Finite Group Databasebeta

← C83×#62147 #35289971

Subgroups — C83×#62147 #35289971

Order 21248.

1734 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3503C211yesmaximal, characteristic, complemented
2C83×#3482C211yesmaximal, characteristic
3Q8×SD16×C83C212yesmaximal, complemented
4C83×#3363C212yesmaximal, complemented
5C83×#3356C216yesmaximal, complemented
6C83×#3331C216yesmaximal, complemented
7C83×#3255C213yesmaximal, complemented
8C83×#3229C213yesmaximal, complemented
9C83×#3107C213yesmaximal, complemented
10C83×#3079C213yesmaximal, complemented
11C83×#2991C211yesmaximal, characteristic, complemented
12Q82×C83C2212yes—
13#557×C83—21no—
14#557×C83C2211yescharacteristic
15#556×C83C2213yes—
16#554×C83C2216yes—
17#552×C83—23no—
18D4×Q8×C83—23no—
19D4×Q8×C83C2211yescharacteristic
20#548×C83—21no—
21#547×C83C2213yes—
22#544×C83—23no—
23#533×C83C2213yes—
24#533×C83C2213yes—
25C2×C4⋊Q8×C83C2213yes—
26#529×C83—23no—
27#520×C83—21no—
28C4×#41×C83C2213yes—
29C4×#41×C83C2211yescharacteristic
30C2×C4×Q8×C83—21no—
31#498×C83C2216yes—
32#487×C83C2216yes—
33#485×C83C2216yes—
34#483×C83C22112yes—
35#477×C83C2216yes—
36#476×C83C2216yes—
37#475×C83C2216yes—
38#475×C83C2216yes—
39#475×C83C2213yes—
40#474×C83C2213yes—
41#470×C83C22112yes—
42#462×C83C2216yes—
43#462×C83C2213yes—
44#461×C83C2211yescharacteristic
45#452×C83C2216yes—
46C8×Q8×C83C2212yes—
47C4×Q16×C83C2216yes—
48C4×SD16×C83C2216yes—
49#436×C83C2216yes—
50#431×C83C2213yes—
51#428×C83C2216yes—
52#423×C83C2213yes—
53#417×C83C2216yes—
54C2×#41×C83D411yescharacteristic
55C2×#41×C83C2313yes—
56C22×Q8×C83—21no—
57C22×Q8×C83—23no—
58C2×Q16×C83C2316yes—
59C2×SD16×C83C2312yes—
60C2×M16×C83C2316yes—
61C4⋊Q8×C83—26no—
62C4⋊Q8×C83—23no—
63C4⋊Q8×C83—23no—
64C4⋊Q8×C83C2313yes—
65C4⋊Q8×C83C2311yescharacteristic
66C4⋊Q8×C83C2313yes—
67C4⋊Q8×C83C2313yes—
68C4⋊Q8×C83C2316yes—
69#126×C83—26no—
70#125×C83—23no—
71#125×C83—26no—
72#125×C83—23no—
73#125×C83—23no—
74#124×C83—23no—
75#123×C83—26no—
76C22⋊Q8×C83—23no—
77C22⋊Q8×C83—23no—
78C22⋊Q8×C83—23no—
79C22⋊Q8×C83—212no—
80C22⋊Q8×C83C2316yes—
81C22⋊Q8×C83C2316yes—
82#121×C83—23no—
83C4×Q8×C83—21no—
84C4×Q8×C83—22no—
85C4×Q8×C83—23no—
86C4×Q8×C83—23no—
87C4×Q8×C83—23no—
88C4×Q8×C83D411yescharacteristic
89C4×Q8×C83C2313yes—
90C4×Q8×C83C2316yes—
91C4×Q8×C83C2313yes—
92C4×Q8×C83C2311yescharacteristic
93C4×D4×C83—26no—
94C4×D4×C83—23no—
95C4×D4×C83—23no—
96C4×D4×C83D413yes—
97C4×D4×C83C2311yescharacteristic
98C4×D4×C83C2313yes—
99C4×D4×C83C2313yes—
100#117×C83—23no—
101#117×C83—23no—
102#117×C83—23no—
103#117×C83D413yes—
104#117×C83C2313yes—
105C2×C4⋊C4×C83—23no—
106C2×C4⋊C4×C83—23no—
107C2×C4⋊C4×C83C2316yes—
108C2×C42×C83—23no—
109C2×C42×C83C2313yes—
110#107×C83C2316yes—
111#106×C83C23112yes—
112#106×C83C2316yes—
113C4⋊C8×C83C2313yes—
114C4⋊C8×C83C2311yescharacteristic
115C4⋊C8×C83C2316yes—
