Finite Group Databasebeta

← #22612051

Subgroups — #22612051

Order 9344.

148 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 49 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#17988857C212yesmaximal, complemented
3#17988417C211yesmaximal, characteristic, complemented
4#17988401C212yesmaximal, complemented
5#504×C73C211yesmaximal, characteristic, complemented
6#14556616—22no—
7C2×D584C2212yes—
8D1168—21no—
9D1168—21no—
10#14556527C2212yes—
11#14556507—22no—
12#131×C73C2211yescharacteristic
13M32×C73—21no—
14M32×C73C2211yescharacteristic
15C2×C16×C73—21no—
16C2×C16×C73C2211yescharacteristic
17C2×D292—22no—
18#11924015—42no—
19D584—22no—
20D584—22no—
21#11924013—42no—
22#11924012—22no—
23#41×C73D411yescharacteristic
24M16×C73—21no—
25M16×C73D411yescharacteristic
26C2×C8×C73—21no—
27C2×C8×C73C2311yescharacteristic
28C16×C73—21no—
29C16×C73D411yescharacteristic
30C16×C73D411yescharacteristic
31C22×D73—42no—
32Q8×C73D811yescharacteristic
33D4×C73—21no—
34D4×C73D811yescharacteristic
35C2×C4×C73—21no—
36C2×C4×C73C2×D411yescharacteristic
37D292—42no—
38D292—42no—
39C8×C73—21no—
40C8×C73C2×D411yescharacteristic
41C8×C73#4111yescharacteristic
42#10596831—42no—
43C22×C73—21no—
44C22×C73#13511yescharacteristic
45C2×D73—82no—
46C2×D73—162no—
47C4×C73—21no—
48C4×C73#12111yescharacteristic
49C4×C73C2×D811yescharacteristic
50C2×C73—21no—
51C2×C73—41no—
52C2×C73#46611yescharacteristic
53D73—162no—
54#2221—731nomaximal, Sylow
55C73#222111yescharacteristic, complemented, Sylow
56C2×D16—731no—
57#504D7311yescharacteristic, complemented
58#472—732no—
59#368—731no—
60#361—732no—
61AGL(1,ℤ/8)—1462no—
62C2×D8—732no—
63#131C2×D7311yescharacteristic
64D16—1461no—
65D16—1461no—
66M32—21no—
67M32C2×D7311yescharacteristic
68C2×C16—21no—
69C2×C16C2×D7311yescharacteristic
70#108—732no—
71#100—1462no—
72#41D29211yescharacteristic
73C2×D4—1462no—
74SD16—2922no—
75D8—2922no—
76D8—1462no—
77D8—1462no—
78M16—21no—
79M16—1462no—
80M16D29211yescharacteristic
81C2×C8—21no—
82C2×C8C22×D7311yescharacteristic
83C16—21no—
84C16C22⋊D7311yescharacteristic
85C16C22⋊D7311yescharacteristic
86C23—2922no—
87Q8D58411yescharacteristic
88D4—21no—
89D4—2922no—
90D4—2922no—
91D4D58411yescharacteristic
92C2×C4—21no—
93C2×C4C2×D29211yescharacteristic
94C8—21no—
95C8—2922no—
96C8C2×C22⋊D7311yescharacteristic
97C8#1192402811yescharacteristic
98C22—21no—
99C22—5842no—
100C22—11682no—
101C22#1455661311yescharacteristic
102C4—21no—
103C4#1455656511yescharacteristic
104C4C2×D58411yescharacteristic
105C2—21no—
106C2—41no—
107C2—11682no—
108C2#1798882311yescharacteristic
subgroupG/H
centerC2#17988823
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#504×C73C2
socleC2×C73#466
hypercenter#504D73
hypocenterC73#2221
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. C2×D1168C2semidirect
2. #17988857C2semidirect
3. #17988417C2semidirect
4. #17988401C2semidirect
5. #504×C73C2semidirect
55. C73#2221semidirect
57. #504D73semidirect