Finite Group Databasebeta

← #17949570

Subgroups — #17949570

Order 4352.

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

normal subgroups only

This group has 142 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#14543921C211yesmaximal, characteristic
2#14543793C211yesmaximal, characteristic
3#14527924C211yesmaximal, characteristic
4#11763732—21no—
5#11763720—21no—
6#11763188C2211yescharacteristic
7#11763104—21no—
8#11762558C411yescharacteristic
9Q8⋊#3622—21no—
10Q82×C17C411yescharacteristic
11C17×C4⋊Q8—41no—
12C17×C4⋊Q8—41no—
13C17×C4⋊Q8C2×C411yescharacteristic
14C4×Q8×C17—21no—
15C4×Q8×C17—41no—
16C2×#63231—41no—
17#10587555D411yescharacteristic
18#10587545—41no—
19#10587538—41no—
20#10587506—41no—
21#10587478—41no—
22C4⋊#3622—21no—
23C4×#3622D411yescharacteristic
24C2×Q8×C17—21no—
25C2×Q8×C17—21no—
26C2×Q8×C17—41no—
27C2×Dic34—21no—
28#63247—81no—
29C4⋊C4×C17—21no—
30C4⋊C4×C17—41no—
31C4⋊C4×C17—42no—
32C4⋊C4×C17—41no—
33C42×C17—41no—
34C42×C17—41no—
35C42×C17C22⋊C411yescharacteristic
36#63231—81no—
37#63231—81no—
38C4⋊Dic17—41no—
39C2×#3622—21no—
40C2×#3622—41no—
41#63216—81no—
42#7522—171nomaximal, Sylow
43Q8×C17—22no—
44Q8×C17—41no—
45Q8×C17—81no—
46Q8×C17—161no—
47C2×C4×C17—21no—
48C2×C4×C17—41no—
49C2×C4×C17—41no—
50C2×C4×C17—41no—
51C2×C4×C17#9911yescharacteristic
52C2×Dic17—41no—
53Dic34—81no—
54#3624—161no—
55#3622—21no—
56#3622—21no—
57#3622—81no—
58#1633—171no—
59#1411—171no—
60#1358—171no—
61C22×C17AΣL(1,𝔽16)11yescharacteristic
62C4×C17—21no—
63C4×C17—21no—
64C4×C17—21no—
65C4×C17—42no—
66C4×C17—81no—
67C4×C17—81no—
68Dic17—81no—
69Q82#59511yescharacteristic
70#494—171no—
71#477—341no—
72#364—341no—
73#356—341no—
74#333—171no—
75Q8⋊C8—341no—
76C2×C17—21no—
77C2×C17#140211yescharacteristic
78C2×Q16—681no—
79C4⋊Q8—41no—
80C4⋊Q8—41no—
81C4⋊Q8—171no—
82C4⋊Q8C2×#59511yescharacteristic
83C4×Q8—21no—
84C4×Q8—41no—
85M32—681no—
86#107—681no—
87C4⋊C8—341no—
88#103—681no—
89#101—681no—
90C4×C8—171no—
91C17#752211yescharacteristic, complemented, Sylow
92C2×Q8—21no—
93C2×Q8—21no—
94C2×Q8—41no—
95C2×Q8—341no—
96Q16—1361no—
97Q16—1361no—
98M16—1361no—
99C2×C8—341no—
100C2×C8—681no—
101C4⋊C4—21no—
102C4⋊C4—41no—
103C4⋊C4—42no—
104C4⋊C4—41no—
105C4⋊C4—681no—
106C42—41no—
107C42—41no—
108C42C22⋊#59511yescharacteristic
109C16—1361no—
110Q8—22no—
111Q8—41no—
112Q8—81no—
113Q8—161no—
114Q8—1361no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—681no—
120C2×C4#1058755111yescharacteristic
121C8—2721no—
122C8—341no—
123C8—341no—
124C8—1361no—
125C22#1176370911yescharacteristic
126C4—21no—
127C4—21no—
128C4—21no—
129C4—42no—
130C4—81no—
131C4—81no—
132C4—1361no—
133C2—21no—
134C2#1454390311yescharacteristic
subgroupG/H
centerC2#14543903
commutatorC17×C4⋊Q8C2×C4
FrattiniC4⋊Q8C2×#595
FittingQ82×C17C4
socleC2×C17#1402
prime radicalC22×C17AΣL(1,𝔽16)
cosocle#11763188C22
hypercenterQ82#595
hypocenterC17#7522
LCSG ▷ C17×C4⋊Q8 ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
91. C17#7522semidirect

Maximal subgroups

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

subgroupindex
#145439212
#145437932
#145279242
#752217