Finite Group Databasebeta

← #28401023

Subgroups — #28401023

Order 14464.

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

normal subgroups only

This group has 656 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×#16813649C212yesmaximal, complemented
2C2×#16813646C212yesmaximal, complemented
3#20299147C211yesmaximal, characteristic, complemented
4#127×D113C211yesmaximal, characteristic, complemented
5#20298988C211yesmaximal, characteristic, complemented
6#20298987C211yesmaximal, characteristic, complemented
7#20298985C211yesmaximal, characteristic, complemented
8#20298973C212yesmaximal, complemented
9#20298969C212yesmaximal, complemented
10#20298550C211yesmaximal, characteristic, complemented
11#496×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×#14268646C2211yescharacteristic
14C2×D4×D113—22no—
15C2×D4×D113C2212yes—
16#16813649—28no—
17#16813646—28no—
18C2×#14268636C2212yescomplemented
19C2×#14268635C2212yescomplemented
20C2×#14268634C2212yescomplemented
21C2×D904C2212yescomplemented
22C2×#14268632C2212yescomplemented
23C2×#14268632C2212yescomplemented
24C2×#14268630C2212yes—
25#16813620C2211yescharacteristic, complemented
26#16813619C2211yescharacteristic
27#16813618—22no—
28#16813618C2212yes—
29#16813618C2211yescharacteristic, complemented
30#16813610C2211yescharacteristic, complemented
31#16813595—22no—
32#16813582—22no—
33C42×D113C2211yescharacteristic
34#16813533C2211yescharacteristic, complemented
35C8×Dic113C2212yescomplemented
36C2×SD16×C113C2212yescomplemented
37C2×D8×C113C2212yescomplemented
38#127×C113C2211yescharacteristic
39#124×C113C2211yescharacteristic, complemented
40#97×C113C2211yescharacteristic, complemented
41C23×D113—22no—
42#14268648—24no—
43#14268646—24no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—22no—
47C2×D452C2311yescharacteristic
48C2×D452C2312yes—
49C2×C22⋊D113—21no—
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52C2×C22⋊D113—24no—
53D4×D113—24no—
54D4×D113—24no—
55D4×D113—48no—
56C22×Dic113—21no—
57C2×C4×D113—21no—
58C2×C4×D113D412yes—
59C2×C4×D113C2311yescharacteristic
60#14268636—24no—
61#14268635—24no—
62#14268634—24no—
63D904—24no—
64#14268632—24no—
65#14268632—24no—
66#14268630D418yescomplemented
67C2×#11744751C2312yes—
68#14268626—22no—
69#14268624—22no—
70C4×Dic113D412yes—
71C4×Dic113C2311yescharacteristic
72C2×Q8×C113C2311yescharacteristic
73C2×D4×C113—22no—
74C2×D4×C113C2312yes—
75C2×D4×C113C2311yescharacteristic
76SD16×C113—24no—
77D8×C113—24no—
78C2×C8×C113C2312yes—
79C22⋊C4×C113—22no—
80C42×C113C2311yescharacteristic
81C23×C113—21no—
82C23×C113—22no—
83C22×D113—21no—
84C22×D113—22no—
85C22×D113—48no—
86C22×D113—44no—
87C22×D113C2×D411yescharacteristic
88Q8×C113—22no—
89D4×C113—22no—
90D4×C113—22no—
91D4×C113—22no—
92D4×C113—44no—
93C2×C4×C113—21no—
94C2×C4×C113C2×D412yes—
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—42no—
97C22⋊D113—44no—
98C22⋊D113—48no—
99C22⋊D113—44no—
100C2×Dic113—21no—
101C2×Dic113—42no—
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D412yes—
104D452—22no—
105D452—22no—
106D452—22no—
107D452—44no—
108D452—42no—
109C4×D113—24no—
110C4×D113—42no—
111C4×D113C2×D414yes—
112Dic226—22no—
113C8×C113C2×D414yescomplemented
114#11744751C2×D414yescomplemented
115C22×C113—41no—
116C22×C113—42no—
117C22×C113—44no—
118C22×C113—42no—
119C22×C113C22×D411yescharacteristic
120C2×D113—22no—
121C2×D113—41no—
122C2×D113—42no—
123C2×D113—44no—
124C2×D113—42no—
125C2×D113—88no—
126C2×D113#12712yes—
127C4×C113—22no—
128C4×C113—41no—
129C4×C113C22×D412yes—
130Dic113—41no—
131Dic113#12712yes—
132Dic113AGL(1,ℤ/8)14yescomplemented
133C2×C113—82no—
134C2×C113—81no—
135C2×C113C2×#12711yescharacteristic
136C2×C113C2×AGL(1,ℤ/8)12yes—
137D113—22no—
138D113—81no—
139D113—82no—
140#3151—1131nomaximal, Sylow
