Finite Group Databasebeta

← #17959834

Subgroups — #17959834

Order 4352.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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#14545159C211yesmaximal, characteristic, complemented
2#14545006C211yesmaximal, characteristic, complemented
3#14543786C214yesmaximal, complemented
4#14539431C211yesmaximal, characteristic
5#11763865—21no—
6#11763731—21no—
7#11763706—21no—
8#11763702—21no—
9#11763701C2212yes—
10#11763701C2212yes—
11#11763413C412yes—
12#11763211C411yescharacteristic
13#11763173C2212yes—
14#11763059—21no—
15#11763042—21no—
16#11762921—21no—
17D8×Dic17—21no—
18#11762763C2211yescharacteristic
19C17×#493C411yescharacteristic
20C2×D8×C17—21no—
21C2×D8×C17—21no—
22C17×#127C2×C412yes—
23#10587625—42no—
24#10587624—22no—
25#10587621—42no—
26D4×Dic17—22no—
27C2×#63218D411yescharacteristic
28C2×C8×D17D411yescharacteristic
29#10587558C2×C411yescharacteristic
30#10587556C2×C412yes—
31#10587538—22no—
32#10587538—22no—
33#10587530—22no—
34#10587529—22no—
35C4×C8×C17C2×C411yescharacteristic
36#10587503—22no—
37#10587503—22no—
38#10587489—21no—
39#10587488—21no—
40#10587486D411yescharacteristic
41C8×Dic17D411yescharacteristic
42#10587474C2311yescharacteristic
43C2×D4×C17—22no—
44C2×D4×C17—42no—
45C2×C22⋊D17—42no—
46C22×Dic17—42no—
47C2×C4×D17C22⋊C411yescharacteristic
48D8×C17—42no—
49D8×C17—41no—
50D8×C17—41no—
51C2×C8×C17C22⋊C411yescharacteristic
52C2×C8×C17C22⋊C411yescharacteristic
53C42×C17C22×C411yescharacteristic
54C22⋊Dic17—42no—
55C22⋊Dic17—42no—
56#63227—21no—
57C4⋊Dic17—22no—
58#63225—21no—
59#63225—42no—
60C4×Dic17C22⋊C411yescharacteristic
61C2×#3622C2×D411yescharacteristic
62C2×#3622C2×D411yescharacteristic
63#63218—41no—
64C8×D17—21no—
65C8×D17—21no—
66#63216—24no—
67#63216—42no—
68#11913—171nomaximal, Sylow
69C23×C17—42no—
70C22×D17#10011yescharacteristic
71D4×C17—42no—
72D4×C17—42no—
73D4×C17—162no—
74C2×C4×C17—21no—
75C2×C4×C17C2×C22⋊C411yescharacteristic
76C22⋊D17—162no—
77C2×Dic17—21no—
78C2×Dic17—42no—
79C2×Dic17—162no—
80C2×Dic17#10011yescharacteristic
81C4×D17—21no—
82C4×D17—21no—
83C8×C17—21no—
84C8×C17#10411yescharacteristic
85C8×C17#10411yescharacteristic
86#3622—21no—
87#3622—21no—
88#3176—171no—
89#2166—171no—
90#2110—171no—
91#1355—174no—
92C22×C17—82no—
93C22×C17—82no—
94C22×C17—82no—
95C22×C17C2×#10011yescharacteristic
96C2×D17—21no—
97C2×D17—41no—
98C4×C17—41no—
99C4×C17C2×#10411yescharacteristic
100C4×C17#42111yescharacteristic
101Dic17—21no—
102Dic17—41no—
103Dic17—82no—
104#540—172no—
105C2×M32—341no—
106#499—171no—
107#493#59511yescharacteristic
108#490—172no—
109#469—341no—
110#466—341no—
111#442—341no—
112C4×D8—341no—
113#405—171no—
114#364—341no—
115#349—341no—
116#347—172no—
117#347—172no—
118#347—341no—
119C2×C17—21no—
120C2×C17—162no—
121C2×C17#153011yescharacteristic
122D17—41no—
123C2×D8—21no—
124C2×D8—21no—
125C2×M16—171no—
126C22×C8—171no—
127#127C2×#59512yes—
128#125—172no—
129#123—682no—
130#121—342no—
131#121—682no—
132C4×D4—342no—
133#117—171no—
134M32—342no—
135M32—342no—
136M32—342no—
137C2×C16—342no—
138#107—341no—
139#106—341no—
140#102—342no—
141#102—342no—
142#97—171no—
143#97—171no—
144C4×C8—171no—
145C4×C8C2×#59511yescharacteristic
146C17#1191311yescharacteristic, complemented, Sylow
147C2×D4—22no—
148C2×D4—42no—
149C2×D4—682no—
150C22×C4—171no—
151C22×C4—682no—
152D8—42no—
153D8—41no—
154D8—41no—
155M16—681no—
156C2×C8—171no—
157C2×C8—171no—
158C2×C8—341no—
159C2×C8—341no—
160C2×C8C22⋊#59511yescharacteristic
161C2×C8C22⋊#59511yescharacteristic
162C4⋊C4—341no—
163C4⋊C4—342no—
164C4⋊C4—682no—
165C22⋊C4—341no—
166C22⋊C4—682no—
167C22⋊C4—682no—
168C42—171no—
169C42C22×#59511yescharacteristic
170C16—344no—
171C16—682no—
172C23—42no—
173C23—171no—
174D4—42no—
175D4—42no—
176D4—162no—
177D4—2722no—
178C2×C4—21no—
179C2×C4—2722no—
180C2×C4—171no—
181C2×C4—341no—
182C2×C4—341no—
183C2×C4—341no—
184C2×C4—682no—
185C2×C4C2×C22⋊#59511yescharacteristic
186C8—21no—
187C8—341no—
188C8—341no—
189C8#1058754811yescharacteristic
190C8#1058754811yescharacteristic
191C22—82no—
192C22—82no—
193C22—82no—
194C22—341no—
195C22—681no—
196C22D17⋊#10011yescharacteristic
197C4—41no—
198C4—341no—
199C4—681no—
200C4—1362no—
201C4C2×#1058754811yescharacteristic
202C4#1176380711yescharacteristic
203C2—21no—
204C2—162no—
205C2—681no—
206C2#1454425411yescharacteristic
subgroupG/H
centerC2#14544254
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#493C4
socleC2×C17#1530
prime radical#14539431C2
cosocle#10587474C23
hypercenter#493#595
hypocenterC17#11913
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #14545159C2semidirect
2. #14545006C2semidirect
3. #14543786C2semidirect
146. C17#11913semidirect

Maximal subgroups

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

subgroupindex
#145451592
#145450062
#145437862
#145394312
#1191317