Finite Group Databasebeta

← #13125983

Subgroups — #13125983

Order 1664.

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

normal subgroups only

This group has 360 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#11719433C211yesmaximal, characteristic
2D13×C4⋊Q8C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic, complemented
4#11718742C211yesmaximal, characteristic, complemented
5#11718739C211yesmaximal, characteristic, complemented
6#11718470C214yesmaximal
7#11718455C214yesmaximal, complemented
8#11718346C211yesmaximal, characteristic
9#11718343C211yesmaximal, characteristic, complemented
10C2×Q8×D13—21no—
11C13×C4⋊Q8C2211yescharacteristic
12C13×C4⋊Q8C2211yescharacteristic
13#88200C2212yes—
14Q8×Dic13C2212yes—
15#88198—21no—
16#88151—21no—
17#88146—21no—
18C4⋊C4×D13—21no—
19C4⋊C4×D13C2212yes—
20#88144—21no—
21#88142—21no—
22#88142C2212yes—
23#88141—21no—
24C42×D13C2211yescharacteristic
25#88123C2211yescharacteristic
26#88123C2211yescharacteristic
27C13×#103C2214yes—
28C4×C8×C13C2211yescharacteristic
29#88075C2214yes—
30#88060C2212yes—
31#88058C2214yes—
32#88054C2212yes—
33#88047C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37Q8×D13—44no—
38C2×C4×D13—22no—
39C2×C4×D13D411yescharacteristic
40C2×C4×D13D411yescharacteristic
41C2×C4×D13C2311yescharacteristic
42C2×Dic26—21no—
43C2×Dic26—21no—
44C2×Dic26—22no—
45C2×C8×C13C2312yes—
46C13×C4⋊C4—21no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C42×C13C2311yescharacteristic
51#6103—22no—
52C4⋊Dic13—21no—
53C4⋊Dic13—21no—
54C4⋊Dic13—22no—
55C4⋊Dic13C2312yes—
56C4⋊Dic13C2312yes—
57#6101—22no—
58#6101—22no—
59#6101—22no—
60C4×Dic13—22no—
61C4×Dic13D411yescharacteristic
62C4×Dic13D411yescharacteristic
63C4×Dic13C2311yescharacteristic
64C2×#1055C2312yes—
65#3230—131nomaximal, Sylow
66C22×D13C2×D411yescharacteristic
67Q8×C13—24no—
68Q8×C13—42no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2411yescharacteristic
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13C2×D411yescharacteristic
77C2×Dic13C2×D411yescharacteristic
78C2×Dic13C2×D411yescharacteristic
79C4×D13—22no—
80C4×D13—22no—
81C4×D13—44no—
82C4×D13Q1614yes—
83Dic26—44no—
84Dic26—42no—
85Dic26—42no—
86C8×C13—22no—
87#1055—22no—
88#533—131no—
89C2×C4⋊Q8—131no—
90#500—131no—
91#500—131no—
92#487—131no—
93#487D1311yescharacteristic, complemented
94#484—134no—
95#477—134no—
96#431—131no—
97C22×C13C22×D411yescharacteristic
98C2×D13—21no—
99C2×D13—21no—
100C2×D13C2×Q1612yes—
101C4×C13—42no—
102C4×C13—42no—
103C4×C13C2×Q1612yes—
104C4×C13AGL(1,ℤ/8)12yes—
105C4×C132−1+412yes—
106Dic13—21no—
107Dic13—21no—
108Dic13—42no—
109Dic13—42no—
110Dic13C2×Q1612yes—
111C22×Q8—261no—
112C4⋊Q8—132no—
113C4⋊Q8—131no—
114C4⋊Q8—131no—
115C4⋊Q8—261no—
116C4⋊Q8—261no—
117C4⋊Q8C2×D1311yescharacteristic
118C4⋊Q8C2×D1311yescharacteristic
119#125—261no—
120C22⋊Q8—132no—
121C22⋊Q8—261no—
122C4×Q8—132no—
123C4×Q8—261no—
124#117—261no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—261no—
127C2×C42—131no—
128#107—134no—
129#107—134no—
130C4⋊C8—132no—
131#103—134no—
132#103C2×D1314yes—
133C22⋊C8—132no—
134C4×C8—131no—
135C4×C8C2×D1311yescharacteristic
136C2×C13#53611yescharacteristic
137C2×C13C22×Q1611yescharacteristic
138C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
139D13—22no—
140C2×Q8—21no—
141C2×Q8—262no—
142C2×Q8—261no—
143C2×Q8—261no—
144C2×Q8—524no—
145C2×Q8C22×D1312yes—
146C22×C4—131no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—262no—
150C2×C8—132no—
151C2×C8C22×D1312yes—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—132no—
156C4⋊C4—132no—
157C4⋊C4—262no—
158C4⋊C4—262no—
159C4⋊C4—262no—
160C4⋊C4—262no—
161C4⋊C4—261no—
162C4⋊C4—261no—
163C4⋊C4C22×D1312yes—
164C22⋊C4—262no—
165C42—131no—
166C42—131no—
167C42—131no—
168C42—262no—
169C42C22×D1311yescharacteristic
170C13#323011yescharacteristic, complemented, Sylow
171C23—131no—
172Q8—24no—
173Q8—42no—
174Q8—524no—
175Q8—522no—
176Q8—522no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—131no—
180C2×C4—134no—
181C2×C4—131no—
182C2×C4—131no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—524no—
188C2×C4D4×D1311yescharacteristic
189C2×C4D4×D1311yescharacteristic
190C2×C4C23×D1311yescharacteristic
191C8—22no—
192C8—262no—
193C22—132no—
194C22—261no—
195C22—261no—
196C22C2×D4×D1311yescharacteristic
197C4—42no—
198C4—42no—
199C4—132no—
200C4—261no—
201C4—261no—
202C4—522no—
203C4—522no—
204C4#8816812yes—
205C4Q16×D1312yes—
206C4#8825712yes—
207C2—262no—
208C2#1171938011yescharacteristic
209C2C2×#8816811yescharacteristic
210C2C2×Q16×D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#487D13
hypocenterC13#3230
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C13×#487C2semidirect
4. #11718742C2semidirect
5. #11718739C2semidirect
7. #11718455C2semidirect
9. #11718343C2semidirect
93. #487D13semidirect
170. C13#3230semidirect

Maximal subgroups

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

subgroupindex
#117194332
D13×C4⋊Q82
C13×#4872
#117187422
#117187392
#117184702
#117184552
#117183462
#117183432
#323013