Finite Group Databasebeta

← #16846696

Subgroups — #16846696

Order 3968.

324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11758501C211yesmaximal, characteristic
2#14520909C211yesmaximal, characteristic
3#14520815C214yesmaximal
4C4×C22⋊C4×C31C211yesmaximal, characteristic
5C23×C4×C31C2211yescharacteristic
6C22×Dic62C411yescharacteristic, complemented
7C2×C22⋊C4×C31C2212yes—
8C2×C42×C31—21no—
9C2×C22⋊Dic31C2212yes—
10C2×C22⋊Dic31C2212yes—
11C2×C4⋊Dic31—21no—
12C2×C4⋊Dic31C411yescharacteristic, complemented
13#11758501—21no—
14#11758501—21no—
15#11758501—21no—
16#11758501—21no—
17C2×Dic31⋊C4C412yescomplemented
18C31×#95—21no—
19C31⋊#95—21no—
20C24×C31C2311yescharacteristic
21C22×C4×C31—22no—
22C22×C4×C31—42no—
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31C2×C411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×Dic31—22no—
30C22×Dic31C2×C412yes—
31C22×Dic31C2×C412yes—
32C2×Dic62—21no—
33C2×Dic62—21no—
34C2×Dic62—42no—
35C22⋊C4×C31—22no—
36C22⋊C4×C31Q814yescomplemented
37C42×C31—42no—
38C22⋊Dic31—22no—
39C22⋊Dic31—22no—
40C22⋊Dic31—24no—
41C4⋊Dic31—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31—42no—
44Dic31⋊C4—22no—
45Dic31⋊C4—22no—
46C23×C31—41no—
47C23×C31—41no—
48C23×C31C22×C411yescharacteristic
49C23×C31C2×D411yescharacteristic
50C23×C31C2×D411yescharacteristic
51C23×C31C2×Q812yes—
52C23×C31#4112yes—
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31—22no—
56C2×C4×C31—24no—
57C2×C4×C31—41no—
58C2×C4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31—42no—
61C2×C4×C31—42no—
62C2×C4×C31C22⋊C411yescharacteristic
63C2×C4×C31C22⋊C411yescharacteristic
64C2×C4×C31C22⋊C411yescharacteristic
65C2×C4×C31C22⋊C411yescharacteristic
66C2×Dic31—22no—
67C2×Dic31—22no—
68C2×Dic31—42no—
69C2×Dic31—42no—
70C2×Dic31—42no—
71C2×Dic31—42no—
72C2×Dic31—42no—
73Dic62—42no—
74Dic62—42no—
75#1996—311nomaximal, Sylow
76C22×C31—21no—
77C22×C31—21no—
78C22×C31—21no—
79C22×C31—21no—
80C22×C31—21no—
81C22×C31—21no—
82C22×C31—42no—
83C22×C31—42no—
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31C4×Q812yes—
86C22×C31C22⋊Q812yes—
87C22×C31#12411yescharacteristic
88C22×C31C4⋊Q811yescharacteristic
89C4×C31—21no—
90C4×C31—21no—
91C4×C31—21no—
92C4×C31—44no—
93C4×C31#9912yes—
94Dic31—42no—
95Dic31—42no—
96Dic31—82no—
97C2×C22⋊Q8—311no—
98#380—311no—
99C4×C22⋊C4D3111yescharacteristic
100#342—314no—
101C2×C31—21no—
102C2×C31—22no—
103C2×C31—22no—
104C2×C31—21no—
105C2×C31#39111yescharacteristic
106C2×C31C2×#9911yescharacteristic
107C2×C31#41011yescharacteristic
108C22×Q8—311no—
109C23×C4C2×D3111yescharacteristic
110C22⋊Q8—621no—
111C22⋊Q8—621no—
112C22⋊Q8—621no—
113C22⋊Q8—621no—
114C2×C4⋊C4—312no—
115C2×C4⋊C4—311no—
116C2×C4⋊C4—621no—
117C2×C22⋊C4—312no—
118C2×C22⋊C4—312no—
119C2×C22⋊C4C2×D3112yes—
120C2×C42—21no—
121#95—21no—
122#95—621no—
123C31#199611yescharacteristic, complemented, Sylow
124C24C22×D3111yescharacteristic
125C2×Q8—621no—
126C2×Q8—621no—
127C2×Q8—1242no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—312no—
131C22×C4—312no—
132C22×C4—622no—
133C22×C4C4×D3111yescharacteristic
134C22×C4C4×D3111yescharacteristic
135C22×C4D12411yescharacteristic
136C22×C4D12411yescharacteristic
137C22×C4C22⋊D3111yescharacteristic
138C22×C4C22⋊D3111yescharacteristic
139C4⋊C4—622no—
140C4⋊C4—622no—
141C4⋊C4—621no—
142C4⋊C4—621no—
143C4⋊C4—1242no—
144C22⋊C4—22no—
145C22⋊C4—622no—
146C22⋊C4—622no—
147C22⋊C4—624no—
148C22⋊C4Dic6214yescomplemented
149C42—42no—
150C23—41no—
151C23—41no—
152C23C2×Dic6212yes—
153C23C2×C4×D3111yescharacteristic
154C23C2×D12411yescharacteristic
155C23#9249512yes—
156C23C2×C22⋊D3111yescharacteristic
157Q8—1242no—
158Q8—1242no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—1242no—
171C2×C4—1242no—
172C2×C4—1242no—
173C2×C4—1242no—
174C2×C4—1242no—
175C2×C4(C2×D31)⋊C411yescharacteristic
176C2×C4(C2×D31)⋊C411yescharacteristic
177C2×C4(C2×D31)⋊C411yescharacteristic
178C2×C4(C2×D31)⋊C411yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C4×Dic6212yes—
188C22#1175844611yescharacteristic
189C22#1175845211yescharacteristic
190C22#1175850112yes—
191C22C2×(C2×D31)⋊C411yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—44no—
196C4—1242no—
197C4—1242no—
198C4—2482no—
199C4#1175839412yes—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2#1452095511yescharacteristic
205C2C2×#1175839411yescharacteristic
206C2#1452102211yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC4×C22⋊C4×C31C2
socleC22×C31C2×C22⋊C4
prime radical, cosocleC24×C31C23
hypercenterC4×C22⋊C4D31
hypocenterC31#1996
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×Dic62C4semidirect
12. C2×C4⋊Dic31C4semidirect
17. C2×Dic31⋊C4C4semidirect
36. C22⋊C4×C31Q8semidirect
123. C31#1996semidirect
148. C22⋊C4Dic62semidirect

Maximal subgroups

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

subgroupindex
C2×#117585012
#145209092
#145208152
C4×C22⋊C4×C312
#199631