Finite Group Databasebeta

← #16846743

Subgroups — #16846743

Order 3968.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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, complemented
2#14521618C211yesmaximal, characteristic
3C2×#11758452C211yesmaximal, characteristic, complemented
4C2×#11758393C211yesmaximal, characteristic, complemented
5#14521057C211yesmaximal, characteristic, complemented
6C2×#11758411C211yesmaximal, characteristic, complemented
7C31×#339C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C22×D124C2211yescharacteristic
10C22×Dic62C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C31×#117C2211yescharacteristic
13C2×C42×C31C2211yescharacteristic
14C2×(C2×D31)⋊C4—22no—
15C2×#92474C2211yescharacteristic
16#11758486—22no—
17#11758486—22no—
18C2×Dic124—21no—
19C2×#92470—21no—
20#11758472—22no—
21#11758459—22no—
22#11758452—21no—
23#11758452—22no—
24#11758452—22no—
25#11758451—21no—
26#11758411—22no—
27#11758398—22no—
28#11758393—22no—
29C23×D31D412yes—
30C22×C4×C31—21no—
31C22×C4×C31C2311yescharacteristic
32C2×C22⋊D31—21no—
33C22×Dic31—21no—
34#92495—21no—
35#92495—21no—
36#92495—21no—
37#92495—21no—
38C2×D124—21no—
39C2×D124—21no—
40C2×D124—21no—
41C2×D124—21no—
42C2×D124—21no—
43C2×D124—21no—
44C2×D124—24no—
45C2×D124D411yescharacteristic
46C2×C4×D31—21no—
47C2×Dic62—21no—
48C2×Dic62—21no—
49C2×Dic62—21no—
50C2×Dic62—21no—
51C2×Dic62—21no—
52C2×Dic62D411yescharacteristic
53C2×Dic62D412yescomplemented
54M16×C31—21no—
55M16×C31D412yescomplemented
56C2×C8×C31—21no—
57C4⋊C4×C31D412yes—
58C22⋊C4×C31—21no—
59C42×C31—21no—
60C42×C31—21no—
61C42×C31D412yescomplemented
62(C2×D31)⋊C4—28no—
63(C2×D31)⋊C4—24no—
64#92474—21no—
65#92474—21no—
66C2×C31⋊C8—21no—
67Dic124—24no—
68#92470—24no—
69C23×C31C2×D411yescharacteristic
70C22×D31—22no—
71C22×D31—22no—
72C22×D31—21no—
73C22×D31—22no—
74C22×D31—44no—
75C2×C4×C31—22no—
76C2×C4×C31—22no—
77C2×C4×C31—42no—
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31#4111yescharacteristic
84C22⋊D31—41no—
85C22⋊D31—41no—
86C2×Dic31—22no—
87C2×Dic31—21no—
88C2×Dic31—41no—
89C2×Dic31—41no—
90D124—21no—
91D124—21no—
92D124—41no—
93D124—41no—
94D124—41no—
95D124—41no—
96D124—84no—
97C4×D31—41no—
98C4×D31—41no—
99Dic62—22no—
100Dic62—21no—
101Dic62—22no—
102Dic62—21no—
103Dic62—41no—
104Dic62—41no—
105C8×C31—22no—
106C31⋊C8—41no—
107#2004—311nomaximal, Sylow
108C22×C31—22no—
109C22×C31#12011yescharacteristic
110C22×C31#12011yescharacteristic
111C22×C31#12111yescharacteristic
112C2×D31—44no—
113C2×D31—41no—
114C2×D31—42no—
115C2×D31—42no—
116C2×D31—44no—
117C2×D31—82no—
118C4×C31—42no—
119C4×C31—42no—
120C4×C31#12011yescharacteristic
121C4×C31#12111yescharacteristic
122C4×C31#12111yescharacteristic
123C4×C31#12711yescharacteristic
124Dic31—42no—
125Dic31—41no—
126C2×#137—311no—
127#535—311no—
128C2×#124—311no—
129C2×#104—311no—
130#419—311no—
131C2×#100—311no—
132#339D3111yescharacteristic, complemented
133C2×C31—21no—
134C2×C31—21no—
135C2×C31#39211yescharacteristic
136C2×C31#45512yes—
