Finite Group Databasebeta

← #13125315

Subgroups — #13125315

Order 1664.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#137C211yesmaximal, characteristic, complemented
2#11719535C211yesmaximal, characteristic, complemented
3C2×#88204C211yesmaximal, characteristic, complemented
4#11719521C211yesmaximal, characteristic, complemented
5C22×#6106C211yesmaximal, characteristic, complemented
6C2×#88162C211yesmaximal, characteristic, complemented
7#11718852C212yesmaximal, complemented
8#11718851C212yesmaximal, complemented
9#11718837C212yesmaximal, complemented
10#11718836C212yesmaximal, complemented
11#11718783C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×Q8×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C22×D52C2211yescharacteristic
16C13×#137—24no—
17C2×C13×Q16C2212yescomplemented
18C2×C13×SD16C2212yescomplemented
19C2×C13×M16C2211yescharacteristic
20#88204—24no—
21#88201C2212yes—
22#88201C2212yescomplemented
23#88200—22no—
24#88198C2212yescomplemented
25C2×#6107C2211yescharacteristic, complemented
26C2×#6106—24no—
27C2×#6106C2212yes—
28C2×#6106C2212yes—
29C2×#6106C2211yescharacteristic, complemented
30#88194C2212yes—
31#88191—22no—
32C2×#6105C2211yescharacteristic, complemented
33C2×#6104C2211yescharacteristic, complemented
34#88184—22no—
35#88183—22no—
36#88180C2211yescharacteristic
37C22×#1055C2211yescharacteristic
38#88162—24no—
39C2×D104C2212yes—
40C2×#6095C2212yes—
41#88055C2212yescomplemented
42C8×Dic13C2212yescomplemented
43C23×D13—21no—
44C13×#41—22no—
45C13×#41—22no—
46C2×Q8×C13—21no—
47C2×Q8×C13—22no—
48C2×Q8×C13—22no—
49C2×Q8×C13C2312yes—
50C2×Q8×C13C2311yescharacteristic
51C2×D4×C13—21no—
52C2×D4×C13C2311yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13C2311yescharacteristic
56C2×C22⋊D13—21no—
57C2×C22⋊D13—24no—
58#6127—22no—
59#6127—22no—
60C2×D52—22no—
61C2×D52—22no—
62C2×D52—21no—
63C2×D52C2312yes—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×Dic26C2311yescharacteristic
67C13×Q16—24no—
68C13×SD16—24no—
69C13×M16D414yescomplemented
70C2×C8×C13C2312yes—
71C22⋊Dic13D412yes—
72#6107—22no—
73#6106—24no—
74#6106—24no—
75#6106—22no—
76#6105—22no—
77#6104—22no—
78#6103—24no—
79#6103—24no—
80C4⋊Dic13D412yes—
81#6101—24no—
82C4×Dic13C2312yes—
83C2×#1055D414yescomplemented
84C2×#1055C2311yescharacteristic
85C2×#1055C2311yescharacteristic
86D104—24no—
87#6095—24no—
88#3154—131nomaximal, Sylow
89C23×C13—21no—
90C23×C13C2×D411yescharacteristic
91C22×D13—21no—
92C22×D13—22no—
93C22×D13—42no—
94C22×D13—82no—
95Q8×C13—22no—
96Q8×C13—21no—
97Q8×C13—22no—
98Q8×C13—21no—
99Q8×C13—42no—
100D4×C13—21no—
101D4×C13—21no—
102D4×C13—42no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13C2×D411yescharacteristic
108C2×C4×C13C2×D412yes—
109C2×C4×C13C2×D412yes—
110C2×C4×C13C2411yescharacteristic
111C22⋊D13—42no—
112C22⋊D13—84no—
113C2×Dic13—21no—
114C2×Dic13C2×D414yes—
115D52—22no—
116D52—21no—
117D52—21no—
118D52—22no—
119D52—42no—
120C4×D13—42no—
121Dic26—21no—
122Dic26—21no—
123C8×C13C2×D414yes—
124#1055C2×D412yes—
125#1055C2×D412yes—
126C2×#137D1311yescharacteristic, complemented
127C2×AGL(1,ℤ/8)—131no—
128C2×#135—131no—
129C22×SD16—131no—
130#536—131no—
131#535—131no—
132#497—132no—
133#496—132no—
134#495—132no—
135#492—132no—
136#405—131no—
137C22×C13—22no—
138C22×C13—41no—
139C22×C13—42no—
140C22×C13#12712yes—
141C22×C13C22×D411yescharacteristic
142C2×D13—41no—
143C2×D13—42no—
144C2×D13—44no—
145C2×D13—42no—
146C2×D13—84no—
147C4×C13—41no—
148C4×C13—42no—
149C4×C13#12712yes—
150C4×C13C22×D411yescharacteristic
151C4×C13C22×D411yescharacteristic
152Dic13—24no—
