Finite Group Databasebeta

← #13125306

Subgroups — #13125306

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
1C22×C13×SD16C211yesmaximal, characteristic, complemented
2#11719521C211yesmaximal, characteristic, complemented
3C2×#88196C211yesmaximal, characteristic, complemented
4#11719510C211yesmaximal, characteristic, complemented
5C2×#88186C211yesmaximal, characteristic, complemented
6C2×#88158C211yesmaximal, characteristic, complemented
7#11718837C212yesmaximal, complemented
8#11718836C212yesmaximal, complemented
9#11718829C212yesmaximal, complemented
10#11718828C212yesmaximal, complemented
11#11718762C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×D4×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C2×#6127C2211yescharacteristic
16C2×C13×SD16—24no—
17C2×C13×SD16C2212yes—
18C2×C13×SD16C2212yes—
19C22×C8×C13C2211yescharacteristic
20#88207—22no—
21#88201C2212yescomplemented
22#88200—22no—
23#88198C2212yescomplemented
24C2×#6107C2212yescomplemented
25#88196—24no—
26C2×#6106C2212yescomplemented
27#88194C2212yes—
28#88192—22no—
29#88190C2212yes—
30C2×#6105C2212yes—
31#88186—24no—
32C2×#6104C2212yes—
33#88183—22no—
34#88180C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C2×Dic52C2211yescharacteristic, complemented
37#88158—24no—
38C2×D104C2211yescharacteristic, complemented
39C2×#6095C2211yescharacteristic, complemented
40C2×#6095C2211yescharacteristic, complemented
41#88055C2212yescomplemented
42C8×Dic13C2212yescomplemented
43C24×C13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13—22no—
46C2×Q8×C13—22no—
47C2×Q8×C13C2312yes—
48C2×D4×C13—22no—
49C2×D4×C13—22no—
50C2×D4×C13—21no—
51C2×D4×C13C2312yes—
52C22×C4×C13—21no—
53C22×C4×C13C2311yescharacteristic
54C2×C22⋊D13—21no—
55C2×C22⋊D13—21no—
56C2×C22⋊D13—24no—
57#6127—22no—
58#6127—22no—
59#6127—22no—
60#6127—22no—
61C2×D52C2311yescharacteristic
62C2×D52C2311yescharacteristic
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×Dic26C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C13×SD16—24no—
68C13×SD16—24no—
69C2×C8×C13D414yescomplemented
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C22⋊Dic13—24no—
73C22⋊Dic13D412yes—
74#6107—24no—
75#6106—24no—
76#6105—24no—
77#6104—24no—
78#6103—24no—
79C4⋊Dic13D412yes—
80#6101—24no—
81C4×Dic13C2312yes—
82#6099D414yescomplemented
83C2×#1055C2312yes—
84Dic52—22no—
85D104—22no—
86#6095—22no—
87#6095—22no—
88#3154—131nomaximal, Sylow
89C23×C13—22no—
90C23×C13—42no—
91C23×C13—82no—
92C23×C13C2×D411yescharacteristic
93C22×D13—21no—
94C22×D13—21no—
95Q8×C13—22no—
96Q8×C13—22no—
97Q8×C13—42no—
98D4×C13—22no—
99D4×C13—22no—
100D4×C13—42no—
101C2×C4×C13—22no—
102C2×C4×C13—42no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2411yescharacteristic
107C22⋊D13—42no—
108C22⋊D13—42no—
109C22⋊D13—84no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13C2×D414yes—
113D52—21no—
114D52—21no—
115D52—21no—
116D52—21no—
117C4×D13—42no—
118C4×D13—42no—
119Dic26—21no—
120Dic26—21no—
121Dic26—21no—
122Dic26—21no—
123C8×C13C2×D412yes—
124C8×C13C2×D412yes—
125#1055C2×D414yes—
126C2×#137—131no—
127C2×AGL(1,ℤ/8)—131no—
128C2×#135—131no—
129C22×SD16D1311yescharacteristic, complemented
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—42no—
139C22×C13—44no—
140C22×C13—84no—
141C22×C13#12712yes—
142C22×C13C22×D411yescharacteristic
143C2×D13—41no—
144C2×D13—41no—
145C2×D13—42no—
146C2×D13—42no—
147C4×C13—42no—
148C4×C13#12712yes—
149C4×C13C22×D411yescharacteristic
150C4×C13C22×D411yescharacteristic
