Finite Group Databasebeta

← C83×#19498 #35247322

Subgroups — C83×#19498 #35247322

Order 21248.

628 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3228C211yesmaximal, characteristic, complemented
2C83×#3116C211yesmaximal, characteristic, complemented
3C83×#3035C211yesmaximal, characteristic
4C83×#2991C211yesmaximal, characteristic, complemented
5C83×#1701C211yesmaximal, characteristic, complemented
6C83×#1697C211yesmaximal, characteristic, complemented
7C83×#1693C211yesmaximal, characteristic, complemented
8C83×#1691C211yesmaximal, characteristic, complemented
9C83×#1682C211yesmaximal, characteristic, complemented
10C83×#1678C211yesmaximal, characteristic, complemented
11C83×#1674C211yesmaximal, characteristic, complemented
12C83×#1672C211yesmaximal, characteristic, complemented
13C83×#1573C211yesmaximal, characteristic, complemented
14C83×#1557C211yesmaximal, characteristic, complemented
15C83×#1550C211yesmaximal, characteristic, complemented
16C2×#135×C83—21no—
17#533×C83C2211yescharacteristic
18#532×C83C2211yescharacteristic
19C4×#41×C83C2211yescharacteristic
20#500×C83C2211yescharacteristic
21#498×C83C2211yescharacteristic
22#486×C83C2211yescharacteristic
23#486×C83C2211yescharacteristic
24#485×C83—21no—
25#482×C83—21no—
26#482×C83—21no—
27#478×C83—21no—
28#478×C83—21no—
29#477×C83C2211yescharacteristic
30#476×C83C2211yescharacteristic
31#464×C83—21no—
32#463×C83—21no—
33#462×C83C2211yescharacteristic
34#462×C83C2211yescharacteristic
35#461×C83C2211yescharacteristic
36#461×C83C2211yescharacteristic
37#460×C83C2211yescharacteristic
38#459×C83C2211yescharacteristic
39#452×C83—21no—
40C8×Q8×C83C2211yescharacteristic
41C8×Q8×C83C2211yescharacteristic
42#441×C83—21no—
43#440×C83—21no—
44#436×C83—21no—
45#436×C83—21no—
46#436×C83C2211yescharacteristic
47#436×C83C2211yescharacteristic
48#432×C83C2211yescharacteristic
49#431×C83—21no—
50#431×C83C2211yescharacteristic
51#423×C83—21no—
52#423×C83C2211yescharacteristic
53C2×C4⋊C8×C83C2211yescharacteristic
54#416×C83—21no—
55#335×C83C2211yescharacteristic
56#335×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#334×C83C2211yescharacteristic
59#333×C83C2211yescharacteristic
60#333×C83C2211yescharacteristic
61#332×C83C2211yescharacteristic
62#332×C83C2211yescharacteristic
63#332×C83C2211yescharacteristic
64#332×C83C2211yescharacteristic
65#331×C83C2211yescharacteristic
66#331×C83C2211yescharacteristic
67C2×#41×C83—21no—
68C2×#41×C83D411yescharacteristic
69#135×C83—44no—
70C2×Q16×C83—21no—
71C2×Q16×C83—21no—
72C2×SD16×C83—21no—
73C2×SD16×C83—21no—
74C2×SD16×C83—21no—
75C2×D8×C83—21no—
76C2×M16×C83—21no—
77C2×M16×C83—21no—
78C2×M16×C83—21no—
79C22×C8×C83—21no—
80C4⋊Q8×C83C2311yescharacteristic
81C4⋊Q8×C83C2311yescharacteristic
82C4⋊Q8×C83C2311yescharacteristic
83#127×C83C2311yescharacteristic
84#125×C83—21no—
85#124×C83—21no—
86C22⋊Q8×C83—21no—
87C22⋊Q8×C83—21no—
88#121×C83—21no—
89#121×C83—21no—
90C4×Q8×C83—21no—
91C4×Q8×C83—21no—
92C4×Q8×C83D411yescharacteristic
93C4×Q8×C83C2311yescharacteristic
94C4×D4×C83—21no—
95C4×D4×C83—21no—
96C4×D4×C83—21no—
97C4×D4×C83—21no—
98C4×D4×C83D411yescharacteristic
99C4×D4×C83C2311yescharacteristic
100#117×C83—21no—
101#117×C83—21no—
102#117×C83D411yescharacteristic
103C2×C42×C83—21no—
104C2×C42×C83C2311yescharacteristic
105#107×C83—21no—
106#107×C83—21no—
107#107×C83—21no—
108#106×C83—21no—
109#106×C83—21no—
