Finite Group Databasebeta

← #16844928

Subgroups — #16844928

Order 3968.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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#14521756C211yesmaximal, characteristic
2#14521400C211yesmaximal, characteristic, complemented
3#14521329C211yesmaximal, characteristic
4#14521260C211yesmaximal, characteristic, complemented
5#14520797C211yesmaximal, characteristic, complemented
6#14520781C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic
8C4×D4×C31C2211yescharacteristic
9D4×Dic31—21no—
10C2×C4⋊Dic31—21no—
11#11758501—21no—
12C2×Dic124—21no—
13#11758467—21no—
14#11758455—22no—
15#11758446C2211yescharacteristic
16#11758446C2211yescharacteristic
17C4×Dic62C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C4×C8×C31C2211yescharacteristic
20#11758420—21no—
21#11758404—22no—
22#11758404—21no—
23#11758395—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×D4×C31D411yescharacteristic
26C22×C4×C31—21no—
27C22×Dic31—22no—
28C2×Dic62—21no—
29C2×Dic62D411yescharacteristic
30C2×Dic62D412yes—
31C2×C8×C31—21no—
32C2×C8×C31—21no—
33C4⋊C4×C31D411yescharacteristic
34C22⋊C4×C31—21no—
35C42×C31C2311yescharacteristic
36C22⋊Dic31—22no—
37C4⋊Dic31—22no—
38C4⋊Dic31—21no—
39C4⋊Dic31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31—21no—
42C4⋊Dic31D411yescharacteristic
43Dic31⋊C4—22no—
44Dic31⋊C4—21no—
45C4×Dic31—21no—
46C2×C31⋊C8—21no—
47Dic124—42no—
48C23×C31—21no—
49D4×C31—21no—
50D4×C31Q1612yescomplemented
51C2×C4×C31—21no—
52C2×C4×C31—41no—
53C2×C4×C31—41no—
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×Dic31—21no—
58C2×Dic31—21no—
59C2×Dic31—22no—
60C2×Dic31—41no—
61C2×Dic31—82no—
62Dic62—21no—
63Dic62—21no—
64Dic62—42no—
65Dic62—41no—
66Dic62—41no—
67C8×C31—41no—
68C8×C31—41no—
69C31⋊C8—41no—
70#1644—311nomaximal, Sylow
71C22×C31—22no—
72C22×C31—41no—
73C22×C31—41no—
74C22×C31#12011yescharacteristic
75C4×C31—21no—
76C4×C31—41no—
77C4×C31C2×Q1611yescharacteristic
78C4×C31#13511yescharacteristic
79C4×C31AGL(1,ℤ/8)11yescharacteristic
80C4×C31#13711yescharacteristic
81Dic31—41no—
82Dic31—42no—
83Dic31—41no—
84Dic31—81no—
85#554—311no—
86#487—311no—
87#474—311no—
88#462—311no—
89#333—311no—
90Q8⋊C8—311no—
91D4⋊C8D3111yescharacteristic
92C2×C31—42no—
93C2×C31#44911yescharacteristic
94C2×C31#45111yescharacteristic
95C2×C31#45511yescharacteristic
96C2×Q16—621no—
97C4⋊Q8—311no—
98C4⋊Q8—311no—
99#125—621no—
100C22⋊Q8—622no—
101C22⋊Q8—621no—
102C4×Q8—311no—
103C4×D4—621no—
104C4×D4C2×D3111yescharacteristic
105C2×C4⋊C4—621no—
106#107—621no—
107C4⋊C8—311no—
108C4⋊C8C2×D3111yescharacteristic
109#103—621no—
110#103—622no—
111#102—621no—
112C4×C8C2×D3111yescharacteristic
113C31#164411yescharacteristic, complemented, Sylow
114C2×Q8—311no—
115C2×Q8—312no—
116C2×Q8—621no—
117C2×D4D12411yescharacteristic
118C22×C4—21no—
119C22×C4—622no—
120Q16—1242no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—621no—
124C4⋊C4—311no—
125C4⋊C4—622no—
126C4⋊C4—622no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C4⋊C4—621no—
130C4⋊C4—621no—
131C4⋊C4—621no—
132C4⋊C4D12411yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—622no—
135C42—621no—
136C42C22×D3111yescharacteristic
137C23—21no—
138Q8—621no—
139Q8—621no—
140Q8—1242no—
141Q8—1241no—
142Q8—1241no—
143D4—21no—
144D4Dic12412yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—621no—
149C2×C4—621no—
150C2×C4—622no—
151C2×C4—1241no—
152C2×C4—2482no—
153C2×C4C2×D12411yescharacteristic
154C2×C4D4×D3111yescharacteristic
155C2×C4D4×D3111yescharacteristic
156C8—41no—
157C8—41no—
158C8—1241no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1175845911yescharacteristic
163C4—21no—
164C4—41no—
165C4—1241no—
166C4—1241no—
167C4—1242no—
168C4—2481no—
169C4C2×Dic12411yescharacteristic
170C4#1175848611yescharacteristic
171C4#1175848811yescharacteristic
172C4#1175849311yescharacteristic
173C2—42no—
174C2#1452119511yescharacteristic
175C2#1452120711yescharacteristic
176C2#1452122811yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31#120
prime radicalC2×D4×C31D4
hypercenterD4⋊C8D31
hypocenterC31#1644
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14521400C2semidirect
4. #14521260C2semidirect
5. #14520797C2semidirect
6. #14520781C2semidirect
50. D4×C31Q16semidirect
113. C31#1644semidirect
144. D4Dic124semidirect

Maximal subgroups

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

subgroupindex
#145217562
#145214002
#145213292
#145212602
#145207972
#145207812
C31×D4⋊C82
#164431