116#103×C83C2316yes—
117#103×C83C23112yes—
118#103×C83C2316yes—
119#103×C83C2312yes—
120#102×C83C2316yes—
121C22⋊C8×C83C2316yes—
122C4×C8×C83C2316yes—
123#41×C83—24no—
124#41×C83—26no—
125#41×C83—43no—
126C2×Q8×C83—23no—
127C2×Q8×C83—23no—
128C2×Q8×C83—26no—
129C2×Q8×C83—44no—
130C2×Q8×C83—86no—
131C2×Q8×C83C2×D411yescharacteristic
132C2×Q8×C83C2413yes—
133C2×Q8×C83C2412yes—
134C2×D4×C83—23no—
135C2×D4×C83C2×D413yes—
136C2×D4×C83C2411yescharacteristic
137C22×C4×C83—26no—
138C22×C4×C83—21no—
139C22×C4×C83—23no—
140C22×C4×C83—23no—
141C22×C4×C83C2×D413yes—
142C22×C4×C83C2×D413yes—
143C22×C4×C83C2413yes—
144Q16×C83—46no—
145SD16×C83—24no—
146M16×C83—46no—
147C2×C8×C83C2412yes—
148C2×C8×C83C2416yes—
149C4⋊C4×C83—23no—
150C4⋊C4×C83—26no—
151C4⋊C4×C83—23no—
152C4⋊C4×C83—26no—
153C4⋊C4×C83—26no—
154C4⋊C4×C83—21no—
155C4⋊C4×C83—23no—
156C4⋊C4×C83—23no—
157C4⋊C4×C83—23no—
158C4⋊C4×C83—23no—
159C4⋊C4×C83—21no—
160C4⋊C4×C83—26no—
161C4⋊C4×C83—26no—
162C4⋊C4×C83C2×D413yes—
163C4⋊C4×C83C2×D413yes—
164C4⋊C4×C83C2416yes—
165C4⋊C4×C83C2413yes—
166C4⋊C4×C83C2411yescharacteristic
167C22⋊C4×C83—26no—
168C22⋊C4×C83—26no—
169C22⋊C4×C83—23no—
170C22⋊C4×C83—21no—
171C22⋊C4×C83—23no—
172C22⋊C4×C83C2×D416yes—
173C42×C83—23no—
174C42×C83—23no—
175C42×C83—23no—
176C42×C83—26no—
177C42×C83C2×D413yes—
178C42×C83C2×D413yes—
179C42×C83C2413yes—
180C42×C83C2411yescharacteristic
181C23×C83—21no—
182C23×C83C22×D413yes—
183Q8×C83—22no—
184Q8×C83—23no—
185Q8×C83—22no—
186Q8×C83—23no—
187Q8×C83—46no—
188Q8×C83—46no—
189Q8×C83—86no—
190Q8×C83#13714yes—
191D4×C83—26no—
192D4×C83—21no—
193D4×C83—46no—
194D4×C832−1+412yes—
195C2×C4×C83—26no—
196C2×C4×C83—26no—
197C2×C4×C83—23no—
198C2×C4×C83—23no—
199C2×C4×C83—21no—
200C2×C4×C83—22no—
201C2×C4×C83—23no—
202C2×C4×C83—23no—
203C2×C4×C83—26no—
204C2×C4×C83—46no—
205C2×C4×C83—46no—
206C2×C4×C83—42no—
207C2×C4×C83—86no—
208C2×C4×C83C22×D413yes—
209C2×C4×C83C22×D411yescharacteristic
210C2×C4×C83C22×D413yes—
211C2×C4×C83C22×D413yes—
212C2×C4×C83C22×D411yescharacteristic
213C2×C4×C83C2511yescharacteristic
214C8×C83—22no—
215C8×C83—26no—
216C22×C83—23no—
217C22×C83—22no—
218C22×C83—23no—
219C22×C83—23no—
220C22×C83—41no—
221C22×C83—41no—
222C22×C83C23×D411yescharacteristic
223C4×C83—23no—
224C4×C83—21no—
225C4×C83—23no—
226C4×C83—43no—
227C4×C83—42no—
228C4×C83—43no—
229C4×C83—41no—
230C4×C83—46no—
231C4×C83C2×#13716yes—
232C4×C83#57712yes—
233C4×C83C2×2−1+411yescharacteristic
234C4×C83#58511yescharacteristic
235#62147C8311yesmaximal, characteristic, direct product factor, Sylow
236C2×C83—43no—
237C2×C83—42no—
238C2×C83#348911yescharacteristic
239C2×C83C22×#13711yescharacteristic
240C2×C83C2×#57711yescharacteristic
241#3503C2×C8311yescharacteristic, complemented
242#3482C2×C8311yescharacteristic
243Q8×SD16C2×C8312yescomplemented
244#3363C2×C8312yescomplemented
