Finite Group Databasebeta

← #15750625

Subgroups — #15750625

Order 3328.

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

normal subgroups only

This group has 170 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
2#13116620C211yesmaximal, characteristic
3C2×C13×#368C211yesmaximal, characteristic
4C22×C13×C16C2211yescharacteristic
5C2×C13×#108—21no—
6#11718767—21no—
7C13×#368—21no—
8C13×#368C412yescomplemented
9#11718097—21no—
10#11718096C412yes—
11C2×#88034—21no—
12C2×#88034—21no—
13C2×#88034C412yescomplemented
14C2×C13×M16—41no—
15C22×C8×C13D411yescharacteristic
16#88180—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#88058—22no—
26#88057—41no—
27#88034—22no—
28#7473—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
39C22⋊Dic13—81no—
40C4⋊Dic13—42no—
41C4×Dic13—81no—
42C13×C16C4211yescharacteristic
43C13×C16C22⋊C411yescharacteristic
44C13×C16C4⋊C411yescharacteristic
45C13×C16C4⋊C411yescharacteristic
46C22×C32—131no—
47C2×#368D1311yescharacteristic
48#2158—131no—
49C23×C13SD3211yescharacteristic
50C2×C4×C13#10211yescharacteristic
51C2×C4×C13#10211yescharacteristic
52C2×C4×C13#10711yescharacteristic
53C2×C4×C13D1611yescharacteristic
54C2×C4×C13SD3211yescharacteristic
55C2×C4×C13Q3211yescharacteristic
56C2×Dic13—82no—
57C8×C13—82no—
58C8×C13#9511yescharacteristic
59C8×C13#10311yescharacteristic
60C8×C13#10311yescharacteristic
61C8×C13#10611yescharacteristic
62C22×C16C2×D1311yescharacteristic
63C2×#108—21no—
64#427—261no—
65C2×C32—132no—
66C2×C32—261no—
67C2×C32—261no—
68#368—21no—
69#368Dic1312yescomplemented
70#367—261no—
71#366—132no—
72C22×C13—22no—
73C22×C13#35711yescharacteristic
74C22×C13#35811yescharacteristic
75C22×C13#36711yescharacteristic
76C4×C13#34011yescharacteristic
77C4×C13#35711yescharacteristic
78C4×C13#35811yescharacteristic
79C4×C13#36611yescharacteristic
80Dic13—162no—
81C2×M16—41no—
82C22×C8C22⋊D1311yescharacteristic
83#117—521no—
84C2×C16Dic2611yescharacteristic
85C2×C16C4×D1311yescharacteristic
86C2×C16C4×D1311yescharacteristic
87C2×C16D5211yescharacteristic
88C2×C16C2×Dic1311yescharacteristic
89C2×C16C22⋊D1311yescharacteristic
90#108—22no—
91#108—41no—
92#107—262no—
93#106—521no—
94C32—262no—
95C2×C13—21no—
96C2×C13—21no—
97C2×C13#138011yescharacteristic
98C2×C13#141712yes—
99C22×C4#610411yescharacteristic
100M16—42no—
101M16—81no—
102C2×C8—81no—
103C2×C8#610111yescharacteristic
104C2×C8#610311yescharacteristic
105C2×C8#610511yescharacteristic
106C2×C8#610611yescharacteristic
107C2×C8#610711yescharacteristic
108C2×C8C22⋊Dic1311yescharacteristic
109C4⋊C4—522no—
110C22⋊C4—1041no—
111C42—1041no—
112C16C4×Dic1311yescharacteristic
113C16#610111yescharacteristic
114C16C4⋊Dic1311yescharacteristic
115C16#610311yescharacteristic
116C13#747311yescharacteristic, complemented, Sylow
117C23#8806811yescharacteristic
118C2×C4—1042no—
119C2×C4#8804711yescharacteristic
120C2×C4#8804911yescharacteristic
121C2×C4#8806611yescharacteristic
122C2×C4#8806711yescharacteristic
123C2×C4#8806911yescharacteristic
124C2×C4#8807211yescharacteristic
125C8—82no—
126C8#8804811yescharacteristic
127C8#8805011yescharacteristic
128C8#8807111yescharacteristic
129C8#8807511yescharacteristic
130C22—22no—
131C22#1171808211yescharacteristic
132C22#1171808311yescharacteristic
133C22#1171815611yescharacteristic
134C4—2082no—
135C4#1171808111yescharacteristic
136C4#1171808411yescharacteristic
137C4#1171812111yescharacteristic
138C4#1171815411yescharacteristic
139C2—21no—
140C2—21no—
141C2#1311292711yescharacteristic
142C2#1311301912yes—
subgroupG/H
centerC2×C4#88066
commutatorC13×C16C42
FrattiniC22×C16C2×D13
FittingC2×C13×#368C2
socleC22×C13#357
prime radicalC23×C13SD32
cosocleC22×C13×C16C22
hypercenterC2×#368D13
hypocenterC13#7473
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
8. C13×#368C4semidirect
13. C2×#88034C4semidirect
69. #368Dic13semidirect
116. C13#7473semidirect

Maximal subgroups

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

subgroupindex
C22×#880342
#131166202
C2×C13×#3682
#747313