Finite Group Databasebeta

← #15767082

Subgroups — #15767082

Order 3328.

342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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#13126230C211yesmaximal, characteristic
2#13115010C211yesmaximal, characteristic
3#13113567C212yesmaximal
4#13113452C212yesmaximal
5C13×#1307C211yesmaximal, characteristic
6#11719175C2212yes—
7C13×#432C2212yes—
8C13×#423C2211yescharacteristic
9#11718798—22no—
10C2×#88062—22no—
11#11718585C2211yescharacteristic
12C2×#88043C2211yescharacteristic
13#11718512—22no—
14#11718510—22no—
15#11718078—22no—
16#11718073—22no—
17#11718057—24no—
18C2×C13×M16D412yes—
19C2×C42×C13C2311yescharacteristic
20#88180—22no—
21#88178—22no—
22#88178—22no—
23C2×#6099—21no—
24C22×#1055—21no—
25C2×Dic52—22no—
26#88124—22no—
27#88123D412yes—
28#88123D412yes—
29C4×Dic26—22no—
30C4×Dic26—22no—
31C13×C4⋊C8—22no—
32C13×C4⋊C8—22no—
33C13×C22⋊C8—22no—
34C13×#97—22no—
35#88062—44no—
36#88057—22no—
37#88056—24no—
38C4⋊#1055—22no—
39#88043—21no—
40#88043D412yes—
41#10528—131nomaximal, Sylow
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13#4112yes—
44C2×Dic26—22no—
45C2×Dic26—22no—
46C13×M16—42no—
47C2×C8×C13—22no—
48C2×C8×C13—42no—
49C42×C13C2×D412yes—
50C42×C13C2×D411yescharacteristic
51C42×C13#4111yescharacteristic
52C22⋊Dic13—42no—
53C4⋊Dic13—22no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13—22no—
57#6101—42no—
58#6101—42no—
59C4×Dic13—42no—
60#6099—42no—
61C2×#1055—22no—
62C2×#1055—22no—
63C2×#1055—22no—
64C2×#1055—41no—
65Dic52—82no—
66#3255—131no—
67#1849—131no—
68#1559—132no—
69#1531—132no—
70#1307D1311yescharacteristic
71C23×C13#12411yescharacteristic
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—42no—
75C2×C4×C13#12011yescharacteristic
76C2×C4×C13#12112yes—
77C2×C4×C13#12111yescharacteristic
78C2×C4×C13#12312yes—
79C2×Dic13—42no—
80C2×Dic13—42no—
81Dic26—42no—
82Dic26—42no—
83Dic26—82no—
84C8×C13—42no—
85C8×C13—82no—
86#1055—24no—
87#1055—81no—
88#533—132no—
89#475—262no—
90#470—262no—
91#462—262no—
92#432C2×D1312yes—
93C2×#108—262no—
94#423—131no—
95#423C2×D1311yescharacteristic
96C2×#97—131no—
97#333—262no—
98#332—262no—
99#330—264no—
100C22×C13—22no—
101C22×C13—21no—
102C22×C13#39411yescharacteristic
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—21no—
106C4×C13#45311yescharacteristic
107C4×C13#45611yescharacteristic
108Dic13—82no—
109Dic13—82no—
110C2×Q16—262no—
111C2×M16—261no—
112C2×M16D5212yes—
113C22×C8—261no—
114C4⋊Q8—132no—
115C4⋊Q8—132no—
116#125—262no—
117C22⋊Q8—262no—
118C22⋊Q8—262no—
119C4×Q8—262no—
120C4×Q8—262no—
121#117—262no—
122C2×C42C22×D1311yescharacteristic
123#108—524no—
124#106—262no—
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—262no—
128#103—264no—
129C22⋊C8—22no—
130#97—22no—
131#97—132no—
132#97—261no—
133C2×C13—41no—
134C2×C13#203911yescharacteristic
135C2×C13#204912yes—
136C2×Q8—262no—
137C2×Q8—262no—
138C22×C4C2×D5211yescharacteristic
139C22×C4#612712yes—
140Q16—1042no—
141M16—42no—
142M16—522no—
143C2×C8—22no—
144C2×C8—42no—
145C2×C8—262no—
146C2×C8—262no—
147C2×C8—262no—
148C2×C8—521no—
149C4⋊C4—262no—
150C4⋊C4—262no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—522no—
154C4⋊C4—522no—
155C22⋊C4—522no—
156C42—522no—
157C42D4×D1312yes—
158C42D4×D1311yescharacteristic
159C42#613111yescharacteristic
160C13#1052811yescharacteristic, complemented, Sylow
161C23#8812911yescharacteristic
162Q8—522no—
163Q8—522no—
164Q8—1042no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4#8813611yescharacteristic
171C2×C4#8813812yes—
172C2×C4#8814812yes—
173C2×C4#8814911yescharacteristic
174C8—42no—
175C8—82no—
176C8—264no—
177C8—1041no—
178C22—21no—
179C22—22no—
180C22#1171833311yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—1042no—
185C4—1042no—
186C4#1171840811yescharacteristic
187C4#1171841311yescharacteristic
188C2—41no—
189C2#1311606111yescharacteristic
190C2#1311611912yes—
subgroupG/H
centerC22#11718333
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1307C2
socleC22×C13#394
prime radicalC23×C13#124
hypercenter#1307D13
hypocenterC13#10528
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
160. C13#10528semidirect

Maximal subgroups

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

subgroupindex
#131262302
#131150102
#131135672
#131134522
C13×#13072
#1052813