Finite Group Databasebeta

← #16845479

Subgroups — #16845479

Order 3968.

336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11758503C211yesmaximal, characteristic
2C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic
3C2×#11758403C211yesmaximal, characteristic, complemented
4C2×C8×Dic31C211yesmaximal, characteristic, complemented
5#14520803C211yesmaximal, characteristic, complemented
6#14520803C211yesmaximal, characteristic, complemented
7C2×C31×C22⋊C8C211yesmaximal, characteristic
8C23×C4×C31C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C22⋊Dic31C412yes—
12#11758503—22no—
13#11758503—22no—
14C2×C4⋊Dic31C412yes—
15C2×C4×Dic31C2211yescharacteristic
16C2×C4×Dic31C2211yescharacteristic
17C22×C31⋊C8C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19C31×C22⋊C8C414yescomplemented
20C22⋊(C31⋊C8)C414yescomplemented
21#11758403—22no—
22C8×Dic31—22no—
23C24×C31C2×C411yescharacteristic
24C22×C4×C31—21no—
25C22×C4×C31—21no—
26C22×C4×C31—21no—
27C22×C4×C31—21no—
28C22×C4×C31C2×C411yescharacteristic
29C22×C4×C31C2×C412yes—
30C22×C4×C31C2×C412yes—
31C22×C4×C31C2311yescharacteristic
32C22×Dic31C2×C412yes—
33C22×Dic31C2×C412yes—
34C2×C8×C31—21no—
35C2×C8×C31—21no—
36C2×C8×C31—21no—
37C2×C8×C31—21no—
38C2×C8×C31C2×C412yes—
39C2×C8×C31C2×C412yes—
40C22⋊Dic31—24no—
41C4⋊Dic31—24no—
42C4×Dic31—21no—
43C4×Dic31—21no—
44C4×Dic31D412yes—
45C4×Dic31D412yes—
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48C2×C31⋊C8—21no—
49C2×C31⋊C8—21no—
50C2×C31⋊C8C2×C412yes—
51C2×C31⋊C8C2×C412yes—
52C23×C31—21no—
53C23×C31—21no—
54C23×C31—22no—
55C23×C31—22no—
56C23×C31C4212yes—
57C23×C31C22×C411yescharacteristic
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—22no—
63C2×C4×C31—22no—
64C2×C4×C31C4212yes—
65C2×C4×C31C22×C411yescharacteristic
66C2×C4×C31C22×C411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31#4111yescharacteristic
70C2×C4×C31#4111yescharacteristic
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31C22⋊C414yes—
77C8×C31—22no—
78C8×C31—22no—
79C31⋊C8—22no—
80C31⋊C8—22no—
81#1750—311nomaximal, Sylow
82C22×C31—22no—
83C22×C31—22no—
84C22×C31—22no—
85C22×C31—42no—
86C22×C31—42no—
87C22×C31C2×C4211yescharacteristic
88C22×C31C2×C22⋊C411yescharacteristic
89C22×C31#11711yescharacteristic
90C22×C31#13112yes—
91C22×C31#13112yes—
92C4×C31—22no—
93C4×C31C4×D411yescharacteristic
94C4×C31C4×D411yescharacteristic
95C4×C31C4×D411yescharacteristic
96C4×C31C4×D411yescharacteristic
97Dic31—24no—
98Dic31—42no—
99C2×#117—311no—
100C2×C22⋊C8—311no—
101C2×C22⋊C8D3111yescharacteristic
102C2×#97—311no—
103C2×C4×C8—311no—
104#336—311no—
105#336—311no—
106C2×C31—42no—
107C2×C31C4×C22⋊C411yescharacteristic
108C2×C31#40511yescharacteristic
109C2×C31#40511yescharacteristic
110C2×C31#40812yes—
111C2×C31#43312yes—
112C23×C4C2×D3111yescharacteristic
113C22×C8—311no—
114C22×C8—311no—
115C22×C8C2×D3111yescharacteristic
116C22×C8C2×D3111yescharacteristic
117#117—622no—
118#117—622no—
119C2×C4⋊C4—312no—
120C2×C22⋊C4—312no—
121C2×C42—311no—
122C2×C42—311no—
123C22⋊C8—314no—
124C22⋊C8Dic3114yescomplemented
125#97—622no—
126C4×C8—622no—
127C31#175011yescharacteristic, complemented, Sylow
128C24C4×D3111yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—312no—
134C22×C4—312no—
135C22×C4C4×D3111yescharacteristic
136C22×C4C4×D3112yes—
137C22×C4C2×Dic3112yes—
138C22×C4C22×D3111yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—312no—
144C2×C8—312no—
145C2×C8—621no—
146C2×C8—621no—
147C2×C8—621no—
148C2×C8—621no—
149C2×C8C2×Dic3112yes—
150C2×C8C2×Dic3112yes—
151C4⋊C4—624no—
152C22⋊C4—624no—
153C42—312no—
154C42—312no—
155C42—621no—
156C42—621no—
157C23—21no—
158C23—21no—
159C23—22no—
160C23—22no—
161C23C4×Dic3112yes—
162C23C2×C4×D3111yescharacteristic
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—314no—
170C2×C4—622no—
171C2×C4—622no—
172C2×C4—622no—
173C2×C4—622no—
174C2×C4—622no—
175C2×C4C4×Dic3112yes—
176C2×C4C2×C4×D3111yescharacteristic
177C2×C4D4×D3111yescharacteristic
178C2×C4D4×D3111yescharacteristic
179C2×C4#9249711yescharacteristic
180C2×C4#9249711yescharacteristic
181C2×C4C22×Dic3111yescharacteristic
182C8—22no—
183C8—22no—
184C8—622no—
185C8—622no—
186C22—22no—
187C22—22no—
188C22—22no—
189C22—42no—
190C22—42no—
191C22#1175845411yescharacteristic
192C22C22⋊C4×D3111yescharacteristic
193C22#1175847812yes—
194C22#1175848412yes—
195C22C2×C4×Dic3111yescharacteristic
196C4—22no—
197C4—624no—
198C4—1242no—
199C4(C22⋊D31)⋊C411yescharacteristic
200C4(C22⋊D31)⋊C411yescharacteristic
201C4D4×Dic3111yescharacteristic
202C4D4×Dic3111yescharacteristic
203C2—42no—
204C2C22⋊C4×Dic3111yescharacteristic
205C2#1452100411yescharacteristic
206C2#1452100711yescharacteristic
207C2#1452101412yes—
208C2#1452110712yes—
subgroupG/H
center, FrattiniC22×C4C22×D31
commutatorC22×C31C2×C42
FittingC2×C31×C22⋊C8C2
socleC23×C31C22×C4
prime radicalC24×C31C2×C4
cosocleC22×C4×C31C23
hypercenterC2×C22⋊C8D31
hypocenterC31#1750
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#11758403C2semidirect
4. C2×C8×Dic31C2semidirect
5. #14520803C2semidirect
6. #14520803C2semidirect
19. C31×C22⋊C8C4semidirect
20. C22⋊(C31⋊C8)C4semidirect
124. C22⋊C8Dic31semidirect
127. C31#1750semidirect

Maximal subgroups

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

subgroupindex
C2×#117585032
C2×C22⋊(C31⋊C8)2
C2×#117584032
C2×C8×Dic312
#145208032
C2×C31×C22⋊C82
#175031