Finite Group Databasebeta

← #17959840

Subgroups — #17959840

Order 4352.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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, complemented
2#14543786C214yesmaximal, complemented
3#14539158C211yesmaximal, characteristic
4#11763732—22no—
5#11763705—22no—
6#11763701C2214yescomplemented
7#11763366C411yescharacteristic
8#11763173C412yes—
9#11763173C2212yes—
10#11763155—22no—
11#11762814—22no—
12C4×#63223C2211yescharacteristic
13C2×C17×#127C411yescharacteristic
14C22×D4×C17—21no—
15C22×D4×C17—41no—
16C17×#127—21no—
17C17×#127—41no—
18C17×#127C2×C412yes—
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#10587503—24no—
28#10587503—24no—
29#10587474C2×C411yescharacteristic
30#10587474C2311yescharacteristic
31C4×#3622D412yes—
32C24×C17—41no—
33C2×D4×C17—22no—
34C2×D4×C17—44no—
35C2×D4×C17—42no—
36C2×D4×C17—42no—
37C2×D4×C17—41no—
38C2×D4×C17—84no—
39C22×C4×C17—21no—
40C22×C4×C17C22⋊C411yescharacteristic
41C2×Dic34—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—42no—
51C2×#3622C22⋊C412yes—
52C2×#3622C2×D412yes—
53#63216—44no—
54#11915—171nomaximal, Sylow
55C23×C17—42no—
56C23×C17—82no—
57C23×C17—84no—
58C23×C17#10011yescharacteristic
59D4×C17—44no—
60D4×C17—82no—
61D4×C17—84no—
62D4×C17—84no—
63C2×C4×C17—21no—
64C2×C4×C17—22no—
65C2×C4×C17—21no—
66C2×C4×C17—42no—
67C2×C4×C17#10011yescharacteristic
68C2×C4×C17C2×C22⋊C411yescharacteristic
69C2×Dic17—42no—
70Dic34—82no—
71#3622—22no—
72#3622—22no—
73#3138—171no—
74#2165—172no—
75#1355—174no—
76C22×C17—21no—
77C22×C17—41no—
78C22×C17—84no—
79C22×C17—82no—
80C22×C17—164no—
81C22×C17C2×#10011yescharacteristic
82C4×C17—22no—
83C4×C17—21no—
84C4×C17—41no—
85C4×C17#42112yes—
86Dic17—82no—
87#533—171no—
88C2×#127#59511yescharacteristic
89#490—172no—
90#490—172no—
91#486—342no—
92#418—342no—
93C4×M16—171no—
94#364—342no—
95#349—342no—
96#347—174no—
97C2×C17—21no—
98C2×C17—41no—
99C2×C17—162no—
100C2×C17#153311yescharacteristic
101C22×D4—21no—
102C22×D4—41no—
103C2×M16—172no—
104C4⋊Q8—341no—
105#127—21no—
106#127—41no—
107#127C2×#59512yes—
108#125—172no—
109C22⋊Q8—681no—
110C4×Q8—681no—
111#117—341no—
112C2×C42C2×#59511yescharacteristic
113M32—344no—
114#102—344no—
115#102—344no—
116#97—171no—
117#97—171no—
118C4×C8—172no—
119C17#1191511yescharacteristic, complemented, Sylow
120C24—41no—
121C2×Q8—681no—
122C2×D4—22no—
123C2×D4—44no—
124C2×D4—42no—
125C2×D4—42no—
126C2×D4—41no—
127C2×D4—84no—
128C22×C4—21no—
129C22×C4C22⋊#59511yescharacteristic
130M16—682no—
131C2×C8—172no—
132C2×C8—172no—
133C4⋊C4—342no—
134C4⋊C4—682no—
135C4⋊C4—681no—
136C22⋊C4—681no—
137C42—21no—
138C42—681no—
139C42C22⋊#59511yescharacteristic
140C42C22×#59511yescharacteristic
141C16—684no—
142C23—42no—
143C23—82no—
144C23—84no—
145C23#1058755311yescharacteristic
146Q8—1362no—
147D4—44no—
148D4—82no—
149D4—84no—
150D4—84no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—42no—
155C2×C4—682no—
156C2×C4#1058755311yescharacteristic
157C2×C4C2×C22⋊#59511yescharacteristic
158C8—342no—
159C8—342no—
160C22—21no—
161C22—41no—
162C22—84no—
163C22—82no—
164C22—164no—
165C22C2×#1058755311yescharacteristic
166C4—22no—
167C4—21no—
168C4—41no—
169C4—1362no—
170C4#1176380712yes—
171C2—21no—
172C2—41no—
173C2—162no—
174C2#1454426311yescharacteristic
subgroupG/H
centerC2#14544263
commutatorC42×C17C22×C4
FrattiniC42C22×#595
Fitting, prime radicalC2×C17×#127C4
socleC2×C17#1533
cosocle#10587474C23
hypercenterC2×#127#595
hypocenterC17#11915
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14545153C2semidirect
2. #14543786C2semidirect
6. #11763701C22semidirect
119. C17#11915semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145437862
#145391582
#1191517