Finite Group Databasebeta

← #22607941

Subgroups — #22607941

Order 9344.

126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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#17988823C211yesmaximal, characteristic
2#17988350C211yesmaximal, characteristic, complemented
3C22⋊C16×C73C211yesmaximal, characteristic, complemented
4C2×D584C411yescharacteristic, complemented
5#14556565—21no—
6C2×C4⋊Dic73—21no—
7#14556525C411yescharacteristic, complemented
8#14556513—21no—
9C22×C8×C73C2211yescharacteristic
10C2×C16×C73—21no—
11C2×D292—21no—
12C2×C22⋊D73—41no—
13C22×Dic73—41no—
14D584—41no—
15C4⋊Dic73—22no—
16C4⋊Dic73—21no—
17C4⋊Dic73—41no—
18#11924005—41no—
19C22×C4×C73D411yescharacteristic
20C2×C8×C73—41no—
21C2×C8×C73C2×C411yescharacteristic
22C2×C8×C73D411yescharacteristic
23C16×C73—41no—
24C23×C73D811yescharacteristic
25C22×D73—41no—
26C2×C4×C73—21no—
27C2×C4×C73—21no—
28C2×C4×C73C22⋊C411yescharacteristic
29C2×C4×C73SD1611yescharacteristic
30C22⋊D73—81no—
31C22⋊D73—81no—
32C2×Dic73—42no—
33C2×Dic73—41no—
34C2×Dic73—81no—
35C2×Dic73—81no—
36D292—41no—
37D292—41no—
38C8×C73—21no—
39C8×C73—21no—
40C22×C73—21no—
41C22×C73—21no—
42C22×C73#10211yescharacteristic
43C22×C73D1611yescharacteristic
44C22×C73SD3211yescharacteristic
45C2×D73—81no—
46C2×D73—81no—
47C2×D73—81no—
48C4×C73—21no—
49C4×C73#9911yescharacteristic
50C4×C73#10411yescharacteristic
51Dic73—82no—
52Dic73—81no—
53C2×C73—21no—
54C2×C73—21no—
55C2×C73#32711yescharacteristic
56C2×C73#35711yescharacteristic
57C2×C73#36011yescharacteristic
58D73—161no—
59#1347—731nomaximal, Sylow
60C73#134711yescharacteristic, complemented, Sylow
61#466—731no—
62C22⋊C16D7311yescharacteristic, complemented
63#340—731no—
64C2×D8—731no—
65C22×C8C2×D7311yescharacteristic
66#121—1461no—
67C2×C4⋊C4—1461no—
68C2×C16—21no—
69#107—731no—
70#102—1461no—
71C2×D4—2921no—
72C2×D4—1461no—
73C22×C4—2921no—
74C22×C4D29211yescharacteristic
75D8—2921no—
76C2×C8—41no—
77C2×C8C4×D7311yescharacteristic
78C2×C8C22⋊D7311yescharacteristic
79C4⋊C4—2921no—
80C4⋊C4—1462no—
81C4⋊C4—1461no—
82C22⋊C4—2921no—
83C16—41no—
84C23—2921no—
85C23D58411yescharacteristic
86D4—2921no—
87D4—2921no—
88D4—5841no—
89D4—5841no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—2922no—
93C2×C4—2921no—
94C2×C4—5841no—
95C2×C4—5841no—
96C2×C4#1192400511yescharacteristic
97C2×C4#1192401711yescharacteristic
98C8—21no—
99C8—21no—
100C22—21no—
101C22—21no—
102C22—5841no—
103C22—5841no—
104C22—5841no—
105C22#1455651311yescharacteristic
106C22D116811yescharacteristic
107C22#1455653611yescharacteristic
108C4—21no—
109C4—5842no—
110C4—5841no—
111C4#1455650511yescharacteristic
112C4#1455651711yescharacteristic
113C2—21no—
114C2—21no—
115C2—11681no—
116C2#1798832211yescharacteristic
117C2#1798838911yescharacteristic
118C2#1798839811yescharacteristic
subgroupG/H
centerC22#14556513
commutatorC2×C8×C73C2×C4
FrattiniC22×C8C2×D73
FittingC22⋊C16×C73C2
socleC22×C73#102
hypercenterC22⋊C16D73
hypocenterC73#1347
LCSG ▷ C2×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. #17988350C2semidirect
3. C22⋊C16×C73C2semidirect
4. C2×D584C4semidirect
7. #14556525C4semidirect
60. C73#1347semidirect
62. C22⋊C16D73semidirect