Finite Group Databasebeta

← #15750621

Subgroups — #15750621

Order 3328.

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

normal subgroups only

This group has 166 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
1C22×#88034C211yesmaximal, characteristic
2C2×#11718098C211yesmaximal, characteristic
3C2×C13×#368C211yesmaximal, characteristic
4C22×C13×C16C2211yescharacteristic
5C2×C13×#108—21no—
6C2×#88059—21no—
7C13×#368—21no—
8C13×#368C412yes—
9#11718098—21no—
10#11718098C412yes—
11C2×#88034—21no—
12C2×#88034—21no—
13C2×#88034C412yes—
14C2×C13×M16—41no—
15C22×C8×C13D411yescharacteristic
16C2×#6099—41no—
17C2×C13×C16C2×C411yescharacteristic
18C2×C13×C16C2×C411yescharacteristic
19C2×C13×C16C2×C411yescharacteristic
20C2×C13×C16D411yescharacteristic
21C2×C13×C16D411yescharacteristic
22C2×C13×C16Q811yescharacteristic
23C13×#108—22no—
24C13×#108—41no—
25#88059—22no—
26#88059—41no—
27#88034—22no—
28#7472—131nomaximal, Sylow
29C22×C4×C13D811yescharacteristic
30C13×M16—42no—
31C13×M16—81no—
32C2×C8×C13—81no—
33C2×C8×C13C22⋊C411yescharacteristic
34C2×C8×C13C22⋊C411yescharacteristic
35C2×C8×C13C4⋊C411yescharacteristic
36C2×C8×C13SD1611yescharacteristic
37C2×C8×C13SD1611yescharacteristic
38C2×C8×C13Q1611yescharacteristic
39#6099—42no—
40#6099—81no—
41C2×#1055—81no—
42C13×C16C4211yescharacteristic
43C13×C16C22⋊C411yescharacteristic
44C13×C16C4⋊C411yescharacteristic
45C13×C16C4⋊C411yescharacteristic
46C22×C32—131no—
47C2×#368—131no—
48C2×#368D1311yescharacteristic
49C23×C13Q3211yescharacteristic
50C2×C4×C13#10211yescharacteristic
51C2×C4×C13#10211yescharacteristic
52C2×C4×C13#10711yescharacteristic
53C2×C4×C13D1611yescharacteristic
54C2×C4×C13SD3211yescharacteristic
55C2×C4×C13SD3211yescharacteristic
56C8×C13—82no—
57C8×C13#9511yescharacteristic
58C8×C13#10311yescharacteristic
59C8×C13#10311yescharacteristic
60C8×C13#10611yescharacteristic
61#1055—82no—
62C22×C16C2×D1311yescharacteristic
63C2×#108—21no—
64C2×#108—261no—
65C2×C32—132no—
66C2×C32—261no—
67C2×C32—261no—
68#368—21no—
69#368—132no—
70#368—261no—
71#368Dic1312yes—
72C22×C13—22no—
73C22×C13#35811yescharacteristic
74C22×C13#35811yescharacteristic
75C22×C13#36611yescharacteristic
76C4×C13#34011yescharacteristic
77C4×C13#35711yescharacteristic
78C4×C13#35711yescharacteristic
79C4×C13#36711yescharacteristic
80C2×M16—41no—
81C2×M16—521no—
82C22×C8C22⋊D1311yescharacteristic
83C2×C16Dic2611yescharacteristic
84C2×C16C4×D1311yescharacteristic
85C2×C16C4×D1311yescharacteristic
86C2×C16D5211yescharacteristic
87C2×C16C2×Dic1311yescharacteristic
88C2×C16C22⋊D1311yescharacteristic
89#108—22no—
90#108—41no—
91#108—262no—
92#108—521no—
93C32—262no—
94C2×C13—21no—
95C2×C13—21no—
96C2×C13#138011yescharacteristic
97C2×C13#142512yes—
98C22×C4#610411yescharacteristic
99M16—42no—
100M16—81no—
101M16—522no—
102M16—1041no—
103C2×C8—81no—
104C2×C8—1041no—
105C2×C8#610111yescharacteristic
106C2×C8#610311yescharacteristic
107C2×C8#610511yescharacteristic
108C2×C8#610611yescharacteristic
109C2×C8#610711yescharacteristic
110C2×C8C22⋊Dic1311yescharacteristic
111C16C4×Dic1311yescharacteristic
112C16#610111yescharacteristic
113C16C4⋊Dic1311yescharacteristic
114C16#610311yescharacteristic
115C13#747211yescharacteristic, complemented, Sylow
116C23#8806911yescharacteristic
117C2×C4#8804711yescharacteristic
118C2×C4#8804911yescharacteristic
119C2×C4#8806611yescharacteristic
120C2×C4#8806711yescharacteristic
121C2×C4#8806811yescharacteristic
122C2×C4#8807211yescharacteristic
123C8—82no—
124C8—1042no—
125C8#8804811yescharacteristic
126C8#8805011yescharacteristic
127C8#8807111yescharacteristic
128C8#8807511yescharacteristic
129C22—22no—
130C22#1171808111yescharacteristic
131C22#1171808411yescharacteristic
132C22#1171815611yescharacteristic
133C4#1171808211yescharacteristic
134C4#1171808311yescharacteristic
135C4#1171812111yescharacteristic
136C4#1171815411yescharacteristic
137C2—21no—
138C2—21no—
139C2#1311292711yescharacteristic
140C2#1311303912yes—
subgroupG/H
centerC2×C4#88066
commutatorC13×C16C42
FrattiniC22×C16C2×D13
FittingC2×C13×#368C2
socleC22×C13#366
prime radicalC23×C13Q32
cosocleC22×C13×C16C22
hypercenterC2×#368D13
hypocenterC13#7472
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#368

Complements

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

NH ≅ G/Ntype
115. C13#7472semidirect

Maximal subgroups

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

subgroupindex
C22×#880342
C2×#117180982
C2×C13×#3682
#747213