Finite Group Databasebeta

← #34001248

Subgroups — #34001248

Order 18688.

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

normal subgroups only

This group has 164 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, complemented
2#22625065C211yesmaximal, characteristic, complemented
3#22609598C211yesmaximal, characteristic
4#17989498—21no—
5#17989492—21no—
6#17988963—21no—
7#17988960C2211yescharacteristic
8#17988933—21no—
9#17988308C411yescharacteristic, complemented
10#493×C73C411yescharacteristic, complemented
11#14556652—41no—
12#14556650—41no—
13C2×#11924017—41no—
14C2×#11924013—42no—
15#14556591D411yescharacteristic
16#14556588D411yescharacteristic
17#14556512—42no—
18C4×#10596831—21no—
19C2×D8×C73—41no—
20#127×C73—21no—
21C4×C8×C73C2×C411yescharacteristic
22#11924037—81no—
23C22⋊#64408—81no—
24C2×Dic146—21no—
25C2×D292—21no—
26C2×D292—41no—
27#11924017—82no—
28#11924013—84no—
29C2×#10596831—22no—
30C4⋊Dic73—41no—
31C2×D4×C73—41no—
32C2×D4×C73—41no—
33C2×D4×C73—41no—
34D8×C73—82no—
35C2×C8×C73—21no—
36C42×C73C22⋊C411yescharacteristic
37C23×C73—81no—
38C22×D73—41no—
39C2×#64408—161no—
40D4×C73—82no—
41D4×C73—82no—
42D4×C73—82no—
43C2×C4×C73—21no—
44C2×C4×C73#9911yescharacteristic
45C2×Dic73—41no—
46D292—81no—
47D292—82no—
48Dic146—81no—
49#10596833—161no—
50C8×C73—22no—
51#10596831—42no—
52C22×C73—161no—
53C22×C73—161no—
54C22×C73—161no—
55C22×C73#35311yescharacteristic
56C2×D73—81no—
57C2×D73—161no—
58#64408—321no—
59C4×C73—22no—
60C4×C73—21no—
61Dic73—81no—
62#7527—731nomaximal, Sylow
63C2×C73—21no—
64C2×C73—321no—
65C2×C73#140811yescharacteristic
66D73—161no—
67#1721—731no—
68#1410—731no—
69#1409—731no—
70C73#752711yescharacteristic, complemented, Sylow
71#493—1461no—
72#493#6440811yescharacteristic, complemented
73#492—731no—
74#486—1461no—
75#356—1461no—
76#353—1461no—
77#322—731no—
78C2×SD16—2921no—
79C2×D8—41no—
80C2×D8—2922no—
81C4⋊Q8—731no—
82#127—21no—
83#127—731no—
84#102—2922no—
85#101—2921no—
86#99—2921no—
87C4×C8—1461no—
88C4×C8C2×#6440811yescharacteristic
89C2×Q8—1461no—
90C2×D4—41no—
91C2×D4—41no—
92C2×D4—41no—
93C2×D4—2921no—
94C2×D4—1461no—
95SD16—5842no—
96D8—82no—
97D8—5844no—
98M16—5841no—
99C2×C8—21no—
100C2×C8—1462no—
101C4⋊C4—2921no—
102C22⋊C4—5841no—
103C42C22⋊#6440811yescharacteristic
104C23—81no—
105C23—2921no—
106Q8—5841no—
107D4—82no—
108D4—82no—
109D4—82no—
110D4—5841no—
111D4—5842no—
112C2×C4—21no—
113C2×C4—2921no—
114C2×C4—11681no—
115C2×C4#1455664911yescharacteristic
116C8—22no—
117C8—2922no—
118C8—11681no—
119C22—161no—
120C22—161no—
121C22—161no—
122C22—5841no—
123C22—11681no—
124C22#1798949111yescharacteristic
125C4—22no—
126C4—21no—
127C4—23361no—
128C4—5841no—
129C2—21no—
130C2—321no—
131C2—11681no—
132C2#2262506211yescharacteristic
subgroupG/H
centerC2#22625062
commutatorC4×C8×C73C2×C4
FrattiniC4×C8C2×#64408
Fitting#493×C73C4
socleC2×C73#1408
prime radical#22609598C2
cosocle#17988960C22
hypercenter#493#64408
hypocenterC73#7527
LCSG ▷ C4×C8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #22625067C2semidirect
2. #22625065C2semidirect
9. #17988308C4semidirect
10. #493×C73C4semidirect
70. C73#7527semidirect
72. #493#64408semidirect

Maximal subgroups

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

subgroupindex
#226250672
#226250652
#226095982
#752773