Finite Group Databasebeta

← #28399033

Subgroups — #28399033

Order 14464.

800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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×#16813668C211yesmaximal, characteristic
2#20299072C212yesmaximal, complemented
3#20298572C211yesmaximal, characteristic, complemented
4#20298571C212yesmaximal, complemented
5#99×D113C218yesmaximal, complemented
6#410×C113C211yesmaximal, characteristic, complemented
7#16813668—24no—
8#16813668—24no—
9C2×#14268648C412yescomplemented
10C2×#14268647C412yescomplemented
11C2×#14268647C2211yescharacteristic
12C22×D452C412yescomplemented
13C22×D452C2211yescharacteristic
14C2×D4×D113C412yescomplemented
15C2×D4×D113C2214yes—
16C4×D452—24no—
17#16813584—24no—
18#16813581C2212yescomplemented
19C22⋊C4×D113C2218yescomplemented
20#16813537C2214yescomplemented
21#16813536C2218yescomplemented
22C2×#41×C113C2211yescharacteristic
23#117×C113C2212yescomplemented
24#99×C113C2214yescomplemented
25C23×D113C2×C414yescomplemented
26C23×D113C2312yes—
27#14268648—28no—
28#14268647—22no—
29#14268647—22no—
30#14268647—24no—
31#14268647—24no—
32C2×Dic226C2×C411yescharacteristic, complemented
33C2×D452—24no—
34C2×D452—24no—
35C2×D452C2×C412yes—
36C2×D452C2×C412yes—
37C2×D452C2×C414yescomplemented
38C2×D452C2×C411yescharacteristic, complemented
39C2×D452D414yes—
40C2×D452D414yes—
41C2×C22⋊D113C2×C414yescomplemented
42C2×C22⋊D113C2312yes—
43D4×D113—216no—
44D4×D113—28no—
45C2×C4×D113—28no—
46C2×C4×D113C2×C412yescomplemented
47C2×C4×D113C2×C414yescomplemented
48C4⋊Dic113—22no—
49C22⋊Dic113C2314yes—
50#14268624—28no—
51C4×Dic113—22no—
52#41×C113—22no—
53#41×C113—22no—
54C2×Q8×C113C2×C411yescharacteristic, complemented
55C2×D4×C113C2×C411yescharacteristic, complemented
56C2×D4×C113C2312yes—
57C22×C4×C113C2×C412yescomplemented
58C22×C4×C113C2311yescharacteristic
59C4⋊C4×C113—22no—
60C22⋊C4×C113C2314yes—
61C42×C113—22no—
62C23×C113C22×C412yes—
63C23×C113C2411yescharacteristic
64C22×D113—28no—
65C22×D113—82no—
66C22×D113—84no—
67C22×D113C22×C412yes—
68C22×D113C22×C414yes—
69C22×D113C2×D418yes—
70Q8×C113—22no—
71D4×C113—24no—
72D4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113—24no—
76C2×C4×C113C22×C412yes—
77C2×C4×C113C22×C411yescharacteristic
78C2×C4×C113C22×C411yescharacteristic
79C2×C4×C113C2×D412yes—
80C2×C4×C113C2×D412yes—
81C22⋊D113—24no—
82C22⋊D113—28no—
83C2×Dic113—24no—
84C2×Dic113C22×C412yes—
85D452—28no—
86D452—21no—
87D452—21no—
88D452C22⋊C418yes—
89D452C22⋊C414yes—
90D452C22⋊C414yes—
91C4×D113—28no—
92C4×D113—24no—
93C4×D113—88no—
94Dic226—21no—
95Dic226—21no—
96C22×C113—22no—
97C22×C113—41no—
98C22×C113—42no—
99C22×C113C23×C411yescharacteristic
100C22×C113C22×D412yes—
101C2×D113—22no—
102C2×D113—48no—
103C2×D113—44no—
104C2×D113—42no—
105C2×D113—88no—
106C2×D113C2×C22⋊C418yes—
107C4×C113—22no—
108C4×C113—44no—
109C4×C113C2×C22⋊C411yescharacteristic
110C4×C113C2×C22⋊C411yescharacteristic
111C4×C113C2×C22⋊C412yes—
112Dic113—22no—
113Dic113—44no—
114C2×C113—22no—
115C2×C113—21no—
116C2×C113—42no—
117C2×C113C22×C22⋊C411yescharacteristic
118D113—28no—
119D113—42no—
120#2883—1131nomaximal, Sylow
121C113#288311yescharacteristic, complemented, Sylow
122C2×H(5,𝔽2)—1131no—
123#518—1132no—
124#410—1131no—
125#410—1132no—
126#410D11311yescharacteristic, complemented
127C2×#99—1138no—
128H(5,𝔽2)—2264no—
