Finite Group Databasebeta

← #13126437

Subgroups — #13126437

Order 1664.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88165C212yesmaximal, complemented
2#11719260C211yesmaximal, characteristic, complemented
3D4×D52C211yesmaximal, characteristic, complemented
4C4×C13×D8C211yesmaximal, characteristic, complemented
5#11718680C211yesmaximal, characteristic, complemented
6#11718676C211yesmaximal, characteristic, complemented
7#11718547C212yesmaximal, complemented
8#11718442C212yesmaximal, complemented
9#11718437C212yesmaximal, complemented
10#11718354C211yesmaximal, characteristic, complemented
11#11718349C211yesmaximal, characteristic, complemented
12C2×#6129C2212yescomplemented
13C2×D4×D13C2212yes—
14C22×D52—21no—
15C2×C13×D8C2211yescharacteristic
16C4×D4×C13C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic, complemented
18C2×#6105C2212yes—
19C2×#6104C2212yescomplemented
20#88184—21no—
21#88184—21no—
22C2×C4⋊Dic13—21no—
23#88165—28no—
24C2×#6095C2212yescomplemented
25C2×#6095C2212yescomplemented
26C2×#6094C2212yescomplemented
27#88151C2212yescomplemented
28#88149C2212yes—
29#88140—22no—
30#88136—22no—
31#88128C2211yescharacteristic
32C4×D52C2211yescharacteristic
33#88123C2211yescharacteristic, complemented
34C13×#107C2211yescharacteristic, complemented
35C13×#102C2211yescharacteristic
36C13×#102C2211yescharacteristic, complemented
37C4×C8×C13C2211yescharacteristic, complemented
38#88060C2212yescomplemented
39#88050C2212yescomplemented
40#88049C2212yescomplemented
41C4⋊#1055C2211yescharacteristic, complemented
42C23×D13—22no—
43C2×D4×C13C2311yescharacteristic
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C22×Dic13—22no—
50#6129—24no—
51#6129—42no—
52D4×D13—24no—
53D4×D13—42no—
54C2×D52—22no—
55C2×D52—21no—
56C2×D52—21no—
57C2×D52—44no—
58C2×D52D411yescharacteristic
59C2×D52C2312yes—
60C2×C4×D13C2312yes—
61C2×Dic26C2312yes—
62C13×D8D414yescomplemented
63C2×C8×C13C2311yescharacteristic
64C2×C8×C13C2311yescharacteristic
65C13×C4⋊C4C2311yescharacteristic
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C13×C22⋊C4—21no—
69C42×C13C2311yescharacteristic
70#6105—24no—
71#6104—24no—
72#6103—22no—
73#6103—22no—
74#6103D412yes—
75C4⋊Dic13—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13—22no—
78C4⋊Dic13D411yescharacteristic
79C2×#1055C2312yes—
80#6095—24no—
81#6095—42no—
82#6094—24no—
83#3272—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13—21no—
86C22×D13—22no—
87C22×D13—44no—
88C22×D13—44no—
89C22×D13—82no—
90C22×D13C2×D412yes—
91D4×C13—21no—
92D4×C13—21no—
93D4×C13C2×D412yes—
94D4×C13C2×D412yescomplemented
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—44no—
103C22⋊D13—44no—
104C2×Dic13—22no—
105C2×Dic13—44no—
106C2×Dic13C2×D412yes—
107D52—22no—
108D52—22no—
109D52—22no—
110D52—44no—
111D52—42no—
112D52—81no—
113C4×D13—22no—
114C4×D13—22no—
115Dic26—22no—
116Dic26—22no—
117C8×C13—21no—
118C8×C13C2×D412yescomplemented
119#1055—22no—
120C2×AGL(1,ℤ/8)—132no—
121#547—131no—
122D42—131no—
123#492—131no—
124#468—132no—
125#461—131no—
126#459—131no—
127#450—132no—
128#449—132no—
129C4×D8D1311yescharacteristic, complemented
130#436—131no—
131C22×C13—22no—
132C22×C13—22no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13C22×D411yescharacteristic
138C2×D13—22no—
139C2×D13—22no—
140C2×D13—22no—
141C2×D13—42no—
142C2×D13—42no—
143C2×D13—42no—
144C2×D13—88no—
145C4×C13—21no—
146C4×C13—41no—
147C4×C13—41no—
148C4×C13AGL(1,ℤ/8)12yescomplemented
149C4×C13C22×D411yescharacteristic
150C4×C13H(5,𝔽2)11yescharacteristic
151Dic13—22no—
152Dic13—42no—
153C2×#41—132no—
154C22×D4—132no—
155C22×D4—261no—
156AGL(1,ℤ/8)—268no—
157C2×SD16—132no—
158C2×SD16—132no—
159C2×SD16—132no—
160C2×D8—132no—
161C2×D8C2×D1311yescharacteristic
162C2×M16—132no—
163C4⋊Q8—131no—
164#127—131no—
165#123—262no—
166C22⋊Q8—132no—
167#121—132no—
168#121—261no—
