Finite Group Databasebeta

← #13126035

Subgroups — #13126035

Order 1664.

366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 111 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#11719430C211yesmaximal, characteristic
2#11719393C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718728C211yesmaximal, characteristic, complemented
6#11718551C212yesmaximal, complemented
7#11718546C212yesmaximal, complemented
8#11718531C212yesmaximal, complemented
9#11718527C212yesmaximal, complemented
10#11718374C211yesmaximal, characteristic, complemented
11#11718366C211yesmaximal, characteristic, complemented
12C2×#6131—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#125C2211yescharacteristic
15#88201—21no—
16#88150—21no—
17#88150—21no—
18#88149—21no—
19#88149C2212yes—
20#88147—21no—
21#88147C2212yes—
22#88146C2211yescharacteristic
23#88146C2211yescharacteristic
24#88142C2211yescharacteristic
25#88142C2211yescharacteristic
26#88141—21no—
27#88141—21no—
28#88128C2211yescharacteristic
29C42×D13C2211yescharacteristic
30#88124C2211yescharacteristic
31C13×#107C2212yes—
32C13×#106C2212yes—
33C13×#97C2211yescharacteristic
34#88061C2212yes—
35#88061C2212yes—
36#88060C2212yes—
37#88054C2212yes—
38#88049C2212yes—
39#88049C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13—21no—
44#6131—44no—
45C2×D52—22no—
46C2×D52—21no—
47C2×D52—21no—
48C2×D52C2312yes—
49C2×C4×D13—22no—
50C2×C4×D13D411yescharacteristic
51C2×C4×D13D411yescharacteristic
52C2×C4×D13C2311yescharacteristic
53C2×Dic26—21no—
54C2×Dic26—21no—
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4C2311yescharacteristic
60C13×C4⋊C4C2312yes—
61C13×C4⋊C4C2311yescharacteristic
62C42×C13C2311yescharacteristic
63#6103—21no—
64#6103—21no—
65#6103—22no—
66#6103—22no—
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69#6101—21no—
70#6101—21no—
71#6101—21no—
72#6101—21no—
73C4×Dic13—21no—
74C4×Dic13—21no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3235—131nomaximal, Sylow
80C22×D13—22no—
81C22×D13C2×D411yescharacteristic
82Q8×C13—42no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13C2×D411yescharacteristic
92C2×Dic13C2×D411yescharacteristic
93C2×Dic13C2×D411yescharacteristic
94D52—24no—
95D52—42no—
96D52—42no—
97D52—44no—
98C4×D13—22no—
99C4×D13—22no—
100C4×D13—41no—
101C4×D13—44no—
102Dic26—42no—
103Dic26—42no—
104C8×C13—22no—
105#1055—22no—
106#533—131no—
107#532—131no—
108#501—131no—
109#501D1311yescharacteristic, complemented
110#490—131no—
111#490—131no—
112#482—132no—
113#482—132no—
114#476—132no—
115#474—132no—
116#432—131no—
117C22×C13C22×D411yescharacteristic
118C2×D13—21no—
119C2×D13—21no—
120C2×D13—21no—
121C2×D13—42no—
122C2×D13—42no—
123C2×D13—42no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—41no—
127C4×C13—42no—
128C4×C13—41no—
129C4×C132−1+412yes—
130Dic13—21no—
131Dic13—21no—
132Dic13—41no—
133Dic13—41no—
134Dic13AGL(1,ℤ/8)12yes—
135C2×#41—261no—
136C4⋊Q8—131no—
137C4⋊Q8—131no—
138C4⋊Q8C2×D1311yescharacteristic
139#127—131no—
140#125—131no—
141#125C2×D1311yescharacteristic
142#124—261no—
143C22⋊Q8—261no—
144C22⋊Q8—261no—
145#121—132no—
146#121—261no—
147C4×Q8—261no—
148C4×Q8—261no—
149C4×D4—132no—
150C4×D4—261no—
151#117—131no—
152#117—131no—
153C2×C42—131no—
154#107—132no—
155#107C2×D1312yes—
156#106—132no—
157#106C2×D1312yes—
158C4⋊C8—132no—
159#102—132no—
160#102—132no—
161#102—132no—
162#102—132no—
163C22⋊C8—132no—
164#97—131no—
165#97C2×D1311yescharacteristic
166C2×C13#53611yescharacteristic
167C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C13#57511yescharacteristic
169D13—41no—
170D13—82no—
171#41—524no—
172C2×Q8—21no—
173C2×Q8—261no—
174C2×Q8—261no—
175C2×D4—132no—
176C2×D4—262no—
177C2×D4—261no—
178C2×D4—261no—
179C22×C4—131no—
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—262no—
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—131no—
189C4⋊C4—131no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4C22×D1311yescharacteristic
195C4⋊C4C22×D1311yescharacteristic
196C4⋊C4C22×D1312yes—
197C22⋊C4—262no—
198C22⋊C4—262no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C42—131no—
202C42—131no—
203C42—131no—
204C42—261no—
205C42—261no—
206C42C22×D1311yescharacteristic
207C13#323511yescharacteristic, complemented, Sylow
208C23—131no—
209C23—262no—
210Q8—42no—
211Q8—522no—
212Q8—522no—
213D4—264no—
214D4—522no—
215D4—522no—
216D4—524no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—131no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—521no—
228C2×C4—524no—
229C2×C4D4×D1311yescharacteristic
230C2×C4D4×D1311yescharacteristic
231C2×C4C23×D1311yescharacteristic
232C8—22no—
233C8—262no—
234C22—261no—
235C22—261no—
236C22—261no—
237C22—522no—
238C22—522no—
239C22—522no—
240C22C2×D4×D1311yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—132no—
247C4—261no—
248C4—261no—
249C4—521no—
250C4—521no—
251C4#8825412yes—
252C2—521no—
253C2—1042no—
254C2#1171942911yescharacteristic
255C2D13×AGL(1,ℤ/8)11yescharacteristic
256C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#501D13
hypocenterC13#3235
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #11719393C2semidirect
3. C13×#501C2semidirect
4. #11718741C2semidirect
5. #11718728C2semidirect
6. #11718551C2semidirect
7. #11718546C2semidirect
8. #11718531C2semidirect
9. #11718527C2semidirect
10. #11718374C2semidirect
11. #11718366C2semidirect
109. #501D13semidirect
207. C13#3235semidirect

Maximal subgroups

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

subgroupindex
#117194302
#117193932
C13×#5012
#117187412
#117187282
#117185512
#117185462
#117185312
#117185272
#117183742
#117183662
#323513