Finite Group Databasebeta

← #35577496

Subgroups — #35577496

Order 21248.

1690 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915813C211yesmaximal, characteristic
2#24915811C211yesmaximal, characteristic
3#24915799C212yesmaximal
4#24913435C212yesmaximal
5#24913279C211yesmaximal, characteristic
6#24913278C211yesmaximal, characteristic
7#24912935C212yesmaximal, complemented
8#24912933C212yesmaximal, complemented
9#24912905C212yesmaximal, complemented
10#24912903C212yesmaximal, complemented
11#24912035C212yesmaximal, complemented
12#24911987C212yesmaximal, complemented
13#24911299C212yesmaximal, complemented
14#24911236C212yesmaximal, complemented
15#24910196C211yesmaximal, characteristic
16#24910063C212yesmaximal
17C4×#14581769C212yesmaximal
18C2×#19127552C211yesmaximal, characteristic
19C83×#2329C211yesmaximal, characteristic
20C2×#14581791C2211yescharacteristic
21C2×#14581790C2211yescharacteristic
22C2×#14581771C2211yescharacteristic
23C2×#14581769C2212yes—
24C2×C4×Dic166C2212yes—
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30#19127642C2212yes—
31#19127642C2212yes—
32#19127641C2212yes—
33#19127641C2212yes—
34#19127639C2212yes—
35#19127639C2212yes—
36#19127635C2212yes—
37#19127634C2212yes—
38#19127634C2212yes—
39#19127634C2212yes—
40#19127632C2212yes—
41#19127631C2212yes—
42#19127631C2212yes—
43#19127631C2212yes—
44#19127622C2212yes—
45#19127620C2212yes—
46#19127608C2211yescharacteristic
47#19127606C2211yescharacteristic
48#19127605C2212yes—
49#19127605C2212yes—
50#19127605C2212yes—
51#19127605C2212yes—
52#19127605C2212yes—
53#19127600C2211yescharacteristic
54#19127598C2212yes—
55#19127598C2212yes—
56#19127598C2212yes—
57#19127597C2211yescharacteristic
58#19127596C2212yes—
59#19127596C2212yes—
60#19127596C2212yes—
61#19127596C2212yes—
62#19127588C2212yes—
63#19127588C2212yes—
64#19127587C2212yes—
65#19127587C2212yes—
66#19127585C2212yes—
67#19127585C2212yes—
68#19127585C2212yes—
69#19127585C2212yes—
70#19127584C2212yes—
71#19127584C2212yes—
72#19127583C2212yes—
73#19127583C2212yes—
74#19127583C2212yes—
75#19127583C2212yes—
76#19127583C2212yes—
77#19127583C2212yes—
78#19127576C2212yes—
79#19127574C2212yes—
80#19127573C2212yes—
81#19127570C2211yescharacteristic
82#19127570C2211yescharacteristic
83#19127562C2212yes—
84#19127562C2212yes—
85#19127561C2211yescharacteristic
86#19127559C2212yes—
87#19127559C2212yes—
88#19127559C2212yes—
89C4×Dic83⋊C4C2212yes—
90C4×Dic83⋊C4C2212yes—
91C4×C4⋊Dic83C2212yes—
92#19127552C2212yes—
93#19127552C2212yes—
94#19127552C2212yes—
95#19127552C2212yes—
96C4×C22⋊Dic83C2212yes—
97C2×C83⋊#95C2211yescharacteristic
98C2×C22⋊Q8×C83C2211yescharacteristic
99#391×C83C2212yes—
100#389×C83C2212yes—
101#387×C83C2212yes—
102#387×C83C2212yes—
103#385×C83C2212yes—
104#380×C83C2211yescharacteristic
