Finite Group Databasebeta

← #28403709

Subgroups — #28403709

Order 14464.

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

normal subgroups only

This group has 364 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
1C2×#16813645C211yesmaximal, characteristic, complemented
2#135×D113C211yesmaximal, characteristic, complemented
3#20299040C212yesmaximal, complemented
4#20299039C211yesmaximal, characteristic, complemented
5#20299036C211yesmaximal, characteristic, complemented
6#20299035C212yesmaximal, complemented
7#20299033C211yesmaximal, characteristic, complemented
8#20299031C212yesmaximal, complemented
9#20299029C212yesmaximal, complemented
10M32×D113C211yesmaximal, characteristic, complemented
11#510×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—21no—
13#41×D113—21no—
14#16813645—21no—
15#16813645—21no—
16#16813645C2212yes—
17#16813645C2212yescomplemented
18#16813645C2211yescharacteristic, complemented
19#16813644C2211yescharacteristic
20#16813643—21no—
21#16813642—21no—
22#16813641C2211yescharacteristic, complemented
23Q16×D113C2211yescharacteristic, complemented
24C2×#14268634—21no—
25SD16×D113—21no—
26C2×D904C2211yescharacteristic, complemented
27D8×D113C2211yescharacteristic, complemented
28C2×C8×D113C2211yescharacteristic
29#16813568C2212yescomplemented
30#16813567C2212yescomplemented
31#16813565C2212yescomplemented
32#16813565C2212yescomplemented
33D1808C2212yescomplemented
34#16813563C2212yescomplemented
35#16813562C2211yescharacteristic, complemented
36#16813561C2212yescomplemented
37C16×D113C2212yescomplemented
38#135×C113C2211yescharacteristic
39C2×Q16×C113C2211yescharacteristic, complemented
40Q32×C113C2212yescomplemented
41SD32×C113C2212yescomplemented
42M32×C113C2211yescharacteristic, complemented
43#14268648—21no—
44#14268648—22no—
45#14268648—22no—
46#14268648—41no—
47#14268648—41no—
48#14268647—21no—
49#14268647—41no—
50#14268646—21no—
51#14268646—41no—
52Q8×D113—21no—
53C2×D452—21no—
54C2×D452—41no—
55D4×D113—21no—
56D4×D113—41no—
57C2×C4×D113—41no—
58C2×C4×D113—41no—
59C2×C4×D113D411yescharacteristic
60Dic452C2311yescharacteristic
61#14268637—21no—
62#14268636—21no—
63#14268635—21no—
64#14268634—21no—
65#14268634—22no—
66#14268634—22no—
67D904—21no—
68D904C2311yescharacteristic
69D904C2312yes—
70#14268632—21no—
71C2×#11744751D411yescharacteristic
72C8×D113D411yescharacteristic
73C8×D113D411yescharacteristic
74C8×D113C2311yescharacteristic
75C8×D113C2311yescharacteristic
76#14268622C2312yes—
77#41×C113—21no—
78C2×Q8×C113—21no—
79Q16×C113—21no—
80Q16×C113C2312yes—
81Q16×C113C2311yescharacteristic
82SD16×C113—21no—
83D8×C113C2311yescharacteristic
84C2×C8×C113C2311yescharacteristic
85C16×C113C2312yes—
86C22×D113—41no—
87C22×D113—41no—
88C22×D113D811yescharacteristic
89Q8×C113—21no—
90Q8×C113—22no—
91Q8×C113—41no—
92D4×C113—21no—
93D4×C113—41no—
94C2×C4×C113—41no—
95C2×C4×C113—41no—
96C2×C4×C113C2×D411yescharacteristic
97C22⋊D113—41no—
98C22⋊D113—41no—
99C22⋊D113—41no—
100C2×Dic113—41no—
101C2×Dic113D811yescharacteristic
102D452—21no—
103D452—22no—
104D452—41no—
105D452—42no—
106D452—42no—
107D452—41no—
108C4×D113—41no—
109C4×D113—41no—
110C4×D113—41no—
111C4×D113—42no—
112C4×D113—42no—
113C4×D113D811yescharacteristic
114C4×D113D811yescharacteristic
115C4×D113C2×D411yescharacteristic
116C4×D113C2×D411yescharacteristic
117Dic226—21no—
118Dic226—41no—
119C8×C113C2×D411yescharacteristic
120C8×C113C2411yescharacteristic
121#11744751C2×D411yescharacteristic
122#11744751C2×D411yescharacteristic
123C22×C113—41no—
124C22×C113C2×D811yescharacteristic
125C2×D113—41no—
126C2×D113—42no—
127C2×D113—41no—
128C2×D113—82no—
129C2×D113—82no—
130C2×D113C2×D811yescharacteristic
131C2×D113C2×D811yescharacteristic
132C4×C113—41no—
133C4×C113—42no—
134C4×C113C2×D811yescharacteristic
135C4×C113C22×D411yescharacteristic
136Dic113—41no—
137Dic113C2×D811yescharacteristic
138Dic113C2×D811yescharacteristic
139C2×C113—21no—
140C2×C113—81no—
141C2×C113C22×D811yescharacteristic
142D113—21no—
143D113—21no—
144D113—82no—
