Finite Group Databasebeta

← C83×#3309 #24904994

Subgroups — C83×#3309 #24904994

Order 10624.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#553×C83C211yesmaximal, characteristic, complemented
2#550×C83C211yesmaximal, characteristic, complemented
3#490×C83C211yesmaximal, characteristic, complemented
4#482×C83C211yesmaximal, characteristic, complemented
5#480×C83C211yesmaximal, characteristic, complemented
6#479×C83C211yesmaximal, characteristic, complemented
7#469×C83C211yesmaximal, characteristic, complemented
8#466×C83C211yesmaximal, characteristic, complemented
9#459×C83C211yesmaximal, characteristic, complemented
10#449×C83C211yesmaximal, characteristic, complemented
11#449×C83C211yesmaximal, characteristic, complemented
12#440×C83C211yesmaximal, characteristic, complemented
13#435×C83C211yesmaximal, characteristic, complemented
14#417×C83C211yesmaximal, characteristic, complemented
15#416×C83C211yesmaximal, characteristic, complemented
16C2×#41×C83C2211yescharacteristic
17C2×#41×C83C2211yescharacteristic
18C2×SD16×C83C2211yescharacteristic
19C2×D8×C83C2211yescharacteristic
20C2×D8×C83C2211yescharacteristic
21C2×M16×C83C2211yescharacteristic
22C22×C8×C83C2211yescharacteristic
23#127×C83—21no—
24#127×C83C2211yescharacteristic
25#126×C83—21no—
26#125×C83C2211yescharacteristic
27#123×C83—21no—
28#121×C83—21no—
29#121×C83—21no—
30#121×C83—21no—
31#121×C83C2211yescharacteristic
32#121×C83C2211yescharacteristic
33#121×C83C2211yescharacteristic
34#121×C83C2211yescharacteristic
35C4×Q8×C83C2211yescharacteristic
36C4×D4×C83—21no—
37C4×D4×C83—21no—
38C4×D4×C83C2211yescharacteristic
39C4×D4×C83C2211yescharacteristic
40#117×C83C2211yescharacteristic
41C2×C4⋊C4×C83C2211yescharacteristic
42#107×C83C2211yescharacteristic
43#107×C83C2211yescharacteristic
44#106×C83C2211yescharacteristic
45C4⋊C8×C83C2211yescharacteristic
46#103×C83C2211yescharacteristic
47#103×C83C2211yescharacteristic
48#103×C83C2211yescharacteristic
49#102×C83C2211yescharacteristic
50#102×C83C2211yescharacteristic
51#102×C83C2211yescharacteristic
52#102×C83C2211yescharacteristic
53#102×C83C2211yescharacteristic
54#102×C83C2211yescharacteristic
55#102×C83C2211yescharacteristic
56C22⋊C8×C83C2211yescharacteristic
57C22⋊C8×C83C2211yescharacteristic
58#97×C83C2211yescharacteristic
59#41×C83—22no—
60#41×C83—22no—
61#41×C83—41no—
62#41×C83—41no—
63C2×Q8×C83C2311yescharacteristic
64C2×D4×C83—21no—
65C2×D4×C83—21no—
66C2×D4×C83—21no—
67C2×D4×C83—21no—
68C2×D4×C83—21no—
69C2×D4×C83—21no—
70C2×D4×C83—21no—
71C2×D4×C83—21no—
72C2×D4×C83D411yescharacteristic
73C2×D4×C83C2311yescharacteristic
74C2×D4×C83C2311yescharacteristic
75C2×D4×C83C2311yescharacteristic
76C22×C4×C83—21no—
77C22×C4×C83—21no—
78C22×C4×C83—21no—
79C22×C4×C83—21no—
80C22×C4×C83C2311yescharacteristic
81C22×C4×C83C2311yescharacteristic
82SD16×C83—22no—
83D8×C83—41no—
84D8×C83—41no—
85M16×C83—41no—
86C2×C8×C83—41no—
87C2×C8×C83C2311yescharacteristic
88C2×C8×C83C2311yescharacteristic
89C2×C8×C83C2311yescharacteristic
90C2×C8×C83C2311yescharacteristic
91C4⋊C4×C83—21no—
92C4⋊C4×C83—21no—
93C4⋊C4×C83—21no—
94C4⋊C4×C83—21no—
95C4⋊C4×C83D411yescharacteristic
96C4⋊C4×C83C2311yescharacteristic
97C4⋊C4×C83C2311yescharacteristic
98C4⋊C4×C83C2311yescharacteristic
99C4⋊C4×C83C2311yescharacteristic
100C22⋊C4×C83—21no—
