Finite Group Databasebeta

← #27205382

Subgroups — #27205382

Order 13184.

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

normal subgroups only

This group has 418 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, complemented
2#20268112C212yesmaximal, complemented
3#20268088C212yesmaximal, complemented
4#20267983C212yesmaximal, complemented
5#20267924C212yesmaximal, complemented
6#20267901C212yesmaximal, complemented
7C4×#13110090C212yesmaximal, complemented
8#20267852C211yesmaximal, characteristic, complemented
9#540×C103C211yesmaximal, characteristic, complemented
10C22×D412C2211yescharacteristic
11C2×#13110090C2212yes—
12C2×#13110090C2212yes—
13C4×D412C2212yes—
14C4×D412C2212yes—
15#15692983—22no—
16#15692980C2211yescharacteristic
17C22⋊C4×D103—22no—
18#15692954C2212yescomplemented
19#15692952C2212yescomplemented
20C4⋊(C103⋊C8)C2212yescomplemented
21#15692942C2212yescomplemented
22#15692942C2212yescomplemented
23#15692941C2212yes—
24#15692941C2212yes—
25C22⋊(C103⋊C8)C2212yes—
26#15692932C2211yescharacteristic, complemented
27C4×C103⋊C8C2211yescharacteristic, complemented
28#127×C103C2211yescharacteristic, complemented
29#125×C103C2211yescharacteristic, complemented
30#123×C103—22no—
31#121×C103—22no—
32#121×C103C2212yes—
33C4×D4×C103C2212yescomplemented
34#117×C103C2211yescharacteristic
35C23×D103—21no—
36C2×D412—21no—
37C2×D412—24no—
38C2×D412C2312yes—
39C2×C4×D103—22no—
40C2×C4×D103—22no—
41#13110090—24no—
42#13110090—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×D4×C103—22no—
51C2×D4×C103—22no—
52C2×D4×C103C2312yes—
53C22×C4×C103—22no—
54C22×C4×C103C2311yescharacteristic
55C4⋊C4×C103—22no—
56C4⋊C4×C103D412yes—
57C4⋊C4×C103C2312yes—
58C22⋊C4×C103—22no—
59C22⋊C4×C103—22no—
60C22⋊C4×C103D412yes—
61C42×C103C2311yescharacteristic
62C42×C103C2311yescharacteristic
63C23×C103—22no—
64C23×C103C2×D411yescharacteristic
65C22×D103—22no—
66C22×D103—24no—
67C22×D103—82no—
68D4×C103—22no—
69D4×C103—22no—
70D4×C103—82no—
71D4×C103—82no—
72C2×C4×C103—22no—
73C2×C4×C103—22no—
74C2×C4×C103—82no—
75C2×C4×C103C2×D412yes—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2411yescharacteristic
79C2×Dic103—22no—
80D412—24no—
81D412—22no—
82D412#4114yes—
83C4×D103—82no—
84C4×D103—82no—
85C103⋊C8—22no—
86C103⋊C8—22no—
87C22×C103—21no—
88C22×C103—22no—
89C22×C103—42no—
90C22×C103—42no—
91C22×C103—42no—
92C22×C103C22×D411yescharacteristic
93C2×D103—24no—
94C2×D103—42no—
95C2×D103—42no—
96C2×D103—84no—
97C4×C103—21no—
98C4×C103—22no—
99C4×C103—22no—
100C4×C103—42no—
101C4×C103C2×#4112yes—
102Dic103—42no—
103C2×C103—41no—
104C2×C103—82no—
105C2×C103#52511yescharacteristic
106C2×C103#57612yes—
107D103—44no—
108#3122—1031nomaximal, Sylow
109C103#312211yescharacteristic, complemented, Sylow
110#540D10311yescharacteristic, complemented
111#518—1031no—
112#482—1032no—
113#478—1032no—
114#459—1032no—
115#447—1032no—
116#442—1032no—
117C4×D8—1032no—
118#433—1031no—
119C22×D4—1031no—
120C2×D8—1032no—
121C2×D8—1032no—
122#127C2×D10311yescharacteristic, complemented
123#125C2×D10311yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D10312yes—
127C4×D4—1032no—
128C4×D4—1032no—
129C4×D4—2062no—
130C4×D4C2×D10312yescomplemented
131#117—1031no—
132#117C2×D10311yescharacteristic
133C2×C22⋊C4—2062no—
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—2061no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—1032no—
148C2×D4—2064no—
149C2×D4—2061no—
150C2×D4C22×D10312yes—
151C22×C4—22no—
152C22×C4—2062no—
153C22×C4—2062no—
154C22×C4C22×D10311yescharacteristic
155D8—2064no—
156D8—2064no—
157C2×C8—1032no—
158C2×C8—1032no—
159C4⋊C4—22no—
160C4⋊C4—1032no—
161C4⋊C4C22⋊D10312yes—
162C4⋊C4C22×D10312yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—2061no—
166C22⋊C4—2062no—
167C22⋊C4—2062no—
168C22⋊C4C22⋊D10312yes—
169C42—2061no—
170C42C22×D10311yescharacteristic
171C42C22×D10311yescharacteristic
172C23—22no—
173C23—8242no—
174C23—2064no—
175C23—2062no—
176C23C2×C22⋊D10311yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—1034no—
182D4—2064no—
183D4—2062no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—8242no—
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—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—8244no—
202C22—4122no—
203C22—4122no—
204C22—2064no—
205C22C22×C22⋊D10311yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—4122no—
211C4#41×D10312yes—
212C2—41no—
213C2—82no—
214C2—4124no—
215C2#2026829811yescharacteristic
216C2#2026859412yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#540×C103C2
socleC22×C103C22×D4
hypercenter#540D103
hypocenterC103#3122
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20268265C2semidirect
2. #20268112C2semidirect
3. #20268088C2semidirect
4. #20267983C2semidirect
5. #20267924C2semidirect
6. #20267901C2semidirect
7. C4×#13110090C2semidirect
8. #20267852C2semidirect
9. #540×C103C2semidirect
18. #15692954C22semidirect
19. #15692952C22semidirect
20. C4⋊(C103⋊C8)C22semidirect
21. #15692942C22semidirect
22. #15692942C22semidirect
26. #15692932C22semidirect
27. C4×C103⋊C8C22semidirect
28. #127×C103C22semidirect
29. #125×C103C22semidirect
33. C4×D4×C103C22semidirect
109. C103#3122semidirect
110. #540D103semidirect
122. #127C2×D103semidirect
123. #125C2×D103semidirect
130. C4×D4C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202682652
#202681122
#202680882
#202679832
#202679242
#202679012
C4×#131100902
#202678522
#540×C1032
#3122103