Finite Group Databasebeta

← C83×#3124 #24904809

Subgroups — C83×#3124 #24904809

Order 10624.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#542×C83C211yesmaximal, characteristic, complemented
2#520×C83C211yesmaximal, characteristic, complemented
3#484×C83C211yesmaximal, characteristic, complemented
4#480×C83C211yesmaximal, characteristic, complemented
5#477×C83C211yesmaximal, characteristic, complemented
6#474×C83C211yesmaximal, characteristic, complemented
7#464×C83C211yesmaximal, characteristic, complemented
8#463×C83C211yesmaximal, characteristic, complemented
9#452×C83C211yesmaximal, characteristic, complemented
10#449×C83C211yesmaximal, characteristic
11#440×C83C211yesmaximal, characteristic, complemented
12#440×C83C211yesmaximal, characteristic, complemented
13C4×Q16×C83C211yesmaximal, characteristic, complemented
14C4×D8×C83C211yesmaximal, characteristic, complemented
15#433×C83C211yesmaximal, characteristic, complemented
16C2×#41×C83C2211yescharacteristic
17C2×Q16×C83C2211yescharacteristic
18C2×SD16×C83C2211yescharacteristic
19C2×SD16×C83C2211yescharacteristic
20C2×D8×C83C2211yescharacteristic
21C4⋊Q8×C83C2211yescharacteristic
22#126×C83—21no—
23#124×C83—21no—
24#124×C83C2211yescharacteristic
25#123×C83—21no—
26C22⋊Q8×C83—21no—
27C22⋊Q8×C83C2211yescharacteristic
28#121×C83C2211yescharacteristic
29C4×Q8×C83C2211yescharacteristic
30C4×Q8×C83C2211yescharacteristic
31C4×Q8×C83C2211yescharacteristic
32C4×D4×C83—21no—
33C4×D4×C83—21no—
34C4×D4×C83C2211yescharacteristic
35C4×D4×C83C2211yescharacteristic
36C4×D4×C83C2211yescharacteristic
37#117×C83—21no—
38#117×C83C2211yescharacteristic
39C2×C4⋊C4×C83—21no—
40C2×C4⋊C4×C83C2211yescharacteristic
41#107×C83C2211yescharacteristic
42#107×C83C2211yescharacteristic
43#107×C83C2211yescharacteristic
44#107×C83C2211yescharacteristic
45C4⋊C8×C83C2211yescharacteristic
46C4⋊C8×C83C2211yescharacteristic
47#103×C83C2211yescharacteristic
48#103×C83C2211yescharacteristic
49#103×C83C2211yescharacteristic
50#103×C83C2211yescharacteristic
51#102×C83C2211yescharacteristic
52#102×C83C2211yescharacteristic
53#102×C83C2211yescharacteristic
54#102×C83C2211yescharacteristic
55C22⋊C8×C83C2211yescharacteristic
56C22⋊C8×C83C2211yescharacteristic
57#97×C83C2211yescharacteristic
58C4×C8×C83C2211yescharacteristic
59#41×C83—22no—
60#41×C83—22no—
61C2×Q8×C83—21no—
62C2×Q8×C83C2311yescharacteristic
63C2×Q8×C83C2311yescharacteristic
64C2×D4×C83—21no—
65C2×D4×C83—21no—
66C2×D4×C83C2311yescharacteristic
67C2×D4×C83C2311yescharacteristic
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83C2311yescharacteristic
74Q16×C83—22no—
75SD16×C83—22no—
76SD16×C83—22no—
77D8×C83—22no—
78C2×C8×C83C2311yescharacteristic
79C2×C8×C83C2311yescharacteristic
80C2×C8×C83C2311yescharacteristic
81C2×C8×C83C2311yescharacteristic
82C4⋊C4×C83—21no—
83C4⋊C4×C83—21no—
84C4⋊C4×C83—21no—
85C4⋊C4×C83—21no—
86C4⋊C4×C83—21no—
87C4⋊C4×C83—21no—
88C4⋊C4×C83D411yescharacteristic
89C4⋊C4×C83D411yescharacteristic
90C4⋊C4×C83C2311yescharacteristic
91C4⋊C4×C83C2311yescharacteristic
92C4⋊C4×C83C2311yescharacteristic
93C4⋊C4×C83C2311yescharacteristic
94C22⋊C4×C83—21no—
95C22⋊C4×C83—21no—
96C22⋊C4×C83—21no—
97C22⋊C4×C83—21no—
98C22⋊C4×C83—21no—
99C22⋊C4×C83—21no—
100C22⋊C4×C83—21no—
