Finite Group Databasebeta

← #22626969

Subgroups — #22626969

Order 9344.

158 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 27 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#17989672C211yesmaximal, characteristic
2#17989672C211yesmaximal, characteristic
3#17989534C211yesmaximal, characteristic
4C22⋊#10596842—21no—
5C22⋊#10596842—21no—
6C23×#64408C411yescharacteristic
7C2×C4⋊#64408—21no—
8C2×C22⋊#64408C2211yescharacteristic
9(C2×#64408)⋊C4—21no—
10C22⋊C4×D73C411yescharacteristic
11C2×#10596842—41no—
12C2×#10596842—41no—
13C22×#64408—21no—
14C22×#64408—42no—
15C22×#64408—41no—
16C22×#64408D411yescharacteristic
17C22×#64408D411yescharacteristic
18C4⋊#64408—42no—
19C22⋊#64408—41no—
20C23×D73C2×C411yescharacteristic
21C2×C4×D73—21no—
22C22⋊Dic73C811yescharacteristic, complemented
23#11924005—21no—
24C22⋊C4×C73C811yescharacteristic, complemented
25C23×C73C2×C811yescharacteristic
26C22×D73—21no—
27C22×D73—21no—
28C22×D73—41no—
29C22×D73—41no—
30C22×D73C22⋊C411yescharacteristic
31C22×D73M1611yescharacteristic
32C2×#64408—22no—
33C2×#64408—21no—
34C2×#64408—21no—
35C2×#64408—41no—
36C2×#64408—42no—
37C2×#64408—41no—
38C2×#64408—41no—
39C2×#64408—41no—
40C2×#64408—42no—
41#10596842—81no—
42#10596842—81no—
43C2×C4×C73—21no—
44C2×Dic73—21no—
45C4×D73—41no—
46C4×D73—41no—
47C22×C73—21no—
48C22×C73—41no—
49C22×C73C22⋊C811yescharacteristic
50C2×D73—21no—
51C2×D73—21no—
52C2×D73—21no—
53C2×D73—42no—
54C2×D73—41no—
55C2×D73—41no—
56C2×D73—41no—
57C2×D73#9911yescharacteristic
58C2×D73#10111yescharacteristic
59#64408—41no—
60#64408—42no—
61#64408—41no—
62C4×C73—41no—
63Dic73—41no—
64C2×C73—21no—
65C2×C73—41no—
66C2×C73#32411yescharacteristic
67D73—21no—
68D73—41no—
69D73AΣL(1,𝔽16)11yescharacteristic
70D73#35211yescharacteristic
71#1326—731nomaximal, Sylow
72C73#132611yescharacteristic, complemented, Sylow
73#385—731no—
74#323—731no—
75#323—731no—
76C23×C4—731no—
77C2×C4⋊C4—1461no—
78C2×C22⋊C4—731no—
79C2×C22⋊C4—731no—
80C22⋊C8—1461no—
81C22⋊C8—1461no—
82#95—1461no—
83C24—731no—
84C22×C4—2921no—
85C22×C4—2922no—
86C22×C4—731no—
87C22×C4—731no—
88C22×C4—1461no—
89C22×C4—1461no—
90C2×C8—2921no—
91C2×C8—2921no—
92C4⋊C4—2922no—
93C22⋊C4—2921no—
94C22⋊C4—731no—
95C22⋊C4—1461no—
96C22⋊C4#1059684211yescharacteristic, complemented
97C23—2921no—
98C23—2921no—
99C23—731no—
100C23—731no—
101C23—1461no—
102C23—1461no—
103C23C2×#1059684211yescharacteristic
104C2×C4—21no—
105C2×C4—2921no—
106C2×C4—2921no—
107C2×C4—2922no—
108C2×C4—2921no—
109C2×C4—2921no—
110C2×C4—2922no—
111C2×C4—2921no—
112C2×C4—2921no—
113C2×C4—1461no—
114C2×C4—1461no—
115C2×C4—1462no—
116C2×C4—1461no—
117C8—5841no—
118C8—5841no—
119C22—21no—
120C22—41no—
121C22—2921no—
122C22—2921no—
123C22—2921no—
124C22—2922no—
125C22—731no—
126C22—731no—
127C22—1461no—
128C22—1461no—
129C22—1461no—
130C22C22⋊#1059684211yescharacteristic
131C4—41no—
132C4—2921no—
133C4—2921no—
134C4—2921no—
135C4—2922no—
136C2—21no—
137C2—41no—
138C2—2921no—
139C2—731no—
140C2—731no—
141C2—1461no—
142C2#1798967311yescharacteristic
subgroupG/H
centerC2#17989673
commutatorC23×C73C2×C8
FrattiniC23C2×#10596842
FittingC22⋊C4×C73C8
socleC2×C73#324
hypercenterC22⋊C4#10596842
hypocenterC73#1326
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C23 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
22. C22⋊Dic73C8semidirect
24. C22⋊C4×C73C8semidirect
72. C73#1326semidirect
96. C22⋊C4#10596842semidirect