Finite Group Databasebeta

← #17949141

Subgroups — #17949141

Order 4352.

178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543716C212yesmaximal
2#14528865C211yesmaximal, characteristic
3#11763705—22no—
4C2×#10587612C411yescharacteristic
5#11762773C2211yescharacteristic
6#11762577—22no—
7C17×#407C411yescharacteristic
8C23×C4×C17C2×C411yescharacteristic
9C2×M16×C17—21no—
10C2×C22⋊Dic17—21no—
11#10587612—41no—
12#10587612—41no—
13C2×C4⋊Dic17—21no—
14C2×C4×Dic17C812yes—
15C2×#63223D412yes—
16#10587538—42no—
17C17×C22⋊C8—41no—
18C22⋊#3622—41no—
19C24×C17M1611yescharacteristic
20C22×C4×C17—21no—
21C22×C4×C17—21no—
22C22×C4×C17—42no—
23C22×C4×C17C22⋊C411yescharacteristic
24C22×C4×C17C2×C811yescharacteristic
25C22×Dic17—22no—
26M16×C17—42no—
27C2×C8×C17—41no—
28C22⋊Dic17—42no—
29C4⋊Dic17—41no—
30C4⋊Dic17—41no—
31C4×Dic17—42no—
32#63223—42no—
33C2×#3622—22no—
34#63216—82no—
35#7350—171nomaximal, Sylow
36C23×C17—21no—
37C23×C17—41no—
38C23×C17—81no—
39C23×C17C22⋊C811yescharacteristic
40C2×C4×C17—22no—
41C2×C4×C17—21no—
42C2×C4×C17—42no—
43C2×C4×C17—42no—
44C2×C4×C17—41no—
45C2×C4×C17#9911yescharacteristic
46C2×C4×C17#10011yescharacteristic
47C2×Dic17—42no—
48C2×Dic17—82no—
49C8×C17—81no—
50#3622—42no—
51#1822—171no—
52#1320—172no—
53C22×C17—21no—
54C22×C17—41no—
55C22×C17—42no—
56C22×C17—41no—
57C22×C17—82no—
58C22×C17#32311yescharacteristic
59C4×C17—21no—
60C4×C17—41no—
61C4×C17#35212yes—
62Dic17—82no—
63C2×#117—171no—
64#407—171no—
65#407#59511yescharacteristic
66#349—342no—
67#343—342no—
68C2×C17—21no—
69C2×C17—41no—
70C2×C17—81no—
71C2×C17#131711yescharacteristic
72C23×C4C2×#59511yescharacteristic
73C2×M16—21no—
74C2×M16—172no—
75#117—681no—
76#117—681no—
77C2×C4⋊C4—341no—
78C2×C22⋊C4—341no—
79C2×C42—172no—
80M32—682no—
81C22⋊C8—41no—
82C22⋊C8—681no—
83C17#735011yescharacteristic, complemented, Sylow
84C24#6324311yescharacteristic
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—42no—
88C22×C4—342no—
89C22×C4#6324211yescharacteristic
90C22×C4C22⋊#59511yescharacteristic
91M16—42no—
92M16—682no—
93C2×C8—41no—
94C2×C8—342no—
95C4⋊C4—681no—
96C4⋊C4—681no—
97C22⋊C4—682no—
98C42—682no—
99C16—1362no—
100C23—21no—
101C23—41no—
102C23—81no—
103C23#1058754311yescharacteristic
104C2×C4—22no—
105C2×C4—21no—
106C2×C4—42no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4—682no—
110C2×C4—1362no—
111C2×C4#1058753911yescharacteristic
112C2×C4#1058755311yescharacteristic
113C8—81no—
114C8—682no—
115C22—21no—
116C22—41no—
117C22—42no—
118C22—41no—
119C22—82no—
120C22#1176365311yescharacteristic
121C4—21no—
122C4—41no—
123C4—1362no—
124C4#1176371212yes—
125C2—21no—
126C2—41no—
127C2—81no—
128C2#1454371111yescharacteristic
subgroupG/H
centerC2#14543711
commutatorC22×C4×C17C2×C8
FrattiniC23×C4C2×#595
FittingC17×#407C4
socleC2×C17#1317
prime radicalC24×C17M16
cosocle#11762773C22
hypercenter#407#595
hypocenterC17#7350
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
83. C17#7350semidirect

Maximal subgroups

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

subgroupindex
#145437162
#145288652
#735017