Finite Group Databasebeta

← #13130821

Subgroups — #13130821

Order 1664.

404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×C4⋊#261C211yesmaximal, characteristic
2D13×C22⋊Q8C211yesmaximal, characteristic
3C2×#88117C212yesmaximal, complemented
4D13⋊(C22⋊C8)C211yesmaximal, characteristic
5#11718246C212yesmaximal, complemented
6C23×#261—21no—
7C2×Q8×D13C2211yescharacteristic
8C22×C4×D13C2211yescharacteristic
9C2×C4⋊#261—21no—
10C2×C4⋊#261—24no—
11C2×C4⋊#261C2212yes—
12C2×D13⋊C8C2212yes—
13C13×C22⋊Q8C411yescharacteristic, complemented
14#88200C411yescharacteristic, complemented
15#88178C411yescharacteristic, complemented
16#88151C411yescharacteristic, complemented
17#88150—21no—
18C4⋊C4×D13—21no—
19C4⋊C4×D13C2211yescharacteristic
20C22⋊C4×D13—21no—
21#88132—21no—
22C22⋊#1057—21no—
23#88117—24no—
24#88111—21no—
25C23×D13D411yescharacteristic
26C22×#261—24no—
27C22×#261—22no—
28C22×#261—42no—
29C22×#261—42no—
30C2×Q8×C13C2×C411yescharacteristic, complemented
31C22×C4×C13C2×C411yescharacteristic
32C22×Dic13D411yescharacteristic
33Q8×D13—22no—
34Q8×D13—22no—
35C2×C4×D13—22no—
36C2×C4×D13—22no—
37C2×C4×D13—21no—
38C2×C4×D13—21no—
39C2×C4×D13C2×C411yescharacteristic
40C2×C4×D13D411yescharacteristic
41C2×C4×D13D411yescharacteristic
42C2×C4×D13C2311yescharacteristic
43C2×Dic26—21no—
44C2×Dic26C2×C411yescharacteristic, complemented
45C2×#1057—22no—
46C4⋊#261—24no—
47C4⋊#261—22no—
48C4⋊#261D414yes—
49D13⋊C8—22no—
50D13⋊C8—22no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2×C411yescharacteristic, complemented
53C13×C22⋊C4—21no—
54C22⋊Dic13—21no—
55#6103—21no—
56#6103—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13C2×C411yescharacteristic, complemented
59#6101—21no—
60#6101—21no—
61#6101—21no—
62#1872—131nomaximal, Sylow
63C23×C13C22⋊C411yescharacteristic
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—21no—
68C22×D13C22⋊C411yescharacteristic
69C22×D13SD1612yes—
70C22×D13Q1612yes—
71C22×D13C2×D411yescharacteristic
72C2×#261—24no—
73C2×#261—48no—
74C2×#261—42no—
75C2×#261—42no—
76Q8×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13C22⋊C411yescharacteristic
81C2×C4×C13C22×C411yescharacteristic
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13C22⋊C411yescharacteristic
86C2×Dic13C2×D411yescharacteristic
87C4×D13—21no—
88C4×D13—21no—
89C4×D13—22no—
90C4×D13—22no—
91C4×D13—41no—
92C4×D13—41no—
93C4×D13—41no—
94C4×D13—41no—
95C4×D13C2×D412yes—
96C4×D13#4112yes—
97Dic26—22no—
98Dic26—42no—
99#1057—42no—
100C2×C22⋊Q8—131no—
101C22×C4⋊C4—131no—
102C2×#103—132no—
103C2×C22⋊C8—131no—
104#340—132no—
105C22×C13—21no—
106C22×C13—21no—
107C22×C13#10312yescomplemented
108C22×C13C2×C22⋊C411yescharacteristic
109C2×D13—21no—
110C2×D13—21no—
111C2×D13—22no—
112C2×D13—22no—
113C2×D13—22no—
114C2×D13—22no—
115C2×D13#10312yescomplemented
116C2×D13#12011yescharacteristic
117C2×D13#12311yescharacteristic
118C2×D13C2×SD1611yescharacteristic
119C2×D13C2×Q1611yescharacteristic
120C2×D13AGL(1,ℤ/8)11yescharacteristic
121C2×D13#13711yescharacteristic
122#261—44no—
123C4×C13—21no—
124C4×C13—41no—
125C4×C13—41no—
126C4×C13C4×D412yes—
127Dic13—21no—
128Dic13—41no—
129Dic13—41no—
130Dic13#12112yes—
131C22×Q8—131no—
132C23×C4—131no—
133C23×C4—261no—
