Finite Group Databasebeta

← #16848469

Subgroups — #16848469

Order 3968.

484 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 217 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#14520956C212yesmaximal, complemented
2#14520942C212yesmaximal
3#14520942C212yesmaximal
4#14520935C212yesmaximal, complemented
5#14520935C212yesmaximal, complemented
6#14520912C211yesmaximal, characteristic
7C4⋊C4×Dic31C212yesmaximal, complemented
8C4×C22⋊Dic31C211yesmaximal, characteristic
9C2×C31×C22⋊Q8C211yesmaximal, characteristic
10C22×Q8×C31C2211yescharacteristic
11C23×C4×C31C2211yescharacteristic
12C31×C22⋊Q8C418yescomplemented
13C2×C4⋊C4×C31C2212yes—
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×C22⋊C4×C31C2212yes—
16C2×C22⋊Dic31C2212yes—
17C2×C22⋊Dic31C2211yescharacteristic
18C2×C22⋊Dic31C2211yescharacteristic
19C2×C4⋊Dic31C2212yes—
20C2×C4⋊Dic31C2212yes—
21C2×C4×Dic31C2212yes—
22C2×C4×Dic31C2211yescharacteristic
23C2×C4×Dic31C2211yescharacteristic
24C2×C4×Dic31C2212yes—
25C31⋊#95C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2212yes—
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C24×C31C2311yescharacteristic
33C2×Q8×C31—41no—
34C2×Q8×C31—41no—
35C2×Q8×C31C2×C414yes—
36C22×C4×C31—41no—
37C22×C4×C31—41no—
38C22×C4×C31C2×C414yes—
39C22×C4×C31C2311yescharacteristic
40C22×C4×C31C2311yescharacteristic
41C22×C4×C31C2312yes—
42C22×C4×C31C2312yes—
43C22×Dic31C2312yes—
44C22×Dic31C2312yes—
45C22×Dic31C2312yes—
46C22×Dic31C2312yes—
47C4⋊C4×C31C2×C414yes—
48C4⋊C4×C31C2×C418yes—
49C22⋊C4×C31C2×C418yes—
50C22⋊Dic31—24no—
51C22⋊Dic31—41no—
52C22⋊Dic31—41no—
53C4⋊Dic31—24no—
54C4⋊Dic31—42no—
55C4×Dic31—24no—
56C4×Dic31—41no—
57C4×Dic31—42no—
58C4×Dic31—41no—
59C23×C31—22no—
60C23×C31—21no—
61C23×C31—21no—
62C23×C31—22no—
63C23×C31C22×C412yes—
64C23×C31C2411yescharacteristic
65Q8×C31—44no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—44no—
75C2×C4×C31C22×C414yes—
76C2×C4×C31C22×C414yes—
77C2×C4×C31C22×C412yes—
78C2×C4×C31C22×C412yes—
79C2×Dic31—22no—
80C2×Dic31—22no—
81C2×Dic31—22no—
82C2×Dic31—22no—
83C2×Dic31—22no—
84C2×Dic31—22no—
85C2×Dic31—22no—
86C2×Dic31—22no—
87C2×Dic31—22no—
88C2×Dic31—22no—
89C2×Dic31—22no—
90C2×Dic31#4114yes—
91#2332—311nomaximal, Sylow
92C22×C31—22no—
93C22×C31—22no—
94C22×C31—22no—
95C22×C31—42no—
96C22×C31—42no—
97C22×C31C23×C411yescharacteristic
98C22×C31C2×#4112yes—
99C22×C31H(5,𝔽2)11yescharacteristic
100C22×C31H(5,𝔽2)11yescharacteristic
101C22×C312−1+412yes—
102C4×C31—24no—
103C4×C31—22no—
104C4×C31—22no—
105C4×C31—24no—
106Dic31—24no—
107Dic31—42no—
108Dic31—42no—
109Dic31—42no—
110C2×C22⋊Q8D3111yescharacteristic
111#391—312no—
112#388—312no—
113#388—312no—
114#387—312no—
115#387—312no—
116#381—311no—
117C4×C4⋊C4—312no—
