Finite Group Databasebeta

← #17981394

Subgroups — #17981394

Order 4352.

184 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 29 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#14545823C212yesmaximal
2#14544970C211yesmaximal, characteristic
3#11763908—22no—
4#11763814C2211yescharacteristic
5C42×#595C411yescharacteristic
6#11763679—22no—
7#11763365C411yescharacteristic
8C2×C4×#595—21no—
9C2×C4×#595—41no—
10C2×#63243D412yes—
11#10587670—42no—
12C17×#125C811yescharacteristic
13#10587582—41no—
14#10587578—21no—
15#10587574—21no—
16#10587573—41no—
17C42×D17C2×C411yescharacteristic
18#10587556C811yescharacteristic
19#10587544—41no—
20C22×#595—41no—
21C2×C4×D17—21no—
22C2×C4×D17C22⋊C411yescharacteristic
23C2×Dic34—41no—
24C2×#3624—22no—
25C4×#595—22no—
26C4×#595—41no—
27C4×#595—44no—
28#63243—42no—
29#63241—82no—
30C4⋊C4×C17—21no—
31C4⋊C4×C17—41no—
32C42×C17C2×C811yescharacteristic
33#63227—41no—
34C4⋊Dic17—21no—
35#63225—41no—
36#63225—41no—
37C4×Dic17—21no—
38C4×Dic17—41no—
39C4×Dic17M1611yescharacteristic
40#7361—171nomaximal, Sylow
41C22×D17#10011yescharacteristic
42C2×#595—42no—
43C2×#595—44no—
44C2×C4×C17—21no—
45C2×C4×C17—41no—
46C2×C4×C17C22⋊C811yescharacteristic
47C2×Dic17—21no—
48C2×Dic17—41no—
49C2×Dic17#9911yescharacteristic
50C4×D17—21no—
51C4×D17—21no—
52C4×D17—42no—
53Dic34—82no—
54#3624—42no—
55#1994—171no—
56#1327—172no—
57C22×C17#32311yescharacteristic
58C2×D17—21no—
59C2×D17—41no—
60#595—44no—
61C4×C17—21no—
62C4×C17—41no—
63C4×C17—81no—
64Dic17—22no—
65Dic17—81no—
66Dic17#35411yescharacteristic
67Dic17#35611yescharacteristic
68#533—171no—
69#423—171no—
70C43—171no—
71#349—342no—
72#339—342no—
73C2×C17—21no—
74C2×C17#131911yescharacteristic
75D17—41no—
76C2×M16—172no—
77C4⋊Q8—341no—
78#125—171no—
79#125#363311yescharacteristic
80C22⋊Q8—681no—
81C4×Q8—681no—
82#117—341no—
83C2×C42—171no—
84C2×C42—341no—
85C2×C42—681no—
86M32—682no—
87C4⋊C8—681no—
88C17#736111yescharacteristic, complemented, Sylow
89C2×Q8—681no—
90C22×C4—171no—
91C22×C4—341no—
92C22×C4—681no—
93M16—682no—
94C2×C8—342no—
95C4⋊C4—21no—
96C4⋊C4—41no—
97C4⋊C4—341no—
98C4⋊C4—681no—
99C4⋊C4—681no—
100C22⋊C4—681no—
101C42—171no—
102C42—341no—
103C42—342no—
104C42—681no—
105C42—681no—
106C42—684no—
107C42C2×#363311yescharacteristic
108C16—1362no—
109C23—171no—
110Q8—1362no—
111C2×C4—21no—
112C2×C4—41no—
113C2×C4—171no—
114C2×C4—341no—
115C2×C4—341no—
116C2×C4—341no—
117C2×C4—682no—
118C2×C4—682no—
119C2×C4—684no—
120C2×C4—681no—
121C2×C4C22⋊#363311yescharacteristic
122C8—682no—
123C22—341no—
124C22—681no—
125C22#1176389411yescharacteristic
126C4—21no—
127C4—41no—
128C4—81no—
129C4—171no—
130C4—171no—
131C4—342no—
132C4—684no—
133C4—1361no—
134C2—21no—
135C2—681no—
136C2#1454581211yescharacteristic
subgroupG/H
centerC2#14545812
commutatorC42×C17C2×C8
FrattiniC42C2×#3633
FittingC17×#125C8
socleC2×C17#1319
prime radicalC22×D17#100
cosocle#11763814C22
hypercenter#125#3633
hypocenterC17#7361
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
88. C17#7361semidirect

Maximal subgroups

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

subgroupindex
#145458232
#145449702
#736117