Finite Group Databasebeta

← #15765667

Subgroups — #15765667

Order 3328.

576 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 113 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#13125980C212yesmaximal
2#13115813C211yesmaximal, characteristic
3#13113508C212yesmaximal
4#13112669C211yesmaximal, characteristic
5C13×#2868C211yesmaximal, characteristic
6C2×C13×C4⋊Q8—22no—
7C2×C13×C4⋊Q8C2212yes—
8#11719175C2211yescharacteristic
9C13×#384—24no—
10C43×C13C2211yescharacteristic
11#11718755—24no—
12#11718754—22no—
13#11718740—22no—
14#11718632—24no—
15#11718586C2212yes—
16#11718585C2211yescharacteristic
17#11718139—24no—
18#11718115—22no—
19C22×Q8×C13—22no—
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8—22no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—44no—
25C13×C4⋊Q8—44no—
26C2×C13×C4⋊C4—28no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4D414yes—
29C2×C42×C13—22no—
30C2×C42×C13D412yes—
31C2×C42×C13C2311yescharacteristic
32#88180—21no—
33#88178—22no—
34C2×#6099—21no—
35#88124—21no—
36#88123D412yes—
37C4×Dic26—22no—
38C22⋊#1055—22no—
39#88050—28no—
40#88048—28no—
41C4⋊#1055—22no—
42C4⋊#1055D414yes—
43C4×#1055—22no—
44#10299—131nomaximal, Sylow
45C2×Q8×C13—42no—
46C2×Q8×C13—42no—
47C2×Q8×C13—44no—
48C2×Q8×C13—44no—
49C22×C4×C13—22no—
50C22×C4×C13—24no—
51C22×C4×C13C2×D412yes—
52C22×C4×C13C2×D411yescharacteristic
53C2×Dic26—22no—
54C13×C4⋊C4—24no—
55C13×C4⋊C4—24no—
56C13×C4⋊C4—416no—
57C13×C4⋊C4—42no—
58C13×C4⋊C4—42no—
59C42×C13—28no—
60C42×C13—22no—
61C42×C13SD1614yes—
62C42×C13C2×D411yescharacteristic
63C42×C13C2×D412yes—
64C42×C13#4111yescharacteristic
65C22⋊Dic13—41no—
66C4⋊Dic13—22no—
67C4⋊Dic13—22no—
68#6101—42no—
69C4×Dic13—41no—
70#6099—42no—
71C2×#1055—24no—
72C2×#1055—41no—
73#3229—132no—
74#2868D1311yescharacteristic
75#1994—131no—
76#1546—132no—
77#1276—131no—
78C23×C13#12011yescharacteristic
79Q8×C13—84no—
80Q8×C13—82no—
81Q8×C13—82no—
82C2×C4×C13—28no—
83C2×C4×C13—24no—
84C2×C4×C13—24no—
85C2×C4×C13—44no—
86C2×C4×C13—48no—
87C2×C4×C13#12012yes—
88C2×C4×C13#12112yes—
89C2×C4×C13#12111yescharacteristic
90C2×C4×C13#12711yescharacteristic
91C2×C4×C13C2×SD1612yes—
92C2×C4×C13AGL(1,ℤ/8)12yes—
93C2×Dic13—42no—
94Dic26—44no—
95#1055—44no—
96#1055—81no—
97#533—131no—
98C2×C4⋊Q8—22no—
99C2×C4⋊Q8C2×D1312yes—
100#498—262no—
101#487—262no—
102#483—264no—
103#475—264no—
104#431—132no—
105#423—131no—
106#384—24no—
107C43C2×D1311yescharacteristic
108#339—262no—
109#332—264no—
110C22×C13—22no—
111C22×C13#39211yescharacteristic
112C22×C13#45012yes—
113C4×C13—28no—
114C4×C13—22no—
115C4×C13—84no—
116C4×C13#45614yes—
117C4×C13#46012yes—
118C4×C13#49211yescharacteristic
119C4×C13#49611yescharacteristic
120Dic13—82no—
121C22×Q8—22no—
122C2×M16—261no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—44no—
128C4⋊Q8—44no—
129C4⋊Q8—132no—
130#125—261no—
131C22⋊Q8—262no—
132C4×Q8—262no—
133#117—261no—
134C2×C4⋊C4—28no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4C22⋊D1314yes—
137C2×C42—22no—
138C2×C42C22⋊D1312yes—
139C2×C42C22×D1311yescharacteristic
140#106—268no—
141C4⋊C8—134no—
142C4⋊C8—262no—
143#103—268no—
144C22⋊C8—262no—
145C4×C8—262no—
146C2×C13—22no—
147C2×C13#200512yes—
148C2×C13#201411yescharacteristic
149C2×Q8—44no—
150C2×Q8—44no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—262no—
154C22×C4—22no—
155C22×C4—24no—
156C22×C4C2×C22⋊D1312yes—
157C22×C4C2×C22⋊D1311yescharacteristic
158M16—522no—
159C2×C8—264no—
160C2×C8—521no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—416no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4—522no—
169C22⋊C4—521no—
170C42—28no—
171C42—22no—
172C42—521no—
173C42#610514yes—
174C42D4×D1311yescharacteristic
175C42D4×D1312yes—
176C42#612911yescharacteristic
177C13#1029911yescharacteristic, complemented, Sylow
178C23#8820711yescharacteristic
179Q8—82no—
180Q8—84no—
181Q8—82no—
182Q8—524no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—48no—
187C2×C4—44no—
188C2×C4—522no—
189C2×C4#8818612yes—
190C2×C4C2×#610512yes—
191C2×C4#8819112yes—
192C2×C4#8819211yescharacteristic
193C2×C4#8819312yes—
194C2×C4#8819411yescharacteristic
195C8—524no—
196C8—1041no—
197C22—22no—
198C22#1171887912yes—
199C22#1171888411yescharacteristic
200C4—28no—
201C4—22no—
202C4—84no—
203C4—1042no—
204C4#1171873511yescharacteristic
205C4#1171873612yes—
206C4#1171873711yescharacteristic
207C4#1171875614yes—
208C2—22no—
209C2#1311587212yes—
210C2#1311592411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2868C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#2868D13
hypocenterC13#10299
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2868

Complements

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

NH ≅ G/Ntype
177. C13#10299semidirect

Maximal subgroups

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

subgroupindex
#131259802
#131158132
#131135082
#131126692
C13×#28682
#1029913