105C4×C22⋊C4×C83C2212yes—
106C2×#95×C83C2211yescharacteristic
107C22×Dic166C2312yes—
108C22×Dic166C2311yescharacteristic
109C23×Dic83C2311yescharacteristic
110C23×Dic83C2311yescharacteristic
111C23×Dic83C2311yescharacteristic
112C23×Dic83C2311yescharacteristic
113#14581791—42no—
114#14581790—42no—
115#14581771—24no—
116#14581769—28no—
117C4×Dic166—44no—
118C2×C4⋊Dic83C2312yes—
119C2×C4⋊Dic83C2311yescharacteristic
120C2×C4⋊Dic83C2312yes—
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×C4⋊Dic83C2312yes—
124C2×Dic83⋊C4—24no—
125C2×Dic83⋊C4Q818yescomplemented
126C2×Dic83⋊C4C2312yes—
127C2×Dic83⋊C4C2312yes—
128C2×Dic83⋊C4C2312yes—
129C2×Dic83⋊C4C2312yes—
130C2×Dic83⋊C4C2312yes—
131C2×Dic83⋊C4C2312yes—
132C2×Dic83⋊C4C2312yes—
133C2×Dic83⋊C4C2312yes—
134C2×Dic83⋊C4C2312yes—
135C2×Dic83⋊C4C2312yes—
136C2×Dic83⋊C4C2312yes—
137C2×Dic83⋊C4C2312yes—
138C2×Dic83⋊C4C2312yes—
139C2×Dic83⋊C4C2312yes—
140C2×Dic83⋊C4C2312yes—
141C2×Dic83⋊C4C2312yes—
142C2×Dic83⋊C4C2312yes—
143C2×C22⋊Dic83C2312yes—
144C2×C22⋊Dic83C2312yes—
145C2×C4×Dic83—24no—
146C2×C4×Dic83—42no—
147C2×C4×Dic83—42no—
148C2×C4×Dic83C2312yes—
149C2×C4×Dic83C2311yescharacteristic
150C2×C4×Dic83C2311yescharacteristic
151C2×C4×Dic83C2312yes—
152C2×C4×Dic83C2312yes—
153C2×C4×Dic83C2312yes—
154C2×C4×Dic83C2311yescharacteristic
155C2×C4×Dic83C2311yescharacteristic
156C2×C4×Dic83C2312yes—
157C2×C4×Dic83C2312yes—
158C83⋊#95C2312yes—
159C83⋊#95C2312yes—
160C83⋊#95C2312yes—
161C83⋊#95C2312yes—
162C83⋊#95C2312yes—
163C83⋊#95C2312yes—
164C83⋊#95C2312yes—
165C83⋊#95C2312yes—
166C83⋊#95C2312yes—
167C83⋊#95C2312yes—
168C83⋊#95C2312yes—
169C83⋊#95C2312yes—
170C83⋊#95C2312yes—
171C83⋊#95C2312yes—
172C83⋊#95C2312yes—
173C83⋊#95C2312yes—
174C83⋊#95C2312yes—
175C83⋊#95C2312yes—
176C83⋊#95C2312yes—
177C83⋊#95C2312yes—
178C83⋊#95C2312yes—
179C83⋊#95C2312yes—
180C83⋊#95C2312yes—
181C83⋊#95C2312yes—
182C83⋊#95C2312yes—
183C22×Q8×C83C2311yescharacteristic
184C23×C4×C83C2311yescharacteristic
185C23×C4×C83C2311yescharacteristic
186C23×C4×C83C2311yescharacteristic
187C22⋊Q8×C83—24no—
188C2×C4⋊C4×C83C2311yescharacteristic
189C2×C4⋊C4×C83C2312yes—
190C2×C4⋊C4×C83C2311yescharacteristic
191C2×C4⋊C4×C83C2312yes—
192C2×C4⋊C4×C83C2312yes—
193C2×C4⋊C4×C83C2311yescharacteristic
194C2×C22⋊C4×C83C2312yes—
195C2×C22⋊C4×C83C2312yes—
196C2×C42×C83C2312yes—
197C2×C42×C83C2312yes—
198#95×C83C2312yes—
199#95×C83C2312yes—
200#95×C83C2312yes—
201#95×C83C2312yes—
202#95×C83C2312yes—
203#95×C83C2312yes—
204#95×C83C2312yes—
205C2×Dic166—24no—
206C2×Dic166—24no—
207C2×Dic166—24no—
208C2×Dic166—22no—
209C2×Dic166—41no—
210C2×Dic166—41no—
211C22×Dic83—22no—
212C22×Dic83—22no—
213C22×Dic83—22no—
214C22×Dic83—22no—
215C22×Dic83—22no—
216C22×Dic83—41no—
217C22×Dic83—41no—
218C22×Dic83—41no—
219C22×Dic83—41no—
220C22×Dic83C2×Q814yes—
221C22×Dic83C2×Q814yes—
