Finite Group Databasebeta

← #28400094

Subgroups — #28400094

Order 14464.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16813655C211yesmaximal, characteristic, complemented
2C22×#14268635C211yesmaximal, characteristic, complemented
3#20299165C211yesmaximal, characteristic
4#20299075C211yesmaximal, characteristic, complemented
5#20298819C214yesmaximal, complemented
6#20298797C214yesmaximal, complemented
7#20298626C211yesmaximal, characteristic, complemented
8#20298592C211yesmaximal, characteristic, complemented
9#418×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×Dic226C2211yescharacteristic
12#16813655—24no—
13C2×Dic452C2212yescomplemented
14C2×#14268636C2212yescomplemented
15C2×#14268635—24no—
16C2×#14268635C2214yes—
17C22×#11744751C2211yescharacteristic
18#16813618C2212yes—
19#16813609C2212yes—
20#16813593—22no—
21#16813591—22no—
22C4×Dic226—22no—
23#16813587C2214yescomplemented
24#16813581C2211yescharacteristic
25#16813578—22no—
26#16813551C2214yescomplemented
27#16813545C2212yescomplemented
28#16813542C2212yescomplemented
29C22×D4×C113C2211yescharacteristic
30C2×M16×C113C2211yescharacteristic
31#117×C113C2211yescharacteristic
32#102×C113C2214yes—
33#14268647—22no—
34#14268647—22no—
35C2×Dic226—21no—
36C2×Dic226—22no—
37C2×Dic226D414yescomplemented
38C2×Dic226C2311yescharacteristic
39C2×Dic226C2312yes—
40C2×D452C2311yescharacteristic
41C2×C22⋊D113—21no—
42C2×C22⋊D113—24no—
43C22×Dic113—21no—
44C2×C4×D113—21no—
45Dic452—24no—
46#14268636—24no—
47#14268635—28no—
48C2×#11744751—22no—
49C2×#11744751C2312yes—
50C4⋊Dic113D412yes—
51#14268626—24no—
52C22⋊Dic113—24no—
53C22⋊Dic113D412yes—
54C4×Dic113—24no—
55C4×Dic113C2312yes—
56C24×C113—21no—
57C2×D4×C113—22no—
58C2×D4×C113—21no—
59C2×D4×C113—22no—
60C2×D4×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62M16×C113—22no—
63C2×C8×C113C2312yes—
64C4⋊C4×C113C2312yes—
65C22⋊C4×C113—21no—
66C42×C113—21no—
67C23×C113—22no—
68C23×C113—42no—
69C23×C113—82no—
70C23×C113C2×D411yescharacteristic
71C22×D113—21no—
72D4×C113—22no—
73D4×C113—22no—
74D4×C113—42no—
75C2×C4×C113—22no—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D412yes—
78C2×C4×C113#4112yes—
79C2×C4×C113C2411yescharacteristic
80C22⋊D113—42no—
81C22⋊D113—84no—
82C2×Dic113—24no—
83C2×Dic113—22no—
84C2×Dic113—21no—
85C2×Dic113C2×D414yes—
86D452—21no—
87D452—21no—
88C4×D113—42no—
89Dic226—24no—
90Dic226—22no—
91Dic226—21no—
92Dic226—21no—
93Dic226C2×D414yes—
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—42no—
105C4×C113#12112yes—
106C4×C113C22×D411yescharacteristic
107C4×C113C2×#4111yescharacteristic
108Dic113—24no—
109Dic113—24no—
110Dic113—41no—
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×SD16—1131no—
120#535—1131no—
121#519—1131no—
122#464—1134no—
123#460—1134no—
124#424—1131no—
125#418D11311yescharacteristic, complemented
126#416—1131no—
127C2×#41—1131no—
128C22×Q8—1131no—
129C22×D4C2×D11311yescharacteristic
130#137—2264no—
131C2×Q16—1132no—
132C2×SD16—1134no—
133C2×SD16—1132no—
134C2×SD16—2264no—
135C2×M16C2×D11311yescharacteristic
136C22×C8—1131no—
137#127—1132no—
138#124—1132no—
139#121—2262no—
140#120—2262no—
141C4×Q8—1134no—
142C4×Q8—2262no—
143#117—1131no—
144#117—2262no—
145#117C2×D11311yescharacteristic
146C4⋊C8—1134no—
147#103—1132no—
148#102—1132no—
149#102C2×D11314yes—
150C24—21no—
151#41—2262no—
152#41—2262no—
153C2×Q8—1134no—
154C2×Q8—1132no—
155C2×Q8—1131no—
156C2×Q8—2261no—
157C2×Q8—2262no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—1131no—
162C2×D4—2264no—
163C2×D4—2261no—
164C2×D4C22×D11312yes—
165C22×C4—2261no—
166C22×C4—2261no—
167C22×C4C22×D11311yescharacteristic
168Q16—2264no—
169SD16—2264no—
170SD16—2268no—
171M16—22no—
172C2×C8—1132no—
173C2×C8—2262no—
174C2×C8C22×D11312yes—
175C4⋊C4—1132no—
176C4⋊C4—2264no—
177C4⋊C4C22×D11312yes—
178C22⋊C4—21no—
179C22⋊C4—1132no—
180C22⋊C4—2264no—
181C42—21no—
182C42—1132no—
183C42—2264no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—2261no—
188C23D4×D11311yescharacteristic
189Q8—1134no—
190Q8—2261no—
191Q8—2261no—
192Q8—2264no—
193Q8—2262no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—9044no—
198D4—4522no—
199D4—2261no—
200D4—2261no—
201C2×C4—22no—
202C2×C4—1134no—
203C2×C4—4522no—
204C2×C4—2261no—
205C2×C4—2264no—
206C2×C4—2262no—
207C2×C4D4×D11311yescharacteristic
208C2×C4D4×D11312yes—
209C2×C4#1426864712yes—
210C2×C4C23×D11311yescharacteristic
211C8—22no—
212C8—2262no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—4521no—
218C22—4522no—
219C22#1681359512yes—
220C22C2×D4×D11311yescharacteristic
221C4—42no—
222C4—4521no—
223C4—2264no—
224C4—2264no—
225C4#1681359512yes—
226C4C2×D4×D11311yescharacteristic
227C4C2×#1426864711yescharacteristic
228C2—22no—
229C2—82no—
230C2—9041no—
231C2C2×#1681359511yescharacteristic
232C2#2029940812yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
prime radical#20299165C2
hypercenter#418D113
hypocenterC113#3043
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C22×#14268635C2semidirect
4. #20299075C2semidirect
5. #20298819C2semidirect
6. #20298797C2semidirect
7. #20298626C2semidirect
8. #20298592C2semidirect
9. #418×C113C2semidirect
13. C2×Dic452C22semidirect
14. C2×#14268636C22semidirect
23. #16813587C22semidirect
26. #16813551C22semidirect
27. #16813545C22semidirect
28. #16813542C22semidirect
37. C2×Dic226D4semidirect
117. C113#3043semidirect
125. #418D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C22×#142686352
#202991652
#202990752
#202988192
#202987972
#202986262
#202985922
#418×C1132
#3043113