Finite Group Databasebeta

← #13125639

Subgroups — #13125639

Order 1664.

462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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×#88192C211yesmaximal, characteristic
2D13×C22⋊Q8C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4#11718879C211yesmaximal, characteristic, complemented
5#11718835C212yesmaximal, complemented
6#11718831C212yesmaximal, complemented
7#11718705C211yesmaximal, characteristic, complemented
8#11718441C212yesmaximal, complemented
9#11718435C212yesmaximal, complemented
10#11718387C211yesmaximal, characteristic, complemented
11#11718383C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13—21no—
14C2×Q8×D13C2211yescharacteristic, complemented
15C22×C4×D13C2211yescharacteristic
16C2×C13×SD16C2212yescomplemented
17C13×C22⋊Q8C2211yescharacteristic
18C2×C22⋊Dic13—21no—
19#88200C2211yescharacteristic, complemented
20#88192—21no—
21#88192—21no—
22#88192C2212yes—
23#88192C2212yes—
24C2×#6105C2212yescomplemented
25C2×C4⋊Dic13C2211yescharacteristic
26#88178C2211yescharacteristic
27C2×#6094C2212yescomplemented
28#88151C2211yescharacteristic, complemented
29#88150—21no—
30C4⋊C4×D13—21no—
31C4⋊C4×D13C2211yescharacteristic, complemented
32C22⋊C4×D13—21no—
33#88132—21no—
34C13×#102C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic
36#88075C2212yescomplemented
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88060C2212yescomplemented
40#88058C2212yescomplemented
41#88056C2212yescomplemented
42#88047C2212yescomplemented
43C24×C13—21no—
44C23×D13D411yescharacteristic
45C2×Q8×C13C2311yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13C2312yes—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—22no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—44no—
53C22×Dic13—21no—
54C22×Dic13D411yescharacteristic
55Q8×D13—42no—
56C2×C4×D13—21no—
57C2×C4×D13—21no—
58C2×C4×D13—42no—
59C2×C4×D13D411yescharacteristic
60C2×C4×D13D411yescharacteristic
61C2×C4×D13C2311yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×Dic26—21no—
64C2×Dic26C2311yescharacteristic
65C13×SD16—42no—
66C2×C8×C13C2312yes—
67C13×C4⋊C4—21no—
68C13×C4⋊C4C2311yescharacteristic
69C13×C22⋊C4—21no—
70C22⋊Dic13—21no—
71C22⋊Dic13—22no—
72C22⋊Dic13—22no—
73#6105—42no—
74#6103—21no—
75#6103—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13—21no—
78C4⋊Dic13C2311yescharacteristic
79C4⋊Dic13C2312yes—
80#6101—21no—
81#6101—21no—
82#6101—21no—
83C2×#1055C2312yes—
84#6094—42no—
85#3193—131nomaximal, Sylow
86C23×C13—22no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13C2×D411yescharacteristic
91C22×D13—22no—
92C22×D13—22no—
93C22×D13—41no—
94C22×D13C2×D411yescharacteristic
95C22×D13C2×D411yescharacteristic
96Q8×C13—22no—
97D4×C13—22no—
98D4×C13—22no—
99D4×C13—42no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2411yescharacteristic
105C22⋊D13—44no—
106C22⋊D13—44no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112C2×Dic13C2×D411yescharacteristic
113C2×Dic13C2×D411yescharacteristic
114C4×D13—22no—
115C4×D13—22no—
116C4×D13—41no—
117C4×D13—41no—
118C4×D13—42no—
119C4×D13—42no—
120Dic26—22no—
121Dic26—42no—
122C8×C13—22no—
123#1055—22no—
124C2×C22⋊Q8—131no—
125C2×#121—131no—
126#484—131no—
127#484—131no—
128#480—132no—
129#468—132no—
130#468—132no—
131#450—131no—
132#450D1311yescharacteristic, complemented
133#448—132no—
134#407—131no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—84no—
141C22×C13#13712yes—
142C22×C13C22×D411yescharacteristic
143C2×D13—21no—
144C2×D13—21no—
145C2×D13—21no—
146C2×D13—21no—
147C2×D13—21no—
148C2×D13—44no—
149C2×D13AGL(1,ℤ/8)12yes—
150C4×C13—21no—
151C4×C13—41no—
152C4×C13—41no—
153C4×C13H(5,𝔽2)12yes—
154Dic13—21no—
