
721C22⋊C4C23×D83124yes—
722C42—832no—
723C42—831no—
724C42—836no—
725C42—833no—
726C42—836no—
727C42—836no—
728C42—836no—
729C42C23×D8311yescharacteristic
730C42C23×D8313yes—
731C42C23×D8316yes—
732C23—224no—
733C23—424no—
734C23—3326no—
735C23—33224no—
736C23—8312no—
737C23—833no—
738C23—831no—
739C23—834no—
740C23—16624no—
741C23C24×D83112yes—
742C23C24×D8313yes—
743Q8—24no—
744Q8—8312no—
745Q8—16624no—
746Q8—16624no—
747Q8—16612no—
748Q8C2×D4×D8314yes—
749D4—224no—
750D4—224no—
751D4—212no—
752D4—224no—
753D4—424no—
754D4—33224no—
755D4—8324no—
756D4—8312no—
757D4—1668no—
758D4—16624no—
759D4—16624no—
760D4—16648no—
761D4—16624no—
762D4—1664no—
763D4—1668no—
764D4C2×D4×D83112yes—
765C2×C4—224no—
766C2×C4—212no—
767C2×C4—3326no—
768C2×C4—3326no—
769C2×C4—3326no—
770C2×C4—8312no—
771C2×C4—831no—
772C2×C4—833no—
773C2×C4—834no—
774C2×C4—8312no—
775C2×C4—8312no—
776C2×C4—8312no—
777C2×C4—832no—
778C2×C4—836no—
779C2×C4—8312no—
780C2×C4—1668no—
781C2×C4—16624no—
782C2×C4—16624no—
783C2×C4—16648no—
784C2×C4—16624no—
785C2×C4—16624no—
786C2×C4—1664no—
787C2×C4—16612no—
788C2×C4C2×D4×D83112yes—
789C2×C4C24×D8316yes—
790C2×C4C24×D8314yes—
791C2×C4C24×D8311yescharacteristic
792C2×C4C24×D8313yes—
793C2×C4C24×D8312yes—
794C22—26no—
795C22—212no—
796C22—224no—
797C22—824no—
798C22—33212no—
799C22—832no—
800C22—836no—
801C22—66424no—
802C22—1664no—
803C22—1668no—
804C22—1662no—
805C22—1666no—
806C22C22×D4×D8316yes—
807C22C25×D8311yescharacteristic
808C4—24no—
809C4—26no—
810C4—832no—
811C4—836no—
812C4—16612no—
813C4—1662no—
814C4—1666no—
815C4C22×D4×D8316yes—
816C4C22×D4×D8312yes—
817C4#1912853614yescomplemented
818C2—26no—
819C2—412no—
820C2—3324no—
821C2—1662no—
822C2—1666no—
823C2C23×D4×D8311yescharacteristic
824C2C2×#1912853612yes—
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3498C2
hypercenter#3498D83
hypocenterC83#62812
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C2×#19128536C2semidirect
2. #24921255C2semidirect
3. #24921251C2semidirect
4. #24921248C2semidirect
5. #24921243C2semidirect
6. #24921239C2semidirect
7. #24921228C2semidirect
8. #24921219C2semidirect
9. #24920953C2semidirect
10. D4×#13050589C2semidirect
11. #24920794C2semidirect
12. C2×#19128249C2semidirect
13. #532×D83C2semidirect
14. C4×#41×D83C2semidirect
15. C83×#3498C2semidirect
17. C2×#14581839C22semidirect
18. C2×#14581839C22semidirect
19. C2×#14581839C22semidirect
20. C2×#14581837C22semidirect
21. C2×#14581837C22semidirect
22. C22×#13050589C22semidirect
23. C22×#13050589C22semidirect
25. C2×#41×D83C22semidirect
26. C2×#41×D83C22semidirect
27. #19128371C22semidirect
28. Q8×D332C22semidirect
29. D4×Dic166C22semidirect
30. #19128358C22semidirect
31. #19128357C22semidirect
32. #19128356C22semidirect
33. #19128355C22semidirect
34. #19128351C22semidirect
35. #19128348C22semidirect
36. #19128345C22semidirect
37. #19128338C22semidirect
38. #19128336C22semidirect
39. D4×C22⋊D83C22semidirect
40. #19128280C22semidirect
41. #19128277C22semidirect
42. #19128272C22semidirect
43. #19128271C22semidirect
44. #19128268C22semidirect
45. #19128264C22semidirect
46. #19128261C22semidirect
47. #19128252C22semidirect
48. #19128251C22semidirect
49. #19128250C22semidirect
50. #19128249C22semidirect
51. #19128249C22semidirect
52. #19128249C22semidirect
53. #19128249C22semidirect
54. #19128249C22semidirect
55. #19128249C22semidirect
56. #19128248C22semidirect
57. #19128247C22semidirect
58. #19128246C22semidirect
59. C2×#14581792C22semidirect
60. C4⋊Q8×D83C22semidirect
61. #127×D83C22semidirect
62. C2×#14581779C22semidirect
63. #124×D83C22semidirect
64. #19128211C22semidirect
65. #19128207C22semidirect
66. C2×#14581763C22semidirect
67. #121×D83C22semidirect
68. #41×Dic83C22semidirect
69. C4×#13050591C22semidirect
70. C4×#13050590C22semidirect
71. #19128169C22semidirect
72. C4×#13050589C22semidirect
73. C4×Q8×D83C22semidirect
74. C2×D4×Dic83C22semidirect
75. C4×D4×D83C22semidirect
76. C4×D4×D83C22semidirect
77. #117×D83C22semidirect
78. C2×C42×D83C22semidirect
79. C2×H(5,𝔽2)×C83C22semidirect
80. #550×C83C22semidirect
81. D42×C83C22semidirect
82. #535×C83C22semidirect
83. #532×C83C22semidirect
84. C2×#127×C83C22semidirect
85. C4×#41×C83C22semidirect
110. #41×D83D4semidirect
216. #13050591C2×D4semidirect
220. #13050590C2×D4semidirect
229. #13050589C2×D4semidirect
238. Q8×D83C2×D4semidirect
255. D4×D83C2×D4semidirect
264. C2×C4×D83C2×D4semidirect
297. #41×C83C2×D4semidirect
399. C4×C83#585semidirect
419. #3498D83semidirect
428. C83#62812semidirect
435. C2×H(5,𝔽2)C2×D83semidirect
442. #550C2×D83semidirect
455. D42C2×D83semidirect
462. #535C2×D83semidirect
476. #532C2×D83semidirect
480. C2×#127C2×D83semidirect
492. C4×#41C2×D83semidirect
646. #41D4×D83semidirect
817. C4#19128536semidirect

Maximal subgroups

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

subgroupindex
C2×#191285362
#249212552
#249212512
#249212482
#249212432
#249212392
#249212282
#249212192
#249209532
D4×#130505892
#249207942
C2×#191282492
#532×D832
C4×#41×D832
C83×#34982
#6281283