Finite Group Databasebeta

← #16844940

Subgroups — #16844940

Order 3968.

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

normal subgroups only

This group has 212 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#14521765C211yesmaximal, characteristic
2#14521399C211yesmaximal, characteristic, complemented
3#14521330C211yesmaximal, characteristic, complemented
4#14521255C211yesmaximal, characteristic, complemented
5#14520776C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic, complemented
7C31×#333C211yesmaximal, characteristic, complemented
8C31×C4⋊Q8C2211yescharacteristic
9#11758524—22no—
10C2×#92470—21no—
11#11758472—21no—
12#11758472—21no—
13#11758469—21no—
14#11758469—21no—
15C4×D124C2211yescharacteristic
16C4×D124C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20#11758423—22no—
21#11758409—21no—
22#11758406—21no—
23#11758404—21no—
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31D412yes—
26C2×D124—22no—
27C2×D124D411yescharacteristic
28C2×D124D411yescharacteristic
29C2×C4×D31—21no—
30C2×C4×D31—21no—
31C2×Dic62—21no—
32C2×C8×C31—21no—
33C2×C8×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31—21no—
36C42×C31C2311yescharacteristic
37(C2×D31)⋊C4—22no—
38(C2×D31)⋊C4—22no—
39(C2×D31)⋊C4—21no—
40(C2×D31)⋊C4—21no—
41C4⋊Dic31—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31D411yescharacteristic
44C4⋊Dic31D411yescharacteristic
45C4×Dic31—22no—
46C2×C31⋊C8—21no—
47#92470—42no—
48C22×D31—21no—
49C22×D31—21no—
50Q8×C31—42no—
51C2×C4×C31—22no—
52C2×C4×C31C2×D411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×Dic31—21no—
56C2×Dic31—21no—
57C2×Dic31—41no—
58D124—21no—
59D124—21no—
60D124—21no—
61D124—21no—
62D124—82no—
63C4×D31—41no—
64C4×D31—41no—
65C4×D31—41no—
66C4×D31—41no—
67Dic62—41no—
68Dic62—41no—
69C8×C31—41no—
70C8×C31—41no—
71C31⋊C8—41no—
72#1646—311nomaximal, Sylow
73C22×C31#12011yescharacteristic
74C2×D31—41no—
75C2×D31—41no—
76C2×D31—41no—
77C2×D31—41no—
78C2×D31—41no—
79C2×D31—41no—
80C4×C31—21no—
81C4×C31—42no—
82C4×C31#13511yescharacteristic
83C4×C31#13511yescharacteristic
84C4×C31AGL(1,ℤ/8)11yescharacteristic
85C4×C31#13711yescharacteristic
86Dic31—41no—
87Dic31—41no—
88Dic31—81no—
89#555—311no—
90#487—311no—
91#474—311no—
92#461—311no—
93#333D3111yescharacteristic, complemented
94D4⋊C8—311no—
95D4⋊C8—311no—
96C2×C31#44911yescharacteristic
97C2×C31#45211yescharacteristic
98C2×C31#45511yescharacteristic
99D31—81no—
100D31—81no—
101C2×SD16—621no—
102C4⋊Q8—311no—
103C4⋊Q8C2×D3111yescharacteristic
104#124—622no—
105#121—621no—
106#121—621no—
107C4×D4—311no—
108C4×D4—311no—
109#117—621no—
110#117—621no—
111#107—621no—
112C4⋊C8C2×D3111yescharacteristic
113C4⋊C8C2×D3111yescharacteristic
114#103—621no—
115#103—622no—
116#102—621no—
117C4×C8—311no—
118C31#164611yescharacteristic, complemented, Sylow
119C2×Q8—621no—
120C2×Q8D12412yes—
121C2×D4—311no—
122C2×D4—311no—
123C2×D4—622no—
124C22×C4—621no—
125C22×C4—621no—
126SD16—1242no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—621no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—311no—
133C4⋊C4—311no—
134C4⋊C4—621no—
135C4⋊C4—621no—
136C22⋊C4—622no—
137C22⋊C4—622no—
138C22⋊C4—621no—
139C22⋊C4—621no—
140C42—622no—
141C42C22×D3111yescharacteristic
142C23—621no—
143C23—621no—
144Q8—42no—
145Q8—1241no—
146Q8—1241no—
147D4—621no—
148D4—621no—
149D4—621no—
150D4—621no—
151D4—2482no—
152C2×C4—22no—
153C2×C4—621no—
154C2×C4—621no—
155C2×C4—1241no—
156C2×C4—1241no—
157C2×C4—1241no—
158C2×C4—1241no—
159C2×C4—1241no—
160C2×C4C2×D12411yescharacteristic
161C2×C4D4×D3111yescharacteristic
162C2×C4D4×D3111yescharacteristic
163C8—41no—
164C8—41no—
165C8—1241no—
166C22—1241no—
167C22—1241no—
168C22—1241no—
169C22—1241no—
170C22—1241no—
171C22—1241no—
172C22#1175845911yescharacteristic
173C4—21no—
174C4—42no—
175C4—1241no—
176C4—1241no—
177C4—2481no—
178C4#1175849111yescharacteristic
179C4#1175849311yescharacteristic
180C4#1175849511yescharacteristic
181C4#1175849611yescharacteristic
182C2—2481no—
183C2—2481no—
184C2#1452119711yescharacteristic
185C2#1452121411yescharacteristic
186C2#1452122911yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#333C2
socleC22×C31#120
prime radical#14521765C2
hypercenter#333D31
hypocenterC31#1646
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #14521399C2semidirect
3. #14521330C2semidirect
4. #14521255C2semidirect
5. #14520776C2semidirect
6. #14520776C2semidirect
7. C31×#333C2semidirect
93. #333D31semidirect
118. C31#1646semidirect

Maximal subgroups

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

subgroupindex
#145217652
#145213992
#145213302
#145212552
#145207762
C31×#3332
#164631