Finite Group Databasebeta

← #16848548

Subgroups — #16848548

Order 3968.

872 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 872 conjugacy classes of subgroups — too many to draw. Only its 233 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
1C22×#92495C211yesmaximal, characteristic
2C2×#11758464C212yesmaximal, complemented
3#14520950C212yesmaximal, complemented
4#14520949C214yesmaximal, complemented
5#14520908C212yesmaximal, complemented
6C4×C22⋊Dic31C211yesmaximal, characteristic, complemented
7#14520896C212yesmaximal, complemented
8C31×#380C211yesmaximal, characteristic, complemented
9C23×C4×C31C2211yescharacteristic
10C22×C22⋊D31C2212yes—
11C2×#92495—28no—
12C2×#92495C418yescomplemented
13C22×D124C2211yescharacteristic
14C22×C4×D31C2212yes—
15C22×Dic62C2211yescharacteristic
16C2×C4⋊C4×C31C2212yes—
17C2×C22⋊C4×C31C2212yes—
18C2×C22⋊Dic31C2212yes—
19C2×(C2×D31)⋊C4C2214yes—
20C2×(C2×D31)⋊C4C2214yes—
21C2×Dic31⋊C4C2214yes—
22C2×C4×Dic31C2214yes—
23C2×C4×Dic31C2212yes—
24#11758464—28no—
25C31×#95C2212yes—
26C31⋊#95C2211yescharacteristic
27C31⋊#95C2211yescharacteristic
28C24×C31C2311yescharacteristic
29C23×D31C2312yes—
30C22×C4×C31—24no—
31C22×C4×C31C2×C414yes—
32C22×C4×C31C2314yes—
33C22×C4×C31C2311yescharacteristic
34C22×C4×C31C2311yescharacteristic
35C2×C22⋊D31—28no—
36C2×C22⋊D31C2×C418yes—
37C22×Dic31C2312yes—
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40#92495—232no—
41C2×D124—24no—
42C2×D124C2×C414yes—
43C2×C4×D31—28no—
44C2×C4×D31C2×C418yes—
45C2×Dic62C2×C414yes—
46C2×Dic62D418yes—
47C4⋊C4×C31—24no—
48C22⋊C4×C31—42no—
49C22⋊Dic31—24no—
50(C2×D31)⋊C4—28no—
51(C2×D31)⋊C4—44no—
52Dic31⋊C4—28no—
53C4×Dic31—24no—
54C4×Dic31—28no—
55C23×C31—22no—
56C23×C31—22no—
57C23×C31—21no—
58C23×C31—21no—
59C23×C31C22×C412yes—
60C23×C31C2411yescharacteristic
61C22×D31—24no—
62C22×D31—24no—
63C22×D31—22no—
64C22×D31—22no—
65C22×D31C22×C414yes—
66C2×C4×C31—22no—
67C2×C4×C31—28no—
68C2×C4×C31—24no—
69C2×C4×C31—24no—
70C2×C4×C31—24no—
71C2×C4×C31C22×C412yes—
72C2×C4×C31C22×C412yes—
73C2×C4×C31C2×D414yes—
74C22⋊D31—216no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—22no—
79C2×Dic31—22no—
80C2×Dic31C22×C414yes—
81C2×Dic31C2×D418yes—
82C2×Dic31#4114yescomplemented
83D124—28no—
84C4×D31—216no—
85Dic62C22⋊C4116yescomplemented
86#2341—311nomaximal, Sylow
87C22×C31—22no—
88C22×C31—22no—
89C22×C31—22no—
90C22×C31—42no—
91C22×C31—42no—
92C22×C31C23×C411yescharacteristic
93C22×C31C22×D412yes—
94C22×C31C2×#4112yes—
95C22×C31H(5,𝔽2)11yescharacteristic
96C22×C312−1+411yescharacteristic
97C2×D31—24no—
98C2×D31—24no—
99C2×D31—24no—
100C2×D31—44no—
101C2×D31—44no—
102C4×C31—22no—
103C4×C31—44no—
104C4×C31C2×C22⋊C414yes—
105Dic31—24no—
106Dic31—42no—
107Dic31C2×C22⋊C418yes—
108C22×#41—311no—
109C2×C4×Q8—312no—
110#390—312no—
111#390—314no—
112#380—312no—
113#380D3111yescharacteristic, complemented
114C4×C22⋊C4—311no—
