Finite Group Databasebeta

← #13126210

Subgroups — #13126210

Order 1664.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#11719184C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3C13×#423C211yesmaximal, characteristic, complemented
4#11718798C212yesmaximal, complemented
5#11718795C212yesmaximal
6#11718511C211yesmaximal, characteristic, complemented
7#11718510C211yesmaximal, characteristic, complemented
8#11718506C212yesmaximal, complemented
9#11718503C211yesmaximal, characteristic, complemented
10#11718502C211yesmaximal, characteristic, complemented
11#11718490C212yesmaximal, complemented
12C2×C13×M16C2212yes—
13C2×C42×C13C2211yescharacteristic
14#88184C2211yescharacteristic
15#88183—21no—
16C4×C22⋊D13—21no—
17#88180—21no—
18#88178—21no—
19#88178C2212yes—
20#88178C2211yescharacteristic
21C2×Dic52C2212yes—
22C2×#6095C2212yes—
23#88130—21no—
24#88129C2211yescharacteristic
25C4×D52C2211yescharacteristic
26#88126—21no—
27#88124—21no—
28#88124C2211yescharacteristic
29#88123C2211yescharacteristic
30#88123C2211yescharacteristic
31C4×Dic26—21no—
32C4×Dic26C2212yes—
33C4×Dic26C2211yescharacteristic
34C13×C4⋊C8C2212yes—
35C13×C4⋊C8C2211yescharacteristic
36C13×C4⋊C8C2211yescharacteristic
37#88061C2212yes—
38#88058C2212yes—
39#88057C2212yes—
40#88056C2212yes—
41#88056C2212yes—
42#88056C2212yes—
43C22×C4×C13D411yescharacteristic
44C22×C4×C13D411yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—21no—
47C2×D52C2311yescharacteristic
48C2×C4×D13—21no—
49C2×Dic26—21no—
50C2×Dic26C2312yes—
51C2×Dic26C2311yescharacteristic
52C13×M16—42no—
53C2×C8×C13C2312yes—
54C2×C8×C13C2312yes—
55C42×C13D411yescharacteristic
56C42×C13D411yescharacteristic
57C42×C13C2311yescharacteristic
58C42×C13C2311yescharacteristic
59C22⋊Dic13—22no—
60C22⋊Dic13—21no—
61#6103—21no—
62#6103—21no—
63#6103—21no—
64#6103—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—22no—
72#6101—22no—
73#6101—21no—
74#6101—21no—
75#6101—21no—
76#6101—21no—
77C4×Dic13—22no—
78C4×Dic13—21no—
79Dic52—42no—
80#6095—42no—
81#3252—131nomaximal, Sylow
82C23×C13C2×D411yescharacteristic
83C22×D13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—41no—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C22⋊D13—42no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100D52—21no—
101D52—21no—
102C4×D13—42no—
103Dic26—22no—
104Dic26—21no—
105Dic26—22no—
106Dic26—21no—
107Dic26—42no—
108C8×C13—22no—
109C8×C13—22no—
110#533—131no—
111#529—131no—
112#479—132no—
113#477—131no—
114#476—131no—
115#470—132no—
116#468—132no—
117#464—132no—
118#462—131no—
119#461—131no—
120#423D1311yescharacteristic, complemented
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—21no—
124C22×C13C22×D411yescharacteristic
125C2×D13—41no—
126C2×D13—41no—
127C2×D13—41no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13#13712yes—
133C4×C13H(5,𝔽2)11yescharacteristic
134C4×C132−1+411yescharacteristic
135Dic13—42no—
136Dic13—41no—
137Dic13—41no—
138Dic13—42no—
139Dic13—41no—
140C2×Q16—132no—
141C2×SD16—132no—
142C2×M16C2×D1312yes—
143C4⋊Q8—131no—
144C4⋊Q8—131no—
145#126—261no—
146#125—131no—
147#125—261no—
148#124—131no—
149#123—261no—
150C22⋊Q8—131no—
151C22⋊Q8—132no—
152C22⋊Q8—261no—
153#121—131no—
154C4×Q8—131no—
155C4×Q8—132no—
156C4×Q8—261no—
157C4×D4—131no—
158C4×D4—261no—
159#117—261no—
160#117—261no—
161C2×C42C2×D1311yescharacteristic
162#107—132no—
163#106—132no—
164C4⋊C8C2×D1311yescharacteristic
165C4⋊C8C2×D1311yescharacteristic
166C4⋊C8C2×D1312yes—
167#103—132no—
168#103—132no—
169#103—132no—
170#102—132no—
171C2×C13—41no—
172C2×C13#53711yescharacteristic
173C2×C13C2×#13711yescharacteristic
174C2×C13#57511yescharacteristic
175D13—81no—
176C2×Q8—131no—
177C2×Q8—132no—
178C2×Q8—261no—
179C2×D4—131no—
180C2×D4—261no—
181C22×C4—261no—
182C22×C4D5211yescharacteristic
183C22×C4D5211yescharacteristic
184C22×C4C22×D1311yescharacteristic
185Q16—522no—
186SD16—522no—
187M16—42no—
188C2×C8C22×D1312yes—
189C2×C8C22×D1312yes—
190C4⋊C4—132no—
191C4⋊C4—131no—
192C4⋊C4—131no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—262no—
199C4⋊C4—261no—
200C4⋊C4—262no—
201C4⋊C4—261no—
202C22⋊C4—262no—
203C22⋊C4—261no—
204C22⋊C4—261no—
205C22⋊C4—261no—
206C22⋊C4—261no—
207C22⋊C4—261no—
208C42—261no—
209C42—262no—
210C42D5211yescharacteristic
211C42D5211yescharacteristic
212C42C22×D1311yescharacteristic
213C42C22×D1311yescharacteristic
214C13#325211yescharacteristic, complemented, Sylow
215C23—261no—
216C23C2×D5211yescharacteristic
217Q8—262no—
218Q8—261no—
219Q8—261no—
220Q8—262no—
221Q8—522no—
222D4—261no—
223D4—261no—
224D4—522no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—522no—
235C2×C4C2×D5211yescharacteristic
236C2×C4C2×D5211yescharacteristic
237C2×C4C2×D5211yescharacteristic
238C2×C4C2×D5211yescharacteristic
239C2×C4C2×D5211yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—22no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—521no—
247C22—521no—
248C22—521no—
249C22C22×D5211yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—521no—
255C4—521no—
256C4—522no—
257C4—521no—
258C4—522no—
259C4#8816312yes—
260C4#8825111yescharacteristic
261C4#8825411yescharacteristic
262C2—41no—
263C2—1041no—
264C2#1171921511yescharacteristic
265C2C2×#8816311yescharacteristic
266C2#1171945311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#423C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#423D13
hypocenterC13#3252
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. C13×#423C2semidirect
4. #11718798C2semidirect
6. #11718511C2semidirect
7. #11718510C2semidirect
8. #11718506C2semidirect
9. #11718503C2semidirect
10. #11718502C2semidirect
11. #11718490C2semidirect
120. #423D13semidirect
214. C13#3252semidirect

Maximal subgroups

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

subgroupindex
#117191842
#117191752
C13×#4232
#117187982
#117187952
#117185112
#117185102
#117185062
#117185032
#117185022
#117184902
#325213