Finite Group Databasebeta

← #28400095

Subgroups — #28400095

Order 14464.

490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C22×#14268634C211yesmaximal, characteristic, complemented
3#20299167C211yesmaximal, characteristic
4#20298820C214yesmaximal, complemented
5#20298798C214yesmaximal, complemented
6#20298625C211yesmaximal, characteristic, complemented
7#20298602C211yesmaximal, characteristic, complemented
8#20298592C211yesmaximal, characteristic, complemented
9#519×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×D452C2211yescharacteristic
12#16813653—24no—
13C2×#14268637C2212yescomplemented
14C2×#14268634—24no—
15C2×#14268634C2214yes—
16C2×#14268634C2212yescomplemented
17C2×#14268631C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19#16813619C2212yes—
20#16813610C2212yes—
21#16813597—22no—
22#16813592—22no—
23C4⋊#11744751C2214yescomplemented
24#16813545C2212yescomplemented
25#16813542C2214yes—
26#16813542C2212yescomplemented
27C22×Q8×C113C2211yescharacteristic
28C4×Q8×C113—22no—
29C4×Q8×C113C2214yescomplemented
30#117×C113—22no—
31#117×C113C2211yescharacteristic
32#117×C113C2211yescharacteristic
33C23×D113—21no—
34#14268647—22no—
35#14268647—22no—
36C2×Dic226C2311yescharacteristic
37C2×D452—22no—
38C2×D452—22no—
39C2×D452—21no—
40C2×D452—24no—
41C2×D452C2312yes—
42C2×D452C2311yescharacteristic
43C2×C22⋊D113—21no—
44C2×C4×D113—21no—
45#14268637—24no—
46#14268634—28no—
47#14268634—24no—
48#14268631—22no—
49C2×#11744751—22no—
50C2×#11744751C2312yes—
51C2×#11744751C2312yes—
52#14268624—24no—
53C2×Q8×C113—21no—
54C2×Q8×C113—22no—
55C2×Q8×C113D414yescomplemented
56C2×Q8×C113C2312yes—
57C22×C4×C113—21no—
58C22×C4×C113C2311yescharacteristic
59C4⋊C4×C113—24no—
60C4⋊C4×C113D412yes—
61C4⋊C4×C113C2312yes—
62C22⋊C4×C113—21no—
63C22⋊C4×C113D412yes—
64C42×C113—24no—
65C42×C113—21no—
66C42×C113C2312yes—
67C23×C113C2×D411yescharacteristic
68C22×D113—22no—
69C22×D113—21no—
70C22×D113—42no—
71C22×D113—82no—
72Q8×C113—24no—
73Q8×C113—22no—
74Q8×C113C2×D414yes—
75C2×C4×C113—24no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113C2×D414yes—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D412yes—
81C2×C4×C113#4112yes—
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—42no—
84C2×Dic113—21no—
85D452—22no—
86D452—21no—
87D452—22no—
88D452—21no—
89D452—42no—
90D452—84no—
91C4×D113—42no—
92Dic226—21no—
93Dic226—21no—
94#11744751—22no—
95#11744751—22no—
96C22×C113—22no—
97C22×C113#12112yes—
98C22×C113C22×D411yescharacteristic
99C2×D113—41no—
100C2×D113—42no—
101C2×D113—42no—
102C2×D113—44no—
103C2×D113—84no—
104C4×C113—24no—
105C4×C113—24no—
106C4×C113—42no—
107C4×C113#12112yes—
108C4×C113C22×D411yescharacteristic
109C4×C113C2×#4111yescharacteristic
110Dic113—41no—
111C2×C113—22no—
112C2×C113C2×#12111yescharacteristic
113C2×C113#57712yes—
114D113—81no—
115D113—82no—
116#3043—1131nomaximal, Sylow
117C113#304311yescharacteristic, complemented, Sylow
118C2×#137—1131no—
119C22×SD16—1131no—
