Finite Group Databasebeta

← #13122542

Subgroups — #13122542

Order 1664.

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

normal subgroups only

This group has 428 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×#382C211yesmaximal, characteristic, complemented
2#11718652C211yesmaximal, characteristic
3#11718651C212yesmaximal, complemented
4#11718640C211yesmaximal, characteristic, complemented
5#11718601C212yesmaximal, complemented
6#11718334C212yesmaximal, complemented
7#11718333C212yesmaximal
8#11718330C212yesmaximal, complemented
9#11718311C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×C4×Dic13C2212yes—
24C13×#95C2212yes—
25C13×#95C2212yes—
26#88071C2211yescharacteristic
27#88071C2212yes—
28#88071C2212yes—
29#88071C2211yescharacteristic
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—
42C2×Dic26—42no—
43C2×Dic26—41no—
44C13×C4⋊C4—41no—
45C13×C4⋊C4—41no—
46C42×C13—22no—
47#6103—24no—
48#6103—24no—
49#6103—24no—
50#6103—42no—
51#6103—42no—
52#6103—42no—
53#6101—42no—
54#6101—42no—
55C4×Dic13—24no—
56#2785—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—22no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
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—
88Dic26—44no—
89#395—131no—
90#394—131no—
91#394—132no—
92#393—132no—
93#388—132no—
94#388—132no—
95#388—132no—
96#382—132no—
97#382D1311yescharacteristic, complemented
98C22×C13C2×#4111yescharacteristic
99C22×C13C2×#4112yes—
100C22×C13H(5,𝔽2)11yescharacteristic
101C22×C13H(5,𝔽2)12yes—
102C22×C132−1+411yescharacteristic
103C2×D13—42no—
104C2×D13—42no—
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C2×D13—42no—
109C2×D13—42no—
110C4×C13—22no—
111C4×C13—42no—
112C4×C13—42no—
113C4×C13—41no—
114C4×C13—41no—
115Dic13—24no—
116Dic13—42no—
117Dic13—42no—
118C22×Q8—131no—
119C22×D4—131no—
120C2×C4⋊C4—132no—
121C2×C4⋊C4—132no—
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—132no—
131C2×C42C2×D1311yescharacteristic
132#95—131no—
133#95—132no—
134#95—132no—
135#95—131no—
136#95—132no—
137#95C2×D1312yes—
138#95C2×D1312yes—
139C2×C13#53911yescharacteristic
140C2×C13#53912yes—
141C2×C13#55512yes—
142C2×C13#55511yescharacteristic
143C2×C13H(3,𝔽4)11yescharacteristic
144D13—82no—
145C24—132no—
146C2×Q8—521no—
147C2×Q8—522no—
148C2×D4—521no—
149C2×D4—522no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4—132no—
153C22×C4C22×D1312yes—
154C22×C4C22×D1312yes—
155C22×C4C22×D1311yescharacteristic
156C22×C4C22×D1311yescharacteristic
157C22×C4C22×D1311yescharacteristic
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—522no—
161C4⋊C4—522no—
162C22⋊C4—264no—
163C22⋊C4—264no—
164C22⋊C4—264no—
165C22⋊C4—522no—
166C22⋊C4—522no—
167C22⋊C4—522no—
168C42—22no—
169C42—264no—
170C13#278511yescharacteristic, complemented, Sylow
171C23—262no—
172C23—262no—
173C23—262no—
174C23—262no—
175C23—262no—
176C23—262no—
177C23—262no—
178C23C23×D1311yescharacteristic
179Q8—524no—
180D4—524no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—134no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4#612712yes—
203C22—522no—
204C22—522no—
205C22—522no—
206C22—522no—
207C22—522no—
208C22—522no—
209C22—522no—
210C22C2×#612711yescharacteristic
211C22#8825111yescharacteristic
212C22#8825411yescharacteristic
213C22#41×D1312yes—
214C22#8825612yes—
215C4—22no—
216C4—42no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—264no—
221C4—522no—
222C4—522no—
223C2—1042no—
224C2#1171922011yescharacteristic
225C2#1171923712yes—
226C2#1171937511yescharacteristic
227C2#1171938811yescharacteristic
228C2#1171939712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#382C2
prime radicalC22×D52C22
hypercenter#382D13
hypocenterC13#2785
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C13×#382C2semidirect
3. #11718651C2semidirect
4. #11718640C2semidirect
5. #11718601C2semidirect
6. #11718334C2semidirect
8. #11718330C2semidirect
9. #11718311C2semidirect
97. #382D13semidirect
170. C13#2785semidirect

Maximal subgroups

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

subgroupindex
C13×#3822
#117186522
#117186512
#117186402
#117186012
#117183342
#117183332
#117183302
#117183112
#278513