Finite Group Databasebeta

← #28399847

Subgroups — #28399847

Order 14464.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813667C211yesmaximal, characteristic
2C2×#16813653C211yesmaximal, characteristic, complemented
3#20299172C211yesmaximal, characteristic, complemented
4#20298757C214yesmaximal, complemented
5#20298747C214yesmaximal, complemented
6#20298603C211yesmaximal, characteristic, complemented
7#20298595C211yesmaximal, characteristic, complemented
8#20298564C211yesmaximal, characteristic, complemented
9C22×SD16×C113C211yesmaximal, characteristic, complemented
10#16813667—24no—
11#16813667—24no—
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2211yescharacteristic
14C2×#14268646—21no—
15C2×#14268646C2212yes—
16C22×C22⋊D113—22no—
17C2×D4×D113—21no—
18C2×D4×D113C2212yes—
19#16813653—24no—
20C2×#14268637C2212yescomplemented
21C2×#14268634C2212yescomplemented
22C2×#14268631C2211yescharacteristic, complemented
23#16813620—21no—
24#16813611—21no—
25#16813605—22no—
26#16813598C2214yescomplemented
27#16813581C2211yescharacteristic, complemented
28#16813547C2212yescomplemented
29#16813544C2212yescomplemented
30#16813543C2214yescomplemented
31#16813534C2214yescomplemented
32C22×Q8×C113C2211yescharacteristic, complemented
33C22×D4×C113C2211yescharacteristic
34C2×SD16×C113—24no—
35C2×SD16×C113C2214yescomplemented
36C22×C8×C113C2211yescharacteristic, complemented
37C23×D113—22no—
38#14268647—22no—
39#14268647—22no—
40#14268647—22no—
41#14268647D414yes—
42#14268646—28no—
43#14268646—24no—
44#14268646—24no—
45C2×Dic226D411yescharacteristic
46C2×Dic226C2311yescharacteristic
47C2×D452D411yescharacteristic
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—216no—
50C2×C22⋊D113—21no—
51C2×C22⋊D113—22no—
52C2×C22⋊D113—22no—
53C2×C22⋊D113D412yes—
54D4×D113—28no—
55D4×D113—24no—
56D4×D113—24no—
57C22×Dic113—22no—
58C2×C4×D113—21no—
59C2×C4×D113C2312yes—
60#14268637—24no—
61#14268634—24no—
62#14268631—22no—
63C2×#11744751C2312yes—
64C4⋊Dic113C2312yes—
65#14268626—24no—
66C22⋊Dic113—21no—
67#14268624—24no—
68C4×Dic113—21no—
69C24×C113—21no—
70C2×Q8×C113—21no—
71C2×Q8×C113—22no—
72C2×Q8×C113—22no—
73C2×Q8×C113C2312yes—
74C2×D4×C113—21no—
75C2×D4×C113—22no—
76C2×D4×C113D414yes—
77C2×D4×C113C2312yes—
78C22×C4×C113—21no—
79C22×C4×C113C2311yescharacteristic
80SD16×C113—28no—
81C2×C8×C113—22no—
82C2×C8×C113C2312yes—
83C23×C113—22no—
84C23×C113—24no—
85C23×C113—82no—
86C23×C113C2×D411yescharacteristic
87C22×D113—21no—
88C22×D113—28no—
89C22×D113—84no—
90C22×D113C2×D412yes—
91Q8×C113—22no—
92Q8×C113—22no—
93Q8×C113—42no—
94D4×C113—24no—
95D4×C113—22no—
96D4×C113C2×D414yes—
97C2×C4×C113—22no—
98C2×C4×C113—42no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D412yes—
101C2×C4×C113C2×D412yes—
102C2×C4×C113C2411yescharacteristic
103C22⋊D113—28no—
104C22⋊D113—28no—
105C22⋊D113—24no—
106C22⋊D113—24no—
107C2×Dic113—28no—
108C2×Dic113—21no—
109C2×Dic113—22no—
110C2×Dic113C2×D412yes—
111D452—22no—
112D452—21no—
113D452C2×D412yes—
114C4×D113—24no—
115C4×D113—22no—
116C4×D113—22no—
117Dic226—22no—
118Dic226—21no—
119Dic226C2×D412yes—
120C8×C113—22no—
121#11744751—22no—
122C22×C113—22no—
123C22×C113—24no—
124C22×C113—44no—
125C22×C113—84no—
126C22×C113#12012yes—
127C22×C113C22×D411yescharacteristic
128C2×D113—22no—
129C2×D113—22no—
130C2×D113—24no—
131C2×D113—42no—
132C2×D113—88no—
133C4×C113—42no—
134C4×C113#12012yes—
135C4×C113C22×D411yescharacteristic
136C4×C113C22×D411yescharacteristic
137Dic113—22no—
138Dic113—22no—
139Dic113—42no—
140C2×C113—22no—
141C2×C113—44no—
142C2×C113C2×#12011yescharacteristic
143C2×C113#57712yes—
144D113—42no—
145D113—42no—
146#3009—1131nomaximal, Sylow
147C113#300911yescharacteristic, complemented, Sylow
148C2×H(5,𝔽2)—1131no—
