Finite Group Databasebeta

← #27204516

Subgroups — #27204516

Order 13184.

736 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 161 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×#15693046C212yesmaximal, complemented
2#20268355C211yesmaximal, characteristic, complemented
3#20267964C214yesmaximal, complemented
4#20267959C214yesmaximal, complemented
5#20267808C212yesmaximal, complemented
6#20267775C211yesmaximal, characteristic, complemented
7#585×C103C211yesmaximal, characteristic, complemented
8C22×D412C2211yescharacteristic, complemented
9#15693046—24no—
10#15693046C2218yescomplemented
11C2×#13110092—22no—
12C2×#13110090—22no—
13C2×#13110089C2212yescomplemented
14#15693017C2212yescomplemented
15#15693010C2212yescomplemented
16#15692995—22no—
17#15692989—22no—
18#15692980C2211yescharacteristic, complemented
19#15692948C2218yescomplemented
20#15692940C2212yescomplemented
21#15692938C2212yescomplemented
222−1+4×C103—22no—
232−1+4×C103C2212yescomplemented
24H(5,𝔽2)×C103—22no—
25H(5,𝔽2)×C103—22no—
26H(5,𝔽2)×C103C2212yescomplemented
27C2×#41×C103—24no—
28C2×#41×C103—22no—
29C2×#41×C103C2212yes—
30C2×#41×C103C2211yescharacteristic
31C23×D103—21no—
32C2×D412—22no—
33C2×D412—22no—
34C2×D412—21no—
35C2×D412C2312yes—
36C2×C22⋊D103—24no—
37#13110092—28no—
38#13110090—28no—
39#13110089—22no—
40#13110089C2314yes—
41C2×C103⋊C8—22no—
42C4⋊Dic103—21no—
43C22⋊Dic103—21no—
44(C2×D103)⋊C4—24no—
45C4×Dic103C2312yes—
46#41×C103—24no—
47#41×C103—28no—
48#41×C103—24no—
49#41×C103—24no—
50#41×C103—24no—
51#41×C103—22no—
52#41×C103—22no—
53#41×C103—24no—
54#41×C103—22no—
55#41×C103—22no—
56#41×C103D414yescomplemented
57#41×C103C2314yes—
58C2×Q8×C103—22no—
59C2×Q8×C103—24no—
60C2×Q8×C103D412yescomplemented
61C2×Q8×C103C2311yescharacteristic
62C2×D4×C103—28no—
63C2×D4×C103—22no—
64C2×D4×C103—24no—
65C2×D4×C103—22no—
66C2×D4×C103—24no—
67C2×D4×C103D412yes—
68C2×D4×C103D412yescomplemented
69C2×D4×C103C2311yescharacteristic
70C22×C4×C103—24no—
71C22×C4×C103—22no—
72C22×C4×C103D412yes—
73C22×C4×C103C2311yescharacteristic
74C23×C103—24no—
75C23×C103—22no—
76C23×C103C2×D412yes—
77C23×C103C2×D411yescharacteristic
78C22×D103—22no—
79C22×D103—42no—
80C22×D103—82no—
81Q8×C103—24no—
82Q8×C103—22no—
83Q8×C103—22no—
84Q8×C103C2×D414yes—
85D4×C103—28no—
86D4×C103—24no—
87D4×C103—24no—
88D4×C103—24no—
89D4×C103—24no—
90D4×C103—22no—
91D4×C103—22no—
92D4×C103C2×D414yes—
93C2×C4×C103—24no—
94C2×C4×C103—28no—
95C2×C4×C103—22no—
96C2×C4×C103—24no—
97C2×C4×C103—22no—
98C2×C4×C103—22no—
99C2×C4×C103—24no—
100C2×C4×C103C2×D412yes—
101C2×C4×C103C2×D411yescharacteristic
102C2×C4×C103C2×D412yes—
103C2×C4×C103C2×D412yes—
104C2×C4×C103C2411yescharacteristic
105C22⋊D103—84no—
106C2×Dic103—22no—
107D412—24no—
108D412—41no—
109D412—41no—
110C103⋊C8—24no—
111C22×C103—22no—
112C22×C103—24no—
113C22×C103—41no—
114C22×C103—42no—
115C22×C103—82no—
116C22×C103—84no—
117C22×C103#12012yes—
118C22×C103C22×D411yescharacteristic
119C2×D103—44no—
120C2×D103—42no—
121C2×D103—84no—
122C4×C103—24no—
123C4×C103—22no—
124C4×C103#12011yescharacteristic
125C4×C103#12011yescharacteristic
126C4×C103C22×D412yes—
127Dic103—42no—
128C2×C103—21no—
129C2×C103—22no—
130C2×C103—42no—
131C2×C103—44no—
132C2×C103C2×#12011yescharacteristic
133D103—82no—
134#3021—1031nomaximal, Sylow
135C103#302111yescharacteristic, complemented, Sylow
136#585D10311yescharacteristic, complemented
137C2×AGL(1,ℤ/8)—1032no—
138#535—1031no—
139#454—1034no—
