Finite Group Databasebeta

← #16856030

Subgroups — #16856030

Order 3968.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#14521597C211yesmaximal, characteristic
3#14521402C214yesmaximal, complemented
4#14521401C211yesmaximal, characteristic, complemented
5#14521400C211yesmaximal, characteristic, complemented
6#14521395C211yesmaximal, characteristic, complemented
7#14521042C214yesmaximal, complemented
8C4×C8×D31C211yesmaximal, characteristic, complemented
9C31×#486C211yesmaximal, characteristic, complemented
10C2×#92497C2212yes—
11C31×C4⋊Q8C2211yescharacteristic
12C31×#127C2211yescharacteristic
13#11758523—21no—
14Q8×Dic31—21no—
15#11758515—21no—
16#11758515—21no—
17#11758513C2212yes—
18D4×Dic31—21no—
19D4×Dic31—21no—
20C2×C8×D31C2212yes—
21#11758474—21no—
22#11758469C2212yes—
23#11758467C2212yes—
24#11758464—21no—
25C42×D31C2211yescharacteristic
26#11758446C2211yescharacteristic
27#11758446C2211yescharacteristic
28C31×#102C2214yes—
29C4×C8×C31C2211yescharacteristic
30#11758420C2214yes—
31#11758404C2214yes—
32C8×Dic31C2212yes—
33#11758398C2214yes—
34C4×C31⋊C8C2211yescharacteristic
35C2×Q8×C31—21no—
36C2×D4×C31—21no—
37C2×D4×C31—21no—
38C2×D4×C31C2312yes—
39C2×C22⋊D31—22no—
40C22×Dic31—22no—
41#92497—28no—
42C2×C4×D31D411yescharacteristic
43C2×C4×D31D411yescharacteristic
44C2×C4×D31C2311yescharacteristic
45C2×Dic62—21no—
46C2×Dic62C2312yes—
47C2×C8×C31C2312yes—
48C4⋊C4×C31—21no—
49C4⋊C4×C31C2312yes—
50C42×C31C2311yescharacteristic
51C22⋊Dic31—22no—
52C22⋊Dic31—22no—
53(C2×D31)⋊C4—22no—
54C4⋊Dic31—21no—
55C4⋊Dic31—21no—
56C4⋊Dic31—21no—
57C4⋊Dic31—22no—
58C4⋊Dic31C2312yes—
59Dic31⋊C4—22no—
60C4×Dic31—22no—
61C4×Dic31D411yescharacteristic
62C4×Dic31D411yescharacteristic
63C4×Dic31C2311yescharacteristic
64C2×C31⋊C8C2312yes—
65C8×D31—24no—
66C23×C31—22no—
67C22×D31C2×D411yescharacteristic
68Q8×C31—42no—
69D4×C31—24no—
70D4×C31—42no—
71D4×C31—42no—
72C2×C4×C31—22no—
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31C2411yescharacteristic
76C22⋊D31—44no—
77C2×Dic31—22no—
78C2×Dic31—22no—
79C2×Dic31—44no—
80C2×Dic31C2×D411yescharacteristic
81C2×Dic31C2×D411yescharacteristic
82C2×Dic31C2×D411yescharacteristic
83C4×D31—22no—
84C4×D31—22no—
85C4×D31#4114yes—
86Dic62—24no—
87Dic62—42no—
88C8×C31—22no—
89C31⋊C8—22no—
90#3131—311nomaximal, Sylow
91C22×C31—42no—
92C22×C31—42no—
93C22×C31—42no—
94C22×C31C22×D411yescharacteristic
95C2×D31—21no—
96C2×D31—21no—
97C2×D31#12412yes—
98C4×C31—42no—
99C4×C31#13512yes—
100C4×C31#13512yes—
101C4×C31C2×#4112yes—
102Dic31—21no—
103Dic31—21no—
104Dic31—42no—
105Dic31—42no—
106Dic31#12412yes—
107#533—311no—
108#532—311no—
109#488—314no—
110#487—311no—
111#487—311no—
112#486—311no—
