Finite Group Databasebeta

← #13127246

Subgroups — #13127246

Order 1664.

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

normal subgroups only

This group has 352 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#11719437C211yesmaximal, characteristic, complemented
2#11719268C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic, complemented
4#11718740C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic, complemented
6#11718549C212yesmaximal, complemented
7#11718541C212yesmaximal, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718495C211yesmaximal, characteristic, complemented
10#11718445C212yesmaximal, complemented
11#11718439C212yesmaximal, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C4×D4×C13C2211yescharacteristic
14#88201—21no—
15Q8×Dic13—21no—
16#88192C2212yes—
17C2×#6105C2211yescharacteristic
18#88184—21no—
19#88180—21no—
20C2×C8×D13C2212yes—
21#88152—22no—
22#88151C2212yes—
23#88146C2212yes—
24#88146C2212yes—
25#88139—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#107C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#102C2212yes—
32#88072C2211yescharacteristic
33#88060C2212yes—
34#88058C2212yes—
35#88056C2212yes—
36#88050C2211yescharacteristic
37#88048C2211yescharacteristic
38#88048C2212yes—
39#88048C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×C22⋊D13—22no—
45C2×D52D411yescharacteristic
46C2×C4×D13C2312yes—
47C2×Dic26—21no—
48C2×Dic26C2311yescharacteristic
49C2×C8×C13C2312yes—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C13×C4⋊C4C2311yescharacteristic
53C13×C22⋊C4—21no—
54C42×C13C2311yescharacteristic
55C22⋊Dic13—22no—
56#6105—22no—
57#6103—22no—
58#6103—22no—
59#6103—22no—
60#6103D412yes—
61C4⋊Dic13—21no—
62C4⋊Dic13—22no—
63C4⋊Dic13D411yescharacteristic
64C4⋊Dic13C2311yescharacteristic
65C4⋊Dic13C2312yes—
66#6101—21no—
67C4×Dic13—21no—
68C4×Dic13—22no—
69C4×Dic13—22no—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72C8×D13—24no—
73#3340—131nomaximal, Sylow
74C23×C13—21no—
75C22×D13C2×D412yes—
76Q8×C13—42no—
77D4×C13—21no—
78D4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—42no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2411yescharacteristic
85C22⋊D13—82no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13C2×D412yes—
90D52—22no—
91C4×D13—22no—
92C4×D13—22no—
93Dic26—21no—
94Dic26—21no—
95Dic26—81no—
96C8×C13—22no—
97#1055—21no—
98#1055#4112yes—
99#556—131no—
100#555—131no—
101#498—131no—
102#485—132no—
103#482—132no—
104#477—131no—
105#474D1311yescharacteristic, complemented
106#465—132no—
107C4×SD16—131no—
108C8×D4—131no—
109#427—132no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13C22×D411yescharacteristic
114C2×D13—22no—
115C2×D13—22no—
116C2×D13—22no—
117C4×C13—21no—
118C4×C13—41no—
119C4×C13—42no—
120C4×C13#13512yes—
121C4×C13C2×#4111yescharacteristic
122C4×C132−1+411yescharacteristic
123Dic13—22no—
124Dic13—41no—
125Dic13—42no—
126Dic13—41no—
127C2×SD16—131no—
128C22×C8—132no—
129C4⋊Q8—131no—
130C4⋊Q8C2×D1311yescharacteristic
131#126—262no—
132#124—262no—
133#124—261no—
134C22⋊Q8—132no—
135#121—132no—
136#121—261no—
137C4×Q8—131no—
138C4×Q8—261no—
139C4×D4—131no—
140C4×D4C2×D1311yescharacteristic
141#117—132no—
142#117—132no—
143#117—261no—
144#107—132no—
145#107C2×D1312yes—
146#106—131no—
147#106—132no—
148#106—132no—
149C4⋊C8C2×D1311yescharacteristic
150#103—132no—
151#103—131no—
152#102—131no—
153#102C2×D1312yes—
154C22⋊C8—132no—
155C4×C8—131no—
156C2×C13—81no—
157C2×C13#54711yescharacteristic
158C2×C13C2×#13511yescharacteristic
159C2×C13#57711yescharacteristic
160D13—42no—
161C2×Q8—21no—
162C2×Q8—131no—
163C2×Q8—261no—
164C2×D4—131no—
165C2×D4—262no—
166C2×D4C22×D1311yescharacteristic
167C22×C4—21no—
168C22×C4—132no—
169SD16—262no—
170C2×C8—131no—
171C2×C8—131no—
172C2×C8—264no—
173C2×C8C22×D1312yes—
174C4⋊C4—21no—
175C4⋊C4—131no—
176C4⋊C4—131no—
177C4⋊C4—132no—
178C4⋊C4—262no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C4⋊C4C22×D1312yes—
182C4⋊C4C22×D1311yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—132no—
185C22⋊C4—262no—
186C22⋊C4—262no—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C42—262no—
190C42—262no—
191C42—261no—
192C42C22×D1311yescharacteristic
193C13#334011yescharacteristic, complemented, Sylow
194C23—21no—
195C23—132no—
196Q8—42no—
197Q8—261no—
198Q8—261no—
199Q8—1041no—
200D4—21no—
201D4—21no—
202D4—262no—
203D4—1042no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—132no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—261no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4D4×D1311yescharacteristic
214C2×C4D4×D1311yescharacteristic
215C2×C4C23×D1311yescharacteristic
216C8—22no—
217C8—132no—
218C8—261no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—262no—
223C22—262no—
224C22—262no—
225C22C2×D4×D1311yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—262no—
230C4—521no—
231C4—522no—
232C4—521no—
233C4#8816612yes—
234C4#8825411yescharacteristic
235C4#41×D1311yescharacteristic
236C2—81no—
237C2—522no—
238C2#1171933611yescharacteristic
239C2C2×#8816611yescharacteristic
240C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radical#11719268C2
hypercenter#474D13
hypocenterC13#3340
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
3. C13×#474C2semidirect
4. #11718740C2semidirect
5. C4×#6105C2semidirect
6. #11718549C2semidirect
7. #11718541C2semidirect
8. #11718511C2semidirect
9. #11718495C2semidirect
10. #11718445C2semidirect
11. #11718439C2semidirect
105. #474D13semidirect
193. C13#3340semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117192682
C13×#4742
#117187402
C4×#61052
#117185492
#117185412
#117185112
#117184952
#117184452
#117184392
#334013