Finite Group Databasebeta

← #16846079

Subgroups — #16846079

Order 3968.

334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11758486C211yesmaximal, characteristic
2#14521530C211yesmaximal, characteristic
3C2×#11758413C211yesmaximal, characteristic
4#14521059C211yesmaximal, characteristic, complemented
5#14520954C211yesmaximal, characteristic, complemented
6#14520810C211yesmaximal, characteristic, complemented
7C31×#343C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C4×C22⋊D31—22no—
14#11758503C2211yescharacteristic
15C2×C4×Dic31C2211yescharacteristic
16#11758486—22no—
17#11758486C414yescomplemented
18C2×Dic124—21no—
19C2×#92470—21no—
20#11758470—21no—
21#11758469—21no—
22C4⋊C4×D31—21no—
23#11758464—21no—
24C31⋊#95—22no—
25#11758413—22no—
26#11758404—21no—
27#11758404—21no—
28C22×C4×C31D412yes—
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—21no—
31C22×Dic31—21no—
32C22×Dic31—21no—
33#92495—21no—
34#92495—21no—
35#92495C2×C412yes—
36#92495D412yes—
37C2×D124D411yescharacteristic
38C2×C4×D31—21no—
39C2×C4×D31—22no—
40C2×Dic62—21no—
41C2×Dic62—21no—
42C2×Dic62—21no—
43C2×Dic62—21no—
44C2×Dic62—21no—
45C2×Dic62C2×C412yescomplemented
46C2×Dic62D411yescharacteristic
47M16×C31—21no—
48M16×C31—21no—
49M16×C31—21no—
50M16×C31C2×C412yescomplemented
51C2×C8×C31—21no—
52C2×C8×C31—21no—
53C4⋊C4×C31—21no—
54C4⋊C4×C31—21no—
55C22⋊Dic31—21no—
56(C2×D31)⋊C4—22no—
57C4⋊Dic31D411yescharacteristic
58C4⋊Dic31D411yescharacteristic
59Dic31⋊C4—22no—
60C4×Dic31—22no—
61C4×Dic31—21no—
62C4×Dic31—21no—
63C4×Dic31—21no—
64Dic124—24no—
65#92470—24no—
66C23×C31C2×D411yescharacteristic
67C22×D31—21no—
68C2×C4×C31—22no—
69C2×C4×C31—42no—
70C2×C4×C31C22×C411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31#4111yescharacteristic
75C2×C4×C31#4111yescharacteristic
76C22⋊D31—22no—
77C22⋊D31—22no—
78C2×Dic31—21no—
79C2×Dic31—22no—
80C2×Dic31—22no—
81C2×Dic31—21no—
82C2×Dic31—21no—
83C2×Dic31—41no—
84C2×Dic31—41no—
85C2×Dic31—41no—
86C2×Dic31—41no—
87D124—21no—
88D124C22⋊C412yes—
89C4×D31—22no—
90C4×D31—22no—
91C4×D31—82no—
92Dic62—21no—
93Dic62—22no—
94Dic62—22no—
95Dic62—41no—
96Dic62—41no—
97Dic62C22⋊C412yes—
98C8×C31—22no—
99C8×C31—41no—
100#1882—311nomaximal, Sylow
101C22×C31—21no—
102C22×C31—21no—
103C22×C31C4×D411yescharacteristic
104C22×C31#12011yescharacteristic
105C22×C31#12111yescharacteristic
106C2×D31—22no—
107C2×D31—41no—
108C2×D31—41no—
109C4×C31—42no—
110C4×C31C2×C22⋊C411yescharacteristic
111C4×C31C4×D411yescharacteristic
112C4×C31#12111yescharacteristic
113C4×C31#12311yescharacteristic
114Dic31—22no—
115Dic31—42no—
116Dic31—42no—
117Dic31—41no—
118Dic31—41no—
119C2×#137—311no—
120#520—311no—
121C2×#104—311no—
122#419—311no—
123#391—311no—
124#343D3111yescharacteristic, complemented
125#339—311no—
126C2×C31—21no—
127C2×C31—21no—
128C2×C31#38611yescharacteristic
129C2×C31#45511yescharacteristic
130C2×C31#45611yescharacteristic
