Finite Group Databasebeta

← #16845809

Subgroups — #16845809

Order 3968.

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

normal subgroups only

This group has 306 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#117×D31C211yesmaximal, characteristic
2#14521012C211yesmaximal, characteristic
3C4×(C2×D31)⋊C4C211yesmaximal, characteristic
4#14520810C211yesmaximal, characteristic, complemented
5#14520809C211yesmaximal, characteristic, complemented
6#14520808C211yesmaximal, characteristic, complemented
7C31×#339C211yesmaximal, characteristic, complemented
8C22×C4×D31C2211yescharacteristic
9C2×M16×C31C2211yescharacteristic
10C31×#117C2211yescharacteristic
11C2×C42×C31C2211yescharacteristic
12C2×(C2×D31)⋊C4—21no—
13#11758503C2211yescharacteristic
14C2×C4×Dic31C2211yescharacteristic
15C2×#92474C2211yescharacteristic
16#11758469C411yescharacteristic, complemented
17#11758469C411yescharacteristic, complemented
18C4⋊C4×D31C411yescharacteristic, complemented
19C4⋊C4×D31C411yescharacteristic, complemented
20C22⋊C4×D31—21no—
21#11758454—21no—
22#11758449—21no—
23C42×D31—21no—
24C31⋊#95—21no—
25(C2×D31)⋊C8—21no—
26(C2×D31)⋊C8—21no—
27C23×D31D411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31D411yescharacteristic
32C2×C4×D31—21no—
33C2×C4×D31—21no—
34C2×C4×D31—21no—
35C2×C4×D31—21no—
36C2×C4×D31—21no—
37C2×C4×D31—21no—
38C2×C4×D31C2×C411yescharacteristic
39C2×C4×D31C2×C411yescharacteristic
40C2×C4×D31D411yescharacteristic
41C2×C4×D31D411yescharacteristic
42M16×C31—21no—
43M16×C31—21no—
44C2×C8×C31—21no—
45C4⋊C4×C31C2×C411yescharacteristic
46C4⋊C4×C31C2×C411yescharacteristic
47C22⋊C4×C31—21no—
48C42×C31—21no—
49C42×C31—21no—
50C42×C31—21no—
51C22⋊Dic31—21no—
52(C2×D31)⋊C4—24no—
53(C2×D31)⋊C4—21no—
54(C2×D31)⋊C4—21no—
55C4⋊Dic31C2×C411yescharacteristic
56C4⋊Dic31C2×C411yescharacteristic
57Dic31⋊C4—21no—
58Dic31⋊C4—21no—
59C4×Dic31—21no—
60C4×Dic31—21no—
61C4×Dic31—21no—
62C4×Dic31—21no—
63C4×Dic31—21no—
64#92474—21no—
65#92474—21no—
66C2×C31⋊C8—21no—
67C23×C31C2×D411yescharacteristic
68C22×D31—21no—
69C22×D31—21no—
70C22×D31—22no—
71C22×D31—41no—
72C22×D31C22⋊C411yescharacteristic
73C22×D31C22⋊C411yescharacteristic
74C2×C4×C31—22no—
75C2×C4×C31—21no—
76C2×C4×C31—21no—
77C2×C4×C31—41no—
78C2×C4×C31—41no—
79C2×C4×C31C22×C411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31#4111yescharacteristic
82C2×C4×C31#4111yescharacteristic
83C2×C4×C31#4111yescharacteristic
84C2×C4×C31#4111yescharacteristic
85C2×Dic31—21no—
86C2×Dic31—21no—
87C2×Dic31—22no—
88C2×Dic31—21no—
89C2×Dic31—21no—
90C2×Dic31—41no—
91C2×Dic31—41no—
92C2×Dic31C22⋊C411yescharacteristic
93C2×Dic31C22⋊C411yescharacteristic
94C4×D31—21no—
95C4×D31—21no—
96C4×D31—21no—
97C4×D31—21no—
98C4×D31—21no—
99C4×D31—21no—
100C4×D31—21no—
101C4×D31—21no—
102C4×D31—42no—
103C4×D31—42no—
104C8×C31—41no—
105C31⋊C8—41no—
106#1826—311nomaximal, Sylow
107C22×C31—21no—
108C22×C31—21no—
109C22×C31C2×C22⋊C411yescharacteristic
110C22×C31#12311yescharacteristic
111C22×C31#12311yescharacteristic
112C2×D31—21no—
113C2×D31—21no—
114C2×D31—21no—
115C2×D31—21no—
116C2×D31—21no—
117C2×D31—42no—
118C2×D31—42no—
119C2×D31#10412yes—
120C4×C31—42no—
121C4×C31—41no—
122C4×C31—41no—
123C4×C31#11711yescharacteristic
124C4×C31#11711yescharacteristic
125C4×C31#12311yescharacteristic
126C4×C31#12311yescharacteristic
127Dic31—21no—
128Dic31—21no—
129Dic31—42no—
130Dic31—41no—
131Dic31—41no—
