Finite Group Databasebeta

← #13126021

Subgroups — #13126021

Order 1664.

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

normal subgroups only

This group has 368 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#11719421C211yesmaximal, characteristic
2D13×#125C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4#11718732C211yesmaximal, characteristic, complemented
5#11718726C211yesmaximal, characteristic, complemented
6#11718438C212yesmaximal, complemented
7#11718435C212yesmaximal, complemented
8#11718427C212yesmaximal, complemented
9#11718424C212yesmaximal, complemented
10#11718366C211yesmaximal, characteristic, complemented
11#11718363C211yesmaximal, characteristic, complemented
12C2×#6129—21no—
13C13×#127C2211yescharacteristic
14C13×#125C2211yescharacteristic
15#88192—21no—
16#88192C2212yes—
17#88190—21no—
18D4×Dic13—21no—
19D4×Dic13C2212yes—
20C4⋊C4×D13—21no—
21C4⋊C4×D13—21no—
22C4⋊C4×D13C2211yescharacteristic
23C4⋊C4×D13C2211yescharacteristic
24#88144C2211yescharacteristic
25#88144C2211yescharacteristic
26#88143—21no—
27#88143—21no—
28C42×D13C2211yescharacteristic
29#88124C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#102C2212yes—
32C13×#102C2212yes—
33C13×#97C2211yescharacteristic
34#88072C2212yes—
35#88072C2212yes—
36#88060C2212yes—
37#88058C2212yes—
38#88057C2212yes—
39#88054C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42#88043C2211yescharacteristic
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13C2312yes—
46C2×C22⋊D13—22no—
47C22×Dic13—22no—
48#6129—44no—
49C2×C4×D13—21no—
50C2×C4×D13—21no—
51C2×C4×D13D411yescharacteristic
52C2×C4×D13D411yescharacteristic
53C2×C4×D13C2311yescharacteristic
54C2×Dic26—21no—
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2311yescharacteristic
59C13×C4⋊C4C2311yescharacteristic
60C42×C13C2311yescharacteristic
61C22⋊Dic13—22no—
62C22⋊Dic13—22no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2312yes—
69#6101—21no—
70#6101—21no—
71#6101—21no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3234—131nomaximal, Sylow
80C23×C13—22no—
81C22×D13C2×D411yescharacteristic
82D4×C13—24no—
83D4×C13—42no—
84D4×C13—42no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2411yescharacteristic
90C22⋊D13—44no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—44no—
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98C4×D13—22no—
99C4×D13—22no—
100C4×D13—41no—
101C4×D13—42no—
102C4×D13—42no—
103Dic26—42no—
104C8×C13—22no—
105#1055—22no—
106#532—131no—
107C2×#125—131no—
108#501—131no—
109#501—131no—
110#490—131no—
111#490D1311yescharacteristic, complemented
112#481—132no—
113#480—132no—
114#478—132no—
115#478—132no—
116#432—131no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13C22×D411yescharacteristic
121C2×D13—21no—
122C2×D13—21no—
123C2×D13AGL(1,ℤ/8)12yes—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—41no—
127C4×C13—41no—
128C4×C132−1+412yes—
129Dic13—21no—
130Dic13—21no—
131Dic13—21no—
132Dic13—42no—
133Dic13—41no—
134Dic13—41no—
135C2×#41—261no—
136C4⋊Q8—131no—
137#127C2×D1311yescharacteristic
138#125—131no—
139#125—131no—
140#125—131no—
141#125—261no—
142#125—261no—
143#125C2×D1311yescharacteristic
144#124—261no—
145#121—132no—
146#121—261no—
147C4×D4—132no—
148C4×D4—261no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4—261no—
153C2×C42—131no—
154#107—132no—
155#107—132no—
156#106—132no—
157#106—132no—
158C4⋊C8—132no—
159#102—132no—
160#102—132no—
161#102C2×D1312yes—
162#102C2×D1312yes—
163C22⋊C8—132no—
164#97—131no—
165#97C2×D1311yescharacteristic
166C2×C13—82no—
167C2×C13#53611yescharacteristic
168C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C13#57511yescharacteristic
170D13—22no—
171#41—524no—
172C2×Q8—261no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—262no—
176C2×D4C22×D1312yes—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—261no—
181C22×C4—261no—
182C22×C4—262no—
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—131no—
188C4⋊C4—131no—
189C4⋊C4—132no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4C22×D1311yescharacteristic
200C4⋊C4C22×D1311yescharacteristic
201C22⋊C4—262no—
202C22⋊C4—262no—
203C42—131no—
204C42—131no—
205C42—131no—
206C42C22×D1311yescharacteristic
207C13#323411yescharacteristic, complemented, Sylow
208C23—22no—
209C23—131no—
210Q8—522no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—524no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—131no—
218C2×C4—131no—
219C2×C4—131no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—521no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4—524no—
229C2×C4D4×D1311yescharacteristic
230C2×C4D4×D1311yescharacteristic
231C2×C4C23×D1311yescharacteristic
232C8—22no—
233C8—262no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—132no—
238C22—261no—
239C22—261no—
240C22C2×D4×D1311yescharacteristic
241C4—21no—
242C4—21no—
243C4—41no—
244C4—41no—
245C4—261no—
246C4—261no—
247C4—261no—
248C4—521no—
249C4—522no—
250C4—521no—
251C4#8825712yes—
252C2—82no—
253C2—262no—
254C2#1171938011yescharacteristic
255C2D13×AGL(1,ℤ/8)11yescharacteristic
256C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#490C2
socleC22×C13C22×D4
prime radical#11719421C2
hypercenter#490D13
hypocenterC13#3234
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. D13×#125C2semidirect
3. C13×#490C2semidirect
4. #11718732C2semidirect
5. #11718726C2semidirect
6. #11718438C2semidirect
7. #11718435C2semidirect
8. #11718427C2semidirect
9. #11718424C2semidirect
10. #11718366C2semidirect
11. #11718363C2semidirect
111. #490D13semidirect
207. C13#3234semidirect

Maximal subgroups

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

subgroupindex
#117194212
D13×#1252
C13×#4902
#117187322
#117187262
#117184382
#117184352
#117184272
#117184242
#117183662
#117183632
#323413