Finite Group Databasebeta

← #508×D113 #28403688

Subgroups — #508×D113 #28403688

Order 14464.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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#135×D113C212yesmaximal, complemented
2#20299031C211yesmaximal, characteristic, complemented
3#20299030C211yesmaximal, characteristic, complemented
4#20299029C212yesmaximal, complemented
5#20299028C212yesmaximal, complemented
6#20299027C211yesmaximal, characteristic, complemented
7Q32×D113C211yesmaximal, characteristic, complemented
8SD32×D113C212yesmaximal, complemented
9D16×D113C211yesmaximal, characteristic, complemented
10C2×C16×D113C211yesmaximal, characteristic, complemented
11#508×C113C211yesmaximal, characteristic, complemented
12#41×D113—22no—
13#16813645C2212yescomplemented
14#16813644C2212yescomplemented
15#16813643—22no—
16#16813642—22no—
17#16813641C2212yescomplemented
18Q16×D113C2212yes—
19SD16×D113—22no—
20D8×D113C2212yes—
21C2×C8×D113C2211yescharacteristic
22Dic904C2211yescharacteristic, complemented
23#16813568C2212yescomplemented
24#16813567C2212yescomplemented
25#16813566C2212yescomplemented
26#16813565C2212yescomplemented
27D1808C2211yescharacteristic, complemented
28#16813563C2212yescomplemented
29C2×#14268622C2211yescharacteristic, complemented
30C16×D113C2211yescharacteristic
31C16×D113C2211yescharacteristic
32C16×D113C2211yescharacteristic, complemented
33C16×D113C2211yescharacteristic, complemented
34#135×C113C2212yescomplemented
35Q32×C113C2211yescharacteristic, complemented
36SD32×C113C2212yescomplemented
37D16×C113C2211yescharacteristic, complemented
38C2×C16×C113C2211yescharacteristic, complemented
39#14268648—22no—
40#14268647—22no—
41#14268647—42no—
42#14268646—22no—
43#14268646—42no—
44Q8×D113—22no—
45D4×D113—22no—
46D4×D113—42no—
47C2×C4×D113—42no—
48C2×C4×D113D411yescharacteristic
49Dic452C2312yes—
50#14268637—22no—
51#14268636—22no—
52#14268635—22no—
53#14268634—22no—
54D904C2312yes—
55#14268632—22no—
56C2×#11744751D411yescharacteristic
57C8×D113D411yescharacteristic
58C8×D113D411yescharacteristic
59C8×D113C2311yescharacteristic
60C8×D113C2311yescharacteristic
61#14268622C2311yescharacteristic
62#14268622C2311yescharacteristic
63#41×C113—22no—
64Q16×C113C2312yes—
65SD16×C113—22no—
66D8×C113C2312yes—
67C2×C8×C113C2311yescharacteristic
68C16×C113C2311yescharacteristic
69C16×C113C2311yescharacteristic
70C22×D113—42no—
71C22×D113D811yescharacteristic
72Q8×C113—22no—
73D4×C113—22no—
74D4×C113—42no—
75C2×C4×C113—42no—
76C2×C4×C113C2×D411yescharacteristic
77C22⋊D113—42no—
78C22⋊D113—42no—
79C22⋊D113—42no—
80C2×Dic113—42no—
81C2×Dic113D811yescharacteristic
82D452—22no—
83D452—42no—
84C4×D113—42no—
85C4×D113—42no—
86C4×D113—42no—
87C4×D113D811yescharacteristic
88C4×D113D811yescharacteristic
89C4×D113C2×D411yescharacteristic
90C4×D113C2×D411yescharacteristic
91Dic226—22no—
92Dic226—42no—
93C8×C113C2×D411yescharacteristic
94C8×C113C2411yescharacteristic
95#11744751C2×D411yescharacteristic
96#11744751C2×D411yescharacteristic
97C22×C113—42no—
98C22×C113C2×D811yescharacteristic
99C2×D113—22no—
100C2×D113—42no—
101C2×D113—84no—
102C2×D113C2×D811yescharacteristic
103C2×D113C2×D811yescharacteristic
104C4×C113—42no—
105C4×C113C2×D811yescharacteristic
106C4×C113C22×D411yescharacteristic
107Dic113—42no—
108Dic113C2×D811yescharacteristic
109Dic113C2×D811yescharacteristic
110C2×C113—21no—
111C2×C113—82no—
112C2×C113C22×D811yescharacteristic
113D113—21no—
114D113—82no—
115D113#50812yesdirect product factor
116C2×#508—1131nomaximal, Sylow
117C113C2×#50811yescharacteristic, complemented, Sylow
