Finite Group Databasebeta

← #28407174

Subgroups — #28407174

Order 14464.

800 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 198 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#20299665C212yesmaximal, complemented
2#20299579C212yesmaximal, complemented
3#20299577C212yesmaximal, complemented
4C2×#16813681C214yesmaximal, complemented
5D113⋊#99C214yesmaximal, complemented
6C2×#16813668C211yesmaximal, characteristic
7D4×#90673—28no—
8#16813701C2214yescomplemented
9C2×C22⋊#90673C2218yescomplemented
10#16813681C2218yescomplemented
11#16813681C2214yescomplemented
12#16813680C2214yescomplemented
13#16813668—28no—
14C2×#14268648C411yescharacteristic, complemented
15C2×#14268648C2211yescharacteristic
16C2×#14268647C412yescomplemented
17C2×#14268647C2211yescharacteristic
18C22×D452C411yescharacteristic, complemented
19C22×D452C2212yes—
20C2×D4×D113C411yescharacteristic, complemented
21C2×D4×D113C412yescomplemented
22C2×D4×D113C2211yescharacteristic
23C2×D4×D113C2212yes—
24C2×#41×C113C411yescharacteristic, complemented
25C22×#90673—28no—
26C4⋊#90673—24no—
27C22⋊#90673—28no—
28C22⋊#90673C2318yes—
29C4×#90673—24no—
30C23×D113C2×C412yescomplemented
31C23×D113C2×C412yescomplemented
32C23×D113C2312yes—
33#14268648—24no—
34#14268648—24no—
35#14268647—28no—
36#14268647—24no—
37C2×Dic226C2×C411yescharacteristic, complemented
38C2×D452—28no—
39C2×D452—24no—
40C2×D452C2×C411yescharacteristic
41C2×D452C2×C411yescharacteristic, complemented
42C2×D452C2×C412yescomplemented
43C2×D452C2×C412yescomplemented
44C2×D452C2312yes—
45C2×D452C2311yescharacteristic
46C2×C22⋊D113C2×C412yes—
47C2×C22⋊D113C2×C411yescharacteristic, complemented
48C2×C22⋊D113C2×C412yescomplemented
49C2×C22⋊D113C2311yescharacteristic
50D4×D113—28no—
51D4×D113—24no—
52D4×D113—28no—
53D4×D113D418yes—
54C2×C4×D113C2×C412yescomplemented
55C2×C4×D113C2×C411yescharacteristic, complemented
56C2×C4×D113C2×C412yescomplemented
57C2×C4×D113C2311yescharacteristic
58#41×C113—24no—
59C2×Q8×C113C2×C411yescharacteristic, complemented
60C2×D4×C113C2×C411yescharacteristic
61C2×D4×C113C2×C412yescomplemented
62C22×C4×C113C2×C411yescharacteristic, complemented
63C22×C4×C113C2×C412yescomplemented
64C23×C113C22×C411yescharacteristic
65C23×C113C22×C412yes—
66C22×D113—24no—
67C22×D113—24no—
68C22×D113—82no—
69C22×D113—82no—
70C22×D113—82no—
71C22×D113C22×C412yes—
72C22×D113C22×C411yescharacteristic
73C22×D113C22×C412yes—
74C22×D113C2×D418yes—
75C22×D113C2411yescharacteristic
76C2×#90673—28no—
77C2×#90673—88no—
78Q8×C113—22no—
79D4×C113—24no—
80D4×C113C22⋊C414yes—
81C2×C4×C113—24no—
82C2×C4×C113—22no—
83C2×C4×C113C22×C411yescharacteristic
84C2×C4×C113C22×C412yes—
85C2×C4×C113C22×C411yescharacteristic
86C22⋊D113—24no—
87C22⋊D113—22no—
88C22⋊D113—22no—
89C22⋊D113C22⋊C418yes—
90C2×Dic113C22×C411yescharacteristic
91C2×Dic113C22×C411yescharacteristic
92D452—24no—
93D452—24no—
94D452—24no—
95D452—22no—
96D452—22no—
97D452C22⋊C414yes—
98C4×D113—24no—
99C4×D113—22no—
100C4×D113—24no—
101C4×D113C2×D414yes—
102Dic226—22no—
103C22×C113—21no—
104C22×C113—42no—
105C22×C113—41no—
106C22×C113C2×C22⋊C414yes—
107C22×C113C23×C411yescharacteristic
108C2×D113—21no—
109C2×D113—22no—
110C2×D113—48no—
111C2×D113—42no—
112C2×D113—41no—
113C2×D113—42no—
114C2×D113—41no—
115C2×D113—84no—
116C2×D113—84no—
117C2×D113C2×C22⋊C414yes—
118C2×D113C22×D412yes—
119#90673—48no—
120C4×C113—21no—
121C4×C113—22no—
122C4×C113C2×C22⋊C412yes—
123Dic113—21no—
124Dic113C2×C22⋊C412yes—
125C2×C113—21no—
126C2×C113—24no—
127C2×C113—41no—
128C2×C113C22×C22⋊C411yescharacteristic
129D113—22no—
130D113—24no—
131D113—42no—
132D113—41no—
133#2883—1131nomaximal, Sylow
134C113#288311yescharacteristic, complemented, Sylow
135C2×H(5,𝔽2)—1131no—
136#518—1132no—
137#410—1132no—
138#410—1132no—
139C2×#99—1134no—
140C2×#99—1134no—
141H(5,𝔽2)—2268no—
