Finite Group Databasebeta

← #28403719

Subgroups — #28403719

Order 14464.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#20299411C211yesmaximal, characteristic, complemented
2#20299400C211yesmaximal, characteristic, complemented
3#20299040C212yesmaximal, complemented
4#20299036C211yesmaximal, characteristic, complemented
5#20299035C212yesmaximal, complemented
6#20299031C212yesmaximal, complemented
7#20299028C211yesmaximal, characteristic, complemented
8C2×#16813565C211yesmaximal, characteristic, complemented
9SD32×D113C212yesmaximal, complemented
10#20299016C211yesmaximal, characteristic, complemented
11#510×C113C211yesmaximal, characteristic, complemented
12#16813670—21no—
13#16813668—21no—
14#16813654—22no—
15#16813653—21no—
16#16813649—22no—
17#16813647—21no—
18#16813645C2212yes—
19#16813645C2212yescomplemented
20#16813644C2211yescharacteristic, complemented
21Q16×D113C2212yescomplemented
22C2×D904C2211yescharacteristic
23D8×D113C2212yes—
24#16813628C2211yescharacteristic
25#16813568C2211yescharacteristic, complemented
26#16813567C2212yescomplemented
27#16813566C2211yescharacteristic, complemented
28#16813565C2212yescomplemented
29#16813565C2212yescomplemented
30#16813565C2211yescharacteristic, complemented
31D1808C2212yescomplemented
32#16813563C2211yescharacteristic, complemented
33#16813561C2212yescomplemented
34C2×#14268622C2211yescharacteristic, complemented
35C16×D113C2212yescomplemented
36#135×C113C2211yescharacteristic
37C2×Q16×C113C2211yescharacteristic, complemented
38Q32×C113C2212yescomplemented
39SD32×C113C2212yescomplemented
40M32×C113C2211yescharacteristic, complemented
41#14268648—22no—
42#14268648—22no—
43#14268648—41no—
44#14268647—21no—
45#14268647—42no—
46#14268647—41no—
47#14268647D411yescharacteristic
48Q8×D113—22no—
49Q8×D113—41no—
50C2×D452—21no—
51C2×D452—41no—
52D4×D113—22no—
53D4×D113—42no—
54Dic452C2311yescharacteristic
55#14268637—22no—
56#14268636—21no—
57#14268634—22no—
58#14268634—22no—
59D904—21no—
60D904C2312yes—
61D904C2311yescharacteristic
62#14268632—22no—
63#14268631D411yescharacteristic
64#14268630D412yes—
65C8×D113C2312yes—
66#14268622C2311yescharacteristic
67#14268622C2311yescharacteristic
68#41×C113—21no—
69C2×Q8×C113—21no—
70Q16×C113—21no—
71Q16×C113C2311yescharacteristic
72Q16×C113C2312yes—
73SD16×C113—21no—
74D8×C113C2311yescharacteristic
75C2×C8×C113C2311yescharacteristic
76C16×C113C2312yes—
77C22×D113—41no—
78C22×D113—42no—
79Q8×C113—21no—
80Q8×C113—22no—
81Q8×C113—41no—
82D4×C113—21no—
83D4×C113—41no—
84C2×C4×C113—41no—
85C2×C4×C113—41no—
86C2×C4×C113C2×D411yescharacteristic
87C22⋊D113—41no—
88C22⋊D113—42no—
89C22⋊D113D812yes—
90D452—22no—
91D452—21no—
92D452—42no—
93D452—42no—
94D452—41no—
95D452D811yescharacteristic
96C4×D113—42no—
97C4×D113—41no—
98C4×D113—42no—
99C4×D113—42no—
100C4×D113C2×D412yes—
101Dic226—21no—
102Dic226—42no—
103Dic226D811yescharacteristic
104C8×C113C2×D411yescharacteristic
105C8×C113C2411yescharacteristic
106#11744751C2×D412yes—
107C22×C113—41no—
108C22×C113C2×D811yescharacteristic
109C2×D113—41no—
110C2×D113—42no—
111C2×D113—162no—
112C2×D113—161no—
113C2×D113C2×D812yes—
114C4×C113—42no—
115C4×C113—41no—
116C4×C113C2×D811yescharacteristic
117C4×C113C22×D411yescharacteristic
118Dic113—41no—
119Dic113C2×D812yes—
120C2×C113—21no—
121C2×C113—81no—
122C2×C113C22×D811yescharacteristic
123D113—22no—
124D113—81no—
125D113—82no—
126#3416—1131nomaximal, Sylow
127C113#341611yescharacteristic, complemented, Sylow
128#578—1131no—
129#576—1131no—
130#510—1132no—
