Finite Group Databasebeta

← #17960049

Subgroups — #17960049

Order 4352.

258 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 64 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#14545153C212yesmaximal
2#14543805C214yesmaximal, complemented
3#14539333C211yesmaximal, characteristic
4#11763732C2214yes—
5#11763705—22no—
6#11763701—22no—
7#11763366C411yescharacteristic
8#11763219—22no—
9#11763208C412yes—
10#11763208C2212yes—
11#11762849—22no—
12C4×#63223C2211yescharacteristic
13C2×C17×#125C411yescharacteristic
14C17×#125—21no—
15C17×#125—41no—
16C17×#125C2×C412yes—
17C2×C4⋊C4×C17—21no—
18C2×C4⋊C4×C17—41no—
19C2×C42×C17C2×C411yescharacteristic
20#10587612—21no—
21#10587610—41no—
22C2×#63223D412yes—
23#10587556C2×C412yes—
24#10587555—21no—
25C4×Dic34—41no—
26#10587538—24no—
27#10587479—22no—
28#10587479—22no—
29#10587478—22no—
30#10587478—22no—
31#10587474D412yes—
32C4×#3622C2×C411yescharacteristic
33C4×#3622C2311yescharacteristic
34C22×C4×C17—21no—
35C22×C4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C2×Dic34—41no—
38C4⋊C4×C17—22no—
39C4⋊C4×C17—42no—
40C4⋊C4×C17—42no—
41C4⋊C4×C17—41no—
42C42×C17—21no—
43C42×C17C22⋊C411yescharacteristic
44C42×C17C22×C411yescharacteristic
45C22⋊Dic17—41no—
46C4⋊Dic17—22no—
47C4⋊Dic17—41no—
48#63225—42no—
49C4×Dic17—41no—
50#63223—24no—
51C2×#3622C22⋊C412yes—
52C2×#3622C2×D412yes—
53#63216—44no—
54#11994—171nomaximal, Sylow
55C23×C17#10011yescharacteristic
56C2×C4×C17—22no—
57C2×C4×C17—21no—
58C2×C4×C17—21no—
59C2×C4×C17—42no—
60C2×C4×C17—81no—
61C2×C4×C17—82no—
62C2×C4×C17#10011yescharacteristic
63C2×C4×C17C2×C22⋊C411yescharacteristic
64C2×Dic17—42no—
65Dic34—82no—
66#3622—22no—
67#3622#13714yes—
68#3166—171no—
69#2165—172no—
70#1366—174no—
71C22×C17—21no—
72C22×C17—41no—
73C22×C17C2×#10011yescharacteristic
74C4×C17—21no—
75C4×C17—41no—
76C4×C17—41no—
77C4×C17—82no—
78C4×C17#41912yes—
79Dic17—82no—
80#533—171no—
81C2×#125#59511yescharacteristic
82#501—342no—
83#499—172no—
84#499—172no—
85#428—342no—
86C4×M16—171no—
87#364—174no—
88#349—342no—
89#347—342no—
90C2×C17—21no—
91C2×C17—41no—
92C2×C17#155811yescharacteristic
93C2×M16—172no—
94C4⋊Q8—341no—
95#125—21no—
96#125—41no—
97#125—172no—
98#125C2×#59512yes—
99C22⋊Q8—681no—
100C4×Q8—681no—
101#117—341no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—41no—
104C2×C42C2×#59511yescharacteristic
105M32—344no—
106#107—342no—
107#107—342no—
108#106—342no—
109#106—342no—
110#97—172no—
111C4×C8—171no—
112C4×C8—171no—
113C17#1199411yescharacteristic, complemented, Sylow
114C2×Q8—681no—
115C22×C4—21no—
116C22×C4—41no—
117C22×C4C22⋊#59511yescharacteristic
118M16—344no—
119C2×C8—172no—
120C2×C8—172no—
121C4⋊C4—22no—
122C4⋊C4—42no—
123C4⋊C4—42no—
124C4⋊C4—41no—
125C4⋊C4—342no—
126C4⋊C4—682no—
127C4⋊C4—681no—
128C22⋊C4—681no—
129C42—21no—
130C42—681no—
131C42C22⋊#59511yescharacteristic
132C42C22×#59511yescharacteristic
133C16—684no—
134C23#1058755311yescharacteristic
135Q8—1362no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—42no—
140C2×C4—81no—
141C2×C4—82no—
142C2×C4—682no—
143C2×C4#1058755311yescharacteristic
144C2×C4C2×C22⋊#59511yescharacteristic
145C8—174no—
146C8—342no—
147C22—21no—
148C22—41no—
149C22C2×#1058755311yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—1362no—
155C4#1176380212yes—
156C2—21no—
157C2—41no—
158C2#1454431711yescharacteristic
subgroupG/H
centerC2#14544317
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×#125C4
socleC2×C17#1558
prime radicalC23×C17#100
cosocleC4×#3622C23
hypercenterC2×#125#595
hypocenterC17#11994
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #14543805C2semidirect
113. C17#11994semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145438052
#145393332
#1199417