Finite Group Databasebeta

← #27205891

Subgroups — #27205891

Order 13184.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#121×D103C212yesmaximal, complemented
2#20268106C212yesmaximal, complemented
3#20268103C212yesmaximal, complemented
4#20268027C211yesmaximal, characteristic, complemented
5#20268025C212yesmaximal, complemented
6#20267926C212yesmaximal, complemented
7#20267923C212yesmaximal, complemented
8C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
9#466×C103C211yesmaximal, characteristic, complemented
10C2×D4×D103—22no—
11C2×D4×D103C2212yescomplemented
12C22×C4×D103C2211yescharacteristic
13C2×D824C2211yescharacteristic, complemented
14C2×#13110090C2212yescomplemented
15C22×C103⋊C8C2211yescharacteristic, complemented
16#15692996C2212yes—
17#15692995C2212yescomplemented
18#15692994—22no—
19#15692993—22no—
20#15692992C2212yes—
21C4⋊C4×D103C2212yescomplemented
22C22⋊C4×D103—22no—
23#15692955C2211yescharacteristic, complemented
24#15692954C2212yescomplemented
25#15692943C2212yescomplemented
26#15692942C2212yescomplemented
27#15692941C2212yescomplemented
28(C2×D103)⋊C8C2212yescomplemented
29(C2×D103)⋊C8C2212yescomplemented
30C2×D8×C103C2211yescharacteristic, complemented
31C22×C8×C103C2211yescharacteristic, complemented
32#121×C103C2212yescomplemented
33#107×C103C2211yescharacteristic, complemented
34#102×C103C2212yescomplemented
35C23×D103—22no—
36C23×D103D411yescharacteristic
37C2×D412—22no—
38C2×D412C2312yes—
39C2×C22⋊D103—22no—
40C2×C22⋊D103—22no—
41C2×C22⋊D103—22no—
42D4×D103—42no—
43D4×D103—42no—
44D4×D103—48no—
45C22×Dic103D411yescharacteristic
46C2×C4×D103—22no—
47C2×C4×D103—41no—
48C2×C4×D103—41no—
49C2×C4×D103D412yes—
50C2×C4×D103C2312yes—
51D824—41no—
52#13110090—42no—
53C2×C103⋊C8—41no—
54C2×C103⋊C8C2312yes—
55C4⋊Dic103C2312yes—
56Dic103⋊C4—22no—
57C22⋊Dic103—22no—
58(C2×D103)⋊C4—22no—
59(C2×D103)⋊C4—22no—
60C2×D4×C103—22no—
61C2×D4×C103C2312yes—
62C22×C4×C103C2311yescharacteristic
63D8×C103—41no—
64C2×C8×C103—41no—
65C2×C8×C103C2311yescharacteristic
66C2×C8×C103C2311yescharacteristic
67C4⋊C4×C103C2312yes—
68C22⋊C4×C103—22no—
69C23×C103—22no—
70C23×C103C2×D411yescharacteristic
71C22×D103—22no—
72C22×D103—41no—
73C22×D103—41no—
74C22×D103—44no—
75C22×D103—44no—
76C22×D103—44no—
77C22×D103D814yescomplemented
78C22×D103C2×D412yes—
79D4×C103—22no—
80D4×C103—22no—
81D4×C103—44no—
82C2×C4×C103—21no—
83C2×C4×C103—21no—
84C2×C4×C103—22no—
85C2×C4×C103C2×D411yescharacteristic
86C2×C4×C103C2411yescharacteristic
87C22⋊D103—44no—
88C22⋊D103—44no—
89C22⋊D103—44no—
90C2×Dic103—22no—
91C2×Dic103—41no—
92C2×Dic103C2×D412yes—
93D412—22no—
94D412—22no—
95D412—44no—
96C4×D103—22no—
97C4×D103—22no—
98C4×D103—42no—
99C4×D103—44no—
100C8×C103—21no—
101C8×C103—21no—
102C103⋊C8—22no—
103C22×C103—21no—
104C22×C103—21no—
105C22×C103—42no—
106C22×C103—42no—
107C22×C103—42no—
108C22×C103C2×D812yes—
109C22×C103C22×D411yescharacteristic
110C2×D103—22no—
111C2×D103—22no—
112C2×D103—44no—
113C2×D103—42no—
114C2×D103—42no—
115C2×D103—42no—
116C2×D103—88no—
117C2×D103C2×D814yes—
118C4×C103—21no—
119C4×C103—42no—
120C4×C103H(5,𝔽2)11yescharacteristic
121C4×C103H(5,𝔽2)11yescharacteristic
122Dic103—22no—
123Dic103—42no—
124C2×C103—22no—
125C2×C103—82no—
126C2×C103#53411yescharacteristic
127C2×C103C22×D811yescharacteristic
128C2×C103#57511yescharacteristic
129D103—24no—
130D103—82no—
131#3186—1031nomaximal, Sylow
132C103#318611yescharacteristic, complemented, Sylow
133C2×#121—1032no—
134#480—1032no—
135#480—1032no—
136#466—1031no—
137#466—1032no—
138#466D10311yescharacteristic, complemented
