Finite Group Databasebeta

← #34001250

Subgroups — #34001250

Order 18688.

142 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 22 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#22625067C211yesmaximal, characteristic
2#22625065C211yesmaximal, characteristic
3#22609603C211yesmaximal, characteristic
4#17989498—21no—
5#17989492—21no—
6#17988990—21no—
7#17988960C2211yescharacteristic
8#17988935—21no—
9#17988308C411yescharacteristic, complemented
10#494×C73C411yescharacteristic, complemented
11#14556652—41no—
12#14556650—41no—
13C2×#11924017—41no—
14#14556591D411yescharacteristic
15#14556588D411yescharacteristic
16#14556524—42no—
17#14556511—42no—
18C4×#10596831—21no—
19C2×Q16×C73—41no—
20C4⋊Q8×C73—21no—
21C4×C8×C73C2×C411yescharacteristic
22#11924037—81no—
23C22⋊#64408—81no—
24C2×Dic146—21no—
25C2×D292—21no—
26C2×D292—41no—
27#11924017—82no—
28C2×#10596831—22no—
29C4⋊Dic73—41no—
30C2×Q8×C73—41no—
31Q16×C73—82no—
32C2×C8×C73—21no—
33C4⋊C4×C73—41no—
34C4⋊C4×C73—41no—
35C42×C73C22⋊C411yescharacteristic
36C22×D73—41no—
37C2×#64408—161no—
38Q8×C73—82no—
39C2×C4×C73—21no—
40C2×C4×C73—81no—
41C2×C4×C73#9911yescharacteristic
42C2×Dic73—41no—
43D292—81no—
44D292—82no—
45Dic146—81no—
46#10596833—161no—
47C8×C73—22no—
48#10596831—42no—
49C22×C73#35311yescharacteristic
50C2×D73—81no—
51C2×D73—161no—
52#64408—321no—
53C4×C73—22no—
54C4×C73—21no—
55C4×C73—161no—
56Dic73—81no—
57#7528—731nomaximal, Sylow
58C2×C73—21no—
59C2×C73#140811yescharacteristic
60D73—161no—
61#1722—731no—
62#1410—731no—
63#1409—731no—
64C73#752811yescharacteristic, complemented, Sylow
65#500—1461no—
66#494#6440811yescharacteristic, complemented
67#492—731no—
68#486—1461no—
69#356—1461no—
70#353—1461no—
71#322—731no—
72C2×Q16—41no—
73C2×SD16—2921no—
74C4⋊Q8—21no—
75C4⋊Q8—731no—
76#127—731no—
77#107—2922no—
78#102—2922no—
79#101—2921no—
80#99—2921no—
81C4×C8—1461no—
82C4×C8C2×#6440811yescharacteristic
83C2×Q8—41no—
84C2×Q8—1461no—
85C2×D4—2921no—
86C2×D4—1461no—
87Q16—82no—
88SD16—5842no—
89M16—5841no—
90C2×C8—21no—
91C2×C8—1462no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—2921no—
95C22⋊C4—5841no—
96C42C22⋊#6440811yescharacteristic
97C23—2921no—
98Q8—82no—
99Q8—5841no—
100D4—5841no—
101D4—5842no—
102C2×C4—21no—
103C2×C4—81no—
104C2×C4—2921no—
105C2×C4—11681no—
106C2×C4#1455664911yescharacteristic
107C8—22no—
108C8—2922no—
109C8—11681no—
110C22—5841no—
111C22—11681no—
112C22#1798949111yescharacteristic
113C4—22no—
114C4—21no—
115C4—161no—
116C4—23361no—
117C4—5841no—
118C2—21no—
119C2—11681no—
120C2#2262506211yescharacteristic
subgroupG/H
centerC2#22625062
commutatorC4×C8×C73C2×C4
FrattiniC4×C8C2×#64408
Fitting#494×C73C4
socleC2×C73#1408
prime radical#14556588D4
cosocle#17988960C22
hypercenter#494#64408
hypocenterC73#7528
LCSG ▷ C4×C8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
9. #17988308C4semidirect
10. #494×C73C4semidirect
64. C73#7528semidirect
66. #494#64408semidirect

Maximal subgroups

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

subgroupindex
#226250672
#226250652
#226096032
#752873