Finite Group Databasebeta

← #24916983

Subgroups — #24916983

Order 10624.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14581825C211yesmaximal, characteristic, complemented
2C22×#13050578C211yesmaximal, characteristic, complemented
3#19128268C211yesmaximal, characteristic
4#19128178C211yesmaximal, characteristic, complemented
5#19127922C214yesmaximal, complemented
6#19127900C214yesmaximal, complemented
7#19127729C211yesmaximal, characteristic, complemented
8#19127695C211yesmaximal, characteristic, complemented
9#418×C83C211yesmaximal, characteristic, complemented
10C2×#13050590C2211yescharacteristic
11C22×Dic166C2211yescharacteristic
12#14581825—24no—
13C2×Dic332C2212yescomplemented
14C2×#13050579C2212yescomplemented
15C2×#13050578—24no—
16C2×#13050578C2214yes—
17C22×C83⋊C8C2211yescharacteristic
18#14581788C2212yes—
19#14581779C2212yes—
20#14581763—22no—
21#14581761—22no—
22C4×Dic166—22no—
23#14581757C2214yescomplemented
24#14581751C2211yescharacteristic
25#14581748—22no—
26Dic83⋊C8C2214yescomplemented
27#14581715C2212yescomplemented
28#14581712C2212yescomplemented
29C22×D4×C83C2211yescharacteristic
30C2×M16×C83C2211yescharacteristic
31#117×C83C2211yescharacteristic
32#102×C83C2214yes—
33#13050590—22no—
34#13050590—22no—
35C2×Dic166—21no—
36C2×Dic166—22no—
37C2×Dic166D414yescomplemented
38C2×Dic166C2311yescharacteristic
39C2×Dic166C2312yes—
40C2×D332C2311yescharacteristic
41C2×C22⋊D83—21no—
42C2×C22⋊D83—24no—
43C22×Dic83—21no—
44C2×C4×D83—21no—
45Dic332—24no—
46#13050579—24no—
47#13050578—28no—
48C2×C83⋊C8—22no—
49C2×C83⋊C8C2312yes—
50C4⋊Dic83D412yes—
51Dic83⋊C4—24no—
52C22⋊Dic83—24no—
53C22⋊Dic83D412yes—
54C4×Dic83—24no—
55C4×Dic83C2312yes—
56C24×C83—21no—
57C2×D4×C83—22no—
58C2×D4×C83—21no—
59C2×D4×C83—22no—
60C2×D4×C83C2312yes—
61C22×C4×C83C2311yescharacteristic
62M16×C83—22no—
63C2×C8×C83C2312yes—
64C4⋊C4×C83C2312yes—
65C22⋊C4×C83—21no—
66C42×C83—21no—
67C23×C83—22no—
68C23×C83—42no—
69C23×C83—82no—
70C23×C83C2×D411yescharacteristic
71C22×D83—21no—
72D4×C83—22no—
73D4×C83—22no—
74D4×C83—42no—
75C2×C4×C83—22no—
76C2×C4×C83C2×D411yescharacteristic
77C2×C4×C83C2×D412yes—
78C2×C4×C83#4112yes—
79C2×C4×C83C2411yescharacteristic
80C22⋊D83—42no—
81C22⋊D83—84no—
82C2×Dic83—24no—
83C2×Dic83—22no—
84C2×Dic83—21no—
85C2×Dic83C2×D414yes—
86D332—21no—
87D332—21no—
88C4×D83—42no—
89Dic166—24no—
90Dic166—22no—
91Dic166—21no—
92Dic166—21no—
93Dic166C2×D414yes—
94C8×C83—22no—
95C83⋊C8—22no—
96C22×C83—22no—
97C22×C83—42no—
98C22×C83—44no—
99C22×C83—84no—
100C22×C83#12112yes—
101C22×C83C22×D411yescharacteristic
102C2×D83—41no—
103C2×D83—42no—
104C4×C83—42no—
105C4×C83#12112yes—
106C4×C83C22×D411yescharacteristic
107C4×C83C2×#4111yescharacteristic
108Dic83—24no—
109Dic83—24no—
110Dic83—41no—
111C2×C83—22no—
112C2×C83—82no—
113C2×C83C2×#12111yescharacteristic
114C2×C83#57712yes—
115D83—81no—
116#3043—831nomaximal, Sylow
