Finite Group Databasebeta

← C83×#8330 #35236154

Subgroups — C83×#8330 #35236154

Order 21248.

908 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C83C211yesmaximal, characteristic
2C83×#1817C211yesmaximal, characteristic, complemented
3C2×#328×C83C212yesmaximal, complemented
4C2×#327×C83C212yesmaximal
5C83×#1434C211yesmaximal, characteristic, complemented
6#529×C83—24no—
7#529×C83—24no—
8C2×#126×C83—21no—
9C2×#125×C83C411yescharacteristic, complemented
10C2×#124×C83C411yescharacteristic, complemented
11C2×#123×C83—21no—
12C2×C22⋊Q8×C83C2211yescharacteristic
13C2×#121×C83C2211yescharacteristic
14C2×C4×Q8×C83C411yescharacteristic, complemented
15C2×C4×D4×C83—21no—
16C2×C4×D4×C83C411yescharacteristic, complemented
17C2×#117×C83—21no—
18C22×C42×C83C2211yescharacteristic
19C2×C22⋊C8×C83C2212yes—
20C2×#95×C83—21no—
21C2×#95×C83—21no—
22C2×#95×C83C2212yes—
23#336×C83—21no—
24#336×C83—21no—
25#328×C83—24no—
26#327×C83—24no—
27C22×Q8×C83C2×C411yescharacteristic
28C22×D4×C83—21no—
29C22×D4×C83C2×C411yescharacteristic
30C23×C4×C83—21no—
31C23×C4×C83—22no—
32C23×C4×C83D411yescharacteristic
33C23×C4×C83D411yescharacteristic
34C23×C4×C83C2311yescharacteristic
35C22×C8×C83—22no—
36#126×C83—28no—
37#125×C83—22no—
38#125×C83—22no—
39#124×C83—22no—
40#124×C83—22no—
41#123×C83—28no—
42C22⋊Q8×C83—22no—
43C22⋊Q8×C83D414yes—
44#121×C83—22no—
45#121×C83D414yes—
46C4×Q8×C83—22no—
47C4×Q8×C83—22no—
48C4×D4×C83—28no—
49C4×D4×C83—22no—
50C4×D4×C83—22no—
51#117×C83—28no—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83—21no—
56C2×C4⋊C4×C83C2×C411yescharacteristic
57C2×C4⋊C4×C83C2×C411yescharacteristic
58C2×C22⋊C4×C83—21no—
59C2×C22⋊C4×C83—21no—
60C2×C22⋊C4×C83—21no—
61C2×C22⋊C4×C83—21no—
62C2×C22⋊C4×C83—21no—
63C2×C42×C83—21no—
64C2×C42×C83—22no—
65C2×C42×C83—22no—
66C2×C42×C83C2×C411yescharacteristic
67C2×C42×C83C2×C411yescharacteristic
68C2×C42×C83D411yescharacteristic
69C2×C42×C83D411yescharacteristic
70C22⋊C8×C83—22no—
71C22⋊C8×C83—22no—
72#95×C83—24no—
73#95×C83—22no—
74#95×C83—22no—
75#95×C83—42no—
76C24×C83—21no—
77C24×C83C2×D411yescharacteristic
78C2×Q8×C83—21no—
79C2×Q8×C83—41no—
80C2×Q8×C83—41no—
81C2×Q8×C83C22⋊C412yes—
82C2×D4×C83—24no—
83C2×D4×C83—21no—
84C2×D4×C83—41no—
85C2×D4×C83—41no—
86C2×D4×C83—42no—
87C2×D4×C83—41no—
88C2×D4×C83—41no—
89C2×D4×C83C22⋊C412yes—
90C22×C4×C83—24no—
91C22×C4×C83—21no—
92C22×C4×C83—21no—
93C22×C4×C83—21no—
94C22×C4×C83—22no—
95C22×C4×C83—22no—
96C22×C4×C83—22no—
97C22×C4×C83—21no—
98C22×C4×C83—21no—
99C22×C4×C83—22no—
100C22×C4×C83—24no—
101C22×C4×C83—41no—
102C22×C4×C83—41no—
103C22×C4×C83—41no—
104C22×C4×C83—42no—
105C22×C4×C83—42no—
106C22×C4×C83—42no—
107C22×C4×C83—42no—
108C22×C4×C83—42no—
109C22×C4×C83—42no—
110C22×C4×C83—42no—
111C22×C4×C83—42no—
112C22×C4×C83C22⋊C411yescharacteristic
113C22×C4×C83C22⋊C411yescharacteristic
114C22×C4×C83C22⋊C411yescharacteristic
115C22×C4×C83C22⋊C411yescharacteristic
116C22×C4×C83C22×C411yescharacteristic
117C22×C4×C83C2×D411yescharacteristic
118C22×C4×C83C2×D412yes—
119C22×C4×C83C2×D412yes—
120C2×C8×C83—42no—
121C2×C8×C83—42no—
122C2×C8×C83—42no—
123C4⋊C4×C83—24no—
124C4⋊C4×C83—24no—
125C4⋊C4×C83—24no—
126C4⋊C4×C83—21no—
127C4⋊C4×C83—21no—
128C4⋊C4×C83—24no—
129C4⋊C4×C83C22⋊C412yes—
130C4⋊C4×C83C22⋊C412yes—
131C22⋊C4×C83—24no—
132C22⋊C4×C83—24no—
133C22⋊C4×C83—24no—
134C22⋊C4×C83—24no—
135C22⋊C4×C83—24no—
136C42×C83—24no—
137C42×C83—21no—
138C42×C83—21no—
139C42×C83—21no—
140C42×C83—21no—
141C42×C83—22no—