131D31—42no—
132C2×#41—311no—
133C22×Q8—311no—
134#137—314no—
135#137—622no—
136C2×Q16—621no—
137C2×SD16—621no—
138C2×M16C2×D3111yescharacteristic
139C2×M16C2×D3111yescharacteristic
140C4×Q8—621no—
141C4×D4—621no—
142C4×D4—622no—
143#117—311no—
144#117—621no—
145C2×C4⋊C4—621no—
146C2×C4⋊C4C2×D3111yescharacteristic
147C2×C42—311no—
148#104—622no—
149#103—621no—
150#103—621no—
151#95—622no—
152C31#188211yescharacteristic, complemented, Sylow
153#41—312no—
154#41—312no—
155#41—621no—
156#41—621no—
157C2×Q8—312no—
158C2×Q8—311no—
159C2×Q8—621no—
160C2×Q8—621no—
161C2×Q8—621no—
162C2×Q8—621no—
163C2×Q8—621no—
164C2×D4—311no—
165C2×D4—621no—
166C22×C4—622no—
167C22×C4—621no—
168C22×C4—621no—
169C22×C4—621no—
170C22×C4D12412yes—
171C22×C4C22×D3111yescharacteristic
172Q16—624no—
173SD16—624no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16C4×D3112yescomplemented
178C2×C8—21no—
179C2×C8—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—311no—
183C4⋊C4—311no—
184C4⋊C4—622no—
185C22⋊C4—622no—
186C22⋊C4—621no—
187C42—622no—
188C42—621no—
189C42—621no—
190C42—621no—
191C23—621no—
192C23C2×D12411yescharacteristic
193Q8—312no—
194Q8—621no—
195Q8—622no—
196Q8—622no—
197Q8—1241no—
198Q8—1241no—
199D4—312no—
200D4—622no—
201D4—622no—
202D4—621no—
203C2×C4—22no—
204C2×C4—42no—
205C2×C4—621no—
206C2×C4—622no—
207C2×C4—622no—
208C2×C4—622no—
209C2×C4—622no—
210C2×C4—621no—
211C2×C4—621no—
212C2×C4—1241no—
213C2×C4—1241no—
214C2×C4—1241no—
215C2×C4—1241no—
216C2×C4—2482no—
217C2×C4C2×C4×D3111yescharacteristic
218C2×C4#9249511yescharacteristic
219C2×C4D4×D3111yescharacteristic
220C2×C4D4×D3111yescharacteristic
221C2×C4D4×D3111yescharacteristic
222C2×C4#9249911yescharacteristic
223C8—22no—
224C8—41no—
225C22—21no—
226C22—21no—
227C22—622no—
228C22—1241no—
229C22—1241no—
230C22C4×D12411yescharacteristic
231C22#1175845911yescharacteristic
232C22#1175847211yescharacteristic
233C4—42no—
234C4—622no—
235C4—1242no—
236C4—1242no—
237C4—1241no—
238C4—1241no—
239C4C22⋊C4×D3111yescharacteristic
240C4#1175846111yescharacteristic
241C4#1175847011yescharacteristic
242C4#1175847111yescharacteristic
243C2—21no—
244C2—21no—
245C2—1242no—
246C2#1452092711yescharacteristic
247C2#1452122911yescharacteristic
248C2#1452123411yescharacteristic
subgroupG/H
centerC22#11758459
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#343C2
socleC22×C31#120
prime radicalC2×#92495C22
cosocleC22×C4×C31C23
hypercenter#343D31
hypocenterC31#1882
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. #14521059C2semidirect
5. #14520954C2semidirect
6. #14520810C2semidirect
7. C31×#343C2semidirect
17. #11758486C4semidirect
45. C2×Dic62C2×C4semidirect
50. M16×C31C2×C4semidirect
124. #343D31semidirect
152. C31#1882semidirect
177. M16C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584862
#145215302
C2×#117584132
#145210592
#145209542
#145208102
C31×#3432
#188231