Finite Group Databasebeta

← #13127078

Subgroups — #13127078

Order 1664.

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
1D42×C13C211yesmaximal, characteristic, complemented
2#11719268C211yesmaximal, characteristic, complemented
3#11718878C212yesmaximal, complemented
4#11718876C212yesmaximal, complemented
5#11718733C211yesmaximal, characteristic, complemented
6#11718731C211yesmaximal, characteristic, complemented
7#11718700C212yesmaximal, complemented
8#11718696C212yesmaximal, complemented
9C4×#6104C211yesmaximal, characteristic, complemented
10#11718673C211yesmaximal, characteristic, complemented
11#11718669C211yesmaximal, characteristic, complemented
12C22×D4×C13—21no—
13C22×D4×C13C2212yes—
14C13×#127C2211yescharacteristic
15C13×#121—21no—
16C13×#121C2212yes—
17C13×#120—22no—
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88192—21no—
21C2×#6104C2211yescharacteristic
22C2×#6104C2212yescomplemented
23#88184C2212yescomplemented
24#88180C2212yescomplemented
25C2×#6099C2212yescomplemented
26#88146—21no—
27#88139—22no—
28C4×D52C2211yescharacteristic, complemented
29#88123C2211yescharacteristic, complemented
30#88072C2212yes—
31#88072C2211yescharacteristic
32#88072C2212yescomplemented
33#88072C2212yescomplemented
34#88072C2212yescomplemented
35C22⋊#1055C2212yescomplemented
36#88049C2211yescharacteristic, complemented
37#88048C2212yescomplemented
38#88047C2211yescharacteristic, complemented
39C4⋊#1055C2211yescharacteristic, complemented
40C4×#1055C2211yescharacteristic, complemented
41C24×C13—22no—
42C2×D4×C13—24no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13—44no—
49C2×D4×C13D411yescharacteristic
50C2×D4×C13C2312yes—
51C2×D4×C13C2311yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13C2312yes—
54C2×C22⋊D13—22no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26—21no—
58C13×C4⋊C4D411yescharacteristic
59C13×C4⋊C4C2311yescharacteristic
60C13×C22⋊C4—21no—
61C13×C22⋊C4—22no—
62C13×C22⋊C4D412yes—
63C42×C13C2311yescharacteristic
64C22⋊Dic13—22no—
65#6104—22no—
66#6104—42no—
67#6103—21no—
68#6103—22no—
69C4⋊Dic13—21no—
70C4⋊Dic13C2312yes—
71C4⋊Dic13C2311yescharacteristic
72C4×Dic13—22no—
73#6099—42no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2312yes—
76C2×#1055C2311yescharacteristic
77#3325—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13—22no—
80C23×C13—44no—
81C23×C13—44no—
82C23×C13—82no—
83C23×C13C2×D412yes—
84C22×D13—21no—
85D4×C13—22no—
86D4×C13—22no—
87D4×C13—21no—
88D4×C13—22no—
89D4×C13—44no—
90D4×C13—44no—
91D4×C13—42no—
92D4×C13—81no—
93D4×C13#4112yes—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—42no—
98C2×C4×C13C2×D412yes—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—82no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105D52—21no—
106D52—21no—
107C4×D13—42no—
108Dic26—81no—
109#1055—21no—
110#1055—21no—
111#1055—22no—
112#555—131no—
113D42D1311yescharacteristic, complemented
114#486—131no—
115#482—132no—
116#476—131no—
117#469—132no—
118#459—131no—
119#447—132no—
120C4×D8—131no—
121#436—131no—
122#418—132no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—22no—
126C22×C13—22no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—88no—
133C22×C13C22×D411yescharacteristic
134C2×D13—41no—
135C2×D13—41no—
136C2×D13—41no—
137C4×C13—22no—
138C4×C13—21no—
139C4×C13—41no—
140C4×C13AGL(1,ℤ/8)12yes—
141C4×C13C2×#4111yescharacteristic
142C4×C13H(5,𝔽2)11yescharacteristic
