Finite Group Databasebeta

← #13124449

Subgroups — #13124449

Order 1664.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#11719533C211yesmaximal, characteristic, complemented
3C2×#88192C211yesmaximal, characteristic, complemented
4C2×M16×D13C211yesmaximal, characteristic, complemented
5#11718893C211yesmaximal, characteristic, complemented
6#11718876C211yesmaximal, characteristic, complemented
7#11718835C212yesmaximal, complemented
8#11718832C212yesmaximal, complemented
9#11718820C212yesmaximal, complemented
10#11718818C212yesmaximal, complemented
11#11718782C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×D4×C13C2211yescharacteristic
14C22×C22⋊D13—21no—
15C22×C4×D13C2211yescharacteristic
16C13×AGL(1,ℤ/8)—24no—
17C2×C13×SD16C2212yescomplemented
18C2×C13×D8C2212yescomplemented
19C2×C13×M16C2211yescharacteristic
20C2×C22⋊Dic13—21no—
21#88200C2211yescharacteristic, complemented
22#88200C2211yescharacteristic, complemented
23#88192—21no—
24#88192—21no—
25#88192C2212yes—
26#88192C2212yes—
27#88192C2211yescharacteristic, complemented
28#88192C2211yescharacteristic, complemented
29#88191—21no—
30#88189—21no—
31C4×C22⋊D13—21no—
32C4×C22⋊D13—21no—
33#88180C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36M16×D13—24no—
37C2×#6094C2212yescomplemented
38C2×C8×D13C2212yescomplemented
39#88075C2212yescomplemented
40#88072C2212yescomplemented
41#88072C2212yescomplemented
42#88072C2212yescomplemented
43#88058C2212yescomplemented
44#88057C2212yescomplemented
45C24×C13—21no—
46C23×D13D411yescharacteristic
47C13×#41—22no—
48C13×#41—22no—
49C2×Q8×C13C2311yescharacteristic
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13C2312yes—
55C2×D4×C13C2311yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13C2311yescharacteristic
58C2×C22⋊D13—21no—
59C2×C22⋊D13—21no—
60C2×C22⋊D13—22no—
61C2×C22⋊D13—22no—
62C2×C22⋊D13—44no—
63C22×Dic13—21no—
64C22×Dic13D411yescharacteristic
65C2×C4×D13—22no—
66C2×C4×D13—22no—
67C2×C4×D13D411yescharacteristic
68C2×C4×D13D411yescharacteristic
69C2×C4×D13C2311yescharacteristic
70C2×C4×D13C2311yescharacteristic
71C13×SD16—24no—
72C13×D8—24no—
73C13×M16D414yescomplemented
74C2×C8×C13C2312yes—
75C22⋊Dic13—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13—22no—
79C22⋊Dic13—22no—
80#6103—21no—
81#6103—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85C4⋊Dic13C2312yes—
86#6101—21no—
87#6101—21no—
88C4×Dic13—21no—
89#6099—22no—
90C2×#1055C2312yes—
91#6094—24no—
92C8×D13—24no—
93#3055—131nomaximal, Sylow
94C23×C13—21no—
95C23×C13—22no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13C2×D411yescharacteristic
100C22×D13—22no—
101C22×D13—22no—
102C22×D13—41no—
103C22×D13C2×D411yescharacteristic
104C22×D13C2×D411yescharacteristic
105Q8×C13—21no—
106Q8×C13—21no—
107D4×C13—21no—
108D4×C13—22no—
109D4×C13—22no—
110D4×C13—21no—
111D4×C13—42no—
112D4×C13—42no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D412yes—
117C2×C4×C13#4112yes—
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—42no—
120C22⋊D13—44no—
121C22⋊D13—42no—
122C22⋊D13—44no—
123C2×Dic13—22no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—22no—
127C2×Dic13—42no—
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C4×D13—22no—
131C4×D13—22no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—21no—
136C8×C13C2×D414yescomplemented
137#1055—22no—
138C2×AGL(1,ℤ/8)D1311yescharacteristic, complemented
139C22×M16—131no—
140#525—131no—
141C2×#121—131no—
142#469—132no—
143#468—132no—
144#466—132no—
145#465—132no—
146#428—131no—
147#418—131no—
148#417—131no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—41no—
152C22×C13—42no—
153C22×C13—42no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—42no—
157C22×C13—84no—
158C22×C13#12112yes—
159C22×C13C22×D411yescharacteristic
160C2×D13—21no—
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—21no—
165C2×D13—44no—
166C2×D13AGL(1,ℤ/8)12yescomplemented
167C4×C13—41no—
168C4×C13#12112yes—
169C4×C13C22×D411yescharacteristic
170C4×C13C2×#4111yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—42no—
174Dic13—41no—
175Dic13—41no—
176C2×#41C2×D1311yescharacteristic
177C22×D4—261no—
