Finite Group Databasebeta

← #27205396

Subgroups — #27205396

Order 13184.

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

normal subgroups only

This group has 394 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#20268403C211yesmaximal, characteristic, complemented
2#20268132C212yesmaximal, complemented
3#20268091C212yesmaximal, complemented
4#20267996C212yesmaximal, complemented
5#20267942C212yesmaximal
6#20267891C212yesmaximal, complemented
7C4×#13110093C212yesmaximal, complemented
8#20267852C211yesmaximal, characteristic, complemented
9#518×C103C211yesmaximal, characteristic
10C2×#13110093C2212yes—
11C2×#13110093C2212yes—
12#15693021C2211yescharacteristic, complemented
13#15693014—22no—
14#15693013C2211yescharacteristic, complemented
15#15693011—22no—
16#15693000C2212yes—
17C4×Dic206C2212yescomplemented
18#15692954C2212yescomplemented
19#15692952C2212yescomplemented
20C4⋊(C103⋊C8)C2212yescomplemented
21#15692944C2212yescomplemented
22#15692944C2212yescomplemented
23#15692942C2212yes—
24#15692942C2212yes—
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×Dic206C2312yes—
36#13110093—24no—
37#13110093—24no—
38C2×C103⋊C8C2312yes—
39C2×C103⋊C8C2312yes—
40C4⋊Dic103—22no—
41C4⋊Dic103C2312yes—
42Dic103⋊C4—22no—
43Dic103⋊C4—22no—
44Dic103⋊C4—22no—
45C22⋊Dic103—22no—
46C4×Dic103—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
67D4×C103—24no—
68D4×C103—22no—
69D4×C103#4114yes—
70C2×C4×C103—22no—
71C2×C4×C103—22no—
72C2×C4×C103—82no—
73C2×C4×C103—82no—
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103C2×D412yes—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2411yescharacteristic
78C2×Dic103—22no—
79C2×Dic103—22no—
80Dic206—22no—
81Dic206—22no—
82C103⋊C8—22no—
83C103⋊C8—22no—
84C22×C103—21no—
85C22×C103—24no—
86C22×C103—22no—
87C22×C103—42no—
88C22×C103—42no—
89C22×C103—84no—
90C22×C103C22×D411yescharacteristic
91C4×C103—21no—
92C4×C103—22no—
93C4×C103—22no—
94C4×C103—42no—
95C4×C103C2×#4112yes—
96Dic103—42no—
97Dic103—42no—
98C2×C103—41no—
99C2×C103—44no—
100C2×C103#52511yescharacteristic
101C2×C103#57712yes—
102#3123—1031nomaximal, Sylow
103C103#312311yescharacteristic, complemented, Sylow
104#541—1031no—
105#518D10311yescharacteristic
106#485—1032no—
107#478—1032no—
108#461—1032no—
109#450—1032no—
110#440—1032no—
111C4×SD16—1032no—
112#433—1031no—
113C22×D4C2×D10311yescharacteristic
114C2×SD16—1032no—
115C2×SD16—1032no—
116C4⋊Q8—1031no—
117#126—2062no—
118#125—1031no—
119#125—2062no—
120C22⋊Q8—1032no—
121C4×Q8—1032no—
122C4×D4—22no—
123C4×D4C2×D10312yes—
124C4×D4C2×D10312yes—
125#117C2×D10311yescharacteristic
126#117C2×D10311yescharacteristic
127C2×C22⋊C4—22no—
128#107—1032no—
129#106—1032no—
130C4⋊C8—1032no—
131#103—1032no—
132#103—1032no—
133#102—1032no—
134#102—1032no—
135C22⋊C8—1032no—
136#97—1031no—
137C4×C8—1031no—
138C24—21no—
139C2×Q8—1032no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D10312yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D10311yescharacteristic
146SD16—2064no—
147SD16—2064no—
148C2×C8—1032no—
149C2×C8—1032no—
150C4⋊C4—1032no—
151C4⋊C4—2062no—
152C4⋊C4—2062no—
153C4⋊C4—2062no—
154C4⋊C4—2062no—
155C4⋊C4C22⋊D10312yes—
156C4⋊C4C22×D10312yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—2062no—
161C22⋊C4C22⋊D10312yes—
162C42—21no—
163C42—2062no—
164C42C22×D10311yescharacteristic
165C42C22×D10311yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D10311yescharacteristic
170Q8—2062no—
171Q8—2062no—
172D4—24no—
173D4—22no—
174D4#1311010514yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—2062no—
180C2×C4—2062no—
181C2×C4C2×C22⋊D10311yescharacteristic
182C2×C4C2×C22⋊D10312yes—
183C2×C4C2×C22⋊D10312yes—
184C2×C4C23×D10311yescharacteristic
185C8—2062no—
186C8—2062no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D10311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—4122no—
199C4—4122no—
200C4C2×#1311010512yes—
201C2—41no—
202C2—44no—
203C2#2026830211yescharacteristic
204C2#2026860212yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#518×C103C2
socleC22×C103C22×D4
prime radicalC22×D4×C103C22
hypercenter#518D103
hypocenterC103#3123
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. #20268403C2semidirect
2. #20268132C2semidirect
3. #20268091C2semidirect
4. #20267996C2semidirect
6. #20267891C2semidirect
7. C4×#13110093C2semidirect
8. #20267852C2semidirect
12. #15693021C22semidirect
14. #15693013C22semidirect
17. C4×Dic206C22semidirect
18. #15692954C22semidirect
19. #15692952C22semidirect
20. C4⋊(C103⋊C8)C22semidirect
21. #15692944C22semidirect
22. #15692944C22semidirect
26. #15692932C22semidirect
27. C4×C103⋊C8C22semidirect
103. C103#3123semidirect

Maximal subgroups

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

subgroupindex
#202684032
#202681322
#202680912
#202679962
#202679422
#202678912
C4×#131100932
#202678522
#518×C1032
#3123103