Finite Group Databasebeta

← #28400209

Subgroups — #28400209

Order 14464.

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

normal subgroups only

This group has 492 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
1C2×#16813628C211yesmaximal, characteristic, complemented
2#20299172C211yesmaximal, characteristic, complemented
3#20299165C211yesmaximal, characteristic
4#20298841C214yesmaximal, complemented
5#20298824C214yesmaximal, complemented
6#20298636C211yesmaximal, characteristic, complemented
7#20298607C211yesmaximal, characteristic, complemented
8#20298603C211yesmaximal, characteristic, complemented
9C22×SD16×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11#16813628—24no—
12C2×#14268631C2211yescharacteristic
13C2×#14268630C2212yescomplemented
14C2×C8×D113C2212yescomplemented
15#16813620—21no—
16#16813618—21no—
17#16813611—21no—
18#16813609—21no—
19#16813605—22no—
20#16813598C2214yescomplemented
21#16813593C2214yes—
22#16813591—22no—
23#16813581C2211yescharacteristic
24#16813581C2211yescharacteristic
25#16813556C2212yescomplemented
26#16813554C2212yescomplemented
27#16813546C2214yescomplemented
28#16813543C2214yes—
29C22×Q8×C113C2211yescharacteristic
30C22×D4×C113C2211yescharacteristic
31C2×SD16×C113—24no—
32C2×SD16×C113C2212yes—
33C2×SD16×C113C2212yes—
34C22×C8×C113C2211yescharacteristic
35#14268647—22no—
36#14268647—22no—
37C2×Dic226D411yescharacteristic
38C2×D452D411yescharacteristic
39C2×C22⋊D113—24no—
40C2×C22⋊D113D412yes—
41C2×C4×D113C2312yes—
42#14268631—22no—
43#14268630—24no—
44C2×#11744751C2312yes—
45C8×D113—24no—
46C4⋊Dic113C2312yes—
47C4⋊Dic113C2312yes—
48#14268626—24no—
49C22⋊Dic113—21no—
50C22⋊Dic113—21no—
51C22⋊Dic113—24no—
52#14268624—24no—
53C4×Dic113—21no—
54C4×Dic113—21no—
55C24×C113—21no—
56C2×Q8×C113—21no—
57C2×Q8×C113—22no—
58C2×Q8×C113—22no—
59C2×Q8×C113C2312yes—
60C2×D4×C113—22no—
61C2×D4×C113—21no—
62C2×D4×C113—22no—
63C2×D4×C113C2312yes—
64C22×C4×C113—21no—
65C22×C4×C113C2311yescharacteristic
66SD16×C113—24no—
67SD16×C113—24no—
68C2×C8×C113D414yescomplemented
69C2×C8×C113C2311yescharacteristic
70C2×C8×C113C2311yescharacteristic
71C23×C113—22no—
72C23×C113—42no—
73C23×C113—82no—
74C23×C113C2×D411yescharacteristic
75C22×D113C2×D412yes—
76Q8×C113—22no—
77Q8×C113—22no—
78Q8×C113—42no—
79D4×C113—22no—
80D4×C113—22no—
81D4×C113—42no—
82C2×C4×C113—22no—
83C2×C4×C113—42no—
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2×D412yes—
86C2×C4×C113#4112yes—
87C2×C4×C113C2411yescharacteristic
88C22⋊D113—24no—
89C22⋊D113—84no—
90C2×Dic113—22no—
91C2×Dic113—22no—
92C2×Dic113C2×D412yes—
93D452—22no—
94C4×D113—22no—
95C4×D113—22no—
96Dic226—22no—
97C8×C113C2×D412yes—
98C8×C113C2×D412yes—
99#11744751—22no—
100C22×C113—22no—
101C22×C113—42no—
102C22×C113—44no—
103C22×C113—84no—
104C22×C113#12112yes—
105C22×C113C22×D411yescharacteristic
106C2×D113—22no—
107C2×D113—24no—
108C4×C113—42no—
109C4×C113#12112yes—
110C4×C113C22×D411yescharacteristic
111C4×C113C2×#4111yescharacteristic
112Dic113—22no—
113Dic113—42no—
114Dic113—42no—
115C2×C113—22no—
116C2×C113—82no—
117C2×C113C2×#12111yescharacteristic
118C2×C113#57712yes—
119D113—42no—
120#3057—1131nomaximal, Sylow
