Finite Group Databasebeta

← #16846158

Subgroups — #16846158

Order 3968.

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

normal subgroups only

This group has 358 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
1#14521561C211yesmaximal, characteristic
2C2×#11758449C211yesmaximal, characteristic, complemented
3C2×#11758393C211yesmaximal, characteristic, complemented
4C2×#11758413C211yesmaximal, characteristic, complemented
5#14521012C211yesmaximal, characteristic, complemented
6#14520808C211yesmaximal, characteristic, complemented
7C31×#339C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C22×C4×D31C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12C2×C42×C31C2211yescharacteristic
13C2×(C2×D31)⋊C4—21no—
14C2×Dic31⋊C4—21no—
15C2×C4×Dic31C2211yescharacteristic
16C2×#92474C2211yescharacteristic
17#11758474C412yescomplemented
18#11758472C412yescomplemented
19#11758463—21no—
20#11758459—21no—
21C4×D124—22no—
22#11758449—22no—
23#11758449—22no—
24#11758413—22no—
25(C2×D31)⋊C8—22no—
26#11758393—22no—
27C23×D31D411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—21no—
31C22×Dic31—21no—
32C22×Dic31D411yescharacteristic
33#92495—21no—
34#92495—21no—
35#92495—21no—
36#92495—21no—
37C2×D124—22no—
38C2×D124C2×C411yescharacteristic
39C2×C4×D31—21no—
40C2×C4×D31—21no—
41C2×C4×D31—21no—
42C2×C4×D31—21no—
43C2×C4×D31—21no—
44C2×C4×D31C2×C412yes—
45C2×C4×D31D412yes—
46C2×Dic62C2×C411yescharacteristic
47M16×C31—21no—
48M16×C31—21no—
49C2×C8×C31—21no—
50C4⋊C4×C31C2×C412yes—
51C22⋊C4×C31—21no—
52C42×C31—21no—
53C42×C31—21no—
54C42×C31D412yescomplemented
55(C2×D31)⋊C4—24no—
56(C2×D31)⋊C4—22no—
57(C2×D31)⋊C4—22no—
58C4⋊Dic31—22no—
59Dic31⋊C4—24no—
60C4×Dic31—21no—
61C4×Dic31D412yescomplemented
62#92474—21no—
63#92474—21no—
64C2×C31⋊C8—21no—
65C23×C31C2×D411yescharacteristic
66C22×D31—21no—
67C22×D31—21no—
68C22×D31—21no—
69C22×D31—42no—
70C22×D31C22⋊C412yes—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—42no—
74C2×C4×C31C22×C411yescharacteristic
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31C2×D411yescharacteristic
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31#4111yescharacteristic
79C2×C4×C31#4111yescharacteristic
80C22⋊D31—41no—
81C22⋊D31—41no—
82C2×Dic31—21no—
83C2×Dic31—21no—
84C2×Dic31—21no—
85C2×Dic31—22no—
86C2×Dic31—42no—
87C2×Dic31C22⋊C412yes—
88D124—21no—
89D124—21no—
90D124—44no—
91C4×D31—22no—
92C4×D31—22no—
93C4×D31—22no—
94C4×D31—22no—
95C4×D31—41no—
96C4×D31—41no—
97Dic62—21no—
98Dic62—21no—
99C8×C31—41no—
100C31⋊C8—41no—
101#1897—311nomaximal, Sylow
102C22×C31—22no—
103C22×C31C2×C22⋊C411yescharacteristic
104C22×C31#12011yescharacteristic
105C22×C31#12311yescharacteristic
106C2×D31—22no—
107C2×D31—22no—
108C2×D31—22no—
109C2×D31—42no—
110C2×D31—42no—
111C2×D31—41no—
112C2×D31—42no—
113C4×C31—42no—
114C4×C31—42no—
115C4×C31C4×D411yescharacteristic
116C4×C31C4×D411yescharacteristic
117C4×C31#12111yescharacteristic
118C4×C31#12111yescharacteristic
119Dic31—22no—
120Dic31—42no—
121Dic31—41no—
122#525—311no—
123C2×#117—311no—
124C2×#104—311no—
125C2×#104—311no—
126#407—311no—
127#339—311no—