142C42×C83—22no—
143C23×C83—21no—
144C23×C83—21no—
145C23×C83—21no—
146C23×C83—21no—
147C23×C83—22no—
148C23×C83—41no—
149C23×C83—41no—
150C23×C83—41no—
151C23×C83—41no—
152C23×C83—41no—
153C23×C83—41no—
154C23×C83C2×C22⋊C411yescharacteristic
155C23×C83#12012yes—
156C23×C83#13512yes—
157C23×C83AGL(1,ℤ/8)11yescharacteristic
158C23×C83#13711yescharacteristic
159Q8×C83—42no—
160Q8×C83—42no—
161D4×C83—42no—
162D4×C83—42no—
163D4×C83—44no—
164D4×C83—44no—
165C2×C4×C83—21no—
166C2×C4×C83—21no—
167C2×C4×C83—21no—
168C2×C4×C83—21no—
169C2×C4×C83—21no—
170C2×C4×C83—21no—
171C2×C4×C83—21no—
172C2×C4×C83—21no—
173C2×C4×C83—21no—
174C2×C4×C83—22no—
175C2×C4×C83—22no—
176C2×C4×C83—22no—
177C2×C4×C83—21no—
178C2×C4×C83—21no—
179C2×C4×C83—21no—
180C2×C4×C83—21no—
181C2×C4×C83—21no—
182C2×C4×C83—21no—
183C2×C4×C83—42no—
184C2×C4×C83—42no—
185C2×C4×C83—44no—
186C2×C4×C83—48no—
187C2×C4×C83—41no—
188C2×C4×C83—41no—
189C2×C4×C83—41no—
190C2×C4×C83—41no—
191C2×C4×C83—41no—
192C2×C4×C83—41no—
193C2×C4×C83—42no—
194C2×C4×C83—42no—
195C2×C4×C83—44no—
196C2×C4×C83—44no—
197C2×C4×C83—44no—
198C2×C4×C83—82no—
199C2×C4×C83—82no—
200C2×C4×C83—82no—
201C2×C4×C83—82no—
202C2×C4×C83#10412yes—
203C2×C4×C83C2×C22⋊C411yescharacteristic
204C2×C4×C83C2×C22⋊C411yescharacteristic
205C2×C4×C83#12012yes—
206C8×C83—82no—
207C22×C83—22no—
208C22×C83—21no—
209C22×C83—21no—
210C22×C83—21no—
211C22×C83—21no—
212C22×C83—22no—
213C22×C83—22no—
214C22×C83—22no—
215C22×C83—42no—
216C22×C83—42no—
217C22×C83—42no—
218C22×C83—81no—
219C22×C83—81no—
220C22×C83—81no—
221C22×C83—81no—
222C22×C83#37911yescharacteristic
223C22×C83#41011yescharacteristic
224C22×C83#41011yescharacteristic
225C22×C83#41611yescharacteristic
226C22×C83#41711yescharacteristic
227C22×C83C2×#10411yescharacteristic
228C22×C83#42111yescharacteristic
229C22×C83#44912yes—
230C22×C83#45212yes—
231C4×C83—22no—
232C4×C83—21no—
233C4×C83—21no—
234C4×C83—22no—
235C4×C83—42no—
236C4×C83—41no—
237C4×C83—41no—
238C4×C83—42no—
239C4×C83—41no—
240C4×C83—42no—
241C4×C83—84no—
242#8330C8311yesmaximal, characteristic, direct product factor, Sylow
243C2×C83—22no—
244C2×C83—22no—
245C2×C83—82no—
246C2×C83#150011yescharacteristic
247C2×C83#150911yescharacteristic
248C2×C83#151211yescharacteristic
249C2×C83#152111yescharacteristic
250C2×C83#178211yescharacteristic
251C2×C83#178811yescharacteristic
252C2×C83#178911yescharacteristic
253C2×#529C2×C8311yescharacteristic
254#1817C2×C8311yescharacteristic, complemented
255C2×#328C2×C8312yescomplemented
256C2×#327C2×C8312yes—
257#1434C2×C8311yescharacteristic, complemented
258C83#833011yescharacteristic, direct product factor, Sylow
259#529—24no—
260#529—24no—
261C2×#126—21no—
262C2×#125C4×C8311yescharacteristic, complemented
263C2×#124C4×C8311yescharacteristic, complemented
264C2×#123—21no—
265C2×C22⋊Q8C22×C8311yescharacteristic
266C2×#121C22×C8311yescharacteristic
267C2×C4×Q8C4×C8311yescharacteristic, complemented
268C2×C4×D4—21no—
269C2×C4×D4C4×C8311yescharacteristic, complemented
270C2×#117—21no—
271C22×C42C22×C8311yescharacteristic
272C2×C22⋊C8C22×C8312yes—
273C2×#95—21no—
274C2×#95—21no—
275C2×#95C22×C8312yes—
276#336—21no—
277#336—21no—
278#328—24no—
279#327—24no—
280C22×Q8C2×C4×C8311yescharacteristic
281C22×D4—21no—
282C22×D4C2×C4×C8311yescharacteristic
283C23×C4—21no—
284C23×C4—22no—
285C23×C4D4×C8311yescharacteristic
286C23×C4D4×C8311yescharacteristic
287C23×C4C23×C8311yescharacteristic
288C22×C8—22no—
289#126—28no—
290#125—22no—
