Finite Group Databasebeta

← #28400812

Subgroups — #28400812

Order 14464.

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#20299072C211yesmaximal, characteristic, complemented
2#20298919C212yesmaximal, complemented
3#20298895C212yesmaximal, complemented
4#20298790C212yesmaximal, complemented
5#20298731C212yesmaximal, complemented
6#20298708C212yesmaximal, complemented
7C4×#14268632C212yesmaximal, complemented
8#20298659C211yesmaximal, characteristic, complemented
9#540×C113C211yesmaximal, characteristic, complemented
10C22×D452C2211yescharacteristic
11C2×#14268632C2212yes—
12C2×#14268632C2212yes—
13C4×D452C2212yes—
14C4×D452C2212yes—
15#16813584—22no—
16#16813581C2211yescharacteristic
17C22⋊C4×D113—22no—
18#16813555C2212yescomplemented
19#16813553C2212yescomplemented
20C4⋊#11744751C2212yescomplemented
21#16813543C2212yescomplemented
22#16813543C2212yescomplemented
23#16813542C2212yes—
24#16813542C2212yes—
25C22⋊#11744751C2212yes—
26#16813533C2211yescharacteristic, complemented
27C4×#11744751C2211yescharacteristic, complemented
28#127×C113C2211yescharacteristic, complemented
29#125×C113C2211yescharacteristic, complemented
30#123×C113—22no—
31#121×C113—22no—
32#121×C113C2212yes—
33C4×D4×C113C2212yescomplemented
34#117×C113C2211yescharacteristic
35C23×D113—21no—
36C2×D452—21no—
37C2×D452—24no—
38C2×D452C2312yes—
39C2×C4×D113—22no—
40C2×C4×D113—22no—
41#14268632—24no—
42#14268632—24no—
43C2×#11744751C2312yes—
44C2×#11744751C2312yes—
45C4⋊Dic113C2312yes—
46C22⋊Dic113—21no—
47#14268624—22no—
48#14268624—22no—
49C4×Dic113—21no—
50C2×D4×C113—22no—
51C2×D4×C113—22no—
52C2×D4×C113C2312yes—
53C22×C4×C113—22no—
54C22×C4×C113C2311yescharacteristic
55C4⋊C4×C113—22no—
56C4⋊C4×C113D412yes—
57C4⋊C4×C113C2312yes—
58C22⋊C4×C113—22no—
59C22⋊C4×C113—22no—
60C22⋊C4×C113D412yes—
61C42×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C23×C113—22no—
64C23×C113C2×D411yescharacteristic
65C22×D113—22no—
66C22×D113—24no—
67C22×D113—82no—
68D4×C113—22no—
69D4×C113—22no—
70D4×C113—82no—
71D4×C113—82no—
72C2×C4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113—82no—
75C2×C4×C113C2×D412yes—
76C2×C4×C113C2×D412yes—
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2411yescharacteristic
79C2×Dic113—22no—
80D452—24no—
81D452—22no—
82D452#4114yes—
83C4×D113—82no—
84C4×D113—82no—
85#11744751—22no—
86#11744751—22no—
87C22×C113—21no—
88C22×C113—22no—
89C22×C113—42no—
90C22×C113—42no—
91C22×C113—42no—
92C22×C113C22×D411yescharacteristic
93C2×D113—24no—
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—84no—
97C4×C113—21no—
98C4×C113—22no—
99C4×C113—22no—
100C4×C113—42no—
101C4×C113C2×#4112yes—
102Dic113—42no—
103C2×C113—41no—
104C2×C113—82no—
105C2×C113#52511yescharacteristic
106C2×C113#57612yes—
107D113—44no—
108#3122—1131nomaximal, Sylow
109C113#312211yescharacteristic, complemented, Sylow
110#540D11311yescharacteristic, complemented
111#518—1131no—
112#482—1132no—
113#478—1132no—
114#459—1132no—
115#447—1132no—
116#442—1132no—
117C4×D8—1132no—
118#433—1131no—
119C22×D4—1131no—
120C2×D8—1132no—
121C2×D8—1132no—
122#127C2×D11311yescharacteristic, complemented
123#125C2×D11311yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D11312yes—
127C4×D4—1132no—
128C4×D4—1132no—
129C4×D4—2262no—
130C4×D4C2×D11312yescomplemented
131#117—1131no—
132#117C2×D11311yescharacteristic
133C2×C22⋊C4—2262no—
134#107—1132no—
135#106—1132no—
136C4⋊C8—1132no—
137#102—1132no—
138#102—1132no—
139#102—1132no—
140#102—1132no—
141C22⋊C8—1132no—
142#97—1131no—
143C4×C8—1131no—
144C24—2261no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—1132no—
148C2×D4—2264no—
149C2×D4—2261no—
150C2×D4C22×D11312yes—
151C22×C4—22no—
152C22×C4—2262no—
153C22×C4—2262no—
154C22×C4C22×D11311yescharacteristic
155D8—2264no—
156D8—2264no—
157C2×C8—1132no—
158C2×C8—1132no—
159C4⋊C4—22no—
160C4⋊C4—1132no—
161C4⋊C4C22⋊D11312yes—
162C4⋊C4C22×D11312yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—2261no—
166C22⋊C4—2262no—
167C22⋊C4—2262no—
168C22⋊C4C22⋊D11312yes—
169C42—2261no—
170C42C22×D11311yescharacteristic
171C42C22×D11311yescharacteristic
172C23—22no—
173C23—9042no—
174C23—2264no—
175C23—2262no—
176C23C2×C22⋊D11311yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—1134no—
182D4—2264no—
183D4—2262no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—9042no—
188C2×C4—9042no—
189C2×C4—2262no—
190C2×C4C2×C22⋊D11311yescharacteristic
191C2×C4C2×C22⋊D11312yes—
192C2×C4C2×C22⋊D11312yes—
193C2×C4C23×D11311yescharacteristic
194C8—2262no—
195C8—2262no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—9044no—
202C22—4522no—
203C22—4522no—
204C22—2264no—
205C22C22×C22⋊D11311yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—4522no—
211C4#41×D11312yes—
212C2—41no—
213C2—82no—
214C2—4524no—
215C2#2029910511yescharacteristic
216C2#2029940112yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#540×C113C2
socleC22×C113C22×D4
hypercenter#540D113
hypocenterC113#3122
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20299072C2semidirect
2. #20298919C2semidirect
3. #20298895C2semidirect
4. #20298790C2semidirect
5. #20298731C2semidirect
6. #20298708C2semidirect
7. C4×#14268632C2semidirect
8. #20298659C2semidirect
9. #540×C113C2semidirect
18. #16813555C22semidirect
19. #16813553C22semidirect
20. C4⋊#11744751C22semidirect
21. #16813543C22semidirect
22. #16813543C22semidirect
26. #16813533C22semidirect
27. C4×#11744751C22semidirect
28. #127×C113C22semidirect
29. #125×C113C22semidirect
33. C4×D4×C113C22semidirect
109. C113#3122semidirect
110. #540D113semidirect
122. #127C2×D113semidirect
123. #125C2×D113semidirect
130. C4×D4C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202990722
#202989192
#202988952
#202987902
#202987312
#202987082
C4×#142686322
#202986592
#540×C1132
#3122113