Finite Group Databasebeta

← #28393557

Subgroups — #28393557

Order 14464.

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

normal subgroups only

This group has 928 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×#16813590C211yesmaximal, characteristic
2C2×C4×C22⋊D113C212yesmaximal, complemented
3C2×C22⋊C4×D113C212yesmaximal, complemented
4#20298501C211yesmaximal, characteristic, complemented
5#20298492C212yesmaximal, complemented
6#20298474C212yesmaximal, complemented
7#20298472C212yesmaximal, complemented
8#20298445C212yesmaximal, complemented
9#386×C113C211yesmaximal, characteristic, complemented
10C24×D113C2211yescharacteristic
11C22×C22⋊D113C2212yes—
12C22×C4×D113C2212yes—
13C22×C4×D113C2212yes—
14#16813590C418yescomplemented
15C4×C22⋊D113—28no—
16C2×C4⋊Dic113C2211yescharacteristic, complemented
17C2×#14268626C2212yescomplemented
18C2×C22⋊Dic113C2212yes—
19C2×C22⋊Dic113C2211yescharacteristic
20C2×C22⋊Dic113C2212yescomplemented
21C2×#14268624C2212yes—
22C2×#14268624C2212yes—
23C2×#14268624C2212yes—
24C22⋊C4×D113—28no—
25C2×C4×Dic113C2212yescomplemented
26C2×C4×Dic113C2211yescharacteristic, complemented
27#16813529C2212yescomplemented
28#16813529C2212yescomplemented
29C22×D4×C113C2211yescharacteristic
30C23×C4×C113C2211yescharacteristic, complemented
31C2×C22⋊C4×C113C2212yes—
32C2×C22⋊C4×C113C2211yescharacteristic, complemented
33#95×C113C2212yescomplemented
34C23×D113—24no—
35C23×D113—24no—
36C23×D113—41no—
37C23×D113—41no—
38C23×D113C2×C414yescomplemented
39C23×D113C2312yes—
40C2×C22⋊D113—24no—
41C2×C22⋊D113—24no—
42C2×C22⋊D113C2×C418yescomplemented
43C22×Dic113C2312yes—
44C22×Dic113C2312yes—
45C22×Dic113C2312yes—
46C2×C4×D113—24no—
47C2×C4×D113—24no—
48C2×C4×D113—24no—
49C2×C4×D113—24no—
50C2×C4×D113—42no—
51C2×C4×D113—42no—
52C4⋊Dic113—41no—
53#14268626—24no—
54C22⋊Dic113—24no—
55C22⋊Dic113—24no—
56C22⋊Dic113C2×C414yescomplemented
57#14268624—24no—
58#14268624C2×C418yescomplemented
59#14268624D418yescomplemented
60C4×Dic113—24no—
61C4×Dic113—41no—
62C24×C113C2311yescharacteristic
63C24×C113C2311yescharacteristic
64C2×D4×C113—41no—
65C2×D4×C113—41no—
66C2×D4×C113C2×C414yescomplemented
67C22×C4×C113—24no—
68C22×C4×C113—41no—
69C22×C4×C113C2312yes—
70C22×C4×C113C2311yescharacteristic
71C22×C4×C113C2312yes—
72C22⋊C4×C113—24no—
73C22⋊C4×C113—41no—
74C23×C113—22no—
75C23×C113—22no—
76C23×C113—22no—
77C23×C113—22no—
78C23×C113—21no—
79C23×C113—21no—
80C23×C113—21no—
81C23×C113—21no—
82C23×C113C22×C412yes—
83C23×C113C22×C412yes—
84C23×C113C2411yescharacteristic
85C22×D113—22no—
86C22×D113—22no—
87C22×D113—22no—
88C22×D113—22no—
89C22×D113—216no—
90C22×D113—44no—
91C22×D113—44no—
92C22×D113—48no—
93C22×D113—44no—
94C22×D113C22×C414yes—
95C22×D113C2×D414yes—
96C22×D113#4114yes—
97D4×C113—44no—
98C2×C4×C113—22no—
99C2×C4×C113—22no—
100C2×C4×C113—21no—
101C2×C4×C113—21no—
102C2×C4×C113—22no—
103C2×C4×C113—22no—
104C2×C4×C113—22no—
105C2×C4×C113—44no—
106C2×C4×C113C22×C412yes—
107C2×C4×C113C2×D414yes—
108C22⋊D113—216no—
109C2×Dic113—22no—
110C2×Dic113—22no—
111C2×Dic113—22no—
112C2×Dic113—22no—
113C2×Dic113—22no—
114C2×Dic113—22no—
115C2×Dic113—22no—
116C2×Dic113C22×C414yes—
117C2×Dic113C2×D414yes—
118C4×D113—48no—
119C4×D113—48no—
120C22×C113—24no—
121C22×C113—24no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—41no—
125C22×C113—41no—
126C22×C113—42no—
127C22×C113—42no—
128C22×C113—41no—
129C22×C113—41no—
130C22×C113C23×C411yescharacteristic
131C22×C113C22×D412yes—
132C22×C113C2×#4112yes—
133C22×C113H(5,𝔽2)11yescharacteristic
134C22×C113H(5,𝔽2)11yescharacteristic
135C2×D113—24no—
136C2×D113—24no—
137C2×D113—24no—
138C2×D113—24no—
139C2×D113—24no—
140C2×D113—24no—
141C2×D113—416no—
142C2×D113C4×D418yescomplemented
143C4×C113—22no—
144C4×C113—24no—
145C4×C113—42no—
146Dic113—24no—
147Dic113—24no—
148Dic113—42no—
149C2×C113—42no—
150C2×C113—42no—
151C2×C113C2×C4×D412yes—
152C2×C113#51811yescharacteristic
153C2×C113D4211yescharacteristic
154C2×C113#54612yes—
155C2×C113#55111yescharacteristic
156D113—28no—
157#2358—1131nomaximal, Sylow
