Finite Group Databasebeta

← #16846126

Subgroups — #16846126

Order 3968.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#14521815C211yesmaximal, characteristic, complemented
2#14521560C211yesmaximal, characteristic
3#14521031C211yesmaximal, characteristic, complemented
4#14521013C211yesmaximal, characteristic, complemented
5#14520821C211yesmaximal, characteristic, complemented
6#14520820C211yesmaximal, characteristic, complemented
7C31×#407C211yesmaximal, characteristic, complemented
8C23×C4×C31C2211yescharacteristic
9C2×#92495C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12#11758530C412yes—
13#11758507—21no—
14#11758506C412yes—
15C4×C22⋊D31—22no—
16#11758503C2211yescharacteristic
17#11758501—21no—
18C2×#92474C2211yescharacteristic
19C2×#92474C2211yescharacteristic
20#11758484—22no—
21M16×D31—22no—
22#11758478—22no—
23C31×C22⋊C8—22no—
24C22⋊(C31⋊C8)—22no—
25#11758412—21no—
26#11758411—21no—
27C24×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31—21no—
30C22×C4×C31—21no—
31C22×C4×C31—21no—
32C22×C4×C31—21no—
33C22×C4×C31—21no—
34C22×C4×C31C2×C411yescharacteristic
35C22×C4×C31C2311yescharacteristic
36C2×C22⋊D31—22no—
37C2×C22⋊D31C2×C412yes—
38#92495—21no—
39#92495—21no—
40#92495—21no—
41#92495—21no—
42C2×D124D411yescharacteristic
43C2×C4×D31D412yes—
44C2×Dic62D411yescharacteristic
45M16×C31—21no—
46M16×C31—21no—
47M16×C31—21no—
48M16×C31—21no—
49C2×C8×C31—21no—
50C2×C8×C31D412yescomplemented
51C22⋊Dic31—22no—
52C22⋊Dic31C2×C412yes—
53(C2×D31)⋊C4—22no—
54C4⋊Dic31—21no—
55Dic31⋊C4—22no—
56C4×Dic31—21no—
57#92474—21no—
58#92474—21no—
59#92474—21no—
60#92474—21no—
61C2×C31⋊C8—21no—
62C2×C31⋊C8D412yescomplemented
63#92469—24no—
64C8×D31—24no—
65C23×C31—21no—
66C23×C31—21no—
67C23×C31—21no—
68C23×C31—42no—
69C23×C31C22×C411yescharacteristic
70C22×D31C22⋊C412yes—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31—41no—
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31#4111yescharacteristic
83C2×C4×C31#4111yescharacteristic
84C22⋊D31—22no—
85C22⋊D31—22no—
86C22⋊D31—44no—
87C2×Dic31—22no—
88C2×Dic31C22⋊C412yes—
89D124—21no—
90D124—21no—
91C4×D31—22no—
92C4×D31—22no—
93Dic62—21no—
94Dic62—21no—
95C8×C31—22no—
96C8×C31—41no—
97C31⋊C8—22no—
98C31⋊C8—41no—
99#1891—311nomaximal, Sylow
100C22×C31—22no—
101C22×C31—22no—
102C22×C31—22no—
103C22×C31—41no—
104C22×C31—41no—
105C22×C31—41no—
106C22×C31—41no—
107C22×C31—41no—
108C22×C31C2×C22⋊C411yescharacteristic
109C22×C31C4×D411yescharacteristic
110C22×C31C4×D411yescharacteristic
111C2×D31—22no—
112C2×D31—42no—
113C4×C31—41no—
114C4×C31#12011yescharacteristic
115C4×C31#12111yescharacteristic
116C4×C31#12111yescharacteristic
117C4×C31#12311yescharacteristic
118Dic31—22no—
119Dic31—42no—
120#568—311no—
121#525—311no—
122#413—311no—
123#407—311no—
124#407D3111yescharacteristic, complemented
125#344—311no—
126#344—311no—
127C2×C31—21no—
128C2×C31—21no—
129C2×C31—21no—
130C2×C31—42no—
131C2×C31#38611yescharacteristic
132D31—42no—
133C2×#41—311no—
134C23×C4C2×D3111yescharacteristic
135#131—622no—
136#131—622no—
137C2×M16—311no—
138C2×M16—311no—
139C2×M16—622no—
140C2×M16C2×D3111yescharacteristic
141C2×M16C2×D3111yescharacteristic
142#123—312no—
143C22⋊Q8—621no—
144#121—621no—
145#120—312no—
146C4×D4—622no—
147#117—311no—
148#101—621no—
149#100—621no—
150C22⋊C8—22no—
151C22⋊C8—622no—
152C31#189111yescharacteristic, complemented, Sylow
153C24C4×D3111yescharacteristic
154#41—621no—
155#41—621no—
156#41—621no—
157#41—621no—
158C2×Q8—311no—
159C2×D4—312no—
160C2×D4—311no—
161C2×D4—622no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—312no—
169C22×C4C4×D3111yescharacteristic
170C22×C4C22×D3111yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—624no—
176M16—621no—
177M16—621no—
178M16—621no—
179M16—621no—
180C2×C8—21no—
181C2×C8—312no—
182C2×C8—624no—
183C2×C8—621no—
184C2×C8C22⋊D3112yescomplemented
185C4⋊C4—622no—
186C4⋊C4—621no—
187C22⋊C4—312no—
188C22⋊C4—622no—
189C22⋊C4—622no—
190C42—621no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23—312no—
196C23C2×C4×D3111yescharacteristic
197Q8—621no—
198Q8—621no—
199D4—622no—
200D4—622no—
201D4—621no—
202D4—621no—
203D4—1244no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—312no—
212C2×C4—622no—
213C2×C4—622no—
214C2×C4—622no—
215C2×C4#9249511yescharacteristic
216C2×C4D4×D3111yescharacteristic
217C2×C4D4×D3111yescharacteristic
218C2×C4D4×D3111yescharacteristic
219C2×C4#9249711yescharacteristic
220C2×C4C2×C22⋊D3111yescharacteristic
221C8—22no—
222C8—41no—
223C8—622no—
224C8—1241no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—622no—
234C22—1242no—
235C22C22⋊C4×D3111yescharacteristic
236C22(C22⋊D31)⋊C411yescharacteristic
237C22C4×C22⋊D3111yescharacteristic
238C4—41no—
239C4—622no—
240C4—1242no—
241C4#1175846011yescharacteristic
242C4#1175846111yescharacteristic
243C4#1175851411yescharacteristic
244C4#1175851511yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—42no—
249C2—1242no—
250C2#1452092511yescharacteristic
subgroupG/H
centerC4#11758514
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#407C2
socleC2×C31#386
prime radical#14521560C2
cosocleC22×C4×C31C23
hypercenter#407D31
hypocenterC31#1891
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14521815C2semidirect
3. #14521031C2semidirect
4. #14521013C2semidirect
5. #14520821C2semidirect
6. #14520820C2semidirect
7. C31×#407C2semidirect
50. C2×C8×C31D4semidirect
62. C2×C31⋊C8D4semidirect
124. #407D31semidirect
152. C31#1891semidirect
184. C2×C8C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145218152
#145215602
#145210312
#145210132
#145208212
#145208202
C31×#4072
#189131