Finite Group Databasebeta

← #27204724

Subgroups — #27204724

Order 13184.

520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15693041C211yesmaximal, characteristic, complemented
2C22×C8×D103C211yesmaximal, characteristic, complemented
3#20268303C211yesmaximal, characteristic, complemented
4#20268298C211yesmaximal, characteristic, complemented
5#20268031C212yesmaximal, complemented
6#20268026C212yesmaximal, complemented
7#20268023C212yesmaximal, complemented
8#20268019C212yesmaximal, complemented
9#20267827C211yesmaximal, characteristic, complemented
10#20267788C211yesmaximal, characteristic, complemented
11#416×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13C22×C4×D103C2211yescharacteristic
14#15693041—24no—
15C2×#13110095C2211yescharacteristic, complemented
16C2×#13110093C2211yescharacteristic, complemented
17C2×#13110092C2211yescharacteristic, complemented
18C2×#13110090C2211yescharacteristic, complemented
19C22×C103⋊C8C2211yescharacteristic
20C2×C8×D103—24no—
21C2×C8×D103C2212yes—
22C2×C8×D103C2212yes—
23#15693005—21no—
24#15693002—21no—
25#15693001C2212yes—
26#15692997C2212yes—
27#15692996C2212yes—
28#15692992C2212yes—
29#15692991—21no—
30#15692989—21no—
31C4×D412—22no—
32C4×C22⋊D103—22no—
33#15692980C2211yescharacteristic
34#15692954C2212yescomplemented
35#15692952C2212yescomplemented
36#15692946C2212yescomplemented
37#15692943C2212yescomplemented
38C2×#41×C103C2211yescharacteristic
39C22×C8×C103C2211yescharacteristic
40#117×C103C2211yescharacteristic
41#103×C103C2212yescomplemented
42#102×C103C2212yescomplemented
43C23×D103D411yescharacteristic
44#13110105—22no—
45#13110105—22no—
46C2×Dic206C2311yescharacteristic
47C2×D412—22no—
48C2×D412C2311yescharacteristic
49C2×C22⋊D103—21no—
50C2×C22⋊D103—22no—
51C22×Dic103D411yescharacteristic
52C2×C4×D103—22no—
53C2×C4×D103—22no—
54C2×C4×D103—21no—
55C2×C4×D103D412yes—
56C2×C4×D103C2312yes—
57#13110095—22no—
58#13110093—22no—
59#13110092—22no—
60#13110090—22no—
61C2×C103⋊C8D414yescomplemented
62C2×C103⋊C8C2311yescharacteristic
63C2×C103⋊C8C2311yescharacteristic
64C8×D103—24no—
65C8×D103—24no—
66C4⋊Dic103—22no—
67C4⋊Dic103C2312yes—
68Dic103⋊C4—22no—
69C22⋊Dic103—21no—
70C22⋊Dic103—22no—
71(C2×D103)⋊C4—22no—
72(C2×D103)⋊C4—22no—
73(C2×D103)⋊C4—22no—
74C4×Dic103—21no—
75#41×C103—22no—
76#41×C103—22no—
77C2×Q8×C103C2311yescharacteristic
78C2×D4×C103—21no—
79C2×D4×C103C2311yescharacteristic
80C22×C4×C103—21no—
81C22×C4×C103C2311yescharacteristic
82C2×C8×C103—22no—
83C2×C8×C103C2312yes—
84C4⋊C4×C103C2312yes—
85C22⋊C4×C103—21no—
86C42×C103—21no—
87C23×C103—21no—
88C23×C103C2×D411yescharacteristic
89C22×D103—22no—
90C22×D103—24no—
91C22×D103—21no—
92C22×D103C2×D412yes—
93Q8×C103—21no—
94Q8×C103—21no—
95D4×C103—21no—
96D4×C103—21no—
97D4×C103—42no—
98C2×C4×C103—22no—
99C2×C4×C103—21no—
100C2×C4×C103—42no—
101C2×C4×C103C2×D412yes—
102C2×C4×C103C2×D411yescharacteristic
103C2×C4×C103#4112yes—
104C2×C4×C103C2411yescharacteristic
105C22⋊D103—42no—
106C22⋊D103—44no—
107C2×Dic103—22no—
108C2×Dic103—22no—
109C2×Dic103—21no—
110C2×Dic103C2×D412yes—
111D412—21no—
112D412—21no—
113D412—44no—
114C4×D103—24no—
115C4×D103—22no—
116C4×D103—22no—
117C4×D103—42no—
118Dic206—21no—
119Dic206—21no—
120C8×C103—22no—
121C103⋊C8C2×D412yes—
122C103⋊C8C2×D412yes—
123C22×C103—22no—
124C22×C103—41no—
125C22×C103—42no—
126C22×C103#12112yes—
127C22×C103C22×D411yescharacteristic
128C2×D103—28no—
129C2×D103—22no—
130C2×D103—22no—
131C2×D103—41no—
132C2×D103—42no—
133C2×D103#13514yescomplemented
134C4×C103—41no—
135C4×C103—42no—
136C4×C103#12112yes—
137C4×C103C22×D411yescharacteristic
138C4×C103C2×#4111yescharacteristic
139Dic103—22no—
140Dic103—41no—
141Dic103—42no—
142C2×C103—22no—
143C2×C103—81no—
144C2×C103C2×#12111yescharacteristic
145C2×C103C2×#13512yes—
146D103—24no—
147D103—81no—
148#3050—1031nomaximal, Sylow
