Finite Group Databasebeta

← #17949606

Subgroups — #17949606

Order 4352.

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#14543920C211yesmaximal, characteristic
2#14543918C211yesmaximal, characteristic
3#14528386C211yesmaximal, characteristic
4#11763720—21no—
5#11763714—21no—
6#11763182C2211yescharacteristic
7#11763159—21no—
8#11763157—21no—
9C8×#3622C411yescharacteristic, complemented
10C17×#498C411yescharacteristic, complemented
11C17×C4⋊Q8—21no—
12C2×#63219—41no—
13#10587560D411yescharacteristic
14#10587555D411yescharacteristic
15#10587545—41no—
16#10587539—41no—
17C17×#106—41no—
18C4×C8×C17C2×C411yescharacteristic
19#10587506—42no—
20#10587480—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
32C4⋊Dic17—41no—
33C2×#3622—22no—
34#63219—82no—
35#7536—171nomaximal, Sylow
36C22×D17—41no—
37C2×#595—161no—
38Q8×C17—82no—
39C2×C4×C17—21no—
40C2×C4×C17—81no—
41C2×C4×C17#9911yescharacteristic
42C2×Dic17—41no—
43D68—81no—
44D68—82no—
45Dic34—81no—
46#3624—161no—
47C8×C17—22no—
48#3622—42no—
49#1708—171no—
50#1410—171no—
51#1409—171no—
52C22×C17#35311yescharacteristic
53C2×D17—81no—
54C2×D17—161no—
55#595—321no—
56C4×C17—22no—
57C4×C17—21no—
58C4×C17—161no—
59Dic17—81no—
60#498#59511yescharacteristic, complemented
61#492—171no—
62#487—341no—
63#486—341no—
64#356—341no—
65#353—341no—
66C82—171no—
67C2×C17—21no—
68C2×C17#140911yescharacteristic
69D17—161no—
70C2×SD16—681no—
71C4⋊Q8—21no—
72C4⋊Q8—171no—
73#127—171no—
74#106—41no—
75#103—682no—
76#102—682no—
77#101—681no—
78#99—681no—
79C4×C8—341no—
80C4×C8C2×#59511yescharacteristic
81C17#753611yescharacteristic, complemented, Sylow
82C2×Q8—41no—
83C2×Q8—341no—
84C2×D4—341no—
85C2×D4—681no—
86SD16—1362no—
87M16—1361no—
88C2×C8—21no—
89C2×C8—342no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—681no—
93C22⋊C4—1361no—
94C42C22⋊#59511yescharacteristic
95C23—681no—
96Q8—82no—
97Q8—1361no—
98D4—1362no—
99D4—1361no—
100C2×C4—21no—
101C2×C4—81no—
102C2×C4—2721no—
103C2×C4—681no—
104C2×C4#1058755111yescharacteristic
105C8—22no—
106C8—2721no—
107C8—682no—
108C22—2721no—
109C22—1361no—
110C22#1176371311yescharacteristic
111C4—22no—
112C4—21no—
113C4—161no—
114C4—5441no—
115C4—1361no—
116C2—21no—
117C2—2721no—
118C2#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#7536
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
60. #498#595semidirect
81. C17#7536semidirect

Maximal subgroups

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

subgroupindex
#145439202
#145439182
#145283862
#753617