Finite Group Databasebeta

← #13125992

Subgroups — #13125992

Order 1664.

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

normal subgroups only

This group has 326 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#11719433C211yesmaximal, characteristic
2#11719433C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic, complemented
4#11718742C211yesmaximal, characteristic, complemented
5#11718740C211yesmaximal, characteristic, complemented
6#11718475C214yesmaximal
7#11718457C214yesmaximal, complemented
8#11718346C211yesmaximal, characteristic
9#11718343C211yesmaximal, characteristic, complemented
10C13×C4⋊Q8C2211yescharacteristic
11C13×C4⋊Q8C2211yescharacteristic
12#88200—21no—
13#88200C2212yes—
14Q8×Dic13—21no—
15Q8×Dic13C2212yes—
16#88151—21no—
17#88151—21no—
18#88146—21no—
19#88146C2212yes—
20#88144—21no—
21#88144C2212yes—
22#88141—21no—
23#88141—21no—
24C42×D13C2211yescharacteristic
25#88123C2211yescharacteristic
26#88123C2211yescharacteristic
27C13×#103C2214yes—
28C4×C8×C13C2211yescharacteristic
29#88075C2214yes—
30#88060C2212yes—
31#88058C2214yes—
32#88054C2212yes—
33#88048C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37C2×C4×D13D411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×C4×D13C2311yescharacteristic
40C2×Dic26—21no—
41C2×Dic26—21no—
42C2×C8×C13C2312yes—
43C13×C4⋊C4—21no—
44C13×C4⋊C4—21no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4C2312yes—
47C42×C13C2311yescharacteristic
48#6103—22no—
49#6103—22no—
50C4⋊Dic13—21no—
51C4⋊Dic13—21no—
52C4⋊Dic13—22no—
53C4⋊Dic13—22no—
54C4⋊Dic13C2312yes—
55C4⋊Dic13C2312yes—
56#6101—22no—
57#6101—22no—
58C4×Dic13—22no—
59C4×Dic13—22no—
60C4×Dic13D411yescharacteristic
61C4×Dic13D411yescharacteristic
62C4×Dic13C2311yescharacteristic
63C2×#1055C2312yes—
64#3231—131nomaximal, Sylow
65C22×D13C2×D411yescharacteristic
66Q8×C13—24no—
67Q8×C13—42no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13C2×D411yescharacteristic
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2411yescharacteristic
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13C2×D411yescharacteristic
76C2×Dic13C2×D411yescharacteristic
77C2×Dic13C2×D411yescharacteristic
78C4×D13—22no—
79C4×D13—22no—
80C4×D13—22no—
81Dic26—42no—
82Dic26—42no—
83C8×C13—22no—
84#1055—22no—
85#533—131no—
86#533—131no—
87#500—131no—
88#498—131no—
89#487—131no—
90#487D1311yescharacteristic, complemented
91#485—134no—
92#479—134no—
93#431—131no—
94C22×C13C22×D411yescharacteristic
95C2×D13—21no—
96C2×D13—21no—
97C2×D13—21no—
98C4×C13—42no—
99C4×C13—42no—
100C4×C13#13512yes—
101C4×C13#13712yes—
102C4×C132−1+412yes—
103Dic13—21no—
104Dic13—21no—
105Dic13—21no—
106Dic13—42no—
107Dic13—42no—
108C4⋊Q8—131no—
109C4⋊Q8—131no—
110C4⋊Q8C2×D1311yescharacteristic
111C4⋊Q8C2×D1311yescharacteristic
112#125—132no—
113#125—261no—
114C22⋊Q8—132no—
115C22⋊Q8—261no—
116C22⋊Q8—261no—
117C22⋊Q8—261no—
118C4×Q8—132no—
119C4×Q8—261no—
120C4×Q8—261no—
121C4×Q8—261no—
122#117—132no—
123#117—261no—
124C2×C42—131no—
125#107—134no—
126#106—134no—
127C4⋊C8—132no—
128#103—134no—
129#103C2×D1314yes—
130C22⋊C8—132no—
131C4×C8—131no—
132C4×C8C2×D1311yescharacteristic
133C2×C13#53611yescharacteristic
134C2×C13C2×#13511yescharacteristic
135C2×C13C2×#13711yescharacteristic
136D13—41no—
137C2×Q8—21no—
138C2×Q8—261no—
139C2×Q8—261no—
140C2×Q8C22×D1312yes—
141C22×C4—131no—
142C22×C4—131no—
143C22×C4—131no—
144C2×C8—132no—
145C2×C8C22×D1312yes—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—132no—
150C4⋊C4—132no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4—262no—
155C4⋊C4—261no—
156C4⋊C4—261no—
157C4⋊C4C22×D1312yes—
158C22⋊C4—262no—
159C22⋊C4—262no—
160C42—131no—
161C42—131no—
162C42—131no—
163C42—262no—
164C42—262no—
165C42C22×D1311yescharacteristic
166C13#323111yescharacteristic, complemented, Sylow
167C23—131no—
168Q8—24no—
169Q8—42no—
170Q8—522no—
171Q8—522no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—131no—
175C2×C4—131no—
176C2×C4—131no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4D4×D1311yescharacteristic
183C2×C4D4×D1311yescharacteristic
184C2×C4C23×D1311yescharacteristic
185C8—22no—
186C8—262no—
187C22—261no—
188C22—261no—
189C22—261no—
190C22C2×D4×D1311yescharacteristic
191C4—42no—
192C4—42no—
193C4—261no—
194C4—261no—
195C4—261no—
196C4—522no—
197C4—522no—
198C4#8816912yes—
199C4#8817312yes—
200C4#8825712yes—
201C2—521no—
202C2#1171938011yescharacteristic
203C2C2×#8816911yescharacteristic
204C2C2×#8817311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#487D13
hypocenterC13#3231
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. #11718740C2semidirect
7. #11718457C2semidirect
9. #11718343C2semidirect
90. #487D13semidirect
166. C13#3231semidirect

Maximal subgroups

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

subgroupindex
#117194332
C13×#4872
#117187422
#117187402
#117184752
#117184572
#117183462
#117183432
#323113