Finite Group Databasebeta

← C83×#8980 #35236804

Subgroups — C83×#8980 #35236804

Order 21248.

692 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C83C211yesmaximal, characteristic
2C83×#2354C211yesmaximal, characteristic, complemented
3C83×#1982C211yesmaximal, characteristic, complemented
4C83×#1957C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C83C211yesmaximal, characteristic, complemented
6C83×#1296C211yesmaximal, characteristic, complemented
7C83×#1279C211yesmaximal, characteristic, complemented
8C22×D8×C83—21no—
9C2×#127×C83C2211yescharacteristic
10C2×C4×D4×C83C2211yescharacteristic
11C2×#117×C83—21no—
12#459×C83—22no—
13#459×C83C414yescomplemented
14C2×C4⋊C8×C83C2211yescharacteristic
15C2×C4⋊C8×C83C2211yescharacteristic
16C2×#102×C83—21no—
17C2×#102×C83—22no—
18C2×#102×C83—21no—
19C2×#102×C83—21no—
20C2×C4×C8×C83C2211yescharacteristic
21#390×C83—21no—
22#388×C83—22no—
23#384×C83C2211yescharacteristic
24#380×C83—21no—
25C4×C4⋊C4×C83—21no—
26C4×C4⋊C4×C83C2211yescharacteristic
27D4⋊C8×C83—22no—
28C22×D4×C83—21no—
29C22×D4×C83—21no—
30C22×D4×C83—21no—
31C22×D4×C83D411yescharacteristic
32C23×C4×C83—21no—
33C2×D8×C83—24no—
34C2×D8×C83—42no—
35C2×D8×C83—42no—
36C22×C8×C83—21no—
37C22×C8×C83—21no—
38C22×C8×C83—21no—
39#127×C83—21no—
40#127×C83—21no—
41#127×C83—21no—
42#127×C83C2×C412yes—
43C4×D4×C83—21no—
44C4×D4×C83—21no—
45C4×D4×C83C2×C412yes—
46C4×D4×C83D412yes—
47#117×C83—42no—
48#117×C83—42no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83D411yescharacteristic
52C2×C4⋊C4×C83D411yescharacteristic
53C2×C4⋊C4×C83D411yescharacteristic
54C2×C4⋊C4×C83D412yes—
55C2×C22⋊C4×C83—21no—
56C2×C22⋊C4×C83—22no—
57C2×C22⋊C4×C83—22no—
58C2×C42×C83—22no—
59C2×C42×C83—21no—
60C2×C42×C83C2311yescharacteristic
61C4⋊C8×C83—21no—
62C4⋊C8×C83—21no—
63C4⋊C8×C83—21no—
64C4⋊C8×C83C2×C412yes—
65#102×C83—24no—
66#102×C83—42no—
67#102×C83—44no—
68#102×C83—42no—
69C4×C8×C83—21no—
70C4×C8×C83—21no—
71#95×C83—22no—
72#95×C83—21no—
73C24×C83—21no—
74C24×C83—41no—
75C2×D4×C83—22no—
76C2×D4×C83—22no—
77C2×D4×C83—22no—
78C2×D4×C83—21no—
79C2×D4×C83—21no—
80C2×D4×C83—21no—
81C2×D4×C83—21no—
82C2×D4×C83—21no—
83C2×D4×C83—42no—
84C2×D4×C83—42no—
85C2×D4×C83—41no—
86C2×D4×C83—41no—
87C2×D4×C83—41no—
88C2×D4×C83—41no—
89C2×D4×C83—41no—
90C2×D4×C83—41no—
91C2×D4×C83—41no—
92C2×D4×C83—41no—
93C2×D4×C83—41no—
94C2×D4×C83—41no—
95C2×D4×C83—41no—
96C2×D4×C83C22⋊C412yes—
97C22×C4×C83—21no—
98C22×C4×C83—21no—
99C22×C4×C83—22no—
100C22×C4×C83—22no—
101C22×C4×C83—21no—
102C22×C4×C83—22no—
103C22×C4×C83—41no—
104C22×C4×C83—41no—
105C22×C4×C83—41no—
106C22×C4×C83—41no—
107C22×C4×C83C2×D411yescharacteristic
108C22×C4×C83C2×D411yescharacteristic
109C22×C4×C83C2×D411yescharacteristic
110D8×C83—48no—
111C2×C8×C83—22no—
112C2×C8×C83—22no—
113C2×C8×C83—41no—
114C2×C8×C83—41no—
115C2×C8×C83—41no—
116C2×C8×C83—41no—
117C2×C8×C83—41no—
118C2×C8×C83—41no—
119C2×C8×C83—41no—
120C4⋊C4×C83—21no—
121C4⋊C4×C83—21no—
122C4⋊C4×C83—21no—
123C4⋊C4×C83—21no—
124C4⋊C4×C83—42no—
125C4⋊C4×C83—41no—
126C4⋊C4×C83—41no—
127C4⋊C4×C83—41no—
128C4⋊C4×C83—41no—
129C4⋊C4×C83C22⋊C412yes—
130C4⋊C4×C83D812yescomplemented
131C22⋊C4×C83—22no—
132C22⋊C4×C83—22no—
133C22⋊C4×C83—44no—
134C22⋊C4×C83—82no—
135C42×C83—44no—
136C42×C83—41no—
137C42×C83—41no—
138C42×C83C22×C411yescharacteristic
139C42×C83C2×D411yescharacteristic
140C42×C83#4111yescharacteristic
141C42×C83#4111yescharacteristic
142C23×C83—22no—
143C23×C83—41no—
144C23×C83—41no—
145C23×C83—41no—
146C23×C83—41no—
147C23×C83—41no—
148C23×C83—41no—
149C23×C83—42no—
150C23×C83—81no—
151C23×C83—81no—
152C23×C83—81no—
153C23×C83—81no—
154C23×C83—81no—
155C23×C83—81no—
156C23×C83#12011yescharacteristic
