Finite Group Databasebeta

← #22611815

Subgroups — #22611815

Order 9344.

144 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 57 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#17989017C211yesmaximal, characteristic
2#17988705C211yesmaximal, characteristic, complemented
3#17988416C211yesmaximal, characteristic, complemented
4#17988394C211yesmaximal, characteristic, complemented
5#17988393C211yesmaximal, characteristic, complemented
6#17988363C211yesmaximal, characteristic, complemented
7#443×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9#14556597—21no—
10#14556537C411yescharacteristic, complemented
11#14556535C411yescharacteristic, complemented
12#14556534C411yescharacteristic, complemented
13#14556532C411yescharacteristic, complemented
14C2×#11924003C2211yescharacteristic
15C2×#11924003C2211yescharacteristic
16#14556527C2211yescharacteristic
17#14556519—21no—
18#135×C73C2211yescharacteristic
19#131×C73—21no—
20#108×C73C2211yescharacteristic
21#104×C73—21no—
22C4×C8×C73C2211yescharacteristic
23#11924028—21no—
24Dic292C2×C411yescharacteristic
25#11924017—21no—
26D584C2×C411yescharacteristic
27#11924012—21no—
28#11924011—41no—
29C8×D73—41no—
30#11924003—21no—
31#11924003C2×C411yescharacteristic
32#11924003C2×C411yescharacteristic
33#41×C73—21no—
34Q16×C73C2×C411yescharacteristic
35SD16×C73—21no—
36D8×C73C2×C411yescharacteristic
37M16×C73—21no—
38M16×C73—41no—
39C2×C8×C73—41no—
40C2×C8×C73D411yescharacteristic
41C2×C8×C73C2311yescharacteristic
42C42×C73D411yescharacteristic
43Q8×C73—21no—
44D4×C73—21no—
45D4×C73—41no—
46C2×C4×C73—21no—
47C2×C4×C73—41no—
48C2×C4×C73C2×D411yescharacteristic
49C22⋊D73—41no—
50D292—21no—
51C4×D73—41no—
52Dic146—21no—
53C8×C73—41no—
54C8×C73D811yescharacteristic
55C8×C73D811yescharacteristic
56C8×C73C22×C411yescharacteristic
57C8×C73#4111yescharacteristic
58#10596831—41no—
59C22×C73—41no—
60C22×C73#13511yescharacteristic
61C2×D73—41no—
62C4×C73—41no—
63C4×C73—41no—
64C4×C73C4×D411yescharacteristic
65C4×C73C2×D811yescharacteristic
66Dic73—41no—
67C2×C73—21no—
68C2×C73—81no—
69C2×C73C4×D811yescharacteristic
70D73—81no—
71#2179—731nomaximal, Sylow
72C73#217911yescharacteristic, complemented, Sylow
73#508—731no—
74#443—731no—
75#443D7311yescharacteristic, complemented
76#368—731no—
77#359—731no—
78#359—731no—
79#346—731no—
80#135—731no—
81#135C2×D7311yescharacteristic
82#131—21no—
83#131—1461no—
84Q32—731no—
85SD32—731no—
86SD32—731no—
87D16—731no—
88C2×C16—731no—
89C2×C16—731no—
90#108—731no—
91#108C2×D7311yescharacteristic
92#104—21no—
93#104—1461no—
94C4×C8C2×D7311yescharacteristic
95#41—21no—
96#41—1461no—
97Q16—731no—
98Q16C4×D7311yescharacteristic
99SD16—21no—
100SD16—1461no—
101D8—731no—
102D8C4×D7311yescharacteristic
103M16—21no—
104M16—41no—
105M16—2921no—
106M16—1461no—
107C2×C8—41no—
108C2×C8—2921no—
109C2×C8C22⋊D7311yescharacteristic
110C2×C8C22×D7311yescharacteristic
111C42C22⋊D7311yescharacteristic
112C16—731no—
113C16—731no—
114C16—1461no—
115Q8—21no—
116Q8—1461no—
117D4—21no—
118D4—41no—
119D4—2921no—
120D4—1461no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—2921no—
124C2×C4C2×C22⋊D7311yescharacteristic
125C8—41no—
126C8—2921no—
127C8#1192401311yescharacteristic
128C8#1192401311yescharacteristic
129C8C2×C4×D7311yescharacteristic
130C8#1192402811yescharacteristic
131C22—41no—
132C22—2921no—
133C22#1455661111yescharacteristic
134C4—41no—
135C4—41no—
136C4—2921no—
137C4C4×C22⋊D7311yescharacteristic
138C4C2×#1192401311yescharacteristic
139C2—21no—
140C2—81no—
141C2—5841no—
142C2C4×#1192401311yescharacteristic
subgroupG/H
centerC4C2×#11924013
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
Fitting#443×C73C2
socleC2×C73C4×D8
hypercenter#443D73
hypocenterC73#2179
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
2. #17988705C2semidirect
3. #17988416C2semidirect
4. #17988394C2semidirect
5. #17988393C2semidirect
6. #17988363C2semidirect
7. #443×C73C2semidirect
10. #14556537C4semidirect
11. #14556535C4semidirect
12. #14556534C4semidirect
13. #14556532C4semidirect
72. C73#2179semidirect
75. #443D73semidirect