149C2×#137—1131no—
150C22×SD16D11311yescharacteristic, complemented
151#536—1131no—
152#452—1134no—
153#450—1134no—
154#418—1131no—
155#416—1131no—
156#408—1131no—
157H(5,𝔽2)—2264no—
158H(5,𝔽2)—2264no—
159C2×#41—1131no—
160C2×#41—1132no—
161C2×#41—1131no—
162C2×#41—2261no—
163C22×Q8C2×D11311yescharacteristic, complemented
164C22×D4—1132no—
165C22×D4—2261no—
166C22×D4—2262no—
167C22×D4C2×D11311yescharacteristic
168#137—2264no—
169C2×Q16—1132no—
170C2×SD16—24no—
171C2×SD16—1132no—
172C2×SD16C2×D11314yescomplemented
173C2×M16—1131no—
174C22×C8C2×D11311yescharacteristic, complemented
175C4⋊Q8—2261no—
176#124—2261no—
177#123—2262no—
178C22⋊Q8—1134no—
179#117—1131no—
180#103—1132no—
181#102—1134no—
182#102—1132no—
183C22⋊C8—1134no—
184C24—21no—
185C24—2262no—
186#41—1134no—
187#41—2264no—
188#41—2268no—
189#41—2264no—
190#41—2262no—
191#41—2262no—
192#41—2262no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—1131no—
197C2×Q8—1131no—
198C2×Q8C22×D11312yes—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—1132no—
202C2×D4—1131no—
203C2×D4—1131no—
204C2×D4—2262no—
205C2×D4—2264no—
206C2×D4—2268no—
207C2×D4—2262no—
208C2×D4—22616no—
209C2×D4—2261no—
210C2×D4—2264no—
211C2×D4C22⋊D11314yes—
212C2×D4C22×D11312yes—
213C22×C4—21no—
214C22×C4—1132no—
215C22×C4—2262no—
216C22×C4—2261no—
217C22×C4C22×D11311yescharacteristic
218Q16—2264no—
219SD16—28no—
220SD16—2264no—
221M16—2262no—
222C2×C8—22no—
223C2×C8—1132no—
224C2×C8C22×D11312yes—
225C4⋊C4—1132no—
226C4⋊C4—2264no—
227C22⋊C4—2264no—
228C22⋊C4—2261no—
229C42—2261no—
230C23—22no—
231C23—24no—
232C23—82no—
233C23—1132no—
234C23—9044no—
235C23—2268no—
236C23—2261no—
237C23D4×D11311yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—42no—
241Q8—1132no—
242Q8—2262no—
243Q8—2261no—
244D4—24no—
245D4—22no—
246D4—1132no—
247D4—2268no—
248D4—2268no—
249D4—2264no—
250D4—2264no—
251D4—2262no—
252D4—2261no—
253D4C2×C22⋊D11314yes—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—1132no—
257C2×C4—2262no—
258C2×C4—2268no—
259C2×C4—2261no—
260C2×C4—2264no—
261C2×C4—2262no—
262C2×C4—2262no—
263C2×C4D4×D11311yescharacteristic
264C2×C4D4×D11312yes—
265C2×C4C2×C22⋊D11312yes—
266C2×C4C23×D11311yescharacteristic
267C8—22no—
268C8—2262no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—84no—
273C22—9048no—
274C22—4522no—
275C22—2262no—
276C22—2262no—
277C22—2264no—
278C22#1681359012yes—
279C22C2×D4×D11311yescharacteristic
280C4—42no—
281C4—4522no—
282C4—2262no—
283C4—2262no—
284C4#1681359012yes—
285C4C2×D4×D11311yescharacteristic
286C4C22×C22⋊D11311yescharacteristic
287C2—22no—
288C2—44no—
289C2—4522no—
290C2—4522no—
291C2C2×#1681359011yescharacteristic
292C2#2029940412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×SD16×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813667C2
hypercenterC22×SD16D113
hypocenterC113#3009
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#16813653C2semidirect
3. #20299172C2semidirect
4. #20298757C2semidirect
5. #20298747C2semidirect
6. #20298603C2semidirect
7. #20298595C2semidirect
8. #20298564C2semidirect
9. C22×SD16×C113C2semidirect
20. C2×#14268637C22semidirect
21. C2×#14268634C22semidirect
22. C2×#14268631C22semidirect
26. #16813598C22semidirect
27. #16813581C22semidirect
28. #16813547C22semidirect
29. #16813544C22semidirect
30. #16813543C22semidirect
31. #16813534C22semidirect
32. C22×Q8×C113C22semidirect
35. C2×SD16×C113C22semidirect
36. C22×C8×C113C22semidirect
147. C113#3009semidirect
150. C22×SD16D113semidirect
163. C22×Q8C2×D113semidirect
172. C2×SD16C2×D113semidirect
174. C22×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136672
C2×#168136532
#202991722
#202987572
#202987472
#202986032
#202985952
#202985642
C22×SD16×C1132
#3009113