101C22⋊C4×C83D411yescharacteristic
102C22⋊C4×C83D411yescharacteristic
103C42×C83—21no—
104C42×C83—21no—
105C42×C83—21no—
106C42×C83C2311yescharacteristic
107C42×C83C2311yescharacteristic
108C23×C83—21no—
109C23×C83—21no—
110C23×C83C2×D411yescharacteristic
111Q8×C83—21no—
112Q8×C83—21no—
113Q8×C83—21no—
114Q8×C83—81no—
115Q8×C83#4112yes—
116D4×C83—24no—
117D4×C83—21no—
118D4×C83—21no—
119D4×C83—21no—
120D4×C83—81no—
121D4×C83#4112yes—
122C2×C4×C83—24no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—81no—
132C2×C4×C83—81no—
133C2×C4×C83—81no—
134C2×C4×C83—81no—
135C2×C4×C83C2×D411yescharacteristic
136C2×C4×C83C2×D411yescharacteristic
137C2×C4×C83C2×D411yescharacteristic
138C2×C4×C83C2×D411yescharacteristic
139C2×C4×C83C2×D411yescharacteristic
140C2×C4×C83C2411yescharacteristic
141C8×C83—21no—
142C8×C83—21no—
143C8×C83—21no—
144C8×C83—21no—
145C22×C83—21no—
146C22×C83—22no—
147C22×C83—21no—
148C22×C83—21no—
149C22×C83—41no—
150C22×C83—41no—
151C22×C83—41no—
152C22×C83—41no—
153C22×C83—41no—
154C22×C83C22×D411yescharacteristic
155C4×C83—21no—
156C4×C83—22no—
157C4×C83—21no—
158C4×C83—21no—
159C4×C83—21no—
160C4×C83—21no—
161C4×C83—41no—
162C4×C83—41no—
163C4×C83—41no—
164C4×C83—41no—
165C4×C83—41no—
166C4×C83C2×#4111yescharacteristic
167C4×C83C2×#4111yescharacteristic
168C2×C83—41no—
169C2×C83—42no—
170C2×C83—81no—
171C2×C83#52511yescharacteristic
172C2×C83#57611yescharacteristic
173C2×C83#57811yescharacteristic
174#3124C8311yesmaximal, characteristic, direct product factor, Sylow
175C83#312411yescharacteristic, direct product factor, Sylow
176#542C2×C8311yescharacteristic, complemented
177#520C2×C8311yescharacteristic, complemented
178#484C2×C8311yescharacteristic, complemented
179#480C2×C8311yescharacteristic, complemented
180#477C2×C8311yescharacteristic, complemented
181#474C2×C8311yescharacteristic, complemented
182#464C2×C8311yescharacteristic, complemented
183#463C2×C8311yescharacteristic, complemented
184#452C2×C8311yescharacteristic, complemented
185#449C2×C8311yescharacteristic
186#440C2×C8311yescharacteristic, complemented
187#440C2×C8311yescharacteristic, complemented
188C4×Q16C2×C8311yescharacteristic, complemented
189C4×D8C2×C8311yescharacteristic, complemented
190#433C2×C8311yescharacteristic, complemented
191C2×#41C22×C8311yescharacteristic
192C2×Q16C22×C8311yescharacteristic
193C2×SD16C22×C8311yescharacteristic
194C2×SD16C22×C8311yescharacteristic
195C2×D8C22×C8311yescharacteristic
196C4⋊Q8C22×C8311yescharacteristic
197#126—21no—
198#124—21no—
199#124C22×C8311yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C22×C8311yescharacteristic
203#121C22×C8311yescharacteristic
204C4×Q8C22×C8311yescharacteristic
205C4×Q8C22×C8311yescharacteristic
206C4×Q8C22×C8311yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4C22×C8311yescharacteristic
210C4×D4C22×C8311yescharacteristic
211C4×D4C22×C8311yescharacteristic
212#117—21no—
213#117C22×C8311yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C22×C8311yescharacteristic
216#107C22×C8311yescharacteristic
217#107C22×C8311yescharacteristic
218#107C22×C8311yescharacteristic
219#107C22×C8311yescharacteristic
220C4⋊C8C22×C8311yescharacteristic
221C4⋊C8C22×C8311yescharacteristic
222#103C22×C8311yescharacteristic
