Finite Group Databasebeta

← #27205387

Subgroups — #27205387

Order 13184.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#20268396C211yesmaximal, characteristic, complemented
2#20268115C212yesmaximal, complemented
3#20268091C212yesmaximal, complemented
4#20267986C212yesmaximal, complemented
5#20267925C212yesmaximal, complemented
6#20267901C212yesmaximal, complemented
7C4×#13110090C212yesmaximal, complemented
8#20267852C211yesmaximal, characteristic, complemented
9#518×C103C211yesmaximal, characteristic, complemented
10C2×#13110090C2212yes—
11C2×#13110090C2212yes—
12#15693018C2211yescharacteristic, complemented
13#15693013C2211yescharacteristic, complemented
14#15693006—22no—
15#15692995C2212yes—
16#15692994—22no—
17C4×D412C2212yescomplemented
18#15692954C2212yescomplemented
19#15692952C2212yescomplemented
20C4⋊(C103⋊C8)C2212yescomplemented
21#15692942C2212yes—
22#15692942C2212yes—
23#15692941C2212yescomplemented
24#15692941C2212yescomplemented
25C22⋊(C103⋊C8)C2212yes—
26#15692932C2211yescharacteristic, complemented
27C4×C103⋊C8C2211yescharacteristic, complemented
28C22×D4×C103C2211yescharacteristic
29C4×D4×C103—22no—
30C4×D4×C103C2212yes—
31C4×D4×C103C2212yes—
32#117×C103C2211yescharacteristic
33#117×C103C2211yescharacteristic
34C2×C22⋊C4×C103—22no—
35C2×D412—22no—
36C2×D412C2312yes—
37C2×C22⋊D103—22no—
38C2×C4×D103—22no—
39#13110090—24no—
40#13110090—24no—
41C2×C103⋊C8C2312yes—
42C2×C103⋊C8C2312yes—
43C4⋊Dic103C2312yes—
44Dic103⋊C4—22no—
45(C2×D103)⋊C4—22no—
46(C2×D103)⋊C4—22no—
47C24×C103—21no—
48C2×D4×C103—24no—
49C2×D4×C103—21no—
50C2×D4×C103C2312yes—
51C22×C4×C103—22no—
52C22×C4×C103—22no—
53C22×C4×C103C2311yescharacteristic
54C4⋊C4×C103D412yes—
55C4⋊C4×C103C2312yes—
56C22⋊C4×C103—21no—
57C22⋊C4×C103—22no—
58C22⋊C4×C103—22no—
59C22⋊C4×C103D412yes—
60C42×C103—21no—
61C42×C103C2311yescharacteristic
62C42×C103C2311yescharacteristic
63C23×C103—24no—
64C23×C103—22no—
65C23×C103—82no—
66C23×C103C2×D411yescharacteristic
67C22×D103—22no—
68D4×C103—24no—
69D4×C103—22no—
70D4×C103#4114yes—
71C2×C4×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103—82no—
74C2×C4×C103—82no—
75C2×C4×C103C2×D411yescharacteristic
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2×D412yes—
78C2×C4×C103C2411yescharacteristic
79C22⋊D103—82no—
80C2×Dic103—22no—
81D412—22no—
82D412—22no—
83D412—82no—
84C4×D103—82no—
85C103⋊C8—22no—
86C103⋊C8—22no—
87C22×C103—21no—
88C22×C103—24no—
89C22×C103—22no—
90C22×C103—42no—
91C22×C103—42no—
92C22×C103—84no—
93C22×C103C22×D411yescharacteristic
94C2×D103—42no—
95C2×D103—42no—
96C2×D103—42no—
97C4×C103—21no—
98C4×C103—22no—
99C4×C103—22no—
100C4×C103—42no—
101C4×C103C2×#4112yes—
102Dic103—42no—
103C2×C103—41no—
104C2×C103—44no—
105C2×C103#52511yescharacteristic
106C2×C103#57612yes—
107D103—82no—
108#3122—1031nomaximal, Sylow
109C103#312211yescharacteristic, complemented, Sylow
110#540—1031no—
111#518D10311yescharacteristic, complemented
112#482—1032no—
113#478—1032no—
114#459—1032no—
115#447—1032no—
116#442—1032no—
117C4×D8—1032no—
118#433—1031no—
119C22×D4C2×D10311yescharacteristic
120C2×D8—1032no—
121C2×D8—1032no—
122#127—1031no—
123#125—1031no—
124#123—2062no—
125#121—1032no—
126#121—2062no—
127C4×D4—22no—
128C4×D4—1032no—
129C4×D4C2×D10312yes—
130C4×D4C2×D10312yes—
131#117C2×D10311yescharacteristic
132#117C2×D10311yescharacteristic
133C2×C22⋊C4—22no—
134#107—1032no—
135#106—1032no—
136C4⋊C8—1032no—
137#102—1032no—
138#102—1032no—
139#102—1032no—
140#102—1032no—
141C22⋊C8—1032no—
142#97—1031no—
143C4×C8—1031no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—1032no—
148C2×D4—2062no—
149C2×D4—2062no—
150C2×D4C22×D10312yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—2062no—
154C22×C4C22×D10311yescharacteristic
155D8—2064no—
156D8—2064no—
157C2×C8—1032no—
158C2×C8—1032no—
159C4⋊C4—1032no—
160C4⋊C4—2062no—
161C4⋊C4C22⋊D10312yes—
162C4⋊C4C22×D10312yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—2062no—
167C22⋊C4—2062no—
168C22⋊C4C22⋊D10312yes—
169C42—21no—
170C42C22×D10311yescharacteristic
171C42C22×D10311yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—2062no—
176C23C2×C22⋊D10311yescharacteristic
177D4—24no—
178D4—22no—
179D4—8242no—
180D4—8242no—
181D4—2062no—
182D4—2062no—
183D4#1311010514yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—8242no—
189C2×C4—2062no—
190C2×C4C2×C22⋊D10311yescharacteristic
191C2×C4C2×C22⋊D10312yes—
192C2×C4C2×C22⋊D10312yes—
193C2×C4C23×D10311yescharacteristic
194C8—2062no—
195C8—2062no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—4122no—
203C22—4122no—
204C22—4122no—
205C22C22×C22⋊D10311yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—4122no—
211C4C2×#1311010512yes—
212C2—41no—
213C2—44no—
214C2—8242no—
215C2#2026830211yescharacteristic
216C2#2026859412yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#518×C103C2
socleC22×C103C22×D4
hypercenter#518D103
hypocenterC103#3122
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #20268396C2semidirect
2. #20268115C2semidirect
3. #20268091C2semidirect
4. #20267986C2semidirect
5. #20267925C2semidirect
6. #20267901C2semidirect
7. C4×#13110090C2semidirect
8. #20267852C2semidirect
9. #518×C103C2semidirect
12. #15693018C22semidirect
13. #15693013C22semidirect
17. C4×D412C22semidirect
18. #15692954C22semidirect
19. #15692952C22semidirect
20. C4⋊(C103⋊C8)C22semidirect
23. #15692941C22semidirect
24. #15692941C22semidirect
26. #15692932C22semidirect
27. C4×C103⋊C8C22semidirect
109. C103#3122semidirect
111. #518D103semidirect

Maximal subgroups

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

subgroupindex
#202683962
#202681152
#202680912
#202679862
#202679252
#202679012
C4×#131100902
#202678522
#518×C1032
#3122103