141C113#315111yescharacteristic, complemented, Sylow
142C2×AGL(1,ℤ/8)—1132no—
143C2×AGL(1,ℤ/8)—1132no—
144#532—1131no—
145C2×#127—1131no—
146#496—1131no—
147#496—1131no—
148#496—1131no—
149#496D11311yescharacteristic, complemented
150#493—1132no—
151#492—1132no—
152C4×M16—1131no—
153C2×#41—1131no—
154C2×#41—1131no—
155C22×D4—1132no—
156C22×D4—2262no—
157AGL(1,ℤ/8)—2268no—
158AGL(1,ℤ/8)—2268no—
159C2×SD16—1132no—
160C2×SD16—1132no—
161C2×SD16—1132no—
162C2×SD16C2×D11312yescomplemented
163C2×D8—1132no—
164C2×D8—1132no—
165C2×D8—1132no—
166C2×D8C2×D11312yescomplemented
167C2×M16—1132no—
168C4⋊Q8—1131no—
169#127—1132no—
170#127—1131no—
171#127—1131no—
172#127—2262no—
173#127C2×D11311yescharacteristic
174#124—1131no—
175#124C2×D11311yescharacteristic, complemented
176#121—2262no—
177C4×D4—2262no—
178C2×C42—1131no—
179#97—1131no—
180#97C2×D11311yescharacteristic, complemented
181C4×C8—1132no—
182C24—2262no—
183#41—2264no—
184#41—2264no—
185C2×Q8—1131no—
186C2×Q8C22×D11311yescharacteristic
187C2×D4—22no—
188C2×D4—1131no—
189C2×D4—1132no—
190C2×D4—4528no—
191C2×D4—2261no—
192C2×D4—2264no—
193C2×D4—2264no—
194C2×D4—2262no—
195C2×D4—2264no—
196C2×D4—2262no—
197C2×D4—2261no—
198C2×D4—2262no—
199C2×D4C22×D11311yescharacteristic
200C2×D4C22×D11312yes—
201C22×C4—1131no—
202C22×C4—1132no—
203C22×C4—2261no—
204C22×C4—2261no—
205SD16—24no—
206SD16—2264no—
207SD16—2264no—
208SD16—2264no—
209D8—24no—
210D8—2264no—
211D8—2264no—
212D8—2264no—
213M16—1138no—
214C2×C8—1132no—
215C2×C8C22×D11312yes—
216C4⋊C4—2262no—
217C22⋊C4—22no—
218C22⋊C4—2262no—
219C42—1132no—
220C42—1131no—
221C42C22×D11311yescharacteristic
222C23—21no—
223C23—22no—
224C23—1131no—
225C23—4524no—
226C23—4528no—
227C23—2261no—
228C23—2262no—
229Q8—22no—
230Q8—2262no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—4524no—
236D4—4522no—
237D4—4528no—
238D4—4524no—
239D4—4524no—
240D4—4522no—
241D4—2262no—
242D4—2262no—
243D4—2262no—
244C2×C4—21no—
245C2×C4—1132no—
246C2×C4—1131no—
247C2×C4—1134no—
248C2×C4—4522no—
249C2×C4—4522no—
250C2×C4—2264no—
251C2×C4—2261no—
252C2×C4D4×D11312yes—
253C2×C4C23×D11311yescharacteristic
254C8—1134no—
255C8D4×D11314yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—1132no—
261C22—9048no—
262C22—4524no—
263C22—4522no—
264C22—4521no—
265C22—4522no—
266C22—2262no—
267C22C2×D4×D11311yescharacteristic
268C4—22no—
269C4—41no—
270C4—1134no—
271C4—1132no—
272C4—4521no—
273C4C2×D4×D11312yes—
274C2—82no—
275C2—81no—
276C2—9042no—
277C2—9041no—
278C2—2262no—
279C2#127×D11311yescharacteristic
280C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3151
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C2×#16813646C2semidirect
3. #20299147C2semidirect
4. #127×D113C2semidirect
5. #20298988C2semidirect
6. #20298987C2semidirect
7. #20298985C2semidirect
8. #20298973C2semidirect
9. #20298969C2semidirect
10. #20298550C2semidirect
11. #496×C113C2semidirect
18. C2×#14268636C22semidirect
19. C2×#14268635C22semidirect
20. C2×#14268634C22semidirect
21. C2×D904C22semidirect
22. C2×#14268632C22semidirect
23. C2×#14268632C22semidirect
25. #16813620C22semidirect
29. #16813618C22semidirect
30. #16813610C22semidirect
34. #16813533C22semidirect
35. C8×Dic113C22semidirect
36. C2×SD16×C113C22semidirect
37. C2×D8×C113C22semidirect
39. #124×C113C22semidirect
40. #97×C113C22semidirect
66. #14268630D4semidirect
113. C8×C113C2×D4semidirect
114. #11744751C2×D4semidirect
132. Dic113AGL(1,ℤ/8)semidirect
141. C113#3151semidirect
149. #496D113semidirect
162. C2×SD16C2×D113semidirect
166. C2×D8C2×D113semidirect
175. #124C2×D113semidirect
180. #97C2×D113semidirect
255. C8D4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×#168136462
#202991472
#127×D1132
#202989882
#202989872
#202989852
#202989732
#202989692
#202985502
#496×C1132
#3151113