157D4×C83—22no—
158D4×C83—22no—
159D4×C83—44no—
160D4×C83—42no—
161D4×C83—42no—
162D4×C83—42no—
163D4×C83—42no—
164D4×C83—41no—
165D4×C83—41no—
166D4×C83—82no—
167D4×C83—81no—
168D4×C83—81no—
169D4×C83—81no—
170D4×C83—81no—
171C2×C4×C83—21no—
172C2×C4×C83—21no—
173C2×C4×C83—22no—
174C2×C4×C83—22no—
175C2×C4×C83—41no—
176C2×C4×C83—41no—
177C2×C4×C83—41no—
178C2×C4×C83—41no—
179C2×C4×C83—42no—
180C2×C4×C83—42no—
181C2×C4×C83—42no—
182C2×C4×C83—42no—
183C2×C4×C83—42no—
184C2×C4×C83—41no—
185C2×C4×C83—41no—
186C2×C4×C83—42no—
187C2×C4×C83—41no—
188C2×C4×C83—42no—
189C2×C4×C83C2×C22⋊C411yescharacteristic
190C2×C4×C83C4×D411yescharacteristic
191C2×C4×C83C4×D411yescharacteristic
192C2×C4×C83#12111yescharacteristic
193C2×C4×C83#12111yescharacteristic
194C2×C4×C83#12311yescharacteristic
195C2×C4×C83C2×D811yescharacteristic
196C2×C4×C83#13511yescharacteristic
197C2×C4×C83#13511yescharacteristic
198C2×C4×C83#13511yescharacteristic
199C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
203C8×C83—42no—
204C8×C83—42no—
205C8×C83—81no—
206C22×C83—42no—
207C22×C83—42no—
208C22×C83—42no—
209C22×C83—81no—
210C22×C83—81no—
211C22×C83—81no—
212C22×C83—81no—
213C22×C83—82no—
214C22×C83—82no—
215C22×C83—82no—
216C22×C83—161no—
217C22×C83—161no—
218C22×C83—161no—
219C22×C83—161no—
220C22×C83#38611yescharacteristic
221C22×C83#44711yescharacteristic
222C22×C83#44911yescharacteristic
223C22×C83#44911yescharacteristic
224C22×C83#44911yescharacteristic
225C22×C83#45311yescharacteristic
226C22×C83#45411yescharacteristic
227C4×C83—21no—
228C4×C83—21no—
229C4×C83—42no—
230C4×C83—42no—
231C4×C83—82no—
232C4×C83—81no—
233C4×C83#41611yescharacteristic
234C4×C83#41811yescharacteristic
235C4×C83C4×D811yescharacteristic
236C4×C83#44211yescharacteristic
237C4×C83#45911yescharacteristic
238C4×C83#46311yescharacteristic
239C4×C83#48211yescharacteristic
240C4×C83#48211yescharacteristic
241#8980C8311yesmaximal, characteristic, direct product factor, Sylow
242C2×C83—82no—
243C2×C83—162no—
244C2×C83#162111yescharacteristic
245C2×C83#162411yescharacteristic
246C2×C83#162511yescharacteristic
247C2×C83#162811yescharacteristic
248C2×C83#187511yescharacteristic
249C2×C83#187911yescharacteristic
250C2×C83#188311yescharacteristic
251C2×#459C2×C8311yescharacteristic
252#2354C2×C8311yescharacteristic, complemented
253#1982C2×C8311yescharacteristic, complemented
254#1957C2×C8311yescharacteristic, complemented
255C2×D4⋊C8C2×C8311yescharacteristic, complemented
256#1296C2×C8311yescharacteristic, complemented
257#1279C2×C8311yescharacteristic, complemented
258C83#898011yescharacteristic, direct product factor, Sylow
259C22×D8—21no—
260C2×#127C22×C8311yescharacteristic
261C2×C4×D4C22×C8311yescharacteristic
262C2×#117—21no—
263#459—22no—
264#459C4×C8314yescomplemented
265C2×C4⋊C8C22×C8311yescharacteristic
266C2×C4⋊C8C22×C8311yescharacteristic
267C2×#102—21no—
268C2×#102—22no—
269C2×#102—21no—
270C2×#102—21no—
271C2×C4×C8C22×C8311yescharacteristic
272#390—21no—
273#388—22no—
274#384C22×C8311yescharacteristic
275#380—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4C22×C8311yescharacteristic
278D4⋊C8—22no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4D4×C8311yescharacteristic
283C23×C4—21no—
284C2×D8—24no—
285C2×D8—42no—
286C2×D8—42no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290#127—21no—
291#127—21no—
292#127—21no—
293#127C2×C4×C8312yes—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4C2×C4×C8312yes—
297C4×D4D4×C8312yes—
298#117—42no—
299#117—42no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4D4×C8311yescharacteristic
303C2×C4⋊C4D4×C8311yescharacteristic
304C2×C4⋊C4D4×C8311yescharacteristic