118C2×#135—1132no—
119#508—1132no—
120#508—1131no—
121#508—1132no—
122#508—1131no—
123#508—1131no—
124#508D11311yescharacteristic, direct product factor
125C2×Q32—1131no—
126C2×SD32—1132no—
127C2×D16—1131no—
128C22×C16—1131no—
129C2×#41—2262no—
130#135—1132no—
131#135—1132no—
132#135—1132no—
133#135—2262no—
134#135—2262no—
135#135C2×D11312yescomplemented
136C2×Q16—1132no—
137C2×SD16—2262no—
138C2×D8—1132no—
139C22×C8—1131no—
140Q32—1132no—
141Q32—1131no—
142Q32C2×D11311yescharacteristic, complemented
143SD32—1132no—
144SD32—1132no—
145SD32—1132no—
146SD32C2×D11312yescomplemented
147D16—1132no—
148D16—1131no—
149D16C2×D11311yescharacteristic, complemented
150C2×C16—1131no—
151C2×C16—1131no—
152C2×C16—1131no—
153C2×C16—1131no—
154C2×C16—1131no—
155C2×C16C2×D11311yescharacteristic, complemented
156#41—22no—
157#41—4522no—
158#41—4522no—
159#41—2262no—
160#41—2262no—
161#41—2262no—
162C2×Q8—2262no—
163C2×D4—4522no—
164C2×D4—2262no—
165C22×C4—1131no—
166C22×C4—4522no—
167Q16—1132no—
168Q16—2262no—
169Q16C22×D11312yes—
170SD16—22no—
171SD16—2262no—
172SD16—2262no—
173SD16—2262no—
174D8—1132no—
175D8—2262no—
176D8C22×D11312yes—
177C2×C8—1131no—
178C2×C8—1131no—
179C2×C8—1131no—
180C2×C8—1131no—
181C2×C8—1131no—
182C2×C8C22×D11311yescharacteristic
183C16—1131no—
184C16—1131no—
185C16C22×D11311yescharacteristic
186C16C22×D11311yescharacteristic
187C23—1131no—
188C23—4522no—
189Q8—22no—
190Q8—4522no—
191Q8—2262no—
192D4—22no—
193D4—42no—
194D4—4522no—
195D4—4522no—
196D4—4522no—
197D4—4522no—
198D4—2262no—
199C2×C4—42no—
200C2×C4—1131no—
201C2×C4—1131no—
202C2×C4—1131no—
203C2×C4—1131no—
204C2×C4—1131no—
205C2×C4—4522no—
206C2×C4—4522no—
207C2×C4—4522no—
208C2×C4—4522no—
209C2×C4D4×D11311yescharacteristic
210C8—1131no—
211C8—1131no—
212C8D4×D11311yescharacteristic
213C8C23×D11311yescharacteristic
214C22—42no—
215C22—1131no—
216C22—1131no—
217C22—9044no—
218C22—4522no—
219C22—2262no—
220C22D8×D11311yescharacteristic
221C4—42no—
222C4—1131no—
223C4—1131no—
224C4—4522no—
225C4D8×D11311yescharacteristic
226C4C2×D4×D11311yescharacteristic
227C2—21no—
228C2—82no—
229C2—1132no—
230C2—9042no—
231C2—2261no—
232C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC4D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#508×C113C2
socleC2×C113C22×D8
hypercenter#508D113
hypocenterC113C2×#508
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D113C2semidirect
2. #20299031C2semidirect
3. #20299030C2semidirect
4. #20299029C2semidirect
5. #20299028C2semidirect
6. #20299027C2semidirect
7. Q32×D113C2semidirect
8. SD32×D113C2semidirect
9. D16×D113C2semidirect
10. C2×C16×D113C2semidirect
11. #508×C113C2semidirect
13. #16813645C22semidirect
14. #16813644C22semidirect
17. #16813641C22semidirect
22. Dic904C22semidirect
23. #16813568C22semidirect
24. #16813567C22semidirect
25. #16813566C22semidirect
26. #16813565C22semidirect
27. D1808C22semidirect
28. #16813563C22semidirect
29. C2×#14268622C22semidirect
32. C16×D113C22semidirect
33. C16×D113C22semidirect
34. #135×C113C22semidirect
35. Q32×C113C22semidirect
36. SD32×C113C22semidirect
37. D16×C113C22semidirect
38. C2×C16×C113C22semidirect
115. D113#508direct (N × H)
117. C113C2×#508semidirect
124. #508D113direct (N × H)
135. #135C2×D113semidirect
142. Q32C2×D113semidirect
146. SD32C2×D113semidirect
149. D16C2×D113semidirect
155. C2×C16C2×D113semidirect

Maximal subgroups

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

subgroupindex
#135×D1132
#202990312
#202990302
#202990292
#202990282
#202990272
Q32×D1132
SD32×D1132
D16×D1132
C2×C16×D1132
#508×C1132
C2×#508113