Finite Group Databasebeta

← #22612060

Subgroups — #22612060

Order 9344.

144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×#14556535C211yesmaximal, characteristic, complemented
2#17989005C211yesmaximal, characteristic, complemented
3#17988863C211yesmaximal, characteristic, complemented
4#17988854C211yesmaximal, characteristic
5#17988416C211yesmaximal, characteristic, complemented
6#17988404C211yesmaximal, characteristic, complemented
7#361×C73C211yesmaximal, characteristic, complemented
8#14556624—21no—
9#14556617—21no—
10C2×Dic292C2211yescharacteristic
11#14556597C2211yescharacteristic
12#14556535—21no—
13#14556535—21no—
14#14556530—21no—
15C2×#11924003C2211yescharacteristic
16C16×D73—21no—
17#14556527C2211yescharacteristic
18#14556509—21no—
19#14556508—21no—
20C2×D8×C73C2211yescharacteristic
21M32×C73C2211yescharacteristic
22#108×C73C2211yescharacteristic
23#11924028D411yescharacteristic
24C2×Dic146—21no—
25Dic292—21no—
26Dic292—21no—
27Dic292—41no—
28#11924017—41no—
29#11924016—41no—
30#11924013—41no—
31#11924012—21no—
32#11924012D411yescharacteristic
33#11924011—21no—
34C8×D73—21no—
35#11924003D411yescharacteristic
36#11924003D411yescharacteristic
37C2×D4×C73—21no—
38D8×C73—21no—
39D8×C73—21no—
40M16×C73—21no—
41C2×C8×C73C2311yescharacteristic
42C16×C73—21no—
43C23×C73—41no—
44D4×C73—41no—
45D4×C73—41no—
46C2×C4×C73C2×D411yescharacteristic
47C22⋊D73—21no—
48C2×Dic73—41no—
49D292D811yescharacteristic
50C4×D73—21no—
51Dic146—41no—
52Dic146—41no—
53Dic146D811yescharacteristic
54C8×C73—41no—
55C8×C73C2×D411yescharacteristic
56C8×C73#4111yescharacteristic
57#10596831—21no—
58#10596831—41no—
59C22×C73—81no—
60C22×C73—161no—
61C22×C73#13511yescharacteristic
62C2×D73—21no—
63C4×C73#12111yescharacteristic
64C4×C73C2×D811yescharacteristic
65Dic73—21no—
66Dic73—81no—
67C2×C73—21no—
68C2×C73—161no—
69C2×C73#46611yescharacteristic
70D73—41no—
71#2223—731nomaximal, Sylow
72C73#222311yescharacteristic, complemented, Sylow
73C2×SD32—731no—
74#504—731no—
75#473—731no—
76#472—731no—
77#368—731no—
78#362—731no—
79#361D7311yescharacteristic, complemented
80#137—1461no—
81AGL(1,ℤ/8)—1461no—
82C2×Q16—731no—
83C2×D8C2×D7311yescharacteristic
84#131—731no—
85SD32—1461no—
86SD32—1461no—
87M32—1461no—
88M32C2×D7311yescharacteristic
89C2×C16—731no—
90C2×C16—1461no—
91#108—731no—
92#108C2×D7311yescharacteristic
93#101—1461no—
94#100—1461no—
95#41—731no—
96C2×Q8—1461no—
97C2×D4—21no—
98Q16—2921no—
99Q16—1461no—
100Q16—1461no—
101SD16—2921no—
102SD16—2921no—
103D8—21no—
104D8—21no—
105D8—2921no—
106M16—21no—
107M16—731no—
108M16—1461no—
109M16—1461no—
110C2×C8—1461no—
111C2×C8C22×D7311yescharacteristic
112C16—21no—
113C16—731no—
114C16—731no—
115C23—41no—
116Q8—2921no—
117Q8—2921no—
118Q8—731no—
119D4—41no—
120D4—41no—
121D4—731no—
122D4—1461no—
123C2×C4—2921no—
124C2×C4—1461no—
125C2×C4D4×D7311yescharacteristic
126C8—41no—
127C8—2921no—
128C8—1461no—
129C8D4×D7311yescharacteristic
130C8#1192402811yescharacteristic
131C22—81no—
132C22—161no—
133C22—1461no—
134C22#1455661211yescharacteristic
135C4—5841no—
136C4—1461no—
137C4#1455656411yescharacteristic
138C4D8×D7311yescharacteristic
139C2—21no—
140C2—161no—
141C2—2921no—
142C2#1798882211yescharacteristic
subgroupG/H
centerC2#17988822
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#361×C73C2
socleC2×C73#466
hypercenter#361D73
hypocenterC73#2223
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. C2×#14556535C2semidirect
2. #17989005C2semidirect
3. #17988863C2semidirect
5. #17988416C2semidirect
6. #17988404C2semidirect
7. #361×C73C2semidirect
72. C73#2223semidirect
79. #361D73semidirect