Finite Group Databasebeta

← #13125750

Subgroups — #13125750

Order 1664.

532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719421C211yesmaximal, characteristic, complemented
2D13×#127C211yesmaximal, characteristic, complemented
3C13×#493C211yesmaximal, characteristic, complemented
4#11718817C214yesmaximal, complemented
5#11718811C214yesmaximal, complemented
6#11718734C211yesmaximal, characteristic, complemented
7#11718731C211yesmaximal, characteristic, complemented
8#11718355C211yesmaximal, characteristic, complemented
9#11718346C211yesmaximal, characteristic, complemented
10C2×#6129—21no—
11C2×D4×D13—21no—
12C2×D4×D13—21no—
13C2×D4×D13C2212yes—
14C2×C13×D8C2214yescomplemented
15C13×#127C2211yescharacteristic
16C13×#127C2211yescharacteristic, complemented
17#88194—21no—
18#88194—21no—
19#88194C2212yes—
20#88192—21no—
21#88192C2212yes—
22#88190—21no—
23D4×Dic13—21no—
24D4×Dic13C2212yescomplemented
25C2×#6104C2214yescomplemented
26#88128C2211yescharacteristic
27C42×D13C2211yescharacteristic
28#88123C2211yescharacteristic, complemented
29C4×C8×C13C2211yescharacteristic, complemented
30#88072C2214yescomplemented
31#88061C2214yescomplemented
32#88060C2212yes—
33#88054C2212yescomplemented
34C4×#1055C2211yescharacteristic, complemented
35C23×D13—22no—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13—21no—
39C2×D4×C13—21no—
40C2×D4×C13C2312yes—
41C2×D4×C13C2312yes—
42C2×C22⋊D13—22no—
43C2×C22⋊D13—22no—
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46C22×Dic13—22no—
47#6129—44no—
48D4×D13—44no—
49D4×D13—44no—
50D4×D13—44no—
51C2×D52—21no—
52C2×D52—21no—
53C2×D52C2312yes—
54C2×C4×D13D411yescharacteristic
55C2×C4×D13D411yescharacteristic
56C2×C4×D13C2311yescharacteristic
57C2×Dic26—21no—
58C13×D8—44no—
59C2×C8×C13C2312yes—
60C42×C13C2311yescharacteristic
61C22⋊Dic13—22no—
62C22⋊Dic13—22no—
63#6104—44no—
64C4⋊Dic13—21no—
65C4⋊Dic13C2312yes—
66C4×Dic13D411yescharacteristic
67C4×Dic13D411yescharacteristic
68C4×Dic13C2311yescharacteristic
69C2×#1055C2312yes—
70#3205—131nomaximal, Sylow
71C23×C13—22no—
72C23×C13—22no—
73C22×D13—22no—
74C22×D13—44no—
75C22×D13—44no—
76C22×D13—44no—
77C22×D13C2×D411yescharacteristic
78D4×C13—24no—
79D4×C13—24no—
80D4×C13—42no—
81D4×C13—42no—
82D4×C13—42no—
83D4×C13—42no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C22⋊D13—44no—
88C22⋊D13—44no—
89C22⋊D13—44no—
90C22⋊D13—44no—
91C2×Dic13—22no—
92C2×Dic13—44no—
93C2×Dic13C2×D411yescharacteristic
94C2×Dic13C2×D411yescharacteristic
95C2×Dic13C2×D411yescharacteristic
96D52—24no—
97D52—42no—
98D52—42no—
99C4×D13—22no—
100C4×D13—22no—
101C4×D13D814yescomplemented
102Dic26—42no—
103C8×C13—22no—
104#1055—22no—
105#532—131no—
106C2×#127—131no—
107#493—131no—
108#493D1311yescharacteristic, complemented
109#486—131no—
110#486—131no—
111#459—134no—
112#447—134no—
113#431—131no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13C22×D411yescharacteristic
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—88no—
127C2×D13C2×D812yes—
128C4×C13C2×D812yes—
129C4×C13AGL(1,ℤ/8)12yes—
130C4×C13H(5,𝔽2)12yes—
131Dic13—21no—
132Dic13—21no—
133Dic13—42no—
134Dic13C2×D812yes—
135C2×#41—261no—
136C22×D4—132no—
137C22×D4—261no—
