Finite Group Databasebeta

← #34000963

Subgroups — #34000963

Order 18688.

150 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 34 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#22625047C211yesmaximal, characteristic, complemented
2#22624999C211yesmaximal, characteristic, complemented
3#22612031C211yesmaximal, characteristic
4#17989597—21no—
5#17989519—21no—
6C2×#14556530C2211yescharacteristic
7#17988820—21no—
8#17988415C411yescharacteristic, complemented
9#17988388—21no—
10C2×D16×C73C411yescharacteristic, complemented
11#14556670—41no—
12#14556660—41no—
13#14556659—22no—
14#14556641—41no—
15C2×C8×D73D411yescharacteristic
16#14556562—41no—
17#14556530—41no—
18C2×#11924003D411yescharacteristic
19#14556525—21no—
20#14556512—41no—
21C2×D8×C73—21no—
22D16×C73—41no—
23C2×C16×C73C2×C411yescharacteristic
24C4⋊#64408—42no—
25C22⋊#64408—81no—
26C4×#64408—81no—
27C2×C22⋊D73—81no—
28C2×C4×D73D811yescharacteristic
29C2×#10596831SD1611yescharacteristic
30C8×D73—21no—
31C8×D73—21no—
32C4⋊Dic73—41no—
33C22⋊Dic73—81no—
34#11924003—21no—
35C2×D4×C73—41no—
36D8×C73—41no—
37D8×C73—41no—
38C2×C8×C73C22⋊C411yescharacteristic
39C16×C73—21no—
40C23×C73—81no—
41C22×D73D1611yescharacteristic
42C2×#64408—82no—
43D4×C73—81no—
44D4×C73—81no—
45C2×C4×C73#10211yescharacteristic
46C22⋊D73—162no—
47C2×Dic73—81no—
48C2×Dic73SD3211yescharacteristic
49C4×D73—21no—
50C4×D73—21no—
51C8×C73#9911yescharacteristic
52C8×C73#10411yescharacteristic
53#10596831—21no—
54C22×C73—161no—
55C22×C73—161no—
56C22×C73—161no—
57C22×C73#35711yescharacteristic
58C2×D73—21no—
59C2×D73—41no—
60#64408—162no—
61C4×C73#32711yescharacteristic
62C4×C73#36011yescharacteristic
63Dic73—21no—
64Dic73—161no—
65#7422—731nomaximal, Sylow
66C2×C73—21no—
67C2×C73—321no—
68C2×C73#134711yescharacteristic
69D73—41no—
70#2218—731no—
71#1400—731no—
72#1384—731no—
73C73#742211yescharacteristic, complemented, Sylow
74C2×D16#6440811yescharacteristic, complemented
75C2×M32—731no—
76#466—1461no—
77#427—1461no—
78M64—1461no—
79#367—731no—
80#357—1461no—
81C2×D8—21no—
82C22×C8—731no—
83#121—2921no—
84#117—2921no—
85D16—41no—
86M32—2921no—
87C2×C16—731no—
88C2×C16C2×#6440811yescharacteristic
89#107—2921no—
90#107—1461no—
91#106—1462no—
92#102—2921no—
93C32—2921no—
94C2×D4—41no—
95C2×D4—5841no—
96C22×C4—731no—
97D8—41no—
98D8—41no—
99C2×C8—731no—
100C2×C8—1461no—
101C2×C8—1461no—
102C2×C8C22⋊#6440811yescharacteristic
103C4⋊C4—2922no—
104C4⋊C4—2921no—
105C22⋊C4—5841no—
106C22⋊C4—5841no—
107C42—5841no—
108C16—21no—
109C16—1461no—
110C23—81no—
111C23—731no—
112D4—81no—
113D4—81no—
114D4—11682no—
115C2×C4—5842no—
116C2×C4—5841no—
117C2×C4—731no—
118C2×C4—1461no—
119C2×C4—1461no—
120C2×C4#1455665311yescharacteristic
121C8—1461no—
122C8#1455664911yescharacteristic
123C8#1455665511yescharacteristic
124C22—161no—
125C22—161no—
126C22—161no—
127C22—2921no—
128C22—1461no—
129C22#1798949911yescharacteristic
130C4—11681no—
131C4—11682no—
132C4—1461no—
133C4#1798943811yescharacteristic
134C4#1798950311yescharacteristic
135C2—21no—
136C2—321no—
137C2—2921no—
138C2#2262491711yescharacteristic
subgroupG/H
centerC2#22624917
commutatorC2×C16×C73C2×C4
FrattiniC2×C16C2×#64408
FittingC2×D16×C73C4
socleC2×C73#1347
prime radical#22612031C2
cosocleC2×#14556530C22
hypercenterC2×D16#64408
hypocenterC73#7422
LCSG ▷ C2×C16×C73 ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #22625047C2semidirect
2. #22624999C2semidirect
8. #17988415C4semidirect
10. C2×D16×C73C4semidirect
73. C73#7422semidirect
74. C2×D16#64408semidirect

Maximal subgroups

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

subgroupindex
#226250472
#226249992
#226120312
#742273