Finite Group Databasebeta

← #13126648

Subgroups — #13126648

Order 1664.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#11719431C211yesmaximal, characteristic, complemented
2#11719422C211yesmaximal, characteristic, complemented
3C13×#486C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718733C211yesmaximal, characteristic, complemented
6#11718436C212yesmaximal, complemented
7#11718435C212yesmaximal, complemented
8#11718434C212yesmaximal, complemented
9D13×#102C212yesmaximal, complemented
10C4×D104C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C2×#6131—21no—
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C13×C4⋊Q8C2211yescharacteristic, complemented
16C13×#127C2211yescharacteristic
17#88200—21no—
18#88192—21no—
19#88192C2212yes—
20#88191—22no—
21C2×#6104C2212yescomplemented
22C2×D104C2211yescharacteristic
23C2×C8×D13C2212yescomplemented
24#88149C2212yescomplemented
25#88148—22no—
26C4⋊C4×D13C2212yescomplemented
27C4×D52C2211yescharacteristic
28C4×D52C2211yescharacteristic
29C4×D52C2211yescharacteristic, complemented
30C13×#102C2212yescomplemented
31C13×#102C2212yescomplemented
32C4×C8×C13C2211yescharacteristic, complemented
33#88072C2212yescomplemented
34#88061C2211yescharacteristic
35#88061C2211yescharacteristic, complemented
36#88060C2212yescomplemented
37#88058C2211yescharacteristic, complemented
38#88049C2212yes—
39#88047C2212yescomplemented
40C4⋊#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×Q8×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13C2312yes—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48#6131—44no—
49D4×D13—24no—
50D4×D13—42no—
51D4×D13—44no—
52C2×D52—22no—
53C2×D52D411yescharacteristic
54C2×D52C2311yescharacteristic
55C2×D52C2311yescharacteristic
56C2×C4×D13—22no—
57C2×C4×D13—21no—
58C2×C4×D13—21no—
59C2×C4×D13C2312yes—
60C2×C8×C13C2311yescharacteristic
61C2×C8×C13C2311yescharacteristic
62C13×C4⋊C4—21no—
63C13×C4⋊C4C2312yes—
64C42×C13C2311yescharacteristic
65C22⋊Dic13—22no—
66#6104—42no—
67#6103—21no—
68#6103—21no—
69#6103—22no—
70#6103D412yes—
71C4⋊Dic13D411yescharacteristic
72C4⋊Dic13C2311yescharacteristic
73C4⋊Dic13C2311yescharacteristic
74#6101—22no—
75C2×#1055C2312yes—
76D104—22no—
77C8×D13—42no—
78#3294—131nomaximal, Sylow
79C23×C13—22no—
80C22×D13—21no—
81C22×D13—21no—
82C22×D13—44no—
83C22×D13—44no—
84C22×D13—82no—
85C22×D13C2×D412yes—
86Q8×C13—42no—
87D4×C13—22no—
88D4×C13—22no—
89D4×C13—42no—
90D4×C13—81no—
91C2×C4×C13—22no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—44no—
96C22⋊D13—44no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13C2×D412yes—
100D52—21no—
101D52—21no—
102D52—21no—
103D52—44no—
104D52D814yescomplemented
105D52#4112yescomplemented
106C4×D13—22no—
107C4×D13—22no—
108C4×D13—44no—
109C4×D13—42no—
110C4×D13—42no—
111C8×C13—21no—
112C8×C13—21no—
113#1055—22no—
114#547—131no—
115D42—131no—
116#486D1311yescharacteristic, complemented
117#480—132no—
118#474—131no—
119#466—132no—
120#459—131no—
121#447—132no—
122C4×D8—131no—
123C8×D4—131no—
124C2×#102—132no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13C22×D411yescharacteristic
129C2×D13—22no—
130C2×D13—22no—
131C2×D13—22no—
132C2×D13—41no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—41no—
136C2×D13—41no—
137C2×D13—88no—
138C2×D13C2×D814yes—
139C4×C13—21no—
140C4×C13—42no—
141C4×C13C2×D812yes—
142C4×C13C2×#4111yescharacteristic
143C4×C13H(5,𝔽2)11yescharacteristic
144Dic13—22no—
145Dic13—41no—
146Dic13—41no—
147C2×#41—261no—
148C22×D4—132no—
149C22×D4—261no—
150C2×D8—132no—
151C2×D8—131no—
152C22×C8—132no—
