Finite Group Databasebeta

← #13121601

Subgroups — #13121601

Order 1664.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88190C212yesmaximal, complemented
2C13×#392C211yesmaximal, characteristic
3#11718883C212yesmaximal, complemented
4#11718881C212yesmaximal, complemented
5#11718614C211yesmaximal, characteristic, complemented
6#11718612C212yesmaximal, complemented
7#11718608C212yesmaximal, complemented
8#11718607C211yesmaximal, characteristic, complemented
9#11718307C212yesmaximal, complemented
10C22×D4×C13C2212yes—
11C22×D4×C13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C22×Dic26C2212yes—
14C2×C13×C22⋊C4C2212yes—
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2211yescharacteristic
22#88190—28no—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2212yes—
25C2×C4×Dic13C2212yes—
26C13×#95C2211yescharacteristic
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2211yescharacteristic
32C24×C13C2312yes—
33C24×C13C2311yescharacteristic
34C2×D4×C13—24no—
35C2×D4×C13—24no—
36C2×D4×C13—42no—
37C2×D4×C13—42no—
38C2×D4×C13—41no—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×Dic13—42no—
43C22×Dic13—41no—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2312yes—
48C2×Dic26—24no—
49C2×Dic26—24no—
50C2×Dic26—42no—
51C13×C22⋊C4—24no—
52C13×C22⋊C4—41no—
53C22⋊Dic13—24no—
54C22⋊Dic13—24no—
55C22⋊Dic13—24no—
56C22⋊Dic13—42no—
57C22⋊Dic13—42no—
58C22⋊Dic13D414yescomplemented
59C4⋊Dic13—41no—
60#6101—42no—
61C4×Dic13—24no—
62#2712—131nomaximal, Sylow
63C23×C13—22no—
64C23×C13—21no—
65C23×C13—22no—
66C23×C13—21no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13C2×D412yes—
75C23×C13C2411yescharacteristic
76D4×C13—48no—
77D4×C13—44no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13#4114yes—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
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×Dic13—44no—
97C2×Dic13C2×D414yes—
98Dic26—48no—
99C2×#124—132no—
100#397—131no—
101#394—132no—
102#393—132no—
103#392D1311yescharacteristic
104#391—132no—
105#388—132no—
106#386—132no—
107#385—131no—
108C22×C13—22no—
109C22×C13—24no—
110C22×C13—42no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13—42no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13C22×D411yescharacteristic
121C22×C13C2×#4112yes—
122C22×C13H(5,𝔽2)11yescharacteristic
123C22×C13H(5,𝔽2)12yes—
124C22×C132−1+411yescharacteristic
125C4×C13—24no—
126C4×C13—41no—
127C4×C13—41no—
128Dic13—24no—
129Dic13—42no—
130Dic13—42no—
131Dic13—42no—
132C22×Q8—132no—
133C22×D4C2×D1312yes—
134C22×D4C2×D1311yescharacteristic
135C23×C4—131no—
136#124—268no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—131no—
139C2×C22⋊C4—131no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—132no—
142C2×C22⋊C4—132no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4C2×D1312yes—
146C2×C22⋊C4C2×D1311yescharacteristic
147C2×C42—132no—
148#95—132no—
149#95—132no—
150#95—132no—
151#95—132no—
152#95—131no—
153#95C2×D1311yescharacteristic
154C2×C13—42no—
155C2×C13—82no—
156C2×C13#53711yescharacteristic
157C2×C13#54212yes—
158C2×C13#54612yes—
159C2×C13#55911yescharacteristic
160C2×C13H(3,𝔽4)11yescharacteristic
161C24C22×D1312yes—
162C24C22×D1311yescharacteristic
163C2×Q8—264no—
164C2×Q8—264no—
165C2×Q8—522no—
166C2×D4—24no—
167C2×D4—24no—
168C2×D4—42no—
169C2×D4—41no—
170C2×D4—42no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4—132no—
175C22×C4—521no—
176C22×C4—522no—
177C22×C4C22×D1311yescharacteristic
178C22×C4C22×D1311yescharacteristic
179C22×C4C22×D1312yes—
180C4⋊C4—522no—
181C4⋊C4—521no—
182C22⋊C4—24no—
183C22⋊C4—41no—
184C22⋊C4—134no—
185C22⋊C4—264no—
186C22⋊C4—264no—
187C22⋊C4—264no—
188C22⋊C4—522no—
189C22⋊C4—522no—
190C42—264no—
191C13#271211yescharacteristic, complemented, Sylow
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23D4×D1312yes—
204C23C23×D1311yescharacteristic
205Q8—528no—
206D4—48no—
207D4—44no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—134no—
215C2×C4—262no—
216C2×C4—262no—
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—262no—
226C2×C4—524no—
227C2×C4#612914yes—
228C22—24no—
229C22—22no—
230C22—41no—
231C22—42no—
232C22—41no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22C2×D4×D1311yescharacteristic
241C22C2×#612912yes—
242C22#8825112yes—
243C22#8825111yescharacteristic
244C22#8825711yescharacteristic
245C4—24no—
246C4—41no—
247C4—41no—
248C4—264no—
249C4—522no—
250C4—522no—
251C4—522no—
252C2—42no—
253C2—82no—
254C2#1171929612yes—
255C2#1171929911yescharacteristic
256C2#1171930211yescharacteristic
257C2#1171930812yes—
258C2#1171941811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC13×#392C2
hypercenter#392D13
hypocenterC13#2712
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#88190C2semidirect
3. #11718883C2semidirect
4. #11718881C2semidirect
5. #11718614C2semidirect
6. #11718612C2semidirect
7. #11718608C2semidirect
8. #11718607C2semidirect
9. #11718307C2semidirect
58. C22⋊Dic13D4semidirect
191. C13#2712semidirect

Maximal subgroups

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

subgroupindex
C2×#881902
C13×#3922
#117188832
#117188812
#117186142
#117186122
#117186082
#117186072
#117183072
#271213