110#106×C83—21no—
111C4⋊C8×C83—21no—
112C4⋊C8×C83—21no—
113C4⋊C8×C83—21no—
114C4⋊C8×C83—21no—
115C4⋊C8×C83D411yescharacteristic
116C4⋊C8×C83D411yescharacteristic
117C4⋊C8×C83C2311yescharacteristic
118C4⋊C8×C83C2311yescharacteristic
119C4⋊C8×C83C2311yescharacteristic
120C4⋊C8×C83C2311yescharacteristic
121C4⋊C8×C83C2311yescharacteristic
122C4⋊C8×C83C2311yescharacteristic
123#103×C83—21no—
124#103×C83—21no—
125#103×C83—21no—
126#103×C83—21no—
127#103×C83—21no—
128#102×C83—21no—
129#102×C83—21no—
130#102×C83—21no—
131#102×C83—21no—
132#102×C83—21no—
133#102×C83—21no—
134#102×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137C22⋊C8×C83—21no—
138C22⋊C8×C83D411yescharacteristic
139C22⋊C8×C83D411yescharacteristic
140#97×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83—21no—
143C4×C8×C83C2311yescharacteristic
144C4×C8×C83C2311yescharacteristic
145#41×C83—22no—
146#41×C83—41no—
147#41×C83—42no—
148#41×C83—42no—
149C2×Q8×C83—21no—
150C2×Q8×C83—21no—
151C2×Q8×C83—21no—
152C2×Q8×C83C2×D411yescharacteristic
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83—41no—
158C2×D4×C83C2×D411yescharacteristic
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—41no—
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83#4111yescharacteristic
166Q16×C83—42no—
167Q16×C83—42no—
168SD16×C83—42no—
169SD16×C83—42no—
170SD16×C83—42no—
171D8×C83—42no—
172M16×C83—81no—
173M16×C83—81no—
174M16×C83—81no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—42no—
182C2×C8×C83C2×D411yescharacteristic
183C2×C8×C83C2×D411yescharacteristic
184C2×C8×C83C2×D411yescharacteristic
185C2×C8×C83C2×D411yescharacteristic
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—41no—
195C4⋊C4×C83—41no—
196C4⋊C4×C83C2×D411yescharacteristic
197C4⋊C4×C83C2×D411yescharacteristic
198C22⋊C4×C83—21no—
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—41no—
202C22⋊C4×C83—41no—
203C22⋊C4×C83—41no—
204C42×C83—21no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—41no—
208C42×C83C2×D411yescharacteristic
209C42×C83C2×D411yescharacteristic
210C42×C83#4111yescharacteristic
211C42×C83C2411yescharacteristic
212C23×C83—21no—
213C23×C83—41no—
214C23×C83#12111yescharacteristic
215Q8×C83—21no—
216Q8×C83—41no—
217Q8×C83—41no—
218Q8×C83—41no—
219Q8×C83—41no—
220Q8×C83—81no—
221Q8×C83AGL(1,ℤ/8)12yes—
222D4×C83—21no—
223D4×C83—21no—
224D4×C83—42no—
225D4×C83—41no—
226D4×C83—41no—
227D4×C83—41no—
228D4×C83—41no—
229D4×C83—81no—
230D4×C83—82no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—41no—
239C2×C4×C83—42no—
240C2×C4×C83—42no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—82no—
247C2×C4×C83#12111yescharacteristic
248C2×C4×C83#12111yescharacteristic
249C2×C4×C83#12111yescharacteristic
250C2×C4×C83C22×D411yescharacteristic
251C2×C4×C83C22×D411yescharacteristic
252C2×C4×C83C2×#4111yescharacteristic
253C8×C83—21no—
254C8×C83—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—41no—
258C8×C83—41no—
259C8×C83—41no—
260C8×C83—41no—
261C8×C83—41no—
262C8×C83—41no—
263C22×C83—21no—
264C22×C83—21no—
265C22×C83—21no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—81no—
270C22×C83—81no—
271C22×C83—81no—
272C22×C83C2×#12111yescharacteristic
273C4×C83—21no—
274C4×C83—21no—
275C4×C83—22no—
276C4×C83—21no—
277C4×C83—21no—
278C4×C83—41no—
279C4×C83—41no—
280C4×C83—81no—
281C4×C83—81no—
282C4×C83—81no—
