Finite Group Databasebeta

← #13125598

Subgroups — #13125598

Order 1664.

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

normal subgroups only

This group has 472 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, complemented
2#11719311C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic, complemented
4#11718879C211yesmaximal, characteristic, complemented
5#11718819C212yesmaximal, complemented
6#11718818C212yesmaximal, complemented
7#11718695C211yesmaximal, characteristic, complemented
8#11718445C212yesmaximal, complemented
9#11718439C212yesmaximal, complemented
10D13×C22⋊C8C211yesmaximal, characteristic, complemented
11#11718383C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13—21no—
14C2×#6129C2211yescharacteristic, complemented
15C22×C4×D13C2211yescharacteristic
16C2×C13×D8C2212yescomplemented
17C13×#121C2211yescharacteristic
18C2×C22⋊Dic13—21no—
19#88192—21no—
20#88192—21no—
21#88192C2212yes—
22#88192C2212yes—
23#88192C2211yescharacteristic, complemented
24#88191—21no—
25D4×Dic13—21no—
26C2×#6105C2212yescomplemented
27C2×C4⋊Dic13C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×C8×D13C2212yescomplemented
30#88151C2211yescharacteristic, complemented
31#88146C2211yescharacteristic, complemented
32#88137—21no—
33#88135—21no—
34C13×#102C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic
36#88072C2212yescomplemented
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88060C2212yescomplemented
40#88058C2212yescomplemented
41#88056C2212yescomplemented
42#88048C2212yescomplemented
43C24×C13—21no—
44C23×D13D411yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13C2311yescharacteristic
49C2×D4×C13C2312yes—
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—21no—
52C2×C22⋊D13—21no—
53C2×C22⋊D13—22no—
54C2×C22⋊D13—22no—
55C2×C22⋊D13—44no—
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13D411yescharacteristic
59#6129—42no—
60C2×C4×D13—42no—
61C2×C4×D13D411yescharacteristic
62C2×C4×D13D411yescharacteristic
63C2×C4×D13C2311yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C13×D8—42no—
67C2×C8×C13C2312yes—
68C13×C4⋊C4C2311yescharacteristic
69C13×C22⋊C4—21no—
70C22⋊Dic13—21no—
71C22⋊Dic13—21no—
72C22⋊Dic13—22no—
73C22⋊Dic13—22no—
74#6105—42no—
75#6103—21no—
76#6103—21no—
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13C2311yescharacteristic
80C4⋊Dic13C2312yes—
81#6101—21no—
82C4×Dic13—21no—
83C2×#1055C2312yes—
84C8×D13—42no—
85#3188—131nomaximal, Sylow
86C23×C13—22no—
87C23×C13—21no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13C2×D411yescharacteristic
92C22×D13—22no—
93C22×D13—22no—
94C22×D13—41no—
95C22×D13C2×D411yescharacteristic
96C22×D13C2×D411yescharacteristic
97D4×C13—22no—
98D4×C13—22no—
99D4×C13—22no—
100D4×C13—42no—
101D4×C13—42no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2411yescharacteristic
106C22⋊D13—42no—
107C22⋊D13—44no—
108C22⋊D13—42no—
109C22⋊D13—44no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—22no—
113C2×Dic13—41no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13C2×D411yescharacteristic
117C2×Dic13C2×D411yescharacteristic
118C4×D13—22no—
119C4×D13—22no—
120C4×D13—41no—
121C4×D13—41no—
122Dic26—22no—
123C8×C13—22no—
124#1055—22no—
125#525—131no—
126C2×#121—131no—
127#484—131no—
128#482—132no—
129#481—131no—
130#466—132no—
131#465—132no—
132#450—131no—
133#449—132no—
134#447D1311yescharacteristic, complemented
135C2×C22⋊C8—131no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—41no—
139C22×C13—42no—
140C22×C13—41no—
141C22×C13—42no—
142C22×C13—42no—
143C22×C13—41no—
144C22×C13—84no—
145C22×C13#13512yes—
146C22×C13C22×D411yescharacteristic
147C2×D13—21no—
148C2×D13—21no—
149C2×D13—21no—
150C2×D13—21no—
151C2×D13—21no—
