Finite Group Databasebeta

← #13124628

Subgroups — #13124628

Order 1664.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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#11719433C211yesmaximal, characteristic, complemented
2C4×D4×D13C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718669C211yesmaximal, characteristic, complemented
6#11718552C212yesmaximal, complemented
7#11718542C212yesmaximal, complemented
8#11718503C211yesmaximal, characteristic, complemented
9#11718498C211yesmaximal, characteristic, complemented
10#11718431C212yesmaximal
11#11718424C212yesmaximal, complemented
12C2×D4×D13C2211yescharacteristic
13C22×C4×D13—21no—
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C4×D4×C13C2211yescharacteristic
16#88200—21no—
17Q8×Dic13—21no—
18D4×Dic13C2211yescharacteristic
19C4×C22⋊D13—21no—
20C2×#6094C2212yes—
21#88151—21no—
22#88147C2211yescharacteristic
23#88146C2212yes—
24C4⋊C4×D13C2211yescharacteristic
25#88144C2212yescomplemented
26#88141—21no—
27#88135—21no—
28C22⋊C4×D13—21no—
29C4×D52C2211yescharacteristic
30C42×D13C2211yescharacteristic
31#88123C2211yescharacteristic, complemented
32C13×#107C2212yescomplemented
33C13×C4⋊C8C2211yescharacteristic, complemented
34C13×#102C2212yes—
35#88072C2212yes—
36#88061C2212yes—
37#88057C2212yescomplemented
38#88054C2212yescomplemented
39#88049C2212yes—
40#88048C2212yescomplemented
41#88047C2212yescomplemented
42C4⋊#1055C2211yescharacteristic, complemented
43C23×D13—21no—
44C2×Q8×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C2×C22⋊D13—21no—
48C22×Dic13—21no—
49D4×D13—22no—
50D4×D13Q814yescomplemented
51C2×D52C2311yescharacteristic
52C2×C4×D13—21no—
53C2×C4×D13—21no—
54C2×C4×D13—21no—
55C2×C4×D13—44no—
56C2×C4×D13D411yescharacteristic
57C2×C4×D13D411yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×Dic26—21no—
60C2×C8×C13C2312yes—
61C13×C4⋊C4—21no—
62C13×C4⋊C4C2312yes—
63C13×C4⋊C4C2311yescharacteristic
64C13×C22⋊C4—21no—
65C42×C13C2311yescharacteristic
66C22⋊Dic13—21no—
67#6103—22no—
68#6103—21no—
69#6103—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13—22no—
72C4⋊Dic13C2312yes—
73C4⋊Dic13C2311yescharacteristic
74#6101—21no—
75#6101—22no—
76C4×Dic13—22no—
77C4×Dic13D411yescharacteristic
78C4×Dic13D411yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81#6094—24no—
82#3077—131nomaximal, Sylow
83C23×C13—21no—
84C22×D13—21no—
85C22×D13—24no—
86C22×D13—42no—
87C22×D13—42no—
88C22×D13C2×D411yescharacteristic
89Q8×C13—42no—
90D4×C13—21no—
91D4×C13C2×Q812yes—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—24no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—42no—
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105D52—21no—
106D52C2×Q812yes—
107C4×D13—22no—
108C4×D13—41no—
109C4×D13—42no—
110C4×D13—42no—
111C4×D13—42no—
112C4×D13C2×Q812yes—
113C4×D13#4112yes—
114Dic26—42no—
115C8×C13—22no—
116#1055—22no—
117#533—131no—
118C2×C4×D4—131no—
119#478—132no—
120#478—132no—
121#476—131no—
122#476—131no—
123#474—131no—
124#474D1311yescharacteristic, complemented
125#428—132no—
126#423—131no—
127#418—132no—
128C22×C13—22no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13C22×D411yescharacteristic
132C2×D13—21no—
133C2×D13—21no—
134C2×D13—22no—
135C2×D13—48no—
136C2×D13—41no—
137C2×D13—41no—
138C2×D13C22⋊Q812yes—
139C4×C13—21no—
140C4×C13—41no—
141C4×C13—42no—
142C4×C13AGL(1,ℤ/8)12yes—
143C4×C13C22×Q811yescharacteristic
144C4×C13C2×#4111yescharacteristic
145Dic13—21no—
146Dic13—21no—
147Dic13—41no—
148Dic13—42no—
149Dic13C22⋊Q812yes—
