Finite Group Databasebeta

← #16844250

Subgroups — #16844250

Order 3968.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#14520915C211yesmaximal, characteristic, complemented
3#14520787C212yesmaximal, complemented
4#14520784C212yesmaximal
5C31×#432C211yesmaximal, characteristic, complemented
6C2×C42×C31C2211yescharacteristic
7#11758507C2211yescharacteristic
8#11758506—21no—
9C4×C22⋊D31—21no—
10C2×C4⋊Dic31—21no—
11#11758501C2211yescharacteristic
12#11758453—21no—
13#11758452C411yescharacteristic, complemented
14C4×D124C411yescharacteristic, complemented
15#11758449—21no—
16#11758447C411yescharacteristic, complemented
17C4×Dic62C411yescharacteristic, complemented
18C31×C4⋊C8—21no—
19C31×C22⋊C8C2212yes—
20C31×#97—21no—
21C31⋊#95—21no—
22C31⋊#95C2212yes—
23C22×C4×C31D411yescharacteristic
24C22×C4×C31D411yescharacteristic
25C22×C4×C31C2311yescharacteristic
26C2×C22⋊D31—21no—
27C22×Dic31—22no—
28C2×D124C2×C411yescharacteristic
29C2×C4×D31—21no—
30C2×Dic62C2×C411yescharacteristic
31C2×C8×C31—22no—
32C42×C31C2×C411yescharacteristic
33C42×C31C2×C411yescharacteristic
34C42×C31D411yescharacteristic
35C42×C31D411yescharacteristic
36C22⋊Dic31—21no—
37(C2×D31)⋊C4—21no—
38(C2×D31)⋊C4—21no—
39(C2×D31)⋊C4—21no—
40(C2×D31)⋊C4—21no—
41C4⋊Dic31—42no—
42C4⋊Dic31C2×C411yescharacteristic
43C4⋊Dic31C2×C411yescharacteristic
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47Dic31⋊C4—21no—
48C4×Dic31—21no—
49C23×C31C2×D411yescharacteristic
50C22×D31—21no—
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C22⋊C411yescharacteristic
59C2×C4×C31C22×C411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C22⋊D31—41no—
62C22⋊D31—41no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—21no—
66C2×Dic31—42no—
67C2×Dic31—42no—
68C2×Dic31—42no—
69D124—41no—
70C4×D31—42no—
71Dic62—41no—
72C8×C31—42no—
73#1512—311nomaximal, Sylow
74C22×C31—21no—
75C22×C31—21no—
76C22×C31C2×C22⋊C411yescharacteristic
77C22×C31AGL(1,ℤ/8)11yescharacteristic
78C22×C31#13711yescharacteristic
79C2×D31—41no—
80C2×D31—41no—
81C2×D31—41no—
82C4×C31—21no—
83C4×C31—21no—
84C4×C31—21no—
85C4×C31—21no—
86C4×C31—21no—
87C4×C31—21no—
88Dic31—41no—
89Dic31—41no—
90Dic31—41no—
91Dic31—82no—
92#529—311no—
93#432D3111yescharacteristic, complemented
94#382—311no—
95#328—312no—
96#327—312no—
97C2×C31—21no—
98C2×C31—21no—
99C2×C31#41011yescharacteristic
100C2×C31#41711yescharacteristic
101C2×C31#42111yescharacteristic
102D31—81no—
103#126—621no—
104#125—311no—
105#124—311no—
106#123—621no—
107C22⋊Q8—311no—
108#121—311no—
109C4×Q8—311no—
110C4×D4—311no—
111C4×D4—621no—
112#117—621no—
113C2×C4⋊C4—621no—
114C2×C42C2×D3111yescharacteristic
115C4⋊C8—21no—
116C22⋊C8C2×D3112yes—
117#97—21no—
118#95—312no—
119#95—621no—
120C31#151211yescharacteristic, complemented, Sylow
121C2×Q8—311no—
122C2×D4—311no—
123C2×D4—621no—
124C22×C4—621no—
125C22×C4—622no—
126C22×C4D12411yescharacteristic
127C22×C4D12411yescharacteristic
128C22×C4C22×D3111yescharacteristic
129C2×C8—22no—
130C4⋊C4—311no—
131C4⋊C4—311no—
132C4⋊C4—621no—
133C4⋊C4—621no—
134C4⋊C4—621no—
135C4⋊C4—621no—
136C4⋊C4—1242no—
137C22⋊C4—621no—
138C22⋊C4—621no—
139C22⋊C4—621no—
140C22⋊C4—621no—
141C22⋊C4—621no—
142C42—621no—
143C42C4×D3111yescharacteristic
144C42C4×D3111yescharacteristic
145C42C22⋊D3111yescharacteristic
146C42C22⋊D3111yescharacteristic
147C23—621no—
148C23C2×D12411yescharacteristic
149Q8—1241no—
150D4—1241no—
151D4—1241no—
152D4—1241no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—621no—
158C2×C4—621no—
159C2×C4—621no—
160C2×C4—1242no—
161C2×C4—1242no—
162C2×C4—1242no—
163C2×C4—1242no—
164C2×C4(C2×D31)⋊C411yescharacteristic
165C2×C4(C2×D31)⋊C411yescharacteristic
166C2×C4(C2×D31)⋊C411yescharacteristic
167C2×C4(C2×D31)⋊C411yescharacteristic
168C2×C4C2×C4×D3111yescharacteristic
169C2×C4C2×C22⋊D3111yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—1241no—
174C22—1241no—
175C22—1241no—
176C22#1175848511yescharacteristic
177C22#1175848611yescharacteristic
178C22C2×(C2×D31)⋊C411yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—1241no—
186C4—1241no—
187C4—1241no—
188C4—2482no—
189C2—21no—
190C2—21no—
191C2—2481no—
192C2#1452102211yescharacteristic
193C2#1452105111yescharacteristic
194C2#1452106511yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#432C2
socleC22×C31C2×C22⋊C4
prime radical#11758507C22
cosocleC22×C4×C31C23
hypercenter#432D31
hypocenterC31#1512
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #14520915C2semidirect
3. #14520787C2semidirect
5. C31×#432C2semidirect
13. #11758452C4semidirect
14. C4×D124C4semidirect
16. #11758447C4semidirect
17. C4×Dic62C4semidirect
93. #432D31semidirect
120. C31#1512semidirect

Maximal subgroups

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

subgroupindex
#145215832
#145209152
#145207872
#145207842
C31×#4322
#151231