Finite Group Databasebeta

← #22612092

Subgroups — #22612092

Order 9344.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×Dic292C211yesmaximal, characteristic
2#17988414C211yesmaximal, characteristic
3#17988412C211yesmaximal, characteristic
4C4⋊#11924003C211yesmaximal, characteristic
5#17988390C211yesmaximal, characteristic
6#17988390C211yesmaximal, characteristic
7#499×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9C4×Dic146—21no—
10C2×#11924003C2211yescharacteristic
11C2×#11924003C2211yescharacteristic
12#14556525C2211yescharacteristic
13#14556516—21no—
14#125×C73—21no—
15#107×C73C2211yescharacteristic
16#107×C73C2211yescharacteristic
17#106×C73—21no—
18C4×C8×C73C2211yescharacteristic
19C2×Dic146—21no—
20Dic292—21no—
21Dic292Q812yes—
22C4⋊Dic73—21no—
23#11924007—41no—
24C4×Dic73—41no—
25#11924003—21no—
26#11924003—21no—
27C2×C8×C73D411yescharacteristic
28C2×C8×C73C2311yescharacteristic
29C4⋊C4×C73—21no—
30C4⋊C4×C73—21no—
31C4⋊C4×C73—41no—
32C4⋊C4×C73—41no—
33C42×C73D411yescharacteristic
34C2×C4×C73—41no—
35C2×C4×C73—41no—
36C2×C4×C73D811yescharacteristic
37C2×C4×C73D811yescharacteristic
38C2×C4×C73C2×D411yescharacteristic
39C2×Dic73—41no—
40C2×Dic73—41no—
41Dic146—22no—
42Dic146—41no—
43C8×C73—21no—
44C8×C73C2×Q811yescharacteristic
45C8×C73#4111yescharacteristic
46C22×C73C2×D811yescharacteristic
47C4×C73—21no—
48C4×C73—21no—
49C4×C73—81no—
50C4×C73—81no—
51C4×C73C22⋊Q811yescharacteristic
52C4×C73#13711yescharacteristic
53Dic73—42no—
54Dic73—81no—
55C2×C73#47411yescharacteristic
56C2×C73#50811yescharacteristic
57C2×C73#51011yescharacteristic
58#2229—731nomaximal, Sylow
59C73#222911yescharacteristic, complemented, Sylow
60#499D7311yescharacteristic
61C4×Q16—731no—
62#367—731no—
63#366—731no—
64C4⋊C16—731no—
65#358—731no—
66#358—731no—
67C2×Q16—731no—
68#125—21no—
69C4×Q8—1461no—
70C2×C16—731no—
71C2×C16—731no—
72#107—731no—
73#107C2×D7311yescharacteristic
74#107C2×D7311yescharacteristic
75#106—21no—
76#103—1461no—
77C4×C8C2×D7311yescharacteristic
78C2×Q8—1461no—
79Q16—732no—
80Q16—1461no—
81C2×C8C22⋊D7311yescharacteristic
82C2×C8C22×D7311yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—2921no—
88C4⋊C4—1461no—
89C42—2921no—
90C42C22⋊D7311yescharacteristic
91C16—1461no—
92C16—1461no—
93Q8—2921no—
94Q8—1462no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—2921no—
98C2×C4—2921no—
99C2×C4#1192401311yescharacteristic
100C2×C4#1192401311yescharacteristic
101C2×C4C2×C22⋊D7311yescharacteristic
102C8—21no—
103C8Q8×D7311yescharacteristic
104C8#1192402911yescharacteristic
105C22C2×#1192401311yescharacteristic
106C4—21no—
107C4—21no—
108C4—81no—
109C4—81no—
110C4—2922no—
111C4—5841no—
112C4#1455656711yescharacteristic
113C4#1455662211yescharacteristic
114C2#1798886411yescharacteristic
115C2#1798901711yescharacteristic
116C2#1798902711yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#499×C73C2
socleC22×C73C2×D8
hypercenter#499D73
hypocenterC73#2229
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
59. C73#2229semidirect