140#453—1034no—
141#421—1032no—
142#413—1031no—
1432−1+4—22no—
1442−1+4C2×D10312yescomplemented
145H(5,𝔽2)—22no—
146H(5,𝔽2)—22no—
147H(5,𝔽2)C2×D10312yescomplemented
148C2×#41—24no—
149C2×#41—22no—
150C2×#41C2×D10312yes—
151C2×#41C2×D10311yescharacteristic
152C22×D4—1031no—
153AGL(1,ℤ/8)—1038no—
154AGL(1,ℤ/8)—2064no—
155C2×SD16—2062no—
156C2×D8—2062no—
157C2×M16—1032no—
158#127—1032no—
159#124—1032no—
160#121—2062no—
161#120—2062no—
162#117—1031no—
163#104—1038no—
164#101—1032no—
165#100—1032no—
166C24—2061no—
167#41—24no—
168#41—28no—
169#41—24no—
170#41—24no—
171#41—24no—
172#41—22no—
173#41—22no—
174#41—24no—
175#41—22no—
176#41—22no—
177#41C22⋊D10314yescomplemented
178#41C22×D10314yes—
179C2×Q8—22no—
180C2×Q8—24no—
181C2×Q8C22⋊D10312yescomplemented
182C2×Q8C22×D10311yescharacteristic
183C2×D4—28no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4—22no—
187C2×D4—24no—
188C2×D4—1032no—
189C2×D4—2064no—
190C2×D4—2061no—
191C2×D4—2062no—
192C2×D4—2062no—
193C2×D4C22⋊D10312yes—
194C2×D4C22⋊D10312yescomplemented
195C2×D4C22×D10311yescharacteristic
196C22×C4—24no—
197C22×C4—22no—
198C22×C4C22⋊D10312yes—
199C22×C4C22×D10311yescharacteristic
200SD16—2068no—
201D8—2068no—
202M16—1034no—
203M16—2062no—
204C2×C8—2062no—
205C4⋊C4—2061no—
206C22⋊C4—2061no—
207C22⋊C4—2064no—
208C42—1032no—
209C23—24no—
210C23—22no—
211C23—8242no—
212C23—4122no—
213C23—2062no—
214C23C2×C22⋊D10312yes—
215C23C2×C22⋊D10311yescharacteristic
216Q8—24no—
217Q8—22no—
218Q8—22no—
219Q8C2×C22⋊D10314yes—
220D4—28no—
221D4—24no—
222D4—24no—
223D4—24no—
224D4—24no—
225D4—22no—
226D4—22no—
227D4—8244no—
228D4—4121no—
229D4—4121no—
230D4—2064no—
231D4C2×C22⋊D10314yes—
232C2×C4—24no—
233C2×C4—28no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—2062no—
240C2×C4C2×C22⋊D10312yes—
241C2×C4C2×C22⋊D10312yes—
242C2×C4C2×C22⋊D10312yes—
243C2×C4C2×C22⋊D10311yescharacteristic
244C2×C4C23×D10311yescharacteristic
245C8—2064no—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—42no—
250C22—82no—
251C22—84no—
252C22—8244no—
253C22—4124no—
254C22—4122no—
255C22#1569299012yes—
256C22C22×C22⋊D10311yescharacteristic
257C4—24no—
258C4—22no—
259C4—4122no—
260C4#1569299011yescharacteristic
261C4#1569299011yescharacteristic
262C4C22×C22⋊D10312yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—44no—
267C2—8242no—
268C2C2×#1569299011yescharacteristic
subgroupG/H
centerC2C2×#15692990
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#585×C103C2
socleC2×C103C2×#120
hypercenter#585D103
hypocenterC103#3021
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#15693046C2semidirect
2. #20268355C2semidirect
3. #20267964C2semidirect
4. #20267959C2semidirect
5. #20267808C2semidirect
6. #20267775C2semidirect
7. #585×C103C2semidirect
8. C22×D412C22semidirect
10. #15693046C22semidirect
13. C2×#13110089C22semidirect
14. #15693017C22semidirect
15. #15693010C22semidirect
18. #15692980C22semidirect
19. #15692948C22semidirect
20. #15692940C22semidirect
21. #15692938C22semidirect
23. 2−1+4×C103C22semidirect
26. H(5,𝔽2)×C103C22semidirect
56. #41×C103D4semidirect
60. C2×Q8×C103D4semidirect
68. C2×D4×C103D4semidirect
135. C103#3021semidirect
136. #585D103semidirect
144. 2−1+4C2×D103semidirect
147. H(5,𝔽2)C2×D103semidirect
177. #41C22⋊D103semidirect
181. C2×Q8C22⋊D103semidirect
194. C2×D4C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930462
#202683552
#202679642
#202679592
#202678082
#202677752
#585×C1032
#3021103