Finite Group Databasebeta

← #24917417

Subgroups — #24917417

Order 10624.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#19128268C211yesmaximal, characteristic
2#19128182C211yesmaximal, characteristic, complemented
3#19128024C212yesmaximal, complemented
4#19128023C212yesmaximal, complemented
5#19128018C212yesmaximal, complemented
6#19128013C212yesmaximal, complemented
7#19127741C211yesmaximal, characteristic, complemented
8#19127739C211yesmaximal, characteristic, complemented
9#19127706C211yesmaximal, characteristic, complemented
10#19127667C211yesmaximal, characteristic, complemented
11C2×#102×C83C211yesmaximal, characteristic, complemented
12C2×#13050590C2211yescharacteristic
13C2×#13050574C2211yescharacteristic
14#14581788—21no—
15#14581779—21no—
16#14581763C2212yes—
17#14581763C2212yes—
18#14581761—22no—
19#14581757—21no—
20#14581754—21no—
21C4×C22⋊D83—22no—
22#14581751C2211yescharacteristic
23#14581751C2211yescharacteristic
24#14581750C2212yescomplemented
25C4⋊C4×D83C2212yescomplemented
26#14581726C2211yescharacteristic, complemented
27#14581726C2211yescharacteristic, complemented
28#14581725C2212yescomplemented
29#14581724C2211yescharacteristic, complemented
30#14581724C2211yescharacteristic, complemented
31#14581723C2212yescomplemented
32#14581713C2212yes—
33#14581713C2212yes—
34(C2×D83)⋊C8C2212yescomplemented
35(C2×D83)⋊C8C2212yescomplemented
36C22×D4×C83C2211yescharacteristic
37C22×C8×C83C2211yescharacteristic
38C2×C4⋊C4×C83C2211yescharacteristic
39#102×C83C2212yes—
40#102×C83C2212yes—
41#13050590—22no—
42#13050590—22no—
43C2×Dic166D411yescharacteristic
44C2×D332D411yescharacteristic
45C2×C22⋊D83—22no—
46C2×C22⋊D83—22no—
47C2×C22⋊D83D412yes—
48C2×C4×D83—22no—
49C2×C4×D83C2312yes—
50#13050574—22no—
51C2×C83⋊C8C2312yes—
52C4⋊Dic83C2311yescharacteristic
53C4⋊Dic83C2311yescharacteristic
54C4⋊Dic83C2311yescharacteristic
55C4⋊Dic83C2311yescharacteristic
56Dic83⋊C4—22no—
57C22⋊Dic83—21no—
58C22⋊Dic83—21no—
59C22⋊Dic83—22no—
60C22⋊Dic83—22no—
61(C2×D83)⋊C4—22no—
62C4×Dic83—21no—
63C4×Dic83—21no—
64C4×Dic83—22no—
65C24×C83—21no—
66C2×D4×C83—21no—
67C2×D4×C83—22no—
68C2×D4×C83—22no—
69C2×D4×C83C2312yes—
70C22×C4×C83—21no—
71C22×C4×C83C2311yescharacteristic
72C2×C8×C83—22no—
73C2×C8×C83C2311yescharacteristic
74C2×C8×C83C2311yescharacteristic
75C4⋊C4×C83—21no—
76C4⋊C4×C83C2312yes—
77C23×C83—22no—
78C23×C83—42no—
79C23×C83—81no—
80C23×C83—81no—
81C23×C83C2×D411yescharacteristic
82C22×D83C2×D412yes—
83D4×C83—22no—
84D4×C83—22no—
85D4×C83—42no—
86C2×C4×C83—22no—
87C2×C4×C83—81no—
88C2×C4×C83C2×D411yescharacteristic
89C2×C4×C83#4112yes—
90C2×C4×C83#4112yes—
91C2×C4×C83C2411yescharacteristic
92C22⋊D83—24no—
93C22⋊D83—82no—
94C22⋊D83—82no—
95C2×Dic83—21no—
96C2×Dic83—21no—
97C2×Dic83—21no—
98C2×Dic83—21no—
99C2×Dic83C2×D412yes—
100D332—22no—
101C4×D83—22no—
102C4×D83—22no—
103C4×D83—82no—
104Dic166—22no—
105C8×C83—21no—
106C8×C83—21no—
107C83⋊C8—22no—
108C22×C83—21no—
109C22×C83—21no—
110C22×C83—42no—
111C22×C83—42no—
112C22×C83—42no—
113C22×C83—84no—
114C22×C83#12312yes—
115C22×C83C22×D411yescharacteristic
116C2×D83—22no—
117C2×D83—22no—
118C2×D83—22no—
119C4×C83—42no—
120C4×C83#12312yes—
121C4×C83C2×#4111yescharacteristic
122C4×C83C2×#4111yescharacteristic
123Dic83—22no—
124Dic83—41no—
125Dic83—41no—
126Dic83—41no—
127Dic83—41no—
128C2×C83—22no—
129C2×C83—82no—
130C2×C83C2×#12311yescharacteristic
131C2×C83#57611yescharacteristic
132C2×C83#57711yescharacteristic
133D83—42no—
