Finite Group Databasebeta

← #15765669

Subgroups — #15765669

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#13125982C212yesmaximal
2#13123234C211yesmaximal, characteristic
3#13115813C211yesmaximal, characteristic
4#13113507C212yesmaximal
5C13×#1276C211yesmaximal, characteristic
6#11719175C2211yescharacteristic
7C2×#88123—22no—
8C2×#88123C2212yes—
9C13×#431C2212yes—
10C43×C13C2211yescharacteristic
11#11718596—24no—
12#11718585C2211yescharacteristic
13#11718512—24no—
14#11718382—24no—
15#11718342—22no—
16#11718341—22no—
17#11718115—22no—
18#11718078—24no—
19C22×Dic26—22no—
20C2×C42×C13—22no—
21C2×C42×C13D412yes—
22C2×C42×C13C2311yescharacteristic
23#88180—21no—
24C2×C4⋊Dic13—28no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13D414yes—
27#88178—22no—
28C2×#6099—21no—
29#88124—21no—
30#88123—22no—
31#88123—22no—
32#88123—22no—
33#88123—22no—
34#88123—44no—
35#88123—44no—
36#88123D412yes—
37C4×Dic26—22no—
38C13×C4⋊C8D414yes—
39C13×C22⋊C8—22no—
40C4×C8×C13—22no—
41#88057—28no—
42#88056—28no—
43C4⋊#1055—22no—
44#10299—131nomaximal, Sylow
45C22×C4×C13—22no—
46C22×C4×C13C2×D411yescharacteristic
47C22×C4×C13C2×D412yes—
48C22×Dic13—24no—
49C2×Dic26—22no—
50C2×Dic26—42no—
51C2×Dic26—42no—
52C2×Dic26—44no—
53C2×Dic26—44no—
54C2×C8×C13—24no—
55C42×C13—28no—
56C42×C13—22no—
57C42×C13SD1614yes—
58C42×C13C2×D412yes—
59C42×C13C2×D411yescharacteristic
60C42×C13#4111yescharacteristic
61C22⋊Dic13—41no—
62C4⋊Dic13—22no—
63C4⋊Dic13—24no—
64C4⋊Dic13—24no—
65C4⋊Dic13—22no—
66C4⋊Dic13—416no—
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69#6101—42no—
70C4×Dic13—41no—
71#6099—42no—
72C2×#1055—41no—
73#3229—132no—
74#2868—131no—
75#1994—131no—
76#1546—132no—
77#1276D1311yescharacteristic
78C23×C13#12011yescharacteristic
79C2×C4×C13—28no—
80C2×C4×C13—24no—
81C2×C4×C13—24no—
82C2×C4×C13#12012yes—
83C2×C4×C13#12112yes—
84C2×C4×C13#12111yescharacteristic
85C2×C4×C13#12711yescharacteristic
86C2×C4×C13C2×SD1612yes—
87C2×C4×C13AGL(1,ℤ/8)12yes—
88C2×Dic13—42no—
89C2×Dic13—44no—
90C2×Dic13—48no—
91Dic26—44no—
92Dic26—84no—
93Dic26—82no—
94Dic26—82no—
95C8×C13—44no—
96#1055—81no—
97#533—131no—
98C2×C4⋊Q8—132no—
99C2×C4⋊Q8—262no—
100#498—262no—
101#487—262no—
102#483—264no—
103#475—264no—
104#431C2×D1312yes—
105#423—131no—
106#384—264no—
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#45614yes—
116C4×C13#46012yes—
117C4×C13#49211yescharacteristic
118C4×C13#49611yescharacteristic
119Dic13—82no—
120Dic13—84no—
121C22×Q8—262no—
122C2×M16—261no—
123C4⋊Q8—132no—
124C4⋊Q8—262no—
125C4⋊Q8—262no—
126C4⋊Q8—262no—
127C4⋊Q8—262no—
128C4⋊Q8—524no—
129C4⋊Q8—524no—
130#125—261no—
131C22⋊Q8—262no—
132C4×Q8—262no—
133#117—261no—
134C2×C4⋊C4—134no—
135C2×C4⋊C4—268no—
136C2×C4⋊C4—262no—
137C2×C42—22no—
138C2×C42D5212yes—
139C2×C42C22×D1311yescharacteristic
140#106—268no—
141C4⋊C8—262no—
142C4⋊C8D5214yes—
143#103—268no—
144C22⋊C8—22no—
145C4×C8—22no—
146C2×C13—22no—
147C2×C13#200512yes—
148C2×C13#201411yescharacteristic
149C2×Q8—262no—
150C2×Q8—522no—
151C2×Q8—522no—
152C2×Q8—524no—
153C2×Q8—524no—
154C22×C4—22no—
155C22×C4—264no—
156C22×C4C2×D5211yescharacteristic
157C22×C4D4×D1312yes—
158M16—522no—
159C2×C8—24no—
160C2×C8—521no—
161C4⋊C4—264no—
162C4⋊C4—262no—
163C4⋊C4—264no—
164C4⋊C4—262no—
165C4⋊C4—5216no—
166C4⋊C4—522no—
167C4⋊C4—522no—
168C4⋊C4—522no—
169C22⋊C4—521no—
170C42—28no—
171C42—22no—
172C42—521no—
173C42#609514yes—
174C42C2×D5212yes—
175C42D4×D1311yescharacteristic
176C42#613111yescharacteristic
177C13#1029911yescharacteristic, complemented, Sylow
178C23#8813611yescharacteristic
179Q8—524no—
180Q8—1044no—
181Q8—1042no—
182Q8—1042no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—522no—
187C2×C4—524no—
188C2×C4—528no—
189C2×C4#8812811yescharacteristic
190C2×C4#8813612yes—
191C2×C4#8814912yes—
192C2×C4#8814911yescharacteristic
193C2×C4C2×#609512yes—
194C2×C4#8816212yes—
195C8—44no—
196C8—1041no—
197C22—22no—
198C22#1171833211yescharacteristic
199C22#1171839212yes—
200C4—28no—
201C4—22no—
202C4—1044no—
203C4—1042no—
204C4#1171835411yescharacteristic
205C4#1171837311yescharacteristic
206C4#1171848714yes—
207C4#1171850912yes—
208C2—22no—
209C2#1311587512yes—
210C2#1311592611yescharacteristic
subgroupG/H
centerC22#11718332
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#1276D13
hypocenterC13#10299
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

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
#131259822
#131232342
#131158132
#131135072
C13×#12762
#1029913