Finite Group Databasebeta

← #13125775

Subgroups — #13125775

Order 1664.

488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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×#88194C211yesmaximal, characteristic
2#11719327C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4#11718879C211yesmaximal, characteristic, complemented
5#11718836C212yesmaximal, complemented
6#11718824C212yesmaximal, complemented
7#11718707C211yesmaximal, characteristic, complemented
8#11718423C212yesmaximal, complemented
9#11718421C212yesmaximal, complemented
10#11718392C211yesmaximal, characteristic, complemented
11#11718379C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13—21no—
14C22×C22⋊D13—21no—
15C22×D52C2211yescharacteristic
16C2×C13×SD16C2212yescomplemented
17C13×C22⋊Q8C2211yescharacteristic
18Q8×Dic13C2211yescharacteristic, complemented
19#88198C2211yescharacteristic, complemented
20C2×#6106C2212yescomplemented
21#88194—21no—
22#88194—21no—
23#88194C2212yes—
24#88194C2212yes—
25C2×#6105C2212yescomplemented
26#88178C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28C2×#6095C2212yescomplemented
29#88143—21no—
30#88142C2211yescharacteristic, complemented
31#88141—21no—
32#88141C2211yescharacteristic, complemented
33#88132—21no—
34#88131—21no—
35C13×#102C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88061C2212yescomplemented
40#88054C2212yescomplemented
41C8×Dic13C2212yescomplemented
42#88049C2212yescomplemented
43C24×C13—21no—
44C23×D13—21no—
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—22no—
53C2×C22⋊D13—22no—
54C2×C22⋊D13—44no—
55C2×C22⋊D13—44no—
56C22×Dic13D411yescharacteristic
57C22×Dic13D411yescharacteristic
58C2×D52—21no—
59C2×D52—42no—
60C2×D52C2312yes—
61C2×Dic26—21no—
62C2×Dic26C2311yescharacteristic
63C13×SD16—42no—
64C2×C8×C13C2312yes—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C22⋊Dic13—21no—
69#6106—42no—
70#6105—42no—
71C4⋊Dic13—21no—
72C4⋊Dic13C2311yescharacteristic
73#6101—21no—
74#6101—21no—
75#6101—21no—
76#6101—21no—
77#6101—21no—
78C4×Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13D411yescharacteristic
81C4×Dic13D411yescharacteristic
82C4×Dic13C2311yescharacteristic
83C4×Dic13C2311yescharacteristic
84C2×#1055C2312yes—
85#6095—42no—
86#3208—131nomaximal, Sylow
87C23×C13—22no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13C2×D411yescharacteristic
92C22×D13—22no—
93C22×D13—42no—
94C22×D13—42no—
95C22×D13—42no—
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—
107C22⋊D13—44no—
108C22⋊D13—44no—
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13SD1614yescomplemented
113C2×Dic13C2×D411yescharacteristic
114C2×Dic13C2×D411yescharacteristic
115C2×Dic13C2×D411yescharacteristic
116C2×Dic13C2×D411yescharacteristic
117D52—22no—
118D52—22no—
119D52—42no—
120Dic26—22no—
121Dic26—42no—
122C8×C13—22no—
123#1055—22no—
124#533—131no—
125C2×#127—131no—
126#492—132no—
127#486—132no—
128#460—132no—
129#460—132no—
130#450—131no—
131#450—131no—
132#450—131no—
133#450D1311yescharacteristic, complemented
134#431—131no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—84no—
141C22×C13C2×SD1612yes—
142C22×C13C22×D411yescharacteristic
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—84no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13H(5,𝔽2)12yes—
151Dic13—21no—
152Dic13—41no—
153Dic13—41no—
154Dic13C2×SD1612yes—
155Dic13C2×SD1612yes—
156Dic13AGL(1,ℤ/8)12yes—
157C22×D4—131no—
158C22×D4—261no—
159C22×D4—261no—
160C22×D4C2×D1311yescharacteristic
161C2×SD16—132no—
162C2×SD16—132no—
163C2×SD16—132no—
164C2×SD16C2×D1312yescomplemented
165C4⋊Q8—131no—
