Finite Group Databasebeta

← #27204722

Subgroups — #27204722

Order 13184.

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

normal subgroups only

This group has 520 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×#15693041C211yesmaximal, characteristic, complemented
2C23×C103⋊C8C211yesmaximal, characteristic, complemented
3#20268302C211yesmaximal, characteristic, complemented
4#20268030C212yesmaximal, complemented
5#20268025C212yesmaximal, complemented
6#20268022C212yesmaximal, complemented
7#20268018C212yesmaximal, complemented
8#20267827C211yesmaximal, characteristic, complemented
9#20267787C211yesmaximal, characteristic, complemented
10#20267785C211yesmaximal, characteristic, complemented
11#525×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13#15693041—24no—
14C2×#13110095C2211yescharacteristic, complemented
15C2×#13110093C2211yescharacteristic, complemented
16C2×#13110092C2211yescharacteristic, complemented
17C2×#13110090C2211yescharacteristic, complemented
18C22×C103⋊C8—24no—
19C22×C103⋊C8C2211yescharacteristic
20C22×C103⋊C8C2212yes—
21C22×C103⋊C8C2212yes—
22C22×C103⋊C8C2211yescharacteristic
23#15693004—21no—
24#15693000C2212yes—
25#15692995C2212yes—
26#15692990—21no—
27C4×C22⋊D103—22no—
28#15692980C2211yescharacteristic
29#15692954C2212yescomplemented
30#15692952C2212yescomplemented
31#15692945C2212yescomplemented
32#15692944C2212yescomplemented
33#15692942C2212yescomplemented
34#15692941C2212yescomplemented
35C2×#41×C103C2211yescharacteristic
36C23×C4×C103C2211yescharacteristic
37#123×C103—21no—
38C22⋊Q8×C103C2212yes—
39#121×C103C2212yes—
40#120×C103—21no—
41C4×D4×C103—22no—
42#117×C103C2211yescharacteristic
43#13110105—22no—
44#13110105—22no—
45C2×Dic206C2311yescharacteristic
46C2×D412C2311yescharacteristic
47C2×C22⋊D103—21no—
48C2×C22⋊D103—22no—
49C2×C4×D103—21no—
50#13110095—22no—
51#13110093—22no—
52#13110092—22no—
53#13110090—22no—
54C2×C103⋊C8—22no—
55C2×C103⋊C8—24no—
56C2×C103⋊C8—24no—
57C2×C103⋊C8D414yescomplemented
58C2×C103⋊C8C2312yes—
59C2×C103⋊C8C2311yescharacteristic
60C2×C103⋊C8C2311yescharacteristic
61C4⋊Dic103C2312yes—
62Dic103⋊C4—22no—
63C22⋊Dic103—21no—
64C22⋊Dic103—22no—
65(C2×D103)⋊C4—22no—
66C4×Dic103—21no—
67C24×C103D411yescharacteristic
68#41×C103—22no—
69#41×C103—22no—
70C2×Q8×C103C2311yescharacteristic
71C2×D4×C103—22no—
72C2×D4×C103—21no—
73C2×D4×C103C2311yescharacteristic
74C22×C4×C103—22no—
75C22×C4×C103—22no—
76C22×C4×C103—21no—
77C22×C4×C103D412yes—
78C22×C4×C103D411yescharacteristic
79C22×C4×C103C2312yes—
80C22×C4×C103C2311yescharacteristic
81C4⋊C4×C103—22no—
82C4⋊C4×C103C2312yes—
83C22⋊C4×C103—21no—
84C22⋊C4×C103—22no—
85C22⋊C4×C103—22no—
86C42×C103—21no—
87C23×C103—22no—
88C23×C103—24no—
89C23×C103—21no—
90C23×C103C2×D411yescharacteristic
91C23×C103C2×D412yes—
92C22×D103—21no—
93Q8×C103—21no—
94Q8×C103—21no—
95D4×C103—21no—
96D4×C103—21no—
97D4×C103—42no—
98D4×C103—44no—
99C2×C4×C103—22no—
100C2×C4×C103—24no—
101C2×C4×C103—22no—
102C2×C4×C103—22no—
103C2×C4×C103—22no—
104C2×C4×C103—21no—
105C2×C4×C103—42no—
106C2×C4×C103C2×D412yes—
107C2×C4×C103C2×D412yes—
108C2×C4×C103C2×D411yescharacteristic
109C2×C4×C103#4112yes—
110C2×C4×C103C2411yescharacteristic
111C22⋊D103—42no—
112C22⋊D103—44no—
113C2×Dic103—22no—
114C2×Dic103—21no—
115D412—21no—
116D412—21no—
117C4×D103—42no—
118Dic206—21no—
119Dic206—21no—
120C103⋊C8—22no—
121C103⋊C8C2×D412yes—
122C103⋊C8C2×D412yes—
123C22×C103—28no—
124C22×C103—22no—
125C22×C103—22no—
126C22×C103—22no—
127C22×C103—41no—
128C22×C103—42no—
129C22×C103#12112yes—
130C22×C103#13514yescomplemented
131C22×C103C22×D411yescharacteristic
132C2×D103—41no—
133C2×D103—42no—
134C4×C103—22no—
135C4×C103—41no—
136C4×C103—42no—
137C4×C103#12112yes—
138C4×C103C22×D411yescharacteristic
139C4×C103C2×#4111yescharacteristic
140Dic103—41no—
141Dic103—42no—
142C2×C103—22no—
143C2×C103—24no—
144C2×C103—81no—
145C2×C103C2×#12111yescharacteristic
146C2×C103C2×#13512yes—
