Finite Group Databasebeta

← #28400092

Subgroups — #28400092

Order 14464.

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

normal subgroups only

This group has 490 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×#16813653C211yesmaximal, characteristic, complemented
2#20299165C211yesmaximal, characteristic
3#20299076C211yesmaximal, characteristic, complemented
4#20298818C214yesmaximal, complemented
5#20298796C214yesmaximal, complemented
6#20298624C211yesmaximal, characteristic, complemented
7#20298603C211yesmaximal, characteristic, complemented
8#20298595C211yesmaximal, characteristic, complemented
9C22×SD16×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11#16813653—24no—
12C2×#14268637C2212yescomplemented
13C2×#14268634C2212yescomplemented
14C2×#14268631C2211yescharacteristic
15#16813618C2212yes—
16#16813609C2212yes—
17#16813593—22no—
18#16813591—22no—
19Q8×Dic113—22no—
20Q8×Dic113C2214yescomplemented
21#16813581—22no—
22#16813581C2211yescharacteristic
23#16813581C2211yescharacteristic
24#16813551C2214yescomplemented
25#16813547C2212yescomplemented
26#16813544C2212yescomplemented
27#16813543C2214yes—
28C22×Q8×C113C2211yescharacteristic
29C22×D4×C113C2211yescharacteristic
30C2×SD16×C113—24no—
31C2×SD16×C113C2214yes—
32C22×C8×C113C2211yescharacteristic
33#14268647—22no—
34#14268647—22no—
35C2×Dic226C2311yescharacteristic
36C2×D452C2311yescharacteristic
37C2×C22⋊D113—21no—
38C2×C22⋊D113—24no—
39C2×C4×D113—21no—
40#14268637—24no—
41#14268634—24no—
42#14268631—22no—
43C2×#11744751C2312yes—
44C4⋊Dic113—24no—
45C4⋊Dic113D412yes—
46C4⋊Dic113C2312yes—
47C22⋊Dic113—21no—
48C22⋊Dic113—24no—
49C22⋊Dic113D412yes—
50C4×Dic113—21no—
51C4×Dic113—24no—
52C4×Dic113C2312yes—
53C24×C113—21no—
54C2×Q8×C113—21no—
55C2×Q8×C113—22no—
56C2×Q8×C113D414yescomplemented
57C2×Q8×C113C2312yes—
58C2×D4×C113—22no—
59C2×D4×C113—21no—
60C2×D4×C113—22no—
61C2×D4×C113C2312yes—
62C22×C4×C113—21no—
63C22×C4×C113C2311yescharacteristic
64SD16×C113—28no—
65C2×C8×C113—22no—
66C2×C8×C113C2312yes—
67C23×C113—22no—
68C23×C113—42no—
69C23×C113—82no—
70C23×C113C2×D411yescharacteristic
71C22×D113—21no—
72Q8×C113—24no—
73Q8×C113—22no—
74Q8×C113C2×D414yes—
75D4×C113—22no—
76D4×C113—22no—
77D4×C113—42no—
78C2×C4×C113—24no—
79C2×C4×C113—22no—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D412yes—
82C2×C4×C113#4112yes—
83C2×C4×C113C2411yescharacteristic
84C22⋊D113—42no—
85C22⋊D113—84no—
86C2×Dic113—22no—
87C2×Dic113—21no—
88C2×Dic113C2×D414yes—
89D452—21no—
90D452—21no—
91C4×D113—42no—
92Dic226—21no—
93Dic226—21no—
94C8×C113—22no—
95#11744751—22no—
96C22×C113—22no—
97C22×C113—42no—
98C22×C113—44no—
99C22×C113—84no—
100C22×C113#12112yes—
101C22×C113C22×D411yescharacteristic
102C2×D113—41no—
103C2×D113—42no—
104C4×C113—24no—
105C4×C113#12112yes—
106C4×C113C22×D411yescharacteristic
107C4×C113C2×#4111yescharacteristic
108Dic113—24no—
109Dic113—41no—
110Dic113—42no—
111C2×C113—22no—
112C2×C113—82no—
113C2×C113C2×#12111yescharacteristic
114C2×C113#57712yes—