305C2×C4⋊C4D4×C8312yes—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C42—22no—
310C2×C42—21no—
311C2×C42C23×C8311yescharacteristic
312C4⋊C8—21no—
313C4⋊C8—21no—
314C4⋊C8—21no—
315C4⋊C8C2×C4×C8312yes—
316#102—24no—
317#102—42no—
318#102—44no—
319#102—42no—
320C4×C8—21no—
321C4×C8—21no—
322#95—22no—
323#95—21no—
324C24—21no—
325C24—41no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4C22⋊C4×C8312yes—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4C2×D4×C8311yescharacteristic
359C22×C4C2×D4×C8311yescharacteristic
360C22×C4C2×D4×C8311yescharacteristic
361D8—48no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—42no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4C22⋊C4×C8312yes—
381C4⋊C4D8×C8312yescomplemented
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—44no—
385C22⋊C4—82no—
386C42—44no—
387C42—41no—
388C42—41no—
389C42C22×C4×C8311yescharacteristic
390C42C2×D4×C8311yescharacteristic
391C42#41×C8311yescharacteristic
392C42#41×C8311yescharacteristic
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—81no—
404C23—81no—
405C23—81no—
406C23—81no—
407C23#120×C8311yescharacteristic
408D4—22no—
409D4—22no—
410D4—44no—
411D4—41no—
412D4—41no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—82no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—81no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4C2×C22⋊C4×C8311yescharacteristic
441C2×C4C4×D4×C8311yescharacteristic
442C2×C4C4×D4×C8311yescharacteristic
443C2×C4#121×C8311yescharacteristic
444C2×C4#121×C8311yescharacteristic
445C2×C4#123×C8311yescharacteristic
446C2×C4C2×D8×C8311yescharacteristic
447C2×C4#135×C8311yescharacteristic
448C2×C4#135×C8311yescharacteristic
449C2×C4#135×C8311yescharacteristic
450C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
451C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
452C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
453C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
454C8—42no—
455C8—42no—
456C8—81no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—161no—
468C22—161no—
469C22—161no—
470C22—161no—
471C22#386×C8311yescharacteristic
472C22#447×C8311yescharacteristic
473C22#449×C8311yescharacteristic
474C22#449×C8311yescharacteristic
475C22#449×C8311yescharacteristic
476C22#453×C8311yescharacteristic
477C22#454×C8311yescharacteristic
478C4—21no—
479C4—21no—
480C4—42no—
481C4—42no—
482C4—82no—
483C4—81no—
484C4#416×C8311yescharacteristic
485C4#418×C8311yescharacteristic
486C4C4×D8×C8311yescharacteristic
487C4#442×C8311yescharacteristic
488C4#459×C8311yescharacteristic
489C4#463×C8311yescharacteristic
490C4#482×C8311yescharacteristic
491C4#482×C8311yescharacteristic
492C2—82no—
493C2—162no—
494C2C83×#162111yescharacteristic
495C2C83×#162411yescharacteristic
496C2C83×#162511yescharacteristic
497C2C83×#162811yescharacteristic
498C2C83×#187511yescharacteristic
499C2C83×#187911yescharacteristic
500C2C83×#188311yescharacteristic
subgroupG/H
center, socleC23×C83#120
commutatorC42C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC2×#459×C83C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2354C2semidirect
3. C83×#1982C2semidirect
4. C83×#1957C2semidirect
5. C2×D4⋊C8×C83C2semidirect
6. C83×#1296C2semidirect
7. C83×#1279C2semidirect
13. #459×C83C4semidirect
130. C4⋊C4×C83D8semidirect
241. #8980C83direct (N × H)
252. #2354C2×C83semidirect
253. #1982C2×C83semidirect
254. #1957C2×C83semidirect
255. C2×D4⋊C8C2×C83semidirect
256. #1296C2×C83semidirect
257. #1279C2×C83semidirect
258. C83#8980direct (N × H)
264. #459C4×C83semidirect
381. C4⋊C4D8×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C832
C83×#23542
C83×#19822
C83×#19572
C2×D4⋊C8×C832
C83×#12962
C83×#12792
#898083