Finite Group Databasebeta

← #27198125

Subgroups — #27198125

Order 13184.

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×#15692989C211yesmaximal, characteristic
2C2×(C22⋊D103)⋊C4C212yesmaximal, complemented
3C2×C22⋊C4×D103C212yesmaximal, complemented
4#20267679C212yesmaximal, complemented
5#20267671C211yesmaximal, characteristic, complemented
6#20267667C212yesmaximal, complemented
7#20267662C212yesmaximal, complemented
8C4×(C2×D103)⋊C4C212yesmaximal, complemented
9#390×C103C211yesmaximal, characteristic, complemented
10C24×D103C2211yescharacteristic
11C22×C22⋊D103C2212yes—
12C23×Dic103C2211yescharacteristic, complemented
13C22×C4×D103C2212yes—
14C22×C4×D103C2212yes—
15#15692989C418yescomplemented
16(C22⋊D103)⋊C4—28no—
17C2×Dic103⋊C4C2212yescomplemented
18C2×C22⋊Dic103C2212yes—
19C2×C22⋊Dic103C2211yescharacteristic
20C2×C22⋊Dic103C2211yescharacteristic, complemented
21C2×(C2×D103)⋊C4C2212yes—
22C2×(C2×D103)⋊C4C2212yes—
23C2×(C2×D103)⋊C4C2212yes—
24C22⋊C4×D103—28no—
25C2×C4×Dic103C2212yescomplemented
26C103⋊#95C2212yescomplemented
27C103⋊#95C2212yescomplemented
28C103⋊#95C2212yescomplemented
29C22×D4×C103C2211yescharacteristic
30C2×C4⋊C4×C103C2211yescharacteristic, complemented
31C2×C22⋊C4×C103C2212yes—
32C2×C22⋊C4×C103C2212yescomplemented
33C2×C42×C103C2211yescharacteristic, complemented
34C23×D103—24no—
35C23×D103—24no—
36C23×D103—41no—
37C23×D103—41no—
38C23×D103C2×C414yescomplemented
39C23×D103C2312yes—
40C2×C22⋊D103—24no—
41C2×C22⋊D103—24no—
42C2×C22⋊D103C2×C418yescomplemented
43C22×Dic103—24no—
44C22×Dic103—41no—
45C22×Dic103C2312yes—
46C22×Dic103C2312yes—
47C22×Dic103C2312yes—
48C2×C4×D103—24no—
49C2×C4×D103—24no—
50C2×C4×D103—24no—
51C2×C4×D103—24no—
52C2×C4×D103—42no—
53C2×C4×D103—42no—
54Dic103⋊C4—24no—
55C22⋊Dic103—24no—
56C22⋊Dic103—41no—
57C22⋊Dic103C2×C414yescomplemented
58(C2×D103)⋊C4—24no—
59(C2×D103)⋊C4C2×C418yescomplemented
60(C2×D103)⋊C4D418yescomplemented
61C4×Dic103—24no—
62C24×C103C2311yescharacteristic
63C24×C103C2311yescharacteristic
64C2×D4×C103—41no—
65C2×D4×C103—41no—
66C2×D4×C103C2×C414yescomplemented
67C22×C4×C103C2312yes—
68C22×C4×C103C2311yescharacteristic
69C22×C4×C103C2312yes—
70C4⋊C4×C103—41no—
71C22⋊C4×C103—24no—
72C22⋊C4×C103—24no—
73C42×C103—41no—
74C23×C103—22no—
75C23×C103—22no—
76C23×C103—22no—
77C23×C103—22no—
78C23×C103—21no—
79C23×C103—21no—
80C23×C103—21no—
81C23×C103—21no—
82C23×C103C22×C412yes—
83C23×C103C22×C412yes—
84C23×C103C2411yescharacteristic
85C22×D103—22no—
86C22×D103—22no—
87C22×D103—22no—
88C22×D103—22no—
89C22×D103—216no—
90C22×D103—44no—
91C22×D103—44no—
92C22×D103—48no—
93C22×D103—44no—
94C22×D103C22×C414yes—
95C22×D103C2×D414yes—
96C22×D103#4114yes—
