Finite Group Databasebeta

← #17949135

Subgroups — #17949135

Order 4352.

200 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 38 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#14543710C212yesmaximal
2#14528861C211yesmaximal, characteristic
3#11763652—22no—
4#11762672C411yescharacteristic
5#11762672C2211yescharacteristic
6#11762576—22no—
7C2×C17×#117C411yescharacteristic
8C23×C4×C17C2×C411yescharacteristic
9C17×#117—41no—
10C17×#117—41no—
11C2×C4⋊C4×C17—21no—
12C2×C22⋊C4×C17—21no—
13C2×C42×C17C812yescomplemented
14C2×C22⋊Dic17—21no—
15C2×C22⋊Dic17D412yes—
16C22⋊#3624—42no—
17#10587502—41no—
18#10587502—41no—
19C24×C17C22⋊C411yescharacteristic
20C22×C4×C17—21no—
21C22×C4×C17—21no—
22C22×C4×C17—22no—
23C22×C4×C17—42no—
24C22×C4×C17C2×C811yescharacteristic
25C22×C4×C17M1611yescharacteristic
26C22×Dic17—22no—
27C22×Dic17—41no—
28C2×#3624—82no—
29C4⋊C4×C17—42no—
30C22⋊C4×C17—41no—
31C22⋊C4×C17—41no—
32C42×C17—42no—
33C22⋊Dic17—42no—
34C22⋊Dic17—42no—
35#7348—171nomaximal, Sylow
36C23×C17—22no—
37C23×C17—81no—
38C23×C17C22⋊C811yescharacteristic
39C23×C17#9911yescharacteristic
40C23×C17#10011yescharacteristic
41C2×C4×C17—21no—
42C2×C4×C17—21no—
43C2×C4×C17—42no—
44C2×C4×C17—42no—
45C2×C4×C17—41no—
46C2×C4×C17—41no—
47C2×C4×C17—42no—
48C2×C4×C17—82no—
49C2×Dic17—42no—
50C2×Dic17—82no—
51C2×Dic17—81no—
52C2×Dic17—82no—
53#3624—162no—
54#1820—171no—
55#1317—172no—
56C22×C17—21no—
57C22×C17—21no—
58C22×C17—41no—
59C22×C17—41no—
60C22×C17—41no—
61C22×C17—82no—
62C22×C17#32311yescharacteristic
63C22×C17#35212yes—
64C4×C17—41no—
65C4×C17—41no—
66C4×C17—82no—
67Dic17—82no—
68Dic17—161no—
69C2×#117#59511yescharacteristic
70#381—171no—
71#381—171no—
72#342—342no—
73#323—342no—
74C2×C17—22no—
75C2×C17—21no—
76C2×C17—41no—
77C2×C17—41no—
78C2×C17#131711yescharacteristic
79C23×C4C2×#59511yescharacteristic
80#117—41no—
81#117—41no—
82C2×C4⋊C4—21no—
83C2×C22⋊C4—21no—
84C2×C22⋊C4—172no—
85C2×C22⋊C4—341no—
86C2×C42#362412yescomplemented
87C22⋊C8—682no—
88#95—681no—
89#95—681no—
90C17#734811yescharacteristic, complemented, Sylow
91C24C22⋊#59511yescharacteristic
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—42no—
96C22×C4—342no—
97C22×C4—681no—
98C22×C4C2×#362411yescharacteristic
99C22×C4#6324711yescharacteristic
100C2×C8—1362no—
101C4⋊C4—42no—
102C22⋊C4—41no—
103C22⋊C4—41no—
104C22⋊C4—682no—
105C22⋊C4—682no—
106C42—42no—
107C23—22no—
108C23—81no—
109C23#1058755111yescharacteristic
110C23C22⋊#362411yescharacteristic
111C23#1058755311yescharacteristic
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4—82no—
120C2×C4—682no—
121C2×C4—1361no—
122C2×C4—1362no—
123C2×C4—1362no—
124C8—2722no—
125C22—21no—
126C22—21no—
127C22—41no—
128C22—41no—
129C22—41no—
130C22—82no—
131C22#1176365211yescharacteristic
132C22#1176371112yes—
133C4—41no—
134C4—41no—
135C4—82no—
136C4—2721no—
137C4—1362no—
138C2—21no—
139C2—22no—
140C2—41no—
141C2—41no—
142C2#1454371011yescharacteristic
subgroupG/H
centerC2#14543710
commutatorC22×C4×C17C2×C8
FrattiniC23×C4C2×#595
FittingC2×C17×#117C4
socleC2×C17#1317
prime radicalC24×C17C22⋊C4
cosocle#11762672C22
hypercenterC2×#117#595
hypocenterC17#7348
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
13. C2×C42×C17C8semidirect
86. C2×C42#3624semidirect
90. C17#7348semidirect

Maximal subgroups

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

subgroupindex
#145437102
#145288612
#734817