Finite Group Databasebeta

← #16856273

Subgroups — #16856273

Order 3968.

412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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#14521604C211yesmaximal, characteristic, complemented
2#14521600C211yesmaximal, characteristic
3#14521445C211yesmaximal, characteristic, complemented
4#14521423C211yesmaximal, characteristic, complemented
5#14521396C211yesmaximal, characteristic, complemented
6#14521281C214yesmaximal, complemented
7#14521134C214yesmaximal, complemented
8C4×C8×D31C211yesmaximal, characteristic, complemented
9C31×#487C211yesmaximal, characteristic, complemented
10C2×#92499—21no—
11C31×C4⋊Q8C2211yescharacteristic
12C31×C4⋊Q8C2211yescharacteristic
13#11758524—21no—
14#11758523C2212yes—
15Q8×Dic31C2212yes—
16C2×#92481C2214yes—
17C2×C8×D31C2212yes—
18#11758474—21no—
19#11758472—21no—
20#11758472C2212yes—
21#11758470—21no—
22#11758470C2212yes—
23#11758469—21no—
24#11758467—21no—
25#11758464—21no—
26#11758451C2211yescharacteristic
27C42×D31C2211yescharacteristic
28#11758446C2211yescharacteristic
29C31×#103C2214yes—
30C4×C8×C31C2211yescharacteristic
31#11758409C2214yes—
32C8×Dic31C2212yes—
33#11758396C2214yes—
34C4×C31⋊C8C2211yescharacteristic
35C2×Q8×C31—21no—
36C2×Q8×C31C2312yes—
37#92499—44no—
38C2×D124—22no—
39C2×D124—21no—
40C2×D124—21no—
41C2×D124C2312yes—
42C2×C4×D31—22no—
43C2×C4×D31D411yescharacteristic
44C2×C4×D31D411yescharacteristic
45C2×C4×D31C2311yescharacteristic
46C2×Dic62—21no—
47C2×C8×C31C2312yes—
48C4⋊C4×C31—21no—
49C4⋊C4×C31—21no—
50C4⋊C4×C31—21no—
51C4⋊C4×C31C2312yes—
52C42×C31C2311yescharacteristic
53#92481—28no—
54(C2×D31)⋊C4—22no—
55(C2×D31)⋊C4—22no—
56(C2×D31)⋊C4—22no—
57C4⋊Dic31—21no—
58C4⋊Dic31—22no—
59C4⋊Dic31C2312yes—
60Dic31⋊C4—22no—
61C4×Dic31—22no—
62C4×Dic31D411yescharacteristic
63C4×Dic31D411yescharacteristic
64C4×Dic31C2311yescharacteristic
65C2×C31⋊C8C2312yes—
66C8×D31—24no—
67C22×D31—22no—
68C22×D31C2×D411yescharacteristic
69Q8×C31—24no—
70Q8×C31—42no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31C2411yescharacteristic
76C2×Dic31—22no—
77C2×Dic31C2×D411yescharacteristic
78C2×Dic31C2×D411yescharacteristic
79C2×Dic31C2×D411yescharacteristic
80D124—24no—
81D124—44no—
82D124—42no—
83D124—42no—
84C4×D31—22no—
85C4×D31—22no—
86C4×D31—44no—
87C4×D31SD1614yescomplemented
88Dic62—42no—
89C8×C31—22no—
90C31⋊C8#4114yescomplemented
91#3167—311nomaximal, Sylow
92C22×C31C22×D411yescharacteristic
93C2×D31—21no—
94C2×D31—21no—
95C2×D31—42no—
96C2×D31—42no—
97C2×D31—42no—
98C2×D31C2×SD1612yes—
99C4×C31—42no—
100C4×C31—42no—
101C4×C31C2×SD1612yes—
102C4×C31#13512yes—
103C4×C31C2×#4112yes—
104Dic31—21no—
105Dic31—21no—
106Dic31—42no—
107Dic31C2×SD1612yes—
108#533—311no—
109#532—311no—
110#498—311no—
111#492—311no—