132C2×#117—311no—
133#407—311no—
134C4×C22⋊C4—311no—
135#339—311no—
136#339—311no—
137#339—311no—
138#339D3111yescharacteristic, complemented
139C2×C31—21no—
140C2×C31—21no—
141C2×C31#38111yescharacteristic
142C2×C31C2×#10411yescharacteristic
143C2×C31#42111yescharacteristic
144D31—22no—
145D31—41no—
146C23×C4—311no—
147C2×M16—311no—
148C2×M16C2×D3111yescharacteristic
149#117—311no—
150#117—311no—
151#117—311no—
152#117—621no—
153#117—621no—
154#117C2×D3111yescharacteristic
155C2×C4⋊C4—311no—
156C2×C4⋊C4—311no—
157C2×C22⋊C4—621no—
158C2×C22⋊C4—621no—
159C2×C42—311no—
160C2×C42—621no—
161C2×C42C2×D3111yescharacteristic
162C22⋊C8—621no—
163C22⋊C8—621no—
164#95—621no—
165C31#182611yescharacteristic, complemented, Sylow
166C24—311no—
167C22×C4—21no—
168C22×C4—311no—
169C22×C4—311no—
170C22×C4—311no—
171C22×C4—311no—
172C22×C4—311no—
173C22×C4—621no—
174C22×C4—621no—
175C22×C4—621no—
176C22×C4—621no—
177C22×C4—621no—
178C22×C4—621no—
179C22×C4—621no—
180C22×C4C22×D3111yescharacteristic
181M16—21no—
182M16—21no—
183M16—621no—
184M16—621no—
185C2×C8—21no—
186C2×C8—621no—
187C4⋊C4—311no—
188C4⋊C4—311no—
189C4⋊C4—621no—
190C4⋊C4—621no—
191C4⋊C4C4×D3111yescharacteristic
192C4⋊C4C4×D3111yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—621no—
195C22⋊C4—621no—
196C22⋊C4—624no—
197C22⋊C4—621no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—621no—
202C42—621no—
203C42—621no—
204C42—621no—
205C42—621no—
206C23—311no—
207C23—311no—
208C23—622no—
209C23—621no—
210C23—621no—
211C23—1241no—
212C23D4×D3111yescharacteristic
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—311no—
219C2×C4—311no—
220C2×C4—621no—
221C2×C4—621no—
222C2×C4—621no—
223C2×C4—621no—
224C2×C4—621no—
225C2×C4—621no—
226C2×C4—621no—
227C2×C4—621no—
228C2×C4—621no—
229C2×C4—621no—
230C2×C4—622no—
231C2×C4—621no—
232C2×C4—621no—
233C2×C4—1242no—
234C2×C4—1242no—
235C2×C4—1241no—
236C2×C4—1241no—
237C2×C4C2×C4×D3111yescharacteristic
238C2×C4#9249511yescharacteristic
239C2×C4#9249511yescharacteristic
240C2×C4D4×D3111yescharacteristic
241C2×C4#9249711yescharacteristic
242C2×C4#9249911yescharacteristic
243C8—41no—
244C8—1241no—
245C22—21no—
246C22—21no—
247C22—312no—
248C22—621no—
249C22—621no—
250C22—621no—
251C22—621no—
252C22—621no—
253C22—1242no—
254C22—1242no—
255C22C22⋊C4×D3111yescharacteristic
256C22#1175846011yescharacteristic
257C22#1175847111yescharacteristic
258C4—42no—
259C4—41no—
260C4—41no—
261C4—621no—
262C4—621no—
263C4—1242no—
264C4—1241no—
265C4—1241no—
266C4#1175844911yescharacteristic
267C4#1175846011yescharacteristic
268C4#1175846911yescharacteristic
269C4#1175847111yescharacteristic
270C2—21no—
271C2—21no—
272C2—622no—
273C2—1241no—
274C2#1452091111yescharacteristic
275C2#104×D3111yescharacteristic
276C2#1452106411yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31C2×C22⋊C4
prime radicalC23×D31D4
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1826
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
4. #14520810C2semidirect
5. #14520809C2semidirect
6. #14520808C2semidirect
7. C31×#339C2semidirect
16. #11758469C4semidirect
17. #11758469C4semidirect
18. C4⋊C4×D31C4semidirect
19. C4⋊C4×D31C4semidirect
138. #339D31semidirect
165. C31#1826semidirect

Maximal subgroups

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

subgroupindex
#117×D312
#145210122
C4×(C2×D31)⋊C42
#145208102
#145208092
#145208082
C31×#3392
#182631