Finite Group Databasebeta

← #28402816

Subgroups — #28402816

Order 14464.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299313C211yesmaximal, characteristic, complemented
2#20298944C211yesmaximal, characteristic, complemented
3#20298919C212yesmaximal, complemented
4#20298888C211yesmaximal, characteristic, complemented
5#20298849C212yesmaximal, complemented
6#20298790C211yesmaximal, characteristic, complemented
7#20298732C212yesmaximal, complemented
8C4×#14268632C211yesmaximal, characteristic, complemented
9#20298676C211yesmaximal, characteristic, complemented
10#20298603C212yesmaximal, complemented
11D42×C113C211yesmaximal, characteristic, complemented
12C2×#14268632C2211yescharacteristic
13C2×#14268632C2212yescomplemented
14C2×#14268631C2212yescomplemented
15#16813622C2211yescharacteristic, complemented
16#16813608—22no—
17#16813596C2212yescomplemented
18#16813593—21no—
19C4×D452C2211yescharacteristic, complemented
20#16813581C2212yescomplemented
21#16813580—21no—
22#16813555C2211yescharacteristic, complemented
23#16813553C2212yescomplemented
24C4⋊#11744751C2211yescharacteristic, complemented
25#16813543C2211yescharacteristic
26#16813543C2212yes—
27#16813543C2212yescomplemented
28#16813543C2212yescomplemented
29#16813543C2212yescomplemented
30#16813542C2211yescharacteristic, complemented
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×D452C2311yescharacteristic
43C2×C22⋊D113—22no—
44C2×C4×D113—21no—
45#14268632—22no—
46#14268632—42no—
47#14268631—42no—
48C2×#11744751C2311yescharacteristic
49C2×#11744751C2312yes—
50C2×#11744751C2311yescharacteristic
51C4⋊Dic113—21no—
52C4⋊Dic113C2311yescharacteristic
53C4⋊Dic113C2312yes—
54C22⋊Dic113—22no—
55#14268624—22no—
56#14268624—21no—
57C4×Dic113—22no—
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—
83C22×D113—21no—
84D4×C113—22no—
85D4×C113—22no—
86D4×C113—21no—
87D4×C113—22no—
88D4×C113—44no—
89D4×C113—44no—
90D4×C113—42no—
91D4×C113—81no—
92D4×C113#4112yes—
93C2×C4×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113—21no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D412yes—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—82no—
102C2×Dic113—21no—
103C2×Dic113—22no—
104D452—21no—
105D452—21no—
106C4×D113—42no—
107Dic226—81no—
108#11744751—21no—
109#11744751—21no—
110#11744751—22no—
111C22×C113—22no—
112C22×C113—22no—
113C22×C113—22no—
114C22×C113—22no—
115C22×C113—41no—
116C22×C113—41no—
117C22×C113—42no—
118C22×C113—42no—
119C22×C113—42no—
120C22×C113—88no—
121C22×C113C22×D411yescharacteristic
122C2×D113—41no—
123C2×D113—41no—
124C2×D113—41no—
125C4×C113—22no—
126C4×C113—21no—
127C4×C113—41no—
128C4×C113AGL(1,ℤ/8)12yes—
129C4×C113C2×#4111yescharacteristic
130C4×C113H(5,𝔽2)11yescharacteristic
131Dic113—41no—
132Dic113—42no—
133C2×C113—42no—
134C2×C113—42no—
135C2×C113—82no—
136C2×C113#54611yescharacteristic
137C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C113#57611yescharacteristic
139D113—81no—
140#3325—1131nomaximal, Sylow
141C113#332511yescharacteristic, complemented, Sylow
142#555—1131no—
143D42D11311yescharacteristic, complemented
144#486—1131no—
145#482—1132no—
146#476—1131no—
147#469—1132no—
148#459—1131no—
149#447—1132no—
150C4×D8—1131no—
151#436—1131no—
152#418—1132no—
153C22×D4—21no—
154C22×D4C2×D11312yes—
155C2×D8—1132no—
