Finite Group Databasebeta

← #13122536

Subgroups — #13122536

Order 1664.

472 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 129 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#11718649C211yesmaximal, characteristic
4#11718640C211yesmaximal, characteristic, complemented
5#11718334C212yesmaximal, complemented
6#11718329C212yesmaximal, complemented
7#11718328C212yesmaximal, complemented
8#11718326C212yesmaximal
9#11718315C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×C4⋊Dic13C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24C13×#95C2212yes—
25C13×#95C2211yescharacteristic
26C13×#95C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C23×D13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×D52—41no—
41C2×D52—41no—
42C2×D52Q814yescomplemented
43C2×C4×D13—24no—
44C2×C4×D13—42no—
45C2×C4×D13—42no—
46C2×Dic26—42no—
47C2×Dic26—41no—
48C13×C4⋊C4—41no—
49C13×C4⋊C4—41no—
50#6103—24no—
51#6103—42no—
52#6103—42no—
53#6103—42no—
54#6103—42no—
55C4⋊Dic13—24no—
56#6101—42no—
57#6101—42no—
58C4×Dic13—41no—
59#2784—131nomaximal, Sylow
60C23×C13C2411yescharacteristic
61C22×D13—22no—
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—22no—
66C22×D13—22no—
67C22×D13C2×Q814yes—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13C2×Q812yes—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13#4114yes—
90D52—44no—
91C4×D13—48no—
92Dic26—44no—
93#400D1311yescharacteristic, complemented
94#396—132no—
95#395—131no—
96#393—132no—
97#390—131no—
98#387—132no—
99#386—132no—
100#385—132no—
101#380—132no—
102C22×C13C22×Q811yescharacteristic
103C22×C13C2×#4112yes—
104C22×C13H(5,𝔽2)11yescharacteristic
105C22×C13H(5,𝔽2)11yescharacteristic
106C22×C13H(5,𝔽2)12yes—
107C2×D13—24no—
108C2×D13—24no—
109C2×D13—24no—
110C2×D13—42no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—42no—
114C4×C13—22no—
115C4×C13—42no—
116C4×C13—42no—
117C4×C13—41no—
118C4×C13—41no—
119Dic13—24no—
120Dic13—42no—
121Dic13—42no—
122C22×Q8—131no—
123C22×D4—131no—
124C23×C4—132no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4C2×D1311yescharacteristic
129C2×C4⋊C4C2×D1311yescharacteristic
130C2×C22⋊C4—132no—
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4—132no—
135C2×C42—131no—
136#95—132no—
137#95—131no—
138#95—132no—
139#95—132no—
140#95C2×D1311yescharacteristic
141#95C2×D1312yes—
142#95C2×D1312yes—
143C2×C13#53812yes—
144C2×C13#54311yescharacteristic
145C2×C13#55412yes—
146C2×C13#55511yescharacteristic
147C2×C13#56011yescharacteristic
148D13—44no—
149C24—132no—
150C2×Q8—521no—
151C2×Q8—522no—
152C2×D4—134no—
153C2×D4—521no—
154C2×D4—521no—
155C22×C4—132no—
156C22×C4—132no—
157C22×C4—132no—
158C22×C4—264no—
159C22×C4—522no—
160C22×C4—522no—
161C22×C4C22×D1312yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C22×C4C22×D1311yescharacteristic
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—264no—
169C4⋊C4—522no—
170C4⋊C4—522no—
171C22⋊C4—264no—
172C22⋊C4—522no—
173C22⋊C4—522no—
174C22⋊C4—522no—
175C22⋊C4—522no—
176C42—521no—
177C13#278411yescharacteristic, complemented, Sylow
178C23—134no—
179C23—262no—
180C23—262no—
181C23—262no—
182C23—262no—
183C23—262no—
184C23—262no—
185C23C23×D1311yescharacteristic
186Q8—524no—
187D4—524no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—134no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—528no—
210C2×C4Q8×D1312yes—
211C22—264no—
212C22—264no—
213C22—264no—
214C22—522no—
215C22—522no—
216C22—522no—
217C22—522no—
218C22#8825111yescharacteristic
219C22C2×Q8×D1311yescharacteristic
220C22#41×D1312yes—
221C22#8825611yescharacteristic
222C22#8825612yes—
223C4—22no—
224C4—41no—
225C4—41no—
226C4—42no—
227C4—42no—
228C4—264no—
229C4—522no—
230C4—522no—
231C2—524no—
232C2#1171933911yescharacteristic
233C2#1171937111yescharacteristic
234C2#1171937511yescharacteristic
235C2#1171939512yes—
236C2#1171940912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#400C2
prime radicalC22×D52C22
hypercenter#400D13
hypocenterC13#2784
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. #11718640C2semidirect
5. #11718334C2semidirect
6. #11718329C2semidirect
7. #11718328C2semidirect
9. #11718315C2semidirect
42. C2×D52Q8semidirect
93. #400D13semidirect
177. C13#2784semidirect

Maximal subgroups

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

subgroupindex
C13×#4002
#117186552
#117186492
#117186402
#117183342
#117183292
#117183282
#117183262
#117183152
#278413