Finite Group Databasebeta

← C83×#19416 #35247240

Subgroups — C83×#19416 #35247240

Order 21248.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3226C211yesmaximal, characteristic, complemented
2C83×#3039C211yesmaximal, characteristic, complemented
3C83×#3035C211yesmaximal, characteristic
4C83×#2988C211yesmaximal, characteristic, complemented
5C83×#1682C212yesmaximal, complemented
6C83×#1681C212yesmaximal, complemented
7C83×#1674C212yesmaximal, complemented
8C83×#1673C212yesmaximal, complemented
9C83×#1571C211yesmaximal, characteristic, complemented
10C83×#1547C211yesmaximal, characteristic, complemented
11C2×#332×C83C211yesmaximal, characteristic, complemented
12C2×#137×C83—21no—
13C2×#135×C83—21no—
14#532×C83C2211yescharacteristic
15C2×C4⋊Q8×C83C2211yescharacteristic
16C4×#41×C83C2211yescharacteristic
17#500×C83C2212yes—
18#486×C83C2212yes—
19#480×C83—22no—
20#474×C83—21no—
21#474×C83—21no—
22#464×C83—21no—
23#463×C83—21no—
24#462×C83—21no—
25#462×C83C2211yescharacteristic
26#462×C83C2212yes—
27#461×C83—21no—
28#461×C83C2211yescharacteristic
29#461×C83C2212yes—
30#460×C83C2211yescharacteristic
31#459×C83C2211yescharacteristic
32C8×Q8×C83C2212yes—
33C8×D4×C83—22no—
34C8×D4×C83C2212yes—
35#431×C83—21no—
36#431×C83C2211yescharacteristic
37#423×C83C2211yescharacteristic
38C2×C4⋊C8×C83—21no—
39C2×C4⋊C8×C83C2211yescharacteristic
40C2×C4⋊C8×C83C2211yescharacteristic
41#419×C83—21no—
42#416×C83—21no—
43#335×C83C2212yes—
44#335×C83C2212yes—
45#332×C83C2212yes—
46#332×C83C2212yes—
47#332×C83C2212yes—
48#331×C83C2212yes—
49C2×#41×C83—21no—
50C2×#41×C83D411yescharacteristic
51C22×Q8×C83—21no—
52#137×C83—44no—
53#135×C83—44no—
54C2×Q16×C83—21no—
55C2×Q16×C83—22no—
56C2×SD16×C83—21no—
57C2×SD16×C83—21no—
58C2×SD16×C83—22no—
59C2×D8×C83—21no—
60C2×M16×C83—21no—
61C22×C8×C83—21no—
62C22×C8×C83—21no—
63C22×C8×C83—22no—
64C4⋊Q8×C83—21no—
65C4⋊Q8×C83—21no—
66C4⋊Q8×C83—21no—
67C4⋊Q8×C83C2312yes—
68C4⋊Q8×C83C2311yescharacteristic
69#127×C83C2311yescharacteristic
70#124×C83—21no—
71#121×C83—21no—
72#121×C83—21no—
73C4×Q8×C83D411yescharacteristic
74C4×Q8×C83C2311yescharacteristic
75C4×D4×C83—21no—
76C4×D4×C83—21no—
77C4×D4×C83—21no—
78C4×D4×C83—21no—
79C4×D4×C83D411yescharacteristic
80C4×D4×C83C2311yescharacteristic
81#117×C83—21no—
82#117×C83D411yescharacteristic
83C2×C4⋊C4×C83—21no—
84C2×C4⋊C4×C83—21no—
85C2×C42×C83—21no—
86C2×C42×C83C2311yescharacteristic
87#107×C83—22no—
88#107×C83—22no—
89C4⋊C8×C83—22no—
90C4⋊C8×C83—21no—
91C4⋊C8×C83—21no—
92C4⋊C8×C83—21no—
93C4⋊C8×C83D411yescharacteristic
94C4⋊C8×C83D411yescharacteristic
95C4⋊C8×C83C2312yes—
96C4⋊C8×C83C2312yes—
97C4⋊C8×C83C2311yescharacteristic
98C4⋊C8×C83C2311yescharacteristic
99#103×C83—21no—
100#103×C83—21no—
101#103×C83—22no—
102#103×C83—22no—
103#102×C83—22no—
104#102×C83—22no—
105#102×C83—21no—
106#102×C83—21no—
107C22⋊C8×C83—22no—
