Finite Group Databasebeta

← #28402398

Subgroups — #28402398

Order 14464.

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

normal subgroups only

This group has 462 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
1#20299305C211yesmaximal, characteristic, complemented
2#20298944C211yesmaximal, characteristic, complemented
3#20298914C212yesmaximal, complemented
4#20298888C211yesmaximal, characteristic, complemented
5#20298825C212yesmaximal, complemented
6#20298795C211yesmaximal, characteristic, complemented
7#20298749C212yesmaximal, complemented
8C4×#14268635C211yesmaximal, characteristic, complemented
9D4×#11744751C211yesmaximal, characteristic, complemented
10C2×#16813543C212yesmaximal, complemented
11D42×C113C211yesmaximal, characteristic
12C2×#14268635C2211yescharacteristic
13C2×#14268635C2212yescomplemented
14C22×#11744751C2212yescomplemented
15#16813622C2211yescharacteristic, complemented
16#16813613—21no—
17#16813601C2212yescomplemented
18#16813599—22no—
19C4×Dic226C2211yescharacteristic, complemented
20D4×Dic113—21no—
21C2×C4⋊Dic113C2212yescomplemented
22#16813553C2212yescomplemented
23#16813553C2211yescharacteristic, complemented
24C4⋊#11744751C2211yescharacteristic, complemented
25#16813545C2211yescharacteristic, complemented
26#16813543C2211yescharacteristic
27#16813543C2212yes—
28#16813543C2212yescomplemented
29#16813543C2212yescomplemented
30#16813543C2212yescomplemented
31C22⋊#11744751C2212yescomplemented
32C4×#11744751C2211yescharacteristic, complemented
33C22×D4×C113—21no—
34C22×D4×C113C2212yes—
35#127×C113C2211yescharacteristic
36#121×C113—21no—
37#121×C113C2212yes—
38#120×C113—22no—
39C4×D4×C113C2211yescharacteristic
40C4×D4×C113C2211yescharacteristic
41C2×Dic226—21no—
42C2×Dic226C2311yescharacteristic
43C22×Dic113—22no—
44#14268635—22no—
45#14268635—42no—
46C2×#11744751—42no—
47C2×#11744751C2311yescharacteristic
48C2×#11744751C2312yes—
49C2×#11744751C2311yescharacteristic
50C4⋊Dic113—22no—
51C4⋊Dic113—21no—
52C4⋊Dic113C2311yescharacteristic
53C4⋊Dic113C2312yes—
54#14268626—21no—
55#14268626—22no—
56C22⋊Dic113—22no—
57C4×Dic113—21no—
58C24×C113—22no—
59C2×D4×C113—24no—
60C2×D4×C113—22no—
61C2×D4×C113—22no—
62C2×D4×C113—21no—
63C2×D4×C113—21no—
64C2×D4×C113—42no—
65C2×D4×C113—44no—
66C2×D4×C113D411yescharacteristic
67C2×D4×C113C2312yes—
68C2×D4×C113C2311yescharacteristic
69C22×C4×C113—21no—
70C22×C4×C113C2312yes—
71C4⋊C4×C113D411yescharacteristic
72C4⋊C4×C113C2311yescharacteristic
73C22⋊C4×C113—21no—
74C22⋊C4×C113—22no—
75C22⋊C4×C113D412yes—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C23×C113—22no—
79C23×C113—44no—
80C23×C113—44no—
81C23×C113—82no—
82C23×C113C2×D412yes—
83D4×C113—22no—
84D4×C113—21no—
85D4×C113—22no—
86D4×C113—44no—
87D4×C113—44no—
88D4×C113—42no—
89D4×C113—81no—
90D4×C113SD1614yescomplemented
91D4×C113#4112yes—
92C2×C4×C113—22no—
93C2×C4×C113—22no—
94C2×C4×C113—21no—
95C2×C4×C113—42no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C2×Dic113—21no—
101C2×Dic113—21no—
102C2×Dic113—22no—
103C2×Dic113—82no—
104Dic226—21no—
105Dic226—21no—
106Dic226—81no—
107#11744751—21no—
108#11744751—21no—
109#11744751—22no—
110C22×C113—22no—
111C22×C113—22no—
112C22×C113—22no—
113C22×C113—41no—
114C22×C113—41no—
115C22×C113—42no—
116C22×C113—42no—
117C22×C113—42no—
118C22×C113—88no—
119C22×C113C2×SD1614yes—
120C22×C113C22×D411yescharacteristic
121C4×C113—22no—
122C4×C113—21no—
123C4×C113—41no—
124C4×C113C2×SD1612yes—
125C4×C113C2×#4111yescharacteristic
126C4×C113H(5,𝔽2)11yescharacteristic
127Dic113—41no—
128Dic113—42no—
129Dic113—41no—
130C2×C113—24no—
131C2×C113—42no—
132C2×C113—82no—
133C2×C113#54611yescharacteristic
