Finite Group Databasebeta

← #16844177

Subgroups — #16844177

Order 3968.

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

normal subgroups only

This group has 216 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#14521073C211yesmaximal, characteristic, complemented
3#14520781C212yesmaximal, complemented
4#14520778C212yesmaximal, complemented
5C31×#431C211yesmaximal, characteristic, complemented
6C2×C42×C31C2211yescharacteristic
7#11758507C411yescharacteristic
8#11758506—21no—
9C4×C22⋊D31—21no—
10#11758501C411yescharacteristic
11C2×#92474—21no—
12#11758453—21no—
13#11758452C411yescharacteristic
14C4×D124C2211yescharacteristic
15#11758449—21no—
16#11758447C411yescharacteristic
17C4×Dic62C2211yescharacteristic
18C31×C4⋊C8—21no—
19C31×C22⋊C8—21no—
20C4×C8×C31C2212yes—
21C4⋊(C31⋊C8)—21no—
22C4⋊(C31⋊C8)C2212yes—
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—
47#92474—42no—
48C2×C31⋊C8—22no—
49C23×C31C22⋊C411yescharacteristic
50C22×D31—21no—
51C2×C4×C31—22no—
52C2×C4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—41no—
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C22×C411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C22⋊D31—42no—
62C2×Dic31—21no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65D124—22no—
66C4×D31—41no—
67C4×D31—41no—
68Dic62—22no—
69C8×C31—42no—
70C31⋊C8—42no—
71#1495—311nomaximal, Sylow
72C22×C31—21no—
73C22×C31—21no—
74C22×C31—21no—
75C22×C31C2×C22⋊C411yescharacteristic
76C2×D31—41no—
77C2×D31—41no—
78C2×D31—41no—
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31#13112yes—
84C4×C31AGL(1,ℤ/8)11yescharacteristic
85C4×C31#13711yescharacteristic
86Dic31—41no—
87Dic31—41no—
88Dic31—41no—
89#529—311no—
90#431D3111yescharacteristic, complemented
91#423—311no—
92Q8⋊C8—312no—
93D4⋊C8—312no—
94C2×C31—41no—
95C2×C31#40811yescharacteristic
96C2×C31#41711yescharacteristic
97C2×C31#42111yescharacteristic
98D31—81no—
99C2×M16—621no—
100#126—621no—
101#125—311no—
102#124—311no—
103#123—621no—
104C22⋊Q8—311no—
105#121—311no—
106C4×Q8—311no—
107C4×D4—311no—
108C4×D4—621no—
109#117—621no—
110C2×C42C2×D3111yescharacteristic
111C4⋊C8—21no—
112C4⋊C8—312no—
113C4⋊C8—621no—
114C22⋊C8—21no—
115C4×C8C2×D3112yes—
116C31#149511yescharacteristic, complemented, Sylow
117C2×Q8—311no—
118C2×D4—311no—
119C2×D4—621no—
120C22×C4—621no—
121C22×C4C4×D3111yescharacteristic
122C22×C4D12411yescharacteristic
123C22×C4C22⋊D3111yescharacteristic
124M16—1242no—
125C2×C8—22no—
126C2×C8—622no—
127C4⋊C4—311no—
128C4⋊C4—311no—
129C4⋊C4—621no—
130C4⋊C4—621no—
131C4⋊C4—621no—
132C4⋊C4—621no—
133C22⋊C4—621no—
134C22⋊C4—621no—
135C22⋊C4—621no—
136C22⋊C4—621no—
137C22⋊C4—621no—
138C42—621no—
139C42C4×D3111yescharacteristic
140C42D12411yescharacteristic
141C42C22⋊D3111yescharacteristic
142C42C22×D3111yescharacteristic
143C23—621no—
144C23(C2×D31)⋊C411yescharacteristic
145Q8—622no—
146D4—622no—
147D4—1242no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—621no—
153C2×C4—621no—
154C2×C4—621no—
155C2×C4—1241no—
156C2×C4—1241no—
157C2×C4(C2×D31)⋊C411yescharacteristic
158C2×C4(C2×D31)⋊C411yescharacteristic
159C2×C4(C2×D31)⋊C411yescharacteristic
160C2×C4C2×C4×D3111yescharacteristic
161C2×C4C2×D12411yescharacteristic
162C2×C4C2×C22⋊D3111yescharacteristic
163C8—42no—
164C8—1242no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—1241no—
169C22—1241no—
170C22—1241no—
171C22C2×(C2×D31)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—1241no—
177C4—1241no—
178C4—1241no—
179C4#1175847812yes—
180C4#1175848511yescharacteristic
181C4#1175848611yescharacteristic
182C2—41no—
183C2—2481no—
184C2#1452101511yescharacteristic
185C2#1452105111yescharacteristic
186C2#1452106711yescharacteristic
subgroupG/H
centerC2×C4C2×D124
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#431C2
socleC22×C31C2×C22⋊C4
prime radical#11758507C4
cosocleC42×C31C23
hypercenter#431D31
hypocenterC31#1495
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. #14521073C2semidirect
3. #14520781C2semidirect
4. #14520778C2semidirect
5. C31×#431C2semidirect
90. #431D31semidirect
116. C31#1495semidirect

Maximal subgroups

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

subgroupindex
#145215832
#145210732
#145207812
#145207782
C31×#4312
#149531