108C22⋊C8×C83D412yes—
109C4×C8×C83—22no—
110C4×C8×C83C2312yes—
111#41×C83—22no—
112#41×C83—42no—
113#41×C83—42no—
114#41×C83D814yes—
115C2×Q8×C83—21no—
116C2×Q8×C83—22no—
117C2×Q8×C83—41no—
118C2×Q8×C83—42no—
119C2×Q8×C83—42no—
120C2×Q8×C83C2×D411yescharacteristic
121C2×D4×C83—21no—
122C2×D4×C83—21no—
123C2×D4×C83—21no—
124C2×D4×C83—21no—
125C2×D4×C83—41no—
126C2×D4×C83C2×D411yescharacteristic
127C22×C4×C83—21no—
128C22×C4×C83—21no—
129C22×C4×C83—21no—
130C22×C4×C83—41no—
131C22×C4×C83—41no—
132C22×C4×C83C2×D411yescharacteristic
133C22×C4×C83C2×D411yescharacteristic
134C22×C4×C83#4111yescharacteristic
135Q16×C83—42no—
136Q16×C83—44no—
137SD16×C83—42no—
138SD16×C83—42no—
139SD16×C83—44no—
140D8×C83—42no—
141M16×C83—42no—
142C2×C8×C83—22no—
143C2×C8×C83—21no—
144C2×C8×C83—21no—
145C2×C8×C83—22no—
146C2×C8×C83—42no—
147C2×C8×C83—82no—
148C2×C8×C83—81no—
149C2×C8×C83C2×D412yes—
150C2×C8×C83C2×D412yes—
151C4⋊C4×C83—21no—
152C4⋊C4×C83—21no—
153C4⋊C4×C83—22no—
154C4⋊C4×C83—21no—
155C4⋊C4×C83—22no—
156C4⋊C4×C83—21no—
157C4⋊C4×C83—41no—
158C4⋊C4×C83—41no—
159C4⋊C4×C83C2×D411yescharacteristic
160C4⋊C4×C83C2×D411yescharacteristic
161C22⋊C4×C83—21no—
162C22⋊C4×C83—21no—
163C22⋊C4×C83—21no—
164C22⋊C4×C83—41no—
165C22⋊C4×C83—41no—
166C42×C83—21no—
167C42×C83—21no—
168C42×C83—21no—
169C42×C83C2×D411yescharacteristic
170C42×C83C2×D411yescharacteristic
171C42×C83#4111yescharacteristic
172C42×C83C2411yescharacteristic
173C23×C83—21no—
174C23×C83—41no—
175C23×C83#12111yescharacteristic
176Q8×C83—21no—
177Q8×C83—42no—
178Q8×C83—41no—
179Q8×C83—42no—
180Q8×C83—41no—
181Q8×C83—82no—
182Q8×C83C2×D812yes—
183D4×C83—24no—
184D4×C83—21no—
185D4×C83—41no—
186D4×C83—41no—
187D4×C83—41no—
188D4×C83—41no—
189D4×C83—81no—
190D4×C83—82no—
191D4×C83C2×D812yes—
192C2×C4×C83—21no—
193C2×C4×C83—21no—
194C2×C4×C83—21no—
195C2×C4×C83—24no—
196C2×C4×C83—21no—
197C2×C4×C83—21no—
198C2×C4×C83—41no—
199C2×C4×C83—41no—
200C2×C4×C83—41no—
201C2×C4×C83—41no—
202C2×C4×C83—42no—
203C2×C4×C83—81no—
204C2×C4×C83—82no—
205C2×C4×C83—82no—
206C2×C4×C83#12111yescharacteristic
207C2×C4×C83#12111yescharacteristic
208C2×C4×C83#12111yescharacteristic
209C2×C4×C83C2×D812yes—
210C2×C4×C83#13512yes—
211C2×C4×C83C22×D411yescharacteristic
212C2×C4×C83C22×D411yescharacteristic
213C2×C4×C83C2×#4111yescharacteristic
214C8×C83—22no—
215C8×C83—22no—
216C8×C83—41no—
217C8×C83—41no—
218C8×C83—42no—
219C8×C83—42no—
220C22×C83—21no—
221C22×C83—21no—
222C22×C83—22no—
223C22×C83—41no—
224C22×C83—41no—
225C22×C83—81no—
226C22×C83—81no—
227C22×C83—81no—
228C22×C83#46612yes—
229C22×C83C2×#12111yescharacteristic
230C4×C83—21no—
231C4×C83—22no—
232C4×C83—21no—
233C4×C83—21no—
234C4×C83—41no—
235C4×C83—41no—
236C4×C83—81no—
237C4×C83—82no—
238C4×C83#46612yes—
239C4×C83C22×D811yescharacteristic
240C4×C83C2×#13511yescharacteristic
241C4×C83#57711yescharacteristic
