Finite Group Databasebeta

← #15757871

Subgroups — #15757871

Order 3328.

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

normal subgroups only

This group has 376 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#13125358C211yesmaximal, characteristic
2#13123942C211yesmaximal, characteristic
3#13113310C212yesmaximal
4#13112736C212yesmaximal
5C13×#1544C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7#11719175C2211yescharacteristic
8C13×#431C2212yes—
9#11718741—22no—
10#11718726C414yes—
11#11718685—24no—
12#11718661—22no—
13#11718659—22no—
14#11718587C2212yes—
15C2×#88043C2211yescharacteristic
16C13×#332—22no—
17#11718048—24no—
18C13×C4⋊Q8D412yes—
19C13×#125C2×C412yes—
20C13×C22⋊Q8—22no—
21C4×Q8×C13—22no—
22C13×#117D412yes—
23C2×C42×C13C2311yescharacteristic
24#88180—21no—
25#88178—22no—
26C22×#1055—21no—
27#88124—21no—
28#88123C2×C412yes—
29C4×Dic26—22no—
30C13×C4⋊C8—22no—
31C13×C22⋊C8—22no—
32C4×C8×C13—22no—
33C22⋊#1055—22no—
34#88048—24no—
35#88047—24no—
36C4⋊#1055—24no—
37C4⋊#1055D414yes—
38#88043—22no—
39#88043—22no—
40#88043—21no—
41#88043C2×C412yes—
42C4×#1055—22no—
43#9006—131nomaximal, Sylow
44C2×Q8×C13—22no—
45C22×C4×C13C2×D411yescharacteristic
46C22×C4×C13#4112yes—
47C2×Dic26—22no—
48C2×C8×C13—42no—
49C13×C4⋊C4—24no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4C22⋊C414yes—
52C13×C22⋊C4—22no—
53C42×C13—22no—
54C42×C13C22×C411yescharacteristic
55C42×C13C2×D412yes—
56C42×C13C2×D411yescharacteristic
57C22⋊Dic13—41no—
58C4⋊Dic13—22no—
59C4⋊Dic13—22no—
60#6101—42no—
61C4×Dic13—41no—
62C2×#1055—24no—
63C2×#1055—22no—
64C2×#1055—24no—
65#3162—131no—
66#2987—131no—
67#1544D1311yescharacteristic
68#1497—132no—
69#1302—132no—
70C23×C13#12311yescharacteristic
71Q8×C13—82no—
72C2×C4×C13—22no—
73C2×C4×C13—24no—
74C2×C4×C13—42no—
75C2×C4×C13C2×C22⋊C411yescharacteristic
76C2×C4×C13C4×D412yes—
77C2×C4×C13#12011yescharacteristic
78C2×C4×C13#12112yes—
79C2×Dic13—42no—
80Dic26—44no—
81C8×C13—82no—
82#1055—24no—
83#1055—44no—
84#533—131no—
85#533C2×D1311yescharacteristic
86#501—134no—
87#501—262no—
88#446—264no—
89#433—262no—
90#432—132no—
91#431C2×D1312yes—
92#427—262no—
93C2×#97—131no—
94#332—22no—
95Q8⋊C8—264no—
96C22×C13—22no—
97C22×C13—21no—
98C22×C13#38611yescharacteristic
99C4×C13—22no—
100C4×C13—22no—
101C4×C13—21no—
102C4×C13—44no—
103C4×C13#45612yes—
104Dic13—82no—
105C22×C8—261no—
106C4⋊Q8—132no—
107C4⋊Q8C22⋊D1312yes—
108#125—261no—
109#125C4×D1312yes—
110C22⋊Q8—22no—
111C22⋊Q8—262no—
112C4×Q8—22no—
113C4×Q8—262no—
114#117—261no—
115#117D5212yes—
116C2×C42C22×D1311yescharacteristic
117#107—264no—
118#106—264no—
119C4⋊C8—22no—
120C4⋊C8—134no—
121C4⋊C8—264no—
122C22⋊C8—22no—
123C22⋊C8—262no—
124#97—132no—
125#97—262no—
126#97—262no—
127#97—261no—
128C4×C8—22no—
129C4×C8—262no—
130C2×C13—41no—
131C2×C13#188112yes—
132C2×C13#188611yescharacteristic
133C2×Q8—22no—
134C2×Q8—262no—
135C22×C4C2×D5211yescharacteristic
136C22×C4#612912yes—
137C2×C8—42no—
138C2×C8—264no—
139C2×C8—262no—
140C2×C8—264no—
141C4⋊C4—24no—
142C4⋊C4—22no—
143C4⋊C4—262no—
144C4⋊C4—262no—
145C4⋊C4—522no—
146C4⋊C4#610314yes—
147C22⋊C4—22no—
148C22⋊C4—521no—
149C42—22no—
150C42—521no—
151C42C2×C4×D1311yescharacteristic
152C42D4×D1312yes—
153C42C2×C22⋊D1311yescharacteristic
154C13#900611yescharacteristic, complemented, Sylow
155C23#8814011yescharacteristic
156Q8—82no—
157Q8—524no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—42no—
161C2×C4—522no—
162C2×C4#8813512yes—
163C2×C4#8813611yescharacteristic
164C2×C4C2×#610311yescharacteristic
165C2×C4#8819312yes—
166C8—82no—
167C8—264no—
168C8—524no—
169C22—22no—
170C22—21no—
171C22#1171861911yescharacteristic
172C4—22no—
173C4—22no—
174C4—21no—
175C4—44no—
176C4—1042no—
177C4#1171841312yes—
178C2—41no—
179C2#1311519612yes—
180C2#1311522711yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1544C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#1544D13
hypocenterC13#9006
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
154. C13#9006semidirect

Maximal subgroups

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

subgroupindex
#131253582
#131239422
#131133102
#131127362
C13×#15442
#900613