Finite Group Databasebeta

← #13124347

Subgroups — #13124347

Order 1664.

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

normal subgroups only

This group has 494 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
1#11719521C211yesmaximal, characteristic, complemented
2C22×#6106C211yesmaximal, characteristic, complemented
3C2×#88162C211yesmaximal, characteristic
4#11719226C211yesmaximal, characteristic, complemented
5C13×#419C211yesmaximal, characteristic, complemented
6#11718780C211yesmaximal, characteristic, complemented
7#11718663C211yesmaximal, characteristic, complemented
8#11718480C214yesmaximal, complemented
9#11718479C214yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C2×#6127C2211yescharacteristic
12C22×D52C2211yescharacteristic
13C2×C13×M16C2211yescharacteristic
14C13×#117C2211yescharacteristic
15#88201C2212yescomplemented
16#88200—22no—
17#88198C2212yescomplemented
18C2×#6106—24no—
19C2×#6106C2214yes—
20#88183—22no—
21#88180C2211yescharacteristic
22C22×#1055C2211yescharacteristic
23#88162—24no—
24C2×D104C2212yes—
25C2×#6095C2212yes—
26#88147C2214yes—
27C22⋊C4×D13—22no—
28C4×D52—22no—
29C13×#103C2214yescomplemented
30#88054C2214yescomplemented
31#88050C2212yescomplemented
32#88049C2212yescomplemented
33C23×D13—21no—
34C2×Q8×C13—21no—
35C2×Q8×C13—22no—
36C2×Q8×C13—22no—
37C2×Q8×C13C2312yes—
38C22×C4×C13—21no—
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—21no—
41#6127—22no—
42#6127—22no—
43C2×D52—21no—
44C2×D52—22no—
45C2×D52D414yes—
46C2×D52C2311yescharacteristic
47C2×D52C2312yes—
48C2×C4×D13—21no—
49C2×C4×D13—24no—
50C2×Dic26C2311yescharacteristic
51C13×M16—22no—
52C2×C8×C13C2312yes—
53C13×C4⋊C4C2312yes—
54C13×C22⋊C4—21no—
55C42×C13—21no—
56C22⋊Dic13D412yes—
57#6106—28no—
58#6103—24no—
59#6103—24no—
60C4⋊Dic13D412yes—
61#6101—24no—
62C4×Dic13C2312yes—
63C2×#1055—22no—
64C2×#1055C2312yes—
65D104—24no—
66#6095—24no—
67#3042—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—22no—
70C22×D13—24no—
71C22×D13—21no—
72C22×D13—82no—
73Q8×C13—22no—
74Q8×C13—22no—
75Q8×C13—42no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—42no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D412yes—
81C2×C4×C13#4112yes—
82C2×C4×C13C2411yescharacteristic
83C22⋊D13—42no—
84C2×Dic13—21no—
85C2×Dic13C2×D414yes—
86D52—24no—
87D52—21no—
88D52—22no—
89D52—21no—
90D52C2×D414yes—
91C4×D13—42no—
92C4×D13—84no—
93Dic26—21no—
94Dic26—21no—
95C8×C13—22no—
96#1055—22no—
97C2×AGL(1,ℤ/8)—131no—
98C22×SD16—131no—
99#536—131no—
100#518—131no—
101#463—134no—
102#461—134no—
103#424—131no—
104#419D1311yescharacteristic, complemented
105#416—131no—
106C22×C13—22no—
107C22×C13#12112yes—
108C22×C13C22×D411yescharacteristic
109C2×D13—24no—
110C2×D13—44no—
111C2×D13—41no—
112C2×D13—42no—
113C2×D13—84no—
114C4×C13—42no—
115C4×C13—42no—
116C4×C13#12112yes—
117C4×C13C22×D411yescharacteristic
118C4×C13C2×#4111yescharacteristic
119Dic13—24no—
120Dic13—41no—
121C2×#41—131no—
122C22×Q8C2×D1311yescharacteristic
123C22×D4—131no—
124AGL(1,ℤ/8)—264no—
125C2×SD16—134no—
126C2×SD16—132no—
127C2×SD16—264no—
128C2×D8—132no—
129C2×M16C2×D1311yescharacteristic
130C22×C8—131no—
131C4⋊Q8—132no—
132#124—132no—
133#123—262no—
134C22⋊Q8—262no—
135C4×D4—134no—
136C4×D4—262no—
137#117—131no—
138#117C2×D1311yescharacteristic
139C2×C22⋊C4—262no—
140C4⋊C8—134no—
141#103—132no—
142#103C2×D1314yescomplemented
143#102—132no—
144C2×C13—22no—
145C2×C13C2×#12111yescharacteristic
146C2×C13#57712yes—
147D13—44no—
148D13—81no—
149C24—261no—
150#41—262no—
151#41—262no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—131no—
156C2×Q8C22×D1312yes—
157C2×D4—134no—
158C2×D4—132no—
159C2×D4—131no—
160C2×D4—261no—
161C2×D4—262no—
162C2×D4—261no—
163C22×C4—21no—
164C22×C4—264no—
165C22×C4—261no—
166C22×C4C22×D1311yescharacteristic
167SD16—264no—
168SD16—268no—
169D8—264no—
170M16—22no—
171C2×C8—132no—
172C2×C8—262no—
173C2×C8C22×D1312yes—
174C4⋊C4—132no—
175C4⋊C4—264no—
176C4⋊C4C22×D1312yes—
177C22⋊C4—21no—
178C22⋊C4—132no—
179C22⋊C4—264no—
180C22⋊C4—264no—
181C42—21no—
182C42—132no—
183C13#304211yescharacteristic, complemented, Sylow
184C23—262no—
185C23—264no—
186C23—261no—
187C23—1042no—
188C23D4×D1311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—261no—
193Q8—261no—
194D4—134no—
195D4—264no—
196D4—262no—
197D4—261no—
198D4—261no—
199D4—522no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—134no—
204C2×C4—261no—
205C2×C4—522no—
206C2×C4—1044no—
207C2×C4#612712yes—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1312yes—
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—262no—
213C22—22no—
214C22—264no—
215C22—524no—
216C22—521no—
217C22—522no—
218C22—1044no—
219C22#8813812yes—
220C22C2×D4×D1311yescharacteristic
221C4—42no—
222C4—42no—
223C4—264no—
224C4—521no—
225C4#8813812yes—
226C4C2×#612711yescharacteristic
227C4C2×D4×D1311yescharacteristic
228C2—22no—
229C2—524no—
230C2—1041no—
231C2C2×#8813811yescharacteristic
232C2#1171948312yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#419C2
socleC22×C13C22×D4
prime radicalC2×#88162C2
hypercenter#419D13
hypocenterC13#3042
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #11719521C2semidirect
2. C22×#6106C2semidirect
4. #11719226C2semidirect
5. C13×#419C2semidirect
6. #11718780C2semidirect
7. #11718663C2semidirect
8. #11718480C2semidirect
9. #11718479C2semidirect
15. #88201C22semidirect
17. #88198C22semidirect
29. C13×#103C22semidirect
30. #88054C22semidirect
31. #88050C22semidirect
32. #88049C22semidirect
104. #419D13semidirect
142. #103C2×D13semidirect
183. C13#3042semidirect

Maximal subgroups

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

subgroupindex
#117195212
C22×#61062
C2×#881622
#117192262
C13×#4192
#117187802
#117186632
#117184802
#117184792
#304213