291#125—22no—
292#124—22no—
293#124—22no—
294#123—28no—
295C22⋊Q8—22no—
296C22⋊Q8D4×C8314yes—
297#121—22no—
298#121D4×C8314yes—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×D4—28no—
302C4×D4—22no—
303C4×D4—22no—
304#117—28no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C2×C4×C8311yescharacteristic
310C2×C4⋊C4C2×C4×C8311yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42C2×C4×C8311yescharacteristic
320C2×C42C2×C4×C8311yescharacteristic
321C2×C42D4×C8311yescharacteristic
322C2×C42D4×C8311yescharacteristic
323C22⋊C8—22no—
324C22⋊C8—22no—
325#95—24no—
326#95—22no—
327#95—22no—
328#95—42no—
329C24—21no—
330C24C2×D4×C8311yescharacteristic
331C2×Q8—21no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8C22⋊C4×C8312yes—
335C2×D4—24no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4C22⋊C4×C8312yes—
343C22×C4—24no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C22⋊C4×C8311yescharacteristic
366C22×C4C22⋊C4×C8311yescharacteristic
367C22×C4C22⋊C4×C8311yescharacteristic
368C22×C4C22⋊C4×C8311yescharacteristic
369C22×C4C22×C4×C8311yescharacteristic
370C22×C4C2×D4×C8311yescharacteristic
371C22×C4C2×D4×C8312yes—
372C22×C4C2×D4×C8312yes—
373C2×C8—42no—
374C2×C8—42no—
375C2×C8—42no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—24no—
382C4⋊C4C22⋊C4×C8312yes—
383C4⋊C4C22⋊C4×C8312yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C42—24no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—21no—
394C42—22no—
395C42—22no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23C2×C22⋊C4×C8311yescharacteristic
408C23#120×C8312yes—
409C23#135×C8312yes—
410C23AGL(1,ℤ/8)×C8311yescharacteristic
411C23#137×C8311yescharacteristic
412Q8—42no—
413Q8—42no—
414D4—42no—
415D4—42no—
416D4—44no—
417D4—44no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—48no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4#104×C8312yes—
456C2×C4C2×C22⋊C4×C8311yescharacteristic
457C2×C4C2×C22⋊C4×C8311yescharacteristic
458C2×C4#120×C8312yes—
459C8—82no—
460C22—22no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22#379×C8311yescharacteristic
476C22#410×C8311yescharacteristic
477C22#410×C8311yescharacteristic
478C22#416×C8311yescharacteristic
479C22#417×C8311yescharacteristic
480C22C2×#104×C8311yescharacteristic
481C22#421×C8311yescharacteristic
482C22#449×C8312yes—
483C22#452×C8312yes—
484C4—22no—
485C4—21no—
486C4—21no—
487C4—22no—
488C4—42no—
489C4—41no—
490C4—41no—
491C4—42no—
492C4—41no—
493C4—42no—
494C4—84no—
495C2—22no—
496C2—22no—
497C2—82no—
498C2C83×#150011yescharacteristic
499C2C83×#150911yescharacteristic
500C2C83×#151211yescharacteristic
501C2C83×#152111yescharacteristic
502C2C83×#178211yescharacteristic
503C2C83×#178811yescharacteristic
504C2C83×#178911yescharacteristic
subgroupG/H
center, socleC23×C83C2×C22⋊C4
commutatorC22×C4C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radicalC2×#121×C83C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#1817C2semidirect
3. C2×#328×C83C2semidirect
5. C83×#1434C2semidirect
9. C2×#125×C83C4semidirect
10. C2×#124×C83C4semidirect
14. C2×C4×Q8×C83C4semidirect
16. C2×C4×D4×C83C4semidirect
242. #8330C83direct (N × H)
254. #1817C2×C83semidirect
255. C2×#328C2×C83semidirect
257. #1434C2×C83semidirect
258. C83#8330direct (N × H)
262. C2×#125C4×C83semidirect
263. C2×#124C4×C83semidirect
267. C2×C4×Q8C4×C83semidirect
269. C2×C4×D4C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C832
C83×#18172
C2×#328×C832
C2×#327×C832
C83×#14342
#833083