Finite Group Databasebeta

← #13125892

Subgroups — #13125892

Order 1664.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719424C211yesmaximal, characteristic, complemented
2#11719380C211yesmaximal, characteristic, complemented
3C13×#496C211yesmaximal, characteristic, complemented
4#11718831C212yesmaximal, complemented
5#11718823C212yesmaximal, complemented
6#11718819C212yesmaximal, complemented
7#11718814C212yesmaximal, complemented
8#11718737C211yesmaximal, characteristic, complemented
9#11718717C211yesmaximal, characteristic, complemented
10#11718370C211yesmaximal, characteristic, complemented
11#11718364C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2211yescharacteristic
13C2×#6129C2211yescharacteristic
14C2×C13×SD16C2212yes—
15C2×C13×D8C2212yes—
16C13×#127C2211yescharacteristic
17C13×#124C2211yescharacteristic
18#88198C2211yescharacteristic
19#88193—22no—
20#88192C2212yes—
21#88190C2211yescharacteristic
22#88189—22no—
23D4×Dic13C2212yes—
24C2×#6105C2212yes—
25C2×#6105C2212yes—
26#88137—22no—
27#88132—22no—
28#88126C2211yescharacteristic
29#88124C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#97C2211yescharacteristic
32#88075C2212yes—
33#88072C2212yes—
34#88060C2212yes—
35#88056C2212yes—
36#88056C2212yes—
37#88054C2212yes—
38C4×#1055C2211yescharacteristic
39C2×Q8×C13C2311yescharacteristic
40C2×D4×C13—22no—
41C2×D4×C13C2311yescharacteristic
42C2×D4×C13C2312yes—
43C2×C22⋊D13—21no—
44C2×C22⋊D13—22no—
45C22×Dic13—21no—
46C22×Dic13—22no—
47Q8×D13—42no—
48#6129—42no—
49C2×C4×D13—21no—
50C2×C4×D13C2311yescharacteristic
51C2×Dic26—21no—
52C2×Dic26C2311yescharacteristic
53C2×Dic26C2311yescharacteristic
54C13×SD16—42no—
55C13×D8—42no—
56C2×C8×C13C2312yes—
57C13×C22⋊C4—22no—
58C42×C13C2311yescharacteristic
59C22⋊Dic13—22no—
60C22⋊Dic13—22no—
61C22⋊Dic13—22no—
62#6105—42no—
63#6105—42no—
64#6103D412yes—
65C4⋊Dic13—22no—
66C4⋊Dic13C2312yes—
67#6101—22no—
68#6101—22no—
69#6101D412yes—
70C4×Dic13C2311yescharacteristic
71C2×#1055C2312yes—
72#3221—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—22no—
75C22×D13C2×D411yescharacteristic
76Q8×C13—22no—
77D4×C13—22no—
78D4×C13—22no—
79D4×C13—22no—
80D4×C13—82no—
81C2×C4×C13—21no—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2411yescharacteristic
84C22⋊D13—42no—
85C22⋊D13—82no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—21no—
89C2×Dic13—42no—
90C2×Dic13—82no—
91C2×Dic13C2×D412yes—
92C2×Dic13C2×D411yescharacteristic
93C4×D13—22no—
94C4×D13—42no—
95Dic26—22no—
96Dic26—22no—
97Dic26—42no—
98C8×C13—22no—
99#1055—22no—
100#540—131no—
101#536—131no—
102#496D1311yescharacteristic, complemented
103#492—131no—
104#491—131no—
105#488—131no—
106#463—132no—
107#461—132no—
108#449—132no—
109#448—132no—
110#433—131no—
111C22×C13—41no—
112C22×C13—42no—
113C22×C13—42no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13C22×D411yescharacteristic
117C2×D13—21no—
118C2×D13—22no—
119C4×C13—22no—
120C4×C13—41no—
121C4×C13H(5,𝔽2)12yes—
122Dic13—21no—
123Dic13—22no—
124Dic13—41no—
125Dic13—41no—
126Dic13—42no—
127C2×#41—131no—
128C22×Q8—131no—
129C2×SD16—132no—
130C2×SD16—132no—
131C2×SD16C2×D1312yes—
132C2×D8C2×D1312yes—
133C4⋊Q8—131no—
134C4⋊Q8—131no—
135#127C2×D1311yescharacteristic
136#125—131no—
137#124—131no—
138#124C2×D1311yescharacteristic
139#123—262no—
140#123—262no—
141C22⋊Q8—262no—
142#121—132no—
143#121—262no—
144C4×D4—132no—
145#117—131no—
146C4⋊C8—132no—
147#103—132no—
148#103—132no—
149#103—132no—
150#102—132no—
151C22⋊C8—132no—
152#97C2×D1311yescharacteristic
153C4×C8—131no—
154C2×C13—81no—
155C2×C13—82no—
156C2×C13#53511yescharacteristic
157C2×C13#57712yes—
158D13—41no—
159#41—522no—
160C2×Q8—131no—
161C2×Q8—131no—
162C2×Q8—261no—
163C2×Q8—522no—
164C2×Q8C22×D1311yescharacteristic
165C2×D4—22no—
166C2×D4—261no—
167C2×D4—262no—
168C2×D4C22×D1311yescharacteristic
169C2×D4C22×D1312yes—
170C22×C4—131no—
171C22×C4—261no—
172C22×C4—261no—
173C22×C4—262no—
174SD16—42no—
175SD16—522no—
176SD16—522no—
177D8—42no—
178C2×C8—132no—
179C2×C8C22×D1312yes—
180C4⋊C4—132no—
181C4⋊C4—132no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C22⋊C4—22no—
186C22⋊C4—132no—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C42—131no—
191C42C22×D1311yescharacteristic
192C13#322111yescharacteristic, complemented, Sylow
193C23—21no—
194C23—22no—
195C23—131no—
196Q8—22no—
197Q8—262no—
198Q8—262no—
199Q8—522no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—522no—
205D4—1042no—
206C2×C4—21no—
207C2×C4—132no—
208C2×C4—131no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—261no—
212C2×C4—261no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—1042no—
216C2×C4D4×D1312yes—
217C2×C4C23×D1311yescharacteristic
218C8—22no—
219C8—262no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—41no—
224C22—42no—
225C22—262no—
226C22—261no—
227C22C2×D4×D1311yescharacteristic
228C4—22no—
229C4—41no—
230C4—262no—
231C4—261no—
232C4—522no—
233C4—521no—
234C4—521no—
235C4#8825112yes—
236C2—82no—
237C2—81no—
238C2—521no—
239C2#1171942011yescharacteristic
240C2#1171948012yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#496C2
socleC22×C13C22×D4
hypercenter#496D13
hypocenterC13#3221
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #11719424C2semidirect
2. #11719380C2semidirect
3. C13×#496C2semidirect
4. #11718831C2semidirect
5. #11718823C2semidirect
6. #11718819C2semidirect
7. #11718814C2semidirect
8. #11718737C2semidirect
9. #11718717C2semidirect
10. #11718370C2semidirect
11. #11718364C2semidirect
102. #496D13semidirect
192. C13#3221semidirect

Maximal subgroups

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

subgroupindex
#117194242
#117193802
C13×#4962
#117188312
#117188232
#117188192
#117188142
#117187372
#117187172
#117183702
#117183642
#322113