150C22×D4—131no—
151C23×C4—261no—
152C2×M16—132no—
153C4⋊Q8—131no—
154C4⋊Q8C2×D1311yescharacteristic, complemented
155#125—132no—
156C22⋊Q8—261no—
157C22⋊Q8—261no—
158C4×Q8—261no—
159C4×Q8—261no—
160C4×D4—131no—
161C4×D4—131no—
162C4×D4—131no—
163C4×D4—261no—
164C4×D4—261no—
165C4×D4C2×D1311yescharacteristic
166#117—132no—
167C2×C4⋊C4—131no—
168C2×C22⋊C4—261no—
169C2×C42—131no—
170#107—132no—
171#107C2×D1312yescomplemented
172#106—132no—
173#106—132no—
174C4⋊C8—132no—
175C4⋊C8—131no—
176C4⋊C8C2×D1311yescharacteristic, complemented
177#102—132no—
178#102—132no—
179#102—132no—
180#102C2×D1312yes—
181C2×C13—42no—
182C2×C13C2×C22⋊Q811yescharacteristic
183C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C13#57511yescharacteristic
185D13—22no—
186D13—42no—
187C24—261no—
188C2×Q8—21no—
189C2×Q8—261no—
190C2×D4—134no—
191C2×D4—131no—
192C2×D4—262no—
193C2×D4—261no—
194C2×D4C22×D1311yescharacteristic
195C22×C4—21no—
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—261no—
200C22×C4—261no—
201C22×C4—261no—
202C22×C4—261no—
203C22×C4—524no—
204M16—264no—
205C2×C8—132no—
206C2×C8C22×D1312yes—
207C4⋊C4—21no—
208C4⋊C4—132no—
209C4⋊C4—131no—
210C4⋊C4—261no—
211C4⋊C4—262no—
212C4⋊C4—262no—
213C4⋊C4—261no—
214C4⋊C4C22×D1312yes—
215C4⋊C4C22×D1311yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—261no—
218C22⋊C4—262no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C42—131no—
222C42—131no—
223C42—131no—
224C42—262no—
225C42C22×D1311yescharacteristic
226C13#307711yescharacteristic, complemented, Sylow
227C23—21no—
228C23—131no—
229C23—264no—
230C23—261no—
231C23—522no—
232C23—522no—
233Q8—42no—
234Q8—522no—
235D4—21no—
236D4—132no—
237D4—264no—
238D4—261no—
239D4Q8×D1312yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—131no—
244C2×C4—132no—
245C2×C4—132no—
246C2×C4—131no—
247C2×C4—131no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—521no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4D4×D1311yescharacteristic
257C2×C4D4×D1311yescharacteristic
258C2×C4C23×D1311yescharacteristic
259C8—22no—
260C8—262no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—132no—
265C22—261no—
266C22—261no—
267C22—262no—
268C22—528no—
269C22—521no—
270C22—521no—
271C22C2×D4×D1311yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—132no—
276C4—261no—
277C4—261no—
278C4—521no—
279C4—522no—
280C4#8816512yes—
281C4C2×Q8×D1311yescharacteristic
282C4#41×D1311yescharacteristic
283C2—42no—
284C2—262no—
285C2—522no—
286C2D13×C22⋊Q811yescharacteristic
287C2C2×#8816511yescharacteristic
288C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenter#474D13
hypocenterC13#3077
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#474C2semidirect
4. #11718748C2semidirect
5. #11718669C2semidirect
6. #11718552C2semidirect
7. #11718542C2semidirect
8. #11718503C2semidirect
9. #11718498C2semidirect
11. #11718424C2semidirect
14. C13×C4⋊Q8C22semidirect
25. #88144C22semidirect
31. #88123C22semidirect
32. C13×#107C22semidirect
33. C13×C4⋊C8C22semidirect
37. #88057C22semidirect
38. #88054C22semidirect
40. #88048C22semidirect
41. #88047C22semidirect
42. C4⋊#1055C22semidirect
50. D4×D13Q8semidirect
124. #474D13semidirect
154. C4⋊Q8C2×D13semidirect
171. #107C2×D13semidirect
176. C4⋊C8C2×D13semidirect
226. C13#3077semidirect

Maximal subgroups

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

subgroupindex
#117194332
C4×D4×D132
C13×#4742
#117187482
#117186692
#117185522
#117185422
#117185032
#117184982
#117184312
#117184242
#307713