Finite Group Databasebeta

← #24917388

Subgroups — #24917388

Order 10624.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128212C211yesmaximal, characteristic
2C22×C4⋊Dic83C211yesmaximal, characteristic, complemented
3#19128037C212yesmaximal, complemented
4#19128032C212yesmaximal, complemented
5#19128020C212yesmaximal, complemented
6#19128015C212yesmaximal, complemented
7#19127743C212yesmaximal, complemented
8#19127703C212yesmaximal, complemented
9#407×C83C211yesmaximal, characteristic, complemented
10C2×#13050590C2211yescharacteristic
11C23×Dic83—21no—
12#14581775—21no—
13#14581771C2211yescharacteristic
14#14581771C2211yescharacteristic
15#14581766C2211yescharacteristic
16#14581766C2211yescharacteristic
17#14581761—21no—
18C4×C22⋊D83—21no—
19C4×C22⋊D83—21no—
20#14581751C2211yescharacteristic
21C2×C4⋊Dic83—21no—
22C2×C4⋊Dic83—21no—
23C2×C4⋊Dic83—21no—
24C2×C4⋊Dic83C2212yes—
25C2×C4⋊Dic83C2212yes—
26C2×C4⋊Dic83C2212yes—
27#14581726C2214yescomplemented
28#14581724C2214yescomplemented
29#14581717C2214yescomplemented
30#14581714C2214yescomplemented
31C23×C4×C83C2211yescharacteristic
32C2×M16×C83C2212yes—
33C22⋊C8×C83C2212yes—
34C22⋊C8×C83C2212yes—
35#13050590—24no—
36C2×Dic166C2311yescharacteristic
37C2×D332C2311yescharacteristic
38C2×C22⋊D83—21no—
39C2×C22⋊D83—21no—
40C2×C22⋊D83—21no—
41C22×Dic83—22no—
42C22×Dic83—22no—
43C22×Dic83—22no—
44C22×Dic83—44no—
45C2×C4×D83—21no—
46C4⋊Dic83—22no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49C4⋊Dic83C2311yescharacteristic
50C4⋊Dic83C2311yescharacteristic
51C4⋊Dic83C2314yes—
52Dic83⋊C4—21no—
53Dic83⋊C4—21no—
54C22⋊Dic83—21no—
55C22⋊Dic83—21no—
56C22⋊Dic83—21no—
57(C2×D83)⋊C4—21no—
58(C2×D83)⋊C4—21no—
59C4×Dic83—21no—
60C24×C83D411yescharacteristic
61C22×C4×C83—24no—
62C22×C4×C83D411yescharacteristic
63C22×C4×C83D411yescharacteristic
64C22×C4×C83D411yescharacteristic
65C22×C4×C83C2311yescharacteristic
66C22×C4×C83C2311yescharacteristic
67C22×C4×C83C2311yescharacteristic
68M16×C83—24no—
69C2×C8×C83C2314yes—
70C23×C83—22no—
71C23×C83—22no—
72C23×C83—22no—
73C23×C83C2×D411yescharacteristic
74C23×C83C2×D411yescharacteristic
75C23×C83C2×D411yescharacteristic
76C22×D83—21no—
77C2×C4×C83—22no—
78C2×C4×C83—22no—
79C2×C4×C83—22no—
80C2×C4×C83—22no—
81C2×C4×C83—22no—
82C2×C4×C83C2×D411yescharacteristic
83C2×C4×C83C2×D411yescharacteristic
84C2×C4×C83C2×D411yescharacteristic
85C2×C4×C83#4114yes—
86C2×C4×C83C2411yescharacteristic
87C22⋊D83—42no—
88C22⋊D83—42no—
89C22⋊D83—42no—
90C2×Dic83—21no—
91C2×Dic83—21no—
92C2×Dic83—21no—
93C2×Dic83—24no—
94C2×Dic83—44no—
95C2×Dic83—44no—
96C2×Dic83—44no—
97D332—22no—
98C4×D83—42no—
99Dic166—22no—
100C8×C83—24no—
101C22×C83—28no—
102C22×C83—21no—
103C22×C83—21no—
104C22×C83—21no—
105C22×C83—21no—
106C22×C83—21no—
107C22×C83—21no—
108C22×C83#12312yes—
109C22×C83AGL(1,ℤ/8)12yes—
110C22×C83#13712yes—
111C22×C83C22×D411yescharacteristic
112C2×D83—41no—
113C2×D83—41no—
114C2×D83—41no—
115C4×C83—21no—
116C4×C83—21no—
117C4×C83#12312yes—
118C4×C83C2×#4112yes—
119Dic83—41no—
120Dic83—44no—
121Dic83—41no—
122Dic83—41no—
123C2×C83—22no—
124C2×C83—22no—
125C2×C83—22no—
126C2×C83C2×#12311yescharacteristic
127C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C83C2×#13711yescharacteristic