166C4⋊Q8—131no—
167#127—132no—
168#127—132no—
169#127—261no—
170#127—261no—
171#125—261no—
172C22⋊Q8—131no—
173C22⋊Q8—261no—
174C22⋊Q8C2×D1311yescharacteristic
175C4×Q8—131no—
176C4×Q8—131no—
177C4×Q8—261no—
178#117—261no—
179C2×C42—131no—
180C4⋊C8—132no—
181#102—132no—
182#102—132no—
183#102—132no—
184#102C2×D1312yescomplemented
185C22⋊C8—131no—
186C22⋊C8C2×D1311yescharacteristic
187C4×C8—132no—
188C2×C13—22no—
189C2×C13—82no—
190C2×C13#53511yescharacteristic
191C2×C13C22×SD1611yescharacteristic
192C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
193D13—82no—
194C24—21no—
195C24—261no—
196C2×Q8—131no—
197C2×Q8—261no—
198C2×Q8C22×D1311yescharacteristic
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—132no—
202C2×D4—262no—
203C2×D4—262no—
204C2×D4—262no—
205C2×D4—262no—
206C2×D4—261no—
207C2×D4—522no—
208C2×D4—524no—
209C2×D4—524no—
210C2×D4C22×D1312yes—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4C22×D1311yescharacteristic
214SD16—42no—
215SD16—522no—
216SD16—522no—
217SD16—522no—
218C2×C8—132no—
219C2×C8C22×D1312yes—
220C4⋊C4—21no—
221C4⋊C4—131no—
222C4⋊C4—261no—
223C4⋊C4—261no—
224C4⋊C4—261no—
225C4⋊C4—261no—
226C4⋊C4—261no—
227C4⋊C4—261no—
228C4⋊C4C22×D1311yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—261no—
231C42—131no—
232C42—131no—
233C42—131no—
234C42—131no—
235C42—261no—
236C42—261no—
237C13#320811yescharacteristic, complemented, Sylow
238C23—22no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—262no—
243C23—522no—
244C23—522no—
245C23—522no—
246C23D4×D1311yescharacteristic
247Q8—22no—
248Q8—262no—
249Q8—522no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—262no—
254D4—262no—
255D4—522no—
256D4—524no—
257D4—524no—
258D4—524no—
259D4—524no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—134no—
264C2×C4—131no—
265C2×C4—131no—
266C2×C4—131no—
267C2×C4—131no—
268C2×C4—262no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4D4×D1311yescharacteristic
272C2×C4C23×D1311yescharacteristic
273C8—22no—
274C8—262no—
275C22—21no—
276C22—21no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—84no—
281C22—522no—
282C22—522no—
283C22—522no—
284C22—1044no—
285C22SD16×D1312yes—
286C22C2×D4×D1311yescharacteristic
287C4—21no—
288C4—41no—
289C4—41no—
290C4—132no—
291C4—132no—
292C4—132no—
293C4—261no—
294C4—521no—
295C4—521no—
296C4#8825112yes—
297C2—22no—
298C2—82no—
299C2—1042no—
300C2#1171929711yescharacteristic
301C2C2×SD16×D1311yescharacteristic
302C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
prime radicalC2×#88194C2
hypercenter#450D13
hypocenterC13#3208
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. #11719327C2semidirect
3. C13×#450C2semidirect
4. #11718879C2semidirect
5. #11718836C2semidirect
6. #11718824C2semidirect
7. #11718707C2semidirect
8. #11718423C2semidirect
9. #11718421C2semidirect
10. #11718392C2semidirect
11. #11718379C2semidirect
16. C2×C13×SD16C22semidirect
18. Q8×Dic13C22semidirect
19. #88198C22semidirect
20. C2×#6106C22semidirect
25. C2×#6105C22semidirect
28. C2×#6095C22semidirect
30. #88142C22semidirect
32. #88141C22semidirect
35. C13×#102C22semidirect
37. #88072C22semidirect
39. #88061C22semidirect
40. #88054C22semidirect
41. C8×Dic13C22semidirect
42. #88049C22semidirect
112. C2×Dic13SD16semidirect
133. #450D13semidirect
164. C2×SD16C2×D13semidirect
184. #102C2×D13semidirect
237. C13#3208semidirect

Maximal subgroups

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

subgroupindex
C2×#881942
#117193272
C13×#4502
#117188792
#117188362
#117188242
#117187072
#117184232
#117184212
#117183922
#117183792
#320813