153Dic13—41no—
154C2×#41—131no—
155C2×#41C2×D1311yescharacteristic
156C22×Q8C2×D1311yescharacteristic
157C22×D4—131no—
158#137—24no—
159AGL(1,ℤ/8)—264no—
160#135—264no—
161C2×Q16—131no—
162C2×Q16C2×D1312yescomplemented
163C2×SD16—132no—
164C2×SD16—132no—
165C2×SD16—131no—
166C2×SD16—131no—
167C2×SD16—132no—
168C2×SD16—264no—
169C2×SD16C2×D1312yescomplemented
170C2×D8—131no—
171C2×D8—132no—
172C2×M16C2×D1311yescharacteristic
173C22×C8—131no—
174C4⋊Q8—132no—
175#127—132no—
176#124—132no—
177#124—132no—
178#123—262no—
179C22⋊Q8—262no—
180#121—262no—
181#120—262no—
182#117—131no—
183#97—132no—
184C4×C8—132no—
185C2×C13—22no—
186C2×C13—81no—
187C2×C13C2×#12711yescharacteristic
188C2×C13#57712yes—
189D13—81no—
190D13—82no—
191C24—261no—
192#41—22no—
193#41—22no—
194#41—262no—
195#41—262no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—131no—
200C2×Q8C22×D1311yescharacteristic
201C2×Q8C22×D1312yes—
202C2×D4—21no—
203C2×D4—131no—
204C2×D4—132no—
205C2×D4—264no—
206C2×D4—261no—
207C2×D4—262no—
208C2×D4—261no—
209C2×D4—262no—
210C2×D4C22×D1311yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—261no—
214C22×C4C22×D1311yescharacteristic
215Q16—24no—
216Q16—262no—
217SD16—24no—
218SD16—262no—
219SD16—264no—
220SD16—264no—
221SD16—262no—
222SD16—264no—
223D8—262no—
224D8—264no—
225M16C22⋊D1314yescomplemented
226C2×C8—134no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1312yes—
230C4⋊C4—132no—
231C4⋊C4—264no—
232C22⋊C4—132no—
233C22⋊C4—264no—
234C22⋊C4—264no—
235C42—132no—
236C13#315411yescharacteristic, complemented, Sylow
237C23—21no—
238C23—261no—
239C23—262no—
240C23—522no—
241C23—1042no—
242C23D4×D1311yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—261no—
249Q8—261no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—261no—
254D4—262no—
255D4—261no—
256D4—262no—
257D4—522no—
258D4—522no—
259D4—1044no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—134no—
265C2×C4—261no—
266C2×C4—522no—
267C2×C4D4×D1311yescharacteristic
268C2×C4D4×D1312yes—
269C2×C4C2×C22⋊D1312yes—
270C2×C4C23×D1311yescharacteristic
271C8—132no—
272C8—132no—
273C8C2×C22⋊D1314yes—
274C22—22no—
275C22—42no—
276C22—41no—
277C22—524no—
278C22—522no—
279C22—521no—
280C22—522no—
281C22—1044no—
282C22#8819412yes—
283C22C2×D4×D1311yescharacteristic
284C4—41no—
285C4—42no—
286C4—264no—
287C4—521no—
288C4#8819412yes—
289C4C2×D4×D1311yescharacteristic
290C4C22×C22⋊D1311yescharacteristic
291C2—22no—
292C2—81no—
293C2—1042no—
294C2—1041no—
295C2#1171948312yes—
296C2C2×#8819411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#137C2
socleC22×C13C22×D4
hypercenterC2×#137D13
hypocenterC13#3154
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C13×#137C2semidirect
2. #11719535C2semidirect
3. C2×#88204C2semidirect
4. #11719521C2semidirect
5. C22×#6106C2semidirect
6. C2×#88162C2semidirect
7. #11718852C2semidirect
8. #11718851C2semidirect
9. #11718837C2semidirect
10. #11718836C2semidirect
11. #11718783C2semidirect
17. C2×C13×Q16C22semidirect
18. C2×C13×SD16C22semidirect
22. #88201C22semidirect
24. #88198C22semidirect
25. C2×#6107C22semidirect
29. C2×#6106C22semidirect
32. C2×#6105C22semidirect
33. C2×#6104C22semidirect
41. #88055C22semidirect
42. C8×Dic13C22semidirect
69. C13×M16D4semidirect
83. C2×#1055D4semidirect
126. C2×#137D13semidirect
162. C2×Q16C2×D13semidirect
169. C2×SD16C2×D13semidirect
225. M16C22⋊D13semidirect
236. C13#3154semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1372
#117195352
C2×#882042
#117195212
C22×#61062
C2×#881622
#117188522
#117188512
#117188372
#117188362
#117187832
#315413