Finite Group Databasebeta

← D8×#1113 #13178464

Subgroups — D8×#1113 #13178464

Order 1728.

1602 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 183 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
1D4×#1113C212yesmaximal, complemented
2C3×D8×C3⋊D3C213yesmaximal, complemented
3#11723702C216yesmaximal, complemented
4#11723647C213yesmaximal, complemented
5C8×#1113C211yesmaximal, characteristic, complemented
6D32×D8—33nomaximal
7C22×#1113—22no—
8C3×D4×C3⋊D3C2216yescomplemented
9#89049—26no—
10C4⋊#1113C2216yescomplemented
11C4×#1113C2211yescharacteristic
12C33×D8C2211yescharacteristic, complemented
13C3×#3753C2216yescomplemented
14C3×#3745C2213yescomplemented
15C3×C8×C3⋊D3C2213yescomplemented
16#88810C2216yescomplemented
17#88808C2213yescomplemented
18D32×D4—36no—
19D8×C3⋊D3D313yescomplemented
20C3×D3×D8—36no—
21C3×D3×D8—63no—
22#63926—36no—
23D3×#213—312no—
24#63797—33no—
25D3×D24—36no—
26D32×C8—33no—
27C22×C3×C3⋊D3—26no—
28C2×#1113—26no—
29C2×#1113—48no—
30C2×#1113D411yescharacteristic
31C33×D4C2312yescomplemented
32C3×#638—26no—
33C3×C4⋊(C3⋊D3)C2316yescomplemented
34C3×C4×C3⋊D3C2313yes—
35#6295—26no—
36#6294D413yes—
37C33×C8C2311yescharacteristic, complemented
38C3×C3⋊(C3⋊C8)C2313yescomplemented
39C2×D3×D8—93no—
40C22×D32—66no—
41D4×C3⋊D3C2×D316yescomplemented
42C3×D3×D4—312no—
43C3×D3×D4—66no—
44#3811—66no—
45D3×#67—612no—
46#3802—36no—
47D3×D12—312no—
48C4×D32—33no—
49C32×D8—23no—
50C32×D8—41no—
51C32×D8C2×D313yescomplemented
52#3753C2×D316yescomplemented
53#3745C2×D313yescomplemented
54C8×C3⋊D3C2×D313yescomplemented
55C3×#213—312no—
56C3×#213—66no—
57C3×D24—36no—
58C3×D24—63no—
59C3×D3×C8—36no—
60C3×D3×C8—63no—
61#3714—312no—
62#3713—36no—
63#3710—33no—
64D3×C3⋊C8—36no—
65C22×C33—22no—
66C2×C3×C3⋊D3—26no—
67C2×C3×C3⋊D3—412no—
68C2×C3×C3⋊D3C2×D413yes—
69#1113—412no—
70#1113D814yesdirect product factor
71C33×C4C2411yescharacteristic
72C3×C3⋊Dic3C2×D413yes—
73C2×D3×D4—96no—
74C2×C3×D8—93no—
75C2×#213—96no—
76D3×D8—36no—
77D3×D8—63no—
78D3×D8—96no—
79D3×D8—912no—
80C2×D24—93no—
81C2×D3×C8—93no—
82C22×C3⋊D3—26no—
83C22×C3×D3—612no—
84C22×C3×D3—126no—
85C2×D32—33no—
86C2×D32—612no—
87C2×D32—66no—
88C2×D32—1224no—
89C32×D4—26no—
90C32×D4—42no—
91C32×D4C22×D316yescomplemented
92#638—26no—
93C4⋊(C3⋊D3)C22×D316yescomplemented
94C4×C3⋊D3C22×D313yes—
95C3×#67—612no—
96C3×#67—126no—
97C3×D12—312no—
98C3×D12—66no—
99C3×C4×D3—36no—
100C3×C4×D3—63no—
101#626—612no—
102#625—66no—
103#624—33no—
104D3×Dic3—36no—
105C32×C8—23no—
106C32×C8—41no—
107C32×C8C22×D313yescomplemented
108C3⋊(C3⋊C8)C22×D313yescomplemented
109C3×C3⋊C8—36no—
110C3×C3⋊C8—63no—
111C22×D8—271noSylow
112C2×C33—42no—
113C2×C33C22×D411yescharacteristic
114C3×C3⋊D3—46no—
115C3×C3⋊D3C2×D816yescomplemented
116C23×D3—186no—
117C2×C3×D4—96no—
118C2×#67—186no—
119D3×D4—312no—
120D3×D4—66no—
121D3×D4—912no—
122D3×D4—1812no—
123C2×D12—96no—
124C2×C4×D3—93no—
125C3×D8—23no—
126C3×D8—41no—
127C3×D8—96no—
128C3×D8—93no—
129C3×D8D3213yescomplemented
130C2×C3×C8—93no—
131#213—312no—
132#213—66no—
133#213—912no—
134C2×C3⋊C8—93no—
135D24—36no—
136D24—63no—
137D24—96no—
138D3×C8—36no—
139D3×C8—63no—
140D3×C8—96no—
141C22×C32—26no—
142C22×C32—46no—
143C22×C32—82no—
144C2×C3⋊D3—26no—
145C2×C3⋊D3—412no—
146C2×C3⋊D3D3×D413yes—
147C2×C3×D3—36no—
148C2×C3×D3—63no—
149C2×C3×D3—612no—
150C2×C3×D3—126no—
151C2×C3×D3—1224no—
152C2×C3×D3—2412no—
153D32—312no—
154D32—1224no—
155D32—1212no—
156C32×C4—23no—
157C32×C4—41no—
158C32×C4C23×D313yes—
159C3⋊Dic3D3×D413yes—
160C3×Dic3—36no—