97D4×C103—44no—
98C2×C4×C103—22no—
99C2×C4×C103—21no—
100C2×C4×C103—22no—
101C2×C4×C103—21no—
102C2×C4×C103—22no—
103C2×C4×C103—22no—
104C2×C4×C103—22no—
105C2×C4×C103C22×C412yes—
106C2×C4×C103C2×D414yes—
107C22⋊D103—216no—
108C2×Dic103—22no—
109C2×Dic103—22no—
110C2×Dic103—22no—
111C2×Dic103—22no—
112C2×Dic103—22no—
113C2×Dic103—22no—
114C2×Dic103—22no—
115C2×Dic103—44no—
116C2×Dic103C22×C414yes—
117C2×Dic103C2×D414yes—
118C4×D103—48no—
119C4×D103—48no—
120C22×C103—24no—
121C22×C103—24no—
122C22×C103—22no—
123C22×C103—22no—
124C22×C103—41no—
125C22×C103—41no—
126C22×C103—42no—
127C22×C103—42no—
128C22×C103—41no—
129C22×C103—41no—
130C22×C103C23×C411yescharacteristic
131C22×C103C22×D412yes—
132C22×C103C2×#4112yes—
133C22×C103H(5,𝔽2)11yescharacteristic
134C22×C103H(5,𝔽2)11yescharacteristic
135C2×D103—24no—
136C2×D103—24no—
137C2×D103—24no—
138C2×D103—24no—
139C2×D103—24no—
140C2×D103—24no—
141C2×D103—416no—
142C2×D103C4×D418yescomplemented
143C4×C103—22no—
144C4×C103—24no—
145C4×C103—42no—
146Dic103—24no—
147Dic103—24no—
148Dic103—42no—
149C2×C103—42no—
150C2×C103—42no—
151C2×C103C2×C4×D412yes—
152C2×C103#51811yescharacteristic
153C2×C103D4211yescharacteristic
154C2×C103#54612yes—
155C2×C103#55111yescharacteristic
156D103—28no—
157#2358—1031nomaximal, Sylow
158C103#235811yescharacteristic, complemented, Sylow
159C2×#120—1031no—
160C2×C4×D4—1032no—
161C22×C22⋊C4—1032no—
162#390D10311yescharacteristic, complemented
163#388—1032no—
164#386—1031no—
165#386—1032no—
166#385—1032no—
167C4×C22⋊C4—1032no—
168C25—1031no—
169C22×D4—1032no—
170C22×D4C2×D10311yescharacteristic
171C23×C4—1031no—
172C23×C4—1032no—
173C23×C4—1032no—
174#120—1038no—
175C4×D4—2068no—
176C2×C4⋊C4—1032no—
177C2×C4⋊C4C2×D10311yescharacteristic, complemented
178C2×C22⋊C4—1031no—
179C2×C22⋊C4—1032no—
180C2×C22⋊C4—1032no—
181C2×C22⋊C4—1031no—
182C2×C22⋊C4—1032no—
183C2×C22⋊C4—1032no—
184C2×C22⋊C4—2068no—
185C2×C22⋊C4C2×D10312yes—
186C2×C22⋊C4C2×D10312yescomplemented
187C2×C42—1032no—
188C2×C42C2×D10311yescharacteristic, complemented
189#95—1032no—
190#95—1032no—
191#95—1032no—
192C24—1032no—
193C24—1034no—
194C24—4121no—
195C24—4121no—
196C24—2064no—
197C24—2064no—
198C24C22×D10311yescharacteristic
199C24C22×D10311yescharacteristic
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—1038no—
203C2×D4—2064no—
204C2×D4—2064no—
205C2×D4C4×D10314yescomplemented
206C22×C4—1032no—
207C22×C4—1032no—
208C22×C4—1032no—
209C22×C4—4122no—
210C22×C4—4122no—
211C22×C4—4121no—
212C22×C4—2064no—
213C22×C4—2064no—
214C22×C4—2064no—
215C22×C4—2064no—
216C22×C4—2064no—
217C22×C4C22×D10312yes—
218C22×C4C22×D10311yescharacteristic
219C22×C4C22×D10312yes—
220C4⋊C4—41no—
