Finite Group Databasebeta

← #13125788

Subgroups — #13125788

Order 1664.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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×#533C211yesmaximal, characteristic, complemented
2#11719182C211yesmaximal, characteristic
3#11718754C211yesmaximal, characteristic, complemented
4#11718753C211yesmaximal, characteristic, complemented
5#11718749C211yesmaximal, characteristic, complemented
6#11718746C211yesmaximal, characteristic, complemented
7#11718708C214yesmaximal, complemented
8#11718689C214yesmaximal, complemented
9#11718586C211yesmaximal, characteristic, complemented
10C2×#6127C2212yes—
11C13×C4⋊Q8C2211yescharacteristic
12C13×C4⋊Q8C2211yescharacteristic
13C13×#125—21no—
14C13×C22⋊Q8—21no—
15C13×C22⋊Q8C2212yes—
16C4×Q8×C13—21no—
17C4×Q8×C13C2212yes—
18C13×#117—21no—
19C2×C42×C13C2211yescharacteristic
20C2×#6107C2214yes—
21C2×#6106C2214yes—
22#88184—21no—
23#88184—21no—
24#88129C2212yes—
25#88128C2211yescharacteristic
26C4×D52—21no—
27C4×D52—21no—
28#88123C2211yescharacteristic
29C22⋊#1055C2212yes—
30#88050C2214yes—
31#88049C2214yes—
32C4⋊#1055C2212yes—
33C4×#1055C2211yescharacteristic
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37C22×C4×C13D411yescharacteristic
38C22×C4×C13D411yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—22no—
41#6127—44no—
42C2×D52—21no—
43C2×D52—21no—
44C2×D52C2312yes—
45C2×C4×D13—22no—
46C2×Dic26C2312yes—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4C2312yes—
53C13×C22⋊C4—22no—
54C42×C13—22no—
55C42×C13D411yescharacteristic
56C42×C13D411yescharacteristic
57C42×C13C2311yescharacteristic
58C42×C13C2311yescharacteristic
59#6107—44no—
60#6106—44no—
61#6103—22no—
62#6103—22no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C2×#1055C2312yes—
66C2×#1055C2312yes—
67#3210—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—22no—
70Q8×C13—24no—
71Q8×C13—42no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2411yescharacteristic
83C22⋊D13—44no—
84C2×Dic13—22no—
85D52—24no—
86D52—42no—
87D52—42no—
88C4×D13—44no—
89Dic26—24no—
90#1055—22no—
91#1055—22no—
92#533D1311yescharacteristic, complemented
93#532—131no—
94#494—131no—
95#492—131no—
96#487—131no—
97#486—131no—
98#464—134no—
99#452—134no—
100#431—131no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13C22×D411yescharacteristic
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—42no—
112C4×C13—42no—
113C4×C13#13512yes—
114C4×C13#13712yes—
115C4×C13H(5,𝔽2)12yes—
116Dic13—42no—
117C2×#41—132no—
118C2×Q16—134no—
119C2×SD16—134no—
120C4⋊Q8—131no—
121C4⋊Q8C2×D1311yescharacteristic
122C4⋊Q8C2×D1311yescharacteristic
123#127—131no—
124#125—21no—
125#124—132no—
126C22⋊Q8—21no—
127C22⋊Q8C2×D1312yes—
128#121—261no—
129#121—261no—
130C4×Q8—21no—
131C4×Q8C2×D1312yes—
132C4×D4—261no—
133C4×D4—261no—
134#117—21no—
135C2×C42C2×D1311yescharacteristic
136C4⋊C8—132no—
137#103—134no—
138#102—134no—
139C22⋊C8—132no—
140C4×C8—131no—
141C4×C8—131no—
142C2×C13—41no—
143C2×C13#53511yescharacteristic
144C2×C13C2×#13511yescharacteristic
145C2×C13C2×#13711yescharacteristic
146D13—82no—
147#41—524no—
148C2×Q8—21no—
149C2×Q8—132no—
150C2×Q8C22×D1312yes—
151C2×D4—132no—
152C2×D4—262no—
153C2×D4—261no—
154C2×D4—261no—
155C22×C4—262no—
156C22×C4C22⋊D1311yescharacteristic
157C22×C4C22⋊D1311yescharacteristic
158C22×C4C22×D1311yescharacteristic
159Q16—524no—
160SD16—524no—
161C2×C8—132no—
162C2×C8—132no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—261no—
169C4⋊C4—261no—
170C4⋊C4C22×D1312yes—
171C22⋊C4—22no—
172C22⋊C4—262no—
173C22⋊C4—262no—
174C42—22no—
175C42C22⋊D1311yescharacteristic
176C42C22⋊D1311yescharacteristic
177C42C22×D1311yescharacteristic
178C42C22×D1311yescharacteristic
179C13#321011yescharacteristic, complemented, Sylow
180C23—262no—
181C23C2×C22⋊D1311yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—264no—
185D4—264no—
186D4—524no—
187D4—522no—
188D4—522no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—262no—
195C2×C4—524no—
196C2×C4C2×C22⋊D1311yescharacteristic
197C2×C4C2×C22⋊D1311yescharacteristic
198C2×C4C2×C22⋊D1311yescharacteristic
199C2×C4C2×C22⋊D1311yescharacteristic
200C2×C4C2×C22⋊D1311yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—262no—
203C8—262no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—522no—
208C22—522no—
209C22—522no—
210C22C22×C22⋊D1311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C4—522no—
217C4#8819612yes—
218C4#8820412yes—
219C4#8825612yes—
220C2—41no—
221C2—1042no—
222C2C2×#8819611yescharacteristic
223C2C2×#8820411yescharacteristic
224C2#1171953511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#533C2
socleC22×C13C22×D4
prime radical#11719182C2
hypercenter#533D13
hypocenterC13#3210
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C13×#533C2semidirect
3. #11718754C2semidirect
4. #11718753C2semidirect
5. #11718749C2semidirect
6. #11718746C2semidirect
7. #11718708C2semidirect
8. #11718689C2semidirect
9. #11718586C2semidirect
92. #533D13semidirect
179. C13#3210semidirect

Maximal subgroups

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

subgroupindex
C13×#5332
#117191822
#117187542
#117187532
#117187492
#117187462
#117187082
#117186892
#117185862
#321013