101C22⋊C4×C83—21no—
102C22⋊C4×C83—21no—
103C22⋊C4×C83—21no—
104C22⋊C4×C83—21no—
105C22⋊C4×C83—21no—
106C22⋊C4×C83D411yescharacteristic
107C22⋊C4×C83D411yescharacteristic
108C42×C83—21no—
109C42×C83—21no—
110C42×C83C2311yescharacteristic
111C23×C83—21no—
112C23×C83—21no—
113C23×C83—21no—
114C23×C83C2×D411yescharacteristic
115C23×C83C2×D411yescharacteristic
116Q8×C83—21no—
117Q8×C83#4112yes—
118D4×C83—21no—
119D4×C83—21no—
120D4×C83—21no—
121D4×C83—21no—
122D4×C83—21no—
123D4×C83—21no—
124D4×C83—41no—
125D4×C83—42no—
126D4×C83—42no—
127D4×C83—42no—
128D4×C83—42no—
129D4×C83—81no—
130D4×C83—81no—
131D4×C83—81no—
132D4×C83—81no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—42no—
143C2×C4×C83—42no—
144C2×C4×C83—81no—
145C2×C4×C83—81no—
146C2×C4×C83C2×D411yescharacteristic
147C2×C4×C83C2×D411yescharacteristic
148C2×C4×C83C2×D411yescharacteristic
149C2×C4×C83C2×D411yescharacteristic
150C2×C4×C83C2411yescharacteristic
151C8×C83—21no—
152C8×C83—21no—
153C8×C83—21no—
154C8×C83—21no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83—41no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83C22×D411yescharacteristic
171C4×C83—21no—
172C4×C83—21no—
173C4×C83—22no—
174C4×C83—21no—
175C4×C83—21no—
176C4×C83—41no—
177C4×C83—41no—
178C4×C83—41no—
179C4×C83—41no—
180C4×C83C2×#4111yescharacteristic
181C4×C83H(5,𝔽2)11yescharacteristic
182C2×C83—41no—
183C2×C83—41no—
184C2×C83—81no—
185C2×C83—81no—
186C2×C83—81no—
187C2×C83#54611yescharacteristic
188C2×C83#57511yescharacteristic
189C2×C83#57611yescharacteristic
190#3309C8311yesmaximal, characteristic, direct product factor, Sylow
191C83#330911yescharacteristic, direct product factor, Sylow
192#553C2×C8311yescharacteristic, complemented
193#550C2×C8311yescharacteristic, complemented
194#490C2×C8311yescharacteristic, complemented
195#482C2×C8311yescharacteristic, complemented
196#480C2×C8311yescharacteristic, complemented
197#479C2×C8311yescharacteristic, complemented
198#469C2×C8311yescharacteristic, complemented
199#466C2×C8311yescharacteristic, complemented
200#459C2×C8311yescharacteristic, complemented
201#449C2×C8311yescharacteristic, complemented
202#449C2×C8311yescharacteristic, complemented
203#440C2×C8311yescharacteristic, complemented
204#435C2×C8311yescharacteristic, complemented
205#417C2×C8311yescharacteristic, complemented
206#416C2×C8311yescharacteristic, complemented
207C2×#41C22×C8311yescharacteristic
208C2×#41C22×C8311yescharacteristic
209C2×SD16C22×C8311yescharacteristic
210C2×D8C22×C8311yescharacteristic
211C2×D8C22×C8311yescharacteristic
212C2×M16C22×C8311yescharacteristic
213C22×C8C22×C8311yescharacteristic
214#127—21no—
215#127C22×C8311yescharacteristic
216#126—21no—
217#125C22×C8311yescharacteristic
218#123—21no—
219#121—21no—
220#121—21no—
221#121—21no—
222#121C22×C8311yescharacteristic
223#121C22×C8311yescharacteristic
224#121C22×C8311yescharacteristic
225#121C22×C8311yescharacteristic
226C4×Q8C22×C8311yescharacteristic
227C4×D4—21no—
228C4×D4—21no—
229C4×D4C22×C8311yescharacteristic
230C4×D4C22×C8311yescharacteristic
231#117C22×C8311yescharacteristic
232C2×C4⋊C4C22×C8311yescharacteristic
233#107C22×C8311yescharacteristic
234#107C22×C8311yescharacteristic
235#106C22×C8311yescharacteristic
236C4⋊C8C22×C8311yescharacteristic
237#103C22×C8311yescharacteristic