161C3×Dic3—63no—
162C22×D4—272no—
163C2×D8—93no—
164C2×D8—273no—
165C2×D8—276no—
166C22×C8—271no—
167C33C22×D811yescharacteristic, complemented, Sylow
168C23×C3—186no—
169C22×D3—612no—
170C22×D3—93no—
171C22×D3—126no—
172C22×D3—1812no—
173C22×D3—186no—
174C22×D3—3624no—
175C3×D4—26no—
176C3×D4—42no—
177C3×D4—96no—
178C3×D4—186no—
179C3×D4C2×D3216yescomplemented
180C2×C3×C4—93no—
181#67—612no—
182#67—126no—
183#67—1812no—
184C2×Dic3—93no—
185D12—312no—
186D12—66no—
187D12—186no—
188C4×D3—36no—
189C4×D3—63no—
190C4×D3—96no—
191C3×C8—23no—
192C3×C8—41no—
193C3×C8—93no—
194C3×C8C2×D3213yescomplemented
195C3⋊C8—36no—
196C3⋊C8—63no—
197C2×C32—23no—
198C2×C32—41no—
199C2×C32—46no—
200C2×C32—86no—
201C2×C32—162no—
202C2×C32C2×D3×D413yes—
203C3⋊D3—46no—
204C3⋊D3D3×D816yescomplemented
205C3×D3—312no—
206C3×D3—66no—
207C3×D3—1212no—
208C3×D3—246no—
209C24—542no—
210C2×D4—96no—
211C2×D4—276no—
212C2×D4—546no—
213C22×C4—271no—
214D8—96no—
215D8—93no—
216D8—276no—
217D8#111311yescharacteristic, direct product factor
218C2×C8—93no—
219C2×C8—273no—
220C22×C3—26no—
221C22×C3—46no—
222C22×C3—82no—
223C22×C3—93no—
224C22×C3—186no—
225C22×C3—3612no—
226C2×D3—36no—
227C2×D3—63no—
228C2×D3—612no—
229C2×D3—912no—
230C2×D3—126no—
231C2×D3—1224no—
232C2×D3—2412no—
233C2×D3—3624no—
234C2×D3—3612no—
235C3×C4—23no—
236C3×C4—41no—
237C3×C4—93no—
238C3×C4C22×D3213yes—
239Dic3—36no—
240Dic3—63no—
241C32—23no—
242C32—41no—
243C32C2×D3×D813yescomplemented
244C23—186no—
245C23—271no—
246C23—546no—
247C23—1088no—
248D4—96no—
249D4—186no—
250D4—546no—
251D4C2×#111312yescomplemented
252C2×C4—93no—
253C2×C4—273no—
254C8—93no—
255C8C2×#111311yescharacteristic, complemented
256C2×C3—23no—
257C2×C3—46no—
258C2×C3—41no—
259C2×C3—86no—
260C2×C3—96no—
261C2×C3—162no—
262C2×C3—366no—
263C2×C3D32×D413yes—
264D3—312no—
265D3—66no—
266D3—1212no—
267D3—246no—
268C22—22no—
269C22—93no—
270C22—186no—
271C22—274no—
272C22—3612no—
273C22—10812no—
274C4—93no—
275C4C22×#111311yescharacteristic
276C3—23no—
277C3—41no—
278C3D32×D813yescomplemented
279C2—42no—
280C2—96no—
281C2—366no—
282C2D4×#111311yescharacteristic
subgroupG/H
centerC2D4×#1113
commutator, cosocleC33×C4C24
FrattiniC4C22×#1113
FittingC33×D8C22
socleC2×C33C22×D4
hypercenterD8#1113
hypocenterC33C22×D8
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D4×#1113C2semidirect
2. C3×D8×C3⋊D3C2semidirect
3. #11723702C2semidirect
4. #11723647C2semidirect
5. C8×#1113C2semidirect
8. C3×D4×C3⋊D3C22semidirect
10. C4⋊#1113C22semidirect
12. C33×D8C22semidirect
13. C3×#3753C22semidirect
14. C3×#3745C22semidirect
15. C3×C8×C3⋊D3C22semidirect
16. #88810C22semidirect
17. #88808C22semidirect
19. D8×C3⋊D3D3semidirect
31. C33×D4C23semidirect
33. C3×C4⋊(C3⋊D3)C23semidirect
37. C33×C8C23semidirect
38. C3×C3⋊(C3⋊C8)C23semidirect
41. D4×C3⋊D3C2×D3semidirect
51. C32×D8C2×D3semidirect
52. #3753C2×D3semidirect
53. #3745C2×D3semidirect
54. C8×C3⋊D3C2×D3semidirect
70. #1113D8direct (N × H)
91. C32×D4C22×D3semidirect
93. C4⋊(C3⋊D3)C22×D3semidirect
107. C32×C8C22×D3semidirect
108. C3⋊(C3⋊C8)C22×D3semidirect
115. C3×C3⋊D3C2×D8semidirect
129. C3×D8D32semidirect
167. C33C22×D8semidirect
179. C3×D4C2×D32semidirect
194. C3×C8C2×D32semidirect
204. C3⋊D3D3×D8semidirect
217. D8#1113direct (N × H)
243. C32C2×D3×D8semidirect
251. D4C2×#1113semidirect
255. C8C2×#1113semidirect
278. C3D32×D8semidirect

Maximal subgroups

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

subgroupindex
D4×#11132
C3×D8×C3⋊D32
#117237022
#117236472
C8×#11132
D32×D83