Finite Group Databasebeta

← C83×#20455 #35248279

Subgroups — C83×#20455 #35248279

Order 21248.

1126 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#427×C83C211yesmaximal, characteristic
2C22×#107×C83C211yesmaximal, characteristic
3C2×#405×C83C211yesmaximal, characteristic
4C83×#2274C212yesmaximal
5C83×#1776C214yesmaximal, complemented
6C4×#107×C83C214yesmaximal, complemented
7C83×#1736C212yesmaximal
8C22×M16×C83C2211yescharacteristic
9C23×C8×C83C2211yescharacteristic
10C2×#117×C83C2212yes—
11C2×#117×C83C2211yescharacteristic
12C22×C4⋊C4×C83C2212yes—
13#427×C83C418yescomplemented
14C2×#107×C83C418yescomplemented
15C2×#107×C83C2212yes—
16C2×#107×C83C2212yes—
17C2×#107×C83C2212yes—
18C2×#106×C83C2212yes—
19#405×C83C418yescomplemented
20C2×#97×C83C2212yes—
21C2×C4×C8×C83C2212yes—
22C4×C4⋊C4×C83—24no—
23C4×C4⋊C4×C83C2218yes—
24C4×C22⋊C4×C83—24no—
25#340×C83C2218yes—
26C23×C4×C83—22no—
27C23×C4×C83C2311yescharacteristic
28C2×M16×C83—22no—
29C2×M16×C83—22no—
30C2×M16×C83C2×C414yes—
31C22×C8×C83C2×C414yes—
32C22×C8×C83C2×C414yes—
33C22×C8×C83C2×C414yes—
34C22×C8×C83C2312yes—
35C22×C8×C83C2311yescharacteristic
36C22×C8×C83C2311yescharacteristic
37#117×C83—24no—
38#117×C83C2×C418yes—
39#117×C83C2×C414yes—
40#117×C83Q814yes—
41C2×C4⋊C4×C83—22no—
42C2×C4⋊C4×C83—24no—
43C2×C4⋊C4×C83C2×C418yes—
44C2×C4⋊C4×C83D412yes—
45C2×C4⋊C4×C83C2314yes—
46C2×C4⋊C4×C83C2314yes—
47C2×C22⋊C4×C83—22no—
48C2×C22⋊C4×C83D412yes—
49C2×C42×C83—22no—
50C2×C42×C83—28no—
51C2×C42×C83C2312yes—
52#107×C83C2×C418yes—
53#107×C83C2×C418yes—
54#107×C83C2×C418yescomplemented
55#106×C83C2×C418yescomplemented
56#97×C83C2×C418yescomplemented
57C4×C8×C83C2×C418yescomplemented
58#95×C83—28no—
59C24×C83C2×D411yescharacteristic
60C22×C4×C83—24no—
61C22×C4×C83—24no—
62C22×C4×C83—28no—
63C22×C4×C83—84no—
64C22×C4×C83C22×C412yes—
65C22×C4×C83C22×C412yes—
66C22×C4×C83C22×C412yes—
67C22×C4×C83C2×D414yes—
68C22×C4×C83C2×D411yescharacteristic
69C22×C4×C83C2×Q812yes—
70C22×C4×C83#4112yes—
71C22×C4×C83#4112yes—
72C22×C4×C83C2411yescharacteristic
73M16×C83—28no—
74C2×C8×C83—22no—
75C2×C8×C83—22no—
76C2×C8×C83C42116yescomplemented
77C2×C8×C83C22×C414yes—
78C2×C8×C83C22×C412yes—
79C2×C8×C83C22×C412yes—
80C2×C8×C83C22×C412yes—
81C2×C8×C83C22×C412yes—
82C2×C8×C83C22×C412yes—
83C2×C8×C83C22×C412yes—
84C4⋊C4×C83—28no—
85C4⋊C4×C83—24no—
86C4⋊C4×C83—24no—
87C4⋊C4×C83C4⋊C418yes—
88C4⋊C4×C83C22×C418yes—
89C4⋊C4×C83C22×C418yes—
90C22⋊C4×C83—28no—
91C22⋊C4×C83C4⋊C418yes—
92C42×C83—28no—
93C42×C83—88no—
94C42×C83C22×C414yes—
95C42×C83C2×Q814yes—
96C23×C83—22no—
97C23×C83—22no—
98C23×C83C2×C4⋊C412yes—
99C23×C83C4×D412yes—
100C23×C83C4×D412yes—
101C23×C83C22×D411yescharacteristic
102C2×C4×C83—24no—
103C2×C4×C83—24no—
104C2×C4×C83—28no—
105C2×C4×C83—28no—
106C2×C4×C83—44no—
107C2×C4×C83—48no—
108C2×C4×C83—44no—
109C2×C4×C83—88no—
110C2×C4×C83C2×C4214yes—
111C2×C4×C83C2×C4⋊C418yes—
112C2×C4×C83C2×C4⋊C412yes—
113C2×C4×C83#11714yes—
