Finite Group Databasebeta

← #16856110

Subgroups — #16856110

Order 3968.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#14521597C211yesmaximal, characteristic
2#125×D31C211yesmaximal, characteristic, complemented
3#14521419C211yesmaximal, characteristic, complemented
4#14521418C211yesmaximal, characteristic, complemented
5#14521413C211yesmaximal, characteristic, complemented
6#14521402C214yesmaximal, complemented
7#14521047C214yesmaximal, complemented
8#14521001C211yesmaximal, characteristic, complemented
9C31×#490C211yesmaximal, characteristic, complemented
10C2×#92497C2212yes—
11C31×#127C2211yescharacteristic
12C31×#125C2211yescharacteristic
13#11758515—22no—
14#11758513C2212yes—
15D4×Dic31—22no—
16C2×#92469C2212yes—
17C4⋊C4×D31—22no—
18C4⋊C4×D31C2212yes—
19#11758467C2212yes—
20#11758466—22no—
21C42×D31C2211yescharacteristic
22#11758447C2211yescharacteristic
23#11758446C2211yescharacteristic
24C31×#102C2214yes—
25C31×#97C2211yescharacteristic
26#11758420C2214yes—
27#11758404C2214yes—
28C8×Dic31C2212yes—
29#11758398C2214yes—
30#11758391C2211yescharacteristic
31C2×D4×C31—22no—
32C2×D4×C31C2312yes—
33C2×C22⋊D31—22no—
34C22×Dic31—22no—
35#92497—28no—
36C2×C4×D31—22no—
37C2×C4×D31D412yes—
38C2×C4×D31C2311yescharacteristic
39C2×Dic62C2312yes—
40C2×C8×C31C2312yes—
41C4⋊C4×C31—22no—
42C4⋊C4×C31C2312yes—
43C42×C31C2311yescharacteristic
44C22⋊Dic31—24no—
45C4⋊Dic31—22no—
46C4⋊Dic31—22no—
47C4⋊Dic31C2312yes—
48Dic31⋊C4—22no—
49Dic31⋊C4—22no—
50Dic31⋊C4—22no—
51C4×Dic31D412yes—
52C4×Dic31C2311yescharacteristic
53C2×C31⋊C8C2312yes—
54#92469—24no—
55C23×C31—22no—
56C22×D31C2×D411yescharacteristic
57D4×C31—24no—
58D4×C31—44no—
59C2×C4×C31—22no—
60C2×C4×C31C2×D412yes—
61C2×C4×C31C2411yescharacteristic
62C22⋊D31—44no—
63C2×Dic31—22no—
64C2×Dic31—22no—
65C2×Dic31—44no—
66C2×Dic31C2×D412yes—
67C2×Dic31C2×D411yescharacteristic
68C4×D31—42no—
69C4×D31—44no—
70C4×D31#4114yes—
71Dic62—24no—
72C8×C31—22no—
73C31⋊C8—22no—
74#3142—311nomaximal, Sylow
75C22×C31—42no—
76C22×C31—44no—
77C22×C31C22×D411yescharacteristic
78C2×D31—22no—
79C2×D31#12412yes—
80C4×C31—22no—
81C4×C31—42no—
82C4×C31C2×#4112yes—
83Dic31—22no—
84Dic31—42no—
85Dic31—42no—
86Dic31#12412yes—
87#532—311no—
88C2×#125—311no—
89#491—311no—
90#491—311no—
91#490—311no—
92#490D3111yescharacteristic, complemented
93#488—314no—
94#417—314no—
95C4×M16—311no—
96C2×C31—82no—
97C2×C31C2×#12411yescharacteristic
98C2×C31#57512yes—
99D31—22no—
100C2×#41—312no—
101C2×M16—312no—
102C4⋊Q8—311no—
103#127C2×D3111yescharacteristic
104#125—312no—
105#125—311no—
106#125—622no—
107#125C2×D3111yescharacteristic
108#124—312no—
109#121—622no—
110C4×D4—622no—
111C2×C4⋊C4—312no—
112C2×C4⋊C4—622no—
113C2×C42—311no—
114#103—314no—
115#103—314no—
116#102—314no—
117#102C2×D3114yes—
118#97—311no—
119#97C2×D3111yescharacteristic
120C4×C8—312no—
121C31#314211yescharacteristic, complemented, Sylow
122#41—628no—
123C2×Q8—312no—
124C2×D4—22no—
125C2×D4—622no—
126C2×D4C22×D3112yes—
127C22×C4—311no—
128C22×C4—312no—
129C22×C4—622no—
130C22×C4—622no—
131M16—624no—
132C2×C8—312no—
133C2×C8C22×D3112yes—
134C4⋊C4—22no—
135C4⋊C4—312no—
136C4⋊C4—622no—
137C4⋊C4—622no—
138C4⋊C4—622no—
139C4⋊C4—622no—
140C4⋊C4—622no—
141C4⋊C4C22×D3112yes—
142C22⋊C4—624no—
143C42—312no—
144C42—311no—
145C42C22×D3111yescharacteristic
146C23—22no—
147C23—311no—
148Q8—624no—
149D4—24no—
150D4—44no—
151D4—1244no—
152C2×C4—22no—
153C2×C4—311no—
154C2×C4—314no—
155C2×C4—312no—
156C2×C4—622no—
157C2×C4—622no—
158C2×C4—1242no—
159C2×C4—1244no—
160C2×C4—1244no—
161C2×C4D4×D3112yes—
162C2×C4C23×D3111yescharacteristic
163C8—22no—
164C8—622no—
165C22—42no—
166C22—44no—
167C22—312no—
168C22—622no—
169C22C2×D4×D3111yescharacteristic
170C4—22no—
171C4—42no—
172C4—312no—
173C4—622no—
174C4—1242no—
175C4—1242no—
176C4#41×D3112yes—
177C2—82no—
178C2—622no—
179C2#124×D3111yescharacteristic
180C2#1452184512yes—
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#490C2
socleC22×C31C22×D4
prime radical#14521597C2
hypercenter#490D31
hypocenterC31#3142
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D31C2semidirect
3. #14521419C2semidirect
4. #14521418C2semidirect
5. #14521413C2semidirect
6. #14521402C2semidirect
7. #14521047C2semidirect
8. #14521001C2semidirect
9. C31×#490C2semidirect
92. #490D31semidirect
121. C31#3142semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145215972
#125×D312
#145214192
#145214182
#145214132
#145214022
#145210472
#145210012
C31×#4902
#314231