Finite Group Databasebeta

← #13125861

Subgroups — #13125861

Order 1664.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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×#88198C211yesmaximal, characteristic, complemented
2#11719305C211yesmaximal, characteristic
3C13×#448C211yesmaximal, characteristic
4#11718889C211yesmaximal, characteristic, complemented
5#11718828C212yesmaximal, complemented
6#11718823C212yesmaximal, complemented
7#11718701C211yesmaximal, characteristic
8#11718458C212yesmaximal, complemented
9#11718454C212yesmaximal, complemented
10#11718400C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×SD16C2212yes—
15C13×#121C2211yescharacteristic
16#88198—21no—
17#88198—21no—
18#88198C2212yes—
19#88198C2212yes—
20C2×#6107C2212yes—
21#88190C2211yescharacteristic
22#88189—21no—
23D4×Dic13—21no—
24D4×Dic13C2211yescharacteristic
25C2×#6105C2212yes—
26#88178C2211yescharacteristic
27C2×#6101—21no—
28C2×#6101—21no—
29C2×C4×Dic13C2211yescharacteristic
30C2×Dic52C2212yes—
31#88144C2211yescharacteristic
32#88141C2211yescharacteristic
33#88133—21no—
34#88131—21no—
35C13×#103C2212yes—
36C13×C22⋊C8C2211yescharacteristic
37#88075C2212yes—
38C22⋊#1055C2211yescharacteristic
39#88056C2212yes—
40#88055C2212yes—
41#88054C2212yes—
42#88050C2212yes—
43C2×Q8×C13—21no—
44C2×Q8×C13—42no—
45C2×Q8×C13C2312yes—
46C2×D4×C13—21no—
47C2×D4×C13C2311yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13D411yescharacteristic
53C22×Dic13D411yescharacteristic
54C2×Dic26—21no—
55C2×Dic26—42no—
56C2×Dic26C2311yescharacteristic
57C2×Dic26C2312yes—
58C13×SD16—42no—
59C2×C8×C13C2312yes—
60C13×C4⋊C4C2311yescharacteristic
61C13×C22⋊C4—21no—
62C22⋊Dic13—21no—
63C22⋊Dic13—21no—
64C22⋊Dic13—21no—
65C22⋊Dic13—21no—
66#6107—42no—
67#6105—42no—
68C4⋊Dic13—21no—
69C4⋊Dic13C2311yescharacteristic
70#6101—21no—
71#6101—21no—
72#6101—21no—
73#6101—22no—
74#6101—22no—
75#6101—22no—
76#6101—22no—
77C4×Dic13—21no—
78C4×Dic13D411yescharacteristic
79C4×Dic13D411yescharacteristic
80C4×Dic13C2311yescharacteristic
81C4×Dic13C2311yescharacteristic
82C2×#1055C2312yes—
83Dic52—42no—
84#3218—131nomaximal, Sylow
85C23×C13—21no—
86C23×C13C2×D411yescharacteristic
87Q8×C13—22no—
88Q8×C13—22no—
89Q8×C13—42no—
90D4×C13—22no—
91D4×C13—42no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—21no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13C2×D411yescharacteristic
106C2×Dic13C2×D411yescharacteristic
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109Dic26—22no—
110Dic26—22no—
111Dic26—22no—
112Dic26—42no—
113C8×C13—22no—
114#1055—22no—
115C2×C4⋊Q8—131no—
116#529—131no—
117#497—132no—
118#491—132no—
119#462—132no—
120#461—132no—
121#451—131no—
122#451—131no—
123#448—131no—
124#448D1311yescharacteristic
125#432—131no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13#13712yes—
132C22×C13C22×D411yescharacteristic
133C4×C13—21no—
134C4×C13—42no—
135C4×C13—41no—
136C4×C13H(5,𝔽2)12yes—
137Dic13—21no—
138Dic13—21no—
139Dic13—21no—
140Dic13—42no—
141Dic13—41no—
142Dic13—41no—
143Dic13#13712yes—
144C22×Q8—131no—
145C22×Q8C2×D1311yescharacteristic
146C2×Q16—132no—
147C2×Q16—132no—
148C2×SD16—132no—
149C2×SD16C2×D1312yes—
150C4⋊Q8—132no—
151C4⋊Q8—132no—
152C4⋊Q8—261no—
153C4⋊Q8—261no—
154#126—261no—
155#125—131no—
156#124—131no—
157#123—261no—
158C22⋊Q8—131no—
159#121C2×D1311yescharacteristic
160C4×Q8—131no—
161C4×D4—131no—
162C4×D4—261no—
163#117—261no—
164C2×C4⋊C4—261no—
165C2×C4⋊C4—261no—
166C2×C42—131no—
167C4⋊C8—132no—
168#103—132no—
169#103—132no—
170#103—132no—
171#103C2×D1312yes—
172C22⋊C8—131no—
173C22⋊C8C2×D1311yescharacteristic
174#97—132no—
175C2×C13—22no—
176C2×C13—81no—
177C2×C13#53511yescharacteristic
178C2×C13C2×#13711yescharacteristic
179C2×C13C2×#13711yescharacteristic
180C2×Q8—21no—
181C2×Q8—42no—
182C2×Q8—132no—
183C2×Q8—131no—
184C2×Q8—261no—
185C2×Q8—522no—
186C2×Q8C22×D1312yes—
187C2×D4—21no—
188C2×D4C22×D1311yescharacteristic
189C22×C4—21no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—261no—
193C22×C4—261no—
194C22×C4C22×D1311yescharacteristic
195Q16—522no—
196Q16—522no—
197SD16—42no—
198SD16—522no—
199C2×C8—132no—
200C2×C8C22×D1312yes—
201C4⋊C4—131no—
202C4⋊C4—262no—
203C4⋊C4—262no—
204C4⋊C4—262no—
205C4⋊C4—262no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4—261no—
209C4⋊C4—261no—
210C4⋊C4C22×D1311yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—261no—
213C22⋊C4—261no—
214C22⋊C4—261no—
215C22⋊C4—261no—
216C42—131no—
217C42—131no—
218C42—131no—
219C42—131no—
220C42—261no—
221C13#321811yescharacteristic, complemented, Sylow
222C23—21no—
223C23D4×D1311yescharacteristic
224Q8—22no—
225Q8—22no—
226Q8—42no—
227Q8—262no—
228Q8—262no—
229Q8—262no—
230Q8—522no—
231D4—22no—
232D4—42no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—131no—
238C2×C4—131no—
239C2×C4—131no—
240C2×C4—131no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—262no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4D4×D1311yescharacteristic
249C2×C4C23×D1311yescharacteristic
250C8—22no—
251C8—262no—
252C22—21no—
253C22—21no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22#8816912yes—
258C22C2×D4×D1311yescharacteristic
259C4—21no—
260C4—41no—
261C4—42no—
262C4—132no—
263C4—261no—
264C4—261no—
265C4—261no—
266C4—521no—
267C4—522no—
268C4—521no—
269C4#8825112yes—
270C2—22no—
271C2—81no—
272C2#1171929711yescharacteristic
273C2C2×#8816911yescharacteristic
274C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#448C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#448D13
hypocenterC13#3218
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#88198C2semidirect
4. #11718889C2semidirect
5. #11718828C2semidirect
6. #11718823C2semidirect
8. #11718458C2semidirect
9. #11718454C2semidirect
10. #11718400C2semidirect
11. #11718380C2semidirect
221. C13#3218semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
#117193052
C13×#4482
#117188892
#117188282
#117188232
#117187012
#117184582
#117184542
#117184002
#117183802
#321813