Finite Group Databasebeta

← #24906002

Subgroups — #24906002

Order 10624.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#19128235C211yesmaximal, characteristic
2#19127567C211yesmaximal, characteristic, complemented
3#19127439C212yesmaximal, complemented
4#19127436C212yesmaximal
5#432×C83C211yesmaximal, characteristic, complemented
6#14581786—21no—
7#14581784C411yescharacteristic, complemented
8#14581780C411yescharacteristic, complemented
9#14581775—21no—
10#14581771C2211yescharacteristic
11#14581766C2211yescharacteristic
12C4×Dic166C411yescharacteristic, complemented
13C4×D332C411yescharacteristic, complemented
14C4×C22⋊D83—21no—
15#14581749—21no—
16C2×C4⋊Dic83—21no—
17C83⋊#95—21no—
18C83⋊#95C2212yes—
19C2×C42×C83C2211yescharacteristic
20C4⋊C8×C83—21no—
21C22⋊C8×C83C2212yes—
22#97×C83—21no—
23C2×Dic166C2×C411yescharacteristic
24C2×D332C2×C411yescharacteristic
25C2×C22⋊D83—21no—
26C22×Dic83—22no—
27C2×C4×D83—21no—
28C4⋊Dic83—42no—
29C4⋊Dic83C2×C411yescharacteristic
30C4⋊Dic83C2×C411yescharacteristic
31Dic83⋊C4—21no—
32Dic83⋊C4—21no—
33Dic83⋊C4—21no—
34Dic83⋊C4—21no—
35C22⋊Dic83—21no—
36(C2×D83)⋊C4—21no—
37(C2×D83)⋊C4—21no—
38(C2×D83)⋊C4—21no—
39(C2×D83)⋊C4—21no—
40C4×Dic83—21no—
41C22×C4×C83D411yescharacteristic
42C22×C4×C83D411yescharacteristic
43C22×C4×C83C2311yescharacteristic
44C2×C8×C83—22no—
45C42×C83C2×C411yescharacteristic
46C42×C83C2×C411yescharacteristic
47C42×C83D411yescharacteristic
48C42×C83D411yescharacteristic
49C23×C83C2×D411yescharacteristic
50C22×D83—21no—
51C2×C4×C83—21no—
52C2×C4×C83—21no—
53C2×C4×C83—41no—
54C2×C4×C83—41no—
55C2×C4×C83C22⋊C411yescharacteristic
56C2×C4×C83C22⋊C411yescharacteristic
57C2×C4×C83C22⋊C411yescharacteristic
58C2×C4×C83C22⋊C411yescharacteristic
59C2×C4×C83C22×C411yescharacteristic
60C2×C4×C83C2×D411yescharacteristic
61C22⋊D83—41no—
62C22⋊D83—41no—
63C2×Dic83—21no—
64C2×Dic83—21no—
65C2×Dic83—21no—
66C2×Dic83—42no—
67C2×Dic83—42no—
68C2×Dic83—42no—
69D332—41no—
70C4×D83—42no—
71Dic166—41no—
72C8×C83—42no—
73C22×C83—21no—
74C22×C83—21no—
75C22×C83C2×C22⋊C411yescharacteristic
76C22×C83AGL(1,ℤ/8)11yescharacteristic
77C22×C83#13711yescharacteristic
78C2×D83—41no—
79C2×D83—41no—
80C2×D83—41no—
81C4×C83—21no—
82C4×C83—21no—
83C4×C83—21no—
84C4×C83—21no—
85C4×C83—21no—
86C4×C83—21no—
87Dic83—41no—
88Dic83—41no—
89Dic83—41no—
90Dic83—82no—
91C2×C83—21no—
92C2×C83—21no—
93C2×C83#41011yescharacteristic
94C2×C83#41711yescharacteristic
95C2×C83#42111yescharacteristic
96D83—81no—
97#1512—831nomaximal, Sylow
98C83#151211yescharacteristic, complemented, Sylow
99#529—831no—
100#432D8311yescharacteristic, complemented
101#382—831no—
102#328—832no—
103#327—832no—
104#126—1661no—
105#125—831no—
106#124—831no—
107#123—1661no—
108C22⋊Q8—831no—
109#121—831no—
110C4×Q8—831no—
111C4×D4—831no—
112C4×D4—1661no—
113#117—1661no—
114C2×C4⋊C4—1661no—
115C2×C42C2×D8311yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C2×D8312yes—
118#97—21no—
119#95—832no—
120#95—1661no—
121C2×Q8—831no—
122C2×D4—831no—
123C2×D4—1661no—
124C22×C4—1662no—
125C22×C4—1661no—
126C22×C4D33211yescharacteristic
127C22×C4D33211yescharacteristic
128C22×C4C22×D8311yescharacteristic
129C2×C8—22no—
130C4⋊C4—3322no—
131C4⋊C4—831no—
132C4⋊C4—831no—
133C4⋊C4—1661no—
134C4⋊C4—1661no—
135C4⋊C4—1661no—
136C4⋊C4—1661no—
137C22⋊C4—1661no—
138C22⋊C4—1661no—
139C22⋊C4—1661no—
140C22⋊C4—1661no—
141C22⋊C4—1661no—
142C42—1661no—
143C42C4×D8311yescharacteristic
144C42C4×D8311yescharacteristic
145C42C22⋊D8311yescharacteristic
146C42C22⋊D8311yescharacteristic
147C23—1661no—
148C23C2×D33211yescharacteristic
149Q8—3321no—
150D4—3321no—
151D4—3321no—
152D4—3321no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—3322no—
158C2×C4—3322no—
159C2×C4—3322no—
160C2×C4—3322no—
161C2×C4—1661no—
162C2×C4—1661no—
163C2×C4—1661no—
164C2×C4(C2×D83)⋊C411yescharacteristic
165C2×C4(C2×D83)⋊C411yescharacteristic
166C2×C4(C2×D83)⋊C411yescharacteristic
167C2×C4(C2×D83)⋊C411yescharacteristic
168C2×C4C2×C4×D8311yescharacteristic
169C2×C4C2×C22⋊D8311yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—3321no—
174C22—3321no—
175C22—3321no—
176C22C2×(C2×D83)⋊C411yescharacteristic
177C22#1458182011yescharacteristic
178C22#1458182511yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—3321no—
186C4—3321no—
187C4—3321no—
188C4—6642no—
189C2—21no—
190C2—21no—
191C2—6641no—
192C2#1912767411yescharacteristic
193C2#1912770311yescharacteristic
194C2#1912771711yescharacteristic
subgroupG/H
centerC22C2×(C2×D83)⋊C4
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#432×C83C2
socleC22×C83C2×C22⋊C4
prime radical#14581766C22
cosocleC22×C4×C83C23
hypercenter#432D83
hypocenterC83#1512
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #19127567C2semidirect
3. #19127439C2semidirect
5. #432×C83C2semidirect
7. #14581784C4semidirect
8. #14581780C4semidirect
12. C4×Dic166C4semidirect
13. C4×D332C4semidirect
98. C83#1512semidirect
100. #432D83semidirect