242C4×C83#57811yescharacteristic
243#19416C8311yesmaximal, characteristic, direct product factor, Sylow
244C2×C83—22no—
245C2×C83—42no—
246C2×C83—161no—
247C2×C83#304611yescharacteristic
248C2×C83C2×#46611yescharacteristic
249C2×C83#306911yescharacteristic
250#3226C2×C8311yescharacteristic, complemented
251#3039C2×C8311yescharacteristic, complemented
252#3035C2×C8311yescharacteristic
253#2988C2×C8311yescharacteristic, complemented
254#1682C2×C8312yescomplemented
255#1681C2×C8312yescomplemented
256#1674C2×C8312yescomplemented
257#1673C2×C8312yescomplemented
258#1571C2×C8311yescharacteristic, complemented
259#1547C2×C8311yescharacteristic, complemented
260C2×#332C2×C8311yescharacteristic, complemented
261C83#1941611yescharacteristic, direct product factor, Sylow
262C2×#137—21no—
263C2×#135—21no—
264#532C22×C8311yescharacteristic
265C2×C4⋊Q8C22×C8311yescharacteristic
266C4×#41C22×C8311yescharacteristic
267#500C22×C8312yes—
268#486C22×C8312yes—
269#480—22no—
270#474—21no—
271#474—21no—
272#464—21no—
273#463—21no—
274#462—21no—
275#462C22×C8311yescharacteristic
276#462C22×C8312yes—
277#461—21no—
278#461C22×C8311yescharacteristic
279#461C22×C8312yes—
280#460C22×C8311yescharacteristic
281#459C22×C8311yescharacteristic
282C8×Q8C22×C8312yes—
283C8×D4—22no—
284C8×D4C22×C8312yes—
285#431—21no—
286#431C22×C8311yescharacteristic
287#423C22×C8311yescharacteristic
288C2×C4⋊C8—21no—
289C2×C4⋊C8C22×C8311yescharacteristic
290C2×C4⋊C8C22×C8311yescharacteristic
291#419—21no—
292#416—21no—
293#335C22×C8312yes—
294#335C22×C8312yes—
295#332C22×C8312yes—
296#332C22×C8312yes—
297#332C22×C8312yes—
298#331C22×C8312yes—
299C2×#41—21no—
300C2×#41D4×C8311yescharacteristic
301C22×Q8—21no—
302#137—44no—
303#135—44no—
304C2×Q16—21no—
305C2×Q16—22no—
306C2×SD16—21no—
307C2×SD16—21no—
308C2×SD16—22no—
309C2×D8—21no—
310C2×M16—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—22no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8C23×C8312yes—
318C4⋊Q8C23×C8311yescharacteristic
319#127C23×C8311yescharacteristic
320#124—21no—
321#121—21no—
322#121—21no—
323C4×Q8D4×C8311yescharacteristic
324C4×Q8C23×C8311yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4D4×C8311yescharacteristic
330C4×D4C23×C8311yescharacteristic
331#117—21no—
332#117D4×C8311yescharacteristic
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C42—21no—
336C2×C42C23×C8311yescharacteristic
337#107—22no—
338#107—22no—
339C4⋊C8—22no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8D4×C8311yescharacteristic
344C4⋊C8D4×C8311yescharacteristic
345C4⋊C8C23×C8312yes—
346C4⋊C8C23×C8312yes—
347C4⋊C8C23×C8311yescharacteristic
348C4⋊C8C23×C8311yescharacteristic
349#103—21no—
350#103—21no—
351#103—22no—
352#103—22no—
353#102—22no—
354#102—22no—
355#102—21no—
356#102—21no—
357C22⋊C8—22no—
358C22⋊C8D4×C8312yes—
359C4×C8—22no—
