Finite Group Databasebeta

← #28400179

Subgroups — #28400179

Order 14464.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#14268630C211yesmaximal, characteristic, complemented
2#20299105C212yesmaximal, complemented
3#20298853C212yesmaximal, complemented
4#20298848C212yesmaximal, complemented
5#20298841C214yesmaximal, complemented
6#20298636C211yesmaximal, characteristic, complemented
7#20298594C212yesmaximal, complemented
8C2×#135×C113C211yesmaximal, characteristic, complemented
9C22×C4×D113C2211yescharacteristic
10C2×#14268630—24no—
11C2×#14268630C2212yes—
12C2×#14268630C2212yes—
13C22×#11744751C2211yescharacteristic
14#16813603—22no—
15#16813598C2214yes—
16#16813593C2214yes—
17#16813590—22no—
18C4×C22⋊D113—24no—
19#16813581C2212yes—
20#16813556C2212yescomplemented
21#16813554C2212yescomplemented
22#16813546C2214yescomplemented
23#16813543C2214yescomplemented
24C2×#41×C113C2212yes—
25#135×C113—24no—
26C2×Q16×C113C2211yescharacteristic, complemented
27C2×SD16×C113C2212yescomplemented
28C2×D8×C113C2211yescharacteristic, complemented
29C22×C8×C113C2211yescharacteristic
30C23×D113D411yescharacteristic
31C2×C22⋊D113—24no—
32C22×Dic113D411yescharacteristic
33C2×C4×D113—22no—
34C2×C4×D113—22no—
35C2×C4×D113D412yes—
36C2×C4×D113C2312yes—
37#14268630—24no—
38#14268630—24no—
39C2×#11744751—22no—
40C2×#11744751C2312yes—
41C4⋊Dic113C2314yes—
42#14268626—24no—
43C22⋊Dic113—22no—
44C22⋊Dic113—24no—
45#14268624—24no—
46C4×Dic113—22no—
47#41×C113—24no—
48#41×C113—24no—
49C2×Q8×C113C2312yes—
50C2×D4×C113—22no—
51C2×D4×C113C2312yes—
52C22×C4×C113—22no—
53C22×C4×C113C2311yescharacteristic
54Q16×C113—22no—
55SD16×C113—24no—
56D8×C113—22no—
57C2×C8×C113D414yescomplemented
58C2×C8×C113C2311yescharacteristic
59C2×C8×C113C2311yescharacteristic
60C23×C113—22no—
61C23×C113C2×D411yescharacteristic
62C22×D113—22no—
63C22×D113—42no—
64C22×D113C2×D412yes—
65Q8×C113—22no—
66Q8×C113—22no—
67D4×C113—22no—
68D4×C113—22no—
69D4×C113—44no—
70C2×C4×C113—22no—
71C2×C4×C113—44no—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2×D412yes—
74C2×C4×C113#4112yes—
75C2×C4×C113C2411yescharacteristic
76C22⋊D113—48no—
77C2×Dic113—22no—
78C2×Dic113—24no—
79C2×Dic113C2×D412yes—
80C4×D113—24no—
81C4×D113—22no—
82C4×D113—22no—
83C8×C113C2×D412yes—
84C8×C113C2×D412yes—
85#11744751—22no—
86C22×C113—22no—
87C22×C113—42no—
88C22×C113—44no—
89C22×C113#12112yes—
90C22×C113C22×D411yescharacteristic
91C2×D113—22no—
92C2×D113—24no—
93C2×D113—44no—
94C4×C113—42no—
95C4×C113#12112yes—
96C4×C113C22×D411yescharacteristic
97C4×C113C2×#4111yescharacteristic
98Dic113—22no—
99Dic113—44no—
100C2×C113—22no—
101C2×C113—82no—
102C2×C113C2×#12111yescharacteristic
103C2×C113#57512yes—
104D113—42no—
105#3054—1131nomaximal, Sylow
106C113#305411yescharacteristic, complemented, Sylow
107C2×#135D11311yescharacteristic, complemented
108C22×M16—1131no—
109#525—1132no—