245#3356C2×C8316yescomplemented
246#3331C2×C8316yescomplemented
247#3255C2×C8313yescomplemented
248#3229C2×C8313yescomplemented
249#3107C2×C8313yescomplemented
250#3079C2×C8313yescomplemented
251#2991C2×C8311yescharacteristic, complemented
252C83#6214711yescharacteristic, direct product factor, Sylow
253Q82C22×C8312yes—
254#557—21no—
255#557C22×C8311yescharacteristic
256#556C22×C8313yes—
257#554C22×C8316yes—
258#552—23no—
259D4×Q8—23no—
260D4×Q8C22×C8311yescharacteristic
261#548—21no—
262#547C22×C8313yes—
263#544—23no—
264#533C22×C8313yes—
265#533C22×C8313yes—
266C2×C4⋊Q8C22×C8313yes—
267#529—23no—
268#520—21no—
269C4×#41C22×C8313yes—
270C4×#41C22×C8311yescharacteristic
271C2×C4×Q8—21no—
272#498C22×C8316yes—
273#487C22×C8316yes—
274#485C22×C8316yes—
275#483C22×C83112yes—
276#477C22×C8316yes—
277#476C22×C8316yes—
278#475C22×C8316yes—
279#475C22×C8316yes—
280#475C22×C8313yes—
281#474C22×C8313yes—
282#470C22×C83112yes—
283#462C22×C8316yes—
284#462C22×C8313yes—
285#461C22×C8311yescharacteristic
286#452C22×C8316yes—
287C8×Q8C22×C8312yes—
288C4×Q16C22×C8316yes—
289C4×SD16C22×C8316yes—
290#436C22×C8316yes—
291#431C22×C8313yes—
292#428C22×C8316yes—
293#423C22×C8313yes—
294#417C22×C8316yes—
295C2×#41D4×C8311yescharacteristic
296C2×#41C23×C8313yes—
297C22×Q8—21no—
298C22×Q8—23no—
299C2×Q16C23×C8316yes—
300C2×SD16C23×C8312yes—
301C2×M16C23×C8316yes—
302C4⋊Q8—26no—
303C4⋊Q8—23no—
304C4⋊Q8—23no—
305C4⋊Q8C23×C8311yescharacteristic
306C4⋊Q8C23×C8313yes—
307C4⋊Q8C23×C8313yes—
308C4⋊Q8C23×C8316yes—
309C4⋊Q8C23×C8313yes—
310#126—26no—
311#125—23no—
312#125—26no—
313#125—23no—
314#125—23no—
315#124—23no—
316#123—26no—
317C22⋊Q8—23no—
318C22⋊Q8—23no—
319C22⋊Q8—23no—
320C22⋊Q8—212no—
321C22⋊Q8C23×C8316yes—
322C22⋊Q8C23×C8316yes—
323#121—23no—
324C4×Q8—21no—
325C4×Q8—22no—
326C4×Q8—23no—
327C4×Q8—23no—
328C4×Q8—23no—
329C4×Q8D4×C8311yescharacteristic
330C4×Q8C23×C8313yes—
331C4×Q8C23×C8313yes—
332C4×Q8C23×C8316yes—
333C4×Q8C23×C8311yescharacteristic
334C4×D4—26no—
335C4×D4—23no—
336C4×D4—23no—
337C4×D4D4×C8313yes—
338C4×D4C23×C8311yescharacteristic
339C4×D4C23×C8313yes—
340C4×D4C23×C8313yes—
341#117—23no—
342#117—23no—
343#117—23no—
344#117D4×C8313yes—
345#117C23×C8313yes—
346C2×C4⋊C4—23no—
347C2×C4⋊C4—23no—
348C2×C4⋊C4C23×C8316yes—
349C2×C42—23no—
350C2×C42C23×C8313yes—
351#107C23×C8316yes—
352#106C23×C83112yes—
353#106C23×C8316yes—
354C4⋊C8C23×C8313yes—
355C4⋊C8C23×C8316yes—
356C4⋊C8C23×C8311yescharacteristic
357#103C23×C83112yes—
358#103C23×C8316yes—
359#103C23×C8312yes—
360#103C23×C8316yes—
361#102C23×C8316yes—
362C22⋊C8C23×C8316yes—
363C4×C8C23×C8316yes—
364#41—24no—
365#41—26no—
366#41—43no—
367C2×Q8—23no—
368C2×Q8—23no—
369C2×Q8—26no—
370C2×Q8—44no—
371C2×Q8—86no—
372C2×Q8C2×D4×C8311yescharacteristic
373C2×Q8C24×C8313yes—
374C2×Q8C24×C8312yes—
375C2×D4—23no—
376C2×D4C2×D4×C8313yes—