283C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C83#57511yescharacteristic
285C4×C83#57711yescharacteristic
286C4×C83#57811yescharacteristic
287#19498C8311yesmaximal, characteristic, direct product factor, Sylow
288C2×C83—41no—
289C2×C83—81no—
290C2×C83—161no—
291C2×C83#304611yescharacteristic
292C2×C83#305511yescharacteristic
293C2×C83#306711yescharacteristic
294#3228C2×C8311yescharacteristic, complemented
295#3116C2×C8311yescharacteristic, complemented
296#3035C2×C8311yescharacteristic
297#2991C2×C8311yescharacteristic, complemented
298#1701C2×C8311yescharacteristic, complemented
299#1697C2×C8311yescharacteristic, complemented
300#1693C2×C8311yescharacteristic, complemented
301#1691C2×C8311yescharacteristic, complemented
302#1682C2×C8311yescharacteristic, complemented
303#1678C2×C8311yescharacteristic, complemented
304#1674C2×C8311yescharacteristic, complemented
305#1672C2×C8311yescharacteristic, complemented
306#1573C2×C8311yescharacteristic, complemented
307#1557C2×C8311yescharacteristic, complemented
308#1550C2×C8311yescharacteristic, complemented
309C83#1949811yescharacteristic, direct product factor, Sylow
310C2×#135—21no—
311#533C22×C8311yescharacteristic
312#532C22×C8311yescharacteristic
313C4×#41C22×C8311yescharacteristic
314#500C22×C8311yescharacteristic
315#498C22×C8311yescharacteristic
316#486C22×C8311yescharacteristic
317#486C22×C8311yescharacteristic
318#485—21no—
319#482—21no—
320#482—21no—
321#478—21no—
322#478—21no—
323#477C22×C8311yescharacteristic
324#476C22×C8311yescharacteristic
325#464—21no—
326#463—21no—
327#462C22×C8311yescharacteristic
328#462C22×C8311yescharacteristic
329#461C22×C8311yescharacteristic
330#461C22×C8311yescharacteristic
331#460C22×C8311yescharacteristic
332#459C22×C8311yescharacteristic
333#452—21no—
334C8×Q8C22×C8311yescharacteristic
335C8×Q8C22×C8311yescharacteristic
336#441—21no—
337#440—21no—
338#436—21no—
339#436—21no—
340#436C22×C8311yescharacteristic
341#436C22×C8311yescharacteristic
342#432C22×C8311yescharacteristic
343#431—21no—
344#431C22×C8311yescharacteristic
345#423—21no—
346#423C22×C8311yescharacteristic
347C2×C4⋊C8C22×C8311yescharacteristic
348#416—21no—
349#335C22×C8311yescharacteristic
350#335C22×C8311yescharacteristic
351#334C22×C8311yescharacteristic
352#334C22×C8311yescharacteristic
353#333C22×C8311yescharacteristic
354#333C22×C8311yescharacteristic
355#332C22×C8311yescharacteristic
356#332C22×C8311yescharacteristic
357#332C22×C8311yescharacteristic
358#332C22×C8311yescharacteristic
359#331C22×C8311yescharacteristic
360#331C22×C8311yescharacteristic
361C2×#41—21no—
362C2×#41D4×C8311yescharacteristic
363#135—44no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×D8—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C22×C8—21no—
374C4⋊Q8C23×C8311yescharacteristic
375C4⋊Q8C23×C8311yescharacteristic
376C4⋊Q8C23×C8311yescharacteristic
377#127C23×C8311yescharacteristic
378#125—21no—
379#124—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8D4×C8311yescharacteristic
387C4×Q8C23×C8311yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4D4×C8311yescharacteristic
393C4×D4C23×C8311yescharacteristic
394#117—21no—
395#117—21no—
396#117D4×C8311yescharacteristic
397C2×C42—21no—
398C2×C42C23×C8311yescharacteristic
399#107—21no—
400#107—21no—
401#107—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8D4×C8311yescharacteristic
410C4⋊C8D4×C8311yescharacteristic
