Finite Group Databasebeta

← #13127548

Subgroups — #13127548

Order 1664.

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

normal subgroups only

This group has 396 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
1#11719435C211yesmaximal, characteristic, complemented
2#11719423C211yesmaximal, characteristic, complemented
3C13×#486C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718733C211yesmaximal, characteristic, complemented
6#11718447C212yesmaximal, complemented
7#11718446C212yesmaximal, complemented
8#11718427C212yesmaximal, complemented
9#11718425C212yesmaximal, complemented
10C4×D104C211yesmaximal, characteristic, complemented
11#11718340C211yesmaximal, characteristic, complemented
12C2×#6129—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#127C2211yescharacteristic
15#88200—22no—
16#88194C2212yes—
17#88193—22no—
18#88192—21no—
19D4×Dic13C2212yes—
20C2×#6104C2212yes—
21C2×D104C2211yescharacteristic
22#88151—21no—
23#88147C2212yes—
24C4⋊C4×D13—21no—
25#88144C2212yes—
26C4×D52C2211yescharacteristic
27C4×D52C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#102C2212yes—
30C13×#102C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88072C2212yes—
33#88061C2211yescharacteristic
34#88061C2211yescharacteristic
35#88058C2211yescharacteristic
36#88055C2212yes—
37#88054C2212yes—
38#88049C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13C2312yes—
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C22×Dic13—22no—
48#6129—44no—
49C2×D52C2311yescharacteristic
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×C4×D13—21no—
53C2×C4×D13—22no—
54C2×Dic26D411yescharacteristic
55C2×C8×C13C2311yescharacteristic
56C2×C8×C13C2311yescharacteristic
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C42×C13C2311yescharacteristic
60C22⋊Dic13—22no—
61#6104—24no—
62#6103—21no—
63#6103—21no—
64#6103—22no—
65C4⋊Dic13—22no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69#6101—22no—
70#6101D412yes—
71C4×Dic13C2312yes—
72C2×#1055C2312yes—
73D104—22no—
74#3366—131nomaximal, Sylow
75C23×C13—22no—
76C22×D13—21no—
77C22×D13—21no—
78Q8×C13—81no—
79D4×C13—22no—
80D4×C13—22no—
81D4×C13—42no—
82D4×C13—81no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C22⋊D13—44no—
88C22⋊D13—82no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—44no—
92C2×Dic13C2×D412yes—
93C2×Dic13C2×D412yes—
94D52—21no—
95D52—21no—
96D52—21no—
97D52#4112yescomplemented
98C4×D13—42no—
99C4×D13—42no—
100C4×D13—82no—
101Dic26—22no—
102C8×C13—21no—
103C8×C13—21no—
104#1055—22no—
105#554—131no—
106#550—131no—
107#490—132no—
108#486D1311yescharacteristic, complemented
109#478—132no—
110#476—131no—
111#459—131no—
112#459—132no—
113#446—131no—
114#442—132no—
115C4×D8—131no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13C22×D411yescharacteristic
120C2×D13—22no—
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—41no—
126C4×C13—21no—
127C4×C13—42no—
128C4×C13AGL(1,ℤ/8)12yes—
129C4×C13C2×#4111yescharacteristic
130C4×C132−1+411yescharacteristic
131Dic13—22no—
132Dic13—22no—
133Dic13—41no—
134Dic13—41no—
135C2×#41—261no—
136C2×D8—132no—
137C2×D8—131no—
138C4⋊Q8C2×D1311yescharacteristic
139#127—132no—
140#127C2×D1311yescharacteristic
141#125—132no—
142C22⋊Q8—261no—
143C22⋊Q8—262no—
144#121—261no—
145#121—262no—
146C4×Q8—131no—
147C4×D4—132no—
148C4×D4—132no—
149C4×D4—131no—
150C4×D4—131no—
151C2×C4⋊C4—261no—
152#107—131no—
153#106—132no—
154C4⋊C8—132no—
155C4⋊C8—131no—
156#102—132no—
157#102—131no—
158#102—131no—
159#102—132no—
160#102C2×D1312yes—
161#102C2×D1312yes—
162#97—132no—
163C4×C8C2×D1311yescharacteristic
164C2×C13—82no—
165C2×C13#54811yescharacteristic
166C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C13#57611yescharacteristic
168D13—42no—
169D13—81no—
170#41—524no—
171C2×Q8—21no—
172C2×Q8—131no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—131no—
176C2×D4—131no—
177C2×D4—262no—
178C2×D4—262no—
179C2×D4C22×D1312yes—
180C22×C4—262no—
181C22×C4—262no—
182C22×C4—261no—
183C22×C4—261no—
184D8—262no—
185D8—264no—
186C2×C8—132no—
187C2×C8C22×D1311yescharacteristic
188C2×C8C22×D1311yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—131no—
191C4⋊C4—132no—
192C4⋊C4—131no—
193C4⋊C4—131no—
194C4⋊C4—262no—
195C4⋊C4—262no—
196C4⋊C4C22×D1312yes—
197C22⋊C4—262no—
198C22⋊C4—262no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C42—132no—
202C42C22×D1311yescharacteristic
203C13#336611yescharacteristic, complemented, Sylow
204C23—22no—
205C23—261no—
206C23—261no—
207Q8—81no—
208Q8—262no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—81no—
213D4—132no—
214D4—261no—
215D4—261no—
216D4—261no—
217D4—524no—
218D4—1042no—
219C2×C4—22no—
220C2×C4—132no—
221C2×C4—132no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—524no—
225C2×C4—522no—
226C2×C4—522no—
227C2×C4—1042no—
228C2×C4D4×D1311yescharacteristic
229C2×C4D4×D1311yescharacteristic
230C2×C4C23×D1311yescharacteristic
231C8—21no—
232C8—21no—
233C8—262no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—262no—
238C22—521no—
239C22—521no—
240C22—521no—
241C22—521no—
242C22—521no—
243C22C2×D4×D1311yescharacteristic
244C4—21no—
245C4—42no—
246C4—262no—
247C4—262no—
248C4—521no—
249C4—521no—
250C4#8816812yes—
251C4#41×D1311yescharacteristic
252C4#8825711yescharacteristic
253C2—82no—
254C2—522no—
255C2—1041no—
256C2#1171938211yescharacteristic
257C2#1171946211yescharacteristic
258C2C2×#8816811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
hypercenter#486D13
hypocenterC13#3366
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
2. #11719423C2semidirect
3. C13×#486C2semidirect
4. #11718745C2semidirect
5. #11718733C2semidirect
6. #11718447C2semidirect
7. #11718446C2semidirect
8. #11718427C2semidirect
9. #11718425C2semidirect
10. C4×D104C2semidirect
11. #11718340C2semidirect
97. D52#41semidirect
108. #486D13semidirect
203. C13#3366semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117194232
C13×#4862
#117187452
#117187332
#117184472
#117184462
#117184272
#117184252
C4×D1042
#117183402
#336613