Finite Group Databasebeta

← #28400053

Subgroups — #28400053

Order 14464.

584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16813650C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic, complemented
3C2×#16813618C211yesmaximal, characteristic, complemented
4#20299066C211yesmaximal, characteristic, complemented
5#20298797C214yesmaximal, complemented
6#20298792C214yesmaximal, complemented
7#20298621C211yesmaximal, characteristic, complemented
8#20298602C211yesmaximal, characteristic, complemented
9#418×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×D452C2211yescharacteristic
12C22×C22⋊D113—22no—
13#16813650—24no—
14#16813648—24no—
15C2×#14268636C2212yescomplemented
16C2×#14268635C2212yescomplemented
17C2×D904C2212yescomplemented
18C2×#14268632C2212yescomplemented
19C2×#14268631C2211yescharacteristic
20#16813618—21no—
21#16813618—21no—
22#16813618C2214yes—
23#16813587C2212yescomplemented
24#16813584C2212yescomplemented
25#16813582—22no—
26#16813579—21no—
27C2×C4×Dic113C2211yescharacteristic
28C42×D113—21no—
29#16813551C2214yescomplemented
30#16813542C2214yescomplemented
31C22×D4×C113C2211yescharacteristic
32C2×M16×C113C2211yescharacteristic
33#117×C113C2211yescharacteristic
34#102×C113C2214yescomplemented
35C23×D113—21no—
36#14268647—22no—
37#14268647D414yescomplemented
38C2×Dic226C2311yescharacteristic
39C2×D452—22no—
40C2×D452—22no—
41C2×D452—21no—
42C2×D452C2312yes—
43C2×D452C2311yescharacteristic
44C2×C22⋊D113—21no—
45C2×C22⋊D113—24no—
46C2×C22⋊D113—24no—
47C2×C22⋊D113—48no—
48C22×Dic113D412yes—
49C2×C4×D113—21no—
50C2×C4×D113—22no—
51#14268636—24no—
52#14268635—24no—
53D904—24no—
54#14268632—24no—
55#14268631—22no—
56C2×#11744751C2312yes—
57#14268626—22no—
58#14268624—22no—
59C4×Dic113—22no—
60C4×Dic113D411yescharacteristic
61C4×Dic113D411yescharacteristic
62C4×Dic113C2312yes—
63C24×C113—21no—
64C2×D4×C113—22no—
65C2×D4×C113—21no—
66C2×D4×C113—22no—
67C2×D4×C113C2312yes—
68C22×C4×C113C2311yescharacteristic
69M16×C113—22no—
70C2×C8×C113C2312yes—
71C4⋊C4×C113C2312yes—
72C22⋊C4×C113—21no—
73C42×C113—21no—
74C23×C113—22no—
75C23×C113—44no—
76C23×C113—42no—
77C23×C113C2×D411yescharacteristic
78C22×D113—21no—
79C22×D113—22no—
80C22×D113—44no—
81C22×D113—42no—
82D4×C113—22no—
83D4×C113—22no—
84D4×C113—42no—
85C2×C4×C113—22no—
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2×D412yes—
88C2×C4×C113#4112yes—
89C2×C4×C113C2411yescharacteristic
90C22⋊D113—24no—
91C22⋊D113—48no—
92C22⋊D113—48no—
93C2×Dic113—21no—
94C2×Dic113—24no—
95C2×Dic113C2×D412yes—
96C2×Dic113C2×D412yes—
97D452—22no—
98D452—21no—
99D452—22no—
100D452—42no—
101D452C2×D412yescomplemented
102C4×D113—24no—
103C4×D113—44no—
104Dic226—21no—
105Dic226C2×D412yescomplemented
106C8×C113—22no—
107#11744751—22no—
108C22×C113—22no—
109C22×C113—42no—
110C22×C113—44no—
111C22×C113—84no—
112C22×C113#12112yes—
113C22×C113C22×D411yescharacteristic
114C2×D113—22no—
115C2×D113—42no—
116C2×D113—42no—
117C2×D113—44no—
118C2×D113—84no—
119C4×C113—42no—
120C4×C113#12112yes—
121C4×C113C22×D411yescharacteristic
122C4×C113C2×#4111yescharacteristic
123Dic113—22no—
124Dic113—22no—
125Dic113AGL(1,ℤ/8)14yescomplemented
126C2×C113—22no—
127C2×C113—82no—
128C2×C113C2×#12111yescharacteristic
129C2×C113C2×AGL(1,ℤ/8)12yes—
130D113—42no—
131D113—82no—
132#3038—1131nomaximal, Sylow