114C2×C4×C83C4×D412yes—
115C2×C4×C83C4×D412yes—
116C2×C4×C83C4×Q814yes—
117C2×C4×C83C4×Q814yes—
118C2×C4×C83C23×C411yescharacteristic
119C2×C4×C83C23×C411yescharacteristic
120C2×C4×C83C23×C411yescharacteristic
121C2×C4×C83C22×Q811yescharacteristic
122C2×C4×C83C2×#4111yescharacteristic
123C2×C4×C83C2×#4111yescharacteristic
124C8×C83—24no—
125C8×C83C2×C4214yes—
126C8×C83C2×C4214yes—
127C22×C83—24no—
128C22×C83—22no—
129C22×C83—22no—
130C22×C83—24no—
131C22×C83C4×C4⋊C414yes—
132C22×C83C22×C4⋊C411yescharacteristic
133C22×C83C2×C4×D411yescharacteristic
134C22×C83C2×C4×D411yescharacteristic
135C22×C83#57612yes—
136C22×C83#57812yes—
137C4×C83—28no—
138C4×C83—48no—
139C4×C83—48no—
140C4×C83C4×C4⋊C414yes—
141C4×C83C22×C4211yescharacteristic
142C4×C83C2×#11711yescharacteristic
143C4×C83C2×C4×Q811yescharacteristic
144C4×C83C2×C4×Q811yescharacteristic
145#20455C8311yesmaximal, characteristic, direct product factor, Sylow
146C2×C83—24no—
147C2×C83C2×C4×C4⋊C411yescharacteristic
148C2×C83#291312yes—
149C2×C83#294811yescharacteristic
150C2×C83#295011yescharacteristic
151C2×C83#295112yes—
152C2×#427C2×C8311yescharacteristic
153C22×#107C2×C8311yescharacteristic
154C2×#405C2×C8311yescharacteristic
155#2274C2×C8312yes—
156#1776C2×C8314yescomplemented
157C4×#107C2×C8314yescomplemented
158#1736C2×C8312yes—
159C83#2045511yescharacteristic, direct product factor, Sylow
160C22×M16C22×C8311yescharacteristic
161C23×C8C22×C8311yescharacteristic
162C2×#117C22×C8312yes—
163C2×#117C22×C8311yescharacteristic
164C22×C4⋊C4C22×C8312yes—
165#427C4×C8318yescomplemented
166C2×#107C4×C8318yescomplemented
167C2×#107C22×C8312yes—
168C2×#107C22×C8312yes—
169C2×#107C22×C8312yes—
170C2×#106C22×C8312yes—
171#405C4×C8318yescomplemented
172C2×#97C22×C8312yes—
173C2×C4×C8C22×C8312yes—
174C4×C4⋊C4—24no—
175C4×C4⋊C4C22×C8318yes—
176C4×C22⋊C4—24no—
177#340C22×C8318yes—
178C23×C4—22no—
179C23×C4C23×C8311yescharacteristic
180C2×M16—22no—
181C2×M16—22no—
182C2×M16C2×C4×C8314yes—
183C22×C8C2×C4×C8314yes—
184C22×C8C2×C4×C8314yes—
185C22×C8C2×C4×C8314yes—
186C22×C8C23×C8312yes—
187C22×C8C23×C8311yescharacteristic
188C22×C8C23×C8311yescharacteristic
189#117—24no—
190#117C2×C4×C8318yes—
191#117C2×C4×C8314yes—
192#117Q8×C8314yes—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4C2×C4×C8318yes—
196C2×C4⋊C4D4×C8312yes—
197C2×C4⋊C4C23×C8314yes—
198C2×C4⋊C4C23×C8314yes—
199C2×C22⋊C4—22no—
200C2×C22⋊C4D4×C8312yes—
201C2×C42—22no—
202C2×C42—28no—
203C2×C42C23×C8312yes—
204#107C2×C4×C8318yes—
205#107C2×C4×C8318yes—
206#107C2×C4×C8318yescomplemented
207#106C2×C4×C8318yescomplemented
208#97C2×C4×C8318yescomplemented
209C4×C8C2×C4×C8318yescomplemented
210#95—28no—
211C24C2×D4×C8311yescharacteristic
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—28no—
215C22×C4—84no—
216C22×C4C22×C4×C8312yes—
217C22×C4C22×C4×C8312yes—
218C22×C4C22×C4×C8312yes—
219C22×C4C2×D4×C8314yes—
220C22×C4C2×D4×C8311yescharacteristic
221C22×C4C2×Q8×C8312yes—
