Finite Group Databasebeta

← #13116180

Subgroups — #13116180

Order 1664.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#11719224C211yesmaximal, characteristic
2#11718782C211yesmaximal, characteristic
3#11718656C211yesmaximal, characteristic
4#11718596C211yesmaximal, characteristic
5C13×#339C211yesmaximal, characteristic
6#11718146C211yesmaximal, characteristic
7#11718115C211yesmaximal, characteristic
8C2×C13×M16C2211yescharacteristic
9C13×#117C2211yescharacteristic
10C2×C42×C13C2211yescharacteristic
11#88180C2211yescharacteristic
12C2×C4⋊Dic13—22no—
13C2×C4⋊Dic13C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×#6099C2211yescharacteristic
16#88144—21no—
17#88142—21no—
18#88132—22no—
19#88124—21no—
20#88123—21no—
21#88058—21no—
22#88057—21no—
23#88048—21no—
24#88047—21no—
25C22×C4×C13—21no—
26C22×C4×C13C2311yescharacteristic
27C22×Dic13—21no—
28C22×Dic13D412yes—
29C2×Dic26—22no—
30C13×M16—21no—
31C13×M16Q812yescomplemented
32C2×C8×C13—21no—
33C13×C4⋊C4D411yescharacteristic
34C13×C4⋊C4D411yescharacteristic
35C13×C22⋊C4—21no—
36C42×C13—21no—
37C42×C13—21no—
38C42×C13Q812yescomplemented
39C22⋊Dic13—21no—
40C4⋊Dic13—22no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13—21no—
45C4⋊Dic13—44no—
46C4⋊Dic13D411yescharacteristic
47C4⋊Dic13D411yescharacteristic
48#6101—22no—
49#6101—22no—
50C4×Dic13—21no—
51#6099—21no—
52#6099Q812yescomplemented
53C2×#1055—21no—
54#2060—131nomaximal, Sylow
55C23×C13C2×D411yescharacteristic
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13C2×D411yescharacteristic
62C2×C4×C13C2×D411yescharacteristic
63C2×C4×C13C2×Q811yescharacteristic
64C2×C4×C13C2×Q811yescharacteristic
65C2×C4×C13C2×Q811yescharacteristic
66C2×C4×C13#4111yescharacteristic
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—22no—
70C2×Dic13—42no—
71C2×Dic13—42no—
72C2×Dic13—41no—
73Dic26—82no—
74C8×C13—22no—
75#1055—22no—
76#544—131no—
77#428—131no—
78#428—131no—
79#384—131no—
80#343—131no—
81#339—131no—
82#339D1311yescharacteristic
83C22×C13—21no—
84C22×C13—21no—
85C22×C13#12011yescharacteristic
86C22×C13C22⋊Q811yescharacteristic
87C22×C13C4⋊Q811yescharacteristic
88C4×C13—24no—
89C4×C13—41no—
90C4×C13—41no—
91C4×C13C22⋊Q811yescharacteristic
92C4×C13C22⋊Q811yescharacteristic
93C4×C13C4⋊Q811yescharacteristic
94C4×C13C4⋊Q811yescharacteristic
95Dic13—41no—
96Dic13—42no—
97Dic13—41no—
98Dic13—81no—
99C2×M16—131no—
100C2×M16C2×D1311yescharacteristic
101C4⋊Q8—261no—
102C4⋊Q8—261no—
103#125—261no—
104#125—261no—
105C22⋊Q8—262no—
106#117—131no—
107#117C2×D1311yescharacteristic
108C2×C4⋊C4—131no—
109C2×C4⋊C4—131no—
110C2×C4⋊C4—262no—
111C2×C42C2×D1311yescharacteristic
112#107—261no—
113#107—261no—
114#106—261no—
115#106—261no—
116C2×C13—21no—
117C2×C13—21no—
118C2×C13#39511yescharacteristic
119C2×C13#45311yescharacteristic
120C2×C13#45611yescharacteristic
121C2×Q8—262no—
122C22×C4—21no—
123C22×C4—132no—
124C22×C4—261no—
125C22×C4C22×D1311yescharacteristic
126M16—21no—
127M16—132no—
128M16—261no—
129M16Dic2612yescomplemented
130C2×C8—21no—
131C2×C8—261no—
132C4⋊C4—131no—
133C4⋊C4—131no—
134C4⋊C4—262no—
135C4⋊C4—262no—
136C4⋊C4—262no—
137C4⋊C4—261no—
138C4⋊C4—261no—
139C4⋊C4—261no—
140C4⋊C4—261no—
141C4⋊C4—524no—
142C4⋊C4D5211yescharacteristic
143C4⋊C4D5211yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—261no—
146C42—21no—
147C42—21no—
148C42—261no—
149C42Dic2612yescomplemented
150C13#206011yescharacteristic, complemented, Sylow
151C23D4×D1311yescharacteristic
152Q8—1042no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—261no—
159C2×C4—261no—
160C2×C4—262no—
161C2×C4—522no—
162C2×C4—522no—
163C2×C4—521no—
164C2×C4C2×Dic2611yescharacteristic
165C2×C4C2×Dic2611yescharacteristic
166C2×C4C2×D5211yescharacteristic
167C2×C4D4×D1311yescharacteristic
168C2×C4#612911yescharacteristic
169C2×C4Q8×D1311yescharacteristic
170C8—22no—
171C8—262no—
172C22—21no—
173C22—21no—
174C22#8813211yescharacteristic
175C22#8813611yescharacteristic
176C22#8814211yescharacteristic
177C4—24no—
178C4—41no—
179C4—41no—
180C4—522no—
181C4—521no—
182C4—521no—
183C4—1041no—
184C4#8812311yescharacteristic
185C4#8813211yescharacteristic
186C4#8814211yescharacteristic
187C4#8815111yescharacteristic
188C2—21no—
189C2—21no—
190C2#1171831711yescharacteristic
191C2#1171848311yescharacteristic
192C2#1171848711yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#339C2
socleC22×C13#120
prime radicalC23×C13C2×D4
hypercenter#339D13
hypocenterC13#2060
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
31. C13×M16Q8semidirect
38. C42×C13Q8semidirect
52. #6099Q8semidirect
129. M16Dic26semidirect
149. C42Dic26semidirect
150. C13#2060semidirect

Maximal subgroups

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

subgroupindex
#117192242
#117187822
#117186562
#117185962
C13×#3392
#117181462
#117181152
#206013