153C4⋊Q8C2×D1311yescharacteristic, complemented
154#127C2×D1311yescharacteristic
155#123—262no—
156C22⋊Q8—261no—
157#121—132no—
158#121—132no—
159#121—261no—
160#120—262no—
161C4×D4—131no—
162C4×D4—131no—
163C4×D4—131no—
164C2×C4⋊C4—132no—
165#107—131no—
166#107—132no—
167C4⋊C8—131no—
168#102—132no—
169#102—131no—
170#102—131no—
171#102—132no—
172#102C2×D1312yescomplemented
173#102C2×D1312yescomplemented
174C22⋊C8—132no—
175C4×C8C2×D1311yescharacteristic, complemented
176C2×C13—82no—
177C2×C13#54611yescharacteristic
178C2×C13C22×D811yescharacteristic
179C2×C13#57711yescharacteristic
180D13—24no—
181D13—42no—
182D13—81no—
183C24—262no—
184#41—524no—
185C2×Q8—21no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—131no—
189C2×D4—131no—
190C2×D4—131no—
191C2×D4—262no—
192C2×D4—262no—
193C2×D4—264no—
194C2×D4—262no—
195C2×D4—522no—
196C2×D4—524no—
197C2×D4C22×D1312yes—
198C22×C4—132no—
199C22×C4—262no—
200C22×C4—261no—
201C22×C4—261no—
202D8—262no—
203D8—522no—
204C2×C8—132no—
205C2×C8—522no—
206C2×C8C22×D1311yescharacteristic
207C2×C8C22×D1311yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—131no—
210C4⋊C4—131no—
211C4⋊C4—131no—
212C4⋊C4—262no—
213C4⋊C4C22×D1312yes—
214C22⋊C4—132no—
215C22⋊C4—262no—
216C22⋊C4—262no—
217C22⋊C4—261no—
218C22⋊C4—261no—
219C42C22×D1311yescharacteristic
220C13#329411yescharacteristic, complemented, Sylow
221C23—22no—
222C23—132no—
223C23—261no—
224C23—261no—
225C23—524no—
226C23—524no—
227C23—1042no—
228Q8—42no—
229D4—22no—
230D4—22no—
231D4—42no—
232D4—81no—
233D4—134no—
234D4—132no—
235D4—261no—
236D4—261no—
237D4—261no—
238D4—524no—
239D4—524no—
240D4—524no—
241C2×C4—22no—
242C2×C4—132no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—524no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4D4×D1311yescharacteristic
251C2×C4D4×D1311yescharacteristic
252C2×C4C23×D1311yescharacteristic
253C8—21no—
254C8—21no—
255C8—262no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—134no—
260C22—262no—
261C22—262no—
262C22—262no—
263C22—521no—
264C22—521no—
265C22—521no—
266C22—521no—
267C22—521no—
268C22—1048no—
269C22C2×D4×D1311yescharacteristic
270C4—21no—
271C4—42no—
272C4—262no—
273C4—521no—
274C4—521no—
275C4D8×D1312yes—
276C4#41×D1311yescharacteristic
277C4#8825611yescharacteristic
278C2—82no—
279C2—264no—
280C2—522no—
281C2—1041no—
282C2#1171938111yescharacteristic
283C2C2×D8×D1311yescharacteristic
284C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
hypercenter#486D13
hypocenterC13#3294
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719431C2semidirect
2. #11719422C2semidirect
3. C13×#486C2semidirect
4. #11718748C2semidirect
5. #11718733C2semidirect
6. #11718436C2semidirect
7. #11718435C2semidirect
8. #11718434C2semidirect
9. D13×#102C2semidirect
10. C4×D104C2semidirect
11. C8×D52C2semidirect
15. C13×C4⋊Q8C22semidirect
21. C2×#6104C22semidirect
23. C2×C8×D13C22semidirect
24. #88149C22semidirect
26. C4⋊C4×D13C22semidirect
29. C4×D52C22semidirect
30. C13×#102C22semidirect
31. C13×#102C22semidirect
32. C4×C8×C13C22semidirect
33. #88072C22semidirect
35. #88061C22semidirect
36. #88060C22semidirect
37. #88058C22semidirect
39. #88047C22semidirect
40. C4⋊#1055C22semidirect
104. D52D8semidirect
105. D52#41semidirect
116. #486D13semidirect
153. C4⋊Q8C2×D13semidirect
172. #102C2×D13semidirect
173. #102C2×D13semidirect
175. C4×C8C2×D13semidirect
220. C13#3294semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117194222
C13×#4862
#117187482
#117187332
#117184362
#117184352
#117184342
D13×#1022
C4×D1042
C8×D522
#329413