Finite Group Databasebeta

← #27204500

Subgroups — #27204500

Order 13184.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15693066C211yesmaximal, characteristic, complemented
2#20268589C212yesmaximal, complemented
3#20267968C214yesmaximal, complemented
4#20267958C214yesmaximal, complemented
5#20267809C212yesmaximal, complemented
6C2×#15692938C211yesmaximal, characteristic, complemented
7#535×C103C211yesmaximal, characteristic, complemented
8#15693066—24no—
9#15693066—22no—
10#15693066C2214yes—
11C2×#13110105C2212yes—
12C2×#13110104—22no—
13C22×C22⋊D103—22no—
14C2×D4×D103—22no—
15#15693052C2214yescomplemented
16#15693051—22no—
17#15693047C2214yescomplemented
18#15693046—22no—
19#15693041—24no—
20C2×#13110089C2212yescomplemented
21#15692949C2218yescomplemented
22#15692938C2214yescomplemented
23C2×#41×C103C2211yescharacteristic, complemented
24C22×D4×C103C2211yescharacteristic
25#127×C103C2212yescomplemented
26#124×C103C2212yescomplemented
27#121×C103—22no—
28#120×C103—22no—
29#117×C103C2211yescharacteristic, complemented
30C23×D103—22no—
31#13110105—22no—
32#13110105—22no—
33#13110105D414yescomplemented
34#13110105C2314yes—
35#13110104—28no—
36#13110104—28no—
37C2×Dic206D412yescomplemented
38C2×D412D412yescomplemented
39C2×C22⋊D103—24no—
40C2×C22⋊D103—28no—
41C2×C22⋊D103—22no—
42C2×C22⋊D103—28no—
43D4×D103—28no—
44D4×D103—28no—
45C22×Dic103—22no—
46C2×C4×D103—22no—
47#13110095—24no—
48#13110093—24no—
49#13110092—24no—
50#13110090—24no—
51#13110089—22no—
52#13110089C2314yescomplemented
53C2×C103⋊C8—22no—
54C24×C103D412yes—
55#41×C103—22no—
56#41×C103—22no—
57C2×Q8×C103C2311yescharacteristic, complemented
58C2×D4×C103—21no—
59C2×D4×C103—24no—
60C2×D4×C103—22no—
61C2×D4×C103—22no—
62C2×D4×C103D412yes—
63C2×D4×C103C2312yes—
64C2×D4×C103C2311yescharacteristic, complemented
65C22×C4×C103—21no—
66C22×C4×C103C2311yescharacteristic
67C4⋊C4×C103—21no—
68C22⋊C4×C103—21no—
69C22⋊C4×C103—24no—
70C42×C103C2312yescomplemented
71C23×C103—22no—
72C23×C103—22no—
73C23×C103—21no—
74C23×C103—82no—
75C23×C103C2×D414yes—
76C23×C103C2×D411yescharacteristic
77C22×D103—22no—
78C22×D103—28no—
79C22×D103—84no—
80Q8×C103—22no—
81D4×C103—24no—
82D4×C103—24no—
83D4×C103—22no—
84D4×C103—41no—
85D4×C103—41no—
86D4×C103—84no—
87C2×C4×C103—22no—
88C2×C4×C103—21no—
89C2×C4×C103—42no—
90C2×C4×C103C2×D412yes—
91C2×C4×C103C2×D412yes—
92C2×C4×C103C2×D411yescharacteristic
93C2×C4×C103C2411yescharacteristic
94C22⋊D103—216no—
95C22⋊D103—24no—
96C22⋊D103—24no—
97C2×Dic103—28no—
98C2×Dic103—22no—
99D412—22no—
100D412C2×D414yes—
101C4×D103—24no—
102C4×D103—24no—
103Dic206—22no—
104Dic206C2×D414yes—
105C103⋊C8—24no—
106C22×C103—24no—
107C22×C103—41no—
108C22×C103—44no—
109C22×C103—44no—
110C22×C103—42no—
111C22×C103—41no—
112C22×C103—82no—
113C22×C103#12011yescharacteristic
114C22×C103#12011yescharacteristic
115C22×C103C22×D411yescharacteristic
116C2×D103—24no—
117C2×D103—44no—
118C2×D103—88no—
119C4×C103—42no—
120C4×C103—41no—
121C4×C103#12012yes—
122C4×C103C22×D412yes—
123Dic103—24no—
124C2×C103—21no—
125C2×C103—21no—
126C2×C103—21no—
127C2×C103—44no—
128C2×C103—81no—
129C2×C103C2×#12011yescharacteristic
130D103—44no—
131#3019—1031nomaximal, Sylow
132C103#301911yescharacteristic, complemented, Sylow
133C2×H(5,𝔽2)—1031no—
134#575—1032no—
135#535D10311yescharacteristic, complemented
136#455—1034no—
137#453—1034no—
138#421—1032no—
