Finite Group Databasebeta

← #13124488

Subgroups — #13124488

Order 1664.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C13×#536C211yesmaximal, characteristic
2#11719530C211yesmaximal, characteristic
3C2×#88202C211yesmaximal, characteristic
4C22×#6107C211yesmaximal, characteristic, complemented
5#11718886C211yesmaximal, characteristic, complemented
6#11718713C214yesmaximal, complemented
7#11718712C214yesmaximal, complemented
8#11718665C211yesmaximal, characteristic, complemented
9#11718659C211yesmaximal, characteristic, complemented
10C2×C13×#41C2211yescharacteristic
11C22×Q8×C13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C13×C4⋊Q8—21no—
14C13×#124—21no—
15C13×#123—22no—
16C13×C22⋊Q8C2214yes—
17C13×#117C2211yescharacteristic
18#88202—24no—
19#88198—21no—
20C2×#6107—24no—
21C2×#6107C2212yes—
22C2×#6107C2212yes—
23#88190—21no—
24#88189—22no—
25#88180C2211yescharacteristic
26#88178C2214yes—
27C2×#6099C2211yescharacteristic
28C2×#6099C2212yes—
29C22×#1055C2212yes—
30C22×#1055C2211yescharacteristic
31#88075C2214yes—
32#88050C2214yes—
33#88048C2212yes—
34#88047C2212yes—
35C13×#41—22no—
36C13×#41—22no—
37C2×Q8×C13—21no—
38C2×Q8×C13—22no—
39C2×Q8×C13—22no—
40C2×Q8×C13D411yescharacteristic
41C2×Q8×C13C2312yes—
42C2×D4×C13D412yes—
43C2×D4×C13D411yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C22×Dic13—21no—
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—21no—
51C2×Dic26C2312yes—
52C13×C4⋊C4—24no—
53C13×C4⋊C4C2312yes—
54C13×C22⋊C4—21no—
55C13×C22⋊C4—24no—
56C42×C13—21no—
57C22⋊Dic13—24no—
58C22⋊Dic13—21no—
59#6107—24no—
60#6107—24no—
61C4⋊Dic13C2312yes—
62#6101—24no—
63C4×Dic13—21no—
64#6099—22no—
65#6099—24no—
66C2×#1055—24no—
67C2×#1055D414yes—
68C2×#1055C2312yes—
69C2×#1055C2311yescharacteristic
70C2×#1055C2311yescharacteristic
71#3059—131nomaximal, Sylow
72C23×C13C2×D412yes—
73C23×C13C2×D411yescharacteristic
74Q8×C13—22no—
75Q8×C13—22no—
76Q8×C13—22no—
77Q8×C13—42no—
78D4×C13—24no—
79D4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D412yes—
88C2×C4×C13#4112yes—
89C2×C4×C13C2411yescharacteristic
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—42no—
93Dic26—22no—
94Dic26—22no—
95Dic26—42no—
96#1055—22no—
97#1055C2×D412yes—
98#1055C2×D412yes—
99C22×Q16—131no—
100C2×#131—131no—
101#536—131no—
102#536D1311yescharacteristic
103#470—134no—
104#467—134no—
105#427—131no—
106#419—131no—
107#419—131no—
108C22×C13—22no—
109C22×C13—22no—
110C22×C13—24no—
111C22×C13#12112yes—
112C22×C13C22×D411yescharacteristic
113C4×C13—22no—
114C4×C13—42no—
115C4×C13—42no—
116C4×C13#12112yes—
117C4×C13C22×D411yescharacteristic
118C4×C13C2×#4111yescharacteristic
119Dic13—42no—
120Dic13—42no—
121C2×#41C2×D1311yescharacteristic
122C22×Q8—131no—
123C22×Q8C2×D1311yescharacteristic
124C2×Q16—132no—
125C2×Q16—132no—
126C2×Q16—264no—
127#131—264no—
128C2×M16—131no—
129C2×M16—132no—
130C22×C8—131no—
131C22×C8—132no—
132C4⋊Q8—21no—
133C4⋊Q8—261no—
134#124—21no—
135#124—261no—
136#123—22no—
137#123—262no—
138C22⋊Q8—134no—
139C22⋊Q8C2×D1314yes—
140#117—131no—
141#117C2×D1311yescharacteristic
142#107—132no—
143#106—132no—
144#103—134no—
145#103—134no—
146C2×C13—22no—
147C2×C13—42no—
148C2×C13C2×#12111yescharacteristic
149C2×C13#57812yes—
150#41—22no—
151#41—22no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—132no—
156C2×Q8—261no—
157C2×Q8—262no—
158C2×Q8—262no—
159C2×Q8C22⋊D1311yescharacteristic
160C2×Q8C22×D1312yes—
161C2×D4C22⋊D1312yes—
162C2×D4C22⋊D1311yescharacteristic
163C22×C4—21no—
164C22×C4—261no—
165C22×C4C22×D1312yes—
166C22×C4C22×D1311yescharacteristic
167Q16—264no—
168Q16—264no—
169M16—264no—
170M16—262no—
171C2×C8—134no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—132no—
175C2×C8—264no—
176C4⋊C4—24no—
177C4⋊C4—132no—
178C4⋊C4—264no—
179C4⋊C4C22×D1312yes—
180C22⋊C4—21no—
181C22⋊C4—24no—
182C22⋊C4—261no—
183C22⋊C4—264no—
184C42—21no—
185C42—261no—
186C13#305911yescharacteristic, complemented, Sylow
187C23C2×C22⋊D1312yes—
188C23C2×C22⋊D1311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—262no—
194Q8—262no—
195Q8—522no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—522no—
206C2×C4D4×D1312yes—
207C2×C4#612912yes—
208C2×C4C2×C22⋊D1312yes—
209C2×C4C2×C22⋊D1311yescharacteristic
210C2×C4C23×D1311yescharacteristic
211C8—132no—
212C8—132no—
213C8—262no—
214C22—22no—
215C22—22no—
216C22—24no—
217C22#8819312yes—
218C22C22×C22⋊D1311yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—522no—
223C4—522no—
224C4#8819312yes—
225C4C2×D4×D1311yescharacteristic
226C4C2×#612911yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#8819311yescharacteristic
230C2#1171954312yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#536C2
socleC22×C13C22×D4
prime radicalC2×C13×#41C22
hypercenter#536D13
hypocenterC13#3059
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
4. C22×#6107C2semidirect
5. #11718886C2semidirect
6. #11718713C2semidirect
7. #11718712C2semidirect
8. #11718665C2semidirect
9. #11718659C2semidirect
186. C13#3059semidirect

Maximal subgroups

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

subgroupindex
C13×#5362
#117195302
C2×#882022
C22×#61072
#117188862
#117187132
#117187122
#117186652
#117186592
#305913