Finite Group Databasebeta

← #22611827

Subgroups — #22611827

Order 9344.

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

normal subgroups only

This group has 154 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#17989023C211yesmaximal, characteristic
2#17988710C211yesmaximal, characteristic, complemented
3#17988409C211yesmaximal, characteristic, complemented
4#17988400C211yesmaximal, characteristic, complemented
5#17988396C211yesmaximal, characteristic, complemented
6#17988365C211yesmaximal, characteristic, complemented
7#442×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9#14556597—21no—
10#14556535C412yescomplemented
11#14556532C412yescomplemented
12#14556531C2211yescharacteristic
13#14556531C2211yescharacteristic
14#14556527C2211yescharacteristic
15#14556519—21no—
16C2×D8×C73C2211yescharacteristic
17C4×D4×C73—21no—
18#106×C73C2211yescharacteristic
19#102×C73—21no—
20#97×C73C2211yescharacteristic
21#11924028—21no—
22Dic292C2×C411yescharacteristic, complemented
23#11924017—21no—
24D584C2×C411yescharacteristic, complemented
25#11924012—21no—
26#11924011—41no—
27C8×D73—41no—
28#11924003—21no—
29#11924003C2×C412yescomplemented
30C2×D4×C73—21no—
31C22×C4×C73—41no—
32D8×C73—21no—
33D8×C73C2×C412yes—
34C2×C8×C73D411yescharacteristic
35C2×C8×C73C2311yescharacteristic
36C4⋊C4×C73—21no—
37C22⋊C4×C73—41no—
38C42×C73D411yescharacteristic
39C23×C73—41no—
40D4×C73—22no—
41D4×C73—41no—
42C2×C4×C73—21no—
43C2×C4×C73—41no—
44C2×C4×C73—82no—
45C2×C4×C73C2×D411yescharacteristic
46C22⋊D73—41no—
47D292—21no—
48C4×D73—41no—
49Dic146—21no—
50C8×C73—21no—
51C8×C73C22×C411yescharacteristic
52C8×C73#4111yescharacteristic
53#10596831—41no—
54C22×C73—42no—
55C22×C73—81no—
56C22×C73—81no—
57C22×C73AGL(1,ℤ/8)11yescharacteristic
58C2×D73—41no—
59C4×C73—41no—
60C4×C73—81no—
61C4×C73C4×D411yescharacteristic
62C4×C73AGL(1,ℤ/8)11yescharacteristic
63Dic73—41no—
64C2×C73—21no—
65C2×C73—82no—
66C2×C73#44211yescharacteristic
67D73—81no—
68AGL(1,ℤ/16)—731nomaximal, Sylow
69C73AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
70#509—731no—
71#444—731no—
72#442D7311yescharacteristic, complemented
73#365—731no—
74#361—731no—
75#360—731no—
76#347—731no—
77#135—731no—
78C2×D8C2×D7311yescharacteristic
79#131—1461no—
80C4×D4—21no—
81SD32—732no—
82D16—732no—
83M32—731no—
84M32—731no—
85#108—731no—
86#106C2×D7311yescharacteristic
87#104—1461no—
88#102—21no—
89#97C2×D7311yescharacteristic
90#41—1461no—
91C2×D4—21no—
92C22×C4—41no—
93Q16—731no—
94SD16—1461no—
95D8—21no—
96D8—731no—
97D8C4×D7312yes—
98M16—2921no—
99M16—1461no—
100C2×C8—2921no—
101C2×C8C22⋊D7311yescharacteristic
102C2×C8C22×D7311yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—41no—
105C42C22⋊D7311yescharacteristic
106C16—732no—
107C16—1461no—
108C23—41no—
109Q8—1461no—
110D4—22no—
111D4—41no—
112D4—2921no—
113D4—1461no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—82no—
117C2×C4—2921no—
118C2×C4C2×C22⋊D7311yescharacteristic
119C8—21no—
120C8—2921no—
121C8C2×C4×D7311yescharacteristic
122C8#1192402811yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—2921no—
127C22#1455661711yescharacteristic
128C4—41no—
129C4—81no—
130C4—2921no—
131C4C4×C22⋊D7311yescharacteristic
132C4#1455661611yescharacteristic
133C2—21no—
134C2—82no—
135C2—5841no—
136C2#1798869711yescharacteristic
subgroupG/H
centerC2#17988697
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
Fitting#442×C73C2
socleC2×C73#442
hypercenter#442D73
hypocenterC73AGL(1,ℤ/16)
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #17988710C2semidirect
3. #17988409C2semidirect
4. #17988400C2semidirect
5. #17988396C2semidirect
6. #17988365C2semidirect
7. #442×C73C2semidirect
10. #14556535C4semidirect
11. #14556532C4semidirect
22. Dic292C2×C4semidirect
24. D584C2×C4semidirect
29. #11924003C2×C4semidirect
69. C73AGL(1,ℤ/16)semidirect
72. #442D73semidirect