152C2×D13—44no—
153C2×D13AGL(1,ℤ/8)12yes—
154C4×C13—21no—
155C4×C13—41no—
156C4×C13H(5,𝔽2)12yes—
157Dic13—21no—
158Dic13—21no—
159Dic13—41no—
160Dic13—42no—
161Dic13—41no—
162C2×#41—131no—
163C22×D4—261no—
164C22×D4C2×D1311yescharacteristic
165C23×C4—131no—
166C2×SD16—132no—
167C2×D8C2×D1312yescomplemented
168C22×C8—132no—
169#123—261no—
170C22⋊Q8—131no—
171C22⋊Q8—131no—
172#121—132no—
173#121—132no—
174#121—131no—
175#121—261no—
176#121—261no—
177#121C2×D1311yescharacteristic
178#120—261no—
179C4×D4—261no—
180C4×D4—261no—
181#117—131no—
182C2×C4⋊C4—131no—
183C2×C22⋊C4—261no—
184#107—132no—
185#106—132no—
186#103—132no—
187#102—132no—
188#102—132no—
189#102C2×D1312yescomplemented
190C22⋊C8—131no—
191C22⋊C8—132no—
192C22⋊C8C2×D1311yescharacteristic
193C2×C13—22no—
194C2×C13—81no—
195C2×C13—82no—
196C2×C13#53411yescharacteristic
197C2×C13C2×#13511yescharacteristic
198C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
199D13—22no—
200D13—41no—
201C24—21no—
202C24—131no—
203#41—522no—
204C2×Q8—131no—
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—42no—
208C2×D4—261no—
209C2×D4—261no—
210C2×D4—262no—
211C2×D4—262no—
212C2×D4—524no—
213C2×D4C22×D1311yescharacteristic
214C2×D4C22×D1312yes—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4—522no—
223C22×C4C22×D1311yescharacteristic
224SD16—522no—
225D8—42no—
226C2×C8—132no—
227C2×C8—522no—
228C2×C8C22×D1312yes—
229C4⋊C4—131no—
230C4⋊C4—132no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4C22×D1311yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—261no—
237C22⋊C4—261no—
238C22⋊C4—262no—
239C22⋊C4—262no—
240C22⋊C4—261no—
241C22⋊C4—261no—
242C42—261no—
243C13#318811yescharacteristic, complemented, Sylow
244C23—21no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—131no—
250C23—131no—
251C23—262no—
252C23—262no—
253C23—521no—
254C23D4×D1311yescharacteristic
255Q8—262no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—522no—
262D4—524no—
263D4—524no—
264D4—522no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—131no—
268C2×C4—131no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4—261no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4D4×D1311yescharacteristic
280C2×C4C23×D1311yescharacteristic
281C8—22no—
282C8—262no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—84no—
292C22—132no—
293C22—261no—
294C22—261no—
295C22—261no—
296C22—261no—
297C22—261no—
298C22—524no—
299C22#8816612yes—
300C22C2×D4×D1311yescharacteristic
301C4—21no—
302C4—41no—
303C4—261no—
304C4—261no—
305C4—522no—
306C4—521no—
307C4—521no—
308C4#8825112yes—
309C2—22no—
310C2—82no—
311C2—81no—
312C2—262no—
313C2—521no—
314C2#1171929411yescharacteristic
315C2C2×#8816611yescharacteristic
316C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3188
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#88192C2semidirect
2. #11719311C2semidirect
3. C13×#447C2semidirect
4. #11718879C2semidirect
5. #11718819C2semidirect
6. #11718818C2semidirect
7. #11718695C2semidirect
8. #11718445C2semidirect
9. #11718439C2semidirect
10. D13×C22⋊C8C2semidirect
11. #11718383C2semidirect
14. C2×#6129C22semidirect
16. C2×C13×D8C22semidirect
23. #88192C22semidirect
26. C2×#6105C22semidirect
29. C2×C8×D13C22semidirect
30. #88151C22semidirect
31. #88146C22semidirect
34. C13×#102C22semidirect
36. #88072C22semidirect
37. #88072C22semidirect
39. #88060C22semidirect
40. #88058C22semidirect
41. #88056C22semidirect
42. #88048C22semidirect
134. #447D13semidirect
167. C2×D8C2×D13semidirect
189. #102C2×D13semidirect
243. C13#3188semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
#117193112
C13×#4472
#117188792
#117188192
#117188182
#117186952
#117184452
#117184392
D13×C22⋊C82
#117183832
#318813