139#447—1032no—
140#447—1032no—
141C2×C22⋊C8—1031no—
142C22×D4—1032no—
143C22×D4—2062no—
144C23×C4—1031no—
145C2×D8—1032no—
146C2×D8—1031no—
147C2×D8C2×D10311yescharacteristic, complemented
148C22×C8—1031no—
149C22×C8C2×D10311yescharacteristic, complemented
150#121—1032no—
151#121—1032no—
152#121—1032no—
153#121—2062no—
154#121—2062no—
155#121C2×D10312yescomplemented
156C2×C4⋊C4—1032no—
157C2×C22⋊C4—2062no—
158#107—1031no—
159#107—1032no—
160#107C2×D10311yescharacteristic, complemented
161#102—1032no—
162#102—1032no—
163#102—1032no—
164#102C2×D10312yescomplemented
165C22⋊C8—1032no—
166C22⋊C8—1032no—
167C24—1031no—
168C24—2062no—
169C2×D4—22no—
170C2×D4—1032no—
171C2×D4—4128no—
172C2×D4—4122no—
173C2×D4—4122no—
174C2×D4—2062no—
175C2×D4—2062no—
176C2×D4—2062no—
177C2×D4—2062no—
178C2×D4C22×D10312yes—
179C22×C4—1031no—
180C22×C4—1032no—
181C22×C4—1032no—
182C22×C4—4121no—
183C22×C4—4121no—
184C22×C4—2062no—
185C22×C4C22×D10311yescharacteristic
186D8—41no—
187D8—4121no—
188D8—4122no—
189C2×C8—41no—
190C2×C8—1032no—
191C2×C8—4121no—
192C2×C8C22×D10311yescharacteristic
193C2×C8C22×D10311yescharacteristic
194C4⋊C4—1032no—
195C4⋊C4—2062no—
196C4⋊C4C22×D10312yes—
197C22⋊C4—22no—
198C22⋊C4—2062no—
199C22⋊C4—2062no—
200C22⋊C4—2062no—
201C23—22no—
202C23—1034no—
203C23—1032no—
204C23—4121no—
205C23—4121no—
206C23—4124no—
207C23—4124no—
208C23—4124no—
209C23—2062no—
210C23D4×D10311yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—4124no—
215D4—4124no—
216D4—4124no—
217D4—4124no—
218D4—2062no—
219D4—2062no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—1032no—
224C2×C4—4122no—
225C2×C4—4124no—
226C2×C4—4121no—
227C2×C4—2062no—
228C2×C4—2062no—
229C2×C4—2062no—
230C2×C4D4×D10311yescharacteristic
231C2×C4C23×D10311yescharacteristic
232C8—21no—
233C8—21no—
234C8—2062no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—8248no—
241C22—1034no—
242C22—4124no—
243C22—4122no—
244C22—4122no—
245C22—4122no—
246C22—2062no—
247C22—2062no—
248C22D8×D10312yes—
249C22C2×D4×D10311yescharacteristic
250C4—21no—
251C4—42no—
252C4—4122no—
253C4—2062no—
254C4#1569306611yescharacteristic
255C4#1569306711yescharacteristic
256C2—22no—
257C2—82no—
258C2—8242no—
259C2—2064no—
260C2#2026834911yescharacteristic
261C2C2×D8×D10311yescharacteristic
262C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#466×C103C2
socleC22×C103C22×D4
hypercenter#466D103
hypocenterC103#3186
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D103C2semidirect
2. #20268106C2semidirect
3. #20268103C2semidirect
4. #20268027C2semidirect
5. #20268025C2semidirect
6. #20267926C2semidirect
7. #20267923C2semidirect
8. C2×(C2×D103)⋊C8C2semidirect
9. #466×C103C2semidirect
11. C2×D4×D103C22semidirect
13. C2×D824C22semidirect
14. C2×#13110090C22semidirect
15. C22×C103⋊C8C22semidirect
17. #15692995C22semidirect
21. C4⋊C4×D103C22semidirect
23. #15692955C22semidirect
24. #15692954C22semidirect
25. #15692943C22semidirect
26. #15692942C22semidirect
27. #15692941C22semidirect
28. (C2×D103)⋊C8C22semidirect
29. (C2×D103)⋊C8C22semidirect
30. C2×D8×C103C22semidirect
31. C22×C8×C103C22semidirect
32. #121×C103C22semidirect
33. #107×C103C22semidirect
34. #102×C103C22semidirect
77. C22×D103D8semidirect
132. C103#3186semidirect
138. #466D103semidirect
147. C2×D8C2×D103semidirect
149. C22×C8C2×D103semidirect
155. #121C2×D103semidirect
160. #107C2×D103semidirect
164. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#121×D1032
#202681062
#202681032
#202680272
#202680252
#202679262
#202679232
C2×(C2×D103)⋊C82
#466×C1032
#3186103