Finite Group Databasebeta

← #34001266

Subgroups — #34001266

Order 18688.

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

normal subgroups only

This group has 138 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#22609533C211yesmaximal, characteristic
4#17989498—21no—
5#17989492—21no—
6#17988960C2211yescharacteristic
7#17988937—21no—
8#17988935—21no—
9C8×#10596831C411yescharacteristic, complemented
10#498×C73C411yescharacteristic, complemented
11#14556652—41no—
12#14556650—41no—
13C2×#11924017—41no—
14#14556591D411yescharacteristic
15#14556588D411yescharacteristic
16#14556515—42no—
17#14556511—42no—
18C4×#10596831—21no—
19C4⋊Q8×C73—21no—
20#106×C73—41no—
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—
31C2×C8×C73—21no—
32C4⋊C4×C73—41no—
33C4⋊C4×C73—41no—
34C42×C73C22⋊C411yescharacteristic
35C22×D73—41no—
36C2×#64408—161no—
37Q8×C73—82no—
38C2×C4×C73—21no—
39C2×C4×C73—81no—
40C2×C4×C73#9911yescharacteristic
41C2×Dic73—41no—
42D292—81no—
43D292—82no—
44Dic146—81no—
45#10596833—161no—
46C8×C73—22no—
47#10596831—42no—
48C22×C73#35311yescharacteristic
49C2×D73—81no—
50C2×D73—161no—
51#64408—321no—
52C4×C73—22no—
53C4×C73—21no—
54C4×C73—161no—
55Dic73—81no—
56#7536—731nomaximal, Sylow
57C2×C73—21no—
58C2×C73#140911yescharacteristic
59D73—161no—
60#1708—731no—
61#1410—731no—
62#1409—731no—
63C73#753611yescharacteristic, complemented, Sylow
64#498#6440811yescharacteristic, complemented
65#492—731no—
66#487—1461no—
67#486—1461no—
68#356—1461no—
69#353—1461no—
70C82—731no—
71C2×SD16—2921no—
72C4⋊Q8—21no—
73C4⋊Q8—731no—
74#127—731no—
75#106—41no—
76#103—2922no—
77#102—2922no—
78#101—2921no—
79#99—2921no—
80C4×C8—1461no—
81C4×C8C2×#6440811yescharacteristic
82C2×Q8—41no—
83C2×Q8—1461no—
84C2×D4—2921no—
85C2×D4—1461no—
86SD16—5842no—
87M16—5841no—
88C2×C8—21no—
89C2×C8—1462no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—2921no—
93C22⋊C4—5841no—
94C42C22⋊#6440811yescharacteristic
95C23—2921no—
96Q8—82no—
97Q8—5841no—
98D4—5841no—
99D4—5842no—
100C2×C4—21no—
101C2×C4—81no—
102C2×C4—2921no—
103C2×C4—11681no—
104C2×C4#1455664911yescharacteristic
105C8—22no—
106C8—2922no—
107C8—11681no—
108C22—5841no—
109C22—11681no—
110C22#1798949111yescharacteristic
111C4—22no—
112C4—21no—
113C4—161no—
114C4—23361no—
115C4—5841no—
116C2—21no—
117C2—11681no—
118C2#2262506411yescharacteristic
subgroupG/H
centerC2#22625064
commutatorC4×C8×C73C2×C4
FrattiniC4×C8C2×#64408
Fitting#498×C73C4
socleC2×C73#1409
prime radical#14556588D4
cosocle#17988960C22
hypercenter#498#64408
hypocenterC73#7536
LCSG ▷ C4×C8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
9. C8×#10596831C4semidirect
10. #498×C73C4semidirect
63. C73#7536semidirect
64. #498#64408semidirect

Maximal subgroups

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

subgroupindex
#226250672
#226250652
#226095332
#753673