Finite Group Databasebeta

← #22612095

Subgroups — #22612095

Order 9344.

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

normal subgroups only

This group has 124 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#17988989C211yesmaximal, characteristic
2#17988414C211yesmaximal, characteristic
3#17988412C211yesmaximal, characteristic
4C4⋊#11924003C211yesmaximal, characteristic
5#17988391C211yesmaximal, characteristic
6#17988391C211yesmaximal, characteristic
7C4×Q16×C73C211yesmaximal, characteristic
8#14556583—21no—
9C2×#11924003C2211yescharacteristic
10C2×#11924003C2211yescharacteristic
11#14556525C2211yescharacteristic
12#14556525C2211yescharacteristic
13#14556523—21no—
14C2×Q16×C73C2211yescharacteristic
15C4×Q8×C73—21no—
16#107×C73C2211yescharacteristic
17#103×C73—21no—
18C4×C8×C73C2211yescharacteristic
19C4⋊Dic73—21no—
20C4⋊Dic73—21no—
21#11924007—41no—
22#11924007—41no—
23#11924003—21no—
24#11924003—21no—
25C2×Q8×C73—21no—
26Q16×C73—21no—
27Q16×C73Q812yes—
28C2×C8×C73D411yescharacteristic
29C2×C8×C73C2311yescharacteristic
30C4⋊C4×C73—21no—
31C4⋊C4×C73—41no—
32C42×C73—41no—
33C42×C73D411yescharacteristic
34Q8×C73—22no—
35Q8×C73—41no—
36C2×C4×C73—41no—
37C2×C4×C73—41no—
38C2×C4×C73D811yescharacteristic
39C2×C4×C73D811yescharacteristic
40C2×C4×C73C2×D411yescharacteristic
41C2×Dic73—41no—
42C2×Dic73—41no—
43C8×C73—21no—
44C8×C73C2×Q811yescharacteristic
45C8×C73#4111yescharacteristic
46C22×C73C2×D811yescharacteristic
47C4×C73—21no—
48C4×C73—21no—
49C4×C73—42no—
50C4×C73—81no—
51C4×C73C22⋊Q811yescharacteristic
52C4×C73#13711yescharacteristic
53Dic73—81no—
54Dic73—81no—
55C2×C73#47411yescharacteristic
56C2×C73#50811yescharacteristic
57C2×C73#51011yescharacteristic
58#2229—731nomaximal, Sylow
59C73#222911yescharacteristic, complemented, Sylow
60#499—731no—
61C4×Q16D7311yescharacteristic
62#367—731no—
63#366—731no—
64C4⋊C16—731no—
65#358—731no—
66#358—731no—
67C2×Q16C2×D7311yescharacteristic
68#125—1461no—
69C4×Q8—21no—
70C2×C16—731no—
71C2×C16—731no—
72#107—731no—
73#107—731no—
74#107C2×D7311yescharacteristic
75#106—1461no—
76#103—21no—
77C4×C8C2×D7311yescharacteristic
78C2×Q8—21no—
79Q16—21no—
80Q16Dic14612yes—
81C2×C8C22⋊D7311yescharacteristic
82C2×C8C22×D7311yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—41no—
85C4⋊C4—2921no—
86C4⋊C4—2921no—
87C4⋊C4—1461no—
88C4⋊C4—1461no—
89C42—41no—
90C42C22⋊D7311yescharacteristic
91C16—1461no—
92C16—1461no—
93Q8—22no—
94Q8—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—2921no—
98C2×C4—2921no—
99C2×C4#1192401311yescharacteristic
100C2×C4#1192401311yescharacteristic
101C2×C4C2×C22⋊D7311yescharacteristic
102C8—21no—
103C8C2×Dic14611yescharacteristic
104C8#1192402811yescharacteristic
105C22C2×#1192401311yescharacteristic
106C4—21no—
107C4—21no—
108C4—42no—
109C4—81no—
110C4—5841no—
111C4—5841no—
112C4#1455657011yescharacteristic
113C4#1455662111yescharacteristic
114C2#1798886711yescharacteristic
115C2#1798901711yescharacteristic
116C2#1798902811yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC4×Q16×C73C2
socleC22×C73C2×D8
hypercenterC4×Q16D73
hypocenterC73#2229
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
59. C73#2229semidirect