Finite Group Databasebeta

← #16848467

Subgroups — #16848467

Order 3968.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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#14520953C212yesmaximal, complemented
3#14520943C212yesmaximal
4#14520937C212yesmaximal
5#14520934C212yesmaximal, complemented
6#14520933C212yesmaximal, complemented
7#14520912C211yesmaximal, characteristic
8C4×Dic31⋊C4C212yesmaximal, complemented
9C4×C22⋊C4×C31C211yesmaximal, characteristic
10C23×C4×C31C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C2×C22⋊C4×C31C2212yes—
13C2×C42×C31C2211yescharacteristic
14C2×C42×C31C2211yescharacteristic
15C2×C22⋊Dic31C2211yescharacteristic
16C2×C22⋊Dic31C2211yescharacteristic
17C2×C22⋊Dic31C2212yes—
18C2×C4⋊Dic31C2211yescharacteristic
19#11758501C418yescomplemented
20C2×Dic31⋊C4C2212yes—
21C2×Dic31⋊C4C2212yes—
22C2×Dic31⋊C4C2212yes—
23C2×C4×Dic31C2212yes—
24C2×C4×Dic31C2212yes—
25C31×#95C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2212yes—
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C24×C31C2311yescharacteristic
33C22×C4×C31—41no—
34C22×C4×C31—41no—
35C22×C4×C31C2×C414yes—
36C22×C4×C31C2312yes—
37C22×C4×C31C2311yescharacteristic
38C22×C4×C31C2311yescharacteristic
39C22×C4×C31C2312yes—
40C22×Dic31C2312yes—
41C22×Dic31C2312yes—
42C22×Dic31C2312yes—
43C22×Dic31C2312yes—
44C2×Dic62—41no—
45C2×Dic62—41no—
46C2×Dic62C2×C414yes—
47C22⋊C4×C31—24no—
48C42×C31—41no—
49C42×C31—41no—
50C22⋊Dic31—41no—
51C22⋊Dic31—41no—
52C22⋊Dic31C2×C418yes—
53C4⋊Dic31C2×C414yes—
54Dic31⋊C4—24no—
55Dic31⋊C4—42no—
56Dic31⋊C4C2×C418yes—
57C4×Dic31—24no—
58C4×Dic31—42no—
59C23×C31—22no—
60C23×C31—21no—
61C23×C31—21no—
62C23×C31—22no—
63C23×C31C22×C412yes—
64C23×C31C2411yescharacteristic
65C2×C4×C31—22no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—44no—
75C2×C4×C31C22×C412yes—
76C2×C4×C31C22×C412yes—
77C2×C4×C31#4114yes—
78C2×Dic31—22no—
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×Dic31C22×C414yes—
89C2×Dic31C22×C414yes—
90Dic62—44no—
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—22no—
103C4×C31—22no—
104C4×C31—24no—
105C4×C31—42no—
106Dic31—24no—
107Dic31—24no—
108Dic31—42no—
109Dic31—42no—
110C2×C22⋊Q8—311no—
111#391—312no—
112#388—312no—
113#388—312no—
114#387—312no—
115#387—312no—
116#381—311no—
117C4×C4⋊C4—312no—
118C4×C22⋊C4D3111yescharacteristic
119C2×C31—42no—
120C2×C31C4×#4111yescharacteristic
121C2×C31#51811yescharacteristic
122C2×C31#51911yescharacteristic
123C2×C31#53912yes—
124C2×C31#54212yes—
125C22×Q8—311no—
126C23×C4C2×D3111yescharacteristic
127C22⋊Q8—318no—
128C2×C4⋊C4—312no—
129C2×C4⋊C4—311no—
130C2×C4⋊C4—312no—
131C2×C4⋊C4—312no—
132C2×C22⋊C4—312no—
133C2×C22⋊C4—311no—
134C2×C22⋊C4—311no—
135C2×C22⋊C4C2×D3112yes—
136C2×C42—312no—
137C2×C42—312no—
138C2×C42C2×D3111yescharacteristic
139C2×C42C2×D3111yescharacteristic
140#95—312no—
141#95—312no—
142#95—312no—
143#95—312no—
144#95—312no—
145#95—312no—
146#95C2×D3112yes—
147C31#233211yescharacteristic, complemented, Sylow
148C24C22×D3111yescharacteristic
149C2×Q8—314no—
150C2×Q8—1241no—
151C2×Q8—1241no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—312no—
155C22×C4—312no—
156C22×C4—312no—
157C22×C4—312no—
158C22×C4C4×D3114yes—
159C22×C4C22×D3112yes—
160C22×C4C22×D3111yescharacteristic
161C22×C4C22×D3111yescharacteristic
162C22×C4C22×D3112yes—
163C4⋊C4—318no—
164C4⋊C4—314no—
165C4⋊C4—624no—
166C4⋊C4—1242no—
167C22⋊C4—24no—
168C22⋊C4—318no—
169C22⋊C4—1241no—
170C22⋊C4—1241no—
171C42—41no—
172C42—41no—
173C42—624no—
174C42—1242no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D3112yes—
180C23C23×D3111yescharacteristic
181Q8—1244no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—314no—
193C2×C4—314no—
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×C4—622no—
204C2×C4C2×C4×D3112yes—
205C2×C4C2×C4×D3112yes—
206C2×C4#9249514yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D3111yescharacteristic
213C22C2×#9249512yes—
214C22#1175856111yescharacteristic
215C22#1175856111yescharacteristic
216C22#1175856712yes—
217C4—24no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—624no—
222C4—624no—
223C4—1242no—
224C4—1242no—
225C2—42no—
226C2C4×#9249511yescharacteristic
227C2#1452152211yescharacteristic
228C2#1452152611yescharacteristic
229C2#1452164112yes—
230C2#1452166412yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC4×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenterC4×C22⋊C4D31
hypocenterC31#2332
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14520953C2semidirect
5. #14520934C2semidirect
6. #14520933C2semidirect
8. C4×Dic31⋊C4C2semidirect
19. #11758501C4semidirect
147. C31#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#117585012
#145209532
#145209432
#145209372
#145209342
#145209332
#145209122
C4×Dic31⋊C42
C4×C22⋊C4×C312
#233231