Finite Group Databasebeta

← #13125865

Subgroups — #13125865

Order 1664.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719184C211yesmaximal, characteristic
2C2×#88123C211yesmaximal, characteristic, complemented
3C13×#432C211yesmaximal, characteristic, complemented
4#11718510C212yesmaximal, complemented
5#11718502C212yesmaximal, complemented
6#11718400C212yesmaximal, complemented
7#11718399C212yesmaximal
8#11718376C212yesmaximal, complemented
9#11718364C212yesmaximal, complemented
10C22×Dic26C2212yes—
11C2×C42×C13C2211yescharacteristic
12#88184C2211yescharacteristic
13#88183—21no—
14C4×C22⋊D13—21no—
15C2×C4⋊Dic13—21no—
16C2×C4⋊Dic13—21no—
17#88178C2211yescharacteristic
18C2×Dic52C2214yes—
19C2×#6095C2214yes—
20#88130—21no—
21#88129C2211yescharacteristic
22C4×D52C2211yescharacteristic
23#88126—21no—
24#88124C2211yescharacteristic
25#88123—21no—
26#88123—21no—
27#88123C2212yes—
28#88123C2212yes—
29C4×Dic26C2211yescharacteristic
30C13×C4⋊C8C2212yes—
31C13×C22⋊C8C2212yes—
32C13×#97C2212yes—
33#88056C2214yes—
34#88056C2214yes—
35C22×C4×C13D411yescharacteristic
36C22×C4×C13D411yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—21no—
39C22×Dic13—22no—
40C2×D52C2311yescharacteristic
41C2×C4×D13—21no—
42C2×Dic26—22no—
43C2×Dic26—44no—
44C2×Dic26C2311yescharacteristic
45C2×Dic26C2314yes—
46C2×C8×C13C2314yes—
47C42×C13D411yescharacteristic
48C42×C13D411yescharacteristic
49C42×C13C2311yescharacteristic
50C42×C13C2311yescharacteristic
51C22⋊Dic13—21no—
52#6103—21no—
53#6103—21no—
54#6103—21no—
55#6103—21no—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13C2311yescharacteristic
61C4⋊Dic13C2311yescharacteristic
62#6101—21no—
63#6101—21no—
64#6101—21no—
65#6101—21no—
66C4×Dic13—21no—
67Dic52—44no—
68#6095—44no—
69#3218—131nomaximal, Sylow
70C23×C13C2×D411yescharacteristic
71C22×D13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C22⋊D13—42no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—24no—
86C2×Dic13—44no—
87D52—22no—
88C4×D13—42no—
89Dic26—24no—
90Dic26—22no—
91Dic26—24no—
92Dic26—44no—
93C8×C13—24no—
94C2×C4⋊Q8—131no—
95#529—131no—
96#497—132no—
97#491—132no—
98#462—132no—
99#461—132no—
100#451—132no—
101#448—132no—
102#432D1311yescharacteristic, complemented
103C22×C13—21no—
104C22×C13—21no—
105C22×C13#13712yes—
106C22×C13C22×D411yescharacteristic
107C2×D13—41no—
108C2×D13—41no—
109C2×D13—41no—
110C4×C13—21no—
111C4×C13—21no—
112C4×C13—21no—
113C4×C13—21no—
114C4×C13#13712yes—
115C4×C13H(5,𝔽2)12yes—
116Dic13—44no—
117Dic13—41no—
118Dic13—41no—
119Dic13—41no—
120C22×Q8—132no—
121C2×Q16—134no—
122C2×SD16—134no—
123C4⋊Q8—132no—
124C4⋊Q8—132no—
125C4⋊Q8—261no—
126C4⋊Q8—261no—
127#126—261no—
128#125—131no—
129#124—131no—
130#123—261no—
131C22⋊Q8—131no—
132#121—131no—
133C4×Q8—131no—
134C4×D4—131no—
135C4×D4—261no—
136#117—261no—
137C2×C4⋊C4—261no—
138C2×C4⋊C4—261no—
139C2×C42C2×D1311yescharacteristic
140C4⋊C8C2×D1312yes—
141#103—134no—
142#103—134no—
143C22⋊C8C2×D1312yes—
144#97C2×D1312yes—
145C2×C13—22no—
146C2×C13#53511yescharacteristic
147C2×C13C2×#13711yescharacteristic
148C2×C13C2×#13711yescharacteristic
149D13—81no—
150C2×Q8—134no—
151C2×Q8—131no—
152C2×Q8—262no—
153C2×Q8—524no—
154C2×D4—131no—
155C2×D4—261no—
156C22×C4—262no—
157C22×C4—261no—
158C22×C4D5211yescharacteristic
159C22×C4D5211yescharacteristic
160C22×C4C22×D1311yescharacteristic
161Q16—524no—
162SD16—524no—
163C2×C8C22×D1314yes—
164C4⋊C4—131no—
165C4⋊C4—131no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—261no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C4⋊C4—261no—
174C22⋊C4—261no—
175C22⋊C4—261no—
176C22⋊C4—261no—
177C22⋊C4—261no—
178C22⋊C4—261no—
179C42—261no—
180C42D5211yescharacteristic
181C42D5211yescharacteristic
182C42C22×D1311yescharacteristic
183C42C22×D1311yescharacteristic
184C13#321811yescharacteristic, complemented, Sylow
185C23—261no—
186C23C2×D5211yescharacteristic
187Q8—264no—
188Q8—262no—
189Q8—264no—
190Q8—524no—
191D4—262no—
192D4—522no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—264no—
200C2×C4—524no—
201C2×C4—522no—
202C2×C4C2×D5211yescharacteristic
203C2×C4C2×D5211yescharacteristic
204C2×C4C2×D5211yescharacteristic
205C2×C4C2×D5211yescharacteristic
206C2×C4C2×D5211yescharacteristic
207C2×C4C23×D1311yescharacteristic
208C8—24no—
209C22—21no—
210C22—21no—
211C22—521no—
212C22—521no—
213C22—521no—
214C22#8816312yes—
215C22C22×D5211yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—521no—
221C4—521no—
222C4—524no—
223C4—521no—
224C4#8816312yes—
225C4#8825612yes—
226C2—22no—
227C2—1041no—
228C2#1171923011yescharacteristic
229C2C2×#8816311yescharacteristic
230C2C2×#8816311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#432C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#432D13
hypocenterC13#3218
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#88123C2semidirect
3. C13×#432C2semidirect
4. #11718510C2semidirect
5. #11718502C2semidirect
6. #11718400C2semidirect
8. #11718376C2semidirect
9. #11718364C2semidirect
102. #432D13semidirect
184. C13#3218semidirect

Maximal subgroups

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

subgroupindex
#117191842
C2×#881232
C13×#4322
#117185102
#117185022
#117184002
#117183992
#117183762
#117183642
#321813