113#486D3111yescharacteristic, complemented
114#416—314no—
115C2×C4×C8—311no—
116C2×C31—82no—
117C2×C31C2×#12411yescharacteristic
118C2×C31C2×#13511yescharacteristic
119C2×C31C2×#13511yescharacteristic
120D31—22no—
121C2×#41—312no—
122C22×C8—312no—
123C4⋊Q8—311no—
124C4⋊Q8—311no—
125C4⋊Q8C2×D3111yescharacteristic
126#127C2×D3111yescharacteristic
127#125—312no—
128#124—312no—
129C22⋊Q8—621no—
130C22⋊Q8—621no—
131#121—621no—
132#121—621no—
133C4×Q8—621no—
134C4×Q8—621no—
135C4×D4—621no—
136C4×D4—621no—
137#117—312no—
138C2×C42—311no—
139#103—314no—
140#103—314no—
141#102—314no—
142#102C2×D3114yes—
143C4×C8—312no—
144C4×C8—311no—
145C4×C8C2×D3111yescharacteristic
146C31#313111yescharacteristic, complemented, Sylow
147#41—628no—
148C2×Q8—21no—
149C2×Q8—312no—
150C2×Q8—621no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—622no—
154C2×D4C22×D3112yes—
155C22×C4—311no—
156C22×C4—311no—
157C22×C4—311no—
158C22×C4—622no—
159C2×C8—312no—
160C2×C8—624no—
161C2×C8C22×D3112yes—
162C4⋊C4—21no—
163C4⋊C4—312no—
164C4⋊C4—622no—
165C4⋊C4—622no—
166C4⋊C4—621no—
167C4⋊C4—621no—
168C4⋊C4—621no—
169C4⋊C4C22×D3112yes—
170C22⋊C4—622no—
171C22⋊C4—622no—
172C22⋊C4—622no—
173C42—311no—
174C42—311no—
175C42—311no—
176C42—622no—
177C42C22×D3111yescharacteristic
178C23—22no—
179C23—311no—
180Q8—42no—
181Q8—624no—
182Q8—1242no—
183D4—24no—
184D4—42no—
185D4—42no—
186D4—1244no—
187C2×C4—22no—
188C2×C4—311no—
189C2×C4—314no—
190C2×C4—311no—
191C2×C4—311no—
192C2×C4—622no—
193C2×C4—622no—
194C2×C4—622no—
195C2×C4—622no—
196C2×C4—1244no—
197C2×C4D4×D3111yescharacteristic
198C2×C4D4×D3111yescharacteristic
199C2×C4C23×D3111yescharacteristic
200C8—22no—
201C8—622no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—312no—
206C22—621no—
207C22—621no—
208C22C2×D4×D3111yescharacteristic
209C4—42no—
210C4—312no—
211C4—621no—
212C4—621no—
213C4—1242no—
214C4—1242no—
215C4#1175848912yes—
216C4#1175849312yes—
217C4#41×D3112yes—
218C2—82no—
219C2—622no—
220C2#124×D3111yescharacteristic
221C2C2×#1175848911yescharacteristic
222C2C2×#1175849311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#486C2
socleC22×C31C22×D4
prime radical#14521597C2
hypercenter#486D31
hypocenterC31#3131
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14521604C2semidirect
3. #14521402C2semidirect
4. #14521401C2semidirect
5. #14521400C2semidirect
6. #14521395C2semidirect
7. #14521042C2semidirect
8. C4×C8×D31C2semidirect
9. C31×#486C2semidirect
113. #486D31semidirect
146. C31#3131semidirect

Maximal subgroups

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

subgroupindex
#145216042
#145215972
#145214022
#145214012
#145214002
#145213952
#145210422
C4×C8×D312
C31×#4862
#313131