Finite Group Databasebeta

← #32973355

Subgroups — #32973355

Order 18688.

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

normal subgroups only

This group has 200 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
1#22607861C212yesmaximal
2C73×#1820C211yesmaximal, characteristic
3#17988311—22no—
4C2×#117×C73C411yescharacteristic
5#381×C73C411yescharacteristic
6#381×C73C2211yescharacteristic
7#342×C73—22no—
8C22⋊#10596831—42no—
9C23×C4×C73C2×C411yescharacteristic
10#117×C73—41no—
11#117×C73—41no—
12C2×C4⋊C4×C73—21no—
13C2×C22⋊C4×C73—21no—
14C2×C22⋊C4×C73—21no—
15C2×C22⋊C4×C73D412yes—
16C2×C42×C73C812yescomplemented
17#95×C73—41no—
18#95×C73—41no—
19C2×#10596831—82no—
20C24×C73C22⋊C411yescharacteristic
21C22×C4×C73—21no—
22C22×C4×C73—21no—
23C22×C4×C73—22no—
24C22×C4×C73—22no—
25C22×C4×C73—42no—
26C22×C4×C73—41no—
27C22×C4×C73C2×C811yescharacteristic
28C22×C4×C73M1611yescharacteristic
29C4⋊C4×C73—42no—
30C22⋊C4×C73—41no—
31C22⋊C4×C73—41no—
32C22⋊C4×C73—42no—
33C22⋊C4×C73—42no—
34C42×C73—42no—
35C23×C73—22no—
36C23×C73—81no—
37C23×C73C22⋊C811yescharacteristic
38C23×C73#9911yescharacteristic
39C23×C73#10011yescharacteristic
40C2×C4×C73—21no—
41C2×C4×C73—21no—
42C2×C4×C73—42no—
43C2×C4×C73—42no—
44C2×C4×C73—41no—
45C2×C4×C73—41no—
46C2×C4×C73—42no—
47C2×C4×C73—42no—
48C2×C4×C73—82no—
49C2×C4×C73—82no—
50C2×C4×C73—81no—
51C2×C4×C73—82no—
52#10596831—162no—
53C22×C73—21no—
54C22×C73—21no—
55C22×C73—41no—
56C22×C73—41no—
57C22×C73—41no—
58C22×C73—82no—
59C22×C73#32311yescharacteristic
60C22×C73#35212yes—
61C4×C73—41no—
62C4×C73—41no—
63C4×C73—82no—
64C4×C73—82no—
65C4×C73—161no—
66#7348—731nomaximal, Sylow
67C2×C73—21no—
68C2×C73—22no—
69C2×C73—41no—
70C2×C73—41no—
71C2×C73#131711yescharacteristic
72#1820D7311yescharacteristic
73#1317—732no—
74C73#734811yescharacteristic, complemented, Sylow
75C2×#117Dic7311yescharacteristic
76#381Dic7311yescharacteristic
77#381C2×D7311yescharacteristic
78#342—22no—
79#323—1462no—
80C23×C4C2×Dic7311yescharacteristic
81#117—41no—
82#117—41no—
83C2×C4⋊C4—21no—
84C2×C22⋊C4—21no—
85C2×C22⋊C4—21no—
86C2×C22⋊C4C22⋊D7312yes—
87C2×C42#1059683112yescomplemented
88C22⋊C8—2922no—
89#95—41no—
90#95—41no—
91C24C22⋊Dic7311yescharacteristic
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—42no—
97C22×C4—41no—
98C22×C4C2×#1059683111yescharacteristic
99C22×C4#1192401211yescharacteristic
100C2×C8—5842no—
101C4⋊C4—42no—
102C22⋊C4—41no—
103C22⋊C4—41no—
104C22⋊C4—42no—
105C22⋊C4—42no—
106C42—42no—
107C23—22no—
108C23—81no—
109C23C22⋊#1059683111yescharacteristic
110C23#1455650611yescharacteristic
111C23#1455650811yescharacteristic
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—82no—
121C2×C4—82no—
122C2×C4—81no—
123C2×C4—82no—
124C8—11682no—
125C22—21no—
126C22—21no—
127C22—41no—
128C22—41no—
129C22—41no—
130C22—82no—
131C22#1798831111yescharacteristic
132C22#1798837712yes—
133C4—41no—
134C4—41no—
135C4—82no—
136C4—82no—
137C4—161no—
138C2—21no—
139C2—22no—
140C2—41no—
141C2—41no—
142C2#2260786111yescharacteristic
subgroupG/H
centerC2#22607861
commutatorC22×C4×C73C2×C8
Frattini#381C2×D73
FittingC73×#1820C2
socleC2×C73#1317
prime radicalC24×C73C22⋊C4
cosocle#381×C73C22
hypercenter#1820D73
hypocenterC73#7348
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1820

Complements

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

NH ≅ G/Ntype
16. C2×C42×C73C8semidirect
74. C73#7348semidirect
87. C2×C42#10596831semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226078612
C73×#18202
#734873