Finite Group Databasebeta

← #13126034

Subgroups — #13126034

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
1C13×#533C211yesmaximal, characteristic, complemented
2#11719182C211yesmaximal, characteristic
3#11718748C212yesmaximal, complemented
4#11718745C212yesmaximal, complemented
5#11718728C212yesmaximal, complemented
6#11718726C212yesmaximal, complemented
7#11718664C214yesmaximal, complemented
8#11718587C211yesmaximal, characteristic, complemented
9C2×#6127—21no—
10C13×C4⋊Q8C2211yescharacteristic
11C13×C4⋊Q8C2211yescharacteristic
12C13×#125C2212yes—
13C13×C22⋊Q8—21no—
14C13×C22⋊Q8—21no—
15C4×Q8×C13—21no—
16C4×Q8×C13—21no—
17C13×#117C2212yes—
18C2×C42×C13C2211yescharacteristic
19#88184—21no—
20#88184C2212yes—
21#88129—21no—
22#88128C2211yescharacteristic
23C4×D52—21no—
24C4×D52C2212yes—
25#88123C2211yescharacteristic
26C22⋊#1055C2212yes—
27#88049C2214yes—
28#88049C2214yes—
29#88048C2214yes—
30#88047C2214yes—
31C4⋊#1055C2212yes—
32#88043C2212yes—
33C2×Q8×C13—21no—
34C2×Q8×C13—21no—
35C22×C4×C13D411yescharacteristic
36C22×C4×C13D411yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—22no—
39#6127—44no—
40C2×D52—21no—
41C2×D52—21no—
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C2×Dic26—21no—
45C13×C4⋊C4—22no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C13×C4⋊C4C2312yes—
51C13×C22⋊C4—22no—
52C42×C13—22no—
53C42×C13D411yescharacteristic
54C42×C13D411yescharacteristic
55C42×C13C2311yescharacteristic
56C42×C13C2311yescharacteristic
57#6103—22no—
58#6103—22no—
59C4⋊Dic13—21no—
60C4⋊Dic13C2312yes—
61C2×#1055C2314yes—
62#3235—131nomaximal, Sylow
63C23×C13C2×D411yescharacteristic
64C22×D13—22no—
65Q8×C13—42no—
66Q8×C13—42no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—41no—
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2411yescharacteristic
78C22⋊D13—44no—
79C2×Dic13—22no—
80D52—24no—
81D52—42no—
82D52—42no—
83C4×D13—44no—
84Dic26—42no—
85#1055—24no—
86#533D1311yescharacteristic, complemented
87#532—131no—
88#501—132no—
89#490—132no—
90#482—134no—
91#476—132no—
92#474—132no—
93#432—131no—
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×C13—42no—
106C4×C13—42no—
107C4×C13AGL(1,ℤ/8)12yes—
108C4×C132−1+412yes—
109Dic13—42no—
110C2×#41—261no—
111C4⋊Q8—131no—
112C4⋊Q8C2×D1311yescharacteristic
113C4⋊Q8C2×D1311yescharacteristic
114#127—131no—
115#125C2×D1312yes—
116#124—261no—
117C22⋊Q8—21no—
118C22⋊Q8—21no—
119#121—132no—
120#121—261no—
121C4×Q8—21no—
122C4×Q8—21no—
123C4×D4—132no—
124C4×D4—261no—
125#117C2×D1312yes—
126C2×C42C2×D1311yescharacteristic
127#107—134no—
128#106—134no—
129C4⋊C8—132no—
130#102—134no—
131#102—134no—
132C22⋊C8—132no—
133#97—132no—
134C2×C13—41no—
135C2×C13#53611yescharacteristic
136C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C13#57511yescharacteristic
138D13—82no—
139#41—524no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—261no—
143C2×D4—132no—
144C2×D4—262no—
145C2×D4—261no—
146C2×D4—261no—
147C22×C4—262no—
148C22×C4C22⋊D1311yescharacteristic
149C22×C4C22⋊D1311yescharacteristic
150C22×C4C22×D1311yescharacteristic
151C2×C8—134no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—132no—
157C4⋊C4—261no—
158C4⋊C4C22×D1312yes—
159C4⋊C4C22×D1312yes—
160C22⋊C4—22no—
161C22⋊C4—262no—
162C22⋊C4—262no—
163C42—22no—
164C42C22⋊D1311yescharacteristic
165C42C22⋊D1311yescharacteristic
166C42C22×D1311yescharacteristic
167C42C22×D1311yescharacteristic
168C13#323511yescharacteristic, complemented, Sylow
169C23—262no—
170C23C2×C22⋊D1311yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—522no—
174D4—264no—
175D4—522no—
176D4—522no—
177D4—524no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—262no—
184C2×C4—524no—
185C2×C4C2×C22⋊D1311yescharacteristic
186C2×C4C2×C22⋊D1311yescharacteristic
187C2×C4C2×C22⋊D1311yescharacteristic
188C2×C4C2×C22⋊D1311yescharacteristic
189C2×C4C2×C22⋊D1311yescharacteristic
190C2×C4C23×D1311yescharacteristic
191C8—264no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—522no—
196C22—522no—
197C22—522no—
198C22C22×C22⋊D1311yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—42no—
205C4—522no—
206C4#8820312yes—
207C4#8825412yes—
208C2—41no—
209C2—1042no—
210C2#1171952111yescharacteristic
211C2C2×#8820311yescharacteristic
212C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#533C2
socleC22×C13C22×D4
prime radical#11719182C2
hypercenter#533D13
hypocenterC13#3235
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C13×#533C2semidirect
3. #11718748C2semidirect
4. #11718745C2semidirect
5. #11718728C2semidirect
6. #11718726C2semidirect
7. #11718664C2semidirect
8. #11718587C2semidirect
86. #533D13semidirect
168. C13#3235semidirect

Maximal subgroups

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

subgroupindex
C13×#5332
#117191822
#117187482
#117187452
#117187282
#117187262
#117186642
#117185872
#323513