115C4×C22⋊C4—312no—
116C2×C31—42no—
117C2×C31C22×C22⋊C411yescharacteristic
118C2×C31C4×#4111yescharacteristic
119C2×C31#52011yescharacteristic
120C2×C31#54812yes—
121C2×C31#55012yes—
122D31—44no—
123C2×#41—318no—
124C2×#41—628no—
125C22×Q8—311no—
126C22×D4—312no—
127C22×D4—311no—
128C23×C4—312no—
129C23×C4C2×D3111yescharacteristic
130C4×Q8—628no—
131C2×C4⋊C4—314no—
132C2×C4⋊C4C2×D3112yes—
133C2×C22⋊C4—312no—
134C2×C22⋊C4—314no—
135C2×C22⋊C4—314no—
136C2×C22⋊C4C2×D3112yes—
137C2×C42—314no—
138C2×C42—312no—
139#95—311no—
140#95—311no—
141#95C2×D3112yes—
142C31#234111yescharacteristic, complemented, Sylow
143C24—312no—
144C24C22×D3111yescharacteristic
145#41—6232no—
146C2×Q8—314no—
147C2×Q8—318no—
148C2×D4—318no—
149C2×D4—314no—
150C2×D4—628no—
151C2×D4—624no—
152C22×C4—24no—
153C22×C4—312no—
154C22×C4—312no—
155C22×C4—318no—
156C22×C4—312no—
157C22×C4—628no—
158C22×C4C4×D3114yes—
159C22×C4C22×D3114yes—
160C22×C4C22×D3111yescharacteristic
161C22×C4C22×D3111yescharacteristic
162C4⋊C4—24no—
163C4⋊C4—628no—
164C22⋊C4—42no—
165C22⋊C4—628no—
166C22⋊C4—624no—
167C22⋊C4—1244no—
168C42—628no—
169C42—624no—
170C23—22no—
171C23—21no—
172C23—21no—
173C23—22no—
174C23—314no—
175C23—624no—
176C23—622no—
177C23—622no—
178C23—624no—
179C23C2×C4×D3112yes—
180C23C23×D3111yescharacteristic
181Q8—3116no—
182D4—6216no—
183D4—628no—
184C2×C4—22no—
185C2×C4—28no—
186C2×C4—24no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—314no—
190C2×C4—318no—
191C2×C4—314no—
192C2×C4—6216no—
193C2×C4—622no—
194C2×C4—622no—
195C2×C4—622no—
196C2×C4—622no—
197C2×C4—622no—
198C2×C4C2×C4×D3112yes—
199C2×C4C2×C4×D3112yes—
200C2×C4D4×D3114yes—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—42no—
205C22—42no—
206C22—624no—
207C22—624no—
208C22—624no—
209C22—1244no—
210C22—1244no—
211C22C22×C4×D3111yescharacteristic
212C22C2×D4×D3112yes—
213C22#1175856111yescharacteristic
214C22#1175856411yescharacteristic
215C22#41×D3112yes—
216C4—22no—
217C4—44no—
218C4—318no—
219C4—624no—
220C4—1242no—
221C4C22⋊C4×D3114yes—
222C2—42no—
223C2—1244no—
224C2C2×C22⋊C4×D3111yescharacteristic
225C2#1452151711yescharacteristic
226C2#1452153011yescharacteristic
227C2#1452170912yes—
228C2#1452171712yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#380C2
socle, cosocleC23×C31C24
prime radicalC22×#92495C2
hypercenter#380D31
hypocenterC31#2341
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#11758464C2semidirect
3. #14520950C2semidirect
4. #14520949C2semidirect
5. #14520908C2semidirect
6. C4×C22⋊Dic31C2semidirect
7. #14520896C2semidirect
8. C31×#380C2semidirect
12. C2×#92495C4semidirect
82. C2×Dic31#41semidirect
85. Dic62C22⋊C4semidirect
113. #380D31semidirect
142. C31#2341semidirect

Maximal subgroups

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

subgroupindex
C22×#924952
C2×#117584642
#145209502
#145209492
#145209082
C4×C22⋊Dic312
#145208962
C31×#3802
#234131