411C4⋊C8C23×C8311yescharacteristic
412C4⋊C8C23×C8311yescharacteristic
413C4⋊C8C23×C8311yescharacteristic
414C4⋊C8C23×C8311yescharacteristic
415C4⋊C8C23×C8311yescharacteristic
416C4⋊C8C23×C8311yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8D4×C8311yescharacteristic
433C22⋊C8D4×C8311yescharacteristic
434#97—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C8311yescharacteristic
438C4×C8C23×C8311yescharacteristic
439#41—22no—
440#41—41no—
441#41—42no—
442#41—42no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×D4×C8311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4C2×D4×C8311yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4C2×D4×C8311yescharacteristic
458C22×C4C2×D4×C8311yescharacteristic
459C22×C4#41×C8311yescharacteristic
460Q16—42no—
461Q16—42no—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465D8—42no—
466M16—81no—
467M16—81no—
468M16—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8C2×D4×C8311yescharacteristic
477C2×C8C2×D4×C8311yescharacteristic
478C2×C8C2×D4×C8311yescharacteristic
479C2×C8C2×D4×C8311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C8311yescharacteristic
491C4⋊C4C2×D4×C8311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C2×D4×C8311yescharacteristic
503C42C2×D4×C8311yescharacteristic
504C42#41×C8311yescharacteristic
505C42C24×C8311yescharacteristic
506C23—21no—
507C23—41no—
508C23#121×C8311yescharacteristic
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515Q8AGL(1,ℤ/8)×C8312yes—
516D4—21no—
517D4—21no—
518D4—42no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4#121×C8311yescharacteristic
542C2×C4#121×C8311yescharacteristic
543C2×C4#121×C8311yescharacteristic
544C2×C4C22×D4×C8311yescharacteristic
545C2×C4C22×D4×C8311yescharacteristic
546C2×C4C2×#41×C8311yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C2×#121×C8311yescharacteristic
567C4—21no—
568C4—21no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×AGL(1,ℤ/8)×C8311yescharacteristic
578C4#575×C8311yescharacteristic
579C4#577×C8311yescharacteristic
580C4#578×C8311yescharacteristic
581C2—41no—
582C2—81no—
583C2—161no—
584C2C83×#304611yescharacteristic
585C2C83×#305511yescharacteristic
586C2C83×#306711yescharacteristic
subgroupG/H
center, socleC22×C83C2×#121
commutator, Frattini, cosocleC42C24×C83
prime radicalC83×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3228C2semidirect
2. C83×#3116C2semidirect
4. C83×#2991C2semidirect
5. C83×#1701C2semidirect
6. C83×#1697C2semidirect
7. C83×#1693C2semidirect
8. C83×#1691C2semidirect
9. C83×#1682C2semidirect
10. C83×#1678C2semidirect
11. C83×#1674C2semidirect
12. C83×#1672C2semidirect
13. C83×#1573C2semidirect
14. C83×#1557C2semidirect
15. C83×#1550C2semidirect
287. #19498C83direct (N × H)
294. #3228C2×C83semidirect
295. #3116C2×C83semidirect
297. #2991C2×C83semidirect
298. #1701C2×C83semidirect
299. #1697C2×C83semidirect
300. #1693C2×C83semidirect
301. #1691C2×C83semidirect
302. #1682C2×C83semidirect
303. #1678C2×C83semidirect
304. #1674C2×C83semidirect
305. #1672C2×C83semidirect
306. #1573C2×C83semidirect
307. #1557C2×C83semidirect
308. #1550C2×C83semidirect
309. C83#19498direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#32282
C83×#31162
C83×#30352
C83×#29912
C83×#17012
C83×#16972
C83×#16932
C83×#16912
C83×#16822
C83×#16782
C83×#16742
C83×#16722
C83×#15732
C83×#15572
C83×#15502
#1949883