134C2×C113C22×SD1611yescharacteristic
135C2×C113#57611yescharacteristic
136#3295—1131nomaximal, Sylow
137C113#329511yescharacteristic, complemented, Sylow
138#554—1131no—
139D42D11311yescharacteristic
140#486—1131no—
141#481—1132no—
142#476—1131no—
143#465—1132no—
144#460—1131no—
145#450—1132no—
146C4×SD16—1131no—
147C8×D4—1131no—
148C2×#102—1132no—
149C22×D4—21no—
150C22×D4C2×D11312yes—
151C2×SD16—1132no—
152C2×SD16—1131no—
153C22×C8—1132no—
154C4⋊Q8—1131no—
155#127C2×D11311yescharacteristic
156#125—2261no—
157C22⋊Q8—1132no—
158C22⋊Q8—2262no—
159#121—21no—
160#121C2×D11312yes—
161#120—22no—
162C4×Q8—1131no—
163C4×D4—2261no—
164C4×D4C2×D11311yescharacteristic
165C4×D4C2×D11311yescharacteristic
166C2×C4⋊C4—1132no—
167#106—1131no—
168#106—1132no—
169C4⋊C8—1131no—
170#103—1131no—
171#102—1131no—
172#102—1132no—
173#102—1132no—
174#102—1132no—
175#102—1132no—
176C22⋊C8—1132no—
177C4×C8—1131no—
178C24—22no—
179C2×Q8—1131no—
180C2×Q8—2261no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4—44no—
188C2×D4C22⋊D11311yescharacteristic
189C2×D4C22×D11312yes—
190C2×D4C22×D11311yescharacteristic
191C22×C4—21no—
192C22×C4—2262no—
193C22×C4C22×D11312yes—
194SD16—4522no—
195SD16—2262no—
196C2×C8—1131no—
197C2×C8—1131no—
198C2×C8—1132no—
199C2×C8—4522no—
200C4⋊C4—1131no—
201C4⋊C4—1132no—
202C4⋊C4—2262no—
203C4⋊C4—2261no—
204C4⋊C4—2261no—
205C4⋊C4—2262no—
206C4⋊C4C22⋊D11311yescharacteristic
207C4⋊C4C22×D11311yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—2262no—
211C22⋊C4C22⋊D11312yes—
212C42—2261no—
213C42C22×D11311yescharacteristic
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D11312yes—
220Q8—9041no—
221Q8—2261no—
222Q8—2261no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1426863514yescomplemented
231D4#1426864612yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—9042no—
237C2×C4—2261no—
238C2×C4—2261no—
239C2×C4—2262no—
240C2×C4C2×C22⋊D11311yescharacteristic
241C2×C4C2×C22⋊D11312yes—
242C2×C4C2×C22⋊D11311yescharacteristic
243C2×C4C23×D11311yescharacteristic
244C8—2261no—
245C8—2261no—
246C8—2262no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#1426863514yes—
257C22C22×C22⋊D11311yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—4521no—
262C4—4522no—
263C4—4521no—
264C4C2×#1426863512yes—
265C4C2×#1426864611yescharacteristic
266C4#1681366711yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2#2029924211yescharacteristic
271C2C22×#1426863511yescharacteristic
272C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radicalD42×C113C2
socleC22×C113C22×D4
hypercenterD42D113
hypocenterC113#3295
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #20299305C2semidirect
2. #20298944C2semidirect
3. #20298914C2semidirect
4. #20298888C2semidirect
5. #20298825C2semidirect
6. #20298795C2semidirect
7. #20298749C2semidirect
8. C4×#14268635C2semidirect
9. D4×#11744751C2semidirect
10. C2×#16813543C2semidirect
13. C2×#14268635C22semidirect
14. C22×#11744751C22semidirect
15. #16813622C22semidirect
17. #16813601C22semidirect
19. C4×Dic226C22semidirect
21. C2×C4⋊Dic113C22semidirect
22. #16813553C22semidirect
23. #16813553C22semidirect
24. C4⋊#11744751C22semidirect
25. #16813545C22semidirect
28. #16813543C22semidirect
29. #16813543C22semidirect
30. #16813543C22semidirect
31. C22⋊#11744751C22semidirect
32. C4×#11744751C22semidirect
90. D4×C113SD16semidirect
137. C113#3295semidirect
230. D4#14268635semidirect

Maximal subgroups

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

subgroupindex
#202993052
#202989442
#202989142
#202988882
#202988252
#202987952
#202987492
C4×#142686352
D4×#117447512
C2×#168135432
D42×C1132
#3295113