134C22×C8—132no—
135C22⋊Q8—131no—
136C22⋊Q8—131no—
137C22⋊Q8—131no—
138C22⋊Q8—261no—
139C22⋊Q8—261no—
140C22⋊Q8#26111yescharacteristic, complemented
141C2×C4⋊C4—132no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—261no—
144C2×C4⋊C4—264no—
145C2×C4⋊C4—261no—
146C2×C22⋊C4—261no—
147#103—264no—
148C22⋊C8—261no—
149C22⋊C8—261no—
150C2×C13—22no—
151C2×C13#38611yescharacteristic
152C2×C13C2×#10311yescharacteristic
153C2×C13#41711yescharacteristic
154D13—22no—
155D13#45011yescharacteristic
156D13#45111yescharacteristic
157D13#48311yescharacteristic
158D13#48411yescharacteristic
159C24—131no—
160C2×Q8—131no—
161C2×Q8—261no—
162C2×Q8—262no—
163C2×Q8—262no—
164C2×Q8C2×#26111yescharacteristic, complemented
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—262no—
171C22×C4—262no—
172C22×C4—261no—
173C22×C4—261no—
174C22×C4—262no—
175C22×C4—264no—
176C22×C4—522no—
177C22×C4—522no—
178C22×C4C2×#26111yescharacteristic
179C2×C8—262no—
180C2×C8—262no—
181C2×C8—262no—
182C4⋊C4—21no—
183C4⋊C4—134no—
184C4⋊C4—131no—
185C4⋊C4—261no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C4⋊C4—262no—
189C4⋊C4—264no—
190C4⋊C4—261no—
191C4⋊C4C2×#26111yescharacteristic, complemented
192C22⋊C4—21no—
193C22⋊C4—261no—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C13#187211yescharacteristic, complemented, Sylow
197C23—131no—
198C23—132no—
199C23—132no—
200C23—131no—
201C23—261no—
202C23—261no—
203C23—261no—
204C23—261no—
205C23C22⋊#26111yescharacteristic
206Q8—22no—
207Q8—262no—
208Q8—522no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—131no—
213C2×C4—132no—
214C2×C4—132no—
215C2×C4—131no—
216C2×C4—262no—
217C2×C4—261no—
218C2×C4—261no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—264no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—521no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—521no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4—528no—
231C2×C4C22⋊#26111yescharacteristic
232C2×C4C22×#26111yescharacteristic
233C8—522no—
234C22—21no—
235C22—21no—
236C22—131no—
237C22—131no—
238C22—131no—
239C22—131no—
240C22—131no—
241C22—131no—
242C22—132no—
243C22—262no—
244C22—262no—
245C22—262no—
246C22—262no—
247C22—261no—
248C22—261no—
249C22#8811712yescomplemented
250C22C2×C22⋊#26111yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—132no—
255C4—261no—
256C4—524no—
257C4—521no—
258C4—521no—
259C4D4×#26112yes—
260C2—22no—
261C2—131no—
262C2—131no—
263C2—131no—
264C2—131no—
265C2—262no—
266C2#1171915011yescharacteristic
267C2C2×#8811711yescharacteristic
268C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC22⋊Q8#261
hypocenterC13#1872
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#88117C2semidirect
5. #11718246C2semidirect
13. C13×C22⋊Q8C4semidirect
14. #88200C4semidirect
15. #88178C4semidirect
16. #88151C4semidirect
30. C2×Q8×C13C2×C4semidirect
44. C2×Dic26C2×C4semidirect
52. C13×C4⋊C4C2×C4semidirect
58. C4⋊Dic13C2×C4semidirect
107. C22×C13#103semidirect
115. C2×D13#103semidirect
140. C22⋊Q8#261semidirect
164. C2×Q8C2×#261semidirect
191. C4⋊C4C2×#261semidirect
196. C13#1872semidirect
249. C22#88117semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#2612
D13×C22⋊Q82
C2×#881172
D13⋊(C22⋊C8)2
#117182462
#187213