Finite Group Databasebeta

← #27205391

Subgroups — #27205391

Order 13184.

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

normal subgroups only

This group has 394 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#20268265C211yesmaximal, characteristic
2#20268129C212yesmaximal, complemented
3#20268088C212yesmaximal, complemented
4#20267993C212yesmaximal, complemented
5#20267941C212yesmaximal
6#20267889C212yesmaximal, complemented
7C4×#13110092C212yesmaximal, complemented
8#20267852C211yesmaximal, characteristic, complemented
9#541×C103C211yesmaximal, characteristic, complemented
10C22×D412C2211yescharacteristic
11C2×#13110092C2212yes—
12C2×#13110092C2212yes—
13C4×D412C2212yes—
14C4×D412C2212yes—
15#15692983—22no—
16#15692980C2211yescharacteristic
17C22⋊C4×D103—22no—
18#15692954C2212yescomplemented
19#15692952C2212yescomplemented
20C4⋊(C103⋊C8)C2212yescomplemented
21#15692945C2212yescomplemented
22#15692945C2212yescomplemented
23#15692941C2212yes—
24#15692941C2212yes—
25C22⋊(C103⋊C8)C2212yes—
26#15692932C2211yescharacteristic, complemented
27C4×C103⋊C8C2211yescharacteristic, complemented
28C4⋊Q8×C103C2211yescharacteristic, complemented
29#126×C103—22no—
30#125×C103—22no—
31#125×C103C2211yescharacteristic, complemented
32C22⋊Q8×C103C2212yes—
33C4×Q8×C103C2212yescomplemented
34#117×C103C2211yescharacteristic
35C23×D103—21no—
36C2×D412—21no—
37C2×D412—24no—
38C2×D412C2312yes—
39C2×C4×D103—22no—
40C2×C4×D103—22no—
41#13110092—24no—
42#13110092—24no—
43C2×C103⋊C8C2312yes—
44C2×C103⋊C8C2312yes—
45C4⋊Dic103C2312yes—
46C22⋊Dic103—21no—
47(C2×D103)⋊C4—22no—
48(C2×D103)⋊C4—22no—
49C4×Dic103—21no—
50C2×Q8×C103C2312yes—
51C22×C4×C103C2311yescharacteristic
52C4⋊C4×C103—22no—
53C4⋊C4×C103—22no—
54C4⋊C4×C103—22no—
55C4⋊C4×C103—22no—
56C4⋊C4×C103D412yes—
57C4⋊C4×C103C2312yes—
58C22⋊C4×C103—22no—
59C22⋊C4×C103D412yes—
60C42×C103—22no—
61C42×C103C2311yescharacteristic
62C42×C103C2311yescharacteristic
63C23×C103C2×D411yescharacteristic
64C22×D103—22no—
65C22×D103—24no—
66C22×D103—82no—
67Q8×C103—22no—
68Q8×C103—22no—
69C2×C4×C103—22no—
70C2×C4×C103—22no—
71C2×C4×C103—22no—
72C2×C4×C103C2×D412yes—
73C2×C4×C103C2×D412yes—
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103C2411yescharacteristic
76C2×Dic103—22no—
77D412—24no—
78D412—22no—
79D412#4114yes—
80C4×D103—82no—
81C4×D103—82no—
82C103⋊C8—22no—
83C103⋊C8—22no—
84C22×C103—21no—
85C22×C103—22no—
86C22×C103C22×D411yescharacteristic
87C2×D103—24no—
88C2×D103—42no—
89C2×D103—42no—
90C2×D103—84no—
91C4×C103—21no—
92C4×C103—22no—
93C4×C103—22no—
94C4×C103—42no—
95C4×C103—42no—
96C4×C103C2×#4112yes—
97Dic103—42no—
98C2×C103—41no—
99C2×C103#52511yescharacteristic
100C2×C103#57712yes—
101D103—44no—
102#3123—1031nomaximal, Sylow
103C103#312311yescharacteristic, complemented, Sylow
104#541D10311yescharacteristic, complemented
105#518—1031no—
106#485—1032no—
107#478—1032no—
108#461—1032no—
109#450—1032no—
110#440—1032no—
111C4×SD16—1032no—
112#433—1031no—
113C22×D4—1031no—
114C2×SD16—1032no—
115C2×SD16—1032no—
116C4⋊Q8C2×D10311yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D10311yescharacteristic, complemented
120C22⋊Q8C2×D10312yes—
121C4×Q8C2×D10312yescomplemented
122C4×D4—1032no—
123C4×D4—1032no—
124C4×D4—2062no—
125#117—1031no—
126#117C2×D10311yescharacteristic
127C2×C22⋊C4—2062no—
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—2061no—
139C2×Q8C22×D10312yes—
140C2×D4—1032no—
141C2×D4—2064no—
142C2×D4—2061no—
143C22×C4—2062no—
144C22×C4—2062no—
145C22×C4C22×D10311yescharacteristic
146SD16—2064no—
147SD16—2064no—
148C2×C8—1032no—
149C2×C8—1032no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—1032no—
155C4⋊C4C22⋊D10312yes—
156C4⋊C4C22×D10312yes—
157C22⋊C4—22no—
158C22⋊C4—2061no—
159C22⋊C4—2062no—
160C22⋊C4—2062no—
161C22⋊C4C22⋊D10312yes—
162C42—22no—
163C42—2061no—
164C42C22×D10311yescharacteristic
165C42C22×D10311yescharacteristic
166C23—8242no—
167C23—2064no—
168C23—2062no—
169C23C2×C22⋊D10311yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—1034no—
173D4—2064no—
174D4—2062no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—8242no—
179C2×C4—8242no—
180C2×C4—2062no—
181C2×C4C2×C22⋊D10312yes—
182C2×C4C2×C22⋊D10311yescharacteristic
183C2×C4C2×C22⋊D10312yes—
184C2×C4C23×D10311yescharacteristic
185C8—2062no—
186C8—2062no—
187C22—21no—
188C22—22no—
189C22—8244no—
190C22—4122no—
191C22—4122no—
192C22—2064no—
193C22C22×C22⋊D10311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—4122no—
200C4#41×D10312yes—
201C2—41no—
202C2—4124no—
203C2#2026829811yescharacteristic
204C2#2026859912yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#541×C103C2
socleC22×C103C22×D4
prime radicalC22×D412C22
hypercenter#541D103
hypocenterC103#3123
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20268129C2semidirect
3. #20268088C2semidirect
4. #20267993C2semidirect
6. #20267889C2semidirect
7. C4×#13110092C2semidirect
8. #20267852C2semidirect
9. #541×C103C2semidirect
18. #15692954C22semidirect
19. #15692952C22semidirect
20. C4⋊(C103⋊C8)C22semidirect
21. #15692945C22semidirect
22. #15692945C22semidirect
26. #15692932C22semidirect
27. C4×C103⋊C8C22semidirect
28. C4⋊Q8×C103C22semidirect
31. #125×C103C22semidirect
33. C4×Q8×C103C22semidirect
103. C103#3123semidirect
104. #541D103semidirect
116. C4⋊Q8C2×D103semidirect
119. #125C2×D103semidirect
121. C4×Q8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202682652
#202681292
#202680882
#202679932
#202679412
#202678892
C4×#131100922
#202678522
#541×C1032
#3123103