Finite Group Databasebeta

← #17953678

Subgroups — #17953678

Order 4352.

438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544032C212yesmaximal
2#14543685C214yesmaximal
3#14531400C211yesmaximal, characteristic
4#11763779C2214yes—
5#11763654—22no—
6#11763654—22no—
7C2×#10587612C411yescharacteristic
8C22×C4⋊Dic17C2211yescharacteristic
9#11762707—22no—
10#11762705—22no—
11#11762667C412yes—
12#11762667C2212yes—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17C2×C411yescharacteristic
16C23×Dic17C2311yescharacteristic
17C2×#63247—24no—
18C17×#117—42no—
19C2×C4⋊C4×C17—21no—
20C2×C22⋊C4×C17C2×C412yes—
21C2×C42×C17—21no—
22C2×C22⋊Dic17C2×C412yes—
23#10587612—42no—
24C2×C4⋊Dic17—21no—
25C2×C4⋊Dic17—24no—
26C2×C4⋊Dic17D412yes—
27C2×C4⋊Dic17D412yes—
28C2×#63225—22no—
29C2×#63225—22no—
30C2×C4×Dic17—21no—
31C22⋊#3624—24no—
32C22⋊#3624—24no—
33#10587502—22no—
34#10587502—22no—
35C24×C17C22×C411yescharacteristic
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17C22⋊C411yescharacteristic
41C22×C4×C17C22⋊C411yescharacteristic
42C22×Dic17—22no—
43C22×Dic17—22no—
44C22×Dic17—81no—
45C22×Dic17—81no—
46C22×Dic17C22⋊C412yes—
47C22×Dic17C2×D412yes—
48C22×Dic17#4114yes—
49#63247—84no—
50C2×#3624—44no—
51C4⋊C4×C17—42no—
52C22⋊C4×C17—42no—
53C42×C17—42no—
54C22⋊Dic17—42no—
55C4⋊Dic17—24no—
56C4⋊Dic17—24no—
57C4⋊Dic17—42no—
58#63225—82no—
59#63225—82no—
60C4×Dic17—42no—
61#8757—171nomaximal, Sylow
62C23×C17—21no—
63C23×C17—21no—
64C23×C17—41no—
65C23×C17—41no—
66C23×C17C2×C22⋊C411yescharacteristic
67C23×C17#11712yes—
68C2×C4×C17—28no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17#10012yes—
77C2×C4×C17#10112yes—
78C2×Dic17—22no—
79C2×Dic17—44no—
80C2×Dic17—42no—
81C2×Dic17—42no—
82C2×Dic17—42no—
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—82no—
86C2×Dic17#12314yes—
87#3624—84no—
88#2316—171no—
89#1463—172no—
90#1305—174no—
91C22×C17—21no—
92C22×C17—21no—
93C22×C17—22no—
94C22×C17—22no—
95C22×C17—22no—
96C22×C17—42no—
97C22×C17—42no—
98C22×C17#38111yescharacteristic
99C22×C17C2×#10011yescharacteristic
100C22×C17C2×#10111yescharacteristic
101C4×C17—22no—
102C4×C17—22no—
103C4×C17—82no—
104Dic17—24no—
105Dic17—42no—
106Dic17—82no—
107C2×#117—171no—
108C2×#117#59511yescharacteristic
109C22×C4⋊C4—171no—
110#407—174no—
111#389—342no—
112#389—342no—
113#380—172no—
114#380—172no—
115#324—342no—
116#324—342no—
117C2×C17—21no—
118C2×C17—21no—
119C2×C17—42no—
120C2×C17#182111yescharacteristic
121C2×C17#182811yescharacteristic
122C2×C17#183011yescharacteristic
123C23×C4—171no—
124C23×C4—171no—
125C23×C4C2×#59511yescharacteristic
126C2×M16—344no—
127#117—42no—
128#117—682no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—172no—
131C2×C4⋊C4—172no—
132C2×C4⋊C4—344no—
133C2×C4⋊C4—341no—
134C2×C4⋊C4—342no—
135C2×C4⋊C4—342no—
136C2×C22⋊C4—172no—
137C2×C22⋊C4C2×#59512yes—
138C2×C42—21no—
139C2×C42—341no—
140C22⋊C8—344no—
141C22⋊C8—344no—
142#95—342no—
143#95—342no—
144C17#875711yescharacteristic, complemented, Sylow
145C24C22×#59511yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—174no—
151C22×C4—172no—
152C22×C4—172no—
153C22×C4—342no—
154C22×C4—342no—
155C22×C4—1361no—
156C22×C4—1361no—
157C22×C4C22⋊#59511yescharacteristic
158C22×C4C22⋊#59511yescharacteristic
159M16—1364no—
160C2×C8—684no—
161C4⋊C4—42no—
162C4⋊C4—344no—
163C4⋊C4—344no—
164C4⋊C4—682no—
165C4⋊C4—1362no—
166C4⋊C4—1362no—
167C22⋊C4—42no—
168C22⋊C4—682no—
169C42—42no—
170C42—682no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23#1058767712yes—
176C23C2×C22⋊#59511yescharacteristic
177C2×C4—28no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—174no—
186C2×C4—342no—
187C2×C4—682no—
188C2×C4—684no—
189C2×C4—682no—
190C2×C4—682no—
191C2×C4—682no—
192C2×C4—682no—
193C2×C4—1362no—
194C2×C4#1058754512yes—
195C2×C4#1058755312yes—
196C8—1364no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22#1176375211yescharacteristic
205C22C2×#1058755311yescharacteristic
206C22C2×#1058754511yescharacteristic
207C4—22no—
208C4—22no—
209C4—82no—
210C4—344no—
211C4—682no—
212C4—1362no—
213C2—21no—
214C2—21no—
215C2—42no—
216C2#1454468311yescharacteristic
217C2#1454469611yescharacteristic
218C2#1454469811yescharacteristic
subgroupG/H
centerC22#11763752
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC2×C17×#117C4
socleC22×C17#381
cosocleC23×Dic17C23
hypercenterC2×#117#595
hypocenterC17#8757
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
144. C17#8757semidirect

Maximal subgroups

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

subgroupindex
#145440322
#145436852
#145314002
#875717