Finite Group Databasebeta

← #24905960

Subgroups — #24905960

Order 10624.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#19127751C211yesmaximal, characteristic
3#19127552C211yesmaximal, 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×Dic83⋊C4—21no—
18C2×C4×Dic83—21no—
19C2×C4×Dic83C2211yescharacteristic
20Dic83⋊C8—21no—
21C22⋊(C83⋊C8)C2211yescharacteristic
22C8×Dic83—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—24no—
36Dic83⋊C4—21no—
37Dic83⋊C4—21no—
38Dic83⋊C4—21no—
39Dic83⋊C4—21no—
40Dic83⋊C4—21no—
41C22⋊Dic83—21no—
42C4×Dic83—21no—
43C4×Dic83—21no—
44C4×Dic83—42no—
45C4×Dic83C2×C411yescharacteristic
46C4×Dic83C2×C411yescharacteristic
47C4×Dic83D411yescharacteristic
48C4×Dic83D411yescharacteristic
49C2×Q8×C83C2×C411yescharacteristic
50C22×C4×C83—21no—
51C22×C4×C83C2311yescharacteristic
52C2×C8×C83—21no—
53C4⋊C4×C83—21no—
54C4⋊C4×C83C2×C411yescharacteristic
55C22⋊C4×C83—21no—
56C23×C83C2×D411yescharacteristic
57Q8×C83—41no—
58C2×C4×C83—22no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—41no—
62C2×C4×C83—41no—
63C2×C4×C83—41no—
64C2×C4×C83C22×C411yescharacteristic
65C2×C4×C83C2×D411yescharacteristic
66C2×Dic83—22no—
67C2×Dic83—22no—
68C2×Dic83—21no—
69C2×Dic83—21no—
70C2×Dic83—41no—
71C2×Dic83—41no—
72C2×Dic83C22⋊C411yescharacteristic
73C2×Dic83C22⋊C411yescharacteristic
74C2×Dic83C22⋊C411yescharacteristic
75C2×Dic83C22⋊C411yescharacteristic
76C2×Dic83SD1612yes—
77C2×Dic83Q1612yes—
78Dic166—42no—
79Dic166—41no—
80C8×C83—41no—
81C83⋊C8—41no—
82C22×C83—21no—
83C22×C83—21no—
84C22×C83C2×C22⋊C411yescharacteristic
85C22×C83C2×SD1611yescharacteristic
86C22×C83C2×Q1611yescharacteristic
87C4×C83—21no—
88C4×C83—21no—
89C4×C83—42no—
90C4×C83—41no—
91C4×C83—41no—
92Dic83—21no—
93Dic83—42no—
94Dic83—41no—
95Dic83—41no—
96Dic83#10312yes—
97Dic83#10312yes—
98Dic83#10412yes—
99C2×C83—21no—
100C2×C83—21no—
101C2×C83#41011yescharacteristic
102C2×C83C2×#10311yescharacteristic
103C2×C83C2×#10411yescharacteristic
104#1503—831nomaximal, Sylow
105C83#150311yescharacteristic, complemented, Sylow
106#533—831no—
107#431—831no—
108C4×C4⋊C4—831no—
109#328—831no—
110#328—831no—
111#328—831no—
112#328D8311yescharacteristic
113C4⋊Q8—831no—
114C4⋊Q8—831no—
115#125—1661no—
116C22⋊Q8—831no—
117C22⋊Q8—1661no—
118C22⋊Q8C2×D8311yescharacteristic
119C4×Q8—831no—
120C4×Q8—831no—
121C4×Q8—1661no—
122#117—1661no—
123C2×C4⋊C4—1661no—
124C2×C42—831no—
125C2×C42—1661no—
126C4⋊C8—1661no—
127C22⋊C8—831no—
128C22⋊C8C2×D8311yescharacteristic
129C4×C8—1661no—
130#95—831no—
131#95C2×D8311yescharacteristic
132C2×Q8—831no—
133C2×Q8—1661no—
134C2×Q8C4×D8311yescharacteristic
135C22×C4—21no—
136C22×C4—831no—
137C22×C4—831no—
138C22×C4—1661no—
139C22×C4C22×D8311yescharacteristic
140C2×C8—21no—
141C2×C8—1661no—
142C4⋊C4—21no—
143C4⋊C4—831no—
144C4⋊C4—1661no—
145C4⋊C4—1661no—
146C4⋊C4—1661no—
147C4⋊C4—1661no—
148C4⋊C4—1661no—
149C4⋊C4—1664no—
150C4⋊C4—1661no—
151C4⋊C4C4×D8311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1661no—
154C42—3322no—
155C42—831no—
156C42—831no—
157C42—831no—
158C42—831no—
159C42—1661no—
160C42—1661no—
161C23D4×D8311yescharacteristic
162Q8—41no—
163Q8—3321no—
164Q8—3322no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3321no—
172C2×C4—3321no—
173C2×C4—832no—
174C2×C4—832no—
175C2×C4—831no—
176C2×C4—831no—
177C2×C4—831no—
178C2×C4—831no—
179C2×C4—1662no—
180C2×C4—1661no—
181C2×C4—1661no—
182C2×C4—1662no—
183C2×C4C2×C4×D8311yescharacteristic
184C2×C4D4×D8311yescharacteristic
185C8—41no—
186C8—3321no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D8311yescharacteristic
190C22SD16×D8311yescharacteristic
191C22Q16×D8311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—3322no—
198C4—3321no—
199C4—3321no—
200C4—832no—
201C4—832no—
202C4—832no—
203C4—1661no—
204C2—21no—
205C2—21no—
206C2#1912767311yescharacteristic
207C2#103×D8311yescharacteristic
208C2#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#1503
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
105. C83#1503semidirect