142C2×#41—1131no—
143C2×#41—1131no—
144C2×#41—1132no—
145C2×#41—1131no—
146C2×#41#9067311yescharacteristic, complemented
147C22×D4—1131no—
148C22×D4—1131no—
149C22×D4—1132no—
150C22×D4—1132no—
151C22×D4—1131no—
152C22×D4—1132no—
153C4×D4—2268no—
154#117—1134no—
155C2×C22⋊C4—1138no—
156#99—1134no—
157#99—1138no—
158#99—1134no—
159C24—1132no—
160C24—1132no—
161C24—1132no—
162#41—24no—
163#41—2264no—
164#41—2268no—
165#41—2264no—
166#41—2264no—
167C2×Q8—1131no—
168C2×Q8C2×#9067311yescharacteristic, complemented
169C2×D4—1132no—
170C2×D4—1138no—
171C2×D4—1131no—
172C2×D4—1131no—
173C2×D4—1132no—
174C2×D4—1131no—
175C2×D4—1132no—
176C2×D4—1131no—
177C2×D4—1132no—
178C2×D4—1132no—
179C2×D4—1131no—
180C2×D4—2264no—
181C2×D4—2268no—
182C2×D4—2268no—
183C2×D4—2268no—
184C2×D4—2264no—
185C2×D4C2×#9067311yescharacteristic
186C2×D4C2×#9067312yescomplemented
187C22×C4—1131no—
188C22×C4—1132no—
189C22×C4—1132no—
190C22×C4—1131no—
191C22×C4—2268no—
192C22×C4C2×#9067312yescomplemented
193C22×C4C2×#9067311yescharacteristic, complemented
194C4⋊C4—2264no—
195C22⋊C4—1138no—
196C22⋊C4—2268no—
197C42—2264no—
198C23—1138no—
199C23—1131no—
200C23—1132no—
201C23—1132no—
202C23—1131no—
203C23—9042no—
204C23—9042no—
205C23—9042no—
206C23—2264no—
207C23—2264no—
208C23C22×#9067311yescharacteristic
209C23C22×#9067312yes—
210Q8—22no—
211Q8—2262no—
212D4—24no—
213D4—1138no—
214D4—1134no—
215D4—2262no—
216D4—2264no—
217D4—2264no—
218D4—2264no—
219D4—2262no—
220D4—2262no—
221D4—2264no—
222D4—2262no—
223D4C22⋊#9067314yes—
224C2×C4—24no—
225C2×C4—22no—
226C2×C4—1131no—
227C2×C4—1134no—
228C2×C4—1131no—
229C2×C4—9048no—
230C2×C4—2264no—
231C2×C4—2264no—
232C2×C4—2268no—
233C2×C4—2262no—
234C2×C4C22×#9067312yes—
235C2×C4C22×#9067311yescharacteristic
236C2×C4C22×#9067311yescharacteristic
237C22—21no—
238C22—42no—
239C22—41no—
240C22—1132no—
241C22—1134no—
242C22—9044no—
243C22—9044no—
244C22—4521no—
245C22—4522no—
246C22—4528no—
247C22—4521no—
248C22—4522no—
249C22—2262no—
250C22—2261no—
251C22C2×C22⋊#9067314yes—
252C22C23×#9067311yescharacteristic
253C4—21no—
254C4—22no—
255C4—1132no—
256C4—4528no—
257C4—2261no—
258C4C2×C22⋊#9067312yes—
259C2—21no—
260C2—24no—
261C2—41no—
262C2—4521no—
263C2—4522no—
264C2—2262no—
265C2—2264no—
266C2C22×C22⋊#9067311yescharacteristic
subgroupG/H
centerC2C22×C22⋊#90673
commutatorC22×C113C23×C4
FrattiniC22C23×#90673
FittingC2×#41×C113C4
socleC2×C113C22×C22⋊C4
prime radicalC2×#16813668C2
cosocleC22×D113C24
hypercenterC2×#41#90673
hypocenterC113#2883
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×D4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20299665C2semidirect
2. #20299579C2semidirect
3. #20299577C2semidirect
4. C2×#16813681C2semidirect
5. D113⋊#99C2semidirect
8. #16813701C22semidirect
9. C2×C22⋊#90673C22semidirect
10. #16813681C22semidirect
11. #16813681C22semidirect
12. #16813680C22semidirect
14. C2×#14268648C4semidirect
16. C2×#14268647C4semidirect
18. C22×D452C4semidirect
20. C2×D4×D113C4semidirect
21. C2×D4×D113C4semidirect
24. C2×#41×C113C4semidirect
30. C23×D113C2×C4semidirect
31. C23×D113C2×C4semidirect
37. C2×Dic226C2×C4semidirect
41. C2×D452C2×C4semidirect
42. C2×D452C2×C4semidirect
43. C2×D452C2×C4semidirect
47. C2×C22⋊D113C2×C4semidirect
48. C2×C22⋊D113C2×C4semidirect
54. C2×C4×D113C2×C4semidirect
55. C2×C4×D113C2×C4semidirect
56. C2×C4×D113C2×C4semidirect
59. C2×Q8×C113C2×C4semidirect
61. C2×D4×C113C2×C4semidirect
62. C22×C4×C113C2×C4semidirect
63. C22×C4×C113C2×C4semidirect
134. C113#2883semidirect
146. C2×#41#90673semidirect
168. C2×Q8C2×#90673semidirect
186. C2×D4C2×#90673semidirect
192. C22×C4C2×#90673semidirect
193. C22×C4C2×#90673semidirect

Maximal subgroups

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

subgroupindex
#202996652
#202995792
#202995772
C2×#168136812
D113⋊#992
C2×#168136682
#2883113