377C2×D4C24×C8311yescharacteristic
378C22×C4—26no—
379C22×C4—21no—
380C22×C4—23no—
381C22×C4—23no—
382C22×C4C2×D4×C8313yes—
383C22×C4C2×D4×C8313yes—
384C22×C4C24×C8313yes—
385Q16—46no—
386SD16—24no—
387M16—46no—
388C2×C8C24×C8312yes—
389C2×C8C24×C8316yes—
390C4⋊C4—23no—
391C4⋊C4—26no—
392C4⋊C4—23no—
393C4⋊C4—26no—
394C4⋊C4—26no—
395C4⋊C4—21no—
396C4⋊C4—23no—
397C4⋊C4—23no—
398C4⋊C4—23no—
399C4⋊C4—23no—
400C4⋊C4—21no—
401C4⋊C4—26no—
402C4⋊C4—26no—
403C4⋊C4C2×D4×C8313yes—
404C4⋊C4C2×D4×C8313yes—
405C4⋊C4C24×C8316yes—
406C4⋊C4C24×C8313yes—
407C4⋊C4C24×C8311yescharacteristic
408C22⋊C4—26no—
409C22⋊C4—26no—
410C22⋊C4—23no—
411C22⋊C4—21no—
412C22⋊C4—23no—
413C22⋊C4C2×D4×C8316yes—
414C42—23no—
415C42—23no—
416C42—23no—
417C42—26no—
418C42C2×D4×C8313yes—
419C42C2×D4×C8313yes—
420C42C24×C8313yes—
421C42C24×C8311yescharacteristic
422C23—21no—
423C23C22×D4×C8313yes—
424Q8—22no—
425Q8—23no—
426Q8—22no—
427Q8—23no—
428Q8—46no—
429Q8—46no—
430Q8—86no—
431Q8#137×C8314yes—
432D4—26no—
433D4—21no—
434D4—46no—
435D42−1+4×C8312yes—
436C2×C4—26no—
437C2×C4—26no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—26no—
445C2×C4—46no—
446C2×C4—46no—
447C2×C4—42no—
448C2×C4—86no—
449C2×C4C22×D4×C8313yes—
450C2×C4C22×D4×C8311yescharacteristic
451C2×C4C22×D4×C8313yes—
452C2×C4C22×D4×C8313yes—
453C2×C4C22×D4×C8311yescharacteristic
454C2×C4C25×C8311yescharacteristic
455C8—22no—
456C8—26no—
457C22—23no—
458C22—23no—
459C22—23no—
460C22—22no—
461C22—41no—
462C22—41no—
463C22C23×D4×C8311yescharacteristic
464C4—21no—
465C4—23no—
466C4—23no—
467C4—43no—
468C4—41no—
469C4—46no—
470C4—43no—
471C4—42no—
472C4C2×#137×C8316yes—
473C4#577×C8312yes—
474C4C2×2−1+4×C8311yescharacteristic
475C4#585×C8311yescharacteristic
476C2—43no—
477C2—42no—
478C2C83×#348911yescharacteristic
479C2C22×#137×C8311yescharacteristic
480C2C2×#577×C8311yescharacteristic
subgroupG/H
center, socleC22×C83C23×D4
commutator, Frattini, cosocleC2×C4C25×C83
prime radicalC83×#3482C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C4×#41×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3503C2semidirect
3. Q8×SD16×C83C2semidirect
4. C83×#3363C2semidirect
5. C83×#3356C2semidirect
6. C83×#3331C2semidirect
7. C83×#3255C2semidirect
8. C83×#3229C2semidirect
9. C83×#3107C2semidirect
10. C83×#3079C2semidirect
11. C83×#2991C2semidirect
235. #62147C83direct (N × H)
241. #3503C2×C83semidirect
243. Q8×SD16C2×C83semidirect
244. #3363C2×C83semidirect
245. #3356C2×C83semidirect
246. #3331C2×C83semidirect
247. #3255C2×C83semidirect
248. #3229C2×C83semidirect
249. #3107C2×C83semidirect
250. #3079C2×C83semidirect
251. #2991C2×C83semidirect
252. C83#62147direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#35032
C83×#34822
Q8×SD16×C832
C83×#33632
C83×#33562
C83×#33312
C83×#32552
C83×#32292
C83×#31072
C83×#30792
C83×#29912
#6214783