Finite Group Databasebeta

← #341×D73 #22609653

Subgroups — #341×D73 #22609653

Order 9344.

392 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 145 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×M16×D73C212yesmaximal
2C22×C8×D73C211yesmaximal, characteristic
3#17988352C211yesmaximal, characteristic, complemented
4#17988351C212yesmaximal, complemented
5#341×C73C211yesmaximal, characteristic, complemented
6C22×C4×D73C2211yescharacteristic
7C2×#11924012C2212yes—
8C2×#11924011—22no—
9M16×D73—24no—
10M16×D73C418yes—
11C22×#10596831C2211yescharacteristic
12C2×C8×D73—24no—
13C2×C8×D73—22no—
14C2×C8×D73C412yes—
15C2×C8×D73C412yes—
16C2×M16×C73C2212yes—
17C22×C8×C73C2211yescharacteristic
18C23×D73Q811yescharacteristic
19C22×Dic73Q811yescharacteristic
20C2×C4×D73C2×C411yescharacteristic
21C2×C4×D73C2×C411yescharacteristic
22C2×C4×D73C2×C414yes—
23C2×C4×D73D411yescharacteristic
24C2×C4×D73D414yes—
25C2×C4×D73D411yescharacteristic
26#11924012—22no—
27#11924012C2×C414yes—
28#11924011—28no—
29C2×#10596831—22no—
30C2×#10596831—22no—
31C2×#10596831C2×C412yes—
32C8×D73—24no—
33C8×D73—24no—
34C8×D73—28no—
35C22×C4×C73C2311yescharacteristic
36M16×C73—22no—
37M16×C73C2×C414yes—
38C2×C8×C73—22no—
39C2×C8×C73—22no—
40C2×C8×C73C2×C412yes—
41C23×C73C2×Q811yescharacteristic
42C22×D73—24no—
43C22×D73C4⋊C411yescharacteristic
44C22×D73C4⋊C414yes—
45C22×D73C4⋊C411yescharacteristic
46C2×C4×C73C22×C411yescharacteristic
47C2×C4×C73C22×C412yes—
48C2×C4×C73C2×D412yes—
49C2×C4×C73C2×D411yescharacteristic
50C2×Dic73C4⋊C414yes—
51C2×Dic73C4⋊C411yescharacteristic
52C2×Dic73C4⋊C411yescharacteristic
53C4×D73C4212yes—
54C4×D73C4212yes—
55C4×D73C22⋊C412yes—
56C4×D73C22⋊C412yes—
57C4×D73C22⋊C414yes—
58C4×D73C22⋊C414yes—
59C8×C73—22no—
60C8×C73—24no—
61#10596831—22no—
62#10596831—24no—
63C22×C73—22no—
64C22×C73C2×C4⋊C412yes—
65C22×C73C2×C4⋊C411yescharacteristic
66C2×D73—22no—
67C2×D73—28no—
68C2×D73#9512yes—
69C2×D73#9512yes—
70C2×D73#10814yes—
71C4×C73C2×C4211yescharacteristic
72C4×C73C2×C22⋊C411yescharacteristic
73C4×C73C2×C22⋊C412yes—
74Dic73#9512yes—
75Dic73#9512yes—
76C2×C73—22no—
77C2×C73C2×#9511yescharacteristic
78C2×C73C2×#10812yes—
79D73—22no—
80D73#34114yesdirect product factor
81C2×#341—731nomaximal, Sylow
82C73C2×#34111yescharacteristic, complemented, Sylow
83C22×M16—732no—
84C23×C8—731no—
85#341—732no—
86#341—731no—
87#341D7311yescharacteristic, direct product factor
88C23×C4—731no—
89C2×M16—732no—
90C2×M16—738no—
91C2×M16—1462no—
92C2×M16—1464no—
93C2×M16C2×D7312yes—
94C22×C8—731no—
95C22×C8—732no—
96C22×C8—732no—
97C22×C8—1464no—
98C22×C8—1462no—
99C22×C8C2×D7311yescharacteristic
100C24—731no—
101C22×C4—731no—
102C22×C4—731no—
103C22×C4—731no—
104C22×C4—734no—
105C22×C4—734no—
106C22×C4—731no—
107C22×C4—731no—
108C22×C4C22×D7311yescharacteristic
109M16—22no—
110M16—734no—
111M16—1468no—
112M16—1462no—
113M16C4×D7314yes—
114C2×C8—22no—
115C2×C8—22no—
116C2×C8—732no—
117C2×C8—1464no—
118C2×C8—1464no—
119C2×C8—1468no—
120C2×C8—1462no—
121C2×C8—1462no—
122C2×C8C4×D7312yes—
123C23—731no—
124C23—734no—
125C23—731no—
126C23—1464no—
127C23Q8×D7311yescharacteristic
128C2×C4—734no—
129C2×C4—731no—
130C2×C4—731no—
131C2×C4—732no—
132C2×C4—732no—
133C2×C4—732no—
134C2×C4—732no—
135C2×C4—734no—
136C2×C4—734no—
137C2×C4C2×C4×D7311yescharacteristic
138C2×C4C2×C4×D7312yes—
139C2×C4D4×D7312yes—
140C2×C4D4×D7311yescharacteristic
141C8—22no—
142C8—24no—
143C8—1462no—
144C8—1464no—
145C22—22no—
146C22—734no—
147C22—732no—
148C22—732no—
149C22—1468no—
150C22—1462no—
151C22C4⋊C4×D7312yes—
152C22C4⋊C4×D7311yescharacteristic
153C4—732no—
154C4—732no—
155C4C42×D7311yescharacteristic
156C4C22⋊C4×D7311yescharacteristic
157C4C22⋊C4×D7312yes—
158C2—22no—
159C2—734no—
160C2—1462no—
161C2#95×D7311yescharacteristic
162C2#108×D7312yes—
subgroupG/H
centerC2×C4D4×D73
commutatorC4×C73C2×C42
FrattiniC22×C4C22×D73
Fitting#341×C73C2
socleC22×C73C2×C4⋊C4
hypercenter#341D73
hypocenterC73C2×#341
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
3. #17988352C2semidirect
4. #17988351C2semidirect
5. #341×C73C2semidirect
80. D73#341direct (N × H)
82. C73C2×#341semidirect
87. #341D73direct (N × H)