Finite Group Databasebeta

← #22612055

Subgroups — #22612055

Order 9344.

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

normal subgroups only

This group has 140 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×#14556537C211yesmaximal, characteristic, complemented
2#17989005C211yesmaximal, characteristic
3#17988863C211yesmaximal, characteristic
4#17988859C211yesmaximal, characteristic
5#17988416C211yesmaximal, characteristic, complemented
6#17988404C211yesmaximal, characteristic, complemented
7#362×C73C211yesmaximal, characteristic, complemented
8#14556624—21no—
9#14556622—21no—
10C2×Dic292C2211yescharacteristic
11#14556597C2211yescharacteristic
12#14556537—21no—
13#14556537—21no—
14#14556530—21no—
15C2×#11924003C2211yescharacteristic
16C16×D73—21no—
17#14556527C2211yescharacteristic
18#14556510—21no—
19#14556509—21no—
20C2×Q16×C73C2211yescharacteristic
21M32×C73C2211yescharacteristic
22#108×C73C2211yescharacteristic
23#11924028D411yescharacteristic
24C2×Dic146—21no—
25Dic292—21no—
26Dic292—21no—
27Dic292—41no—
28#11924018—41no—
29#11924017—41no—
30#11924015—41no—
31#11924012—21no—
32#11924012D411yescharacteristic
33#11924011—21no—
34C8×D73—21no—
35#11924003D411yescharacteristic
36#11924003D411yescharacteristic
37C2×Q8×C73—21no—
38Q16×C73—21no—
39Q16×C73—21no—
40M16×C73—21no—
41C2×C8×C73C2311yescharacteristic
42C16×C73—21no—
43Q8×C73—41no—
44Q8×C73—41no—
45C2×C4×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#13511yescharacteristic
60C2×D73—21no—
61C4×C73—81no—
62C4×C73#12111yescharacteristic
63C4×C73C2×D811yescharacteristic
64Dic73—21no—
65Dic73—81no—
66C2×C73—21no—
67C2×C73#46611yescharacteristic
68D73—41no—
69#2222—731nomaximal, Sylow
70C73#222211yescharacteristic, complemented, Sylow
71C2×Q32—731no—
72#504—731no—
73#473—731no—
74#473—731no—
75#368—731no—
76#362—731no—
77#362D7311yescharacteristic, complemented
78#137—1461no—
79#137—1461no—
80C2×Q16—731no—
81C2×Q16C2×D7311yescharacteristic
82#131—731no—
83Q32—1461no—
84Q32—1461no—
85M32—1461no—
86M32C2×D7311yescharacteristic
87C2×C16—731no—
88C2×C16—1461no—
89#108—731no—
90#108C2×D7311yescharacteristic
91#101—1461no—
92#101—1461no—
93#41—731no—
94C2×Q8—21no—
95C2×Q8—1461no—
96Q16—21no—
97Q16—21no—
98Q16—2921no—
99Q16—2921no—
100Q16—1461no—
101Q16—1461no—
102SD16—2921no—
103SD16—2921no—
104M16—21no—
105M16—731no—
106M16—1461no—
107M16—1461no—
108C2×C8—1461no—
109C2×C8C22×D7311yescharacteristic
110C16—21no—
111C16—731no—
112C16—731no—
113Q8—41no—
114Q8—41no—
115Q8—2921no—
116Q8—2921no—
117Q8—731no—
118D4—731no—
119D4—1461no—
120C2×C4—41no—
121C2×C4—2921no—
122C2×C4—1461no—
123C2×C4D4×D7311yescharacteristic
124C8—41no—
125C8—2921no—
126C8—1461no—
127C8D4×D7311yescharacteristic
128C8#1192402811yescharacteristic
129C22—1461no—
130C22#1455661211yescharacteristic
131C4—81no—
132C4—5841no—
133C4—1461no—
134C4#1455656411yescharacteristic
135C4D8×D7311yescharacteristic
136C2—21no—
137C2—2921no—
138C2#1798882211yescharacteristic
subgroupG/H
centerC2#17988822
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#362×C73C2
socleC2×C73#466
hypercenter#362D73
hypocenterC73#2222
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. C2×#14556537C2semidirect
5. #17988416C2semidirect
6. #17988404C2semidirect
7. #362×C73C2semidirect
70. C73#2222semidirect
77. #362D73semidirect