223#103C22×C8311yescharacteristic
224#103C22×C8311yescharacteristic
225#103C22×C8311yescharacteristic
226#102C22×C8311yescharacteristic
227#102C22×C8311yescharacteristic
228#102C22×C8311yescharacteristic
229#102C22×C8311yescharacteristic
230C22⋊C8C22×C8311yescharacteristic
231C22⋊C8C22×C8311yescharacteristic
232#97C22×C8311yescharacteristic
233C4×C8C22×C8311yescharacteristic
234#41—22no—
235#41—22no—
236C2×Q8—21no—
237C2×Q8C23×C8311yescharacteristic
238C2×Q8C23×C8311yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C23×C8311yescharacteristic
242C2×D4C23×C8311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4C23×C8311yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—22no—
252D8—22no—
253C2×C8C23×C8311yescharacteristic
254C2×C8C23×C8311yescharacteristic
255C2×C8C23×C8311yescharacteristic
256C2×C8C23×C8311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4D4×C8311yescharacteristic
264C4⋊C4D4×C8311yescharacteristic
265C4⋊C4C23×C8311yescharacteristic
266C4⋊C4C23×C8311yescharacteristic
267C4⋊C4C23×C8311yescharacteristic
268C4⋊C4C23×C8311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4D4×C8311yescharacteristic
277C22⋊C4D4×C8311yescharacteristic
278C42—21no—
279C42—21no—
280C42—21no—
281C42C23×C8311yescharacteristic
282C42C23×C8311yescharacteristic
283C23—21no—
284C23—21no—
285C23C2×D4×C8311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—81no—
290Q8#41×C8312yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#41×C8312yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4C2×D4×C8311yescharacteristic
311C2×C4C2×D4×C8311yescharacteristic
312C2×C4C2×D4×C8311yescharacteristic
313C2×C4C2×D4×C8311yescharacteristic
314C2×C4C2×D4×C8311yescharacteristic
315C2×C4C24×C8311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C22×D4×C8311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4C2×#41×C8311yescharacteristic
342C4C2×#41×C8311yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#525×C8311yescharacteristic
347C2#576×C8311yescharacteristic
348C2#578×C8311yescharacteristic
subgroupG/H
center, socleC22×C83C22×D4
commutator, Frattini, cosocleC2×C4C24×C83
prime radical#449×C83C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ #117×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. #542×C83C2semidirect
2. #520×C83C2semidirect
3. #484×C83C2semidirect
4. #480×C83C2semidirect
5. #477×C83C2semidirect
6. #474×C83C2semidirect
7. #464×C83C2semidirect
8. #463×C83C2semidirect
9. #452×C83C2semidirect
11. #440×C83C2semidirect
12. #440×C83C2semidirect
13. C4×Q16×C83C2semidirect
14. C4×D8×C83C2semidirect
15. #433×C83C2semidirect
174. #3124C83direct (N × H)
175. C83#3124direct (N × H)
176. #542C2×C83semidirect
177. #520C2×C83semidirect
178. #484C2×C83semidirect
179. #480C2×C83semidirect
180. #477C2×C83semidirect
181. #474C2×C83semidirect
182. #464C2×C83semidirect
183. #463C2×C83semidirect
184. #452C2×C83semidirect
186. #440C2×C83semidirect
187. #440C2×C83semidirect
188. C4×Q16C2×C83semidirect
189. C4×D8C2×C83semidirect
190. #433C2×C83semidirect

Maximal subgroups

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

subgroupindex
#542×C832
#520×C832
#484×C832
#480×C832
#477×C832
#474×C832
#464×C832
#463×C832
#452×C832
#449×C832
#440×C832
C4×Q16×C832
C4×D8×C832
#433×C832
#312483