169#121—261no—
170#120—262no—
171C4×D4—131no—
172C4×D4C2×D1311yescharacteristic
173C4×D4C2×D1311yescharacteristic, complemented
174C2×C4⋊C4—261no—
175#107C2×D1311yescharacteristic, complemented
176C4⋊C8—131no—
177#103—132no—
178#102—132no—
179#102C2×D1311yescharacteristic
180#102C2×D1311yescharacteristic, complemented
181C22⋊C8—132no—
182C4×C8C2×D1311yescharacteristic, complemented
183C2×C13—42no—
184C2×C13—42no—
185C2×C13D4211yescharacteristic
186C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C13#57711yescharacteristic
188D13—42no—
189D13—82no—
190C24—262no—
191#41—264no—
192#41—522no—
193C2×Q8—132no—
194C2×D4—131no—
195C2×D4—132no—
196C2×D4—262no—
197C2×D4—262no—
198C2×D4—264no—
199C2×D4—262no—
200C2×D4—261no—
201C2×D4—261no—
202C2×D4—524no—
203C2×D4—522no—
204C2×D4C22×D1311yescharacteristic
205C2×D4C22×D1311yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—132no—
209C22×C4—262no—
210SD16—264no—
211SD16—264no—
212SD16—522no—
213D8—264no—
214D8D5214yescomplemented
215M16—264no—
216C2×C8—132no—
217C2×C8C22×D1311yescharacteristic
218C2×C8C22×D1311yescharacteristic
219C4⋊C4—131no—
220C4⋊C4—262no—
221C4⋊C4—261no—
222C4⋊C4—261no—
223C4⋊C4C22×D1311yescharacteristic
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—21no—
227C22⋊C4—132no—
228C22⋊C4—262no—
229C22⋊C4—262no—
230C42C22×D1311yescharacteristic
231C13#327211yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—132no—
235C23—262no—
236C23—524no—
237C23—524no—
238C23—1042no—
239Q8—262no—
240Q8—262no—
241D4—21no—
242D4—21no—
243D4—262no—
244D4—262no—
245D4—262no—
246D4—524no—
247D4—524no—
248D4—524no—
249D4—522no—
250D4—1041no—
251D4C2×D5212yes—
252D4C2×D5212yescomplemented
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—132no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—524no—
262C2×C4D4×D1311yescharacteristic
263C2×C4D4×D1311yescharacteristic
264C2×C4C23×D1311yescharacteristic
265C8—21no—
266C8—262no—
267C8C2×D5212yescomplemented
268C22—22no—
269C22—22no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—262no—
275C22—262no—
276C22—262no—
277C22—522no—
278C22—522no—
279C22—522no—
280C22—1048no—
281C22C2×D4×D1311yescharacteristic
282C4—21no—
283C4—41no—
284C4—41no—
285C4—262no—
286C4—522no—
287C4#8816512yescomplemented
288C4C22×D5211yescharacteristic
289C4#8825611yescharacteristic
290C2—42no—
291C2—42no—
292C2—522no—
293C2—1042no—
294C2D4×D5211yescharacteristic
295C2C2×#8816511yescharacteristic
296C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×D8C2
socleC22×C13C22×D4
hypercenterC4×D8D13
hypocenterC13#3272
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#88165C2semidirect
2. #11719260C2semidirect
3. D4×D52C2semidirect
4. C4×C13×D8C2semidirect
5. #11718680C2semidirect
6. #11718676C2semidirect
7. #11718547C2semidirect
8. #11718442C2semidirect
9. #11718437C2semidirect
10. #11718354C2semidirect
11. #11718349C2semidirect
12. C2×#6129C22semidirect
17. C4×D4×C13C22semidirect
19. C2×#6104C22semidirect
24. C2×#6095C22semidirect
25. C2×#6095C22semidirect
26. C2×#6094C22semidirect
27. #88151C22semidirect
33. #88123C22semidirect
34. C13×#107C22semidirect
36. C13×#102C22semidirect
37. C4×C8×C13C22semidirect
38. #88060C22semidirect
39. #88050C22semidirect
40. #88049C22semidirect
41. C4⋊#1055C22semidirect
62. C13×D8D4semidirect
94. D4×C13C2×D4semidirect
118. C8×C13C2×D4semidirect
129. C4×D8D13semidirect
148. C4×C13AGL(1,ℤ/8)semidirect
173. C4×D4C2×D13semidirect
175. #107C2×D13semidirect
180. #102C2×D13semidirect
182. C4×C8C2×D13semidirect
214. D8D52semidirect
231. C13#3272semidirect
252. D4C2×D52semidirect
267. C8C2×D52semidirect
287. C4#88165semidirect

Maximal subgroups

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

subgroupindex
C2×#881652
#117192602
D4×D522
C4×C13×D82
#117186802
#117186762
#117185472
#117184422
#117184372
#117183542
#117183492
#327213