Finite Group Databasebeta

← #28400083

Subgroups — #28400083

Order 14464.

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

normal subgroups only

This group has 494 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×#16813648C211yesmaximal, characteristic
2#20299172C211yesmaximal, characteristic, complemented
3#20299073C211yesmaximal, characteristic, complemented
4#20298815C214yesmaximal, complemented
5#20298801C214yesmaximal, complemented
6#20298624C211yesmaximal, characteristic, complemented
7#20298607C211yesmaximal, characteristic, complemented
8#20298595C211yesmaximal, characteristic, complemented
9C22×SD16×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11#16813648—24no—
12C2×#14268635C2212yes—
13C2×#14268632C2212yes—
14C2×#14268631C2211yescharacteristic
15#16813620C2212yescomplemented
16#16813611C2212yescomplemented
17#16813605—22no—
18#16813598—22no—
19D4×Dic113—22no—
20D4×Dic113C2214yes—
21#16813581C2211yescharacteristic
22#16813581C2211yescharacteristic
23C2×C22⋊Dic113—22no—
24#16813551C2214yescomplemented
25#16813547C2212yescomplemented
26#16813546C2214yescomplemented
27#16813544C2212yescomplemented
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—
38C22×Dic113—24no—
39C2×C4×D113—21no—
40#14268635—24no—
41#14268632—24no—
42#14268631—22no—
43C2×#11744751C2312yes—
44C4⋊Dic113D412yes—
45C4⋊Dic113C2312yes—
46#14268626—24no—
47C22⋊Dic113—21no—
48C22⋊Dic113—24no—
49C22⋊Dic113D412yes—
50#14268624—24no—
51C4×Dic113—21no—
52C4×Dic113C2312yes—
53C24×C113—21no—
54C2×Q8×C113—21no—
55C2×Q8×C113—22no—
56C2×Q8×C113—22no—
57C2×Q8×C113C2312yes—
58C2×D4×C113—21no—
59C2×D4×C113—22no—
60C2×D4×C113D414yes—
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—24no—
69C23×C113—82no—
70C23×C113C2×D411yescharacteristic
71C22×D113—21no—
72Q8×C113—22no—
73Q8×C113—22no—
74Q8×C113—42no—
75D4×C113—24no—
76D4×C113—22no—
77D4×C113C2×D414yes—
78C2×C4×C113—22no—
79C2×C4×C113—42no—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D412yes—
82C2×C4×C113#4112yes—
83C2×C4×C113C2411yescharacteristic
84C22⋊D113—42no—
85C2×Dic113—22no—
86C2×Dic113—21no—
87C2×Dic113—84no—
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—24no—
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—41no—
110Dic113—42no—
111C2×C113—22no—
112C2×C113—44no—
113C2×C113C2×#12111yescharacteristic
114C2×C113#57712yes—
115D113—81no—
116#3042—1131nomaximal, Sylow
117C113#304211yescharacteristic, complemented, Sylow
118C2×AGL(1,ℤ/8)—1131no—
119C22×SD16D11311yescharacteristic, complemented
120#536—1131no—
121#518—1131no—
122#463—1134no—
123#461—1134no—
124#424—1131no—
125#419—1131no—
126#416—1131no—
127C2×#41—1131no—
128C22×Q8C2×D11311yescharacteristic
129C22×D4C2×D11311yescharacteristic
130AGL(1,ℤ/8)—2264no—
131C2×SD16—24no—
132C2×SD16—1132no—
133C2×SD16C2×D11314yes—
134C2×D8—1132no—
135C2×M16—1131no—
136C22×C8C2×D11311yescharacteristic
137C4⋊Q8—1132no—
138#124—1132no—
139#123—2262no—
140C22⋊Q8—2262no—
141C4×D4—1134no—
142C4×D4—2262no—
143#117—1131no—
144#117—1131no—
145C2×C22⋊C4—2262no—
146C4⋊C8—1134no—
147#103—1134no—
148#103—1132no—
149#102—1132no—
150C24—21no—
151#41—2262no—
152#41—2262no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—1131no—
157C2×Q8C22×D11312yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—1131no—
161C2×D4—2261no—
162C2×D4C22⋊D11314yes—
163C2×D4C22×D11312yes—
164C22×C4—21no—
165C22×C4—2264no—
166C22×C4—2261no—
167C22×C4C22×D11311yescharacteristic
168SD16—28no—
169SD16—2264no—
170D8—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—2264no—
181C22⋊C4—2261no—
182C42—1132no—
183C42—2261no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—2261no—
188C23D4×D11311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—2261no—
193Q8—2261no—
194D4—24no—
195D4—22no—
196D4—4522no—
197D4—2261no—
198D4—2261no—
199D4C2×C22⋊D11314yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—1134no—
203C2×C4—9044no—
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—24no—
215C22—44no—
216C22—84no—
217C22—4521no—
218C22—4522no—
219C22#1681359412yes—
220C22C2×D4×D11311yescharacteristic
221C4—42no—
222C4—4521no—
223C4—4522no—
224C4—2264no—
225C4#1681359412yes—
226C4C22×C22⋊D11311yescharacteristic
227C4C2×#1426864611yescharacteristic
228C2—22no—
229C2—44no—
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 radicalC2×#16813648C2
hypercenterC22×SD16D113
hypocenterC113#3042
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
2. #20299172C2semidirect
3. #20299073C2semidirect
4. #20298815C2semidirect
5. #20298801C2semidirect
6. #20298624C2semidirect
7. #20298607C2semidirect
8. #20298595C2semidirect
9. C22×SD16×C113C2semidirect
15. #16813620C22semidirect
16. #16813611C22semidirect
24. #16813551C22semidirect
25. #16813547C22semidirect
26. #16813546C22semidirect
27. #16813544C22semidirect
117. C113#3042semidirect
119. C22×SD16D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202991722
#202990732
#202988152
#202988012
#202986242
#202986072
#202985952
C22×SD16×C1132
#3042113