Finite Group Databasebeta

← #22608093

Subgroups — #22608093

Order 9344.

120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 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#17988963C211yesmaximal, characteristic
2#17988380C211yesmaximal, characteristic, complemented
3#353×C73C211yesmaximal, characteristic, complemented
4C2×#11924013—21no—
5C2×#11924013—21no—
6#14556588C411yescharacteristic, complemented
7#14556506—21no—
8C4×#10596831C411yescharacteristic, complemented
9#127×C73C2211yescharacteristic
10#99×C73—21no—
11C2×D292—21no—
12C2×D292—41no—
13#11924013—42no—
14#11924013—42no—
15C2×#10596831—21no—
16C22⋊Dic73—41no—
17C2×D4×C73—41no—
18C2×D4×C73D411yescharacteristic
19C2×D4×C73D411yescharacteristic
20C22⋊C4×C73—41no—
21C42×C73C2×C411yescharacteristic
22C23×C73—21no—
23C23×C73—21no—
24C22×D73—41no—
25D4×C73—41no—
26D4×C73—41no—
27D4×C73—82no—
28C2×C4×C73—21no—
29C2×C4×C73—81no—
30C2×C4×C73C22⋊C411yescharacteristic
31C2×Dic73—81no—
32D292—41no—
33D292—41no—
34D292—82no—
35#10596831—22no—
36C22×C73—41no—
37C22×C73—41no—
38C22×C73—81no—
39C22×C73—81no—
40C22×C73#9911yescharacteristic
41C2×D73—82no—
42C2×D73—81no—
43C4×C73—22no—
44C4×C73—21no—
45C4×C73—161no—
46Dic73—161no—
47C2×C73—21no—
48C2×C73—81no—
49C2×C73—81no—
50C2×C73#35311yescharacteristic
51D73—161no—
52#1408—731nomaximal, Sylow
53C73#140811yescharacteristic, complemented, Sylow
54#493—731no—
55#353—731no—
56#353D7311yescharacteristic, complemented
57C2×D8—1461no—
58C2×D8—1461no—
59#127—731no—
60#127C2×D7311yescharacteristic
61#99—21no—
62#99—1461no—
63C4×C8—731no—
64C2×D4—41no—
65C2×D4—2921no—
66C2×D4—1461no—
67C2×D4D29211yescharacteristic
68C2×D4C22⋊D7311yescharacteristic
69D8—2922no—
70D8—2922no—
71C2×C8—1461no—
72C22⋊C4—41no—
73C22⋊C4—2921no—
74C42C4×D7311yescharacteristic
75C23—21no—
76C23—21no—
77C23—2921no—
78D4—41no—
79D4—41no—
80D4—82no—
81D4—2921no—
82D4—2921no—
83D4—5842no—
84C2×C4—21no—
85C2×C4—81no—
86C2×C4—5841no—
87C2×C4#1192400511yescharacteristic
88C8—1462no—
89C22—41no—
90C22—41no—
91C22—81no—
92C22—81no—
93C22—5842no—
94C22—5841no—
95C22#1455650511yescharacteristic
96C4—22no—
97C4—21no—
98C4—161no—
99C4—11681no—
100C2—21no—
101C2—81no—
102C2—81no—
103C2—11681no—
104C2#1798837911yescharacteristic
subgroupG/H
centerC2#17988379
commutatorC42×C73C2×C4
Frattini#127C2×D73
Fitting#353×C73C2
socleC2×C73#353
hypercenter#353D73
hypocenterC73#1408
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #17988380C2semidirect
3. #353×C73C2semidirect
6. #14556588C4semidirect
8. C4×#10596831C4semidirect
53. C73#1408semidirect
56. #353D73semidirect