Finite Group Databasebeta

← #17949152

Subgroups — #17949152

Order 4352.

216 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 40 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#14543726C212yesmaximal
2#14529586C211yesmaximal, characteristic
3#11763654—22no—
4C2×#10587555C411yescharacteristic
5C2×#10587487—22no—
6#11762679C2211yescharacteristic
7C2×C4×C8×C17C411yescharacteristic
8C22×Dic34—21no—
9C22×C8×C17—21no—
10C2×C42×C17C2×C411yescharacteristic
11C2×C4⋊Dic17—41no—
12C2×C4⋊Dic17—41no—
13C2×C4⋊Dic17D412yes—
14#10587555—21no—
15#10587555—41no—
16#10587555C812yescomplemented
17C22⋊#3624—42no—
18C4×C8×C17—41no—
19#10587487—44no—
20C22×C4×C17—21no—
21C22×C4×C17C22⋊C411yescharacteristic
22C22×Dic17—22no—
23C22×Dic17—41no—
24C2×Dic34—22no—
25C2×Dic34—42no—
26C2×Dic34—42no—
27C2×Dic34—41no—
28C2×#3624—82no—
29C2×C8×C17—22no—
30C2×C8×C17—41no—
31C2×C8×C17—41no—
32C42×C17—21no—
33C42×C17C2×C811yescharacteristic
34C42×C17M1611yescharacteristic
35C4⋊Dic17—42no—
36C4⋊Dic17—42no—
37C4⋊Dic17—42no—
38C4⋊Dic17—82no—
39#7355—171nomaximal, Sylow
40C23×C17#9911yescharacteristic
41C2×C4×C17—22no—
42C2×C4×C17—22no—
43C2×C4×C17—21no—
44C2×C4×C17—21no—
45C2×C4×C17—21no—
46C2×C4×C17—21no—
47C2×C4×C17C22⋊C811yescharacteristic
48C2×C4×C17#10011yescharacteristic
49C2×Dic17—42no—
50C2×Dic17—42no—
51C2×Dic17—81no—
52C2×Dic17—81no—
53C2×Dic17—82no—
54Dic34—44no—
55Dic34—82no—
56#3624—162no—
57C8×C17—42no—
58#1956—171no—
59#1325—172no—
60C22×C17—21no—
61C22×C17—21no—
62C22×C17#32311yescharacteristic
63C22×C17#35311yescharacteristic
64C22×C17#35511yescharacteristic
65C4×C17—22no—
66C4×C17—22no—
67C4×C17—21no—
68C4×C17—21no—
69Dic17—82no—
70Dic17—82no—
71C2×C4⋊Q8—171no—
72C2×#103—342no—
73C2×C4×C8#59511yescharacteristic
74#384—171no—
75#324—342no—
76C2×C17—21no—
77C2×C17—21no—
78C2×C17#131811yescharacteristic
79C2×C17#140911yescharacteristic
80C2×C17#141111yescharacteristic
81C22×Q8—341no—
82C22×C8—21no—
83C4⋊Q8—172no—
84C4⋊Q8—341no—
85C4⋊Q8—681no—
86C2×C4⋊C4—172no—
87C2×C4⋊C4—681no—
88C2×C4⋊C4—681no—
89C2×C42C2×#59511yescharacteristic
90#103—684no—
91C22⋊C8—682no—
92C4×C8—41no—
93C17#735511yescharacteristic, complemented, Sylow
94C2×Q8—342no—
95C2×Q8—682no—
96C2×Q8—682no—
97C2×Q8—681no—
98C22×C4—21no—
99C22×C4—342no—
100C22×C4—681no—
101C22×C4C22⋊#59511yescharacteristic
102C2×C8—22no—
103C2×C8—41no—
104C2×C8—41no—
105C2×C8—1362no—
106C4⋊C4—682no—
107C4⋊C4—682no—
108C4⋊C4—682no—
109C4⋊C4—1362no—
110C42—21no—
111C42#6324211yescharacteristic
112C42#6324311yescharacteristic
113C23#1058753911yescharacteristic
114Q8—684no—
115Q8—1362no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—682no—
123C2×C4—682no—
124C2×C4—1361no—
125C2×C4—1361no—
126C2×C4—1362no—
127C2×C4#1058754311yescharacteristic
128C2×C4#1058755311yescharacteristic
129C8—42no—
130C8—2722no—
131C22—21no—
132C22—21no—
133C22#1176365311yescharacteristic
134C22#1176371411yescharacteristic
135C22#1176371811yescharacteristic
136C4—22no—
137C4—22no—
138C4—21no—
139C4—21no—
140C4—1362no—
141C4—1362no—
142C2—21no—
143C2—21no—
144C2#1454371311yescharacteristic
145C2#1454391811yescharacteristic
146C2#1454392211yescharacteristic
subgroupG/H
centerC22#11763714
commutatorC42×C17C2×C8
FrattiniC2×C42C2×#595
FittingC2×C4×C8×C17C4
socleC22×C17#353
prime radicalC23×C17#99
cosocle#11762679C22
hypercenterC2×C4×C8#595
hypocenterC17#7355
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
16. #10587555C8semidirect
93. C17#7355semidirect

Maximal subgroups

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

subgroupindex
#145437262
#145295862
#735517