145D113—81no—
146#3414—1131nomaximal, Sylow
147C113#341411yescharacteristic, complemented, Sylow
148C2×#135—1131no—
149C2×#135—1131no—
150#510—1131no—
151#510—1132no—
152#510D11311yescharacteristic, complemented
153#509—1131no—
154#509—1132no—
155#509—1131no—
156#508—1132no—
157#508—1132no—
158C2×M32—1131no—
159C2×#41—2261no—
160C2×#41—2261no—
161#135—1132no—
162#135—1131no—
163#135—1132no—
164#135—1131no—
165#135—1131no—
166#135—2261no—
167#135—2261no—
168#135—2261no—
169#135—2261no—
170#135C2×D11311yescharacteristic
171C2×Q16—1131no—
172C2×Q16C2×D11311yescharacteristic, complemented
173C2×SD16—2261no—
174C2×SD16—2261no—
175C2×D8—1131no—
176C2×D8—1131no—
177C22×C8—1131no—
178Q32—1132no—
179Q32C2×D11312yescomplemented
180SD32—1132no—
181SD32—1132no—
182SD32—1132no—
183SD32C2×D11312yescomplemented
184D16—1132no—
185D16—1132no—
186M32—1131no—
187M32—1132no—
188M32C2×D11311yescharacteristic, complemented
189C2×C16—1132no—
190#41—21no—
191#41—4521no—
192#41—4521no—
193#41—4521no—
194#41—4521no—
195#41—2261no—
196#41—2262no—
197#41—2261no—
198#41—2262no—
199#41—2261no—
200C2×Q8—21no—
201C2×Q8—2261no—
202C2×D4—4521no—
203C2×D4—4521no—
204C2×D4—2261no—
205C2×D4—2261no—
206C22×C4—1131no—
207C22×C4—4521no—
208C22×C4—4521no—
209Q16—21no—
210Q16—1131no—
211Q16—2261no—
212Q16C22×D11311yescharacteristic
213Q16C22×D11312yes—
214SD16—21no—
215SD16—2261no—
216SD16—2262no—
217SD16—2261no—
218SD16—2262no—
219SD16—2261no—
220D8—1132no—
221D8—1131no—
222D8—2261no—
223D8—2261no—
224D8C22×D11311yescharacteristic
225C2×C8—1131no—
226C2×C8—1131no—
227C2×C8—1131no—
228C2×C8—1131no—
229C2×C8—1131no—
230C2×C8C22×D11311yescharacteristic
231C16—1132no—
232C16C22×D11312yes—
233C23—1131no—
234C23—4521no—
235C23—4521no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—4521no—
240Q8—2261no—
241D4—21no—
242D4—41no—
243D4—4521no—
244D4—4522no—
245D4—4522no—
246D4—4521no—
247D4—4521no—
248D4—4521no—
249D4—4521no—
250D4—2261no—
251D4—2262no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—1131no—
255C2×C4—1131no—
256C2×C4—1131no—
257C2×C4—1131no—
258C2×C4—1131no—
259C2×C4—4521no—
260C2×C4—4522no—
261C2×C4—4522no—
262C2×C4—4521no—
263C2×C4—4521no—
264C2×C4—4521no—
265C2×C4D4×D11311yescharacteristic
266C8—1131no—
267C8—1131no—
268C8D4×D11311yescharacteristic
269C8C23×D11311yescharacteristic
270C22—41no—
271C22—1131no—
272C22—1131no—
273C22—9042no—
274C22—9042no—
275C22—4521no—
276C22—4522no—
277C22—4521no—
278C22D8×D11311yescharacteristic
279C4—41no—
280C4—42no—
281C4—1131no—
282C4—1131no—
283C4—4521no—
284C4D8×D11311yescharacteristic
285C4C2×D4×D11311yescharacteristic
286C2—21no—
287C2—81no—
288C2—9042no—
289C2—9041no—
290C2—2261no—
291C2—2261no—
292C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC2C2×D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#510×C113C2
socleC2×C113C22×D8
hypercenter#510D113
hypocenterC113#3414
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. C2×#16813645C2semidirect
2. #135×D113C2semidirect
3. #20299040C2semidirect
4. #20299039C2semidirect
5. #20299036C2semidirect
6. #20299035C2semidirect
7. #20299033C2semidirect
8. #20299031C2semidirect
9. #20299029C2semidirect
10. M32×D113C2semidirect
11. #510×C113C2semidirect
17. #16813645C22semidirect
18. #16813645C22semidirect
22. #16813641C22semidirect
23. Q16×D113C22semidirect
26. C2×D904C22semidirect
27. D8×D113C22semidirect
29. #16813568C22semidirect
30. #16813567C22semidirect
31. #16813565C22semidirect
32. #16813565C22semidirect
33. D1808C22semidirect
34. #16813563C22semidirect
35. #16813562C22semidirect
36. #16813561C22semidirect
37. C16×D113C22semidirect
39. C2×Q16×C113C22semidirect
40. Q32×C113C22semidirect
41. SD32×C113C22semidirect
42. M32×C113C22semidirect
147. C113#3414semidirect
152. #510D113semidirect
172. C2×Q16C2×D113semidirect
179. Q32C2×D113semidirect
183. SD32C2×D113semidirect
188. M32C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136452
#135×D1132
#202990402
#202990392
#202990362
#202990352
#202990332
#202990312
#202990292
M32×D1132
#510×C1132
#3414113