Finite Group Databasebeta

← #13127823

Subgroups — #13127823

Order 1664.

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

normal subgroups only

This group has 360 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#11719437C211yesmaximal, characteristic, complemented
2#11719247C211yesmaximal, characteristic, complemented
3C13×#461C211yesmaximal, characteristic, complemented
4#11718829C212yesmaximal
5#11718827C212yesmaximal, complemented
6#11718753C211yesmaximal, characteristic, complemented
7C4×#6104C211yesmaximal, characteristic
8#11718502C211yesmaximal, characteristic, complemented
9#11718491C211yesmaximal, characteristic, complemented
10#11718459C212yesmaximal, complemented
11#11718451C212yesmaximal, complemented
12C2×C13×SD16C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15#88201C2212yes—
16Q8×Dic13C2212yes—
17C2×#6107C2212yes—
18C2×#6107C2212yes—
19#88190C2212yes—
20C2×#6104C2211yescharacteristic
21#88180—21no—
22#88178—21no—
23C2×#6095C2212yes—
24#88152—22no—
25#88151—21no—
26#88146—21no—
27#88141C2212yes—
28#88133—22no—
29C4×D52C2211yescharacteristic
30#88123C2211yescharacteristic
31C4×Dic26C2211yescharacteristic
32C13×C4⋊C8C2211yescharacteristic
33C13×#103C2212yes—
34#88072C2211yescharacteristic
35#88056C2212yes—
36#88054C2212yes—
37C8×Dic13C2212yes—
38#88049C2211yescharacteristic
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×D52C2311yescharacteristic
45C2×C4×D13—21no—
46C2×Dic26D411yescharacteristic
47C2×Dic26C2312yes—
48C13×SD16—42no—
49C2×C8×C13C2312yes—
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2311yescharacteristic
53C13×C22⋊C4—21no—
54C42×C13C2311yescharacteristic
55C22⋊Dic13—22no—
56C22⋊Dic13—22no—
57#6107—24no—
58#6107—42no—
59#6104—22no—
60#6103—21no—
61#6103—22no—
62#6103—22no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68#6101—22no—
69#6101D412yes—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13C2312yes—
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75#6095—42no—
76#3393—131nomaximal, Sylow
77C23×C13—21no—
78C22×D13—21no—
79Q8×C13—22no—
80Q8×C13—22no—
81D4×C13—21no—
82D4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—42no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13C2×D412yes—
92C2×Dic13C2×D412yes—
93D52—21no—
94D52—21no—
95C4×D13—42no—
96Dic26—22no—
97Dic26—22no—
98Dic26—22no—
99C8×C13—22no—
100#1055—21no—
101#1055#4112yes—
102#556—131no—
103#556—131no—
104#495—132no—
105#494—131no—
106#464—132no—
107#464—132no—
108#461—131no—
109#461D1311yescharacteristic, complemented
110C8×Q8—131no—
111C4×Q16—132no—
112C4×D8—131no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13C22×D411yescharacteristic
117C2×D13—41no—
118C2×D13—41no—
119C2×D13—41no—
120C4×C13—21no—
121C4×C13—42no—
122C4×C13—41no—
123C4×C13#13512yes—
124C4×C13C2×#4111yescharacteristic
125C4×C13H(5,𝔽2)11yescharacteristic
126Dic13—22no—
127Dic13—22no—
128Dic13—42no—
129Dic13—41no—
130C2×Q16—132no—
131C2×Q16—132no—
132C2×SD16—132no—
133C2×SD16C2×D1312yes—
134C2×D8—131no—
135C4⋊Q8—131no—
136C4⋊Q8C2×D1311yescharacteristic
137#126—262no—
138#126—262no—
139#124—132no—
140#124—132no—
141C22⋊Q8—261no—
142C22⋊Q8—261no—
143C4×Q8—131no—
144C4×Q8—132no—
145C4×Q8—132no—
146C4×D4—131no—
147C4×D4C2×D1311yescharacteristic
148#117—261no—
149#117—261no—
150#107—131no—
151C4⋊C8—132no—
152C4⋊C8C2×D1311yescharacteristic
153#103—132no—
154#103C2×D1312yes—
155#102—131no—
156#102—131no—
157C4×C8—132no—
158C4×C8—131no—
159C2×C13—81no—
160C2×C13#55011yescharacteristic
161C2×C13C2×#13511yescharacteristic
162C2×C13#57811yescharacteristic
163D13—81no—
164C2×Q8—131no—
165C2×Q8—132no—
166C2×Q8C22×D1312yes—
167C2×D4—131no—
168C2×D4C22×D1311yescharacteristic
169C22×C4—21no—
170C22×C4—261no—
171Q16—264no—
172Q16—522no—
173SD16—42no—
174SD16—522no—
175D8—262no—
176C2×C8—131no—
177C2×C8—131no—
178C2×C8C22×D1312yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—131no—
182C4⋊C4—132no—
183C4⋊C4—131no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C4⋊C4C22×D1311yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—262no—
191C22⋊C4—262no—
192C22⋊C4—262no—
193C22⋊C4—262no—
194C22⋊C4—261no—
195C42—132no—
196C42—262no—
197C42—262no—
198C42C22×D1311yescharacteristic
199C13#339311yescharacteristic, complemented, Sylow
200C23—21no—
201C23—261no—
202Q8—22no—
203Q8—22no—
204Q8—262no—
205Q8—262no—
206Q8—262no—
207D4—21no—
208D4—21no—
209D4—261no—
210D4—261no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—132no—
215C2×C4—132no—
216C2×C4—261no—
217C2×C4—262no—
218C2×C4—522no—
219C2×C4D4×D1311yescharacteristic
220C2×C4D4×D1311yescharacteristic
221C2×C4C23×D1311yescharacteristic
222C8—22no—
223C8—132no—
224C8—261no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—521no—
229C22—521no—
230C22—521no—
231C22C2×D4×D1311yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—262no—
236C4—262no—
237C4—521no—
238C4—522no—
239C4#8817012yes—
240C4#8825111yescharacteristic
241C4#41×D1311yescharacteristic
242C2—81no—
243C2—1041no—
244C2#1171930411yescharacteristic
245C2C2×#8817011yescharacteristic
246C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#461D13
hypocenterC13#3393
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. #11719437C2semidirect
2. #11719247C2semidirect
3. C13×#461C2semidirect
5. #11718827C2semidirect
6. #11718753C2semidirect
8. #11718502C2semidirect
9. #11718491C2semidirect
10. #11718459C2semidirect
11. #11718451C2semidirect
109. #461D13semidirect
199. C13#3393semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117192472
C13×#4612
#117188292
#117188272
#117187532
C4×#61042
#117185022
#117184912
#117184592
#117184512
#339313