Finite Group Databasebeta

← #36352864

Subgroups — #36352864

Order 22144.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C173⋊#564C211yesmaximal, characteristic, complemented
2#26011855C212yesmaximal
3#26011233C211yesmaximal, characteristic, complemented
4#26011232C212yesmaximal, complemented
5#490×C173C211yesmaximal, characteristic
6#19149671C2212yes—
7#19149670—22no—
8#19149669—22no—
9#19149669—22no—
10#19149600—22no—
11#19149600—22no—
12#19149590C2212yes—
13#127×C173C2211yescharacteristic
14#125×C173C2211yescharacteristic
15#102×C173—22no—
16#97×C173C2211yescharacteristic
17C2×#13063436—22no—
18C4⋊Dic173—22no—
19C4⋊Dic173D412yes—
20C4⋊Dic173D412yes—
21#14583805—22no—
22#14583805—22no—
23#14583805—22no—
24#14583805—22no—
25C4×Dic173—22no—
26C2×D4×C173—22no—
27C2×D4×C173—21no—
28C2×C8×C173—21no—
29C4⋊C4×C173—22no—
30C4⋊C4×C173D412yes—
31C42×C173C2311yescharacteristic
32C2×Dic173—22no—
33C2×Dic173—22no—
34#13063436—42no—
35C23×C173—41no—
36D4×C173—42no—
37D4×C173—44no—
38C2×C4×C173—22no—
39C2×C4×C173C2×D412yes—
40C2×C4×C173C2×D411yescharacteristic
41C8×C173—41no—
42C22×C173—82no—
43C22×C173—81no—
44C22×C173#12011yescharacteristic
45C4×C173—21no—
46C4×C173—22no—
47C4×C173—42no—
48Dic173—42no—
49Dic173—42no—
50C2×C173—161no—
51C2×C173#45412yes—
52C2×C173#45411yescharacteristic
53C173#165811yescharacteristic, complemented, Sylow
54#1658—1731nomaximal, Sylow
55#564—1731no—
56#490—1732no—
57#490D17311yescharacteristic
58#330—1731no—
59#330—1732no—
60#127C2×D17311yescharacteristic
61#125—3462no—
62#125—3462no—
63#125—3462no—
64#125—1732no—
65#125C2×D17311yescharacteristic
66#102—22no—
67#102—3462no—
68#102—3462no—
69#97—1732no—
70#97C2×D17311yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—3462no—
75C4⋊C4—22no—
76C4⋊C4—3462no—
77C4⋊C4—3462no—
78C4⋊C4—3462no—
79C4⋊C4—3462no—
80C4⋊C4—3462no—
81C4⋊C4—1732no—
82C4⋊C4—1732no—
83C4⋊C4C22⋊D17312yes—
84C42—3462no—
85C42C22×D17311yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—3462no—
91C2×C4—3462no—
92C2×C4D4×D17312yes—
93C2×C4C2×C22⋊D17311yescharacteristic
94C8—41no—
95C8—6922no—
96C22—82no—
97C22—81no—
98C22#1914964711yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—6922no—
103C4—6922no—
104C2—161no—
105C2#2601166212yes—
106C2#2601166311yescharacteristic
subgroupG/H
centerC22#19149647
commutator, cosocleC42×C173C23
FrattiniC42C22×D173
Fitting#490×C173C2
socleC22×C173#120
prime radical#127×C173C22
hypercenter#490D173
hypocenterC173#1658
LCSG ▷ C42×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C173⋊#564C2semidirect
3. #26011233C2semidirect
4. #26011232C2semidirect
53. C173#1658semidirect

Maximal subgroups

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

subgroupindex
C173⋊#5642
#260118552
#260112332
#260112322
#490×C1732
#1658173