Finite Group Databasebeta

← #13122670

Subgroups — #13122670

Order 1664.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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×#400C211yesmaximal, characteristic, complemented
2#11718655C212yesmaximal, complemented
3#11718652C211yesmaximal, characteristic
4#11718637C211yesmaximal, characteristic, complemented
5#11718333C212yesmaximal
6#11718331C212yesmaximal, complemented
7#11718331C212yesmaximal, complemented
8#11718330C212yesmaximal, complemented
9#11718315C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×#6103C2212yes—
14C2×#6103C2212yes—
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×C4⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24C2×C4×Dic13C2212yes—
25C13×#95C2212yes—
26C13×#95C2211yescharacteristic
27C13×#95C2212yes—
28#88071C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31C23×D13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×D52—42no—
41C2×D52—41no—
42C13×C4⋊C4—41no—
43C13×C4⋊C4—41no—
44#6103—24no—
45#6103—24no—
46#6103—24no—
47#6103—42no—
48#6103—42no—
49#6103—42no—
50C4⋊Dic13—24no—
51C4⋊Dic13—41no—
52#6101—42no—
53#6101—42no—
54C4×Dic13—22no—
55C4×Dic13—42no—
56#2795—131nomaximal, Sylow
57C23×C13C2411yescharacteristic
58C22×D13—22no—
59C22×D13—22no—
60C22×D13—22no—
61C22×D13—22no—
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13#4112yes—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13#4114yes—
87D52—44no—
88#400D1311yescharacteristic, complemented
89#396—132no—
90#394—131no—
91#394—132no—
92#388—132no—
93#388—132no—
94#388—132no—
95#387—132no—
96#384—131no—
97C22×C13C2×#4111yescharacteristic
98C22×C13C2×#4112yes—
99C22×C13H(5,𝔽2)11yescharacteristic
100C22×C13H(5,𝔽2)12yes—
101C22×C132−1+411yescharacteristic
102C2×D13—42no—
103C2×D13—42no—
104C2×D13—42no—
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C2×D13—42no—
109C4×C13—22no—
110C4×C13—42no—
111C4×C13—42no—
112C4×C13—41no—
113C4×C13—41no—
114Dic13—24no—
115Dic13—42no—
116Dic13—42no—
117C22×D4—131no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—132no—
121C2×C4⋊C4—131no—
122C2×C4⋊C4C2×D1311yescharacteristic
123C2×C4⋊C4C2×D1311yescharacteristic
124C2×C22⋊C4—132no—
125C2×C22⋊C4—132no—
126C2×C22⋊C4—132no—
127C2×C22⋊C4—132no—
128C2×C22⋊C4—132no—
129C2×C22⋊C4—132no—
130C2×C42—131no—
131C2×C42—132no—
132#95—131no—
133#95—132no—
134#95—132no—
135#95C2×D1312yes—
136#95C2×D1311yescharacteristic
137#95C2×D1312yes—
138C2×C13#53911yescharacteristic
139C2×C13#54212yes—
140C2×C13#55312yes—
141C2×C13#55511yescharacteristic
142C2×C13#56011yescharacteristic
143D13—82no—
144C24—132no—
145C2×D4—521no—
146C2×D4—522no—
147C22×C4—132no—
148C22×C4—132no—
149C22×C4—132no—
150C22×C4C22×D1312yes—
151C22×C4C22×D1312yes—
152C22×C4C22×D1311yescharacteristic
153C22×C4C22×D1311yescharacteristic
154C22×C4C22×D1311yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—264no—
158C4⋊C4—522no—
159C4⋊C4—522no—
160C4⋊C4—521no—
161C22⋊C4—264no—
162C22⋊C4—264no—
163C22⋊C4—264no—
164C22⋊C4—522no—
165C22⋊C4—522no—
166C22⋊C4—522no—
167C42—262no—
168C42—522no—
169C13#279511yescharacteristic, complemented, Sylow
170C23—262no—
171C23—262no—
172C23—262no—
173C23—262no—
174C23—262no—
175C23—262no—
176C23—262no—
177C23C23×D1311yescharacteristic
178D4—524no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—134no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4#613112yes—
201C22—522no—
202C22—522no—
203C22—522no—
204C22—522no—
205C22—522no—
206C22—522no—
207C22—522no—
208C22#8825111yescharacteristic
209C22C2×#613111yescharacteristic
210C22#41×D1312yes—
211C22#8825612yes—
212C22#8825711yescharacteristic
213C4—22no—
214C4—41no—
215C4—41no—
216C4—42no—
217C4—42no—
218C4—264no—
219C4—522no—
220C4—522no—
221C2—1042no—
222C2#1171935011yescharacteristic
223C2#1171937111yescharacteristic
224C2#1171937511yescharacteristic
225C2#1171940012yes—
226C2#1171941512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#400C2
prime radicalC22×D52C22
hypercenter#400D13
hypocenterC13#2795
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C13×#400C2semidirect
2. #11718655C2semidirect
4. #11718637C2semidirect
6. #11718331C2semidirect
7. #11718331C2semidirect
8. #11718330C2semidirect
9. #11718315C2semidirect
88. #400D13semidirect
169. C13#2795semidirect

Maximal subgroups

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

subgroupindex
C13×#4002
#117186552
#117186522
#117186372
#117183332
#117183312
#117183302
#117183152
#279513