Finite Group Databasebeta

← #15756445

Subgroups — #15756445

Order 3328.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#13117439C211yesmaximal, characteristic
2#13114916C211yesmaximal, characteristic
3#13112745C214yesmaximal
4C13×#1821C211yesmaximal, characteristic
5C22×C13×C4⋊C4C2211yescharacteristic
6C13×#407C2212yes—
7#11718873C412yes—
8#11718872C2212yes—
9C4×C22⋊Dic13C412yes—
10#11718868C2212yes—
11#11718642—22no—
12#11718642—22no—
13C13×#343—22no—
14#11718122—22no—
15C23×C4×C13C2×C411yescharacteristic
16C23×C4×C13C2×C411yescharacteristic
17C23×C4×C13C2311yescharacteristic
18C2×C13×M16—22no—
19C2×C13×C4⋊C4—24no—
20C2×C13×C4⋊C4D412yes—
21C2×C13×C4⋊C4D412yes—
22C2×C22⋊Dic13C2×C414yes—
23C2×C4⋊Dic13—22no—
24C2×C4×Dic13—22no—
25C2×#6099—22no—
26C13×C22⋊C8—24no—
27#88071—22no—
28#88071—22no—
29#88071—22no—
30#88071—22no—
31C22⋊#1055—24no—
32#8755—131nomaximal, Sylow
33C24×C13C22×C411yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—42no—
37C22×C4×C13—81no—
38C22×C4×C13—81no—
39C22×C4×C13C22⋊C412yes—
40C22×C4×C13C22⋊C412yes—
41C22×C4×C13C2×D411yescharacteristic
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13#4114yes—
44C22×Dic13—24no—
45C13×M16—44no—
46C2×C8×C13—42no—
47C13×C4⋊C4—24no—
48C13×C4⋊C4—24no—
49C22⋊Dic13—44no—
50C4⋊Dic13—82no—
51C4×Dic13—82no—
52#6099—44no—
53C2×#1055—42no—
54#2313—131no—
55#1821—131no—
56#1821D1311yescharacteristic
57#1306—134no—
58C23×C13—22no—
59C23×C13—41no—
60C23×C13—41no—
61C23×C13C2×C22⋊C411yescharacteristic
62C23×C13#11712yes—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—44no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—82no—
71C2×C4×C13—82no—
72C2×C4×C13#12312yes—
73C2×C4×C13#12312yes—
74C2×Dic13—44no—
75C2×Dic13—44no—
76C2×Dic13—44no—
77C8×C13—82no—
78#1055—82no—
79C22×C4⋊C4C2×D1311yescharacteristic
80#407—132no—
81#407C2×D1312yes—
82#387—262no—
83#387—262no—
84#381—132no—
85#380—132no—
86C4×C22⋊C4—132no—
87#343—22no—
88#343—262no—
89C22×C13—21no—
90C22×C13—21no—
91C22×C13—22no—
92C22×C13—22no—
93C22×C13—22no—
94C22×C13—44no—
95C22×C13#38111yescharacteristic
96C22×C13#41012yes—
97C4×C13—22no—
98C4×C13—22no—
99C4×C13—42no—
100C4×C13—42no—
101Dic13—84no—
102C23×C4C4×D1311yescharacteristic
103C23×C4C4×D1311yescharacteristic
104C23×C4C22×D1311yescharacteristic
105C2×M16—22no—
106C2×M16—262no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—262no—
109C2×C4⋊C4D5212yes—
110C2×C4⋊C4C22⋊D1312yes—
111C2×C22⋊C4—134no—
112C2×C42—262no—
113C22⋊C8—24no—
114C22⋊C8—264no—
115#95—262no—
116#95—262no—
117#95—262no—
118#95—262no—
119C2×C13—22no—
120C2×C13—42no—
121C2×C13#182011yescharacteristic
122C2×C13#182911yescharacteristic
123C2×C13#183011yescharacteristic
124C24C2×C4×D1311yescharacteristic
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—42no—
128C22×C4—81no—
129C22×C4—81no—
130C22×C4—264no—
131C22×C4#610312yes—
132C22×C4#610312yes—
133C22×C4C2×D5211yescharacteristic
134C22×C4#612914yes—
135C22×C4C2×C22⋊D1311yescharacteristic
136M16—44no—
137M16—524no—
138C2×C8—42no—
139C2×C8—522no—
140C4⋊C4—24no—
141C4⋊C4—24no—
142C4⋊C4—1042no—
143C22⋊C4—524no—
144C42—1042no—
145C13#875511yescharacteristic, complemented, Sylow
146C23—22no—
147C23—41no—
148C23—41no—
149C23#8813112yes—
150C23C2×#610311yescharacteristic
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—524no—
161C2×C4—524no—
162C2×C4—524no—
163C2×C4#8814012yes—
164C2×C4#8818912yes—
165C8—82no—
166C8—1042no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—44no—
173C22#1171860411yescharacteristic
174C22#1171866712yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—1044no—
180C2—22no—
181C2—42no—
182C2#1311491111yescharacteristic
183C2#1311494511yescharacteristic
184C2#1311494811yescharacteristic
subgroupG/H
centerC22#11718604
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1821C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenter#1821D13
hypocenterC13#8755
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
145. C13#8755semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131149162
#131127452
C13×#18212
#875513