Finite Group Databasebeta

← #13126452

Subgroups — #13126452

Order 1664.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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
1D42×C13C211yesmaximal, characteristic, complemented
2C2×#88186C212yesmaximal, complemented
3#11719258C211yesmaximal, characteristic, complemented
4#11718878C212yesmaximal, complemented
5#11718736C211yesmaximal, characteristic, complemented
6#11718734C211yesmaximal, characteristic, complemented
7#11718700C212yesmaximal, complemented
8#11718698C212yesmaximal, complemented
9C4×#6105C211yesmaximal, characteristic, complemented
10#11718676C211yesmaximal, characteristic, complemented
11#11718673C211yesmaximal, characteristic, complemented
12C22×D4×C13—21no—
13C22×D4×C13C2212yes—
14C2×#6127C2212yescomplemented
15C13×#127C2211yescharacteristic
16C13×#121—21no—
17C13×#121C2212yes—
18C13×#120—22no—
19C4×D4×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88194—21no—
22C2×#6105C2211yescharacteristic
23C2×#6105C2212yescomplemented
24#88186—28no—
25C2×#6104C2212yes—
26C2×#6104C2212yescomplemented
27C2×#6104C2212yescomplemented
28#88184C2212yescomplemented
29C2×#6099C2212yescomplemented
30#88147—21no—
31#88138—22no—
32#88128C2211yescharacteristic, complemented
33C4×Dic26C2211yescharacteristic, complemented
34#88072C2211yescharacteristic
35#88072C2212yescomplemented
36C22⋊#1055C2212yescomplemented
37#88050C2211yescharacteristic, complemented
38#88049C2212yescomplemented
39#88048C2211yescharacteristic, complemented
40C4⋊#1055C2211yescharacteristic, complemented
41C4×#1055C2211yescharacteristic, complemented
42C24×C13—22no—
43C2×D4×C13—24no—
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—42no—
49C2×D4×C13—44no—
50C2×D4×C13D411yescharacteristic
51C2×D4×C13C2312yes—
52C2×D4×C13C2311yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13C2312yes—
55C2×C22⋊D13—22no—
56C2×C22⋊D13—22no—
57#6127—24no—
58#6127—42no—
59C2×D52—21no—
60C2×D52—21no—
61C2×D52C2312yes—
62C2×C4×D13—22no—
63C2×Dic26C2311yescharacteristic
64C13×C4⋊C4D411yescharacteristic
65C13×C4⋊C4C2311yescharacteristic
66C13×C22⋊C4—21no—
67C13×C22⋊C4—22no—
68C13×C22⋊C4D412yes—
69C42×C13C2311yescharacteristic
70#6105—24no—
71#6105D414yescomplemented
72#6104—24no—
73#6104—24no—
74#6104—42no—
75#6103—22no—
76C4⋊Dic13C2311yescharacteristic
77#6101—21no—
78C4×Dic13—21no—
79#6099—24no—
80C2×#1055C2311yescharacteristic
81C2×#1055C2312yes—
82C2×#1055C2311yescharacteristic
83#3274—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13—22no—
86C23×C13—44no—
87C23×C13—44no—
88C23×C13—82no—
89C23×C13C2×D412yes—
90C22×D13—22no—
91D4×C13—22no—
92D4×C13—22no—
93D4×C13—21no—
94D4×C13—22no—
95D4×C13—44no—
96D4×C13—44no—
97D4×C13—42no—
98D4×C13—81no—
99D4×C13C2×D412yes—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2411yescharacteristic
108C22⋊D13—44no—
109C22⋊D13—82no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112D52—22no—
113D52—22no—
114D52—42no—
115D52—81no—
116C4×D13—44no—
117Dic26—21no—
118Dic26C2×D412yescomplemented
119#1055—22no—
120#1055—21no—
121#1055C2×D412yescomplemented
122C2×AGL(1,ℤ/8)—132no—
123#550—131no—
124D42D1311yescharacteristic, complemented
125#493—131no—
126#469—132no—
127#460—131no—
128#459—131no—
129#449—132no—
130#447—132no—
131C4×SD16—131no—
132#436—131no—
133C22×C13—22no—
134C22×C13—22no—
135C22×C13—22no—
136C22×C13—22no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—42no—
142C22×C13—88no—
143C22×C13C22×D411yescharacteristic
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—42no—
147C4×C13—22no—
148C4×C13—21no—
149C4×C13—41no—
150C4×C13AGL(1,ℤ/8)12yescomplemented
151C4×C13C22×D411yescharacteristic
152C4×C13H(5,𝔽2)11yescharacteristic
153Dic13—22no—