143Dic13—41no—
144Dic13—42no—
145C22×D4—21no—
146C22×D4C2×D1312yes—
147C2×D8—131no—
148C2×D8—132no—
149C2×M16—132no—
150C4⋊Q8—131no—
151#127C2×D1311yescharacteristic
152#124—262no—
153#121—21no—
154#121—132no—
155#121—261no—
156#121C2×D1312yes—
157#120—22no—
158C4×D4—131no—
159C4×D4C2×D1311yescharacteristic
160C4×D4C2×D1311yescharacteristic
161#117—132no—
162#117—261no—
163#107—131no—
164#106—132no—
165C4⋊C8—131no—
166#102—131no—
167#102—132no—
168#102—132no—
169#102—132no—
170#102—132no—
171#102—131no—
172C22⋊C8—132no—
173C4×C8—131no—
174C2×C13—42no—
175C2×C13—42no—
176C2×C13—82no—
177C2×C13#54611yescharacteristic
178C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C13#57611yescharacteristic
180D13—81no—
181C24—22no—
182C2×Q8—261no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—42no—
189C2×D4—44no—
190C2×D4—131no—
191C2×D4—262no—
192C2×D4C22⋊D1311yescharacteristic
193C2×D4C22×D1312yes—
194C2×D4C22×D1311yescharacteristic
195C22×C4—21no—
196C22×C4—261no—
197C22×C4C22×D1312yes—
198D8—262no—
199D8—522no—
200M16—522no—
201C2×C8—131no—
202C2×C8—131no—
203C2×C8—132no—
204C4⋊C4—132no—
205C4⋊C4—131no—
206C4⋊C4—261no—
207C4⋊C4C22⋊D1311yescharacteristic
208C4⋊C4C22×D1311yescharacteristic
209C22⋊C4—21no—
210C22⋊C4—22no—
211C22⋊C4—262no—
212C22⋊C4—262no—
213C22⋊C4—261no—
214C22⋊C4C22⋊D1312yes—
215C42—262no—
216C42C22×D1311yescharacteristic
217C13#332511yescharacteristic, complemented, Sylow
218C23—21no—
219C23—22no—
220C23—44no—
221C23—44no—
222C23—82no—
223C23—261no—
224C23C2×C22⋊D1312yes—
225Q8—1041no—
226D4—22no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—44no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—261no—
235D4—261no—
236D4—1042no—
237D4#612912yes—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—261no—
243C2×C4—262no—
244C2×C4—522no—
245C2×C4C2×C22⋊D1312yes—
246C2×C4C2×C22⋊D1311yescharacteristic
247C2×C4C2×C22⋊D1311yescharacteristic
248C2×C4C23×D1311yescharacteristic
249C8—261no—
250C8—261no—
251C8—262no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—88no—
262C22—521no—
263C22—521no—
264C22—521no—
265C22C22×C22⋊D1311yescharacteristic
266C4—22no—
267C4—21no—
268C4—41no—
269C4—521no—
270C4—522no—
271C4#8818612yes—
272C4C2×#612911yescharacteristic
273C4#8825111yescharacteristic
274C2—42no—
275C2—42no—
276C2—82no—
277C2—1041no—
278C2C2×#8818611yescharacteristic
279C2#1171951111yescharacteristic
280C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3325
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. D42×C13C2semidirect
2. #11719268C2semidirect
3. #11718878C2semidirect
4. #11718876C2semidirect
5. #11718733C2semidirect
6. #11718731C2semidirect
7. #11718700C2semidirect
8. #11718696C2semidirect
9. C4×#6104C2semidirect
10. #11718673C2semidirect
11. #11718669C2semidirect
22. C2×#6104C22semidirect
23. #88184C22semidirect
24. #88180C22semidirect
25. C2×#6099C22semidirect
28. C4×D52C22semidirect
29. #88123C22semidirect
32. #88072C22semidirect
33. #88072C22semidirect
34. #88072C22semidirect
35. C22⋊#1055C22semidirect
36. #88049C22semidirect
37. #88048C22semidirect
38. #88047C22semidirect
39. C4⋊#1055C22semidirect
40. C4×#1055C22semidirect
113. D42D13semidirect
217. C13#3325semidirect

Maximal subgroups

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

subgroupindex
D42×C132
#117192682
#117188782
#117188762
#117187332
#117187312
#117187002
#117186962
C4×#61042
#117186732
#117186692
#332513