Finite Group Databasebeta

← #22612129

Subgroups — #22612129

Order 9344.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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#17988828C211yesmaximal, characteristic
2C2×#14556525C211yesmaximal, characteristic
3#17988415C212yesmaximal, complemented
4#17988392C212yesmaximal, complemented
5C22⋊C16×C73C211yesmaximal, characteristic
6C2×Dic292C2211yescharacteristic
7#14556570—21no—
8C2×C4⋊Dic73—21no—
9#14556525—21no—
10#14556525C2212yes—
11#14556525C2211yescharacteristic
12#14556516—21no—
13C22×C8×C73C2211yescharacteristic
14C2×C16×C73C2212yes—
15C2×Dic146—21no—
16C22×Dic73—41no—
17Dic292—22no—
18C4⋊Dic73—21no—
19C4⋊Dic73—22no—
20C4⋊Dic73—41no—
21#11924007—41no—
22C22⋊Dic73—41no—
23C22×C4×C73D411yescharacteristic
24C2×C8×C73—22no—
25C2×C8×C73D411yescharacteristic
26C2×C8×C73C2311yescharacteristic
27C16×C73—22no—
28C23×C73D811yescharacteristic
29C2×C4×C73—21no—
30C2×C4×C73—21no—
31C2×C4×C73D811yescharacteristic
32C2×C4×C73C2×D411yescharacteristic
33C2×Dic73—41no—
34C2×Dic73—41no—
35C2×Dic73—42no—
36C2×Dic73—82no—
37Dic146—41no—
38Dic146—41no—
39C8×C73—21no—
40C8×C73#4112yes—
41C22×C73—21no—
42C22×C73—21no—
43C22×C73SD3212yes—
44C22×C73C2×D811yescharacteristic
45C4×C73—21no—
46C4×C73#12311yescharacteristic
47C4×C73#13711yescharacteristic
48Dic73—81no—
49Dic73—82no—
50Dic73—81no—
51C2×C73—22no—
52C2×C73#48011yescharacteristic
53C2×C73C2×SD3211yescharacteristic
54C2×C73#51011yescharacteristic
55#2235—731nomaximal, Sylow
56C73#223511yescharacteristic, complemented, Sylow
57#467—731no—
58C2×#107—731no—
59#367—732no—
60#358—732no—
61C22⋊C16D7311yescharacteristic
62C2×Q16—731no—
63C22×C8C2×D7311yescharacteristic
64C22⋊Q8—1461no—
65C2×C4⋊C4—1461no—
66C2×C16C2×D7312yes—
67#107—732no—
68#107—731no—
69#107—1461no—
70#103—1461no—
71C2×Q8—1461no—
72C22×C4—2921no—
73C22×C4D29211yescharacteristic
74Q16—1462no—
75C2×C8—22no—
76C2×C8D29211yescharacteristic
77C2×C8C22×D7311yescharacteristic
78C4⋊C4—2921no—
79C4⋊C4—2921no—
80C4⋊C4—1461no—
81C4⋊C4—1462no—
82C22⋊C4—2921no—
83C16—22no—
84C23D58411yescharacteristic
85Q8—2921no—
86Q8—2921no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—2921no—
90C2×C4—2921no—
91C2×C4—2922no—
92C2×C4—5842no—
93C2×C4D58411yescharacteristic
94C2×C4C2×D29211yescharacteristic
95C8—21no—
96C8#1192402712yes—
97C22—21no—
98C22—21no—
99C22#1455653612yes—
100C22C2×D58411yescharacteristic
101C4—21no—
102C4—5841no—
103C4—5842no—
104C4—5841no—
105C4#1455657511yescharacteristic
106C4#1455662411yescharacteristic
107C2—22no—
108C2#1798890111yescharacteristic
109C2C2×#1455653611yescharacteristic
110C2#1798903011yescharacteristic
subgroupG/H
centerC22C2×D584
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC22⋊C16×C73C2
socleC22×C73C2×D8
hypercenterC22⋊C16D73
hypocenterC73#2235
LCSG ▷ C2×C8×C73 ▷ 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
3. #17988415C2semidirect
4. #17988392C2semidirect
56. C73#2235semidirect