154Dic13—41no—
155C2×#41—132no—
156C22×D4—21no—
157C22×D4C2×D1312yes—
158AGL(1,ℤ/8)—268no—
159C2×SD16—131no—
160C2×SD16—132no—
161C2×D8—132no—
162C2×D8—132no—
163C2×D8—132no—
164C2×M16—132no—
165#127—131no—
166#127—261no—
167#127C2×D1311yescharacteristic
168#121—21no—
169#121—132no—
170#121—262no—
171#121C2×D1312yes—
172#120—22no—
173C4×Q8—131no—
174C4×D4—261no—
175C4×D4C2×D1311yescharacteristic
176C4×D4C2×D1311yescharacteristic
177#106—131no—
178C4⋊C8—131no—
179#103—131no—
180#102—131no—
181#102—132no—
182#102—132no—
183C22⋊C8—132no—
184C4×C8—131no—
185C2×C13—42no—
186C2×C13—42no—
187C2×C13—82no—
188C2×C13D4211yescharacteristic
189C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C13#57611yescharacteristic
191D13—82no—
192C24—22no—
193#41—264no—
194#41—522no—
195C2×Q8—131no—
196C2×D4—24no—
197C2×D4—22no—
198C2×D4—22no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—42no—
202C2×D4—44no—
203C2×D4—132no—
204C2×D4—262no—
205C2×D4—262no—
206C2×D4—261no—
207C2×D4—261no—
208C2×D4C22⋊D1311yescharacteristic
209C2×D4C22×D1312yes—
210C2×D4C22×D1311yescharacteristic
211C22×C4—21no—
212C22×C4—262no—
213C22×C4C22×D1312yes—
214SD16—134no—
215SD16—264no—
216D8—264no—
217D8—264no—
218D8—522no—
219M16—264no—
220C2×C8—131no—
221C2×C8—131no—
222C2×C8—132no—
223C4⋊C4—131no—
224C4⋊C4—261no—
225C4⋊C4C22⋊D1311yescharacteristic
226C4⋊C4C22×D1311yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—22no—
229C22⋊C4—262no—
230C22⋊C4C22⋊D1312yes—
231C42—261no—
232C42C22×D1311yescharacteristic
233C13#327411yescharacteristic, complemented, Sylow
234C23—21no—
235C23—22no—
236C23—44no—
237C23—44no—
238C23—82no—
239C23—262no—
240C23C2×C22⋊D1312yes—
241Q8—132no—
242Q8—261no—
243D4—22no—
244D4—22no—
245D4—21no—
246D4—22no—
247D4—44no—
248D4—44no—
249D4—42no—
250D4—81no—
251D4—262no—
252D4—262no—
253D4—524no—
254D4—522no—
255D4—1041no—
256D4—1042no—
257D4D4×D1312yes—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—524no—
265C2×C4C2×C22⋊D1311yescharacteristic
266C2×C4C2×C22⋊D1312yes—
267C2×C4C2×C22⋊D1311yescharacteristic
268C2×C4C23×D1311yescharacteristic
269C8—132no—
270C8—262no—
271C8—261no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—88no—
282C22—522no—
283C22—522no—
284C22—522no—
285C22C22×C22⋊D1311yescharacteristic
286C4—22no—
287C4—21no—
288C4—41no—
289C4—262no—
290C4—521no—
291C4#8818612yescomplemented
292C4C2×D4×D1311yescharacteristic
293C4#8825111yescharacteristic
294C2—42no—
295C2—42no—
296C2—82no—
297C2—1042no—
298C2C2×#8818611yescharacteristic
299C2D4×C22⋊D1311yescharacteristic
300C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3274
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. D42×C13C2semidirect
2. C2×#88186C2semidirect
3. #11719258C2semidirect
4. #11718878C2semidirect
5. #11718736C2semidirect
6. #11718734C2semidirect
7. #11718700C2semidirect
8. #11718698C2semidirect
9. C4×#6105C2semidirect
10. #11718676C2semidirect
11. #11718673C2semidirect
14. C2×#6127C22semidirect
23. C2×#6105C22semidirect
26. C2×#6104C22semidirect
27. C2×#6104C22semidirect
28. #88184C22semidirect
29. C2×#6099C22semidirect
32. #88128C22semidirect
33. C4×Dic26C22semidirect
35. #88072C22semidirect
36. C22⋊#1055C22semidirect
37. #88050C22semidirect
38. #88049C22semidirect
39. #88048C22semidirect
40. C4⋊#1055C22semidirect
41. C4×#1055C22semidirect
71. #6105D4semidirect
118. Dic26C2×D4semidirect
121. #1055C2×D4semidirect
124. D42D13semidirect
150. C4×C13AGL(1,ℤ/8)semidirect
233. C13#3274semidirect
291. C4#88186semidirect

Maximal subgroups

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

subgroupindex
D42×C132
C2×#881862
#117192582
#117188782
#117187362
#117187342
#117187002
#117186982
C4×#61052
#117186762
#117186732
#327413