128#339D3111yescharacteristic, complemented
129C2×C31—21no—
130C2×C31—21no—
131C2×C31#38611yescharacteristic
132C2×C31#42112yes—
133D31—42no—
134D31—81no—
135C2×#41—311no—
136C23×C4—311no—
137C2×M16—311no—
138C2×M16C2×D3111yescharacteristic
139#123—621no—
140C22⋊Q8—312no—
141#121—312no—
142#120—621no—
143C4×D4—622no—
144#117—622no—
145#117—622no—
146#117C2×D3111yescharacteristic
147C2×C4⋊C4—621no—
148C2×C22⋊C4—621no—
149C2×C42—311no—
150C2×C42C2×D3111yescharacteristic
151#104—622no—
152#104—622no—
153C22⋊C8—622no—
154C31#189711yescharacteristic, complemented, Sylow
155C24—311no—
156#41—621no—
157#41—621no—
158#41—621no—
159#41—621no—
160C2×Q8—311no—
161C2×D4—311no—
162C2×D4—622no—
163C2×D4—621no—
164C22×C4—21no—
165C22×C4—311no—
166C22×C4—312no—
167C22×C4—312no—
168C22×C4—621no—
169C22×C4—621no—
170C22×C4—621no—
171C22×C4—621no—
172C22×C4—621no—
173C22×C4—621no—
174C22×C4C22×D3111yescharacteristic
175M16—21no—
176M16—21no—
177M16—621no—
178M16—621no—
179C2×C8—21no—
180C2×C8—621no—
181C4⋊C4—622no—
182C4⋊C4—624no—
183C4⋊C4C4×D3112yes—
184C22⋊C4—21no—
185C22⋊C4—622no—
186C22⋊C4—622no—
187C22⋊C4—624no—
188C42—21no—
189C42—21no—
190C42—312no—
191C42—621no—
192C42D12412yescomplemented
193C23—312no—
194C23—621no—
195C23—621no—
196C23—621no—
197C23—1242no—
198C23D4×D3111yescharacteristic
199Q8—621no—
200Q8—621no—
201D4—621no—
202D4—621no—
203D4—1244no—
204D4—1241no—
205D4—1241no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—312no—
210C2×C4—621no—
211C2×C4—621no—
212C2×C4—622no—
213C2×C4—622no—
214C2×C4—622no—
215C2×C4—622no—
216C2×C4—621no—
217C2×C4—622no—
218C2×C4—1242no—
219C2×C4—1241no—
220C2×C4—1241no—
221C2×C4C2×C4×D3111yescharacteristic
222C2×C4C2×D12411yescharacteristic
223C2×C4#9249511yescharacteristic
224C2×C4D4×D3111yescharacteristic
225C2×C4D4×D3111yescharacteristic
226C2×C4#9249911yescharacteristic
227C8—41no—
228C8—1241no—
229C22—22no—
230C22—622no—
231C22—622no—
232C22—622no—
233C22—1242no—
234C22—1242no—
235C22—1241no—
236C22—1242no—
237C22C22⋊C4×D3111yescharacteristic
238C22#1175845911yescharacteristic
239C22#1175847111yescharacteristic
240C4—42no—
241C4—42no—
242C4—622no—
243C4—1242no—
244C4—1241no—
245C4C4×D12411yescharacteristic
246C4#1175846111yescharacteristic
247C4#1175847011yescharacteristic
248C4#1175847211yescharacteristic
249C2—21no—
250C2—21no—
251C2—1242no—
252C2—2481no—
253C2#1452092711yescharacteristic
254C2#1452106412yes—
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31C2×C22⋊C4
prime radical#14521561C2
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1897
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#11758449C2semidirect
3. C2×#11758393C2semidirect
4. C2×#11758413C2semidirect
5. #14521012C2semidirect
6. #14520808C2semidirect
7. C31×#339C2semidirect
17. #11758474C4semidirect
18. #11758472C4semidirect
54. C42×C31D4semidirect
61. C4×Dic31D4semidirect
128. #339D31semidirect
154. C31#1897semidirect
192. C42D124semidirect

Maximal subgroups

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

subgroupindex
#145215612
C2×#117584492
C2×#117583932
C2×#117584132
#145210122
#145208082
C31×#3392
#189731