137D31—81no—
138D31—82no—
139C2×#41—311no—
140C22×Q8—311no—
141C22×D4—311no—
142#137—622no—
143#137—622no—
144C2×Q16—621no—
145C2×SD16—621no—
146C2×M16—311no—
147C2×M16C2×D3111yescharacteristic
148#127—621no—
149#124—622no—
150#124—621no—
151#124—622no—
152#121—622no—
153#120—622no—
154#117C2×D3111yescharacteristic
155C2×C22⋊C4—622no—
156C2×C42C2×D3111yescharacteristic
157#104—622no—
158#103—622no—
159#100—622no—
160C31#200411yescharacteristic, complemented, Sylow
161C24—312no—
162#41—621no—
163#41—621no—
164#41—621no—
165#41—621no—
166C2×Q8—311no—
167C2×Q8—312no—
168C2×Q8—621no—
169C2×Q8—621no—
170C2×Q8—621no—
171C2×Q8—621no—
172C2×Q8—621no—
173C2×D4—311no—
174C2×D4—624no—
175C2×D4—621no—
176C2×D4—621no—
177C2×D4—621no—
178C2×D4—621no—
179C2×D4—621no—
180C2×D4—621no—
181C2×D4—621no—
182C22×C4—21no—
183C22×C4—621no—
184C22×C4—621no—
185C22×C4C22×D3111yescharacteristic
186Q16—624no—
187SD16—624no—
188M16—21no—
189M16—621no—
190M16—621no—
191M16D12412yescomplemented
192C2×C8—21no—
193C2×C8—621no—
194C4⋊C4D12412yes—
195C22⋊C4—21no—
196C22⋊C4—628no—
197C22⋊C4—624no—
198C42—21no—
199C42—21no—
200C42D12412yescomplemented
201C23—622no—
202C23—622no—
203C23—621no—
204C23—622no—
205C23—1244no—
206C23D4×D3111yescharacteristic
207Q8—622no—
208Q8—621no—
209Q8—622no—
210Q8—621no—
211Q8—1241no—
212Q8—1241no—
213D4—621no—
214D4—621no—
215D4—1241no—
216D4—1241no—
217D4—1241no—
218D4—1241no—
219D4—1241no—
220D4—1241no—
221D4—2484no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—622no—
226C2×C4—621no—
227C2×C4—1241no—
228C2×C4—1241no—
229C2×C4—1241no—
230C2×C4—1241no—
231C2×C4C2×D12411yescharacteristic
232C2×C4C2×D12411yescharacteristic
233C2×C4C2×D12411yescharacteristic
234C2×C4D4×D3111yescharacteristic
235C2×C4D4×D3111yescharacteristic
236C2×C4#9249911yescharacteristic
237C8—22no—
238C8—1241no—
239C22—22no—
240C22—1244no—
241C22—1241no—
242C22—1242no—
243C22—1242no—
244C22—1244no—
245C22—2482no—
246C22#1175845911yescharacteristic
247C22#1175845911yescharacteristic
248C22#1175847211yescharacteristic
249C4—42no—
250C4—42no—
251C4—1241no—
252C4—1242no—
253C4#1175845111yescharacteristic
254C4#1175845911yescharacteristic
255C4#1175847211yescharacteristic
256C4#1175847211yescharacteristic
257C2—21no—
258C2—21no—
259C2—2482no—
260C2—2481no—
261C2#1452095911yescharacteristic
262C2#1452122812yes—
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31#120
prime radical#14521618C2
hypercenter#339D31
hypocenterC31#2004
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#11758486C2semidirect
3. C2×#11758452C2semidirect
4. C2×#11758393C2semidirect
5. #14521057C2semidirect
6. C2×#11758411C2semidirect
7. C31×#339C2semidirect
53. C2×Dic62D4semidirect
55. M16×C31D4semidirect
61. C42×C31D4semidirect
132. #339D31semidirect
160. C31#2004semidirect
191. M16D124semidirect
200. C42D124semidirect

Maximal subgroups

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

subgroupindex
C2×#117584862
#145216182
C2×#117584522
C2×#117583932
#145210572
C2×#117584112
C31×#3392
#200431