129D83—81no—
130#3092—831nomaximal, Sylow
131C83#309211yescharacteristic, complemented, Sylow
132#525—831no—
133C22×C4⋊C4—831no—
134#484—832no—
135#483—832no—
136#481—832no—
137#480—832no—
138#428—832no—
139#417—832no—
140#407D8311yescharacteristic, complemented
141C2×#41—831no—
142C23×C4—1661no—
143C23×C4C2×D8311yescharacteristic
144C2×M16C2×D8312yes—
145#123—1661no—
146C22⋊Q8—831no—
147C22⋊Q8—831no—
148#121—831no—
149#121—831no—
150#120—1661no—
151C4×D4—1661no—
152C4×D4—1661no—
153#117—831no—
154C2×C4⋊C4—832no—
155C2×C4⋊C4—832no—
156C2×C4⋊C4—832no—
157C2×C4⋊C4—1661no—
158C2×C4⋊C4—1661no—
159C2×C4⋊C4—1661no—
160#107—834no—
161#106—834no—
162#103—834no—
163#102—834no—
164C22⋊C8C2×D8312yes—
165C22⋊C8C2×D8312yes—
166C24D33211yescharacteristic
167#41—1664no—
168C2×Q8—831no—
169C2×D4—831no—
170C2×D4—1661no—
171C2×D4—1661no—
172C2×D4—1661no—
173C22×C4—24no—
174C22×C4—3324no—
175C22×C4—1662no—
176C22×C4—1662no—
177C22×C4—1662no—
178C22×C4—1661no—
179C22×C4D33211yescharacteristic
180C22×C4D33211yescharacteristic
181C22×C4D33211yescharacteristic
182C22×C4C22×D8311yescharacteristic
183C22×C4C22×D8311yescharacteristic
184C22×C4C22×D8311yescharacteristic
185M16—24no—
186C2×C8C22×D8314yes—
187C4⋊C4—834no—
188C4⋊C4—831no—
189C4⋊C4—831no—
190C4⋊C4—1662no—
191C4⋊C4—1662no—
192C4⋊C4—1662no—
193C4⋊C4—1661no—
194C4⋊C4—1661no—
195C22⋊C4—1661no—
196C22⋊C4—1661no—
197C22⋊C4—1661no—
198C22⋊C4—1661no—
199C22⋊C4—1661no—
200C42—1661no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—1661no—
205C23C2×D33211yescharacteristic
206C23C2×D33211yescharacteristic
207C23C2×D33211yescharacteristic
208Q8—1662no—
209D4—3322no—
210D4—3322no—
211D4—3322no—
212D4—1662no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—3324no—
219C2×C4—3324no—
220C2×C4—3324no—
221C2×C4—3322no—
222C2×C4—1661no—
223C2×C4—1661no—
224C2×C4—1661no—
225C2×C4—1664no—
226C2×C4C2×D33211yescharacteristic
227C2×C4C2×D33211yescharacteristic
228C2×C4C2×D33211yescharacteristic
229C2×C4#1305058914yes—
230C2×C4C23×D8311yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—3321no—
240C22—3321no—
241C22—3321no—
242C22#1458177612yes—
243C22#1458182012yes—
244C22#1458182512yes—
245C22C22×D33211yescharacteristic
246C4—21no—
247C4—21no—
248C4—3321no—
249C4—3324no—
250C4—3321no—
251C4—3321no—
252C4#1458177612yes—
253C4C2×#1305058912yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—6641no—
258C2C2×#1458177611yescharacteristic
259C2C2×#1458182011yescharacteristic
260C2C2×#1458182511yescharacteristic
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#407×C83C2
socleC22×C83C22×D4
prime radical#19128212C2
hypercenter#407D83
hypocenterC83#3092
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic83C2semidirect
3. #19128037C2semidirect
4. #19128032C2semidirect
5. #19128020C2semidirect
6. #19128015C2semidirect
7. #19127743C2semidirect
8. #19127703C2semidirect
9. #407×C83C2semidirect
27. #14581726C22semidirect
28. #14581724C22semidirect
29. #14581717C22semidirect
30. #14581714C22semidirect
131. C83#3092semidirect
140. #407D83semidirect

Maximal subgroups

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

subgroupindex
#191282122
C22×C4⋊Dic832
#191280372
#191280322
#191280202
#191280152
#191277432
#191277032
#407×C832
#309283