Finite Group Databasebeta

← #22620483

Subgroups — #22620483

Order 9344.

348 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 165 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#17989144C211yesmaximal, characteristic
2C2×#14556583C211yesmaximal, characteristic
3#17988996C214yesmaximal, complemented
4#17988989C214yesmaximal, complemented
5#17988629C214yesmaximal
6C4×M16×C73C211yesmaximal, characteristic
7#14556591C2212yes—
8#14556583—22no—
9#14556583C2212yes—
10#14556583C2212yes—
11#14556583C2212yes—
12#14556570—22no—
13C4×Dic146—22no—
14#14556550C2212yes—
15C2×C4⋊Dic73C2212yes—
16C2×#11924007—22no—
17#14556525C2218yes—
18#14556523C2218yes—
19C2×M16×C73C2212yes—
20C2×C42×C73C2211yescharacteristic
21#97×C73C2212yes—
22C4×C8×C73C2212yes—
23C2×Dic146—22no—
24C22×Dic73—22no—
25C4⋊Dic73—22no—
26C4⋊Dic73—22no—
27C4⋊Dic73C2314yes—
28C4⋊Dic73C2314yes—
29#11924007—24no—
30#11924007—24no—
31#11924007—24no—
32C22⋊Dic73—22no—
33C4×Dic73—22no—
34C22×C4×C73D412yes—
35C22×C4×C73C2311yescharacteristic
36M16×C73Q818yescomplemented
37C2×C8×C73C2314yes—
38C42×C73D412yes—
39C42×C73C2311yescharacteristic
40C42×C73C2311yescharacteristic
41C23×C73C2×D411yescharacteristic
42C2×C4×C73—42no—
43C2×C4×C73C2×D412yes—
44C2×C4×C73C2×D412yes—
45C2×C4×C73C2×D411yescharacteristic
46C2×C4×C73C2×Q814yes—
47C2×C4×C73C2411yescharacteristic
48C2×Dic73—24no—
49C2×Dic73—24no—
50C2×Dic73—44no—
51Dic146—44no—
52C8×C73C2×Q818yes—
53C22×C73—22no—
54C22×C73C4⋊Q812yes—
55C22×C73C22×D411yescharacteristic
56C4×C73—22no—
57C4×C73—22no—
58C4×C73C4⋊Q812yes—
59C4×C73C22×Q812yes—
60Dic73—44no—
61Dic73—44no—
62C2×C73—22no—
63C2×C73C2×C4⋊Q811yescharacteristic
64C2×C73#57512yes—
65#3166—731nomaximal, Sylow
66C73#316611yescharacteristic, complemented, Sylow
67#533—731no—
68C2×#125—731no—
69#501—734no—
70#499—734no—
71#428—734no—
72C4×M16D7311yescharacteristic
73C2×M16C2×D7312yes—
74C4⋊Q8—732no—
75#125—732no—
76#125—732no—
77#125—732no—
78#125—1462no—
79C22⋊Q8—1462no—
80C4×Q8—1462no—
81#117—732no—
82C2×C4⋊C4—732no—
83C2×C4⋊C4—1462no—
84C2×C42C2×D7311yescharacteristic
85#107—738no—
86#106—738no—
87#97C2×D7312yes—
88C4×C8C2×D7312yes—
89C2×Q8—1462no—
90C22×C4—1462no—
91C22×C4D29212yes—
92C22×C4C22×D7311yescharacteristic
93M16Dic14618yescomplemented
94C2×C8C22×D7314yes—
95C4⋊C4—734no—
96C4⋊C4—734no—
97C4⋊C4—1464no—
98C4⋊C4—1464no—
99C4⋊C4—1464no—
100C4⋊C4—1462no—
101C4⋊C4—1462no—
102C22⋊C4—1462no—
103C42—1462no—
104C42D29212yes—
105C42C22×D7311yescharacteristic
106C42C22×D7311yescharacteristic
107C23C2×D29211yescharacteristic
108Q8—2924no—
109C2×C4—42no—
110C2×C4—2924no—
111C2×C4—1464no—
112C2×C4—1464no—
113C2×C4C2×D29212yes—
114C2×C4C2×D29212yes—
115C2×C4C2×D29211yescharacteristic
116C2×C4C2×Dic14614yes—
117C2×C4C23×D7311yescharacteristic
118C8C2×Dic14618yes—
119C22—22no—
120C22#1455659112yes—
121C22C22×D29211yescharacteristic
122C4—22no—
123C4—22no—
124C4—2924no—
125C4—2924no—
126C4#1455659112yes—
127C4C22×Dic14612yes—
128C2—22no—
129C2C2×#1455659111yescharacteristic
130C2#1798938712yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×M16×C73C2
socleC22×C73C22×D4
hypercenterC4×M16D73
hypocenterC73#3166
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #17988996C2semidirect
4. #17988989C2semidirect
36. M16×C73Q8semidirect
66. C73#3166semidirect
93. M16Dic146semidirect