Finite Group Databasebeta

← #24906012

Subgroups — #24906012

Order 10624.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#19127568C211yesmaximal, 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×Dic83C2211yescharacteristic
18Dic83⋊C8—21no—
19C22⋊(C83⋊C8)C2211yescharacteristic
20#14581702—21no—
21C83⋊#95—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—21no—
42C4×Dic83—21no—
43C4×Dic83C2×C411yescharacteristic
44C4×Dic83C2×C411yescharacteristic
45C4×Dic83D411yescharacteristic
46C4×Dic83D411yescharacteristic
47C2×Q8×C83C2×C411yescharacteristic
48C22×C4×C83—21no—
49C22×C4×C83C2311yescharacteristic
50C2×C8×C83—21no—
51C4⋊C4×C83—21no—
52C4⋊C4×C83C2×C411yescharacteristic
53C22⋊C4×C83—21no—
54C23×C83C2×D411yescharacteristic
55Q8×C83—41no—
56C2×C4×C83—21no—
57C2×C4×C83—21no—
58C2×C4×C83—41no—
59C2×C4×C83—41no—
60C2×C4×C83—41no—
61C2×C4×C83—41no—
62C2×C4×C83C22×C411yescharacteristic
63C2×C4×C83C2×D411yescharacteristic
64C2×Dic83—21no—
65C2×Dic83—21no—
66C2×Dic83—21no—
67C2×Dic83—21no—
68C2×Dic83—41no—
69C2×Dic83—41no—
70C2×Dic83—41no—
71C2×Dic83—41no—
72C2×Dic83C22⋊C411yescharacteristic
73C2×Dic83C22⋊C411yescharacteristic
74C2×Dic83C22⋊C411yescharacteristic
75C2×Dic83C22⋊C411yescharacteristic
76Dic166—42no—
77Dic166—41no—
78C8×C83—41no—
79C83⋊C8—41no—
80C22×C83—21no—
81C22×C83—21no—
82C22×C83C2×C22⋊C411yescharacteristic
83C22×C83#13711yescharacteristic
84C22×C83#13711yescharacteristic
85C4×C83—21no—
86C4×C83—21no—
87C4×C83—41no—
88C4×C83—41no—
89C4×C83—81no—
90Dic83—21no—
91Dic83—21no—
92Dic83—21no—
93Dic83—21no—
94Dic83—41no—
95Dic83—41no—
96Dic83—81no—
97C2×C83—21no—
98C2×C83—21no—
99C2×C83#41011yescharacteristic
100C2×C83#41911yescharacteristic
101C2×C83#42111yescharacteristic
102#1515—831nomaximal, Sylow
103C83#151511yescharacteristic, complemented, Sylow
104#533—831no—
105#432—831no—
106#383—831no—
107#328—831no—
108#328—831no—
109#328—831no—
110#328D8311yescharacteristic
111C4⋊Q8—831no—
112C4⋊Q8—831no—
113#125—1661no—
114C22⋊Q8—831no—
115C22⋊Q8—1661no—
116C22⋊Q8C2×D8311yescharacteristic
117C4×Q8—831no—
118C4×Q8—831no—
119C4×Q8—1661no—
120#117—1661no—
121C2×C42—831no—
122C4⋊C8—1661no—
123C22⋊C8—831no—
124C22⋊C8C2×D8311yescharacteristic
125#97—1661no—
126#95—831no—
127#95—1661no—
128#95—1661no—
129#95C2×D8311yescharacteristic
130C2×Q8—831no—
131C2×Q8—1661no—
132C2×Q8C4×D8311yescharacteristic
133C22×C4—21no—
134C22×C4—831no—
135C22×C4—831no—
136C22×C4—1661no—
137C22×C4C22×D8311yescharacteristic
138C2×C8—21no—
139C2×C8—1661no—
140C4⋊C4—21no—
141C4⋊C4—831no—
142C4⋊C4—1661no—
143C4⋊C4—1661no—
144C4⋊C4—1661no—
145C4⋊C4—1661no—
146C4⋊C4—1661no—
147C4⋊C4—1661no—
148C4⋊C4C4×D8311yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—1661no—
151C42—831no—
152C42—831no—
153C42—831no—
154C42—831no—
155C42—1661no—
156C42—1661no—
157C23D4×D8311yescharacteristic
158Q8—41no—
159Q8—3321no—
160Q8—3322no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—3321no—
168C2×C4—3321no—
169C2×C4—3321no—
170C2×C4—3321no—
171C2×C4—831no—
172C2×C4—831no—
173C2×C4—831no—
174C2×C4—831no—
175C2×C4—1661no—
176C2×C4—1661no—
177C2×C4—1661no—
178C2×C4—1661no—
179C2×C4C2×C4×D8311yescharacteristic
180C2×C4D4×D8311yescharacteristic
181C8—41no—
182C8—3321no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D8311yescharacteristic
186C22#1458182111yescharacteristic
187C22#1458182411yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—3321no—
194C4—3321no—
195C4—6641no—
196C4—1661no—
197C4—1661no—
198C4—1661no—
199C4—1661no—
200C2—21no—
201C2—21no—
202C2#1912767311yescharacteristic
203C2#1912770811yescharacteristic
204C2#1912771611yescharacteristic
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#1515
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
103. C83#1515semidirect