147D103—81no—
148#3050—1031nomaximal, Sylow
149C103#305011yescharacteristic, complemented, Sylow
150C2×#135—1031no—
151C23×C8—1031no—
152#525—1031no—
153#525D10311yescharacteristic, complemented
154#467—1032no—
155#466—1032no—
156#465—1032no—
157#465—1032no—
158#427—1031no—
159#416—1031no—
160#416—1031no—
161C2×#41—1031no—
162C2×#41C2×D10311yescharacteristic
163C23×C4C2×D10311yescharacteristic
164#135—2064no—
165C2×Q16—1031no—
166C2×SD16—1031no—
167C2×SD16—1031no—
168C2×D8—1031no—
169C22×C8—1031no—
170C22×C8—1031no—
171C22×C8—1032no—
172C22×C8—1032no—
173C22×C8—2064no—
174#123—21no—
175#123—2061no—
176C22⋊Q8—1032no—
177C22⋊Q8C2×D10312yes—
178#121—1032no—
179#121C2×D10312yes—
180#120—21no—
181#120—2061no—
182C4×D4—22no—
183C4×D4—2062no—
184#117—1031no—
185#117C2×D10311yescharacteristic
186#107—1032no—
187#106—1032no—
188#103—1032no—
189#103—1032no—
190#102—1032no—
191#102—1032no—
192C24C22⋊D10311yescharacteristic
193#41—22no—
194#41—22no—
195#41—2062no—
196#41—2062no—
197C2×Q8—1031no—
198C2×Q8C22×D10311yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—1031no—
202C2×D4—2062no—
203C2×D4—2061no—
204C2×D4C22×D10311yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—2061no—
209C22×C4C22⋊D10311yescharacteristic
210C22×C4C22⋊D10312yes—
211C22×C4C22×D10312yes—
212C22×C4C22×D10311yescharacteristic
213Q16—2062no—
214SD16—2062no—
215SD16—2062no—
216D8—2062no—
217C2×C8—1034no—
218C2×C8—1031no—
219C2×C8—1031no—
220C2×C8—1032no—
221C2×C8—2064no—
222C2×C8—2064no—
223C2×C8—2062no—
224C4⋊C4—22no—
225C4⋊C4—1032no—
226C4⋊C4—2062no—
227C4⋊C4C22×D10312yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—2061no—
232C22⋊C4—2062no—
233C22⋊C4—2062no—
234C42—21no—
235C42—2061no—
236C23—22no—
237C23—24no—
238C23—21no—
239C23—2061no—
240C23C2×C22⋊D10311yescharacteristic
241C23C2×C22⋊D10312yes—
242Q8—21no—
243Q8—21no—
244Q8—2061no—
245Q8—2061no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—44no—
250D4—4122no—
251D4—4124no—
252D4—2061no—
253D4—2061no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—24no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—4122no—
262C2×C4—2062no—
263C2×C4—2061no—
264C2×C4D4×D10312yes—
265C2×C4C2×C22⋊D10312yes—
266C2×C4C2×C22⋊D10311yescharacteristic
267C2×C4#1311010412yes—
268C2×C4C23×D10311yescharacteristic
269C8—1032no—
270C8—1032no—
271C8—2062no—
272C22—28no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—41no—
278C22—4122no—
279C22—4121no—
280C22#1569299312yes—
281C22#1569304114yescomplemented
282C22C22×C22⋊D10311yescharacteristic
283C4—22no—
284C4—42no—
285C4—41no—
286C4—4122no—
287C4—4121no—
288C4#1569299312yes—
289C4C2×D4×D10311yescharacteristic
290C4C2×#1311010411yescharacteristic
291C2—22no—
292C2—24no—
293C2—81no—
294C2—8241no—
295C2C2×#1569299311yescharacteristic
296C2C2×#1569304112yes—
subgroupG/H
centerC2×C4C2×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#525×C103C2
socleC22×C103C22×D4
hypercenter#525D103
hypocenterC103#3050
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#15693041C2semidirect
2. C23×C103⋊C8C2semidirect
3. #20268302C2semidirect
4. #20268030C2semidirect
5. #20268025C2semidirect
6. #20268022C2semidirect
7. #20268018C2semidirect
8. #20267827C2semidirect
9. #20267787C2semidirect
10. #20267785C2semidirect
11. #525×C103C2semidirect
14. C2×#13110095C22semidirect
15. C2×#13110093C22semidirect
16. C2×#13110092C22semidirect
17. C2×#13110090C22semidirect
29. #15692954C22semidirect
30. #15692952C22semidirect
31. #15692945C22semidirect
32. #15692944C22semidirect
33. #15692942C22semidirect
34. #15692941C22semidirect
57. C2×C103⋊C8D4semidirect
130. C22×C103#135semidirect
149. C103#3050semidirect
153. #525D103semidirect
281. C22#15693041semidirect

Maximal subgroups

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

subgroupindex
C2×#156930412
C23×C103⋊C82
#202683022
#202680302
#202680252
#202680222
#202680182
#202678272
#202677872
#202677852
#525×C1032
#3050103