149C103#305011yescharacteristic, complemented, Sylow
150C2×#135—1031no—
151C23×C8—1031no—
152#525—1031no—
153#525—1031no—
154#467—1032no—
155#466—1032no—
156#465—1032no—
157#465—1032no—
158#427—1031no—
159#416—1031no—
160#416D10311yescharacteristic, complemented
161C2×#41—1031no—
162C2×#41C2×D10311yescharacteristic
163C23×C4—1031no—
164#135—2064no—
165C2×Q16—1031no—
166C2×SD16—1031no—
167C2×SD16—1031no—
168C2×D8—1031no—
169C22×C8—1031no—
170C22×C8—1032no—
171C22×C8—1032no—
172C22×C8—2064no—
173C22×C8C2×D10311yescharacteristic
174#123—2061no—
175#123—2061no—
176C22⋊Q8—1032no—
177C22⋊Q8—1032no—
178#121—1032no—
179#121—1032no—
180#120—2061no—
181#120—2061no—
182C4×D4—2062no—
183C4×D4—2062no—
184#117—1031no—
185#117C2×D10311yescharacteristic
186#107—1032no—
187#106—1032no—
188#103—1032no—
189#103C2×D10312yescomplemented
190#102—1032no—
191#102C2×D10312yescomplemented
192C24—1031no—
193#41—22no—
194#41—22no—
195#41—2062no—
196#41—2062no—
197C2×Q8—1031no—
198C2×Q8C22×D10311yescharacteristic
199C2×D4—21no—
200C2×D4—1031no—
201C2×D4—2062no—
202C2×D4—2062no—
203C2×D4—2061no—
204C2×D4C22×D10311yescharacteristic
205C22×C4—21no—
206C22×C4—1031no—
207C22×C4—1032no—
208C22×C4—1032no—
209C22×C4—2061no—
210C22×C4—2062no—
211C22×C4—2062no—
212C22×C4C22×D10311yescharacteristic
213Q16—2062no—
214SD16—2062no—
215SD16—2062no—
216D8—2062no—
217C2×C8—22no—
218C2×C8—1034no—
219C2×C8—1031no—
220C2×C8—1031no—
221C2×C8—2064no—
222C2×C8—2064no—
223C2×C8C22×D10312yes—
224C4⋊C4—1032no—
225C4⋊C4—2062no—
226C4⋊C4—2062no—
227C4⋊C4C22×D10312yes—
228C22⋊C4—21no—
229C22⋊C4—2062no—
230C22⋊C4—2062no—
231C22⋊C4—2062no—
232C22⋊C4—2062no—
233C22⋊C4—2061no—
234C42—21no—
235C42—2061no—
236C23—21no—
237C23—1032no—
238C23—2064no—
239C23—2061no—
240C23—2062no—
241C23D4×D10311yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—2061no—
245Q8—2061no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—4124no—
250D4—4124no—
251D4—4122no—
252D4—2061no—
253D4—2061no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—1032no—
258C2×C4—4122no—
259C2×C4—2062no—
260C2×C4—2061no—
261C2×C4—2062no—
262C2×C4—2062no—
263C2×C4—2062no—
264C2×C4—2064no—
265C2×C4D4×D10312yes—
266C2×C4D4×D10311yescharacteristic
267C2×C4#1311010512yes—
268C2×C4C23×D10311yescharacteristic
269C8—22no—
270C8—1032no—
271C8—1032no—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—1034no—
276C22—4122no—
277C22—4121no—
278C22—2068no—
279C22—2062no—
280C22—2062no—
281C22#1569299412yes—
282C22C2×D4×D10311yescharacteristic
283C4—42no—
284C4—41no—
285C4—4122no—
286C4—4121no—
287C4—2062no—
288C4#1569299412yes—
289C4C2×D4×D10311yescharacteristic
290C4C2×#1311010511yescharacteristic
291C2—22no—
292C2—81no—
293C2—8241no—
294C2—2064no—
295C2C2×#1569299411yescharacteristic
296C2#135×D10312yes—
subgroupG/H
centerC2×C4D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#416×C103C2
socleC22×C103C22×D4
hypercenter#416D103
hypocenterC103#3050
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#15693041C2semidirect
2. C22×C8×D103C2semidirect
3. #20268303C2semidirect
4. #20268298C2semidirect
5. #20268031C2semidirect
6. #20268026C2semidirect
7. #20268023C2semidirect
8. #20268019C2semidirect
9. #20267827C2semidirect
10. #20267788C2semidirect
11. #416×C103C2semidirect
15. C2×#13110095C22semidirect
16. C2×#13110093C22semidirect
17. C2×#13110092C22semidirect
18. C2×#13110090C22semidirect
34. #15692954C22semidirect
35. #15692952C22semidirect
36. #15692946C22semidirect
37. #15692943C22semidirect
41. #103×C103C22semidirect
42. #102×C103C22semidirect
61. C2×C103⋊C8D4semidirect
133. C2×D103#135semidirect
149. C103#3050semidirect
160. #416D103semidirect
189. #103C2×D103semidirect
191. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930412
C22×C8×D1032
#202683032
#202682982
#202680312
#202680262
#202680232
#202680192
#202678272
#202677882
#416×C1032
#3050103