Finite Group Databasebeta

← #13127163

Subgroups — #13127163

Order 1664.

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

normal subgroups only

This group has 430 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
1C13×#550C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic, complemented
3#11718899C212yesmaximal, complemented
4#11718893C212yesmaximal, complemented
5#11718733C211yesmaximal, characteristic, complemented
6#11718731C211yesmaximal, characteristic, complemented
7#11718700C212yesmaximal, complemented
8#11718695C212yesmaximal, complemented
9C4×#6106C211yesmaximal, characteristic, complemented
10#11718681C211yesmaximal, characteristic, complemented
11#11718673C211yesmaximal, characteristic, complemented
12C2×C13×#41C2212yes—
13C2×#6129—21no—
14C13×#127—21no—
15C13×#127C2211yescharacteristic
16C13×#121—22no—
17C13×#121C2212yes—
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13C2211yescharacteristic
21C2×#6106C2211yescharacteristic
22C2×#6104C2212yes—
23#88184C2212yes—
24C2×C4⋊Dic13C2212yes—
25C2×#6099C2212yes—
26#88151—21no—
27#88140—22no—
28C4×D52C2211yescharacteristic
29#88123C2211yescharacteristic
30#88075C2212yes—
31#88075C2211yescharacteristic
32#88072C2212yes—
33#88072C2212yes—
34#88072C2212yes—
35C22⋊#1055C2212yes—
36#88049C2211yescharacteristic
37#88048C2212yes—
38#88048C2211yescharacteristic
39C4⋊#1055C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C13×#41—24no—
42C13×#41—42no—
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13D411yescharacteristic
49C2×D4×C13C2312yes—
50C22×C4×C13—22no—
51C22×C4×C13C2312yes—
52C2×C22⋊D13—22no—
53C22×Dic13—22no—
54#6129—44no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4D411yescharacteristic
60C13×C4⋊C4C2311yescharacteristic
61C13×C22⋊C4—22no—
62C13×C22⋊C4D412yes—
63C42×C13—21no—
64C42×C13C2311yescharacteristic
65#6106—22no—
66#6104—42no—
67#6103—21no—
68#6103—22no—
69C4⋊Dic13—21no—
70C4⋊Dic13—22no—
71C4⋊Dic13C2312yes—
72C4⋊Dic13C2311yescharacteristic
73#6099—42no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2312yes—
76C2×#1055C2311yescharacteristic
77#3332—131nomaximal, Sylow
78C23×C13—22no—
79C23×C13C2×D412yes—
80C22×D13—21no—
81Q8×C13—21no—
82Q8×C13#4112yescomplemented
83D4×C13—22no—
84D4×C13—22no—
85D4×C13—22no—
86D4×C13—44no—
87D4×C13—42no—
88D4×C13—81no—
89D4×C13—82no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—44no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D412yes—
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2411yescharacteristic
99C22⋊D13—44no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—44no—
103D52—21no—
104D52—21no—
105C4×D13—42no—
106Dic26—42no—
107#1055—21no—
108#1055—21no—
109#1055—22no—
110#550D1311yescharacteristic, complemented
111#547—131no—
112#486—131no—
113#481—132no—
114#475—131no—
115#469—132no—
116#459—131no—
117#449—132no—
118C4×SD16—131no—
119#436—131no—
120#417—132no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13C22×D411yescharacteristic
128C2×D13—41no—
129C2×D13—41no—
130C2×D13—41no—
131C4×C13—22no—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—41no—
135C4×C13AGL(1,ℤ/8)12yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—42no—
139Dic13—41no—
140C2×#41—261no—
141C2×#41C2×D1312yes—
142C2×SD16—131no—
143C2×D8—132no—
144C2×M16—132no—
145C4⋊Q8—131no—
146#127—21no—
147#127C2×D1311yescharacteristic
148#123—262no—
149C22⋊Q8—261no—
150#121—22no—
151#121—132no—
152#121C2×D1312yes—
153C4×Q8C2×D1311yescharacteristic
154C4×D4—21no—
155C4×D4—131no—
156C4×D4C2×D1311yescharacteristic
157C2×C4⋊C4—132no—
158#106—131no—
159#106—132no—
160C4⋊C8—131no—
161#103—131no—
162#103—132no—
163#102—132no—
164#102—132no—
165#102—132no—
166#102—131no—
167C22⋊C8—132no—
168C4×C8—131no—
169C2×C13—42no—
170C2×C13—82no—
171C2×C13#54611yescharacteristic
172C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C13#57711yescharacteristic
174D13—81no—
175#41—24no—
176#41—42no—
177#41—524no—
178C2×Q8—261no—
179C2×Q8C22×D1311yescharacteristic
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—131no—
185C2×D4—262no—
186C2×D4C22⋊D1311yescharacteristic
187C2×D4C22×D1312yes—
188C22×C4—22no—
189C22×C4—262no—
190C22×C4—261no—
191C22×C4C22×D1312yes—
192SD16—262no—
193D8—522no—
194M16—522no—
195C2×C8—131no—
196C2×C8—131no—
197C2×C8—132no—
198C4⋊C4—21no—
199C4⋊C4—131no—
200C4⋊C4—132no—
201C4⋊C4—262no—
202C4⋊C4—261no—
203C4⋊C4C22⋊D1311yescharacteristic
204C4⋊C4C22×D1311yescharacteristic
205C22⋊C4—22no—
206C22⋊C4—261no—
207C22⋊C4—262no—
208C22⋊C4C22⋊D1312yes—
209C42—21no—
210C42C22×D1311yescharacteristic
211C13#333211yescharacteristic, complemented, Sylow
212C23—22no—
213C23—261no—
214C23C2×C22⋊D1312yes—
215Q8—21no—
216Q8—522no—
217Q8#612912yescomplemented
218D4—22no—
219D4—22no—
220D4—22no—
221D4—44no—
222D4—42no—
223D4—81no—
224D4—82no—
225D4—261no—
226D4—261no—
227D4—524no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—44no—
233C2×C4—261no—
234C2×C4—262no—
235C2×C4—524no—
236C2×C4—522no—
237C2×C4C2×C22⋊D1311yescharacteristic
238C2×C4C2×C22⋊D1312yes—
239C2×C4C2×C22⋊D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—261no—
242C8—261no—
243C8—262no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—521no—
251C22—521no—
252C22—521no—
253C22C22×C22⋊D1311yescharacteristic
254C4—22no—
255C4—22no—
256C4—21no—
257C4—41no—
258C4—521no—
259C4—522no—
260C4#8820312yes—
261C4C2×#612911yescharacteristic
262C4#8825111yescharacteristic
263C2—42no—
264C2—82no—
265C2—1041no—
266C2#1171951111yescharacteristic
267C2C2×#8820311yescharacteristic
268C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#550C2
socleC22×C13C22×D4
hypercenter#550D13
hypocenterC13#3332
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C13×#550C2semidirect
2. #11719260C2semidirect
3. #11718899C2semidirect
4. #11718893C2semidirect
5. #11718733C2semidirect
6. #11718731C2semidirect
7. #11718700C2semidirect
8. #11718695C2semidirect
9. C4×#6106C2semidirect
10. #11718681C2semidirect
11. #11718673C2semidirect
82. Q8×C13#41semidirect
110. #550D13semidirect
211. C13#3332semidirect
217. Q8#6129semidirect

Maximal subgroups

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

subgroupindex
C13×#5502
#117192602
#117188992
#117188932
#117187332
#117187312
#117187002
#117186952
C4×#61062
#117186812
#117186732
#333213