Finite Group Databasebeta

← #17953104

Subgroups — #17953104

Order 4352.

1026 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 124 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#14544618C212yesmaximal
2#14544032C214yesmaximal
3C22×#10587555C211yesmaximal, characteristic
4C2×#10587545—24no—
5#11763779C2214yes—
6#11763654—28no—
7C23×Dic34C411yescharacteristic
8C23×Dic34C2211yescharacteristic
9C2×#10587555—28no—
10C2×#10587555—24no—
11C22×C4⋊Dic17C412yes—
12C22×C4⋊Dic17C2212yes—
13C22×C42×C17C411yescharacteristic
14C23×C4×C17C2×C412yes—
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17C2×C411yescharacteristic
17C23×Dic17C2×C412yes—
18C23×Dic17C2311yescharacteristic
19C22×Dic34—22no—
20C22×Dic34—24no—
21C22×Dic34—24no—
22C22×Dic34—44no—
23C22×Dic34—44no—
24C22×Dic34D414yes—
25C2×#63247—24no—
26C2×C42×C17—24no—
27C2×C42×C17—22no—
28C2×C4⋊Dic17—24no—
29C2×C4⋊Dic17—24no—
30C2×C4⋊Dic17—24no—
31C2×C4⋊Dic17—24no—
32C2×C4⋊Dic17—24no—
33C2×C4⋊Dic17D418yes—
34#10587555—232no—
35C22⋊#3624—28no—
36#10587545—48no—
37C24×C17C22×C411yescharacteristic
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—24no—
42C22×C4×C17—28no—
43C22×C4×C17C22⋊C412yes—
44C22×C4×C17C22⋊C414yes—
45C22×Dic17—22no—
46C22×Dic17—22no—
47C22×Dic17—22no—
48C22×Dic17—42no—
49C22×Dic17—42no—
50C22×Dic17—44no—
51C22×Dic17C22⋊C412yes—
52C22×Dic17C22⋊C414yes—
53C22×Dic17C2×D412yes—
54C22×Dic17C2×D414yes—
55C2×Dic34—28no—
56C2×Dic34—28no—
57C2×Dic34—28no—
58C2×Dic34—44no—
59C2×Dic34—416no—
60C2×Dic34—416no—
61C2×Dic34—44no—
62C2×Dic34—44no—
63#63247—48no—
64C2×#3624—44no—
65C42×C17—28no—
66C4⋊Dic17—216no—
67C4⋊Dic17—216no—
68#8551—171nomaximal, Sylow
69C23×C17—22no—
70C23×C17—24no—
71C23×C17C2×C22⋊C411yescharacteristic
72C23×C17C2×C22⋊C412yes—
73C2×C4×C17—28no—
74C2×C4×C17—28no—
75C2×C4×C17—28no—
76C2×C4×C17—22no—
77C2×C4×C17—24no—
78C2×C4×C17—22no—
79C2×C4×C17—24no—
80C2×C4×C17#9914yes—
81C2×C4×C17#10118yescomplemented
82C2×Dic17—24no—
83C2×Dic17—22no—
84C2×Dic17—24no—
85C2×Dic17—24no—
86C2×Dic17—44no—
87C2×Dic17—44no—
88C2×Dic17—44no—
89C2×Dic17—44no—
90C2×Dic17—44no—
91C2×Dic17#12014yes—
92Dic34—416no—
93Dic34—416no—
94#3624—84no—
95C22×C4⋊Q8—171no—
96#1784—172no—
97#1463—174no—
98C22×C17—28no—
99C22×C17—22no—
100C22×C17—22no—
101C22×C17—22no—
102C22×C17#37911yescharacteristic
103C22×C17C2×#9912yes—
104C22×C17C2×#10114yes—
105C4×C17—24no—
106C4×C17—28no—
107Dic17—24no—
108Dic17—42no—
109Dic17—44no—
110C23×Q8—171no—
111C23×Q8—171no—
112C2×C4⋊Q8—348no—
113C2×C4⋊Q8—344no—
114C22×C4⋊C4—172no—
115C22×C4⋊C4—172no—
116C22×C42#59511yescharacteristic
117C2×#101—344no—
118#407—174no—
119#324—348no—
120C2×C17—22no—
121C2×C17—24no—
122C2×C17#178111yescharacteristic
123C2×C17#178412yes—
124C22×Q8—174no—
125C22×Q8—344no—
126C22×Q8—344no—
127C22×Q8—342no—
128C22×Q8—684no—
129C22×Q8—684no—
130C23×C4—171no—
131C23×C4—171no—
132C23×C4—172no—
133C23×C4C2×#59512yes—
134C23×C4C2×#59511yescharacteristic
135C2×M16—344no—
136C4⋊Q8—3432no—
137C2×C4⋊C4—178no—
138C2×C4⋊C4—344no—
139C2×C4⋊C4—344no—
140C2×C4⋊C4—344no—
141C2×C4⋊C4—344no—
142C2×C4⋊C4—344no—
143C2×C42—22no—
144C2×C42—24no—
145#101—688no—
146C22⋊C8—348no—
147C17#855111yescharacteristic, complemented, Sylow
148C24C22×#59511yescharacteristic
149C2×Q8—348no—
150C2×Q8—348no—
151C2×Q8—348no—
152C2×Q8—684no—
153C2×Q8—6816no—
154C2×Q8—6816no—
155C2×Q8—684no—
156C2×Q8—684no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—24no—
161C22×C4—28no—
162C22×C4—172no—
163C22×C4—174no—
164C22×C4—172no—
165C22×C4—174no—
166C22×C4—342no—
167C22×C4—342no—
168C22×C4—342no—
169C22×C4—682no—
170C22×C4—682no—
171C22×C4—684no—
172C22×C4C22⋊#59512yes—
173C22×C4C22⋊#59514yes—
174M16—688no—
175C2×C8—684no—
176C4⋊C4—3416no—
177C4⋊C4—3416no—
178C42—28no—
179C23—22no—
180C23—24no—
181C23C2×C22⋊#59511yescharacteristic
182C23C2×C22⋊#59512yes—
183Q8—6816no—
184Q8—6816no—
185C2×C4—28no—
186C2×C4—28no—
187C2×C4—28no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—174no—
193C2×C4—344no—
194C2×C4—342no—
195C2×C4—344no—
196C2×C4—344no—
197C2×C4—684no—
198C2×C4—684no—
199C2×C4—684no—
200C2×C4—684no—
201C2×C4—684no—
202C2×C4#1058753914yes—
203C2×C4#1058754518yescomplemented
204C8—1364no—
205C22—28no—
206C22—22no—
207C22—22no—
208C22—22no—
209C22#1176375011yescharacteristic
210C22C2×#1058753912yes—
211C22C2×#1058754514yes—
212C4—24no—
213C4—28no—
214C4—344no—
215C4—682no—
216C4—684no—
217C2—22no—
218C2—24no—
219C2#1454461211yescharacteristic
220C2#1454461812yes—
subgroupG/H
centerC22#11763750
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC22×C17#379
cosocleC23×Dic17C23
hypercenterC22×C42#595
hypocenterC17#8551
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
81. C2×C4×C17#101semidirect
147. C17#8551semidirect
203. C2×C4#10587545semidirect

Maximal subgroups

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

subgroupindex
#145446182
#145440322
C22×#105875552
#855117