222C22×C4#41×C8312yes—
223C22×C4#41×C8312yes—
224C22×C4C24×C8311yescharacteristic
225M16—28no—
226C2×C8—22no—
227C2×C8—22no—
228C2×C8C42×C83116yescomplemented
229C2×C8C22×C4×C8314yes—
230C2×C8C22×C4×C8312yes—
231C2×C8C22×C4×C8312yes—
232C2×C8C22×C4×C8312yes—
233C2×C8C22×C4×C8312yes—
234C2×C8C22×C4×C8312yes—
235C2×C8C22×C4×C8312yes—
236C4⋊C4—28no—
237C4⋊C4—24no—
238C4⋊C4—24no—
239C4⋊C4C4⋊C4×C8318yes—
240C4⋊C4C22×C4×C8318yes—
241C4⋊C4C22×C4×C8318yes—
242C22⋊C4—28no—
243C22⋊C4C4⋊C4×C8318yes—
244C42—28no—
245C42—88no—
246C42C22×C4×C8314yes—
247C42C2×Q8×C8314yes—
248C23—22no—
249C23—22no—
250C23C2×C4⋊C4×C8312yes—
251C23C4×D4×C8312yes—
252C23C4×D4×C8312yes—
253C23C22×D4×C8311yescharacteristic
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—28no—
257C2×C4—28no—
258C2×C4—44no—
259C2×C4—48no—
260C2×C4—44no—
261C2×C4—88no—
262C2×C4C2×C42×C8314yes—
263C2×C4C2×C4⋊C4×C8318yes—
264C2×C4C2×C4⋊C4×C8312yes—
265C2×C4#117×C8314yes—
266C2×C4C4×D4×C8312yes—
267C2×C4C4×D4×C8312yes—
268C2×C4C4×Q8×C8314yes—
269C2×C4C4×Q8×C8314yes—
270C2×C4C23×C4×C8311yescharacteristic
271C2×C4C23×C4×C8311yescharacteristic
272C2×C4C23×C4×C8311yescharacteristic
273C2×C4C22×Q8×C8311yescharacteristic
274C2×C4C2×#41×C8311yescharacteristic
275C2×C4C2×#41×C8311yescharacteristic
276C8—24no—
277C8C2×C42×C8314yes—
278C8C2×C42×C8314yes—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—24no—
283C22C4×C4⋊C4×C8314yes—
284C22C22×C4⋊C4×C8311yescharacteristic
285C22C2×C4×D4×C8311yescharacteristic
286C22C2×C4×D4×C8311yescharacteristic
287C22#576×C8312yes—
288C22#578×C8312yes—
289C4—28no—
290C4—48no—
291C4—48no—
292C4C4×C4⋊C4×C8314yes—
293C4C22×C42×C8311yescharacteristic
294C4C2×#117×C8311yescharacteristic
295C4C2×C4×Q8×C8311yescharacteristic
296C4C2×C4×Q8×C8311yescharacteristic
297C2—24no—
298C2C2×C4×C4⋊C4×C8311yescharacteristic
299C2C83×#291312yes—
300C2C83×#294811yescharacteristic
301C2C83×#295011yescharacteristic
302C2C83×#295112yes—
subgroupG/H
center, socleC23×C83C22×D4
commutatorC4C22×C42×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC24×C83C2×D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×#117×C83 ◁ G

Complements

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

NH ≅ G/Ntype
5. C83×#1776C2semidirect
6. C4×#107×C83C2semidirect
13. #427×C83C4semidirect
14. C2×#107×C83C4semidirect
19. #405×C83C4semidirect
54. #107×C83C2×C4semidirect
55. #106×C83C2×C4semidirect
56. #97×C83C2×C4semidirect
57. C4×C8×C83C2×C4semidirect
76. C2×C8×C83C42semidirect
145. #20455C83direct (N × H)
156. #1776C2×C83semidirect
157. C4×#107C2×C83semidirect
159. C83#20455direct (N × H)
165. #427C4×C83semidirect
166. C2×#107C4×C83semidirect
171. #405C4×C83semidirect
206. #107C2×C4×C83semidirect
207. #106C2×C4×C83semidirect
208. #97C2×C4×C83semidirect
209. C4×C8C2×C4×C83semidirect
228. C2×C8C42×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#427×C832
C22×#107×C832
C2×#405×C832
C83×#22742
C83×#17762
C4×#107×C832
C83×#17362
#2045583