Finite Group Databasebeta

← #13124356

Subgroups — #13124356

Order 1664.

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

normal subgroups only

This group has 490 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#11719510C211yesmaximal, characteristic
2C22×#6105C211yesmaximal, characteristic, complemented
3C2×#88163C211yesmaximal, characteristic, complemented
4#11719221C211yesmaximal, characteristic, complemented
5C13×#418C211yesmaximal, characteristic, complemented
6#11718780C211yesmaximal, characteristic, complemented
7#11718663C211yesmaximal, characteristic, complemented
8#11718428C214yesmaximal, complemented
9#11718423C214yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C2×#6127C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×M16C2211yescharacteristic
14C13×#117C2211yescharacteristic
15#88207—22no—
16#88194C2212yes—
17#88192—22no—
18#88190C2212yes—
19C2×#6105—24no—
20C2×#6105C2214yes—
21#88180C2211yescharacteristic
22C22×#1055C2211yescharacteristic
23#88163—24no—
24C2×Dic52C2212yescomplemented
25C2×#6095C2212yescomplemented
26#88141C2214yescomplemented
27#88131—22no—
28C4×Dic26—22no—
29C13×#102C2214yes—
30#88054C2214yescomplemented
31#88050C2212yescomplemented
32#88049C2212yescomplemented
33C24×C13—21no—
34C2×D4×C13—22no—
35C2×D4×C13—21no—
36C2×D4×C13—22no—
37C2×D4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C2×C22⋊D13—21no—
40C2×C22⋊D13—24no—
41C22×Dic13—21no—
42#6127—22no—
43#6127—22no—
44C2×D52C2311yescharacteristic
45C2×C4×D13—21no—
46C2×Dic26—21no—
47C2×Dic26—22no—
48C2×Dic26D414yescomplemented
49C2×Dic26C2311yescharacteristic
50C2×Dic26C2312yes—
51C13×M16—22no—
52C2×C8×C13C2312yes—
53C13×C4⋊C4C2312yes—
54C13×C22⋊C4—21no—
55C42×C13—21no—
56C22⋊Dic13—24no—
57C22⋊Dic13D412yes—
58#6105—28no—
59C4⋊Dic13D412yes—
60#6101—24no—
61C4×Dic13—24no—
62C4×Dic13C2312yes—
63C2×#1055—22no—
64C2×#1055C2312yes—
65Dic52—24no—
66#6095—24no—
67#3043—131nomaximal, Sylow
68C23×C13—22no—
69C23×C13—42no—
70C23×C13—82no—
71C23×C13C2×D411yescharacteristic
72C22×D13—21no—
73D4×C13—22no—
74D4×C13—22no—
75D4×C13—42no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D412yes—
79C2×C4×C13#4112yes—
80C2×C4×C13C2411yescharacteristic
81C22⋊D13—42no—
82C22⋊D13—84no—
83C2×Dic13—24no—
84C2×Dic13—22no—
85C2×Dic13—21no—
86C2×Dic13C2×D414yes—
87D52—21no—
88D52—21no—
89C4×D13—42no—
90Dic26—24no—
91Dic26—22no—
92Dic26—21no—
93Dic26—21no—
94Dic26C2×D414yes—
95C8×C13—22no—
96#1055—22no—
97C2×#137—131no—
98C22×SD16—131no—
99#535—131no—
100#519—131no—
101#464—134no—
102#460—134no—
103#424—131no—
104#418D1311yescharacteristic, complemented
105#416—131no—
106C22×C13—22no—
107C22×C13—42no—
108C22×C13—44no—
109C22×C13—84no—
110C22×C13#12112yes—
111C22×C13C22×D411yescharacteristic
112C2×D13—41no—
113C2×D13—42no—
114C4×C13—42no—
115C4×C13#12112yes—
116C4×C13C22×D411yescharacteristic
117C4×C13C2×#4111yescharacteristic
118Dic13—24no—
119Dic13—24no—
120Dic13—41no—
121C2×#41—131no—
122C22×Q8—131no—
123C22×D4C2×D1311yescharacteristic
124#137—264no—
125C2×Q16—132no—
126C2×SD16—134no—
127C2×SD16—132no—
128C2×SD16—264no—
129C2×M16C2×D1311yescharacteristic
130C22×C8—131no—
131#127—132no—
132#124—132no—
133#121—262no—
134#120—262no—
135C4×Q8—134no—
136C4×Q8—262no—
137#117—131no—
138#117—262no—
139#117C2×D1311yescharacteristic
140C4⋊C8—134no—
141#103—132no—
142#102—132no—
143#102C2×D1314yes—
144C2×C13—22no—
145C2×C13—82no—
146C2×C13C2×#12111yescharacteristic
147C2×C13#57712yes—
148D13—81no—
149C24—21no—
150#41—262no—
151#41—262no—
152C2×Q8—134no—
153C2×Q8—132no—
154C2×Q8—131no—
155C2×Q8—262no—
156C2×Q8—261no—
157C2×D4—22no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—131no—
161C2×D4—264no—
162C2×D4—261no—
163C2×D4C22×D1312yes—
164C22×C4—261no—
165C22×C4—261no—
166C22×C4C22×D1311yescharacteristic
167Q16—264no—
168SD16—264no—
169SD16—268no—
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—
180C42—21no—
181C42—132no—
182C42—264no—
183C13#304311yescharacteristic, complemented, Sylow
184C23—22no—
185C23—42no—
186C23—82no—
187C23—261no—
188C23D4×D1311yescharacteristic
189Q8—134no—
190Q8—264no—
191Q8—262no—
192Q8—261no—
193Q8—261no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—261no—
198D4—261no—
199D4—522no—
200D4—1044no—
201C2×C4—22no—
202C2×C4—134no—
203C2×C4—264no—
204C2×C4—262no—
205C2×C4—261no—
206C2×C4—522no—
207C2×C4#612712yes—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1312yes—
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—262no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—521no—
218C22—522no—
219C22#8813812yes—
220C22C2×D4×D1311yescharacteristic
221C4—42no—
222C4—264no—
223C4—264no—
224C4—521no—
225C4#8813812yes—
226C4C2×#612711yescharacteristic
227C4C2×D4×D1311yescharacteristic
228C2—22no—
229C2—82no—
230C2—1041no—
231C2C2×#8813811yescharacteristic
232C2#1171948012yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#418C2
socleC22×C13C22×D4
prime radical#11719510C2
hypercenter#418D13
hypocenterC13#3043
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C22×#6105C2semidirect
3. C2×#88163C2semidirect
4. #11719221C2semidirect
5. C13×#418C2semidirect
6. #11718780C2semidirect
7. #11718663C2semidirect
8. #11718428C2semidirect
9. #11718423C2semidirect
24. C2×Dic52C22semidirect
25. C2×#6095C22semidirect
26. #88141C22semidirect
30. #88054C22semidirect
31. #88050C22semidirect
32. #88049C22semidirect
48. C2×Dic26D4semidirect
104. #418D13semidirect
183. C13#3043semidirect

Maximal subgroups

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

subgroupindex
#117195102
C22×#61052
C2×#881632
#117192212
C13×#4182
#117187802
#117186632
#117184282
#117184232
#304313