Finite Group Databasebeta

← #28403720

Subgroups — #28403720

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#20299412C211yesmaximal, characteristic, complemented
2#20299399C211yesmaximal, characteristic, complemented
3#20299041C211yesmaximal, characteristic, complemented
4#20299037C212yesmaximal, complemented
5#20299032C212yesmaximal, complemented
6#20299028C211yesmaximal, characteristic, complemented
7#20299027C212yesmaximal, complemented
8C2×#16813566C211yesmaximal, characteristic, complemented
9SD32×D113C212yesmaximal, complemented
10#20299016C211yesmaximal, characteristic, complemented
11#509×C113C211yesmaximal, characteristic, complemented
12#16813669—21no—
13#16813667—21no—
14#16813652—21no—
15#16813651—22no—
16#16813648—21no—
17#16813646—22no—
18#16813644C2211yescharacteristic
19#16813641C2212yes—
20#16813641C2212yescomplemented
21C2×Dic452C2211yescharacteristic, complemented
22Q16×D113C2212yescomplemented
23D8×D113C2212yes—
24#16813628C2211yescharacteristic
25Dic904C2212yescomplemented
26#16813568C2211yescharacteristic, complemented
27#16813567C2212yescomplemented
28#16813566C2212yescomplemented
29#16813566C2212yescomplemented
30#16813566C2211yescharacteristic, complemented
31#16813565C2211yescharacteristic, complemented
32#16813563C2211yescharacteristic, complemented
33#16813561C2212yescomplemented
34C2×#14268622C2211yescharacteristic, complemented
35C16×D113C2212yescomplemented
36#135×C113C2211yescharacteristic, complemented
37C2×D8×C113C2211yescharacteristic
38SD32×C113C2212yescomplemented
39D16×C113C2212yescomplemented
40M32×C113C2211yescharacteristic, complemented
41#14268647—21no—
42#14268647—41no—
43#14268647D411yescharacteristic
44#14268646—22no—
45#14268646—22no—
46#14268646—42no—
47#14268646—41no—
48C2×Dic226—21no—
49C2×Dic226—41no—
50Q8×D113—22no—
51C2×C22⋊D113—42no—
52D4×D113—22no—
53D4×D113—41no—
54Dic452—21no—
55Dic452C2311yescharacteristic
56Dic452C2312yes—
57#14268637—22no—
58#14268636—21no—
59#14268635—22no—
60#14268635—22no—
61D904C2311yescharacteristic
62#14268632—22no—
63#14268631D411yescharacteristic
64#14268630D412yes—
65C8×D113C2312yes—
66#14268622C2311yescharacteristic
67#14268622C2311yescharacteristic
68#41×C113—21no—
69C2×D4×C113—21no—
70Q16×C113C2311yescharacteristic
71SD16×C113—21no—
72D8×C113—21no—
73D8×C113C2312yes—
74D8×C113C2311yescharacteristic
75C2×C8×C113C2311yescharacteristic
76C16×C113C2312yes—
77C23×C113—41no—
78C22×D113—42no—
79Q8×C113—21no—
80D4×C113—22no—
81D4×C113—21no—
82D4×C113—41no—
83D4×C113—41no—
84C2×C4×C113—41no—
85C2×C4×C113C2×D411yescharacteristic
86C22⋊D113—41no—
87C22⋊D113—42no—
88C22⋊D113—42no—
89C22⋊D113—42no—
90C22⋊D113D812yes—
91C2×Dic113—41no—
92C2×Dic113—42no—
93C2×Dic113—42no—
94D452—21no—
95D452D811yescharacteristic
96C4×D113—42no—
97C4×D113—41no—
98C4×D113C2×D412yes—
99Dic226—21no—
100Dic226—22no—
101Dic226—41no—
102Dic226—42no—
103Dic226D811yescharacteristic
104C8×C113C2×D411yescharacteristic
105C8×C113C2411yescharacteristic
106#11744751C2×D412yes—
107C22×C113—41no—
108C22×C113—42no—
109C22×C113—161no—
110C22×C113C2×D811yescharacteristic
111C2×D113—41no—
112C2×D113—162no—
113C2×D113C2×D812yes—
114C4×C113—41no—
115C4×C113C2×D811yescharacteristic
116C4×C113C22×D411yescharacteristic
117Dic113—42no—
118Dic113—41no—
119Dic113C2×D812yes—
120C2×C113—21no—
121C2×C113—82no—
122C2×C113—81no—
123C2×C113C22×D811yescharacteristic
124D113—22no—
125D113—81no—