110#470—1132no—
111#469—1132no—
112#468—1134no—
113#427—1131no—
114#416—1132no—
115C2×#41C2×D11312yes—
116C23×C4—1131no—
117#135—24no—
118C2×Q16C2×D11311yescharacteristic, complemented
119C2×SD16C2×D11312yescomplemented
120C2×D8C2×D11311yescharacteristic, complemented
121C2×M16—1132no—
122C2×M16—1132no—
123C2×M16—2264no—
124C22×C8—1131no—
125C22×C8C2×D11311yescharacteristic
126#123—2262no—
127C22⋊Q8—1134no—
128#121—1134no—
129#120—2262no—
130C4×D4—2264no—
131#117—1132no—
132#107—1132no—
133#106—1132no—
134#103—1134no—
135#102—1134no—
136C24—1131no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D11312yes—
140C2×D4—22no—
141C2×D4—2264no—
142C2×D4C22×D11312yes—
143C22×C4—22no—
144C22×C4—1131no—
145C22×C4—1132no—
146C22×C4—1132no—
147C22×C4—2262no—
148C22×C4—2262no—
149C22×C4C22×D11311yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—2264no—
154M16—2264no—
155C2×C8—1132no—
156C2×C8—2262no—
157C2×C8C22⋊D11314yescomplemented
158C2×C8C22×D11311yescharacteristic
159C2×C8C22×D11311yescharacteristic
160C4⋊C4—1134no—
161C4⋊C4—2264no—
162C22⋊C4—2264no—
163C22⋊C4—2264no—
164C22⋊C4—2262no—
165C42—2262no—
166C23—22no—
167C23—1132no—
168C23—4522no—
169C23—2262no—
170C23D4×D11311yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—4528no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—1132no—
180C2×C4—2264no—
181C2×C4—2262no—
182C2×C4—2264no—
183C2×C4—2262no—
184C2×C4—2262no—
185C2×C4D4×D11311yescharacteristic
186C2×C4C2×C22⋊D11312yes—
187C2×C4#1426864612yes—
188C2×C4C23×D11311yescharacteristic
189C8—2262no—
190C8C2×C22⋊D11312yes—
191C8C2×C22⋊D11312yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—4524no—
196C22—2262no—
197C22—2264no—
198C22#1681359312yes—
199C22C2×D4×D11311yescharacteristic
200C4—42no—
201C4—4524no—
202C4—2262no—
203C4#1681359312yes—
204C4C22×C22⋊D11311yescharacteristic
205C4C2×#1426864611yescharacteristic
206C2—22no—
207C2—82no—
208C2—4522no—
209C2C2×#1681359311yescharacteristic
210C2#2029939512yes—
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#135×C113C2
socleC22×C113C22×D4
hypercenterC2×#135D113
hypocenterC113#3054
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#14268630C2semidirect
2. #20299105C2semidirect
3. #20298853C2semidirect
4. #20298848C2semidirect
5. #20298841C2semidirect
6. #20298636C2semidirect
7. #20298594C2semidirect
8. C2×#135×C113C2semidirect
20. #16813556C22semidirect
21. #16813554C22semidirect
22. #16813546C22semidirect
23. #16813543C22semidirect
26. C2×Q16×C113C22semidirect
27. C2×SD16×C113C22semidirect
28. C2×D8×C113C22semidirect
57. C2×C8×C113D4semidirect
106. C113#3054semidirect
107. C2×#135D113semidirect
118. C2×Q16C2×D113semidirect
119. C2×SD16C2×D113semidirect
120. C2×D8C2×D113semidirect
157. C2×C8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686302
#202991052
#202988532
#202988482
#202988412
#202986362
#202985942
C2×#135×C1132
#3054113