117C83#304311yescharacteristic, complemented, Sylow
118C2×#137—831no—
119C22×SD16—831no—
120#535—831no—
121#519—831no—
122#464—834no—
123#460—834no—
124#424—831no—
125#418D8311yescharacteristic, complemented
126#416—831no—
127C2×#41—831no—
128C22×Q8—831no—
129C22×D4C2×D8311yescharacteristic
130#137—1664no—
131C2×Q16—832no—
132C2×SD16—834no—
133C2×SD16—832no—
134C2×SD16—1664no—
135C2×M16C2×D8311yescharacteristic
136C22×C8—831no—
137#127—832no—
138#124—832no—
139#121—1662no—
140#120—1662no—
141C4×Q8—834no—
142C4×Q8—1662no—
143#117—831no—
144#117—1662no—
145#117C2×D8311yescharacteristic
146C4⋊C8—834no—
147#103—832no—
148#102—832no—
149#102C2×D8314yes—
150C24—21no—
151#41—1662no—
152#41—1662no—
153C2×Q8—834no—
154C2×Q8—832no—
155C2×Q8—831no—
156C2×Q8—1661no—
157C2×Q8—1662no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—831no—
162C2×D4—1664no—
163C2×D4—1661no—
164C2×D4C22×D8312yes—
165C22×C4—1661no—
166C22×C4—1661no—
167C22×C4C22×D8311yescharacteristic
168Q16—1664no—
169SD16—1664no—
170SD16—1668no—
171M16—22no—
172C2×C8—832no—
173C2×C8—1662no—
174C2×C8C22×D8312yes—
175C4⋊C4—832no—
176C4⋊C4—1664no—
177C4⋊C4C22×D8312yes—
178C22⋊C4—21no—
179C22⋊C4—832no—
180C22⋊C4—1664no—
181C42—21no—
182C42—832no—
183C42—1664no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—1661no—
188C23D4×D8311yescharacteristic
189Q8—834no—
190Q8—1661no—
191Q8—1661no—
192Q8—1664no—
193Q8—1662no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—3322no—
198D4—6644no—
199D4—1661no—
200D4—1661no—
201C2×C4—22no—
202C2×C4—3322no—
203C2×C4—834no—
204C2×C4—1661no—
205C2×C4—1664no—
206C2×C4—1662no—
207C2×C4D4×D8311yescharacteristic
208C2×C4D4×D8312yes—
209C2×C4#1305059012yes—
210C2×C4C23×D8311yescharacteristic
211C8—22no—
212C8—1662no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—3321no—
218C22—3322no—
219C22#1458176512yes—
220C22C2×D4×D8311yescharacteristic
221C4—42no—
222C4—3321no—
223C4—1664no—
224C4—1664no—
225C4#1458176512yes—
226C4C2×D4×D8311yescharacteristic
227C4C2×#1305059011yescharacteristic
228C2—22no—
229C2—82no—
230C2—6641no—
231C2C2×#1458176511yescharacteristic
232C2#1912851112yes—
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#418×C83C2
socleC22×C83C22×D4
prime radical#19128268C2
hypercenter#418D83
hypocenterC83#3043
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#14581825C2semidirect
2. C22×#13050578C2semidirect
4. #19128178C2semidirect
5. #19127922C2semidirect
6. #19127900C2semidirect
7. #19127729C2semidirect
8. #19127695C2semidirect
9. #418×C83C2semidirect
13. C2×Dic332C22semidirect
14. C2×#13050579C22semidirect
23. #14581757C22semidirect
26. Dic83⋊C8C22semidirect
27. #14581715C22semidirect
28. #14581712C22semidirect
37. C2×Dic166D4semidirect
117. C83#3043semidirect
125. #418D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145818252
C22×#130505782
#191282682
#191281782
#191279222
#191279002
#191277292
#191276952
#418×C832
#304383