156C2×D8—1131no—
157C2×M16—1132no—
158C4⋊Q8—1131no—
159#127C2×D11311yescharacteristic
160#124—2262no—
161#121—21no—
162#121—1132no—
163#121—2261no—
164#121C2×D11312yes—
165#120—22no—
166C4×D4—1131no—
167C4×D4C2×D11311yescharacteristic
168C4×D4C2×D11311yescharacteristic
169#117—1132no—
170#117—2261no—
171#107—1131no—
172#106—1132no—
173C4⋊C8—1131no—
174#102—1131no—
175#102—1132no—
176#102—1132no—
177#102—1132no—
178#102—1132no—
179#102—1131no—
180C22⋊C8—1132no—
181C4×C8—1131no—
182C24—22no—
183C2×Q8—2261no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—42no—
190C2×D4—44no—
191C2×D4—1131no—
192C2×D4—2262no—
193C2×D4C22⋊D11311yescharacteristic
194C2×D4C22×D11312yes—
195C2×D4C22×D11311yescharacteristic
196C22×C4—21no—
197C22×C4—2261no—
198C22×C4C22×D11312yes—
199D8—4522no—
200D8—2262no—
201M16—4522no—
202C2×C8—1131no—
203C2×C8—1131no—
204C2×C8—1132no—
205C4⋊C4—1132no—
206C4⋊C4—1131no—
207C4⋊C4—2261no—
208C4⋊C4C22⋊D11311yescharacteristic
209C4⋊C4C22×D11311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—22no—
212C22⋊C4—2262no—
213C22⋊C4—2262no—
214C22⋊C4—2261no—
215C22⋊C4C22⋊D11312yes—
216C42—2262no—
217C42C22×D11311yescharacteristic
218C23—21no—
219C23—22no—
220C23—44no—
221C23—44no—
222C23—82no—
223C23—2261no—
224C23C2×C22⋊D11312yes—
225Q8—9041no—
226D4—22no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—44no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—9042no—
235D4—2261no—
236D4—2261no—
237D4#1426864612yes—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—4522no—
243C2×C4—2261no—
244C2×C4—2262no—
245C2×C4C2×C22⋊D11312yes—
246C2×C4C2×C22⋊D11311yescharacteristic
247C2×C4C2×C22⋊D11311yescharacteristic
248C2×C4C23×D11311yescharacteristic
249C8—2261no—
250C8—2261no—
251C8—2262no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—88no—
262C22—4521no—
263C22—4521no—
264C22—4521no—
265C22C22×C22⋊D11311yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—4521no—
270C4—4522no—
271C4#1681364812yes—
272C4C2×#1426864611yescharacteristic
273C4#1681366711yescharacteristic
274C2—42no—
275C2—42no—
276C2—82no—
277C2—9041no—
278C2#2029924211yescharacteristic
279C2C2×#1681364811yescharacteristic
280C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD42×C113C2
socleC22×C113C22×D4
hypercenterD42D113
hypocenterC113#3325
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. #20299313C2semidirect
2. #20298944C2semidirect
3. #20298919C2semidirect
4. #20298888C2semidirect
5. #20298849C2semidirect
6. #20298790C2semidirect
7. #20298732C2semidirect
8. C4×#14268632C2semidirect
9. #20298676C2semidirect
10. #20298603C2semidirect
11. D42×C113C2semidirect
13. C2×#14268632C22semidirect
14. C2×#14268631C22semidirect
15. #16813622C22semidirect
17. #16813596C22semidirect
19. C4×D452C22semidirect
20. #16813581C22semidirect
22. #16813555C22semidirect
23. #16813553C22semidirect
24. C4⋊#11744751C22semidirect
27. #16813543C22semidirect
28. #16813543C22semidirect
29. #16813543C22semidirect
30. #16813542C22semidirect
31. C22⋊#11744751C22semidirect
32. C4×#11744751C22semidirect
141. C113#3325semidirect
143. D42D113semidirect

Maximal subgroups

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

subgroupindex
#202993132
#202989442
#202989192
#202988882
#202988492
#202987902
#202987322
C4×#142686322
#202986762
#202986032
D42×C1132
#3325113