221C4⋊C4—2064no—
222C22⋊C4—24no—
223C22⋊C4—24no—
224C22⋊C4—1034no—
225C22⋊C4—1038no—
226C22⋊C4—1038no—
227C22⋊C4—4121no—
228C22⋊C4—2064no—
229C22⋊C4—2064no—
230C42—41no—
231C42—2064no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—1034no—
241C23—1034no—
242C23—1034no—
243C23—4124no—
244C23—4124no—
245C23—4128no—
246C23—4124no—
247C23—20616no—
248C23—2062no—
249C23—2062no—
250C23—2062no—
251C23—2062no—
252C23C2×C4×D10312yes—
253C23C2×C4×D10312yes—
254C23C23×D10311yescharacteristic
255D4—44no—
256D4—20616no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—1034no—
265C2×C4—1034no—
266C2×C4—4128no—
267C2×C4—4128no—
268C2×C4—4124no—
269C2×C4—2062no—
270C2×C4—2062no—
271C2×C4—2062no—
272C2×C4—2062no—
273C2×C4—2062no—
274C2×C4—2062no—
275C2×C4—2062no—
276C2×C4C2×C4×D10312yes—
277C2×C4D4×D10314yes—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—41no—
287C22—41no—
288C22—1038no—
289C22—41216no—
290C22—2064no—
291C22—2064no—
292C22—2064no—
293C22—2064no—
294C22—2064no—
295C22—2064no—
296C22C22×C4×D10311yescharacteristic
297C22C2×D4×D10312yes—
298C22#41×D10312yes—
299C22#1569306611yescharacteristic
300C22#1569306611yescharacteristic
301C4—24no—
302C4—22no—
303C4—42no—
304C4—4122no—
305C4—2064no—
306C4—2064no—
307C2—42no—
308C2—42no—
309C2—2068no—
310C2C4×D4×D10312yes—
311C2#2026826411yescharacteristic
312C2#2026842611yescharacteristic
313C2#2026843012yes—
314C2#2026847111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#390×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692989C2
hypercenter#390D103
hypocenterC103#2358
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D103)⋊C4C2semidirect
3. C2×C22⋊C4×D103C2semidirect
4. #20267679C2semidirect
5. #20267671C2semidirect
6. #20267667C2semidirect
7. #20267662C2semidirect
8. C4×(C2×D103)⋊C4C2semidirect
9. #390×C103C2semidirect
12. C23×Dic103C22semidirect
15. #15692989C4semidirect
17. C2×Dic103⋊C4C22semidirect
20. C2×C22⋊Dic103C22semidirect
25. C2×C4×Dic103C22semidirect
26. C103⋊#95C22semidirect
27. C103⋊#95C22semidirect
28. C103⋊#95C22semidirect
30. C2×C4⋊C4×C103C22semidirect
32. C2×C22⋊C4×C103C22semidirect
33. C2×C42×C103C22semidirect
38. C23×D103C2×C4semidirect
42. C2×C22⋊D103C2×C4semidirect
57. C22⋊Dic103C2×C4semidirect
59. (C2×D103)⋊C4C2×C4semidirect
60. (C2×D103)⋊C4D4semidirect
66. C2×D4×C103C2×C4semidirect
142. C2×D103C4×D4semidirect
158. C103#2358semidirect
162. #390D103semidirect
177. C2×C4⋊C4C2×D103semidirect
186. C2×C22⋊C4C2×D103semidirect
188. C2×C42C2×D103semidirect
205. C2×D4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929892
C2×(C22⋊D103)⋊C42
C2×C22⋊C4×D1032
#202676792
#202676712
#202676672
#202676622
C4×(C2×D103)⋊C42
#390×C1032
#2358103