Finite Group Databasebeta

← #13118093

Subgroups — #13118093

Order 1664.

560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×C13×#117C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D13C211yesmaximal, characteristic
3C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic, complemented
5#11718653C211yesmaximal, characteristic, complemented
6#11718643C211yesmaximal, characteristic, complemented
7#11718641C211yesmaximal, characteristic, complemented
8#11718620C212yesmaximal
9#11718613C212yesmaximal, complemented
10C4×#6103C212yesmaximal, complemented
11C4×#6101C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C13×#117—24no—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×C42×C13C2212yes—
20C2×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊Dic13C2212yes—
22C4×C22⋊D13—24no—
23C2×#6103C2211yescharacteristic
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6101C2211yescharacteristic
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30C2×C4×Dic13C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2211yescharacteristic
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13—24no—
40C22×C4×C13D414yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2312yes—
53C2×C4×D13—22no—
54C2×C4×D13—24no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C22⋊C4—24no—
58C42×C13—24no—
59C22⋊Dic13—22no—
60C22⋊Dic13—24no—
61#6103—24no—
62#6103—22no—
63#6103—24no—
64#6101—22no—
65#6101—24no—
66#6101—24no—
67C4×Dic13—22no—
68C4×Dic13—24no—
69#2395—131nomaximal, Sylow
70C23×C13—22no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—22no—
74C23×C13C2×D412yes—
75C23×C13C2411yescharacteristic
76C22×D13—21no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—21no—
80C22×D13#4112yes—
81C2×C4×C13—22no—
82C2×C4×C13—28no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13C2×D412yes—
90C2×C4×C13C2×D412yes—
91C2×C4×C13#4114yes—
92C22⋊D13—28no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13#4112yes—
105C2×Dic13#4114yes—
106C4×D13—44no—
107C2×C4×D4—131no—
108C2×#117D1311yescharacteristic, complemented
109#400—131no—
110#399—131no—
111#398—131no—
112#397—131no—
113#397—132no—
114#394—132no—
115C4×C4⋊C4—132no—
116C4×C22⋊C4—131no—
117C4×C22⋊C4—132no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13C22×D411yescharacteristic
124C22×C13C2×#4112yes—
125C22×C13C2×#4111yescharacteristic
126C22×C13C2×#4111yescharacteristic
127C22×C13C2×#4112yes—
128C2×D13—22no—
129C2×D13—24no—
130C2×D13—41no—
131C2×D13—42no—
132C2×D13—41no—
133C4×C13—22no—
134C4×C13—42no—
135C4×C13—42no—
136C4×C13#12314yes—
137Dic13—22no—
138Dic13—24no—
139Dic13—41no—
140Dic13—42no—
141Dic13—41no—
142C22×D4—131no—
143C23×C4—131no—
144C23×C4C2×D1311yescharacteristic
145C4×D4—264no—
146#117—24no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—132no—
150C2×C4⋊C4C2×D1311yescharacteristic
151C2×C4⋊C4C2×D1311yescharacteristic
152C2×C22⋊C4—131no—
153C2×C22⋊C4—132no—
154C2×C22⋊C4—131no—
155C2×C22⋊C4—132no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4C2×D1312yes—
158C2×C42—131no—
159C2×C42—132no—
160C2×C42C2×D1312yes—
161#95—132no—
162#95—131no—
163#95—132no—
164#95—131no—
165#95—132no—
166#95—132no—
167C2×C13—42no—
168C2×C13C2×#12311yescharacteristic
169C2×C13#52511yescharacteristic
170C2×C13#52912yes—
171C2×C13#52912yes—
172C2×C13#53211yescharacteristic
173D13—42no—
174C24—131no—
175C24C22×D1311yescharacteristic
176C2×D4—262no—
177C2×D4—262no—
178C2×D4—262no—
179C22×C4—24no—
180C22×C4—132no—
181C22×C4—131no—
182C22×C4—132no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—264no—
186C22×C4—262no—
187C22×C4C22⋊D1314yes—
188C22×C4C22×D1312yes—
189C22×C4C22×D1312yes—
190C22×C4C22×D1311yescharacteristic
191C22×C4C22×D1311yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—264no—
195C4⋊C4—264no—
196C4⋊C4—262no—
197C22⋊C4—24no—
198C22⋊C4—264no—
199C22⋊C4—264no—
200C22⋊C4—264no—
201C22⋊C4—262no—
202C22⋊C4—262no—
203C42—24no—
204C42—264no—
205C42—262no—
206C13#239511yescharacteristic, complemented, Sylow
207C23—22no—
208C23—22no—
209C23—21no—
210C23—21no—
211C23—132no—
212C23—262no—
213C23—262no—
214C23—261no—
215C23—261no—
216C23C2×C22⋊D1312yes—
217C23C23×D1311yescharacteristic
218D4—268no—
219C2×C4—22no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—134no—
228C2×C4—132no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—524no—
241C2×C4#612714yes—
242C2×C4C2×C22⋊D1312yes—
243C2×C4C2×C22⋊D1312yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—264no—
250C22—262no—
251C22—522no—
252C22—521no—
253C22—521no—
254C22C2×#612712yes—
255C22#41×D1311yescharacteristic
256C22#41×D1311yescharacteristic
257C22#41×D1312yes—
258C22C22×C22⋊D1311yescharacteristic
259C4—22no—
260C4—42no—
261C4—42no—
262C4—264no—
263C4—262no—
264C4—522no—
265C4—521no—
266C4—521no—
267C4#8818314yes—
268C2—42no—
269C2—522no—
270C2#1171923312yes—
271C2#1171923312yes—
272C2C2×#8818311yescharacteristic
273C2#1171953311yescharacteristic
274C2#1171953711yescharacteristic
subgroupG/H
centerC22×C4C22×D13
commutator, socle, cosocleC23×C13C24
FrattiniC23C23×D13
FittingC2×C13×#117C2
prime radicalC22×C22⋊D13C22
hypercenterC2×#117D13
hypocenterC13#2395
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C13×#117C2semidirect
3. C4×C22⋊Dic13C2semidirect
4. #11718654C2semidirect
5. #11718653C2semidirect
6. #11718643C2semidirect
7. #11718641C2semidirect
9. #11718613C2semidirect
10. C4×#6103C2semidirect
11. C4×#6101C2semidirect
108. C2×#117D13semidirect
206. C13#2395semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1172
C2×C4×C22⋊D132
C4×C22⋊Dic132
#117186542
#117186532
#117186432
#117186412
#117186202
#117186132
C4×#61032
C4×#61012
#239513