Finite Group Databasebeta

← #13127149

Subgroups — #13127149

Order 1664.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719435C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic
3C13×#476C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic, complemented
6#11718529C212yesmaximal, complemented
7#11718523C212yesmaximal, complemented
8#11718510C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718444C212yesmaximal, complemented
11#11718432C212yesmaximal, complemented
12C2×#6129C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15#88200—22no—
16C2×#6105C2211yescharacteristic
17#88184—21no—
18C2×C4⋊Dic13—21no—
19C2×Dic52C2212yes—
20C2×#6094C2212yes—
21#88151C2212yes—
22#88151C2212yes—
23#88147—21no—
24C4⋊C4×D13C2212yes—
25#88144—21no—
26#88140—22no—
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×#106C2212yes—
31C13×C4⋊C8C2211yescharacteristic
32C13×#102C2212yes—
33#88072C2211yescharacteristic
34#88060C2212yes—
35#88056C2212yes—
36#88050C2211yescharacteristic
37#88050C2212yes—
38#88050C2212yes—
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×C22⋊D13—22no—
45C22×Dic13—22no—
46#6129—24no—
47#6129—42no—
48C2×D52D411yescharacteristic
49C2×C4×D13—22no—
50C2×C4×D13C2312yes—
51C2×Dic26C2311yescharacteristic
52C2×Dic26C2312yes—
53C2×C8×C13C2312yes—
54C13×C4⋊C4—21no—
55C13×C4⋊C4C2312yes—
56C13×C4⋊C4C2311yescharacteristic
57C13×C22⋊C4—21no—
58C42×C13C2311yescharacteristic
59#6105—22no—
60#6103—22no—
61#6103—22no—
62#6103D412yes—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4⋊Dic13—22no—
67C4⋊Dic13D411yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69#6101—21no—
70#6101—22no—
71C4×Dic13—21no—
72C2×#1055C2311yescharacteristic
73C2×#1055C2311yescharacteristic
74Dic52—42no—
75#6094—42no—
76#3331—131nomaximal, Sylow
77C23×C13—21no—
78C22×D13C2×D412yes—
79Q8×C13—81no—
80D4×C13—21no—
81D4×C13#4112yes—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C22⋊D13—44no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—44no—
93C2×Dic13C2×D412yes—
94D52—22no—
95C4×D13—22no—
96C4×D13—22no—
97C4×D13—82no—
98Dic26—21no—
99Dic26—22no—
100Dic26—21no—
101Dic26—22no—
102C8×C13—22no—
103#1055—21no—
104#1055—21no—
105#554—131no—
106#547—131no—
107#487—131no—
108#483—132no—
109#476D1311yescharacteristic, complemented
110#470—132no—
111#462—131no—
112#452—132no—
113C4×SD16—131no—
114#436—131no—
115#417—132no—
116C22×C13—22no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13C22×D411yescharacteristic
120C2×D13—22no—
121C2×D13—22no—
122C2×D13—22no—
123C4×C13—21no—
124C4×C13—41no—
125C4×C13—42no—
126C4×C13#13712yes—
127C4×C13C2×#4111yescharacteristic
128C4×C13H(5,𝔽2)11yescharacteristic
129Dic13—22no—
130Dic13—41no—
131Dic13—42no—
132Dic13—41no—
133C2×#41—132no—
134C2×Q16—132no—
135C2×SD16—131no—
136C2×M16—132no—
137C4⋊Q8—131no—
138C4⋊Q8C2×D1311yescharacteristic
139#125—261no—
140#123—262no—
141C22⋊Q8—132no—
142C22⋊Q8—132no—
143C22⋊Q8—262no—
144#121—261no—
145C4×Q8—131no—
146C4×D4—131no—
147C4×D4—261no—
148C4×D4C2×D1311yescharacteristic
149C2×C4⋊C4—132no—
150C2×C4⋊C4—261no—
151#106—131no—
152#106C2×D1312yes—
153C4⋊C8C2×D1311yescharacteristic
154#103—132no—
155#103—132no—
156#103—131no—
157#103—132no—
158#102—131no—
159#102C2×D1312yes—
160C22⋊C8—132no—
161C4×C8—131no—
162C2×C13—42no—
163C2×C13#54611yescharacteristic
164C2×C13C2×#13711yescharacteristic
165C2×C13#57711yescharacteristic
166D13—42no—
167#41—264no—
168#41—522no—
169C2×Q8—21no—
170C2×Q8—132no—
171C2×Q8—131no—
172C2×D4—131no—
173C2×D4—262no—
174C2×D4C22×D1311yescharacteristic
175C22×C4—21no—
176C22×C4—132no—
177C22×C4—262no—
178C22×C4—262no—
179Q16—522no—
180SD16—262no—
181M16—522no—
182C2×C8—131no—
183C2×C8—131no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—131no—
187C4⋊C4—131no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4C22×D1312yes—
195C4⋊C4C22×D1311yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—132no—
198C22⋊C4—262no—
199C22⋊C4—262no—
200C42—261no—
201C42C22×D1311yescharacteristic
202C13#333111yescharacteristic, complemented, Sylow
203C23—21no—
204C23—132no—
205Q8—81no—
206Q8—261no—
207Q8—262no—
208Q8—261no—
209Q8—262no—
210D4—21no—
211D4—262no—
212D4—524no—
213D4#613112yes—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—132no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—262no—
223C2×C4—524no—
224C2×C4—1042no—
225C2×C4D4×D1311yescharacteristic
226C2×C4D4×D1311yescharacteristic
227C2×C4C23×D1311yescharacteristic
228C8—22no—
229C8—261no—
230C8—261no—
231C22—22no—
232C22—41no—
233C22—41no—
234C22—262no—
235C22—262no—
236C22—262no—
237C22C2×D4×D1311yescharacteristic
238C4—21no—
239C4—41no—
240C4—42no—
241C4—262no—
242C4—521no—
243C4—522no—
244C4—521no—
245C4#8816912yes—
246C4C2×#613111yescharacteristic
247C4#8825611yescharacteristic
248C2—42no—
249C2—522no—
250C2#1171933511yescharacteristic
251C2C2×#8816911yescharacteristic
252C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#476C2
socleC22×C13C22×D4
prime radical#11719260C2
hypercenter#476D13
hypocenterC13#3331
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
3. C13×#476C2semidirect
4. #11718754C2semidirect
5. C4×#6105C2semidirect
6. #11718529C2semidirect
7. #11718523C2semidirect
8. #11718510C2semidirect
9. #11718499C2semidirect
10. #11718444C2semidirect
11. #11718432C2semidirect
109. #476D13semidirect
202. C13#3331semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117192602
C13×#4762
#117187542
C4×#61052
#117185292
#117185232
#117185102
#117184992
#117184442
#117184322
#333113