155Dic13—21no—
156Dic13—41no—
157Dic13—41no—
158Dic13—42no—
159C22×Q8—131no—
160C22×D4—261no—
161C22×D4C2×D1311yescharacteristic
162C23×C4—131no—
163C2×SD16—132no—
164C2×SD16C2×D1312yescomplemented
165C2×M16—132no—
166C22⋊Q8—131no—
167C22⋊Q8—131no—
168C22⋊Q8—131no—
169C22⋊Q8—261no—
170C22⋊Q8—261no—
171C22⋊Q8C2×D1311yescharacteristic
172#121—132no—
173#121—132no—
174#121—261no—
175#121—261no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—261no—
179C2×C22⋊C4—261no—
180C2×C22⋊C4—261no—
181#107—132no—
182#107—132no—
183#103—132no—
184#103—132no—
185#102—132no—
186#102C2×D1312yescomplemented
187C22⋊C8—131no—
188C22⋊C8—132no—
189C22⋊C8C2×D1311yescharacteristic
190C2×C13—22no—
191C2×C13—82no—
192C2×C13#53411yescharacteristic
193C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C13C2×#13711yescharacteristic
195D13—22no—
196D13—41no—
197C24—21no—
198C24—131no—
199C2×Q8—131no—
200C2×Q8—261no—
201C2×Q8—522no—
202C2×Q8C22×D1311yescharacteristic
203C2×D4—21no—
204C2×D4—42no—
205C2×D4—262no—
206C2×D4—262no—
207C2×D4—524no—
208C2×D4C22×D1312yes—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—522no—
218C22×C4C22×D1311yescharacteristic
219SD16—42no—
220SD16—522no—
221M16—522no—
222C2×C8—132no—
223C2×C8C22×D1312yes—
224C4⋊C4—21no—
225C4⋊C4—131no—
226C4⋊C4—132no—
227C4⋊C4—261no—
228C4⋊C4—261no—
229C4⋊C4—261no—
230C4⋊C4—261no—
231C4⋊C4—261no—
232C4⋊C4C22×D1311yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—261no—
235C22⋊C4—261no—
236C22⋊C4—262no—
237C22⋊C4—262no—
238C22⋊C4—261no—
239C13#319311yescharacteristic, complemented, Sylow
240C23—22no—
241C23—42no—
242C23—42no—
243C23—42no—
244C23—131no—
245C23—131no—
246C23—262no—
247C23—262no—
248C23—521no—
249C23D4×D1311yescharacteristic
250Q8—22no—
251Q8—262no—
252Q8—522no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—524no—
257D4—524no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—131no—
262C2×C4—131no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—261no—
266C2×C4—262no—
267C2×C4—261no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4—521no—
273C2×C4—522no—
274C2×C4D4×D1311yescharacteristic
275C2×C4C23×D1311yescharacteristic
276C8—22no—
277C8—262no—
278C22—21no—
279C22—21no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—84no—
284C22—132no—
285C22—261no—
286C22—261no—
287C22—261no—
288C22—261no—
289C22—261no—
290C22—524no—
291C22#8816912yes—
292C22C2×D4×D1311yescharacteristic
293C4—21no—
294C4—41no—
295C4—41no—
296C4—261no—
297C4—261no—
298C4—521no—
299C4—522no—
300C4—521no—
301C4#8825112yes—
302C2—22no—
303C2—82no—
304C2—262no—
305C2—521no—
306C2#1171929411yescharacteristic
307C2C2×#8816911yescharacteristic
308C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
prime radicalC2×#88192C2
hypercenter#450D13
hypocenterC13#3193
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. D13×C22⋊Q8C2semidirect
3. C13×#450C2semidirect
4. #11718879C2semidirect
5. #11718835C2semidirect
6. #11718831C2semidirect
7. #11718705C2semidirect
8. #11718441C2semidirect
9. #11718435C2semidirect
10. #11718387C2semidirect
11. #11718383C2semidirect
14. C2×Q8×D13C22semidirect
16. C2×C13×SD16C22semidirect
19. #88200C22semidirect
24. C2×#6105C22semidirect
27. C2×#6094C22semidirect
28. #88151C22semidirect
31. C4⋊C4×D13C22semidirect
34. C13×#102C22semidirect
36. #88075C22semidirect
37. #88072C22semidirect
39. #88060C22semidirect
40. #88058C22semidirect
41. #88056C22semidirect
42. #88047C22semidirect
132. #450D13semidirect
164. C2×SD16C2×D13semidirect
186. #102C2×D13semidirect
239. C13#3193semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
D13×C22⋊Q82
C13×#4502
#117188792
#117188352
#117188312
#117187052
#117184412
#117184352
#117183872
#117183832
#319313