Finite Group Databasebeta

← #16844117

Subgroups — #16844117

Order 3968.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521583C211yesmaximal, characteristic
2#14521102C211yesmaximal, characteristic, complemented
3#14520779C212yesmaximal, complemented
4#14520776C212yesmaximal, complemented
5C31×#431C211yesmaximal, characteristic, complemented
6C2×C42×C31C2211yescharacteristic
7#11758507C411yescharacteristic
8#11758506—21no—
9C4×C22⋊D31—21no—
10#11758501C411yescharacteristic
11#11758453—21no—
12#11758452C411yescharacteristic
13C4×D124C2211yescharacteristic
14#11758449—21no—
15#11758447C411yescharacteristic
16C4×Dic62C2211yescharacteristic
17C31×C4⋊C8C2212yes—
18C31×C22⋊C8—21no—
19C4×C8×C31—21no—
20C22⋊(C31⋊C8)—21no—
21C4⋊(C31⋊C8)—21no—
22C4×C31⋊C8C2212yes—
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C2×C22⋊D31—21no—
27C2×D124C2×C411yescharacteristic
28C2×C4×D31—21no—
29C2×Dic62C2×C411yescharacteristic
30C2×C8×C31—22no—
31C42×C31C2×C411yescharacteristic
32C42×C31D411yescharacteristic
33C42×C31D411yescharacteristic
34C42×C31C2311yescharacteristic
35C22⋊Dic31—21no—
36(C2×D31)⋊C4—21no—
37(C2×D31)⋊C4—21no—
38(C2×D31)⋊C4—21no—
39(C2×D31)⋊C4—21no—
40C4⋊Dic31C2×C411yescharacteristic
41C4⋊Dic31C2×C411yescharacteristic
42Dic31⋊C4—21no—
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46C4×Dic31—21no—
47C2×C31⋊C8—22no—
48C23×C31C22⋊C411yescharacteristic
49C22×D31—21no—
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—41no—
53C2×C4×C31C22⋊C411yescharacteristic
54C2×C4×C31C22⋊C411yescharacteristic
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22×C411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C22⋊D31—42no—
60C2×Dic31—21no—
61C2×Dic31—21no—
62C2×Dic31—21no—
63D124—22no—
64C4×D31—42no—
65Dic62—22no—
66C8×C31—42no—
67C31⋊C8—42no—
68#1482—311nomaximal, Sylow
69C22×C31—21no—
70C22×C31—21no—
71C22×C31—21no—
72C22×C31C2×C22⋊C411yescharacteristic
73C2×D31—41no—
74C2×D31—41no—
75C2×D31—41no—
76C4×C31—21no—
77C4×C31—21no—
78C4×C31—21no—
79C4×C31—21no—
80C4×C31#13112yes—
81C4×C31#13512yes—
82Dic31—41no—
83Dic31—41no—
84Dic31—41no—
85#529—311no—
86#431—311no—
87#431D3111yescharacteristic, complemented
88Q8⋊C8—312no—
89D4⋊C8—312no—
90C2×C31—41no—
91C2×C31#40811yescharacteristic
92C2×C31#41611yescharacteristic
93C2×C31#42111yescharacteristic
94D31—81no—
95#126—621no—
96#125—311no—
97#124—311no—
98#123—621no—
99C22⋊Q8—311no—
100#121—311no—
101C4×Q8—311no—
102C4×D4—311no—
103C4×D4—621no—
104#117—621no—
105C2×C42C2×D3111yescharacteristic
106C4⋊C8—621no—
107C4⋊C8C2×D3112yes—
108C22⋊C8—21no—
109C22⋊C8—621no—
110C4×C8—21no—
111C4×C8—312no—
112C31#148211yescharacteristic, complemented, Sylow
113C2×Q8—311no—
114C2×D4—311no—
115C2×D4—621no—
116C22×C4—621no—
117C22×C4C4×D3111yescharacteristic
118C22×C4D12411yescharacteristic
119C22×C4C22⋊D3111yescharacteristic
120C2×C8—22no—
121C2×C8—622no—
122C4⋊C4—311no—
123C4⋊C4—311no—
124C4⋊C4—621no—
125C4⋊C4—621no—
126C4⋊C4—621no—
127C4⋊C4—621no—
128C22⋊C4—621no—
129C22⋊C4—621no—
130C22⋊C4—621no—
131C22⋊C4—621no—
132C22⋊C4—621no—
133C42—621no—
134C42C4×D3111yescharacteristic
135C42D12411yescharacteristic
136C42C22⋊D3111yescharacteristic
137C42C22×D3111yescharacteristic
138C23—621no—
139C23(C2×D31)⋊C411yescharacteristic
140Q8—622no—
141D4—622no—
142D4—1242no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—621no—
147C2×C4—621no—
148C2×C4—621no—
149C2×C4—1242no—
150C2×C4(C2×D31)⋊C411yescharacteristic
151C2×C4(C2×D31)⋊C411yescharacteristic
152C2×C4(C2×D31)⋊C411yescharacteristic
153C2×C4C2×C4×D3111yescharacteristic
154C2×C4C2×D12411yescharacteristic
155C2×C4C2×C22⋊D3111yescharacteristic
156C8—42no—
157C8—1242no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—1241no—
162C22—1241no—
163C22—1241no—
164C22C2×(C2×D31)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—1241no—
170C4—1241no—
171C4—1241no—
172C4#1175847812yes—
173C4#1175852712yes—
174C2—41no—
175C2—2481no—
176C2#1452101511yescharacteristic
177C2#1452104311yescharacteristic
178C2#1452106511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#431C2
socleC22×C31C2×C22⋊C4
prime radical#11758507C4
cosocleC42×C31C23
hypercenter#431D31
hypocenterC31#1482
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #14521102C2semidirect
3. #14520779C2semidirect
4. #14520776C2semidirect
5. C31×#431C2semidirect
87. #431D31semidirect
112. C31#1482semidirect

Maximal subgroups

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

subgroupindex
#145215832
#145211022
#145207792
#145207762
C31×#4312
#148231