Finite Group Databasebeta

← #13127070

Subgroups — #13127070

Order 1664.

448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719422C211yesmaximal, characteristic
2#11719289C211yesmaximal, characteristic, complemented
3C13×#460C211yesmaximal, characteristic, complemented
4#11718835C212yesmaximal, complemented
5#11718830C212yesmaximal, complemented
6#11718731C211yesmaximal, characteristic, complemented
7C4×#6106C211yesmaximal, characteristic, complemented
8#11718507C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718445C212yesmaximal, complemented
11#11718431C212yesmaximal, complemented
12C2×D4×D13—21no—
13C2×D4×D13C2212yes—
14C2×C13×SD16C2212yescomplemented
15C13×#127C2211yescharacteristic
16C4×Q8×C13C2211yescharacteristic, complemented
17#88200C2212yescomplemented
18C2×#6106C2211yescharacteristic
19#88192—21no—
20#88192C2212yes—
21#88191—22no—
22C2×#6094C2212yescomplemented
23#88152—22no—
24#88146C2212yescomplemented
25#88129—21no—
26C4×D52C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic, complemented
29C4×Dic26—21no—
30C13×C4⋊C8C2211yescharacteristic, complemented
31C13×#102C2212yescomplemented
32#88075C2211yescharacteristic, complemented
33#88072C2212yescomplemented
34#88072C2212yescomplemented
35#88061C2212yes—
36#88060C2212yescomplemented
37#88058C2212yescomplemented
38#88049C2211yescharacteristic
39#88048C2211yescharacteristic, complemented
40C4×#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×Q8×C13C2311yescharacteristic
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13C2312yes—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48D4×D13—24no—
49D4×D13—42no—
50D4×D13—44no—
51C2×D52D411yescharacteristic
52C2×D52C2311yescharacteristic
53C2×C4×D13—21no—
54C2×C4×D13C2312yes—
55C2×Dic26—21no—
56C13×SD16—42no—
57C2×C8×C13C2312yes—
58C13×C4⋊C4—21no—
59C13×C4⋊C4C2311yescharacteristic
60C42×C13—21no—
61C42×C13C2311yescharacteristic
62C22⋊Dic13—22no—
63#6106—22no—
64#6103—22no—
65#6103—22no—
66#6103—21no—
67#6103D412yes—
68C4⋊Dic13—21no—
69C4⋊Dic13D411yescharacteristic
70C4⋊Dic13C2312yes—
71C4⋊Dic13C2311yescharacteristic
72#6101—22no—
73C4×Dic13—22no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76#6094—42no—
77#3324—131nomaximal, Sylow
78C23×C13—22no—
79C22×D13—21no—
80C22×D13—44no—
81C22×D13—44no—
82C22×D13—82no—
83C22×D13C2×D412yes—
84Q8×C13—21no—
85Q8×C13—21no—
86D4×C13—22no—
87D4×C13—22no—
88D4×C13—42no—
89D4×C13—81no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—44no—
96C22⋊D13—44no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13C2×D412yes—
100D52—22no—
101D52—21no—
102D52#4112yes—
103C4×D13—22no—
104C4×D13—22no—
105C4×D13—42no—
106Dic26—42no—
107C8×C13—22no—
108#1055—21no—
109#1055—21no—
110#556—131no—
111D42—131no—
112#486—131no—
113#482—132no—
114#474—131no—
115#468—132no—
116#460D1311yescharacteristic, complemented
117#450—132no—
118C4×SD16—131no—
119#436—131no—
120#418—132no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13C22×D411yescharacteristic
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—22no—
128C2×D13—22no—
129C2×D13—41no—
130C2×D13—41no—
131C2×D13—88no—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13AGL(1,ℤ/8)12yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—22no—
139Dic13—42no—
140Dic13—41no—
141C22×D4—132no—
142C22×D4—261no—
143C2×SD16—131no—
144C2×SD16C2×D1312yescomplemented
145C2×M16—132no—
146C4⋊Q8—131no—
147#127C2×D1311yescharacteristic
