Finite Group Databasebeta

← #13124760

Subgroups — #13124760

Order 1664.

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

normal subgroups only

This group has 458 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#11719332C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
3C13×#483C211yesmaximal, characteristic, complemented
4#11718704C211yesmaximal, characteristic, complemented
5#11718628C211yesmaximal, characteristic, complemented
6#11718524C212yesmaximal, complemented
7#11718522C212yesmaximal, complemented
8#11718470C212yesmaximal, complemented
9#11718464C212yesmaximal, complemented
10#11718397C211yesmaximal, characteristic, complemented
11#11718387C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C22×C4×D13—21no—
14C22×C4×D13C2211yescharacteristic
15C13×C22⋊Q8C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17#88200C2211yescharacteristic
18#88184C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20C2×#6101—21no—
21C2×#6094C2212yes—
22#88149C2211yescharacteristic
23#88148—21no—
24#88147—21no—
25#88146C2211yescharacteristic
26C4⋊C4×D13—21no—
27C4⋊C4×D13—21no—
28C4⋊C4×D13C2212yes—
29C4⋊C4×D13C2212yes—
30#88136—21no—
31#88135—21no—
32C13×#106C2212yescomplemented
33C13×#103C2212yescomplemented
34C13×C22⋊C8C2211yescharacteristic
35#88075C2212yescomplemented
36C22⋊#1055C2211yescharacteristic
37#88061C2212yescomplemented
38#88060C2212yes—
39#88058C2212yescomplemented
40#88049C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13D411yescharacteristic
44C2×Q8×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C22×Dic13—21no—
49C22×Dic13D411yescharacteristic
50#6131—24no—
51C2×D52—21no—
52C2×D52—21no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—24no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—21no—
58C2×C4×D13—44no—
59C2×C4×D13D411yescharacteristic
60C2×C4×D13D411yescharacteristic
61C2×C4×D13C2311yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×C8×C13C2312yes—
64C13×C4⋊C4—21no—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2312yes—
67C13×C4⋊C4C2311yescharacteristic
68C13×C22⋊C4—21no—
69#6103—21no—
70#6103—21no—
71#6103—21no—
72#6103—21no—
73C4⋊Dic13—21no—
74C4⋊Dic13C2312yes—
75C4⋊Dic13C2311yescharacteristic
76#6101—21no—
77#6101—22no—
78#6101—22no—
79C4×Dic13—21no—
80C2×#1055C2312yes—
81#6094—24no—
82#3092—131nomaximal, Sylow
83C23×C13C2×D411yescharacteristic
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—21no—
88C22×D13C2×D411yescharacteristic
89C22×D13C2×D411yescharacteristic
90Q8×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—42no—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—42no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—42no—
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105D52—22no—
106D52—42no—
107D52—42no—
108C4×D13—22no—
109C4×D13—22no—
110C4×D13—22no—
111C4×D13—44no—
112C4×D13—44no—
113C4×D13—42no—
114C4×D13#4114yes—
115C8×C13—22no—
116#1055—22no—
117#525—131no—
118C22×C4⋊C4—131no—
119#484—132no—
120#483—131no—
121#483D1311yescharacteristic, complemented
122#481—132no—
123#480—131no—
124#480—131no—
125#428—132no—
126#417—132no—
127#407—131no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13AGL(1,ℤ/8)12yes—
131C22×C13C22×D411yescharacteristic
132C2×D13—28no—
133C2×D13—21no—
134C2×D13—21no—
135C2×D13—21no—
136C2×D13—21no—
137C2×D13—41no—
138C2×D13—41no—
139C2×D13—41no—
140C2×D13#12312yes—
141C2×D13#13712yes—
142C4×C13—21no—
143C4×C13—41no—