129H(5,𝔽2)—2264no—
130C2×#41—1132no—
131C2×#41—1132no—
132C2×#41—1131no—
133C2×#41C2×D11311yescharacteristic
134C22×D4—1132no—
135C22×D4—1134no—
136C22×D4—1132no—
137C22×D4—1131no—
138C4×D4—2264no—
139C4×D4—2264no—
140#117—1132no—
141#117C2×D11312yescomplemented
142C2×C22⋊C4—1138no—
143#99—1134no—
144#99—1138no—
145#99C2×D11314yescomplemented
146C24—1132no—
147C24—1134no—
148#41—22no—
149#41—22no—
150#41—2264no—
151#41—2264no—
152#41—2268no—
153#41—2262no—
154#41—2262no—
155C2×Q8—1131no—
156C2×Q8C4×D11311yescharacteristic, complemented
157C2×D4—1134no—
158C2×D4—1132no—
159C2×D4—1132no—
160C2×D4—1132no—
161C2×D4—1134no—
162C2×D4—1131no—
163C2×D4—1134no—
164C2×D4—1134no—
165C2×D4—2264no—
166C2×D4—2264no—
167C2×D4—2268no—
168C2×D4—22616no—
169C2×D4C4×D11311yescharacteristic, complemented
170C2×D4C22×D11312yes—
171C22×C4—1134no—
172C22×C4—1132no—
173C22×C4—2268no—
174C22×C4C4×D11312yescomplemented
175C22×C4C22×D11311yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—2262no—
178C22⋊C4—1134no—
179C22⋊C4—2268no—
180C22⋊C4C22×D11314yes—
181C42—22no—
182C42—2262no—
183C23—1134no—
184C23—1138no—
185C23—1132no—
186C23—9044no—
187C23—9042no—
188C23—2268no—
189C23C2×C4×D11312yes—
190C23C23×D11311yescharacteristic
191Q8—22no—
192Q8—2261no—
193Q8—2261no—
194D4—24no—
195D4—22no—
196D4—1134no—
197D4—1134no—
198D4—1138no—
199D4—2268no—
200D4—2268no—
201D4—2264no—
202D4—2261no—
203D4—2261no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—1132no—
208C2×C4—9048no—
209C2×C4—2268no—
210C2×C4—2264no—
211C2×C4—2264no—
212C2×C4C2×C4×D11312yes—
213C2×C4C2×C4×D11311yescharacteristic
214C2×C4C2×C4×D11311yescharacteristic
215C2×C4D4×D11312yes—
216C2×C4D4×D11312yes—
217C22—22no—
218C22—41no—
219C22—42no—
220C22—1138no—
221C22—9048no—
222C22—4522no—
223C22—4528no—
224C22—4524no—
225C22—2262no—
226C22C22×C4×D11311yescharacteristic
227C22C2×D4×D11312yes—
228C4—22no—
229C4—44no—
230C4—4524no—
231C4—2262no—
232C4C22⋊C4×D11311yescharacteristic
233C4C22⋊C4×D11311yescharacteristic
234C4C22⋊C4×D11312yes—
235C2—22no—
236C2—21no—
237C2—42no—
238C2—4522no—
239C2—2268no—
240C2C2×C22⋊C4×D11311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
Fitting#410×C113C2
socleC2×C113C22×C22⋊C4
prime radicalC2×#16813668C2
cosocleC23×C113C24
hypercenter#410D113
hypocenterC113#2883
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #20299072C2semidirect
3. #20298572C2semidirect
4. #20298571C2semidirect
5. #99×D113C2semidirect
6. #410×C113C2semidirect
9. C2×#14268648C4semidirect
10. C2×#14268647C4semidirect
12. C22×D452C4semidirect
14. C2×D4×D113C4semidirect
18. #16813581C22semidirect
19. C22⋊C4×D113C22semidirect
20. #16813537C22semidirect
21. #16813536C22semidirect
23. #117×C113C22semidirect
24. #99×C113C22semidirect
25. C23×D113C2×C4semidirect
32. C2×Dic226C2×C4semidirect
37. C2×D452C2×C4semidirect
38. C2×D452C2×C4semidirect
41. C2×C22⋊D113C2×C4semidirect
46. C2×C4×D113C2×C4semidirect
47. C2×C4×D113C2×C4semidirect
54. C2×Q8×C113C2×C4semidirect
55. C2×D4×C113C2×C4semidirect
57. C22×C4×C113C2×C4semidirect
121. C113#2883semidirect
126. #410D113semidirect
141. #117C2×D113semidirect
145. #99C2×D113semidirect
156. C2×Q8C4×D113semidirect
169. C2×D4C4×D113semidirect
174. C22×C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136682
#202990722
#202985722
#202985712
#99×D1132
#410×C1132
#2883113