158C113#235811yescharacteristic, complemented, Sylow
159C2×#120—1131no—
160C2×C4×D4—1132no—
161C22×C22⋊C4—1132no—
162#390—1131no—
163#388—1132no—
164#386—1132no—
165#386D11311yescharacteristic, complemented
166#385—1132no—
167C4×C22⋊C4—1132no—
168C25—1131no—
169C22×D4—1132no—
170C22×D4C2×D11311yescharacteristic
171C23×C4—1132no—
172C23×C4—1132no—
173C23×C4C2×D11311yescharacteristic, complemented
174#120—1138no—
175C4×D4—2268no—
176C2×C4⋊C4—1131no—
177C2×C4⋊C4—1132no—
178C2×C22⋊C4—1131no—
179C2×C22⋊C4—1132no—
180C2×C22⋊C4—1132no—
181C2×C22⋊C4—1132no—
182C2×C22⋊C4—1132no—
183C2×C22⋊C4—1132no—
184C2×C22⋊C4—2268no—
185C2×C22⋊C4C2×D11312yes—
186C2×C22⋊C4C2×D11311yescharacteristic, complemented
187C2×C42—1131no—
188C2×C42—1132no—
189#95—1132no—
190#95—1132no—
191#95C2×D11312yescomplemented
192C24—1132no—
193C24—1134no—
194C24—4521no—
195C24—4521no—
196C24—2264no—
197C24—2264no—
198C24C22×D11311yescharacteristic
199C24C22×D11311yescharacteristic
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—1138no—
203C2×D4—2264no—
204C2×D4—2264no—
205C2×D4C4×D11314yescomplemented
206C22×C4—24no—
207C22×C4—41no—
208C22×C4—1132no—
209C22×C4—1132no—
210C22×C4—1132no—
211C22×C4—4522no—
212C22×C4—4522no—
213C22×C4—2264no—
214C22×C4—2264no—
215C22×C4—2264no—
216C22×C4—2264no—
217C22×C4C22×D11312yes—
218C22×C4C22×D11311yescharacteristic
219C22×C4C22×D11312yes—
220C4⋊C4—4521no—
221C4⋊C4—2264no—
222C22⋊C4—24no—
223C22⋊C4—41no—
224C22⋊C4—1134no—
225C22⋊C4—1138no—
226C22⋊C4—1138no—
227C22⋊C4—2264no—
228C22⋊C4—2264no—
229C22⋊C4—2264no—
230C42—4521no—
231C42—2264no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—1134no—
241C23—1134no—
242C23—1134no—
243C23—4524no—
244C23—4524no—
245C23—4524no—
246C23—4528no—
247C23—22616no—
248C23—2262no—
249C23—2262no—
250C23—2262no—
251C23—2262no—
252C23C2×C4×D11312yes—
253C23C2×C4×D11312yes—
254C23C23×D11311yescharacteristic
255D4—44no—
256D4—22616no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—44no—
265C2×C4—1134no—
266C2×C4—1134no—
267C2×C4—4528no—
268C2×C4—4528no—
269C2×C4—2262no—
270C2×C4—2262no—
271C2×C4—2262no—
272C2×C4—2262no—
273C2×C4—2262no—
274C2×C4—2262no—
275C2×C4—2262no—
276C2×C4C2×C4×D11312yes—
277C2×C4D4×D11314yes—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—1138no—
289C22—45216no—
290C22—2264no—
291C22—2264no—
292C22—2264no—
293C22—2264no—
294C22—2264no—
295C22—2264no—
296C22C22×C4×D11311yescharacteristic
297C22C2×D4×D11312yes—
298C22#41×D11312yes—
299C22#1681366711yescharacteristic
300C22#1681366711yescharacteristic
301C4—22no—
302C4—24no—
303C4—42no—
304C4—4522no—
305C4—2264no—
306C4—2264no—
307C2—42no—
308C2—42no—
309C2—2268no—
310C2C4×D4×D11312yes—
311C2#2029907111yescharacteristic
312C2#2029923011yescharacteristic
313C2#2029924512yes—
314C2#2029927611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#386×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813590C2
hypercenter#386D113
hypocenterC113#2358
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D113C2semidirect
3. C2×C22⋊C4×D113C2semidirect
4. #20298501C2semidirect
5. #20298492C2semidirect
6. #20298474C2semidirect
7. #20298472C2semidirect
8. #20298445C2semidirect
9. #386×C113C2semidirect
14. #16813590C4semidirect
16. C2×C4⋊Dic113C22semidirect
17. C2×#14268626C22semidirect
20. C2×C22⋊Dic113C22semidirect
25. C2×C4×Dic113C22semidirect
26. C2×C4×Dic113C22semidirect
27. #16813529C22semidirect
28. #16813529C22semidirect
30. C23×C4×C113C22semidirect
32. C2×C22⋊C4×C113C22semidirect
33. #95×C113C22semidirect
38. C23×D113C2×C4semidirect
42. C2×C22⋊D113C2×C4semidirect
56. C22⋊Dic113C2×C4semidirect
58. #14268624C2×C4semidirect
59. #14268624D4semidirect
66. C2×D4×C113C2×C4semidirect
142. C2×D113C4×D4semidirect
158. C113#2358semidirect
165. #386D113semidirect
173. C23×C4C2×D113semidirect
186. C2×C22⋊C4C2×D113semidirect
191. #95C2×D113semidirect
205. C2×D4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135902
C2×C4×C22⋊D1132
C2×C22⋊C4×D1132
#202985012
#202984922
#202984742
#202984722
#202984452
#386×C1132
#2358113