222C22×Dic83#4114yes—
223C22×Dic83C2412yes—
224C22×Dic83C2412yes—
225C22×Dic83C2412yes—
226C22×Dic83C2412yes—
227C22×Dic83C2412yes—
228C22×Dic83C2412yes—
229C22×Dic83C2411yescharacteristic
230C22×Dic83C2411yescharacteristic
231C22×Dic83C2411yescharacteristic
232C22×Dic83C2411yescharacteristic
233C4⋊Dic83—22no—
234C4⋊Dic83—24no—
235C4⋊Dic83—41no—
236C4⋊Dic83—41no—
237C4⋊Dic83—42no—
238C4⋊Dic83—42no—
239Dic83⋊C4—24no—
240Dic83⋊C4—24no—
241Dic83⋊C4—24no—
242Dic83⋊C4—24no—
243Dic83⋊C4—24no—
244Dic83⋊C4—24no—
245Dic83⋊C4—24no—
246Dic83⋊C4—42no—
247Dic83⋊C4—42no—
248Dic83⋊C4—42no—
249Dic83⋊C4—42no—
250Dic83⋊C4—42no—
251Dic83⋊C4—42no—
252Dic83⋊C4—42no—
253Dic83⋊C4—42no—
254Dic83⋊C4C2×Q818yes—
255Dic83⋊C4C2×Q818yes—
256C22⋊Dic83—24no—
257C22⋊Dic83—24no—
258C4×Dic83—24no—
259C4×Dic83—24no—
260C4×Dic83—22no—
261C4×Dic83—22no—
262C4×Dic83—24no—
263C4×Dic83—41no—
264C4×Dic83—41no—
265C4×Dic83—42no—
266C4×Dic83—42no—
267C4×Dic83—42no—
268C24×C83C2411yescharacteristic
269C2×Q8×C83—22no—
270C2×Q8×C83—41no—
271C2×Q8×C83—41no—
272C22×C4×C83—22no—
273C22×C4×C83—41no—
274C22×C4×C83—41no—
275C22×C4×C83—41no—
276C22×C4×C83—41no—
277C22×C4×C83—41no—
278C22×C4×C83—41no—
279C22×C4×C83C2×Q814yes—
280C22×C4×C83#4114yes—
281C22×C4×C83C2412yes—
282C22×C4×C83C2412yes—
283C22×C4×C83C2412yes—
284C22×C4×C83C2412yes—
285C22×C4×C83C2412yes—
286C22×C4×C83C2412yes—
287C22×C4×C83C2411yescharacteristic
288C22×C4×C83C2411yescharacteristic
289C4⋊C4×C83—22no—
290C4⋊C4×C83—24no—
291C4⋊C4×C83—41no—
292C4⋊C4×C83—41no—
293C4⋊C4×C83—42no—
294C4⋊C4×C83—42no—
295C22⋊C4×C83—24no—
296C22⋊C4×C83—24no—
297C42×C83—42no—
298C42×C83—42no—
299C23×C83—21no—
300C23×C83—21no—
301C23×C83—21no—
302C23×C83—21no—
303C23×C83C22×Q812yes—
304C23×C83C2×#4112yes—
305C23×C83C2×#4112yes—
306C23×C83C2511yescharacteristic
307Q8×C83—82no—
308C2×C4×C83—22no—
309C2×C4×C83—21no—
310C2×C4×C83—21no—
311C2×C4×C83—22no—
312C2×C4×C83—21no—
313C2×C4×C83—21no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—44no—
330C2×C4×C83—44no—
331C2×C4×C83—44no—
332C2×C4×C83C22×Q814yes—
333C2×C4×C83C2×#4112yes—
334C2×C4×C83C2×#4112yes—
335C2×Dic83—28no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—21no—
339C2×Dic83—21no—
340C2×Dic83—21no—
341C2×Dic83—21no—
342C2×Dic83—21no—
343C2×Dic83—21no—
344C2×Dic83—28no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83—22no—
355C2×Dic83—22no—
356C2×Dic83—22no—
357C2×Dic83—22no—
358C2×Dic83—22no—
359C2×Dic83—22no—
360C2×Dic83—44no—
361C2×Dic83—44no—
362C2×Dic83C22×Q814yes—
363C2×Dic83C22×Q812yes—
364C2×Dic83C22×Q812yes—
365C2×Dic83C2×#4112yes—
366C2×Dic83C2×#4112yes—
367C2×Dic83H(5,𝔽2)12yes—
368C2×Dic832−1+412yes—
369Dic166—48no—
370Dic166—82no—
371C22×C83—22no—
372C22×C83—22no—
373C22×C83—22no—
374C22×C83—22no—
375C22×C83—22no—
376C22×C83—22no—
377C22×C83#53314yes—