178C22×D4C2×D1311yescharacteristic
179C23×C4—131no—
180AGL(1,ℤ/8)—24no—
181C2×SD16C2×D1312yescomplemented
182C2×D8C2×D1312yescomplemented
183C2×M16—131no—
184C2×M16—132no—
185C2×M16—264no—
186C2×M16C2×D1311yescharacteristic
187C22×C8—132no—
188#123—261no—
189C22⋊Q8—131no—
190C22⋊Q8—131no—
191#121—132no—
192#121—132no—
193#121—131no—
194#121—131no—
195#121—261no—
196#121—261no—
197#120—261no—
198C4×D4—261no—
199C4×D4—261no—
200#117—131no—
201C2×C4⋊C4—131no—
202C2×C22⋊C4—261no—
203#107—132no—
204#106—132no—
205#103—132no—
206#102—132no—
207#102—132no—
208#102—132no—
209C2×C13—22no—
210C2×C13—81no—
211C2×C13—82no—
212C2×C13C2×#12111yescharacteristic
213C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C13#57511yescharacteristic
215D13—22no—
216D13—41no—
217C24—21no—
218C24—131no—
219#41—22no—
220#41—22no—
221C2×Q8C22×D1311yescharacteristic
222C2×D4—21no—
223C2×D4—21no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—261no—
227C2×D4—261no—
228C2×D4—262no—
229C2×D4—262no—
230C2×D4—524no—
231C2×D4C22×D1311yescharacteristic
232C2×D4C22×D1312yes—
233C22×C4—21no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—262no—
240C22×C4—262no—
241C22×C4—261no—
242C22×C4C22×D1311yescharacteristic
243SD16—24no—
244D8—24no—
245M16—262no—
246M16—264no—
247M16C22⋊D1314yescomplemented
248C2×C8—132no—
249C2×C8—264no—
250C2×C8C22×D1312yes—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—132no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—262no—
260C22⋊C4—262no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—261no—
265C13#305511yescharacteristic, complemented, Sylow
266C23—21no—
267C23—22no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—131no—
272C23—131no—
273C23—262no—
274C23—262no—
275C23—521no—
276C23D4×D1311yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—22no—
280D4—21no—
281D4—21no—
282D4—22no—
283D4—42no—
284D4—42no—
285D4—522no—
286D4—524no—
287D4—522no—
288D4—524no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—262no—
294C2×C4—262no—
295C2×C4—262no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—262no—
303C2×C4—522no—
304C2×C4D4×D1311yescharacteristic
305C2×C4#612912yes—
306C2×C4C2×C22⋊D1312yes—
307C2×C4C23×D1311yescharacteristic
308C8—262no—
309C8C2×C22⋊D1314yescomplemented
310C22—21no—
311C22—21no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—42no—
318C22—84no—
319C22—132no—
320C22—261no—
321C22—261no—
322C22—261no—
323C22—261no—
324C22—261no—
325C22—524no—
326C22#8819212yes—
327C22C2×D4×D1311yescharacteristic
328C4—41no—
329C4—261no—
330C4—261no—
331C4—522no—
332C4—521no—
333C4—521no—
334C4#8819212yes—
335C4C2×#612911yescharacteristic
336C4C22×C22⋊D1311yescharacteristic
337C2—22no—
338C2—82no—
339C2—81no—
340C2—262no—
341C2—521no—
342C2D13×AGL(1,ℤ/8)11yescharacteristic
343C2#1171947811yescharacteristic
344C2C2×#8819211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×AGL(1,ℤ/8)C2
socleC22×C13C22×D4
hypercenterC2×AGL(1,ℤ/8)D13
hypocenterC13#3055
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C13×AGL(1,ℤ/8)C2semidirect
2. #11719533C2semidirect
3. C2×#88192C2semidirect
4. C2×M16×D13C2semidirect
5. #11718893C2semidirect
6. #11718876C2semidirect
7. #11718835C2semidirect
8. #11718832C2semidirect
9. #11718820C2semidirect
10. #11718818C2semidirect
11. #11718782C2semidirect
17. C2×C13×SD16C22semidirect
18. C2×C13×D8C22semidirect
21. #88200C22semidirect
22. #88200C22semidirect
27. #88192C22semidirect
28. #88192C22semidirect
37. C2×#6094C22semidirect
38. C2×C8×D13C22semidirect
39. #88075C22semidirect
40. #88072C22semidirect
41. #88072C22semidirect
42. #88072C22semidirect
43. #88058C22semidirect
44. #88057C22semidirect
73. C13×M16D4semidirect
136. C8×C13C2×D4semidirect
138. C2×AGL(1,ℤ/8)D13semidirect
166. C2×D13AGL(1,ℤ/8)semidirect
181. C2×SD16C2×D13semidirect
182. C2×D8C2×D13semidirect
247. M16C22⋊D13semidirect
265. C13#3055semidirect
309. C8C2×C22⋊D13semidirect

Maximal subgroups

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

subgroupindex
C2×C13×AGL(1,ℤ/8)2
#117195332
C2×#881922
C2×M16×D132
#117188932
#117188762
#117188352
#117188322
#117188202
#117188182
#117187822
#305513