Finite Group Databasebeta

← #16854082

Subgroups — #16854082

Order 3968.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11758467C211yesmaximal, characteristic, complemented
2C2×#11758513C211yesmaximal, characteristic
3#14520955C211yesmaximal, characteristic, complemented
4#14520954C211yesmaximal, characteristic, complemented
5#14520952C211yesmaximal, characteristic
6#14520942C214yesmaximal, complemented
7#14520937C214yesmaximal, complemented
8C42×Dic31C211yesmaximal, characteristic, complemented
9C31×#390C211yesmaximal, characteristic
10C22×D4×C31C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C22⋊C4×C31C2214yes—
14C2×C42×C31C2211yescharacteristic
15C2×C22⋊Dic31C2212yes—
16C2×C22⋊Dic31C2214yes—
17C2×C22⋊Dic31C2212yes—
18#11758513—24no—
19C2×C4⋊Dic31C2212yes—
20C2×C4⋊Dic31C2211yescharacteristic
21C2×Dic31⋊C4C2212yes—
22C2×C4×Dic31C2212yes—
23C2×C4×Dic31C2212yes—
24C2×C4×Dic31C2211yescharacteristic
25C2×C4×Dic31C2211yescharacteristic
26#11758467—24no—
27C31⋊#95C2214yes—
28C31⋊#95C2214yes—
29C24×C31C2312yes—
30C2×D4×C31—22no—
31C2×D4×C31—22no—
32C2×D4×C31—22no—
33C22×C4×C31C2312yes—
34C22×C4×C31C2312yes—
35C22×C4×C31C2311yescharacteristic
36C22×Dic31C2312yes—
37C22×Dic31C2312yes—
38C22×Dic31C2311yescharacteristic
39C22×Dic31C2311yescharacteristic
40C22×Dic31C2312yes—
41C2×Dic62—22no—
42C2×Dic62—22no—
43C2×Dic62—22no—
44C4⋊C4×C31—22no—
45C22⋊C4×C31—28no—
46C42×C31—22no—
47C22⋊Dic31—24no—
48C22⋊Dic31—24no—
49C22⋊Dic31—28no—
50C4⋊Dic31—22no—
51C4⋊Dic31—24no—
52Dic31⋊C4—24no—
53C4×Dic31—22no—
54C4×Dic31—24no—
55C4×Dic31—24no—
56C4×Dic31D414yes—
57C23×C31—22no—
58C23×C31—24no—
59C23×C31—24no—
60C23×C31—22no—
61C23×C31—22no—
62C23×C31C2411yescharacteristic
63D4×C31—44no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—24no—
68C2×C4×C31C2×D412yes—
69C2×C4×C31#4112yes—
70C2×C4×C31#4114yes—
71C2×C4×C31#4112yes—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—24no—
79C2×Dic31—22no—
80C2×Dic31—22no—
81C2×Dic31C2×D412yes—
82C2×Dic31C2×D412yes—
83C2×Dic31#4114yes—
84Dic62—44no—
85#2861—311nomaximal, Sylow
86C22×C31—42no—
87C22×C31—44no—
88C22×C31—44no—
89C22×C31—42no—
90C22×C31—42no—
91C22×C31C22×D411yescharacteristic
92C22×C31C2×#4111yescharacteristic
93C22×C31C2×#4111yescharacteristic
94C22×C31C2×#4112yes—
95C22×C31C2×#4112yes—
96C4×C31—24no—
97C4×C31—42no—
98C4×C31#12414yes—
99Dic31—24no—
100Dic31—22no—
101Dic31—22no—
102Dic31—42no—
103Dic31—42no—
104C2×#125—311no—
105C2×#124—311no—
106#391—311no—
107#391—311no—
108#390—311no—
109#390D3111yescharacteristic
110#388—314no—
111#388—314no—
112C43—311no—
113C2×C31—82no—
114C2×C31C2×#12411yescharacteristic
115C2×C31#52912yes—
116C2×C31#52912yes—
117C2×C31#53211yescharacteristic
118C2×C31#53211yescharacteristic
119C22×Q8—311no—
120C22×D4C2×D3111yescharacteristic
121#125—624no—
122#124—624no—
123C2×C4⋊C4—312no—
124C2×C4⋊C4—312no—
125C2×C4⋊C4—311no—
126C2×C4⋊C4C2×D3111yescharacteristic
127C2×C22⋊C4—312no—
128C2×C22⋊C4—312no—
129C2×C22⋊C4—314no—
130C2×C22⋊C4C2×D3114yes—
131C2×C42—311no—
132C2×C42—312no—
133C2×C42—312no—
134C2×C42—311no—
135C2×C42C2×D3111yescharacteristic
136#95—314no—
137#95—314no—
138C31#286111yescharacteristic, complemented, Sylow
139C24C22×D3112yes—
140C2×Q8—622no—
141C2×Q8—622no—
142C2×Q8—622no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4—22no—
146C22×C4—312no—
147C22×C4—311no—
148C22×C4—311no—
149C22×C4—312no—
150C22×C4—312no—
151C22×C4C22×D3112yes—
152C22×C4C22×D3112yes—
153C22×C4C22×D3111yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—624no—
156C4⋊C4—624no—
157C4⋊C4—622no—
158C22⋊C4—28no—
159C22⋊C4—628no—
160C22⋊C4—624no—
161C22⋊C4—624no—
162C42—22no—
163C42—314no—
164C42—624no—
165C42—622no—
166C42—624no—
167C23—22no—
168C23—22no—
169C23—24no—
170C23—22no—
171C23—24no—
172C23C23×D3111yescharacteristic
173Q8—1244no—
174D4—44no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—312no—
180C2×C4—312no—
181C2×C4—314no—
182C2×C4—622no—
183C2×C4—622no—
184C2×C4—622no—
185C2×C4—622no—
186C2×C4—622no—
187C2×C4—622no—
188C2×C4—622no—
189C2×C4—622no—
190C2×C4—624no—
191C2×C4#9249512yes—
192C2×C4D4×D3112yes—
193C2×C4#9249714yes—
194C2×C4#9249712yes—
195C22—42no—
196C22—44no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22C2×#9249511yescharacteristic
201C22C2×D4×D3111yescharacteristic
202C22C2×#9249711yescharacteristic
203C22C2×#9249712yes—
204C22#41×D3112yes—
205C4—24no—
206C4—42no—
207C4—624no—
208C4—622no—
209C4—622no—
210C4—1242no—
211C4—1242no—
212C4#1175846214yes—
213C2—82no—
214C2C2×#1175846211yescharacteristic
215C2#1452158012yes—
216C2#1452158112yes—
217C2#1452159711yescharacteristic
218C2#1452159811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#390C2
prime radicalC22×D4×C31C22
hypercenter#390D31
hypocenterC31#2861
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#11758467C2semidirect
3. #14520955C2semidirect
4. #14520954C2semidirect
6. #14520942C2semidirect
7. #14520937C2semidirect
8. C42×Dic31C2semidirect
138. C31#2861semidirect

Maximal subgroups

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

subgroupindex
C2×#117584672
C2×#117585132
#145209552
#145209542
#145209522
#145209422
#145209372
C42×Dic312
C31×#3902
#286131