Finite Group Databasebeta

← #13126209

Subgroups — #13126209

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
1C13×#529C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3#11718724C212yesmaximal, complemented
4#11718715C212yesmaximal, complemented
5#11718713C212yesmaximal, complemented
6#11718703C212yesmaximal
7#11718692C211yesmaximal, characteristic, complemented
8#11718682C211yesmaximal, characteristic, complemented
9#11718680C211yesmaximal, characteristic, complemented
10#11718669C211yesmaximal, characteristic, complemented
11#11718585C211yesmaximal, characteristic, complemented
12C13×#126—21no—
13C13×#125C2211yescharacteristic
14C13×#124C2211yescharacteristic
15C13×#123—21no—
16C13×C22⋊Q8C2211yescharacteristic
17C13×#121C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13C2211yescharacteristic
21C13×#117—21no—
22C2×C42×C13C2211yescharacteristic
23C2×#6107C2212yes—
24C2×#6105C2212yes—
25#88180—21no—
26#88178—21no—
27#88178C2212yes—
28C2×#6099C2212yes—
29#88124—21no—
30#88123C2211yescharacteristic
31#88123C2211yescharacteristic
32C4×Dic26—21no—
33C4×Dic26C2212yes—
34#88075C2212yes—
35#88072C2212yes—
36#88050C2212yes—
37#88050C2212yes—
38#88048C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C4⋊#1055C2211yescharacteristic
42C4⋊#1055C2212yes—
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13D411yescharacteristic
48C22×C4×C13D411yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C13×C22⋊C4—21no—
60C13×C22⋊C4—21no—
61C13×C22⋊C4—21no—
62C13×C22⋊C4—21no—
63C42×C13—21no—
64C42×C13D411yescharacteristic
65C42×C13D411yescharacteristic
66C42×C13C2311yescharacteristic
67C42×C13C2311yescharacteristic
68C22⋊Dic13—22no—
69#6107—42no—
70#6105—42no—
71C4⋊Dic13—21no—
72C4⋊Dic13—21no—
73C4⋊Dic13—21no—
74C4⋊Dic13C2312yes—
75#6101—22no—
76#6101—22no—
77C4×Dic13—22no—
78#6099—42no—
79C2×#1055C2312yes—
80C2×#1055C2312yes—
81#3252—131nomaximal, Sylow
82C23×C13—21no—
83C23×C13C2×D411yescharacteristic
84Q8×C13—21no—
85Q8×C13—21no—
86D4×C13—21no—
87D4×C13—21no—
88D4×C13—42no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2411yescharacteristic
103C2×Dic13—22no—
104C2×Dic13—22no—
105Dic26—22no—
106Dic26—22no—
107Dic26—42no—
108#1055—22no—
109#1055—22no—
110#533—131no—
111#529D1311yescharacteristic
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#423—131no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—21no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13C22×D411yescharacteristic
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—41no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13#13712yes—
136C4×C13H(5,𝔽2)11yescharacteristic
137C4×C132−1+411yescharacteristic
138Dic13—42no—
139Dic13—42no—
140C2×Q16—132no—
141C2×SD16—132no—
142C2×M16—132no—
143C4⋊Q8—131no—
144C4⋊Q8—131no—
145#126—21no—
146#125—261no—
147#125C2×D1311yescharacteristic
148#124C2×D1311yescharacteristic
149#123—21no—
150C22⋊Q8—132no—
151C22⋊Q8—261no—
152C22⋊Q8C2×D1311yescharacteristic
153#121C2×D1311yescharacteristic
154C4×Q8—132no—
155C4×Q8—261no—
156C4×Q8C2×D1311yescharacteristic
157C4×D4—21no—
158C4×D4C2×D1311yescharacteristic
159#117—21no—
160#117—261no—
161C2×C42C2×D1311yescharacteristic
162#107—132no—
163#106—132no—
164C4⋊C8—131no—
165C4⋊C8—131no—
166C4⋊C8—132no—
167#103—132no—
168#103—132no—
169#103—132no—
170#102—132no—
171C2×C13—41no—
172C2×C13—81no—
173C2×C13#53711yescharacteristic
174C2×C13C2×#13711yescharacteristic
175C2×C13#57511yescharacteristic
176C2×Q8—132no—
177C2×Q8—261no—
178C2×Q8C22×D1311yescharacteristic
179C2×D4—21no—
180C2×D4C22×D1311yescharacteristic
181C22×C4—21no—
182C22×C4C22⋊D1311yescharacteristic
183C22×C4C22⋊D1311yescharacteristic
184C22×C4C22×D1311yescharacteristic
185Q16—522no—
186SD16—522no—
187M16—522no—
188C2×C8—132no—
189C2×C8—132no—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—132no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—262no—
198C4⋊C4—262no—
199C4⋊C4—261no—
200C4⋊C4C22×D1311yescharacteristic
201C4⋊C4C22×D1311yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—262no—
208C42—21no—
209C42—262no—
210C42C22⋊D1311yescharacteristic
211C42C22⋊D1311yescharacteristic
212C42C22×D1311yescharacteristic
213C42C22×D1311yescharacteristic
214C13#325211yescharacteristic, complemented, Sylow
215C23—21no—
216C23C2×C22⋊D1311yescharacteristic
217Q8—21no—
218Q8—21no—
219Q8—262no—
220Q8—262no—
221Q8—522no—
222D4—21no—
223D4—21no—
224D4—42no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4C2×C22⋊D1311yescharacteristic
236C2×C4C2×C22⋊D1311yescharacteristic
237C2×C4C2×C22⋊D1311yescharacteristic
238C2×C4C2×C22⋊D1311yescharacteristic
239C2×C4C2×C22⋊D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—262no—
242C8—262no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22C22×C22⋊D1311yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—41no—
255C4—41no—
256C4—41no—
257C4—522no—
258C4—522no—
259C4#8820512yes—
260C4#8825611yescharacteristic
261C4#8825711yescharacteristic
262C2—41no—
263C2—81no—
264C2#1171952711yescharacteristic
265C2C2×#8820511yescharacteristic
266C2#1171953811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#529C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#529D13
hypocenterC13#3252
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. #11718724C2semidirect
4. #11718715C2semidirect
5. #11718713C2semidirect
7. #11718692C2semidirect
8. #11718682C2semidirect
9. #11718680C2semidirect
10. #11718669C2semidirect
11. #11718585C2semidirect
214. C13#3252semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117191752
#117187242
#117187152
#117187132
#117187032
#117186922
#117186822
#117186802
#117186692
#117185852
#325213