Finite Group Databasebeta

← #26011667

Subgroups — #26011667

Order 11072.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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#19149725C211yesmaximal, characteristic
2#19149710C211yesmaximal, characteristic, complemented
3#19149668C211yesmaximal, characteristic, complemented
4#19149606C211yesmaximal, characteristic, complemented
5#19149605C211yesmaximal, characteristic, complemented
6#19149595C211yesmaximal, characteristic, complemented
7#137×C173C211yesmaximal, characteristic, complemented
8#14583827—21no—
9#14583826—21no—
10#14583826C2211yescharacteristic
11C2×D692—21no—
12C2×D692C2211yescharacteristic
13D4×D173—22no—
14D4×D173—21no—
15#14583816—21no—
16#14583813—21no—
17#14583810C2211yescharacteristic, complemented
18#14583803—22no—
19C4×Dic173C2211yescharacteristic, complemented
20#41×C173C2211yescharacteristic
21C2×Q8×C173C2211yescharacteristic, complemented
22Q16×C173—21no—
23SD16×C173—21no—
24M16×C173C2211yescharacteristic, complemented
25C22×D173—22no—
26C22×D173D412yes—
27Dic346D411yescharacteristic
28D692—22no—
29D692—21no—
30D692—21no—
31D692D411yescharacteristic
32C22⋊D173—22no—
33C22⋊D173—21no—
34C2×Dic173—21no—
35C4×D173—22no—
36C4×D173—21no—
37#13063436—21no—
38Q8×C173—21no—
39Q8×C173—21no—
40Q8×C173D411yescharacteristic
41D4×C173—21no—
42D4×C173D411yescharacteristic
43C2×C4×C173—21no—
44C2×C4×C173—21no—
45C2×C4×C173C2311yescharacteristic
46C8×C173—21no—
47C22×C173—21no—
48C22×C173C2×D411yescharacteristic
49C2×D173—22no—
50C2×D173—21no—
51C2×D173—42no—
52C2×D173—82no—
53C4×C173—21no—
54C4×C173—41no—
55C4×C173C2×D411yescharacteristic
56C4×C173C2×D411yescharacteristic
57Dic173—21no—
58Dic173—41no—
59C2×C173—21no—
60C2×C173—41no—
61C2×C173#12011yescharacteristic
62D173—42no—
63D173—41no—
64C173#45511yescharacteristic, complemented, Sylow
65#455—1731nomaximal, Sylow
66H(5,𝔽2)—1731no—
67#137—1731no—
68#137D17311yescharacteristic, complemented
69#124—1731no—
70#104—1731no—
71#104—1731no—
72#100—1731no—
73#41—3461no—
74#41—3461no—
75#41—1731no—
76#41C2×D17311yescharacteristic
77C2×Q8C2×D17311yescharacteristic, complemented
78C2×D4—3461no—
79C2×D4—3462no—
80C2×D4—3461no—
81C2×D4—1731no—
82Q16—21no—
83Q16—3461no—
84SD16—21no—
85SD16—3461no—
86M16—1731no—
87M16C2×D17311yescharacteristic, complemented
88C22⋊C4—3462no—
89C42—1731no—
90C23—3462no—
91C23—1732no—
92Q8—21no—
93Q8—21no—
94Q8—1731no—
95Q8C22⋊D17311yescharacteristic
96D4—21no—
97D4—3462no—
98D4—3462no—
99D4—3461no—
100D4—3461no—
101D4—3461no—
102D4—1731no—
103D4C22⋊D17311yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—3462no—
107C2×C4—3461no—
108C2×C4—3461no—
109C2×C4C22×D17311yescharacteristic
110C8—21no—
111C8—3461no—
112C22—21no—
113C22—3462no—
114C22—3461no—
115C22—13842no—
116C22—6922no—
117C22D4×D17311yescharacteristic
118C4—21no—
119C4—41no—
120C4—3461no—
121C4—6921no—
122C4D4×D17311yescharacteristic
123C4C2×C22⋊D17311yescharacteristic
124C2—21no—
125C2—41no—
126C2—6921no—
127C2—6922no—
128C2#1914964711yescharacteristic
subgroupG/H
centerC2#19149647
commutator, cosocleC2×C4×C173C23
FrattiniC2×C4C22×D173
Fitting#137×C173C2
socleC2×C173#120
prime radical#19149725C2
hypercenter#137D173
hypocenterC173#455
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #19149710C2semidirect
3. #19149668C2semidirect
4. #19149606C2semidirect
5. #19149605C2semidirect
6. #19149595C2semidirect
7. #137×C173C2semidirect
17. #14583810C22semidirect
19. C4×Dic173C22semidirect
21. C2×Q8×C173C22semidirect
24. M16×C173C22semidirect
64. C173#455semidirect
68. #137D173semidirect
77. C2×Q8C2×D173semidirect
87. M16C2×D173semidirect

Maximal subgroups

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

subgroupindex
#191497252
#191497102
#191496682
#191496062
#191496052
#191495952
#137×C1732
#455173