151Dic13—24no—
152Dic13—41no—
153Dic13—41no—
154C2×#41—131no—
155C2×#41—131no—
156C22×Q8C2×D1311yescharacteristic
157C22×D4C2×D1311yescharacteristic
158#137—264no—
159AGL(1,ℤ/8)—264no—
160#135—264no—
161C2×Q16—132no—
162C2×Q16—131no—
163C2×SD16—24no—
164C2×SD16—132no—
165C2×SD16—132no—
166C2×SD16—131no—
167C2×SD16—131no—
168C2×SD16C2×D1312yes—
169C2×SD16C2×D1312yes—
170C2×D8—132no—
171C2×D8—131no—
172C2×M16—131no—
173C22×C8C2×D1311yescharacteristic
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—82no—
187C2×C13C2×#12711yescharacteristic
188C2×C13#57712yes—
189D13—81no—
190D13—81no—
191C24—21no—
192#41—262no—
193#41—262no—
194#41—262no—
195#41—262no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—131no—
200C2×Q8—131no—
201C2×Q8C22×D1312yes—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—131no—
206C2×D4—131no—
207C2×D4—264no—
208C2×D4—261no—
209C2×D4—261no—
210C2×D4C22×D1312yes—
211C22×C4—21no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4C22×D1311yescharacteristic
215Q16—264no—
216Q16—262no—
217SD16—24no—
218SD16—24no—
219SD16—264no—
220SD16—264no—
221SD16—262no—
222SD16—262no—
223D8—264no—
224D8—262no—
225M16—134no—
226C2×C8—132no—
227C2×C8C22⋊D1314yescomplemented
228C2×C8C22×D1311yescharacteristic
229C2×C8C22×D1311yescharacteristic
230C4⋊C4—132no—
231C4⋊C4—264no—
232C22⋊C4—132no—
233C22⋊C4—264no—
234C22⋊C4—264no—
235C42—132no—
236C13#315411yescharacteristic, complemented, Sylow
237C23—22no—
238C23—42no—
239C23—82no—
240C23—261no—
241C23—261no—
242C23D4×D1311yescharacteristic
243Q8—22no—
244Q8—22no—
245Q8—42no—
246Q8—261no—
247Q8—261no—
248Q8—261no—
249Q8—261no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—261no—
254D4—261no—
255D4—261no—
256D4—261no—
257D4—522no—
258D4—522no—
259D4—1044no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—134no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4D4×D1311yescharacteristic
268C2×C4D4×D1312yes—
269C2×C4C2×C22⋊D1312yes—
270C2×C4C23×D1311yescharacteristic
271C8—134no—
272C8C2×C22⋊D1312yes—
273C8C2×C22⋊D1312yes—
274C22—22no—
275C22—44no—
276C22—42no—
277C22—84no—
278C22—522no—
279C22—522no—
280C22—521no—
281C22—521no—
282C22#8819412yes—
283C22C2×D4×D1311yescharacteristic
284C4—42no—
285C4—264no—
286C4—521no—
287C4—521no—
288C4#8819412yes—
289C4C2×D4×D1311yescharacteristic
290C4C22×C22⋊D1311yescharacteristic
291C2—22no—
292C2—82no—
293C2—1041no—
294C2—1041no—
295C2#1171946712yes—
296C2C2×#8819411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×SD16C2
socleC22×C13C22×D4
hypercenterC22×SD16D13
hypocenterC13#3154
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C13×SD16C2semidirect
2. #11719521C2semidirect
3. C2×#88196C2semidirect
4. #11719510C2semidirect
5. C2×#88186C2semidirect
6. C2×#88158C2semidirect
7. #11718837C2semidirect
8. #11718836C2semidirect
9. #11718829C2semidirect
10. #11718828C2semidirect
11. #11718762C2semidirect
21. #88201C22semidirect
23. #88198C22semidirect
24. C2×#6107C22semidirect
26. C2×#6106C22semidirect
36. C2×Dic52C22semidirect
38. C2×D104C22semidirect
39. C2×#6095C22semidirect
40. C2×#6095C22semidirect
41. #88055C22semidirect
42. C8×Dic13C22semidirect
69. C2×C8×C13D4semidirect
82. #6099D4semidirect
129. C22×SD16D13semidirect
227. C2×C8C22⋊D13semidirect
236. C13#3154semidirect

Maximal subgroups

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

subgroupindex
C22×C13×SD162
#117195212
C2×#881962
#117195102
C2×#881862
C2×#881582
#117188372
#117188362
#117188292
#117188282
#117187622
#315413