378C22×C83C23×Q811yescharacteristic
379C22×C83C22×#4111yescharacteristic
380C22×C83C22×#4111yescharacteristic
381C22×C83C2×H(5,𝔽2)11yescharacteristic
382C22×C83C2×2−1+411yescharacteristic
383C22×C83#58511yescharacteristic
384C22×C83#58511yescharacteristic
385C4×C83—24no—
386C4×C83—22no—
387C4×C83—22no—
388C4×C83—42no—
389C4×C83—42no—
390C4×C83—42no—
391C4×C83—42no—
392C4×C83—42no—
393Dic83—24no—
394Dic83—22no—
395Dic83—22no—
396Dic83—22no—
397Dic83—42no—
398Dic83—42no—
399Dic83—42no—
400Dic83—42no—
401Dic83—42no—
402Dic83#53914yes—
403#35015—831nomaximal, Sylow
404C2×C83—24no—
405C2×C83C2×#53311yescharacteristic
406C2×C83C2×#53911yescharacteristic
407C2×C83#345511yescharacteristic
408C2×C83#350111yescharacteristic
409C2×C83#350211yescharacteristic
410C2×C83#350511yescharacteristic
411C2×C83#350711yescharacteristic
412#2857—831no—
413#2857—831no—
414#2855—832no—
415#2646—832no—
416#2627—831no—
417#2627—831no—
418#2590—832no—
419#2590—832no—
420#2588—832no—
421#2588—832no—
422#2511—832no—
423#2507—832no—
424#2451—832no—
425#2446—832no—
426#2329—831no—
427#2329D8311yescharacteristic
428#2313—832no—
429C4×C22⋊Q8—832no—
430C2×C4×C4⋊C4—831no—
431C83#3501511yescharacteristic, complemented, Sylow
432C2×C4⋊Q8—831no—
433C2×C4⋊Q8—831no—
434C2×C22⋊Q8—831no—
435C2×C22⋊Q8—832no—
436C2×C22⋊Q8C2×D8311yescharacteristic
437C2×C4×Q8—832no—
438C22×C4⋊C4—831no—
439C22×C4⋊C4—831no—
440C22×C42—831no—
441C22×C42—831no—
442C22×C42—831no—
443#400—832no—
444#400—832no—
445#400—832no—
446#400—832no—
447#400—832no—
448#400—832no—
449#398—832no—
450#398—832no—
451#398—832no—
452#398—832no—
453#398—832no—
454#398—832no—
455#398—832no—
456#398—832no—
457#395—832no—
458#395—832no—
459#391—831no—
460#391—831no—
461#391—832no—
462#391—832no—
463#391—832no—
464#391—832no—
465#391—832no—
466#391C2×D8312yes—
467#389—832no—
468#389—831no—
469#389—831no—
470#389—832no—
471#389—832no—
472#389—832no—
473#389—832no—
474#389—832no—
475#389—832no—
476#389C2×D8312yes—
477#387—832no—
478#387—832no—
479#387—832no—
480#387—832no—
481#387—832no—
482#387—832no—
483#387—832no—
484#387—832no—
485#387—832no—
486#387—832no—
487#387—832no—
488#387—832no—
489#387—832no—
490#387—832no—
491#387—832no—
492#387—832no—
493#387C2×D8312yes—
494#387C2×D8312yes—
495#385—832no—
496#385—832no—
497#385—832no—
498#385C2×D8312yes—
499#384—831no—
500#384—831no—
501#381—832no—
502#381—832no—
503#380—831no—
504#380—832no—
505#380—832no—
506#380—832no—
507#380C2×D8311yescharacteristic
508C4×C4⋊C4—832no—
509C4×C4⋊C4—832no—
510C4×C4⋊C4—832no—
511C4×C4⋊C4—832no—
512C4×C4⋊C4—832no—
513C4×C4⋊C4—832no—
514C4×C4⋊C4—832no—
515C4×C22⋊C4—832no—
516C4×C22⋊C4C2×D8312yes—
517C2×#95—831no—
518C2×#95C2×D8311yescharacteristic
519C22×Q8—831no—
520C22×Q8—832no—
521C22×Q8C22×D8311yescharacteristic
522C23×C4—831no—
523C23×C4—831no—