118C4×C22⋊C4—311no—
119C2×C31—42no—
120C2×C31C4×#4111yescharacteristic
121C2×C31#51811yescharacteristic
122C2×C31#51911yescharacteristic
123C2×C31#53912yes—
124C2×C31#54212yes—
125C22×Q8C2×D3111yescharacteristic
126C23×C4C2×D3111yescharacteristic
127C22⋊Q8Dic3118yescomplemented
128C2×C4⋊C4—312no—
129C2×C4⋊C4—312no—
130C2×C4⋊C4C2×D3112yes—
131C2×C4⋊C4C2×D3111yescharacteristic
132C2×C22⋊C4—312no—
133C2×C22⋊C4—311no—
134C2×C22⋊C4—311no—
135C2×C22⋊C4C2×D3112yes—
136C2×C42—312no—
137C2×C42—311no—
138C2×C42—311no—
139C2×C42—312no—
140#95—312no—
141#95—312no—
142#95—312no—
143#95—312no—
144#95—312no—
145#95—312no—
146#95—312no—
147C31#233211yescharacteristic, complemented, Sylow
148C24C22×D3111yescharacteristic
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8C2×Dic3114yes—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—312no—
155C22×C4—312no—
156C22×C4—312no—
157C22×C4—312no—
158C22×C4C2×Dic3114yes—
159C22×C4C22×D3111yescharacteristic
160C22×C4C22×D3111yescharacteristic
161C22×C4C22×D3112yes—
162C22×C4C22×D3112yes—
163C4⋊C4—624no—
164C4⋊C4—1242no—
165C4⋊C4C2×Dic3114yes—
166C4⋊C4C2×Dic3118yes—
167C22⋊C4—624no—
168C22⋊C4—1241no—
169C22⋊C4—1241no—
170C22⋊C4C2×Dic3118yes—
171C42—624no—
172C42—1241no—
173C42—1241no—
174C42—1242no—
175C23—21no—
176C23—21no—
177C23—22no—
178C23—22no—
179C23C22×Dic3112yes—
180C23C23×D3111yescharacteristic
181Q8—44no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—44no—
191C2×C4—314no—
192C2×C4—622no—
193C2×C4—622no—
194C2×C4—622no—
195C2×C4—622no—
196C2×C4—622no—
197C2×C4—622no—
198C2×C4—622no—
199C2×C4—622no—
200C2×C4—622no—
201C2×C4—622no—
202C2×C4—622no—
203C2×C4C22×Dic3114yes—
204C2×C4C22×Dic3114yes—
205C2×C4C22×Dic3112yes—
206C2×C4C22×Dic3112yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22#1175856111yescharacteristic
213C22#1175856111yescharacteristic
214C22#1175856412yes—
215C22#41×D3112yes—
216C22C23×Dic3111yescharacteristic
217C4—24no—
218C4—22no—
219C4—22no—
220C4—24no—
221C4—624no—
222C4—1242no—
223C4—1242no—
224C4—1242no—
225C2—42no—
226C2#41×Dic3111yescharacteristic
227C2#1452152411yescharacteristic
228C2#1452152711yescharacteristic
229C2#1452164512yes—
230C2#1452166912yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC2×C31×C22⋊Q8C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenterC2×C22⋊Q8D31
hypocenterC31#2332
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14520956C2semidirect
4. #14520935C2semidirect
5. #14520935C2semidirect
7. C4⋊C4×Dic31C2semidirect
12. C31×C22⋊Q8C4semidirect
127. C22⋊Q8Dic31semidirect
147. C31#2332semidirect

Maximal subgroups

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

subgroupindex
#145209562
#145209422
#145209352
#145209122
C4⋊C4×Dic312
C4×C22⋊Dic312
C2×C31×C22⋊Q82
#233231