144C4×C13—42no—
145C4×C13—41no—
146C4×C13C2×#4112yes—
147Dic13—21no—
148Dic13—42no—
149Dic13—41no—
150Dic13#12312yes—
151C2×#41—131no—
152C23×C4—131no—
153C23×C4—261no—
154C2×M16—132no—
155#123—261no—
156C22⋊Q8—131no—
157C22⋊Q8C2×D1311yescharacteristic
158#121—131no—
159#121—131no—
160#120—261no—
161C4×D4—261no—
162C4×D4—261no—
163#117—131no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4C2×D1311yescharacteristic
171#107—132no—
172#107—132no—
173#106—132no—
174#106C2×D1312yescomplemented
175#103—132no—
176#103C2×D1312yescomplemented
177#102—132no—
178#102—132no—
179C22⋊C8—131no—
180C22⋊C8—132no—
181C22⋊C8C2×D1311yescharacteristic
182C2×C13—22no—
183C2×C13C2×#12311yescharacteristic
184C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C13C2×#13711yescharacteristic
186D13—22no—
187D13—22no—
188D13—81no—
189C24—131no—
190#41—264no—
191C2×Q8C22×D1311yescharacteristic
192C2×D4—131no—
193C2×D4—261no—
194C2×D4—261no—
195C2×D4—261no—
196C22×C4—21no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—264no—
203C22×C4—261no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—261no—
207C22×C4—524no—
208C22×C4C22×D1311yescharacteristic
209M16—264no—
210C2×C8—132no—
211C2×C8C22×D1312yes—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—132no—
215C4⋊C4—131no—
216C4⋊C4—262no—
217C4⋊C4—262no—
218C4⋊C4—261no—
219C4⋊C4—261no—
220C4⋊C4C22×D1312yes—
221C4⋊C4C22×D1311yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—261no—
224C22⋊C4—261no—
225C22⋊C4—261no—
226C22⋊C4—261no—
227C42—261no—
228C13#309211yescharacteristic, complemented, Sylow
229C23—131no—
230C23—131no—
231C23—262no—
232C23—262no—
233C23—262no—
234C23—261no—
235C23D4×D1311yescharacteristic
236Q8—22no—
237D4—262no—
238D4—522no—
239D4—522no—
240D4—522no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—131no—
247C2×C4—134no—
248C2×C4—131no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—261no—
254C2×C4—262no—
255C2×C4—522no—
256C2×C4—524no—
257C2×C4—524no—
258C2×C4—522no—
259C2×C4D4×D1311yescharacteristic
260C2×C4C23×D1311yescharacteristic
261C8—22no—
262C8—262no—
263C22—21no—
264C22—21no—
265C22—132no—
266C22—132no—
267C22—268no—
268C22—261no—
269C22—261no—
270C22—261no—
271C22—261no—
272C22—521no—
273C22—521no—
274C22—521no—
275C22#8816812yes—
276C22C2×D4×D1311yescharacteristic
277C4—21no—
278C4—42no—
279C4—41no—
280C4—41no—
281C4—132no—
282C4—261no—
283C4—522no—
284C4—521no—
285C4#41×D1312yes—
286C2—22no—
287C2—262no—
288C2—262no—
289C2—1041no—
290C2D13×#12311yescharacteristic
291C2C2×#8816811yescharacteristic
292C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radical#11719332C2
hypercenter#483D13
hypocenterC13#3092
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D13C2semidirect
3. C13×#483C2semidirect
4. #11718704C2semidirect
5. #11718628C2semidirect
6. #11718524C2semidirect
7. #11718522C2semidirect
8. #11718470C2semidirect
9. #11718464C2semidirect
10. #11718397C2semidirect
11. #11718387C2semidirect
32. C13×#106C22semidirect
33. C13×#103C22semidirect
35. #88075C22semidirect
37. #88061C22semidirect
39. #88058C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
121. #483D13semidirect
174. #106C2×D13semidirect
176. #103C2×D13semidirect
228. C13#3092semidirect

Maximal subgroups

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

subgroupindex
#117193322
C2×C4⋊C4×D132
C13×#4832
#117187042
#117186282
#117185242
#117185222
#117184702
#117184642
#117183972
#117183872
#309213