Finite Group Databasebeta

← #16844043

Subgroups — #16844043

Order 3968.

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

normal subgroups only

This group has 252 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
1C2×#11758449C211yesmaximal, characteristic
2#14521106C211yesmaximal, characteristic, complemented
3#14520774C212yesmaximal, complemented
4#14520772C212yesmaximal
5C31×#432C211yesmaximal, characteristic, complemented
6C22×C4×D31C411yescharacteristic
7C2×C42×C31C2211yescharacteristic
8C2×(C2×D31)⋊C4C411yescharacteristic
9C2×(C2×D31)⋊C4C2211yescharacteristic
10C2×Dic31⋊C4C411yescharacteristic
11C2×Dic31⋊C4C2211yescharacteristic
12C2×C4×Dic31C411yescharacteristic
13#11758449—21no—
14#11758449—21no—
15#11758449—21no—
16#11758449—21no—
17C31×C4⋊C8—21no—
18C31×C22⋊C8C2212yes—
19C31×#97—21no—
20C22⋊(C31⋊C8)C2212yes—
21C4⋊(C31⋊C8)—21no—
22#11758391—21no—
23C23×D31C2×C411yescharacteristic
24C22×C4×C31C2×C411yescharacteristic
25C22×C4×C31C2×C411yescharacteristic
26C22×C4×C31C2311yescharacteristic
27C22×Dic31C2×C411yescharacteristic
28C22×Dic31C2×C411yescharacteristic
29C22×Dic31C2×C411yescharacteristic
30C2×C4×D31—22no—
31C2×C4×D31—21no—
32C2×C4×D31—21no—
33C2×C4×D31—22no—
34C2×C8×C31—22no—
35C42×C31D411yescharacteristic
36C42×C31D411yescharacteristic
37C42×C31D411yescharacteristic
38C42×C31D411yescharacteristic
39(C2×D31)⋊C4—21no—
40(C2×D31)⋊C4—21no—
41(C2×D31)⋊C4—21no—
42(C2×D31)⋊C4—21no—
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47C4×Dic31—21no—
48C4×Dic31—21no—
49C2×C31⋊C8—22no—
50C23×C31C22×C411yescharacteristic
51C22×D31—21no—
52C22×D31—21no—
53C22×D31—41no—
54C22×D31—41no—
55C22×D31M1612yes—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31C22⋊C411yescharacteristic
61C2×C4×C31C22⋊C411yescharacteristic
62C2×C4×C31C22⋊C411yescharacteristic
63C2×C4×C31C22⋊C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C2×Dic31—21no—
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—41no—
71C2×Dic31—41no—
72C2×Dic31M1612yes—
73C4×D31—24no—
74C4×D31—24no—
75C8×C31—42no—
76C31⋊C8—42no—
77#1464—311nomaximal, Sylow
78C22×C31—21no—
79C22×C31—21no—
80C22×C31C2×C22⋊C411yescharacteristic
81C22×C31C2×M1611yescharacteristic
82C22×C31C2×M1611yescharacteristic
83C2×D31—22no—
84C2×D31—42no—
85C2×D31—41no—
86C2×D31—41no—
87C2×D31—42no—
88C4×C31—21no—
89C4×C31—21no—
90C4×C31—21no—
91C4×C31—21no—
92C4×C31—21no—
93C4×C31—21no—
94Dic31—22no—
95Dic31—41no—
96Dic31—41no—
97C2×#117—311no—
98#432—311no—
99#432D3111yescharacteristic, complemented
100#324—312no—
101#323—312no—
102C2×C31—21no—
103C2×C31—21no—
104C2×C31#40711yescharacteristic
105C2×C31#41011yescharacteristic
106C2×C31#41311yescharacteristic
107D31—42no—
108C23×C4—311no—
109#117—621no—
110#117—621no—
111#117—621no—
112#117—621no—
113C2×C4⋊C4—311no—
114C2×C4⋊C4—311no—
115C2×C22⋊C4—311no—
116C2×C22⋊C4—311no—
117C2×C42—311no—
118C2×C42C2×D3111yescharacteristic
119C4⋊C8—21no—
120C4⋊C8—621no—
121C22⋊C8—312no—
122C22⋊C8C2×D3112yes—
123#97—21no—
124#97—621no—
125C31#146411yescharacteristic, complemented, Sylow
126C24—311no—
127C22×C4—311no—
128C22×C4—311no—
129C22×C4—311no—
130C22×C4—622no—
131C22×C4—622no—
132C22×C4—621no—
133C22×C4—621no—
134C22×C4C4×D3111yescharacteristic
135C22×C4C4×D3111yescharacteristic
136C22×C4C22×D3111yescharacteristic
137C2×C8—22no—
138C2×C8—622no—
139C4⋊C4—621no—
140C4⋊C4—621no—
141C4⋊C4—621no—
142C4⋊C4—621no—
143C22⋊C4—621no—
144C22⋊C4—621no—
145C22⋊C4—621no—
146C22⋊C4—621no—
147C42—621no—
148C42—621no—
149C42D12411yescharacteristic
150C42D12411yescharacteristic
151C42C22⋊D3111yescharacteristic
152C42C22⋊D3111yescharacteristic
153C23—312no—
154C23—621no—
155C23—621no—
156C23—1241no—
157C23—1241no—
158C23C2×C4×D3111yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—312no—
164C2×C4—624no—
165C2×C4—624no—
166C2×C4—621no—
167C2×C4—621no—
168C2×C4—621no—
169C2×C4—621no—
170C2×C4—1241no—
171C2×C4—1241no—
172C2×C4(C2×D31)⋊C411yescharacteristic
173C2×C4(C2×D31)⋊C411yescharacteristic
174C2×C4(C2×D31)⋊C411yescharacteristic
175C2×C4(C2×D31)⋊C411yescharacteristic
176C2×C4C2×D12411yescharacteristic
177C2×C4C2×C22⋊D3111yescharacteristic
178C8—42no—
179C8—1242no—
180C22—21no—
181C22—21no—
182C22—622no—
183C22—1242no—
184C22—1242no—
185C22—1241no—
186C22—1241no—
187C22M16×D3111yescharacteristic
188C22M16×D3111yescharacteristic
189C22C2×(C2×D31)⋊C411yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—622no—
197C4—1241no—
198C4—1241no—
199C2—21no—
200C2—21no—
201C2—1242no—
202C2#1452101211yescharacteristic
203C2#1452102211yescharacteristic
204C2#1452103111yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#432C2
socleC22×C31C2×C22⋊C4
prime radicalC23×D31C2×C4
cosocleC22×C4×C31C23
hypercenter#432D31
hypocenterC31#1464
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #14521106C2semidirect
3. #14520774C2semidirect
5. C31×#432C2semidirect
99. #432D31semidirect
125. C31#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#117584492
#145211062
#145207742
#145207722
C31×#4322
#146431