133C113#303811yescharacteristic, complemented, Sylow
134C2×AGL(1,ℤ/8)—1131no—
135C2×AGL(1,ℤ/8)—1131no—
136C2×#127—1131no—
137C4×#41—1131no—
138#460—1134no—
139#459—1134no—
140#423—1131no—
141#418—1131no—
142#418D11311yescharacteristic, complemented
143C2×#41—1131no—
144C22×D4—1131no—
145C22×D4—2262no—
146C22×D4C2×D11311yescharacteristic
147AGL(1,ℤ/8)—2264no—
148AGL(1,ℤ/8)—2264no—
149C2×SD16—1132no—
150C2×SD16—1132no—
151C2×D8—1132no—
152C2×D8—1132no—
153C2×M16—1131no—
154C2×M16C2×D11311yescharacteristic
155#127—1134no—
156#127—2261no—
157#127—2261no—
158C4×Q8—1132no—
159C4×D4—1132no—
160C4×D4—2262no—
161#117—2261no—
162#117C2×D11311yescharacteristic
163C2×C42—1131no—
164C2×C42—2261no—
165C4⋊C8—1134no—
166#102—1134no—
167#102C2×D11314yescomplemented
168C24—21no—
169C24—2261no—
170#41—1134no—
171#41—2262no—
172C2×Q8—1131no—
173C2×D4—22no—
174C2×D4—21no—
175C2×D4—22no—
176C2×D4—1131no—
177C2×D4—1132no—
178C2×D4—4528no—
179C2×D4—2264no—
180C2×D4—2264no—
181C2×D4—2261no—
182C2×D4—2261no—
183C2×D4—2262no—
184C2×D4—2262no—
185C2×D4C22×D11312yes—
186C22×C4—1132no—
187C22×C4—2262no—
188C22×C4—2261no—
189C22×C4C22×D11311yescharacteristic
190SD16—2264no—
191SD16—2264no—
192D8—2264no—
193D8—2264no—
194M16—22no—
195M16—2262no—
196C2×C8—1132no—
197C2×C8C22×D11312yes—
198C4⋊C4—2262no—
199C4⋊C4C22×D11312yes—
200C22⋊C4—21no—
201C22⋊C4—2262no—
202C42—21no—
203C42—1131no—
204C42—1131no—
205C42—1132no—
206C42—2262no—
207C23—22no—
208C23—44no—
209C23—42no—
210C23—4524no—
211C23—4522no—
212C23—2262no—
213C23—2261no—
214C23D4×D11311yescharacteristic
215Q8—1132no—
216Q8—2261no—
217D4—22no—
218D4—22no—
219D4—42no—
220D4—1132no—
221D4—4528no—
222D4—4528no—
223D4—4522no—
224D4—2264no—
225D4—2262no—
226D4—2262no—
227D4—2261no—
228C2×C4—22no—
229C2×C4—1132no—
230C2×C4—1132no—
231C2×C4—4524no—
232C2×C4—2264no—
233C2×C4—2261no—
234C2×C4—2264no—
235C2×C4D4×D11311yescharacteristic
236C2×C4D4×D11312yes—
237C2×C4#1426864712yes—
238C2×C4C23×D11311yescharacteristic
239C8—22no—
240C8—2262no—
241C22—22no—
242C22—42no—
243C22—44no—
244C22—84no—
245C22—9044no—
246C22—4522no—
247C22—4524no—
248C22—4522no—
249C22—2262no—
250C22#1681359512yes—
251C22C2×D4×D11311yescharacteristic
252C4—42no—
253C4—1134no—
254C4—2262no—
255C4—2262no—
256C4#1681359512yes—
257C4C2×D4×D11311yescharacteristic
258C4C2×#1426864711yescharacteristic
259C2—22no—
260C2—82no—
261C2—9042no—
262C2—4522no—
263C2C2×#1681359511yescharacteristic
264C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
hypercenter#418D113
hypocenterC113#3038
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C2×#16813648C2semidirect
3. C2×#16813618C2semidirect
4. #20299066C2semidirect
5. #20298797C2semidirect
6. #20298792C2semidirect
7. #20298621C2semidirect
8. #20298602C2semidirect
9. #418×C113C2semidirect
15. C2×#14268636C22semidirect
16. C2×#14268635C22semidirect
17. C2×D904C22semidirect
18. C2×#14268632C22semidirect
23. #16813587C22semidirect
24. #16813584C22semidirect
29. #16813551C22semidirect
30. #16813542C22semidirect
34. #102×C113C22semidirect
37. #14268647D4semidirect
101. D452C2×D4semidirect
105. Dic226C2×D4semidirect
125. Dic113AGL(1,ℤ/8)semidirect
133. C113#3038semidirect
142. #418D113semidirect
167. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C2×#168136482
C2×#168136182
#202990662
#202987972
#202987922
#202986212
#202986022
#418×C1132
#3038113