Finite Group Databasebeta

← #34033070

Subgroups — #34033070

Order 18688.

190 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 31 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#22626968C212yesmaximal
2#22625866C211yesmaximal, characteristic
3#17989673—22no—
4C2×#14556659—22no—
5#17989533C411yescharacteristic
6#17989533C2211yescharacteristic
7C4×C8×D73C411yescharacteristic
8C22⋊#10596842—42no—
9C2×C4⋊#64408—21no—
10C2×C4⋊#64408—41no—
11C2×C4⋊#64408—41no—
12C2×C4⋊#64408D412yes—
13#14556659—44no—
14C2×C8×D73—21no—
15C42×D73C2×C411yescharacteristic
16C4×#10596831C811yescharacteristic, complemented
17C8×Dic73—21no—
18C4×C8×C73C811yescharacteristic, complemented
19C2×#10596842—82no—
20C22×#64408—22no—
21C22×#64408—41no—
22C4⋊#64408—42no—
23C4⋊#64408—42no—
24C4⋊#64408—82no—
25C4⋊#64408—82no—
26C2×C4×D73—21no—
27C2×C4×D73C22⋊C411yescharacteristic
28C2×#10596831—21no—
29C8×D73—22no—
30C8×D73—22no—
31C4×Dic73—21no—
32C4×Dic73M1611yescharacteristic
33C2×C8×C73—21no—
34C42×C73C2×C811yescharacteristic
35C22×D73#9911yescharacteristic
36C2×#64408—42no—
37C2×#64408—82no—
38C2×#64408—82no—
39C2×#64408—81no—
40#10596842—162no—
41C2×C4×C73—21no—
42C2×C4×C73C22⋊C811yescharacteristic
43C2×Dic73—21no—
44C2×Dic73#10111yescharacteristic
45C4×D73—22no—
46C4×D73—22no—
47C4×D73—21no—
48C4×D73—21no—
49C8×C73—22no—
50#10596831—22no—
51C22×C73#32411yescharacteristic
52C2×D73—21no—
53C2×D73—21no—
54C2×D73#35311yescharacteristic
55C2×D73#35611yescharacteristic
56#64408—82no—
57#64408—161no—
58C4×C73—22no—
59C4×C73—21no—
60Dic73—22no—
61Dic73—21no—
62#7371—731nomaximal, Sylow
63C2×C73—21no—
64C2×C73#132511yescharacteristic
65D73—21no—
66D73#140911yescharacteristic
67D73#141011yescharacteristic
68#1844—731no—
69#1325—732no—
70C73#737111yescharacteristic, complemented, Sylow
71C2×#106—1462no—
72C2×C4×C8—731no—
73#384—731no—
74#384—731no—
75#324—1462no—
76C22×C8—1461no—
77C2×C4⋊C4—2921no—
78C2×C4⋊C4—2921no—
79C2×C4⋊C4—732no—
80C2×C4⋊C4—1461no—
81C2×C42—731no—
82#106—2924no—
83C22⋊C8—2922no—
84C4×C8—731no—
85C4×C8—1461no—
86C4×C8#1059684211yescharacteristic, complemented
87C22×C4—2921no—
88C22×C4—731no—
89C22×C4—1461no—
90C22×C4—1462no—
91C2×C8—21no—
92C2×C8—5842no—
93C2×C8—1462no—
94C2×C8—1462no—
95C2×C8—1461no—
96C4⋊C4—2922no—
97C4⋊C4—2922no—
98C4⋊C4—5842no—
99C4⋊C4—5842no—
100C42—731no—
101C42—1461no—
102C42C2×#1059684211yescharacteristic
103C23—731no—
104C2×C4—21no—
105C2×C4—2922no—
106C2×C4—5842no—
107C2×C4—5841no—
108C2×C4—5842no—
109C2×C4—731no—
110C2×C4—1461no—
111C2×C4—1461no—
112C2×C4—1462no—
113C2×C4—1462no—
114C2×C4—1461no—
115C2×C4C22⋊#1059684211yescharacteristic
116C8—22no—
117C8—11682no—
118C8—1462no—
119C22—731no—
120C22—731no—
121C22—1461no—
122C22—1461no—
123C22#1798967311yescharacteristic
124C4—22no—
125C4—21no—
126C4—5842no—
127C4—11681no—
128C4—1462no—
129C4—1461no—
130C2—21no—
131C2—731no—
132C2—731no—
133C2—1461no—
134C2#2262696811yescharacteristic
subgroupG/H
centerC2#22626968
commutatorC42×C73C2×C8
FrattiniC42C2×#10596842
FittingC4×C8×C73C8
socleC2×C73#1325
prime radicalC22×D73#99
cosocle#17989533C22
hypercenterC4×C8#10596842
hypocenterC73#7371
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
16. C4×#10596831C8semidirect
18. C4×C8×C73C8semidirect
70. C73#7371semidirect
86. C4×C8#10596842semidirect

Maximal subgroups

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

subgroupindex
#226269682
#226258662
#737173