126#3416—1131nomaximal, Sylow
127C113#341611yescharacteristic, complemented, Sylow
128#578—1131no—
129#576—1131no—
130#510—1132no—
131#510—1131no—
132#509—1132no—
133#509D11311yescharacteristic, complemented
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, complemented
149C2×Q16—1132no—
150C2×Q16—1131no—
151C2×D8—1132no—
152C2×D8C2×D11311yescharacteristic
153#131—1131no—
154Q32—1131no—
155Q32—1132no—
156SD32—1131no—
157SD32—1132no—
158SD32—1132no—
159SD32—1131no—
160SD32—1132no—
161SD32C2×D11312yescomplemented
162D16—1131no—
163D16C2×D11312yescomplemented
164M32—1132no—
165M32C2×D11311yescharacteristic, complemented
166C2×C16—1131no—
167C2×C16—1132no—
168#41—21no—
169#41—1131no—
170#41—4521no—
171#41—4522no—
172#41—4521no—
173#41—2262no—
174#41—2262no—
175#41—2261no—
176C2×Q8—4521no—
177C2×Q8—2262no—
178C2×Q8—2261no—
179C2×D4—21no—
180C2×D4—4521no—
181C2×D4—4522no—
182C2×D4—2262no—
183Q16—1132no—
184Q16—1131no—
185Q16—2262no—
186Q16—2261no—
187Q16C22×D11311yescharacteristic
188SD16—21no—
189SD16—2262no—
190SD16—2262no—
191SD16—2261no—
192D8—21no—
193D8—1131no—
194D8—2262no—
195D8C22×D11311yescharacteristic
196D8C22×D11312yes—
197M16—1131no—
198M16—1132no—
199C2×C8—1132no—
200C2×C8C22×D11311yescharacteristic
201C16—1131no—
202C16—1131no—
203C16C22×D11312yes—
204C23—41no—
205C23—4522no—
206Q8—21no—
207Q8—1131no—
208Q8—4522no—
209Q8—4521no—
210Q8—2261no—
211Q8—2262no—
212D4—22no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—1132no—
217D4—1131no—
218D4—4522no—
219D4—4522no—
220D4—4522no—
221D4—4521no—
222D4—2261no—
223C2×C4—41no—
224C2×C4—1132no—
225C2×C4—4522no—
226C2×C4—4522no—
227C2×C4—4522no—
228C2×C4—4521no—
229C2×C4—4521no—
230C2×C4D4×D11311yescharacteristic
231C8—1132no—
232C8D4×D11311yescharacteristic
233C8C23×D11311yescharacteristic
234C22—41no—
235C22—42no—
236C22—161no—
237C22—18082no—
238C22—1132no—
239C22—4521no—
240C22D8×D11311yescharacteristic
241C4—41no—
242C4—1132no—
243C4—4521no—
244C4—4522no—
245C4D8×D11311yescharacteristic
246C4C2×D4×D11311yescharacteristic
247C2—21no—
248C2—82no—
249C2—81no—
250C2—9041no—
251C2—2262no—
252C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC2C2×D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#509×C113C2
socleC2×C113C22×D8
hypercenter#509D113
hypocenterC113#3416
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #20299412C2semidirect
2. #20299399C2semidirect
3. #20299041C2semidirect
4. #20299037C2semidirect
5. #20299032C2semidirect
6. #20299028C2semidirect
7. #20299027C2semidirect
8. C2×#16813566C2semidirect
9. SD32×D113C2semidirect
10. #20299016C2semidirect
11. #509×C113C2semidirect
20. #16813641C22semidirect
21. C2×Dic452C22semidirect
22. Q16×D113C22semidirect
25. Dic904C22semidirect
26. #16813568C22semidirect
27. #16813567C22semidirect
28. #16813566C22semidirect
29. #16813566C22semidirect
30. #16813566C22semidirect
31. #16813565C22semidirect
32. #16813563C22semidirect
33. #16813561C22semidirect
34. C2×#14268622C22semidirect
35. C16×D113C22semidirect
36. #135×C113C22semidirect
38. SD32×C113C22semidirect
39. D16×C113C22semidirect
40. M32×C113C22semidirect
127. C113#3416semidirect
133. #509D113semidirect
148. #135C2×D113semidirect
161. SD32C2×D113semidirect
163. D16C2×D113semidirect
165. M32C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994122
#202993992
#202990412
#202990372
#202990322
#202990282
#202990272
C2×#168135662
SD32×D1132
#202990162
#509×C1132
#3416113