Finite Group Databasebeta

← #15760439

Subgroups — #15760439

Order 3328.

384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 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#13125218C211yesmaximal, characteristic
2#13123942C211yesmaximal, characteristic
3#13113552C212yesmaximal
4#13112709C212yesmaximal
5C13×#1537C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#432C2212yes—
9#11718754C414yes—
10#11718730—22no—
11#11718685—24no—
12#11718665—22no—
13#11718661—22no—
14#11718587C2212yes—
15C4×#6099C2211yescharacteristic
16C13×#330—22no—
17#11718078—24no—
18C22×Dic26—21no—
19C13×C4⋊Q8C2×C412yes—
20C13×#125D412yes—
21C13×C22⋊Q8—22no—
22C4×Q8×C13—22no—
23C13×#117D412yes—
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—22no—
26C2×#6099—21no—
27#88123—22no—
28#88123—21no—
29#88123C2×C412yes—
30C13×C4⋊C8—22no—
31C13×C22⋊C8—22no—
32C13×#97—22no—
33C22⋊#1055—22no—
34#88050—28no—
35C4⋊#1055—24no—
36C4⋊#1055D414yes—
37#88043—22no—
38#88043—22no—
39#88043—21no—
40C4×#1055—22no—
41C4×#1055C2×C412yes—
42#9422—131nomaximal, Sylow
43C2×Q8×C13—22no—
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13#4112yes—
46C22×Dic13—41no—
47C2×Dic26—22no—
48C2×Dic26—44no—
49C2×Dic26—41no—
50C2×C8×C13—42no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—24no—
53C13×C4⋊C4C22⋊C414yes—
54C13×C22⋊C4—22no—
55C42×C13—22no—
56C42×C13C22×C411yescharacteristic
57C42×C13C2×D412yes—
58C42×C13C2×D411yescharacteristic
59C4⋊Dic13—24no—
60C4⋊Dic13—42no—
61#6099—42no—
62C2×#1055—22no—
63C2×#1055—24no—
64#3139—131no—
65#2987—131no—
66#1556—132no—
67#1537D1311yescharacteristic
68#1291—132no—
69C23×C13#12311yescharacteristic
70Q8×C13—82no—
71C2×C4×C13—22no—
72C2×C4×C13—24no—
73C2×C4×C13—42no—
74C2×C4×C13C2×C22⋊C411yescharacteristic
75C2×C4×C13C4×D412yes—
76C2×C4×C13#12011yescharacteristic
77C2×C4×C13#12112yes—
78C2×Dic13—42no—
79C2×Dic13—82no—
80Dic26—44no—
81Dic26—82no—
82C8×C13—82no—
83#1055—42no—
84#1055—44no—
85#533C2×D1311yescharacteristic
86C2×C4⋊Q8—131no—
87#491—262no—
88#487—134no—
89#446—264no—
90#433—262no—
91#432—132no—
92#432C2×D1312yes—
93#419—262no—
94C4×M16—131no—
95#332—264no—
96#330—22no—
97C22×C13—21no—
98C22×C13—22no—
99C22×C13#38611yescharacteristic
100C4×C13—21no—
101C4×C13—22no—
102C4×C13—22no—
103C4×C13—44no—
104C4×C13#45412yes—
105Dic13—82no—
106C22×Q8—261no—
107C2×M16—261no—
108C4⋊Q8—132no—
109C4⋊Q8—262no—
110C4⋊Q8—261no—
111C4⋊Q8C4×D1312yes—
112#125C22⋊D1312yes—
113C22⋊Q8—22no—
114C4×Q8—22no—
115#117D5212yes—
116C2×C4⋊C4—262no—
117C2×C42C22×D1311yescharacteristic
118C4⋊C8—22no—
119C4⋊C8—134no—
120C4⋊C8—264no—
121#103—268no—
122C22⋊C8—22no—
123C22⋊C8—262no—
124#97—22no—
125#97—262no—
126#97—262no—
127#97—261no—
128C4×C8—132no—
129C4×C8—262no—
130C2×C13—41no—
131C2×C13#188811yescharacteristic
132C2×C13#190212yes—
133C2×Q8—22no—
134C2×Q8—262no—
135C2×Q8—524no—
136C2×Q8—521no—
137C22×C4—521no—
138C22×C4C2×D5211yescharacteristic
139C22×C4#612912yes—
140M16—522no—
141C2×C8—42no—
142C2×C8—264no—
143C2×C8—262no—
144C4⋊C4—22no—
145C4⋊C4—24no—
146C4⋊C4—264no—
147C4⋊C4—522no—
148C4⋊C4#610314yes—
149C22⋊C4—22no—
150C42—22no—
151C42C2×C4×D1311yescharacteristic
152C42D4×D1312yes—
153C42C2×C22⋊D1311yescharacteristic
154C13#942211yescharacteristic, complemented, Sylow
155C23#8814011yescharacteristic
156Q8—82no—
157Q8—524no—
158Q8—1042no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—42no—
162C2×C4—522no—
163C2×C4—1042no—
164C2×C4#8813512yes—
165C2×C4#8813611yescharacteristic
166C2×C4C2×#610311yescharacteristic
167C2×C4#8819312yes—
168C8—82no—
169C8—522no—
170C8—524no—
171C22—21no—
172C22—22no—
173C22#1171861911yescharacteristic
174C4—21no—
175C4—22no—
176C4—22no—
177C4—44no—
178C4—1042no—
179C4#1171841412yes—
180C2—41no—
181C2#1311523711yescharacteristic
182C2#1311530712yes—
subgroupG/H
centerC22#11718619
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1537C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#1537D13
hypocenterC13#9422
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
154. C13#9422semidirect

Maximal subgroups

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

subgroupindex
#131252182
#131239422
#131135522
#131127092
C13×#15372
#942213