238#103C22×C8311yescharacteristic
239#103C22×C8311yescharacteristic
240#102C22×C8311yescharacteristic
241#102C22×C8311yescharacteristic
242#102C22×C8311yescharacteristic
243#102C22×C8311yescharacteristic
244#102C22×C8311yescharacteristic
245#102C22×C8311yescharacteristic
246#102C22×C8311yescharacteristic
247C22⋊C8C22×C8311yescharacteristic
248C22⋊C8C22×C8311yescharacteristic
249#97C22×C8311yescharacteristic
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C23×C8311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4D4×C8311yescharacteristic
264C2×D4C23×C8311yescharacteristic
265C2×D4C23×C8311yescharacteristic
266C2×D4C23×C8311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4C23×C8311yescharacteristic
272C22×C4C23×C8311yescharacteristic
273SD16—22no—
274D8—41no—
275D8—41no—
276M16—41no—
277C2×C8—41no—
278C2×C8C23×C8311yescharacteristic
279C2×C8C23×C8311yescharacteristic
280C2×C8C23×C8311yescharacteristic
281C2×C8C23×C8311yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4D4×C8311yescharacteristic
287C4⋊C4C23×C8311yescharacteristic
288C4⋊C4C23×C8311yescharacteristic
289C4⋊C4C23×C8311yescharacteristic
290C4⋊C4C23×C8311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4D4×C8311yescharacteristic
298C22⋊C4D4×C8311yescharacteristic
299C42—21no—
300C42—21no—
301C42C23×C8311yescharacteristic
302C23—21no—
303C23—21no—
304C23—21no—
305C23C2×D4×C8311yescharacteristic
306C23C2×D4×C8311yescharacteristic
307Q8—21no—
308Q8#41×C8312yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—41no—
316D4—42no—
317D4—42no—
318D4—42no—
319D4—42no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C2×D4×C8311yescharacteristic
338C2×C4C2×D4×C8311yescharacteristic
339C2×C4C2×D4×C8311yescharacteristic
340C2×C4C2×D4×C8311yescharacteristic
341C2×C4C24×C8311yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×D4×C8311yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4C2×#41×C8311yescharacteristic
372C4H(5,𝔽2)×C8311yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—81no—
378C2#546×C8311yescharacteristic
379C2#575×C8311yescharacteristic
380C2#576×C8311yescharacteristic
subgroupG/H
center, socleC22×C83C22×D4
commutator, Frattini, cosocleC2×C4C24×C83
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. #553×C83C2semidirect
2. #550×C83C2semidirect
3. #490×C83C2semidirect
4. #482×C83C2semidirect
5. #480×C83C2semidirect
6. #479×C83C2semidirect
7. #469×C83C2semidirect
8. #466×C83C2semidirect
9. #459×C83C2semidirect
10. #449×C83C2semidirect
11. #449×C83C2semidirect
12. #440×C83C2semidirect
13. #435×C83C2semidirect
14. #417×C83C2semidirect
15. #416×C83C2semidirect
190. #3309C83direct (N × H)
191. C83#3309direct (N × H)
192. #553C2×C83semidirect
193. #550C2×C83semidirect
194. #490C2×C83semidirect
195. #482C2×C83semidirect
196. #480C2×C83semidirect
197. #479C2×C83semidirect
198. #469C2×C83semidirect
199. #466C2×C83semidirect
200. #459C2×C83semidirect
201. #449C2×C83semidirect
202. #449C2×C83semidirect
203. #440C2×C83semidirect
204. #435C2×C83semidirect
205. #417C2×C83semidirect
206. #416C2×C83semidirect

Maximal subgroups

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

subgroupindex
#553×C832
#550×C832
#490×C832
#482×C832
#480×C832
#479×C832
#469×C832
#466×C832
#459×C832
#449×C832
#440×C832
#435×C832
#417×C832
#416×C832
#330983