Finite Group Databasebeta

← #13126169

Subgroups — #13126169

Order 1664.

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

normal subgroups only

This group has 354 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
1#11719433C211yesmaximal, characteristic, complemented
2#11719262C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic, complemented
4#11718832C212yesmaximal
5#11718827C212yesmaximal, complemented
6#11718751C211yesmaximal, characteristic, complemented
7#11718668C211yesmaximal, characteristic, complemented
8#11718512C211yesmaximal, characteristic, complemented
9D13×C4⋊C8C211yesmaximal, characteristic, complemented
10#11718474C212yesmaximal, complemented
11#11718460C212yesmaximal, complemented
12C2×C13×SD16C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15#88200C2212yes—
16Q8×Dic13C2212yes—
17C2×#6107C2212yes—
18#88192C2211yescharacteristic
19#88190C2211yescharacteristic
20C4×C22⋊D13—21no—
21#88180—21no—
22C2×C8×D13C2212yes—
23#88151—21no—
24#88151C2211yescharacteristic
25#88146—21no—
26#88144—21no—
27#88144C2211yescharacteristic
28#88141—21no—
29#88137—21no—
30#88133—21no—
31C42×D13C2211yescharacteristic
32#88123C2211yescharacteristic
33C4×Dic26C2211yescharacteristic
34C13×C4⋊C8C2211yescharacteristic
35C13×#103C2212yes—
36#88075C2212yes—
37#88072C2212yes—
38#88057C2212yes—
39#88056C2212yes—
40#88054C2212yes—
41#88047C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13C2312yes—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C2×C22⋊D13—21no—
47C2×C4×D13D411yescharacteristic
48C2×C4×D13D411yescharacteristic
49C2×C4×D13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26C2311yescharacteristic
52C13×SD16—42no—
53C2×C8×C13C2312yes—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C13×C22⋊C4—21no—
58C42×C13C2311yescharacteristic
59C22⋊Dic13—21no—
60C22⋊Dic13—21no—
61C22⋊Dic13—21no—
62#6107—42no—
63#6103—21no—
64#6103—22no—
65C4⋊Dic13—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68C4⋊Dic13—22no—
69C4⋊Dic13C2312yes—
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—21no—
73#6101—22no—
74C4×Dic13—21no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80C8×D13—42no—
81#3248—131nomaximal, Sylow
82C23×C13—21no—
83C22×D13C2×D411yescharacteristic
84Q8×C13—22no—
85Q8×C13—22no—
86D4×C13—21no—
87D4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C22⋊D13—42no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13C2×D411yescharacteristic
99C2×Dic13C2×D411yescharacteristic
100C2×Dic13C2×D411yescharacteristic
101C4×D13—22no—
102C4×D13—22no—
103C4×D13—21no—
104C4×D13—21no—
105Dic26—21no—
106Dic26—21no—
107Dic26—42no—
108C8×C13—22no—
109#1055—22no—
110#533—131no—
111#529—131no—
112#479—132no—
113#475—131no—
114#474—131no—
115#467—132no—
116#465—132no—
117#464—132no—
118#462—131no—
119#461D1311yescharacteristic, complemented
120C2×C4⋊C8—131no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13C22×D411yescharacteristic
125C2×D13—21no—
126C2×D13—21no—
127C2×D13#13712yes—
128C4×C13—21no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13#13512yes—
132C4×C13H(5,𝔽2)11yescharacteristic
133C4×C132−1+411yescharacteristic
134Dic13—21no—
135Dic13—21no—
136Dic13—21no—
137Dic13—41no—
138Dic13—42no—
139Dic13—41no—
140C2×Q16—132no—
141C2×SD16C2×D1312yes—
142C22×C8—132no—
143C4⋊Q8—131no—
144C4⋊Q8C2×D1311yescharacteristic
145#126—261no—
146#125—131no—
147#125—261no—
148#124—131no—
149#123—261no—
150C22⋊Q8—132no—
151C22⋊Q8—131no—
152C22⋊Q8—261no—
153#121—131no—
154C4×Q8—132no—
155C4×Q8—131no—
156C4×Q8—261no—
157C4×D4—261no—
158C4×D4C2×D1311yescharacteristic
159#117—261no—
160#117—261no—
161C2×C42—131no—
162#107—132no—
163#106—132no—
164C4⋊C8—132no—
165C4⋊C8—131no—
166C4⋊C8C2×D1311yescharacteristic
167#103—132no—
168#103—132no—
169#103C2×D1312yes—
170#102—132no—
171C2×C13—81no—
172C2×C13#53711yescharacteristic
173C2×C13C2×#13511yescharacteristic
174C2×C13C2×#13711yescharacteristic
175D13—22no—
176C2×Q8—131no—
177C2×Q8—261no—
178C2×Q8C22×D1312yes—
179C2×D4—261no—
180C2×D4C22×D1311yescharacteristic
181C22×C4—21no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185Q16—522no—
186SD16—42no—
187C2×C8—132no—
188C2×C8—522no—
189C2×C8C22×D1312yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—132no—
193C4⋊C4—131no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—262no—
198C4⋊C4—262no—
199C4⋊C4—261no—
200C4⋊C4—261no—
201C4⋊C4C22×D1311yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—262no—
204C22⋊C4—261no—
205C22⋊C4—261no—
206C22⋊C4—261no—
207C22⋊C4—261no—
208C42—131no—
209C42—131no—
210C42—131no—
211C42—262no—
212C42—261no—
213C42C22×D1311yescharacteristic
214C13#324811yescharacteristic, complemented, Sylow
215C23—21no—
216C23—131no—
217Q8—22no—
218Q8—22no—
219Q8—261no—
220Q8—261no—
221Q8—522no—
222D4—21no—
223D4—21no—
224D4—522no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—131no—
229C2×C4—131no—
230C2×C4—131no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—262no—
238C2×C4D4×D1311yescharacteristic
239C2×C4D4×D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—22no—
242C8—262no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—132no—
247C22—261no—
248C22—261no—
249C22C2×D4×D1311yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—261no—
254C4—261no—
255C4—261no—
256C4—522no—
257C4—521no—
258C4—521no—
259C4#8817012yes—
260C4#8825111yescharacteristic
261C4#8825711yescharacteristic
262C2—81no—
263C2—262no—
264C2#1171931311yescharacteristic
265C2C2×#8817011yescharacteristic
266C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#461D13
hypocenterC13#3248
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#461C2semidirect
5. #11718827C2semidirect
6. #11718751C2semidirect
7. #11718668C2semidirect
8. #11718512C2semidirect
9. D13×C4⋊C8C2semidirect
10. #11718474C2semidirect
11. #11718460C2semidirect
119. #461D13semidirect
214. C13#3248semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117192622
C13×#4612
#117188322
#117188272
#117187512
#117186682
#117185122
D13×C4⋊C82
#117184742
#117184602
#324813