131#510D11311yescharacteristic, complemented
132#509—1132no—
133#509—1131no—
134#508—1131no—
135#508—1132no—
136C2×SD32—1131no—
137C2×SD32—1132no—
138#504—1131no—
1392−1+4—2261no—
140H(5,𝔽2)—2261no—
141#137—2262no—
142#137—2261no—
143AGL(1,ℤ/8)—2262no—
144AGL(1,ℤ/8)—2261no—
145#135—1132no—
146#135—1132no—
147#135—1131no—
148#135C2×D11311yescharacteristic
149C2×Q16—1132no—
150C2×Q16C2×D11311yescharacteristic, complemented
151C2×D8—1132no—
152C2×D8—1131no—
153#131—1131no—
154Q32—1131no—
155Q32C2×D11312yescomplemented
156SD32—1132no—
157SD32—1132no—
158SD32—1131no—
159SD32—1131no—
160SD32—1132no—
161SD32C2×D11312yescomplemented
162D16—1131no—
163D16—1132no—
164M32—1132no—
165M32C2×D11311yescharacteristic, complemented
166C2×C16—1131no—
167C2×C16—1132no—
168#41—21no—
169#41—1131no—
170#41—4522no—
171#41—4521no—
172#41—4521no—
173#41—2262no—
174#41—2262no—
175#41—2261no—
176C2×Q8—21no—
177C2×Q8—4521no—
178C2×Q8—2262no—
179C2×D4—4521no—
180C2×D4—4522no—
181C2×D4—2262no—
182C2×D4—2261no—
183Q16—21no—
184Q16—1131no—
185Q16—2262no—
186Q16C22×D11312yes—
187Q16C22×D11311yescharacteristic
188SD16—21no—
189SD16—2262no—
190SD16—2262no—
191SD16—2261no—
192D8—1131no—
193D8—1132no—
194D8—2262no—
195D8—2261no—
196D8C22×D11311yescharacteristic
197M16—1131no—
198M16—1132no—
199C2×C8—1132no—
200C2×C8C22×D11311yescharacteristic
201C16—1131no—
202C16—1131no—
203C16C22×D11312yes—
204C23—4522no—
205C23—4521no—
206Q8—21no—
207Q8—22no—
208Q8—41no—
209Q8—1131no—
210Q8—4522no—
211Q8—2261no—
212D4—21no—
213D4—41no—
214D4—1132no—
215D4—1131no—
216D4—4522no—
217D4—4522no—
218D4—4522no—
219D4—4521no—
220D4—4521no—
221D4—2262no—
222D4—2261no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—1132no—
226C2×C4—4522no—
227C2×C4—4522no—
228C2×C4—4522no—
229C2×C4—4521no—
230C2×C4D4×D11311yescharacteristic
231C8—1132no—
232C8D4×D11311yescharacteristic
233C8C23×D11311yescharacteristic
234C22—41no—
235C22—18081no—
236C22—18082no—
237C22—1132no—
238C22—4521no—
239C22—4522no—
240C22D8×D11311yescharacteristic
241C4—41no—
242C4—42no—
243C4—1132no—
244C4—4521no—
245C4D8×D11311yescharacteristic
246C4C2×D4×D11311yescharacteristic
247C2—21no—
248C2—81no—
249C2—9042no—
250C2—9041no—
251C2—2262no—
252C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC2C2×D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#510×C113C2
socleC2×C113C22×D8
hypercenter#510D113
hypocenterC113#3416
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. #20299411C2semidirect
2. #20299400C2semidirect
3. #20299040C2semidirect
4. #20299036C2semidirect
5. #20299035C2semidirect
6. #20299031C2semidirect
7. #20299028C2semidirect
8. C2×#16813565C2semidirect
9. SD32×D113C2semidirect
10. #20299016C2semidirect
11. #510×C113C2semidirect
19. #16813645C22semidirect
20. #16813644C22semidirect
21. Q16×D113C22semidirect
25. #16813568C22semidirect
26. #16813567C22semidirect
27. #16813566C22semidirect
28. #16813565C22semidirect
29. #16813565C22semidirect
30. #16813565C22semidirect
31. D1808C22semidirect
32. #16813563C22semidirect
33. #16813561C22semidirect
34. C2×#14268622C22semidirect
35. C16×D113C22semidirect
37. C2×Q16×C113C22semidirect
38. Q32×C113C22semidirect
39. SD32×C113C22semidirect
40. M32×C113C22semidirect
127. C113#3416semidirect
131. #510D113semidirect
150. C2×Q16C2×D113semidirect
155. Q32C2×D113semidirect
161. SD32C2×D113semidirect
165. M32C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994112
#202994002
#202990402
#202990362
#202990352
#202990312
#202990282
C2×#168135652
SD32×D1132
#202990162
#510×C1132
#3416113