120#535—1131no—
121#519D11311yescharacteristic, complemented
122#464—1134no—
123#460—1134no—
124#424—1131no—
125#418—1131no—
126#416—1131no—
127C2×#41—1131no—
128C22×Q8C2×D11311yescharacteristic
129C22×D4—1131no—
130#137—2264no—
131C2×Q16—1132no—
132C2×SD16—1134no—
133C2×SD16—1132no—
134C2×SD16—2264no—
135C2×M16—1131no—
136C22×C8—1131no—
137#127—1132no—
138#124—1132no—
139#121—2262no—
140#120—2262no—
141C4×Q8—22no—
142C4×Q8C2×D11314yescomplemented
143#117—22no—
144#117C2×D11311yescharacteristic
145#117C2×D11311yescharacteristic
146C4⋊C8—1134no—
147#103—1132no—
148#102—1132no—
149#102—1134no—
150C24—2261no—
151#41—2262no—
152#41—2262no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—1131no—
156C2×Q8D45214yescomplemented
157C2×Q8C22×D11312yes—
158C2×D4—1132no—
159C2×D4—1131no—
160C2×D4—2261no—
161C2×D4—2264no—
162C2×D4—2261no—
163C2×D4—2262no—
164C2×D4—2262no—
165C22×C4—21no—
166C22×C4—2261no—
167C22×C4C22×D11311yescharacteristic
168Q16—2264no—
169SD16—2268no—
170SD16—2264no—
171M16—2262no—
172C2×C8—1132no—
173C2×C8—1132no—
174C2×C8—2262no—
175C4⋊C4—24no—
176C4⋊C4C22⋊D11312yes—
177C4⋊C4C22×D11312yes—
178C22⋊C4—21no—
179C22⋊C4—2264no—
180C22⋊C4C22⋊D11312yes—
181C42—24no—
182C42—21no—
183C42C22×D11312yes—
184C23—9042no—
185C23—4522no—
186C23—2262no—
187C23—2261no—
188C23C2×C22⋊D11311yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—2261no—
192Q8—2261no—
193Q8C2×D45214yes—
194D4—9044no—
195D4—4522no—
196D4—4522no—
197D4—2262no—
198D4—2261no—
199D4—2262no—
200D4—2261no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—4522no—
205C2×C4—2261no—
206C2×C4C2×C22⋊D11314yes—
207C2×C4C2×C22⋊D11311yescharacteristic
208C2×C4C2×D45212yes—
209C2×C4#1426864712yes—
210C2×C4C23×D11311yescharacteristic
211C8—2262no—
212C8—2262no—
213C22—22no—
214C22—9044no—
215C22—4521no—
216C22—4522no—
217C22—4522no—
218C22—4524no—
219C22#1681359612yes—
220C22C22×C22⋊D11311yescharacteristic
221C4—24no—
222C4—24no—
223C4—42no—
224C4—4521no—
225C4#1681359612yes—
226C4C22×D45211yescharacteristic
227C4C2×#1426864711yescharacteristic
228C2—22no—
229C2—9042no—
230C2—9041no—
231C2C2×#1681359611yescharacteristic
232C2#2029940612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#519×C113C2
socleC22×C113C22×D4
prime radical#20299167C2
hypercenter#519D113
hypocenterC113#3043
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C22×#14268634C2semidirect
4. #20298820C2semidirect
5. #20298798C2semidirect
6. #20298625C2semidirect
7. #20298602C2semidirect
8. #20298592C2semidirect
9. #519×C113C2semidirect
13. C2×#14268637C22semidirect
16. C2×#14268634C22semidirect
23. C4⋊#11744751C22semidirect
24. #16813545C22semidirect
26. #16813542C22semidirect
29. C4×Q8×C113C22semidirect
55. C2×Q8×C113D4semidirect
117. C113#3043semidirect
121. #519D113semidirect
142. C4×Q8C2×D113semidirect
156. C2×Q8D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C22×#142686342
#202991672
#202988202
#202987982
#202986252
#202986022
#202985922
#519×C1132
#3043113