115D113—81no—
116#3043—1131nomaximal, Sylow
117C113#304311yescharacteristic, complemented, Sylow
118C2×#137—1131no—
119C22×SD16D11311yescharacteristic, complemented
120#535—1131no—
121#519—1131no—
122#464—1134no—
123#460—1134no—
124#424—1131no—
125#418—1131no—
126#416—1131no—
127C2×#41—1131no—
128C22×Q8C2×D11311yescharacteristic
129C22×D4C2×D11311yescharacteristic
130#137—2264no—
131C2×Q16—1132no—
132C2×SD16—24no—
133C2×SD16—1132no—
134C2×SD16C2×D11314yes—
135C2×M16—1131no—
136C22×C8C2×D11311yescharacteristic
137#127—1132no—
138#124—1132no—
139#121—2262no—
140#120—2262no—
141C4×Q8—1134no—
142C4×Q8—2262no—
143#117—1131no—
144#117—1131no—
145#117—2262no—
146C4⋊C8—1134no—
147#103—1132no—
148#102—1134no—
149#102—1132no—
150C24—21no—
151#41—2262no—
152#41—2262no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—1131no—
156C2×Q8C22⋊D11314yescomplemented
157C2×Q8C22×D11312yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4—1131no—
162C2×D4—2264no—
163C2×D4—2261no—
164C2×D4C22×D11312yes—
165C22×C4—21no—
166C22×C4—2261no—
167C22×C4C22×D11311yescharacteristic
168Q16—2264no—
169SD16—28no—
170SD16—2264no—
171M16—2262no—
172C2×C8—22no—
173C2×C8—1132no—
174C2×C8C22×D11312yes—
175C4⋊C4—1132no—
176C4⋊C4—1132no—
177C4⋊C4—2264no—
178C22⋊C4—1132no—
179C22⋊C4—2264no—
180C22⋊C4—2261no—
181C42—1132no—
182C42—2264no—
183C42—2261no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—2261no—
188C23D4×D11311yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—2261no—
192Q8—2261no—
193Q8C2×C22⋊D11314yes—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—9044no—
198D4—4522no—
199D4—2261no—
200D4—2261no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—1134no—
204C2×C4—4522no—
205C2×C4—2262no—
206C2×C4—2261no—
207C2×C4D4×D11311yescharacteristic
208C2×C4C2×C22⋊D11312yes—
209C2×C4#1426864612yes—
210C2×C4C23×D11311yescharacteristic
211C8—22no—
212C8—2262no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—4521no—
218C22—4522no—
219C22#1681359412yes—
220C22C2×D4×D11311yescharacteristic
221C4—24no—
222C4—4521no—
223C4—4522no—
224C4—2264no—
225C4#1681359412yes—
226C4C22×C22⋊D11311yescharacteristic
227C4C2×#1426864611yescharacteristic
228C2—22no—
229C2—82no—
230C2—9041no—
231C2C2×#1681359411yescharacteristic
232C2#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#3043
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×#16813653C2semidirect
3. #20299076C2semidirect
4. #20298818C2semidirect
5. #20298796C2semidirect
6. #20298624C2semidirect
7. #20298603C2semidirect
8. #20298595C2semidirect
9. C22×SD16×C113C2semidirect
12. C2×#14268637C22semidirect
13. C2×#14268634C22semidirect
20. Q8×Dic113C22semidirect
24. #16813551C22semidirect
25. #16813547C22semidirect
26. #16813544C22semidirect
56. C2×Q8×C113D4semidirect
117. C113#3043semidirect
119. C22×SD16D113semidirect
156. C2×Q8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
#202991652
#202990762
#202988182
#202987962
#202986242
#202986032
#202985952
C22×SD16×C1132
#3043113