524C23×C4—831no—
525C23×C4—831no—
526C23×C4C22×D8311yescharacteristic
527C23×C4C22×D8311yescharacteristic
528C23×C4C22×D8311yescharacteristic
529C4⋊Q8—3322no—
530C4⋊Q8—3322no—
531C22⋊Q8—24no—
532C22⋊Q8—1668no—
533C22⋊Q8—1664no—
534C4×Q8—3324no—
535C2×C4⋊C4—832no—
536C2×C4⋊C4—832no—
537C2×C4⋊C4—832no—
538C2×C4⋊C4—831no—
539C2×C4⋊C4—832no—
540C2×C4⋊C4—832no—
541C2×C4⋊C4—832no—
542C2×C4⋊C4—832no—
543C2×C4⋊C4—832no—
544C2×C4⋊C4—831no—
545C2×C4⋊C4—832no—
546C2×C4⋊C4—832no—
547C2×C4⋊C4—838no—
548C2×C4⋊C4—832no—
549C2×C4⋊C4—832no—
550C2×C4⋊C4—832no—
551C2×C4⋊C4—832no—
552C2×C4⋊C4—832no—
553C2×C4⋊C4—832no—
554C2×C4⋊C4—832no—
555C2×C4⋊C4—832no—
556C2×C4⋊C4—831no—
557C2×C4⋊C4—832no—
558C2×C4⋊C4—832no—
559C2×C4⋊C4—1664no—
560C2×C4⋊C4C22×D8311yescharacteristic
561C2×C4⋊C4C22×D8312yes—
562C2×C4⋊C4C22×D8311yescharacteristic
563C2×C4⋊C4C22×D8311yescharacteristic
564C2×C4⋊C4C22×D8312yes—
565C2×C4⋊C4C22×D8312yes—
566C2×C22⋊C4—832no—
567C2×C22⋊C4—832no—
568C2×C22⋊C4C22×D8312yes—
569C2×C22⋊C4C22×D8312yes—
570C2×C42—3322no—
571C2×C42—3322no—
572C2×C42—832no—
573C2×C42—832no—
574C2×C42—832no—
575C2×C42—831no—
576C2×C42—831no—
577C2×C42—832no—
578C2×C42—831no—
579C2×C42—831no—
580C2×C42—832no—
581C2×C42—832no—
582C2×C42—1664no—
583C2×C42C22×D8312yes—
584C2×C42C22×D8312yes—
585#95—832no—
586#95—832no—
587#95—832no—
588#95—832no—
589#95—832no—
590#95—832no—
591#95—832no—
592#95—832no—
593#95—832no—
594#95—832no—
595#95—832no—
596#95—832no—
597#95—832no—
598#95—832no—
599#95—832no—
600#95—832no—
601#95—832no—
602#95—832no—
603#95—832no—
604#95—832no—
605#95—832no—
606#95—832no—
607#95—832no—
608#95—832no—
609#95—832no—
610#95C22×D8312yes—
611#95C22×D8312yes—
612#95C22×D8312yes—
613#95C22×D8312yes—
614#95C22×D8312yes—
615#95C22×D8312yes—
616#95C22×D8312yes—
617C24C23×D8311yescharacteristic
618C2×Q8—22no—
619C2×Q8—41no—
620C2×Q8—41no—
621C2×Q8—3321no—
622C2×Q8—3321no—
623C2×Q8—1664no—
624C2×Q8—1664no—
625C2×Q8—1664no—
626C2×Q8—1662no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—3321no—
635C22×C4—3321no—
636C22×C4—3321no—
637C22×C4—3321no—
638C22×C4—834no—
639C22×C4—831no—
640C22×C4—834no—
641C22×C4—834no—
642C22×C4—832no—
643C22×C4—831no—
644C22×C4—831no—
645C22×C4—831no—
646C22×C4—832no—
647C22×C4—832no—
648C22×C4—832no—
649C22×C4—832no—
650C22×C4—832no—
651C22×C4—1662no—
652C22×C4—1662no—
653C22×C4—1662no—
654C22×C4—1662no—
655C22×C4—1662no—
656C22×C4Q8×D8314yes—
657C22×C4#1305059014yes—
658C22×C4C23×D8312yes—
659C22×C4C23×D8312yes—
660C22×C4C23×D8312yes—
661C22×C4C23×D8312yes—
662C22×C4C23×D8312yes—
663C22×C4C23×D8312yes—
664C22×C4C23×D8311yescharacteristic
665C22×C4C23×D8311yescharacteristic
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—3322no—
673C4⋊C4—3322no—
674C4⋊C4—3322no—
675C4⋊C4—3322no—
676C4⋊C4—3321no—
677C4⋊C4—3322no—
678C4⋊C4—3322no—
