Finite Group Databasebeta

← #13121852

Subgroups — #13121852

Order 1664.

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

normal subgroups only

This group has 528 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
1C2×#88150C212yesmaximal, complemented
2C13×#389C211yesmaximal, characteristic, complemented
3#11718655C212yesmaximal, complemented
4#11718653C212yesmaximal, complemented
5#11718650C212yesmaximal, complemented
6#11718600C211yesmaximal, characteristic
7#11718590C211yesmaximal, characteristic, complemented
8#11718326C212yesmaximal
9#11718318C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27#88150—28no—
28C13×#95C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32C23×D13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C2×D52—41no—
42C2×D52—41no—
43C2×D52Q814yescomplemented
44C2×C4×D13—24no—
45C2×C4×D13—42no—
46C2×C4×D13—42no—
47C2×Dic26—41no—
48C2×Dic26—41no—
49C2×Dic26D414yescomplemented
50C13×C4⋊C4—24no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—41no—
53C42×C13—41no—
54#6103—24no—
55#6103—24no—
56#6103—24no—
57#6103—42no—
58#6103—42no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61#6101—24no—
62#6101—24no—
63#6101—42no—
64#2732—131nomaximal, Sylow
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—22no—
72C22×D13C2×Q814yes—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×Q812yes—
87C2×C4×C13#4112yes—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13C2×D414yes—
97D52—44no—
98C4×D13—48no—
99Dic26—44no—
100C2×C22⋊Q8—132no—
101#399—132no—
102#398—132no—
103#396—132no—
104#391—131no—
105#390—131no—
106#389D1311yescharacteristic, complemented
107#386—132no—
108#385—132no—
109C22×C13C22×D411yescharacteristic
110C22×C13C22×Q811yescharacteristic
111C22×C13C2×#4111yescharacteristic
112C22×C13H(5,𝔽2)11yescharacteristic
113C22×C13H(5,𝔽2)11yescharacteristic
114C22×C13H(5,𝔽2)11yescharacteristic
115C22×C132−1+411yescharacteristic
116C2×D13—24no—
117C2×D13—24no—
118C2×D13—24no—
119C2×D13—42no—
120C2×D13—42no—
121C2×D13—42no—
122C2×D13—42no—
123C4×C13—22no—
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—42no—
127C4×C13—42no—
128Dic13—24no—
129Dic13—42no—
130Dic13—42no—
131C22×Q8—131no—
132C22×D4—131no—
133C23×C4—132no—
134C22⋊Q8—268no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4C2×D1312yes—
141C2×C4⋊C4C2×D1311yescharacteristic
142C2×C4⋊C4C2×D1311yescharacteristic
143C2×C22⋊C4—132no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C42C2×D1311yescharacteristic
149#95—132no—
150#95—132no—
151#95—132no—
152#95C2×D1312yes—
153C2×C13#53411yescharacteristic
154C2×C13#53911yescharacteristic
155C2×C13#54311yescharacteristic
156C2×C13D4×Q811yescharacteristic
157C2×C13#55011yescharacteristic
158C2×C13#55411yescharacteristic
159C2×C13#56211yescharacteristic
160D13—44no—
161C24—132no—
162C2×Q8—134no—
163C2×Q8—521no—
164C2×Q8—521no—
165C2×D4—134no—
166C2×D4—521no—
167C2×D4—521no—
168C22×C4—132no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4—264no—
172C22×C4—522no—
173C22×C4—522no—
174C22×C4C22×D1312yes—
175C22×C4C22×D1312yes—
176C22×C4C22×D1311yescharacteristic
177C22×C4C22×D1311yescharacteristic
178C22×C4C22×D1311yescharacteristic
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—41no—
182C4⋊C4—264no—
183C4⋊C4—264no—
184C4⋊C4—522no—
185C4⋊C4—521no—
186C4⋊C4—521no—
187C22⋊C4—264no—
188C22⋊C4—264no—
189C22⋊C4—264no—
190C22⋊C4—522no—
191C22⋊C4—522no—
192C42—41no—
193C13#273211yescharacteristic, complemented, Sylow
194C23—134no—
195C23—262no—
196C23—262no—
197C23—262no—
198C23—262no—
199C23—262no—
200C23—262no—
201C23C23×D1311yescharacteristic
202Q8—524no—
203D4—524no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—134no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—528no—
226C2×C4#612712yes—
227C2×C4D4×D1312yes—
228C2×C4Q8×D1312yes—
229C22—264no—
230C22—264no—
231C22—264no—
232C22—522no—
233C22—522no—
234C22—522no—
235C22—522no—
236C22C2×#612711yescharacteristic
237C22C2×D4×D1311yescharacteristic
238C22#8825111yescharacteristic
239C22C2×Q8×D1311yescharacteristic
240C22#8825411yescharacteristic
241C22#8825611yescharacteristic
242C22#8825611yescharacteristic
243C4—22no—
244C4—22no—
245C4—22no—
246C4—42no—
247C4—42no—
248C4—264no—
249C4—522no—
250C4—522no—
251C2—524no—
252C2#1171922011yescharacteristic
253C2#1171925811yescharacteristic
254C2#1171928411yescharacteristic
255C2#1171931011yescharacteristic
256C2#1171933911yescharacteristic
257C2#1171940511yescharacteristic
258C2#1171943211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC22×D52C22
hypercenter#389D13
hypocenterC13#2732
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#88150C2semidirect
2. C13×#389C2semidirect
3. #11718655C2semidirect
4. #11718653C2semidirect
5. #11718650C2semidirect
7. #11718590C2semidirect
9. #11718318C2semidirect
43. C2×D52Q8semidirect
49. C2×Dic26D4semidirect
106. #389D13semidirect
193. C13#2732semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C13×#3892
#117186552
#117186532
#117186502
#117186002
#117185902
#117183262
#117183182
#273213