Finite Group Databasebeta

← #17953683

Subgroups — #17953683

Order 4352.

474 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 72 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#14544031C212yesmaximal
2#14543685C214yesmaximal, complemented
3#14531379C211yesmaximal, characteristic
4#11763779C2214yes—
5#11763653—22no—
6#11763653—22no—
7C22×#63227C2211yescharacteristic
8#11762700—22no—
9#11762698—22no—
10#11762667C2212yes—
11#11762664C412yes—
12C4×C22⋊Dic17C411yescharacteristic
13C4×C22⋊C4×C17C411yescharacteristic
14C24×D17C2×C411yescharacteristic
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17C2311yescharacteristic
17C2×#63247—24no—
18C2×C22⋊C4×C17C2×C412yes—
19C2×C42×C17—21no—
20C2×C22⋊Dic17C2×C412yes—
21C2×#63227—22no—
22C2×#63227—22no—
23C2×#63227—24no—
24C2×#63227D412yes—
25C2×#63227D412yes—
26C2×#63225—22no—
27C2×C4×Dic17—21no—
28C22⋊#3624—24no—
29C22⋊#3624—24no—
30C17×#95—21no—
31#10587502—21no—
32#10587502—22no—
33C24×C17C22×C411yescharacteristic
34C23×D17—22no—
35C23×D17—42no—
36C23×D17—81no—
37C23×D17—81no—
38C23×D17C22⋊C412yes—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—81no—
42C22×C4×C17C22⋊C411yescharacteristic
43C22×C4×C17C22⋊C411yescharacteristic
44C22×Dic17—22no—
45C22×Dic17—81no—
46C22×Dic17C2×D412yes—
47C22×Dic17#4114yes—
48#63247—84no—
49C2×#3624—44no—
50C22⋊C4×C17—42no—
51C42×C17—81no—
52C22⋊Dic17—42no—
53#63227—24no—
54#63227—24no—
55#63227—82no—
56#63227—82no—
57#63225—82no—
58C4×Dic17—81no—
59#8759—171nomaximal, Sylow
60C23×C17—22no—
61C23×C17—41no—
62C23×C17—41no—
63C23×C17C2×C22⋊C411yescharacteristic
64C23×C17#11712yes—
65C22×D17—22no—
66C22×D17—24no—
67C22×D17—44no—
68C22×D17—42no—
69C22×D17—42no—
70C22×D17—82no—
71C22×D17—82no—
72C22×D17—88no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—41no—
76C2×C4×C17—41no—
77C2×C4×C17—42no—
78C2×C4×C17—42no—
79C2×C4×C17—42no—
80C2×C4×C17—82no—
81C2×Dic17—44no—
82C2×Dic17—42no—
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17#12314yes—
87#3624—84no—
88#2312—171no—
89#1462—172no—
90#1305—174no—
91C22×C17—21no—
92C22×C17—21no—
93C22×C17—22no—
94C22×C17—22no—
95C22×C17—22no—
96C22×C17—44no—
97C22×C17#38111yescharacteristic
98C22×C17#41312yes—
99C2×D17—42no—
100C2×D17—42no—
101C2×D17—42no—
102C2×D17—88no—
103C2×D17—84no—
104C4×C17—41no—
105C4×C17—41no—
106C4×C17—82no—
107Dic17—24no—
108Dic17—82no—
109C22×C22⋊C4—171no—
110#407—174no—
111#388—342no—
112#388—342no—
113#380—172no—
114#379—172no—
115C4×C22⋊C4—171no—
116C4×C22⋊C4#59511yescharacteristic
117#323—342no—
118#323—342no—
119C2×C17—22no—
120C2×C17—42no—
121C2×C17#182211yescharacteristic
122C2×C17#182811yescharacteristic
123C2×C17#182911yescharacteristic
124D17—82no—
125C25—171no—
126C23×C4—171no—
127C23×C4C2×#59511yescharacteristic
128C2×M16—344no—
129C2×C4⋊C4—342no—
130C2×C22⋊C4—172no—
131C2×C22⋊C4—172no—
132C2×C22⋊C4—172no—
133C2×C22⋊C4—344no—
134C2×C22⋊C4—342no—
135C2×C22⋊C4—342no—
136C2×C22⋊C4C2×#59512yes—
137C2×C42—21no—
138C2×C42—341no—
139C22⋊C8—344no—
140C22⋊C8—344no—
141#95—21no—
142#95—342no—
143#95—341no—
144C17#875911yescharacteristic, complemented, Sylow
145C24—172no—
146C24—342no—
147C24—682no—
148C24—1361no—
149C24—1361no—
150C24C22×#59511yescharacteristic
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—81no—
154C22×C4—174no—
155C22×C4—172no—
156C22×C4—342no—
157C22×C4—1361no—
158C22×C4C22⋊#59511yescharacteristic
159C22×C4C22⋊#59511yescharacteristic
160M16—1364no—
161C2×C8—684no—
162C4⋊C4—1362no—
163C22⋊C4—42no—
164C22⋊C4—344no—
165C22⋊C4—344no—
166C22⋊C4—682no—
167C22⋊C4—1362no—
168C22⋊C4—1362no—
169C42—81no—
170C42—1361no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—342no—
175C23—344no—
176C23—684no—
177C23—682no—
178C23—682no—
179C23—1362no—
180C23—1362no—
181C23—1368no—
182C23#1058767712yes—
183C23C2×C22⋊#59511yescharacteristic
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—82no—
192C2×C4—174no—
193C2×C4—682no—
194C2×C4—684no—
195C2×C4—682no—
196C2×C4—682no—
197C2×C4—682no—
198C8—1364no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—44no—
205C22—682no—
206C22—682no—
207C22—682no—
208C22—1364no—
209C22—1368no—
210C22#1176375211yescharacteristic
211C22#1176379512yes—
212C4—41no—
213C4—41no—
214C4—82no—
215C4—344no—
216C4—1362no—
217C2—22no—
218C2—42no—
219C2—1362no—
220C2#1454468511yescharacteristic
221C2#1454469611yescharacteristic
222C2#1454469711yescharacteristic
subgroupG/H
centerC22#11763752
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC4×C22⋊C4×C17C4
socleC22×C17#381
prime radicalC24×D17C2×C4
cosocleC23×Dic17C23
hypercenterC4×C22⋊C4#595
hypocenterC17#8759
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14543685C2semidirect
144. C17#8759semidirect

Maximal subgroups

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

subgroupindex
#145440312
#145436852
#145313792
#875917