121C113#305711yescharacteristic, complemented, Sylow
122C22×SD16D11311yescharacteristic, complemented
123C2×#131—1131no—
124#536—1131no—
125#535—1131no—
126#468—1134no—
127#465—1134no—
128#427—1131no—
129#419—1131no—
130#418—1131no—
131C2×#41—1131no—
132C22×Q8C2×D11311yescharacteristic
133C22×D4C2×D11311yescharacteristic
134C2×SD16—24no—
135C2×SD16C2×D11312yes—
136C2×SD16C2×D11312yes—
137#131—2264no—
138C2×M16—1131no—
139C2×M16—1132no—
140C22×C8—1132no—
141C22×C8C2×D11311yescharacteristic
142C4⋊Q8—2261no—
143#127—2261no—
144#124—2261no—
145#124—2261no—
146#123—2262no—
147C22⋊Q8—1134no—
148#121—1134no—
149#120—2262no—
150#117—1131no—
151#117—1131no—
152#107—1132no—
153#106—1132no—
154#103—1134no—
155#102—1134no—
156C24—21no—
157#41—2262no—
158#41—2262no—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—1131no—
163C2×Q8C22×D11312yes—
164C2×D4—21no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—1132no—
168C2×D4—1131no—
169C2×D4—2264no—
170C2×D4C22×D11312yes—
171C22×C4—21no—
172C22×C4—1132no—
173C22×C4C22×D11311yescharacteristic
174SD16—24no—
175SD16—24no—
176M16—2262no—
177M16—2264no—
178C2×C8—1132no—
179C2×C8—2264no—
180C2×C8C22⋊D11314yescomplemented
181C2×C8C22×D11311yescharacteristic
182C2×C8C22×D11311yescharacteristic
183C4⋊C4—1132no—
184C4⋊C4—1132no—
185C4⋊C4—2264no—
186C22⋊C4—2264no—
187C22⋊C4—2264no—
188C22⋊C4—2261no—
189C22⋊C4—2261no—
190C42—2261no—
191C42—2261no—
192C23—22no—
193C23—42no—
194C23—82no—
195C23—1132no—
196C23D4×D11311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—42no—
200Q8—2262no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—9044no—
205D4—2264no—
206D4—2262no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—1132no—
210C2×C4—2262no—
211C2×C4—2262no—
212C2×C4—2262no—
213C2×C4—2262no—
214C2×C4D4×D11311yescharacteristic
215C2×C4C2×C22⋊D11312yes—
216C2×C4#1426864612yes—
217C2×C4C23×D11311yescharacteristic
218C8—2262no—
219C8C2×C22⋊D11312yes—
220C8C2×C22⋊D11312yes—
221C22—22no—
222C22—42no—
223C22—44no—
224C22—84no—
225C22—2262no—
226C22—2264no—
227C22#1681359312yes—
228C22C2×D4×D11311yescharacteristic
229C4—42no—
230C4—4522no—
231C4—4522no—
232C4—2262no—
233C4#1681359312yes—
234C4C22×C22⋊D11311yescharacteristic
235C4C2×#1426864611yescharacteristic
236C2—22no—
237C2—82no—
238C2—4522no—
239C2C2×#1681359311yescharacteristic
240C2#2029940412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×SD16×C113C2
socleC22×C113C22×D4
prime radical#20299165C2
hypercenterC22×SD16D113
hypocenterC113#3057
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16813628C2semidirect
2. #20299172C2semidirect
4. #20298841C2semidirect
5. #20298824C2semidirect
6. #20298636C2semidirect
7. #20298607C2semidirect
8. #20298603C2semidirect
9. C22×SD16×C113C2semidirect
13. C2×#14268630C22semidirect
14. C2×C8×D113C22semidirect
20. #16813598C22semidirect
25. #16813556C22semidirect
26. #16813554C22semidirect
27. #16813546C22semidirect
68. C2×C8×C113D4semidirect
121. C113#3057semidirect
122. C22×SD16D113semidirect
180. C2×C8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136282
#202991722
#202991652
#202988412
#202988242
#202986362
#202986072
#202986032
C22×SD16×C1132
#3057113