148#126—262no—
149#124—261no—
150C22⋊Q8—132no—
151#121—132no—
152#121—261no—
153#120—262no—
154C4×Q8—261no—
155C4×Q8C2×D1311yescharacteristic, complemented
156C4×D4—131no—
157C4×D4—131no—
158#117—132no—
159#107—132no—
160#106—131no—
161C4⋊C8C2×D1311yescharacteristic, complemented
162#103—131no—
163#102—132no—
164#102—132no—
165#102—132no—
166#102—131no—
167#102C2×D1312yescomplemented
168C22⋊C8—132no—
169C4×C8—131no—
170C2×C13—82no—
171C2×C13#54611yescharacteristic
172C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C13#57711yescharacteristic
174D13—42no—
175D13—42no—
176C24—262no—
177C2×Q8—261no—
178C2×Q8C22×D1311yescharacteristic
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—131no—
182C2×D4—131no—
183C2×D4—262no—
184C2×D4—264no—
185C2×D4—262no—
186C2×D4—522no—
187C2×D4—524no—
188C2×D4C22×D1312yes—
189C22×C4—132no—
190C22×C4—261no—
191SD16—42no—
192SD16—262no—
193M16—522no—
194C2×C8—131no—
195C2×C8—131no—
196C2×C8C22×D1312yes—
197C4⋊C4—21no—
198C4⋊C4—131no—
199C4⋊C4—132no—
200C4⋊C4—131no—
201C4⋊C4—262no—
202C4⋊C4—261no—
203C4⋊C4C22×D1311yescharacteristic
204C22⋊C4—132no—
205C22⋊C4—262no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4—261no—
209C42—21no—
210C42—262no—
211C42C22×D1311yescharacteristic
212C13#332411yescharacteristic, complemented, Sylow
213C23—22no—
214C23—132no—
215C23—261no—
216C23—524no—
217C23—524no—
218C23—1042no—
219Q8—21no—
220Q8—21no—
221Q8—522no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—81no—
226D4—132no—
227D4—262no—
228D4—261no—
229D4—524no—
230D4—524no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—132no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—261no—
238C2×C4—522no—
239C2×C4D4×D1311yescharacteristic
240C2×C4D4×D1311yescharacteristic
241C2×C4C23×D1311yescharacteristic
242C8—22no—
243C8—261no—
244C8—261no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—262no—
249C22—262no—
250C22—262no—
251C22—262no—
252C22—521no—
253C22—521no—
254C22—1048no—
255C22C2×D4×D1311yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—262no—
260C4—521no—
261C4—522no—
262C4#8816812yes—
263C4#8825111yescharacteristic
264C4#41×D1311yescharacteristic
265C2—82no—
266C2—522no—
267C2—522no—
268C2#1171931711yescharacteristic
269C2C2×#8816811yescharacteristic
270C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
prime radical#11719422C2
hypercenter#460D13
hypocenterC13#3324
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #11719289C2semidirect
3. C13×#460C2semidirect
4. #11718835C2semidirect
5. #11718830C2semidirect
6. #11718731C2semidirect
7. C4×#6106C2semidirect
8. #11718507C2semidirect
9. #11718499C2semidirect
10. #11718445C2semidirect
11. #11718431C2semidirect
14. C2×C13×SD16C22semidirect
16. C4×Q8×C13C22semidirect
17. #88200C22semidirect
22. C2×#6094C22semidirect
24. #88146C22semidirect
28. #88123C22semidirect
30. C13×C4⋊C8C22semidirect
31. C13×#102C22semidirect
32. #88075C22semidirect
33. #88072C22semidirect
34. #88072C22semidirect
36. #88060C22semidirect
37. #88058C22semidirect
39. #88048C22semidirect
40. C4×#1055C22semidirect
116. #460D13semidirect
144. C2×SD16C2×D13semidirect
155. C4×Q8C2×D13semidirect
161. C4⋊C8C2×D13semidirect
167. #102C2×D13semidirect
212. C13#3324semidirect

Maximal subgroups

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

subgroupindex
#117194222
#117192892
C13×#4602
#117188352
#117188302
#117187312
C4×#61062
#117185072
#117184992
#117184452
#117184312
#332413