Finite Group Databasebeta

← #13114052

Subgroups — #13114052

Order 1664.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#11719284C211yesmaximal, characteristic
2#11718692C211yesmaximal, characteristic, complemented
3#11718507C211yesmaximal, characteristic
4#11718342C211yesmaximal, characteristic, complemented
5C13×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11718073C211yesmaximal, characteristic, complemented
7#11718051C211yesmaximal, characteristic
8C4×Q8×C13C2211yescharacteristic
9#88200—21no—
10C2×#6107—21no—
11#88150—22no—
12C4⋊C4×D13—21no—
13C4×D52—21no—
14C4×D52C2211yescharacteristic
15#88124—21no—
16#88123C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C4×C8×C13C2211yescharacteristic
20#88061—21no—
21#88058—21no—
22#88056—22no—
23#88050—21no—
24C4⋊#1055C2211yescharacteristic
25C2×Q8×C13D411yescharacteristic
26C2×D52D411yescharacteristic
27C2×C4×D13—21no—
28C2×C4×D13—22no—
29C2×Dic26—21no—
30C2×Dic26D412yes—
31C2×C8×C13—21no—
32C2×C8×C13—21no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4D411yescharacteristic
35C42×C13—21no—
36C42×C13C2311yescharacteristic
37#6107—42no—
38#6103—22no—
39#6103—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13D411yescharacteristic
45#6101—22no—
46#6101—22no—
47C2×#1055—21no—
48#1644—131nomaximal, Sylow
49C22×D13—21no—
50Q8×C13—21no—
51Q8×C13—21no—
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13C2×D411yescharacteristic
55C2×C4×C13C2×D411yescharacteristic
56C2×C4×C13C2×D411yescharacteristic
57C2×Dic13—21no—
58C2×Dic13—22no—
59C2×Dic13—41no—
60D52—21no—
61D52Q1612yescomplemented
62C4×D13—41no—
63C4×D13—41no—
64C4×D13—82no—
65Dic26—42no—
66Dic26—41no—
67Dic26—41no—
68C8×C13—41no—
69C8×C13—41no—
70#1055—41no—
71#554—131no—
72#487—131no—
73#474—131no—
74#462—131no—
75#333—131no—
76Q8⋊C8D1311yescharacteristic, complemented
77D4⋊C8—131no—
78C22×C13#12011yescharacteristic
79C2×D13—22no—
80C2×D13—41no—
81C2×D13—41no—
82C4×C13—21no—
83C4×C13—41no—
84C4×C13—41no—
85C4×C13C2×Q1611yescharacteristic
86C4×C13#13511yescharacteristic
87C4×C13AGL(1,ℤ/8)11yescharacteristic
88C4×C13#13711yescharacteristic
89Dic13—41no—
90Dic13—42no—
91Dic13—81no—
92C2×Q16—261no—
93C4⋊Q8—131no—
94C4⋊Q8—131no—
95#125—261no—
96C22⋊Q8—262no—
97C22⋊Q8—261no—
98C4×Q8C2×D1311yescharacteristic
99C4×D4—131no—
100C4×D4—261no—
101C2×C4⋊C4—261no—
102#107—261no—
103C4⋊C8—131no—
104C4⋊C8C2×D1311yescharacteristic
105#103—262no—
106#103—261no—
107#102—261no—
108C4×C8C2×D1311yescharacteristic
109C2×C13#44911yescharacteristic
110C2×C13#45111yescharacteristic
111C2×C13#45511yescharacteristic
112D13—42no—
113C2×Q8—132no—
114C2×Q8—261no—
115C2×Q8D5211yescharacteristic
116C2×D4—131no—
117C22×C4—262no—
118C22×C4—261no—
119Q16—522no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—261no—
123C4⋊C4—21no—
124C4⋊C4—131no—
125C4⋊C4—262no—
126C4⋊C4—262no—
127C4⋊C4—261no—
128C4⋊C4—261no—
129C4⋊C4—261no—
130C4⋊C4—261no—
131C4⋊C4D5211yescharacteristic
132C22⋊C4—262no—
133C22⋊C4—261no—
134C42—21no—
135C42C22×D1311yescharacteristic
136C13#164411yescharacteristic, complemented, Sylow
137C23—261no—
138Q8—21no—
139Q8—21no—
140Q8—522no—
141Q8—521no—
142Q8—521no—
143D4—132no—
144D4—261no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—261no—
148C2×C4—262no—
149C2×C4—521no—
150C2×C4—521no—
151C2×C4—521no—
152C2×C4—1042no—
153C2×C4C2×D5211yescharacteristic
154C2×C4D4×D1311yescharacteristic
155C2×C4D4×D1311yescharacteristic
156C8—41no—
157C8—41no—
158C8—521no—
159C22—262no—
160C22—521no—
161C22—521no—
162C22#8813611yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—522no—
167C4—521no—
168C4—1041no—
169C4#8815811yescharacteristic
170C4#8816211yescharacteristic
171C4#8816911yescharacteristic
172C4Q16×D1311yescharacteristic
173C2—522no—
174C2#1171839511yescharacteristic
175C2#1171846911yescharacteristic
176C2#1171848611yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×Q8⋊C8C2
socleC22×C13#120
prime radicalC2×D52D4
hypercenterQ8⋊C8D13
hypocenterC13#1644
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #11718692C2semidirect
4. #11718342C2semidirect
5. C13×Q8⋊C8C2semidirect
6. #11718073C2semidirect
61. D52Q16semidirect
76. Q8⋊C8D13semidirect
136. C13#1644semidirect

Maximal subgroups

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

subgroupindex
#117192842
#117186922
#117185072
#117183422
C13×Q8⋊C82
#117180732
#117180512
#164413