360C4×C8C23×C8312yes—
361#41—22no—
362#41—42no—
363#41—42no—
364#41D8×C8314yes—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×Q8C2×D4×C8311yescharacteristic
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4C2×D4×C8311yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4C2×D4×C8311yescharacteristic
383C22×C4C2×D4×C8311yescharacteristic
384C22×C4#41×C8311yescharacteristic
385Q16—42no—
386Q16—44no—
387SD16—42no—
388SD16—42no—
389SD16—44no—
390D8—42no—
391M16—42no—
392C2×C8—22no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—42no—
397C2×C8—82no—
398C2×C8—81no—
399C2×C8C2×D4×C8312yes—
400C2×C8C2×D4×C8312yes—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4C2×D4×C8311yescharacteristic
410C4⋊C4C2×D4×C8311yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42C2×D4×C8311yescharacteristic
420C42C2×D4×C8311yescharacteristic
421C42#41×C8311yescharacteristic
422C42C24×C8311yescharacteristic
423C23—21no—
424C23—41no—
425C23#121×C8311yescharacteristic
426Q8—21no—
427Q8—42no—
428Q8—41no—
429Q8—42no—
430Q8—41no—
431Q8—82no—
432Q8C2×D8×C8312yes—
433D4—24no—
434D4—21no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—81no—
440D4—82no—
441D4C2×D8×C8312yes—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4#121×C8311yescharacteristic
457C2×C4#121×C8311yescharacteristic
458C2×C4#121×C8311yescharacteristic
459C2×C4C2×D8×C8312yes—
460C2×C4#135×C8312yes—
461C2×C4C22×D4×C8311yescharacteristic
462C2×C4C22×D4×C8311yescharacteristic
463C2×C4C2×#41×C8311yescharacteristic
464C8—22no—
465C8—22no—
466C8—41no—
467C8—41no—
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22#466×C8312yes—
479C22C2×#121×C8311yescharacteristic
480C4—21no—
481C4—22no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—82no—
488C4#466×C8312yes—
489C4C22×D8×C8311yescharacteristic
490C4C2×#135×C8311yescharacteristic
491C4#577×C8311yescharacteristic
492C4#578×C8311yescharacteristic
493C2—22no—
494C2—42no—
495C2—161no—
496C2C83×#304611yescharacteristic
497C2C2×#466×C8311yescharacteristic
498C2C83×#306911yescharacteristic
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×#3226C2semidirect
2. C83×#3039C2semidirect
4. C83×#2988C2semidirect
5. C83×#1682C2semidirect
6. C83×#1681C2semidirect
7. C83×#1674C2semidirect
8. C83×#1673C2semidirect
9. C83×#1571C2semidirect
10. C83×#1547C2semidirect
11. C2×#332×C83C2semidirect
243. #19416C83direct (N × H)
250. #3226C2×C83semidirect
251. #3039C2×C83semidirect
253. #2988C2×C83semidirect
254. #1682C2×C83semidirect
255. #1681C2×C83semidirect
256. #1674C2×C83semidirect
257. #1673C2×C83semidirect
258. #1571C2×C83semidirect
259. #1547C2×C83semidirect
260. C2×#332C2×C83semidirect
261. C83#19416direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#32262
C83×#30392
C83×#30352
C83×#29882
C83×#16822
C83×#16812
C83×#16742
C83×#16732
C83×#15712
C83×#15472
C2×#332×C832
#1941683