679C4⋊C4—3322no—
680C4⋊C4—3322no—
681C4⋊C4—3322no—
682C4⋊C4—3321no—
683C4⋊C4—3322no—
684C4⋊C4—838no—
685C4⋊C4—838no—
686C4⋊C4—1664no—
687C4⋊C4—1664no—
688C4⋊C4—1664no—
689C4⋊C4—1664no—
690C4⋊C4—1664no—
691C4⋊C4—1664no—
692C4⋊C4—1664no—
693C4⋊C4—1664no—
694C4⋊C4—1662no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—1664no—
698C22⋊C4—1664no—
699C42—42no—
700C42—42no—
701C42—3322no—
702C42—3321no—
703C42—3321no—
704C42—3322no—
705C42—3322no—
706C42—1664no—
707C42—1662no—
708C42—1662no—
709C42—1664no—
710C42—1664no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23C2×Q8×D8312yes—
716C23#41×D8312yes—
717C23C2×#1305059012yes—
718C23C24×D8311yescharacteristic
719Q8—82no—
720Q8—3328no—
721Q8—6642no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—3324no—
747C2×C4—3324no—
748C2×C4—832no—
749C2×C4—832no—
750C2×C4—832no—
751C2×C4—834no—
752C2×C4—832no—
753C2×C4—832no—
754C2×C4—832no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4—1668no—
771C2×C4—1668no—
772C2×C4—1662no—
773C2×C4—1662no—
774C2×C4—1661no—
775C2×C4—1661no—
776C2×C4—1661no—
777C2×C4—1661no—
778C2×C4—1661no—
779C2×C4—1661no—
780C2×C4C2×Q8×D8314yes—
781C2×C4C2×#1305059012yes—
782C2×C4C2×#1305059012yes—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22#1912825514yes—
790C22C22×Q8×D8311yescharacteristic
791C22C2×#41×D8311yescharacteristic
792C22C22×#1305059011yescharacteristic
793C22H(5,𝔽2)×D8311yescharacteristic
794C222−1+4×D8311yescharacteristic
795C22#1912853611yescharacteristic
796C22#1912853611yescharacteristic
797C4—24no—
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—3322no—
806C4—3322no—
807C4—3322no—
808C4—3322no—
809C4—3322no—
810C4—834no—
811C4—1664no—
812C4—1662no—
813C4—1662no—
814C4—1662no—
815C2—24no—
816C2C2×#1912825511yescharacteristic
817C2#539×D8311yescharacteristic
818C2#2492084511yescharacteristic
819C2#2492126311yescharacteristic
820C2#2492127111yescharacteristic
821C2#2492129311yescharacteristic
822C2#2492132111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2329C2
prime radicalC24×C83C24
hypercenter#2329D83
hypocenterC83#35015
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2329

Complements

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

NH ≅ G/Ntype
7. #24912935C2semidirect
8. #24912933C2semidirect
9. #24912905C2semidirect
10. #24912903C2semidirect
11. #24912035C2semidirect
12. #24911987C2semidirect
13. #24911299C2semidirect
14. #24911236C2semidirect
125. C2×Dic83⋊C4Q8semidirect
431. C83#35015semidirect

Maximal subgroups

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

subgroupindex
#249158132
#249158112
#249157992
#249134352
#249132792
#249132782
#249129352
#249129332
#249129052
#249129032
#249120352
#249119872
#249112992
#249112362
#249101962
#249100632
C4×#145817692
C2×#191275522
C83×#23292
#3501583