139C2×#100—1031no—
140H(5,𝔽2)—1034no—
141H(5,𝔽2)—2064no—
142H(5,𝔽2)—2062no—
143C2×#41—1032no—
144C2×#41—2062no—
145C2×#41C2×D10311yescharacteristic, complemented
146C22×D4—2062no—
147C22×D4—2062no—
148C22×D4C2×D10311yescharacteristic
149#137—1034no—
150#137—2062no—
151AGL(1,ℤ/8)—1034no—
152AGL(1,ℤ/8)—2062no—
153#135—2064no—
154C2×M16—1032no—
155#127C2×D10312yescomplemented
156#124C2×D10312yescomplemented
157#121—22no—
158#120—22no—
159#117C2×D10311yescharacteristic, complemented
160#104—1038no—
161#100—1034no—
162C24—2062no—
163C24C22⋊D10312yes—
164#41—22no—
165#41—22no—
166#41—1034no—
167#41—1034no—
168#41—2068no—
169#41—2068no—
170#41—2062no—
171#41—2062no—
172C2×Q8—1032no—
173C2×Q8C22×D10311yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—1032no—
179C2×D4—2068no—
180C2×D4—2068no—
181C2×D4—2064no—
182C2×D4—2068no—
183C2×D4—2062no—
184C2×D4—2068no—
185C2×D4C22⋊D10312yes—
186C2×D4C22×D10312yes—
187C2×D4C22×D10311yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—2062no—
190C22×C4—2062no—
191C22×C4C22×D10311yescharacteristic
192Q16—2064no—
193SD16—2064no—
194SD16—2064no—
195D8—2064no—
196M16—1034no—
197M16—2062no—
198C2×C8—2062no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D10312yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—8244no—
208C23—2068no—
209C23—2062no—
210C23C2×C22⋊D10314yes—
211C23C2×C22⋊D10311yescharacteristic
212Q8—22no—
213Q8—1034no—
214Q8—2062no—
215D4—24no—
216D4—22no—
217D4—24no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—1034no—
222D4—20616no—
223D4—2064no—
224D4—2064no—
225D4—2062no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—2068no—
230C2×C4—2062no—
231C2×C4—2064no—
232C2×C4—2064no—
233C2×C4D4×D10312yes—
234C2×C4D4×D10312yes—
235C2×C4C2×C22⋊D10311yescharacteristic
236C2×C4C23×D10311yescharacteristic
237C8—2064no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—8248no—
246C22—4124no—
247C22—2064no—
248C22#1569298911yescharacteristic
249C22#1569298911yescharacteristic
250C22C22×C22⋊D10311yescharacteristic
251C4—42no—
252C4—41no—
253C4—2064no—
254C4#1569298912yes—
255C4C2×D4×D10312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—4124no—
262C2C2×#1569298911yescharacteristic
subgroupG/H
centerC2C2×#15692989
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#535×C103C2
socleC2×C103C2×#120
hypercenter#535D103
hypocenterC103#3019
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#15693066C2semidirect
2. #20268589C2semidirect
3. #20267968C2semidirect
4. #20267958C2semidirect
5. #20267809C2semidirect
6. C2×#15692938C2semidirect
7. #535×C103C2semidirect
15. #15693052C22semidirect
17. #15693047C22semidirect
20. C2×#13110089C22semidirect
21. #15692949C22semidirect
22. #15692938C22semidirect
23. C2×#41×C103C22semidirect
25. #127×C103C22semidirect
26. #124×C103C22semidirect
29. #117×C103C22semidirect
33. #13110105D4semidirect
37. C2×Dic206D4semidirect
38. C2×D412D4semidirect
52. #13110089C23semidirect
57. C2×Q8×C103C23semidirect
64. C2×D4×C103C23semidirect
70. C42×C103C23semidirect
132. C103#3019semidirect
135. #535D103semidirect
145. C2×#41C2×D103semidirect
155. #127C2×D103semidirect
156. #124C2×D103semidirect
159. #117C2×D103semidirect
173. C2×Q8C22×D103semidirect
187. C2×D4C22×D103semidirect
202. C42C22×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930662
#202685892
#202679682
#202679582
#202678092
C2×#156929382
#535×C1032
#3019103