Finite Group Databasebeta

← #24905973

Subgroups — #24905973

Order 10624.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#19128253C211yesmaximal, characteristic
2#19127755C211yesmaximal, characteristic
3#19127546C211yesmaximal, characteristic
4#19127439C211yesmaximal, characteristic
5#19127438C211yesmaximal, characteristic
6#19127437C211yesmaximal, characteristic
7#328×C83C211yesmaximal, characteristic
8#14581791C411yescharacteristic, complemented
9#14581790C411yescharacteristic, complemented
10#14581782—21no—
11#14581771C2211yescharacteristic
12#14581769—21no—
13Q8×Dic83C411yescharacteristic, complemented
14#14581757—21no—
15#14581757C411yescharacteristic, complemented
16#14581748—21no—
17C2×C4×Dic83—21no—
18C2×C4×Dic83C2211yescharacteristic
19Dic83⋊C8—21no—
20C22⋊(C83⋊C8)C2211yescharacteristic
21#14581702—21no—
22C83⋊#95—21no—
23C83⋊#95C2211yescharacteristic
24C22⋊Q8×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic
26#95×C83C2211yescharacteristic
27C2×Dic166—21no—
28C2×Dic166C2×C411yescharacteristic
29C22×Dic83—21no—
30C22×Dic83D411yescharacteristic
31C22×Dic83D411yescharacteristic
32C2×C83⋊C8—21no—
33C4⋊Dic83—21no—
34C4⋊Dic83C2×C411yescharacteristic
35Dic83⋊C4—21no—
36Dic83⋊C4—21no—
37Dic83⋊C4—21no—
38Dic83⋊C4—21no—
39Dic83⋊C4—21no—
40C22⋊Dic83—21no—
41C4×Dic83—24no—
42C4×Dic83—21no—
43C4×Dic83—21no—
44C4×Dic83C2×C411yescharacteristic
45C4×Dic83C2×C411yescharacteristic
46C4×Dic83D411yescharacteristic
47C4×Dic83D411yescharacteristic
48C2×Q8×C83C2×C411yescharacteristic
49C22×C4×C83—21no—
50C22×C4×C83C2311yescharacteristic
51C2×C8×C83—21no—
52C4⋊C4×C83—21no—
53C4⋊C4×C83C2×C411yescharacteristic
54C22⋊C4×C83—21no—
55C23×C83C2×D411yescharacteristic
56Q8×C83—41no—
57C2×C4×C83—22no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—41no—
61C2×C4×C83—41no—
62C2×C4×C83—41no—
63C2×C4×C83C22×C411yescharacteristic
64C2×C4×C83C2×D411yescharacteristic
65C2×Dic83—21no—
66C2×Dic83—21no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—21no—
70C2×Dic83—21no—
71C2×Dic83—41no—
72C2×Dic83—41no—
73C2×Dic83C22⋊C411yescharacteristic
74C2×Dic83C22⋊C411yescharacteristic
75C2×Dic83C22⋊C411yescharacteristic
76C2×Dic83C22⋊C411yescharacteristic
77Dic166—42no—
78Dic166—41no—
79C8×C83—41no—
80C83⋊C8—41no—
81C22×C83—21no—
82C22×C83—21no—
83C22×C83C2×C22⋊C411yescharacteristic
84C22×C83#13711yescharacteristic
85C22×C83#13711yescharacteristic
86C4×C83—21no—
87C4×C83—21no—
88C4×C83—42no—
89C4×C83—41no—
90C4×C83—41no—
91Dic83—21no—
92Dic83—21no—
93Dic83—21no—
94Dic83—42no—
95Dic83—41no—
96Dic83—41no—
97Dic83#10412yes—
98C2×C83—21no—
99C2×C83—21no—
100C2×C83#41011yescharacteristic
101C2×C83#41911yescharacteristic
102C2×C83C2×#10411yescharacteristic
103#1506—831nomaximal, Sylow
104C83#150611yescharacteristic, complemented, Sylow
105#533—831no—
106#432—831no—
107#376—831no—
108#328—831no—
109#328—831no—
110#328—831no—
111#328D8311yescharacteristic
112C4⋊Q8—831no—
113C4⋊Q8—831no—
114#125—1661no—
115C22⋊Q8—831no—
116C22⋊Q8—1661no—
117C22⋊Q8C2×D8311yescharacteristic
118C4×Q8—831no—
119C4×Q8—831no—
120C4×Q8—1661no—
121#117—1661no—
122C2×C42—831no—
123C2×C42—1661no—
124C4⋊C8—1661no—
125C22⋊C8—831no—
126C22⋊C8C2×D8311yescharacteristic
127#97—1661no—
128#95—831no—
129#95—1661no—
130#95C2×D8311yescharacteristic
131C2×Q8—831no—
132C2×Q8—1661no—
133C2×Q8C4×D8311yescharacteristic
134C22×C4—21no—
135C22×C4—831no—
136C22×C4—831no—
137C22×C4—1661no—
138C22×C4C22×D8311yescharacteristic
139C2×C8—21no—
140C2×C8—1661no—
141C4⋊C4—21no—
142C4⋊C4—831no—
143C4⋊C4—1661no—
144C4⋊C4—1661no—
145C4⋊C4—1661no—
146C4⋊C4—1661no—
147C4⋊C4—1661no—
148C4⋊C4—1661no—
149C4⋊C4C4×D8311yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—1661no—
152C42—831no—
153C42—831no—
154C42—831no—
155C42—831no—
156C42—1661no—
157C42—1661no—
158C42—1664no—
159C23D4×D8311yescharacteristic
160Q8—41no—
161Q8—3321no—
162Q8—3322no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3321no—
170C2×C4—3321no—
171C2×C4—831no—
172C2×C4—831no—
173C2×C4—831no—
174C2×C4—831no—
175C2×C4—1662no—
176C2×C4—1661no—
177C2×C4—1661no—
178C2×C4—1662no—
179C2×C4—1661no—
180C2×C4—1661no—
181C2×C4C2×C4×D8311yescharacteristic
182C2×C4D4×D8311yescharacteristic
183C8—41no—
184C8—3321no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D8311yescharacteristic
188C22#1458182111yescharacteristic
189C22#1458182411yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—3322no—
196C4—3321no—
197C4—3321no—
198C4—832no—
199C4—1661no—
200C4—1661no—
201C4—1661no—
202C2—21no—
203C2—21no—
204C2#1912767311yescharacteristic
205C2#1912770811yescharacteristic
206C2#104×D8311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#328×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC23×C83C2×D4
cosocleC22×C4×C83C23
hypercenter#328D83
hypocenterC83#1506
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #14581791C4semidirect
9. #14581790C4semidirect
13. Q8×Dic83C4semidirect
15. #14581757C4semidirect
104. C83#1506semidirect