112#487D3111yescharacteristic, complemented
113#486—311no—
114#465—314no—
115C4×SD16—314no—
116C2×C4×C8—311no—
117C2×C31#53211yescharacteristic
118C2×C31C22×SD1611yescharacteristic
119C2×C31C2×#13511yescharacteristic
120D31—22no—
121D31—82no—
122C2×#41—621no—
123C2×SD16—314no—
124C22×C8—312no—
125C4⋊Q8—311no—
126C4⋊Q8C2×D3111yescharacteristic
127C4⋊Q8C2×D3111yescharacteristic
128#127—311no—
129#125—621no—
130#124—621no—
131C22⋊Q8—312no—
132C22⋊Q8—621no—
133#121—312no—
134#121—621no—
135C4×Q8—312no—
136C4×Q8—621no—
137C4×D4—312no—
138C4×D4—621no—
139#117—621no—
140C2×C42—311no—
141#106—314no—
142#103C2×D3114yes—
143#102—314no—
144C4×C8—312no—
145C4×C8—311no—
146C4×C8C2×D3111yescharacteristic
147C31#316711yescharacteristic, complemented, Sylow
148#41—1244no—
149C2×Q8—21no—
150C2×Q8—621no—
151C2×Q8C22×D3112yes—
152C2×D4—312no—
153C2×D4—622no—
154C2×D4—621no—
155C2×D4—621no—
156C22×C4—311no—
157C22×C4—311no—
158C22×C4—311no—
159C22×C4—622no—
160SD16—628no—
161C2×C8—312no—
162C2×C8—624no—
163C2×C8C22×D3112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—312no—
168C4⋊C4—622no—
169C4⋊C4—622no—
170C4⋊C4—621no—
171C4⋊C4C22×D3112yes—
172C22⋊C4—622no—
173C22⋊C4—622no—
174C22⋊C4—622no—
175C42—311no—
176C42—311no—
177C42—311no—
178C42—622no—
179C42C22×D3111yescharacteristic
180C23—311no—
181C23—622no—
182Q8—24no—
183Q8—42no—
184Q8—1242no—
185D4—624no—
186D4—1244no—
187D4—1242no—
188D4—1242no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—311no—
192C2×C4—314no—
193C2×C4—311no—
194C2×C4—311no—
195C2×C4—622no—
196C2×C4—622no—
197C2×C4—622no—
198C2×C4—1244no—
199C2×C4D4×D3111yescharacteristic
200C2×C4D4×D3111yescharacteristic
201C2×C4C23×D3111yescharacteristic
202C8—22no—
203C8—314no—
204C22—312no—
205C22—621no—
206C22—621no—
207C22—1242no—
208C22—1242no—
209C22—1242no—
210C22C2×D4×D3111yescharacteristic
211C4—42no—
212C4—42no—
213C4—312no—
214C4—621no—
215C4—621no—
216C4—1242no—
217C4SD16×D3112yes—
218C4#1175849612yes—
219C4#41×D3112yes—
220C2—622no—
221C2—2482no—
222C2#1452159811yescharacteristic
223C2C2×SD16×D3111yescharacteristic
224C2C2×#1175849611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#487C2
socleC22×C31C22×D4
prime radical#14521600C2
hypercenter#487D31
hypocenterC31#3167
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14521604C2semidirect
3. #14521445C2semidirect
4. #14521423C2semidirect
5. #14521396C2semidirect
6. #14521281C2semidirect
7. #14521134C2semidirect
8. C4×C8×D31C2semidirect
9. C31×#487C2semidirect
87. C4×D31SD16semidirect
90. C31⋊C8#41semidirect
112. #487D31semidirect
147. C31#3167semidirect

Maximal subgroups

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

subgroupindex
#145216042
#145216002
#145214452
#145214232
#145213962
#145212812
#145211342
C4×C8×D312
C31×#4872
#316731