Finite Group Databasebeta

← #13126036

Subgroups — #13126036

Order 1664.

366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 121 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#11719182C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3C13×#432C211yesmaximal, characteristic, complemented
4#11718507C212yesmaximal, complemented
5#11718503C212yesmaximal, complemented
6#11718398C214yesmaximal, complemented
7#11718374C212yesmaximal, complemented
8#11718363C212yesmaximal, complemented
9C2×#6127—21no—
10C2×C42×C13C2211yescharacteristic
11#88184—21no—
12#88184C2212yes—
13#88180C2212yes—
14#88178—21no—
15#88178—21no—
16#88129—21no—
17#88128C2211yescharacteristic
18C4×D52—21no—
19C4×D52C2212yes—
20#88124C2212yes—
21#88123C2211yescharacteristic
22#88123C2211yescharacteristic
23#88123C2211yescharacteristic
24C4×Dic26—21no—
25C4×Dic26—21no—
26C13×C4⋊C8C2212yes—
27C13×C22⋊C8C2212yes—
28C13×#97C2212yes—
29#88061C2214yes—
30#88061C2214yes—
31#88058C2214yes—
32#88057C2214yes—
33C22×C4×C13D411yescharacteristic
34C22×C4×C13D411yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C2×C22⋊D13—22no—
37#6127—44no—
38C2×D52—21no—
39C2×D52—21no—
40C2×D52C2312yes—
41C2×C4×D13—22no—
42C2×Dic26—21no—
43C2×Dic26—21no—
44C2×Dic26—21no—
45C2×C8×C13C2314yes—
46C42×C13D411yescharacteristic
47C42×C13D411yescharacteristic
48C42×C13C2311yescharacteristic
49C42×C13C2311yescharacteristic
50C22⋊Dic13—22no—
51#6103—22no—
52#6103—22no—
53C4⋊Dic13—21no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13C2312yes—
57C4⋊Dic13C2312yes—
58C4⋊Dic13C2312yes—
59#6101—22no—
60#6101—22no—
61C4×Dic13—22no—
62#3235—131nomaximal, Sylow
63C23×C13C2×D411yescharacteristic
64C22×D13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—41no—
68C2×C4×C13C2×D411yescharacteristic
69C2×C4×C13C2×D411yescharacteristic
70C2×C4×C13C2×D411yescharacteristic
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2411yescharacteristic
74C22⋊D13—44no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78D52—24no—
79D52—42no—
80D52—42no—
81C4×D13—44no—
82Dic26—42no—
83Dic26—42no—
84Dic26—42no—
85C8×C13—24no—
86#533—131no—
87#532—131no—
88#501—132no—
89#490—132no—
90#482—134no—
91#476—132no—
92#474—132no—
93#432D1311yescharacteristic, complemented
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13C22×D411yescharacteristic
98C2×D13—42no—
99C2×D13—42no—
100C2×D13—42no—
101C4×C13—21no—
102C4×C13—21no—
103C4×C13—21no—
104C4×C13—21no—
105C4×C13AGL(1,ℤ/8)12yes—
106C4×C132−1+412yes—
107Dic13—42no—
108Dic13—42no—
109Dic13—42no—
110C2×#41—261no—
111C4⋊Q8—131no—
112C4⋊Q8—131no—
113C4⋊Q8—131no—
114#127—131no—
115#125—132no—
116#124—261no—
117C22⋊Q8—261no—
118C22⋊Q8—261no—
119#121—132no—
120#121—261no—
121C4×Q8—261no—
122C4×Q8—261no—
123C4×D4—132no—
124C4×D4—261no—
125#117—132no—
126C2×C42C2×D1311yescharacteristic
127#107—134no—
128#106—134no—
129C4⋊C8C2×D1312yes—
130#102—134no—
131#102—134no—
132C22⋊C8C2×D1312yes—
133#97C2×D1312yes—
134C2×C13—41no—
135C2×C13#53611yescharacteristic
136C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C13#57511yescharacteristic
138D13—82no—
139#41—524no—
140C2×Q8—261no—
141C2×Q8—261no—
142C2×Q8—261no—
143C2×D4—132no—
144C2×D4—262no—
145C2×D4—261no—
146C2×D4—261no—
147C22×C4—262no—
148C22×C4D5211yescharacteristic
149C22×C4D5211yescharacteristic
150C22×C4C22×D1311yescharacteristic
151C2×C8C22×D1314yes—
152C4⋊C4—132no—
153C4⋊C4—132no—
154C4⋊C4—132no—
155C4⋊C4—261no—
156C4⋊C4—262no—
157C4⋊C4—262no—
158C4⋊C4—261no—
159C4⋊C4—261no—
160C22⋊C4—262no—
161C22⋊C4—262no—
162C22⋊C4—262no—
163C42—262no—
164C42D5211yescharacteristic
165C42D5211yescharacteristic
166C42C22×D1311yescharacteristic
167C42C22×D1311yescharacteristic
168C13#323511yescharacteristic, complemented, Sylow
169C23—262no—
170C23C2×D5211yescharacteristic
171Q8—522no—
172Q8—522no—
173Q8—522no—
174D4—264no—
175D4—522no—
176D4—522no—
177D4—524no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—524no—
185C2×C4C2×D5211yescharacteristic
186C2×C4C2×D5211yescharacteristic
187C2×C4C2×D5211yescharacteristic
188C2×C4C2×D5211yescharacteristic
189C2×C4C2×D5211yescharacteristic
190C2×C4C23×D1311yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—522no—
196C22—522no—
197C22—522no—
198C22C22×D5211yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—522no—
204C4—522no—
205C4—522no—
206C4#8816212yes—
207C4#8825712yes—
208C2—41no—
209C2—1042no—
210C2#1171923111yescharacteristic
211C2C2×#8816211yescharacteristic
212C2#1171945311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#432C2
socleC22×C13C22×D4
prime radical#11719182C2
hypercenter#432D13
hypocenterC13#3235
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. #11719175C2semidirect
3. C13×#432C2semidirect
4. #11718507C2semidirect
5. #11718503C2semidirect
6. #11718398C2semidirect
7. #11718374C2semidirect
8. #11718363C2semidirect
93. #432D13semidirect
168. C13#3235semidirect

Maximal subgroups

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

subgroupindex
#117191822
#117191752
C13×#4322
#117185072
#117185032
#117183982
#117183742
#117183632
#323513