Finite Group Databasebeta

← #15750143

Subgroups — #15750143

Order 3328.

202 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 103 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#13113595C211yesmaximal, characteristic
2C2×#11718050C211yesmaximal, characteristic
3C13×#2162C211yesmaximal, characteristic
4C2×C4×C8×C13C2211yescharacteristic
5#11718585—21no—
6C2×C4⋊#1055—21no—
7C13×C4⋊C16—21no—
8C13×C22⋊C16C412yes—
9C4×C13×C16—21no—
10#11718050—21no—
11#11718050—21no—
12#11718050C412yes—
13#11718050C412yes—
14C22×C8×C13C2×C411yescharacteristic
15C22×C8×C13Q811yescharacteristic
16C2×C42×C13D411yescharacteristic
17C2×#6099—41no—
18C22×#1055—41no—
19C2×C13×C16—22no—
20C4×C8×C13C2×C411yescharacteristic
21C4×C8×C13C2×C411yescharacteristic
22C4×C8×C13D411yescharacteristic
23C4×C8×C13D411yescharacteristic
24C4⋊#1055—22no—
25C4⋊#1055—22no—
26C4⋊#1055—41no—
27C4⋊#1055—41no—
28#7288—131nomaximal, Sylow
29C22×C4×C13C4⋊C411yescharacteristic
30C22×C4×C13D811yescharacteristic
31C22×C4×C13Q1611yescharacteristic
32C2×C8×C13—22no—
33C2×C8×C13—41no—
34C2×C8×C13C4211yescharacteristic
35C2×C8×C13C22⋊C411yescharacteristic
36C2×C8×C13C4⋊C411yescharacteristic
37C2×C8×C13C4⋊C411yescharacteristic
38C42×C13C22⋊C411yescharacteristic
39C42×C13C22⋊C411yescharacteristic
40C42×C13SD1611yescharacteristic
41C42×C13SD1611yescharacteristic
42#6099—81no—
43#6099—81no—
44C2×#1055—42no—
45C2×#1055—42no—
46C2×#1055—81no—
47C2×#1055—81no—
48C13×C16—42no—
49#2162D1311yescharacteristic
50#1567—131no—
51C2×#335—131no—
52C23×C13#10711yescharacteristic
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—41no—
56C2×C4×C13#9511yescharacteristic
57C2×C4×C13#10211yescharacteristic
58C2×C4×C13#10211yescharacteristic
59C2×C4×C13#10311yescharacteristic
60C2×C4×C13#10311yescharacteristic
61C2×C4×C13#10611yescharacteristic
62C2×C4×C13D1611yescharacteristic
63C2×C4×C13SD3211yescharacteristic
64C2×C4×C13SD3211yescharacteristic
65C2×C4×C13Q3211yescharacteristic
66C8×C13—21no—
67C8×C13—21no—
68C8×C13—21no—
69C8×C13#10812yes—
70#1055—82no—
71#1055—82no—
72#423—261no—
73C2×C4⋊C8—261no—
74C2×C4×C8C2×D1311yescharacteristic
75C4⋊C16—21no—
76C22⋊C16Dic1312yes—
77C4×C16—21no—
78#335—132no—
79#335—132no—
80#335—261no—
81#335—261no—
82C22×C13—21no—
83C22×C13—21no—
84C22×C13#34011yescharacteristic
85C22×C13#36611yescharacteristic
86C22×C13#36711yescharacteristic
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13#34111yescharacteristic
91C4×C13#34411yescharacteristic
92C4×C13#35711yescharacteristic
93C4×C13#35711yescharacteristic
94C4×C13#35811yescharacteristic
95C4×C13#35811yescharacteristic
96C2×M16—521no—
97C22×C8—521no—
98C22×C8Dic2611yescharacteristic
99C22×C8C2×Dic1311yescharacteristic
100C2×C42D5211yescharacteristic
101C2×C16—22no—
102C4⋊C8—262no—
103C4⋊C8—262no—
104C4⋊C8—521no—
105C4⋊C8—521no—
106C4×C8C4×D1311yescharacteristic
107C4×C8C4×D1311yescharacteristic
108C4×C8C22⋊D1311yescharacteristic
109C4×C8C22⋊D1311yescharacteristic
110C2×C13—21no—
111C2×C13—21no—
112C2×C13#130111yescharacteristic
113C2×C13#138011yescharacteristic
114C2×C13#138811yescharacteristic
115C22×C4D10411yescharacteristic
116C22×C4Dic5211yescharacteristic
117C22×C4C4⋊Dic1311yescharacteristic
118M16—1041no—
119M16—1041no—
120C2×C8—22no—
121C2×C8—41no—
122C2×C8—522no—
123C2×C8—522no—
124C2×C8—1041no—
125C2×C8—1041no—
126C2×C8C4×Dic1311yescharacteristic
127C2×C8#610111yescharacteristic
128C2×C8#610111yescharacteristic
129C2×C8C22⋊Dic1311yescharacteristic
130C42#609511yescharacteristic
131C42#609511yescharacteristic
132C42#610311yescharacteristic
133C42#610311yescharacteristic
134C16—42no—
135C13#728811yescharacteristic, complemented, Sylow
136C23#8805811yescharacteristic
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4D20811yescharacteristic
141C2×C4#8804011yescharacteristic
142C2×C4#8804011yescharacteristic
143C2×C4Dic10411yescharacteristic
144C2×C4#8805611yescharacteristic
145C2×C4#8805611yescharacteristic
146C2×C4#8805711yescharacteristic
147C2×C4#8806111yescharacteristic
148C2×C4#8806111yescharacteristic
149C2×C4#8807111yescharacteristic
150C8—21no—
151C8—21no—
152C8—21no—
153C8—1042no—
154C8—1042no—
155C8#8806212yes—
156C22—21no—
157C22—21no—
158C22#1171809611yescharacteristic
159C22#1171809711yescharacteristic
160C22#1171814311yescharacteristic
161C4—21no—
162C4—21no—
163C4—21no—
164C4#1171809511yescharacteristic
165C4#1171809511yescharacteristic
166C4#1171810111yescharacteristic
167C4#1171810111yescharacteristic
168C4#1171812511yescharacteristic
169C4#1171815011yescharacteristic
170C2—21no—
171C2—21no—
172C2#1311273211yescharacteristic
173C2#1311292811yescharacteristic
174C2#1311294811yescharacteristic
subgroupG/H
centerC2×C4#88061
commutatorC2×C8×C13C42
FrattiniC2×C4×C8C2×D13
FittingC13×#2162C2
socleC22×C13#340
prime radicalC23×C13#107
cosocleC2×C4×C8×C13C22
hypercenter#2162D13
hypocenterC13#7288
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
135. C13#7288semidirect

Maximal subgroups

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

subgroupindex
#131135952
C2×#117180502
C13×#21622
#728813