Finite Group Databasebeta

← #16844880

Subgroups — #16844880

Order 3968.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521773C211yesmaximal, characteristic
2#14521341C211yesmaximal, characteristic, complemented
3#14521336C211yesmaximal, characteristic
4#14520795C211yesmaximal, characteristic, complemented
5#14520781C211yesmaximal, characteristic, complemented
6#14520778C211yesmaximal, characteristic
7C31×#487C211yesmaximal, characteristic, complemented
8C31×C4⋊Q8C2211yescharacteristic
9C31×C4⋊Q8C2211yescharacteristic
10#11758524—21no—
11Q8×Dic31—21no—
12#11758475—22no—
13#11758474—21no—
14#11758469—21no—
15C4×D124C2211yescharacteristic
16C4×Dic62C2211yescharacteristic
17C31×#103—22no—
18C4×C8×C31C2211yescharacteristic
19#11758398—21no—
20#11758397—21no—
21#11758396—21no—
22#11758395—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×Q8×C31—21no—
27C2×D124D411yescharacteristic
28C2×C4×D31—21no—
29C2×Dic62D411yescharacteristic
30C2×C8×C31—21no—
31C4⋊C4×C31—21no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31D412yes—
35C42×C31C2311yescharacteristic
36(C2×D31)⋊C4—22no—
37(C2×D31)⋊C4—22no—
38(C2×D31)⋊C4—21no—
39C4⋊Dic31—22no—
40C4⋊Dic31D411yescharacteristic
41C4⋊Dic31D411yescharacteristic
42Dic31⋊C4—21no—
43C4×Dic31—22no—
44C4×Dic31—21no—
45C2×C31⋊C8—21no—
46C2×C31⋊C8—21no—
47C22×D31—21no—
48Q8×C31—42no—
49Q8×C31—41no—
50Q8×C31—41no—
51C2×C4×C31—22no—
52C2×C4×C31—41no—
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×Dic31—21no—
57C2×Dic31—21no—
58C2×Dic31—21no—
59D124—21no—
60D124—21no—
61C4×D31—41no—
62C4×D31—41no—
63Dic62—21no—
64Dic62—21no—
65C8×C31—41no—
66C31⋊C8—41no—
67C31⋊C8—41no—
68#1638—311nomaximal, Sylow
69C22×C31#12011yescharacteristic
70C2×D31—41no—
71C2×D31—41no—
72C2×D31—41no—
73C4×C31—21no—
74C4×C31—42no—
75C4×C31—81no—
76C4×C31#13511yescharacteristic
77C4×C31#13511yescharacteristic
78C4×C31#13711yescharacteristic
79C4×C31#13711yescharacteristic
80Dic31—41no—
81Dic31—41no—
82Dic31—41no—
83#556—311no—
84#487D3111yescharacteristic, complemented
85#477—311no—
86#476—311no—
87#332—311no—
88Q8⋊C8—311no—
89D4⋊C8—311no—
90C2×C31#45211yescharacteristic
91C2×C31#45211yescharacteristic
92C2×C31#45411yescharacteristic
93D31—81no—
94C4⋊Q8C2×D3111yescharacteristic
95C4⋊Q8C2×D3111yescharacteristic
96#126—622no—
97#124—621no—
98C22⋊Q8—621no—
99C4×Q8—311no—
100C4×Q8—621no—
101C4×D4—311no—
102#117—621no—
103#107—621no—
104#106—621no—
105C4⋊C8—311no—
106C4⋊C8—311no—
107#103—22no—
108#103—621no—
109#102—621no—
110C4×C8C2×D3111yescharacteristic
111C31#163811yescharacteristic, complemented, Sylow
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—311no—
115C2×D4—311no—
116C22×C4—621no—
117C2×C8—21no—
118C2×C8—621no—
119C2×C8—621no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—311no—
124C4⋊C4—311no—
125C4⋊C4—622no—
126C4⋊C4—621no—
127C4⋊C4C22⋊D3112yes—
128C22⋊C4—622no—
129C22⋊C4—622no—
130C22⋊C4—621no—
131C42—622no—
132C42—621no—
133C42C22×D3111yescharacteristic
134C23—621no—
135Q8—42no—
136Q8—41no—
137Q8—41no—
138Q8—621no—
139Q8—621no—
140D4—621no—
141D4—621no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—621no—
145C2×C4—621no—
146C2×C4—621no—
147C2×C4—1241no—
148C2×C4—1241no—
149C2×C4D4×D3111yescharacteristic
150C2×C4D4×D3111yescharacteristic
151C2×C4C2×C22⋊D3111yescharacteristic
152C8—41no—
153C8—1241no—
154C8—1241no—
155C22—1241no—
156C22—1241no—
157C22—1241no—
158C22#1175851411yescharacteristic
159C4—21no—
160C4—42no—
161C4—81no—
162C4—1241no—
163C4—1241no—
164C4—1241no—
165C4#1175849211yescharacteristic
166C4#1175849311yescharacteristic
167C4#1175849511yescharacteristic
168C4#1175849611yescharacteristic
169C2—2481no—
170C2#1452120811yescharacteristic
171C2#1452121011yescharacteristic
172C2#1452122111yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#487C2
socleC22×C31#120
prime radicalC2×D124D4
hypercenter#487D31
hypocenterC31#1638
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #14521341C2semidirect
4. #14520795C2semidirect
5. #14520781C2semidirect
7. C31×#487C2semidirect
84. #487D31semidirect
111. C31#1638semidirect

Maximal subgroups

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

subgroupindex
#145217732
#145213412
#145213362
#145207952
#145207812
#145207782
C31×#4872
#163831