134#3096—831nomaximal, Sylow
135C83#309611yescharacteristic, complemented, Sylow
136#535—831no—
137#520—831no—
138#482—832no—
139#482—832no—
140#481—832no—
141#480—832no—
142#428—831no—
143#427—831no—
144#418—831no—
145C2×#102D8311yescharacteristic, complemented
146#408—831no—
147C2×#41—831no—
148C22×D4C2×D8311yescharacteristic
149C2×M16—831no—
150C22×C8C2×D8311yescharacteristic
151#127—1661no—
152#124—1661no—
153#121—832no—
154#121—832no—
155#120—1662no—
156C4×Q8—1661no—
157C4×D4—1661no—
158C4×D4—1662no—
159#117—831no—
160#117—831no—
161#117—832no—
162C2×C4⋊C4—832no—
163C2×C4⋊C4C2×D8311yescharacteristic
164#107—831no—
165#107—831no—
166#107—832no—
167#106—831no—
168#106—831no—
169#106—832no—
170#102—832no—
171#102—832no—
172#102C2×D8312yes—
173#102C2×D8312yes—
174C22⋊C8—832no—
175C22⋊C8—832no—
176C24—21no—
177#41—1662no—
178#41—1662no—
179C2×Q8—831no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—832no—
184C2×D4—831no—
185C2×D4—1662no—
186C2×D4—1662no—
187C2×D4C22×D8312yes—
188C22×C4—21no—
189C22×C4—832no—
190C22×C4—1662no—
191C22×C4C22×D8311yescharacteristic
192M16—1662no—
193C2×C8—22no—
194C2×C8—832no—
195C2×C8C22×D8311yescharacteristic
196C2×C8C22×D8311yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—831no—
199C4⋊C4—831no—
200C4⋊C4—831no—
201C4⋊C4—831no—
202C4⋊C4—1662no—
203C4⋊C4C22×D8312yes—
204C22⋊C4—1662no—
205C22⋊C4—1662no—
206C22⋊C4—1662no—
207C22⋊C4—1661no—
208C22⋊C4—1661no—
209C42—1662no—
210C42—1661no—
211C42—1661no—
212C23—22no—
213C23—42no—
214C23—81no—
215C23—81no—
216C23—832no—
217C23D4×D8311yescharacteristic
218Q8—1662no—
219D4—22no—
220D4—22no—
221D4—42no—
222D4—6642no—
223D4—6642no—
224D4—1664no—
225D4—1662no—
226C2×C4—22no—
227C2×C4—81no—
228C2×C4—832no—
229C2×C4—6642no—
230C2×C4—1661no—
231C2×C4—1661no—
232C2×C4—1661no—
233C2×C4—1661no—
234C2×C4—1662no—
235C2×C4—1662no—
236C2×C4D4×D8311yescharacteristic
237C2×C4#1305058912yes—
238C2×C4#1305059012yes—
239C2×C4C23×D8311yescharacteristic
240C8—21no—
241C8—21no—
242C8—1662no—
243C22—21no—
244C22—21no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—84no—
249C22—1662no—
250C22—1662no—
251C22—1662no—
252C22#1458177412yes—
253C22C2×D4×D8311yescharacteristic
254C4—42no—
255C4—3321no—
256C4—3321no—
257C4—3321no—
258C4—3321no—
259C4—1662no—
260C4#1458177412yes—
261C4C2×#1305058911yescharacteristic
262C4C2×#1305059011yescharacteristic
263C2—22no—
264C2—82no—
265C2—3322no—
266C2C2×#1458177411yescharacteristic
267C2#1912850211yescharacteristic
268C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#102×C83C2
socleC22×C83C22×D4
prime radical#19128268C2
hypercenterC2×#102D83
hypocenterC83#3096
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. #19128182C2semidirect
3. #19128024C2semidirect
4. #19128023C2semidirect
5. #19128018C2semidirect
6. #19128013C2semidirect
7. #19127741C2semidirect
8. #19127739C2semidirect
9. #19127706C2semidirect
10. #19127667C2semidirect
11. C2×#102×C83C2semidirect
24. #14581750C22semidirect
25. C4⋊C4×D83C22semidirect
26. #14581726C22semidirect
27. #14581726C22semidirect
28. #14581725C22semidirect
29. #14581724C22semidirect
30. #14581724C22semidirect
31. #14581723C22semidirect
34. (C2×D83)⋊C8C22semidirect
35. (C2×D83)⋊C8C22semidirect
135. C83#3096semidirect
145. C2×#102D83semidirect

Maximal subgroups

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

subgroupindex
#191282682
#191281822
#191280242
#191280232
#191280182
#191280132
#191277412
#191277392
#191277062
#191276672
C2×#102×C832
#309683