Finite Group Databasebeta

← #22612052

Subgroups — #22612052

Order 9344.

148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C2×D1168C211yesmaximal, characteristic, complemented
2#17989003C211yesmaximal, characteristic, complemented
3#17988858C212yesmaximal, complemented
4#17988399C212yesmaximal, complemented
5#368×C73C211yesmaximal, characteristic, complemented
6#14556619—22no—
7C2×D584C2212yes—
8#14556597C2211yescharacteristic
9D1168—21no—
10D1168—21no—
11#14556531C2211yescharacteristic
12#14556530—21no—
13C16×D73—21no—
14#14556507—22no—
15C2×C16×C73C2211yescharacteristic
16#108×C73C2212yes—
17#11924028D411yescharacteristic
18C2×D292—22no—
19#11924017—42no—
20D584—22no—
21D584—22no—
22D584—42no—
23#11924012D411yescharacteristic
24#11924011—21no—
25C8×D73—21no—
26#11924003—21no—
27M16×C73—22no—
28C2×C8×C73C2311yescharacteristic
29C16×C73D411yescharacteristic
30C16×C73D411yescharacteristic
31C22×D73—42no—
32C2×C4×C73C2×D411yescharacteristic
33C22⋊D73—21no—
34D292—42no—
35D292—42no—
36D292D811yescharacteristic
37C4×D73—21no—
38Dic146D811yescharacteristic
39C8×C73—42no—
40C8×C73C2×D411yescharacteristic
41C8×C73#4111yescharacteristic
42#10596831—21no—
43C22×C73#13511yescharacteristic
44C2×D73—21no—
45C2×D73—82no—
46C2×D73—162no—
47C4×C73#12111yescharacteristic
48C4×C73C2×D811yescharacteristic
49Dic73—21no—
50C2×C73—21no—
51C2×C73#46611yescharacteristic
52D73—41no—
53D73—162no—
54#2221—731nomaximal, Sylow
55C73#222111yescharacteristic, complemented, Sylow
56C2×D16—731no—
57#504—731no—
58#472—732no—
59#368D7311yescharacteristic, complemented
60#361—732no—
61AGL(1,ℤ/8)—1462no—
62C2×D8—732no—
63#131—731no—
64D16—1461no—
65D16—1461no—
66M32—731no—
67M32—1461no—
68C2×C16—1461no—
69C2×C16C2×D7311yescharacteristic
70#108C2×D7312yes—
71#100—1462no—
72#41—731no—
73C2×D4—1462no—
74SD16—2922no—
75D8—2922no—
76D8—1462no—
77D8—1462no—
78M16—22no—
79M16—731no—
80M16—1461no—
81C2×C8—1461no—
82C2×C8C22×D7311yescharacteristic
83C16—1461no—
84C16D29211yescharacteristic
85C16D29211yescharacteristic
86C23—2922no—
87Q8—731no—
88D4—2922no—
89D4—2922no—
90D4—731no—
91D4—1461no—
92C2×C4—1461no—
93C2×C4D4×D7311yescharacteristic
94C8—42no—
95C8—1461no—
96C8C2×D29211yescharacteristic
97C8#1192402911yescharacteristic
98C22—5842no—
99C22—11682no—
100C22—1461no—
101C22#1455661411yescharacteristic
102C4—1461no—
103C4#1455656611yescharacteristic
104C4D8×D7311yescharacteristic
105C2—21no—
106C2—2921no—
107C2—11682no—
108C2#1798882411yescharacteristic
subgroupG/H
centerC2#17988824
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#368×C73C2
socleC2×C73#466
hypercenter#368D73
hypocenterC73#2221
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
1. C2×D1168C2semidirect
2. #17989003C2semidirect
3. #17988858C2semidirect
4. #17988399C2semidirect
5. #368×C73C2semidirect
55. C73#2221semidirect
59. #368D73semidirect