138C22×D4—261no—
139C2×D8—134no—
140C2×D8C2×D1314yescomplemented
141C4⋊Q8—131no—
142#127—132no—
143#127—131no—
144#127—261no—
145#127—261no—
146#127C2×D1311yescharacteristic
147#127C2×D1311yescharacteristic, complemented
148#124—261no—
149#121—132no—
150#121—261no—
151C4×D4—132no—
152C4×D4—261no—
153C2×C42—131no—
154C4⋊C8—132no—
155#102—134no—
156#102—134no—
157C22⋊C8—132no—
158C4×C8—131no—
159C4×C8C2×D1311yescharacteristic, complemented
160C2×C13—82no—
161C2×C13—82no—
162C2×C13#53511yescharacteristic
163C2×C13C22×D811yescharacteristic
164C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
165D13—22no—
166D13—82no—
167C24—262no—
168#41—524no—
169C2×Q8—261no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—132no—
175C2×D4—262no—
176C2×D4—262no—
177C2×D4—262no—
178C2×D4—262no—
179C2×D4—261no—
180C2×D4—261no—
181C2×D4—524no—
182C2×D4—524no—
183C2×D4—524no—
184C2×D4C22×D1312yes—
185C2×D4C22×D1312yes—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—262no—
190D8—44no—
191D8—524no—
192C2×C8—132no—
193C2×C8C22×D1312yes—
194C4⋊C4—132no—
195C4⋊C4—261no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C42—131no—
199C42—131no—
200C42—131no—
201C42C22×D1311yescharacteristic
202C13#320511yescharacteristic, complemented, Sylow
203C23—22no—
204C23—22no—
205C23—131no—
206C23—262no—
207C23—524no—
208C23—524no—
209C23—524no—
210Q8—522no—
211D4—24no—
212D4—24no—
213D4—42no—
214D4—42no—
215D4—42no—
216D4—42no—
217D4—264no—
218D4—524no—
219D4—524no—
220D4—524no—
221D4—524no—
222D4—522no—
223D4—522no—
224C2×C4—131no—
225C2×C4—134no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—524no—
232C2×C4D4×D1311yescharacteristic
233C2×C4D4×D1311yescharacteristic
234C2×C4C23×D1311yescharacteristic
235C8—22no—
236C8—262no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—132no—
244C22—261no—
245C22—261no—
246C22—522no—
247C22—522no—
248C22—522no—
249C22—1048no—
250C22C2×D4×D1311yescharacteristic
251C4—132no—
252C4—261no—
253C4—261no—
254C4—522no—
255C4D8×D1312yes—
256C4#8816512yes—
257C4#8825112yes—
258C2—82no—
259C2—82no—
260C2—262no—
261C2—1042no—
262C2#1171942011yescharacteristic
263C2C2×D8×D1311yescharacteristic
264C2C2×#8816511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#493C2
socleC22×C13C22×D4
hypercenter#493D13
hypocenterC13#3205
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #11719421C2semidirect
2. D13×#127C2semidirect
3. C13×#493C2semidirect
4. #11718817C2semidirect
5. #11718811C2semidirect
6. #11718734C2semidirect
7. #11718731C2semidirect
8. #11718355C2semidirect
9. #11718346C2semidirect
14. C2×C13×D8C22semidirect
16. C13×#127C22semidirect
24. D4×Dic13C22semidirect
25. C2×#6104C22semidirect
28. #88123C22semidirect
29. C4×C8×C13C22semidirect
30. #88072C22semidirect
31. #88061C22semidirect
33. #88054C22semidirect
34. C4×#1055C22semidirect
101. C4×D13D8semidirect
108. #493D13semidirect
140. C2×D8C2×D13semidirect
147. #127C2×D13semidirect
159. C4×C8C2×D13semidirect
202. C13#3205semidirect

Maximal subgroups

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

subgroupindex
#117194212
D13×#1272
C13×#4932
#117188172
#117188112
#117187342
#117187312
#117183552
#117183462
#320513