Finite Group Databasebeta

← #22626943

Subgroups — #22626943

Order 9344.

160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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#17989700C211yesmaximal, characteristic
2C2×C4⋊#10596842C211yesmaximal, characteristic
3M16×#64408C211yesmaximal, characteristic
4C22×#10596842C412yes—
5C4⋊#10596842—21no—
6C4⋊#10596842—21no—
7C4⋊#10596842—21no—
8C22⋊#10596842C412yes—
9C4×#10596842—21no—
10D73⋊M16C411yescharacteristic
11C2×C4×#64408C2211yescharacteristic
12#14556645—21no—
13C8×#64408—21no—
14M16×D73C411yescharacteristic
15C2×#10596842—22no—
16C2×#10596842—22no—
17C2×#10596842—42no—
18C22×#64408C2×C411yescharacteristic
19C22×#64408C2×C411yescharacteristic
20#11924038—21no—
21#11924037C812yescomplemented
22#11924036—21no—
23C4×#64408D411yescharacteristic
24C4×#64408D411yescharacteristic
25C4×#64408D411yescharacteristic
26C4×#64408Q811yescharacteristic
27C2×C4×D73C2×C411yescharacteristic
28#11924012C811yescharacteristic, complemented
29#11924011—21no—
30C8×D73—21no—
31M16×C73C811yescharacteristic, complemented
32C22×D73C4211yescharacteristic
33C2×#64408—21no—
34C2×#64408—21no—
35C2×#64408—41no—
36C2×#64408C22⋊C411yescharacteristic
37C2×#64408C22⋊C411yescharacteristic
38C2×#64408C4⋊C411yescharacteristic
39C2×#64408C4⋊C411yescharacteristic
40#10596842—42no—
41#10596842—42no—
42C2×C4×C73C2×C811yescharacteristic
43C2×Dic73C2×C811yescharacteristic
44C4×D73C22⋊C411yescharacteristic
45C4×D73C4⋊C411yescharacteristic
46C4×D73M1611yescharacteristic
47C4×D73M1611yescharacteristic
48#10596833—22no—
49C8×C73—21no—
50#10596831—21no—
51C22×C73C4×C811yescharacteristic
52C2×D73—21no—
53C2×D73—21no—
54C2×D73#9511yescharacteristic
55C2×D73#9711yescharacteristic
56#64408—21no—
57#64408—21no—
58#64408—21no—
59#64408#10011yescharacteristic
60#64408#10111yescharacteristic
61C4×C73C22⋊C811yescharacteristic
62C4×C73C4⋊C811yescharacteristic
63Dic73C22⋊C811yescharacteristic
64Dic73C4⋊C811yescharacteristic
65C2×C73—21no—
66C2×C73#33611yescharacteristic
67D73—21no—
68D73#34311yescharacteristic
69D73#34411yescharacteristic
70#1283—731nomaximal, Sylow
71C73#128311yescharacteristic, complemented, Sylow
72#431—731no—
73C2×C4⋊C8—731no—
74C4×M16—731no—
75C2×M16—731no—
76C2×M16—731no—
77C22×C8—732no—
78C2×C42—731no—
79C4⋊C8—1461no—
80C4⋊C8—1461no—
81C4⋊C8—1461no—
82C22⋊C8—732no—
83#97—1461no—
84C4×C8—1461no—
85C4×C8—1461no—
86C22×C4—731no—
87C22×C4—731no—
88C22×C4—731no—
89M16—732no—
90M16—731no—
91M16—1461no—
92M16—1461no—
93M16#1059684211yescharacteristic, complemented
94C2×C8—2922no—
95C2×C8—1461no—
96C2×C8—1462no—
97C2×C8—1462no—
98C2×C8—1461no—
99C42—731no—
100C42—731no—
101C42—731no—
102C42—731no—
103C23—731no—
104C2×C4—2921no—
105C2×C4—731no—
106C2×C4—731no—
107C2×C4—731no—
108C2×C4—731no—
109C2×C4—731no—
110C2×C4—731no—
111C2×C4—731no—
112C2×C4—731no—
113C2×C4—731no—
114C2×C4—1461no—
115C2×C4—1461no—
116C2×C4C2×#1059684211yescharacteristic
117C8—21no—
118C8—2922no—
119C8—2922no—
120C8—1462no—
121C8—1461no—
122C22—731no—
123C22—731no—
124C22—1461no—
125C22—1461no—
126C22C4×#1059684211yescharacteristic
127C4—731no—
128C4—731no—
129C4—731no—
130C4—731no—
131C4—1461no—
132C4—1461no—
133C4—1461no—
134C4C22⋊#1059684211yescharacteristic
135C4C4⋊#1059684211yescharacteristic
136C2—21no—
137C2—731no—
138C2—731no—
139C2—1461no—
140C2(C2×#10596842)⋊C411yescharacteristic
subgroupG/H
centerC2(C2×#10596842)⋊C4
commutatorC22×C73C4×C8
FrattiniC2×C4C2×#10596842
FittingM16×C73C8
socleC2×C73#336
hypercenterM16#10596842
hypocenterC73#1283
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
21. #11924037C8semidirect
28. #11924012C8semidirect
31. M16×C73C8semidirect
71. C73#1283semidirect
93. M16#10596842semidirect