Finite Group Databasebeta

← #24906063

Subgroups — #24906063

Order 10624.

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

normal subgroups only

This group has 212 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#125×D83C211yesmaximal, characteristic
2#19127756C211yesmaximal, characteristic
3#19127653C211yesmaximal, characteristic
4#19127443C211yesmaximal, characteristic, complemented
5#19127442C211yesmaximal, characteristic, complemented
6#19127442C211yesmaximal, characteristic, complemented
7#330×C83C211yesmaximal, characteristic, complemented
8C2×#13050573—21no—
9#14581784C2211yescharacteristic
10#14581783C411yescharacteristic
11#14581783C411yescharacteristic
12#14581782—21no—
13#14581782—21no—
14C4⋊C4×D83—21no—
15C4⋊C4×D83—21no—
16C4⋊C4×D83C411yescharacteristic
17C4⋊C4×D83C411yescharacteristic
18C42×D83C2211yescharacteristic
19Dic83⋊C8—21no—
20(C2×D83)⋊C8—21no—
21#14581703C2211yescharacteristic
22#14581703C2211yescharacteristic
23C8×Dic83—21no—
24#125×C83C2211yescharacteristic
25#97×C83C2211yescharacteristic
26#97×C83C2211yescharacteristic
27C2×C4×D83—21no—
28C2×C4×D83—21no—
29C2×C4×D83C2×C411yescharacteristic
30C2×C4×D83D411yescharacteristic
31C2×C4×D83D411yescharacteristic
32#13050573—24no—
33C2×C83⋊C8—21no—
34C2×C83⋊C8—21no—
35C4⋊Dic83—21no—
36C4⋊Dic83—21no—
37C4⋊Dic83C2×C411yescharacteristic
38C4⋊Dic83C2×C411yescharacteristic
39Dic83⋊C4—21no—
40Dic83⋊C4—21no—
41Dic83⋊C4—21no—
42Dic83⋊C4—21no—
43Dic83⋊C4—21no—
44Dic83⋊C4—21no—
45C4×Dic83C2×C411yescharacteristic
46C4×Dic83D411yescharacteristic
47C4×Dic83D411yescharacteristic
48C2×C8×C83—21no—
49C2×C8×C83—21no—
50C4⋊C4×C83—21no—
51C4⋊C4×C83—21no—
52C4⋊C4×C83C2×C411yescharacteristic
53C4⋊C4×C83C2×C411yescharacteristic
54C42×C83C2311yescharacteristic
55C22×D83C22⋊C411yescharacteristic
56C2×C4×C83—21no—
57C2×C4×C83—21no—
58C2×C4×C83C22×C411yescharacteristic
59C2×C4×C83C2×D411yescharacteristic
60C2×C4×C83C2×D411yescharacteristic
61C2×Dic83—21no—
62C2×Dic83—21no—
63C2×Dic83C22⋊C411yescharacteristic
64C2×Dic83C22⋊C411yescharacteristic
65C2×Dic83C22⋊C411yescharacteristic
66C4×D83—22no—
67C4×D83—22no—
68C4×D83—41no—
69C4×D83—42no—
70C4×D83—42no—
71C8×C83—22no—
72C8×C83—41no—
73C83⋊C8—22no—
74C83⋊C8—41no—
75C22×C83C2×C22⋊C411yescharacteristic
76C2×D83—21no—
77C2×D83—21no—
78C2×D83#10412yes—
79C4×C83—21no—
80C4×C83—21no—
81C4×C83—21no—
82C4×C83—41no—
83C4×C83—41no—
84Dic83—21no—
85Dic83—21no—
86Dic83—41no—
87Dic83—41no—
88Dic83#10112yes—
89C2×C83C2×#10111yescharacteristic
90C2×C83C2×#10411yescharacteristic
91C2×C83#42111yescharacteristic
92D83—22no—
93#1528—831nomaximal, Sylow
94C83#152811yescharacteristic, complemented, Sylow
95C2×#125—831no—
96#432—831no—
97C4×M16—831no—
98#330—831no—
99#330—831no—
100#330—831no—
101#330D8311yescharacteristic, complemented
102C2×M16—1661no—
103#125—831no—
104#125—831no—
105#125—831no—
106#125—1661no—
107#125—1661no—
108#125C2×D8311yescharacteristic
109C2×C4⋊C4—831no—
110C2×C4⋊C4—831no—
111C2×C4⋊C4—1661no—
112C2×C4⋊C4—1661no—
113C2×C42—831no—
114C4⋊C8—1661no—
115C22⋊C8—1661no—
116#97—831no—
117#97—831no—
118#97C2×D8311yescharacteristic
119#97C2×D8311yescharacteristic
120C4×C8—1661no—
121C22×C4—831no—
122C22×C4—831no—
123C22×C4—831no—
124C22×C4—1661no—
125C22×C4—1661no—
126M16—1664no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1661no—
130C2×C8—1661no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—831no—
134C4⋊C4—831no—
135C4⋊C4—1661no—
136C4⋊C4—1661no—
137C4⋊C4—1661no—
138C4⋊C4—1661no—
139C4⋊C4—1661no—
140C4⋊C4—1661no—
141C4⋊C4—1661no—
142C4⋊C4—1661no—
143C4⋊C4C4×D8311yescharacteristic
144C4⋊C4C4×D8311yescharacteristic
145C42—831no—
146C42—831no—
147C42—831no—
148C42C22×D8311yescharacteristic
149C23—831no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—3321no—
153C2×C4—3322no—
154C2×C4—3322no—
155C2×C4—831no—
156C2×C4—831no—
157C2×C4—831no—
158C2×C4—1662no—
159C2×C4—1662no—
160C2×C4—1661no—
161C2×C4—1661no—
162C2×C4C2×C4×D8311yescharacteristic
163C2×C4D4×D8311yescharacteristic
164C2×C4D4×D8311yescharacteristic
165C8—22no—
166C8—41no—
167C8—3321no—
168C8—1662no—
169C22—832no—
170C22—1661no—
171C22—1661no—
172C22C22⋊C4×D8311yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—3321no—
179C4—3321no—
180C4—832no—
181C4—1661no—
182C4—1661no—
183C2—1662no—
184C2#101×D8311yescharacteristic
185C2#104×D8311yescharacteristic
186C2#1912771611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC42C22×D83
Fitting#330×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC22×D83C22⋊C4
cosocleC42×C83C23
hypercenter#330D83
hypocenterC83#1528
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #19127443C2semidirect
5. #19127442C2semidirect
6. #19127442C2semidirect
7. #330×C83C2semidirect
94. C83#1528semidirect
101. #330D83semidirect