Finite Group Databasebeta

← #17949604

Subgroups — #17949604

Order 4352.

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

normal subgroups only

This group has 150 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#14543920C211yesmaximal, characteristic
2#14543918C211yesmaximal, characteristic
3#14528372C211yesmaximal, characteristic
4#11763720—21no—
5#11763714—21no—
6#11763205—21no—
7#11763183—21no—
8#11763182C2211yescharacteristic
9C8×#3622C411yescharacteristic, complemented
10C17×#498C411yescharacteristic, complemented
11C17×C4⋊Q8—21no—
12C2×#63230—42no—
13C2×#63219—41no—
14#10587560D411yescharacteristic
15#10587555D411yescharacteristic
16#10587545—41no—
17#10587539—41no—
18C17×#106—41no—
19C4×C8×C17C2×C411yescharacteristic
20#10587479—42no—
21C4×#3622—21no—
22C2×Q8×C17—41no—
23C2×D68—21no—
24C2×D68—41no—
25C2×Dic34—21no—
26C22⋊#595—81no—
27#63247—81no—
28C2×C8×C17—21no—
29C4⋊C4×C17—41no—
30C4⋊C4×C17—41no—
31C42×C17C22⋊C411yescharacteristic
32#63230—84no—
33C4⋊Dic17—41no—
34C2×#3622—22no—
35#63219—82no—
36#7535—171nomaximal, Sylow
37C22×D17—41no—
38C2×#595—161no—
39Q8×C17—82no—
40C2×C4×C17—21no—
41C2×C4×C17—81no—
42C2×C4×C17#9911yescharacteristic
43C2×Dic17—41no—
44D68—81no—
45D68—82no—
46Dic34—81no—
47#3624—161no—
48C8×C17—22no—
49#3622—24no—
50#1705—171no—
51#1410—171no—
52#1409—171no—
53C22×C17#35311yescharacteristic
54C2×D17—81no—
55C2×D17—161no—
56#595—321no—
57C4×C17—22no—
58C4×C17—21no—
59C4×C17—161no—
60Dic17—81no—
61#498—341no—
62#498#59511yescharacteristic, complemented
63#492—171no—
64#492—341no—
65#356—341no—
66#353—341no—
67C82—171no—
68C2×C17—21no—
69C2×C17#140911yescharacteristic
70D17—161no—
71C2×SD16—681no—
72C2×SD16—682no—
73C4⋊Q8—21no—
74C4⋊Q8—171no—
75#127—171no—
76#106—41no—
77#106—682no—
78#101—681no—
79#99—681no—
80C4×C8—341no—
81C4×C8C2×#59511yescharacteristic
82C17#753511yescharacteristic, complemented, Sylow
83C2×Q8—41no—
84C2×Q8—341no—
85C2×D4—341no—
86C2×D4—681no—
87SD16—1362no—
88SD16—1364no—
89M16—1361no—
90C2×C8—21no—
91C2×C8—342no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—681no—
95C22⋊C4—1361no—
96C42C22⋊#59511yescharacteristic
97C23—681no—
98Q8—82no—
99Q8—1361no—
100D4—1362no—
101D4—1361no—
102C2×C4—21no—
103C2×C4—81no—
104C2×C4—2721no—
105C2×C4—681no—
106C2×C4#1058755111yescharacteristic
107C8—22no—
108C8—2721no—
109C8—344no—
110C22—2721no—
111C22—1361no—
112C22#1176371311yescharacteristic
113C4—22no—
114C4—21no—
115C4—161no—
116C4—5441no—
117C4—1361no—
118C2—21no—
119C2—2721no—
120C2#1454391711yescharacteristic
subgroupG/H
centerC2#14543917
commutatorC4×C8×C17C2×C4
FrattiniC4×C8C2×#595
FittingC17×#498C4
socleC2×C17#1409
prime radical#10587560D4
cosocle#11763182C22
hypercenter#498#595
hypocenterC17#7535
LCSG ▷ C4×C8×C17 ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
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×#3622C4semidirect
10. C17×#498C4semidirect
62. #498#595semidirect
82. C17#7535semidirect

Maximal subgroups

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

subgroupindex
#145439202
#145439182
#145283722
#753517