Finite Group Databasebeta

← #17953105

Subgroups — #17953105

Order 4352.

1026 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 116 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#14544034C214yesmaximal
3C22×#10587630C211yesmaximal, characteristic
4C2×#10587545—24no—
5#11763779C2214yes—
6#11763655—28no—
7C23×Dic34C2211yescharacteristic
8C2×#10587630—28no—
9C2×#10587630—24no—
10C22×#63225C412yes—
11C22×#63225C2212yes—
12C22×C4×Dic17C411yescharacteristic
13C23×Q8×C17C411yescharacteristic
14C22×Q8×C17—24no—
15C22×Q8×C17—22no—
16C22×Q8×C17—44no—
17C23×C4×C17C2×C411yescharacteristic
18C23×C4×C17C2×C412yes—
19C23×Dic17C2×C412yes—
20C23×Dic17C2×C411yescharacteristic
21C23×Dic17C2311yescharacteristic
22C22×Dic34—24no—
23C22×Dic34—44no—
24C22×Dic34D414yes—
25C2×#63247—24no—
26#10587630—232no—
27C2×#63225—24no—
28C2×#63225—24no—
29C2×#63225—24no—
30C2×#63225—24no—
31C2×#63225—24no—
32C2×#63225D418yes—
33C2×C4×Dic17—22no—
34C2×C4×Dic17—24no—
35C22⋊#3624—28no—
36#10587545—48no—
37C24×C17C22×C411yescharacteristic
38C2×Q8×C17—28no—
39C2×Q8×C17—416no—
40C2×Q8×C17—44no—
41C2×Q8×C17—44no—
42C22×C4×C17—22no—
43C22×C4×C17—24no—
44C22×C4×C17—22no—
45C22×C4×C17—22no—
46C22×C4×C17—44no—
47C22×C4×C17C22⋊C412yes—
48C22×C4×C17C22⋊C414yes—
49C22×Dic17—22no—
50C22×Dic17—22no—
51C22×Dic17—28no—
52C22×Dic17—22no—
53C22×Dic17—42no—
54C22×Dic17—42no—
55C22×Dic17C22⋊C412yes—
56C22×Dic17C22⋊C414yes—
57C22×Dic17C2×D412yes—
58C22×Dic17C2×D414yes—
59C2×Dic34—28no—
60C2×Dic34—28no—
61C2×Dic34—44no—
62C2×Dic34—416no—
63#63247—48no—
64C2×#3624—44no—
65#63225—216no—
66#63225—216no—
67C4×Dic17—28no—
68#8551—171nomaximal, Sylow
69C23×C17—22no—
70C23×C17—24no—
71C23×C17C2×C22⋊C411yescharacteristic
72C23×C17C2×C22⋊C412yes—
73Q8×C17—416no—
74C2×C4×C17—28no—
75C2×C4×C17—22no—
76C2×C4×C17—22no—
77C2×C4×C17—24no—
78C2×C4×C17—44no—
79C2×C4×C17—44no—
80C2×C4×C17—44no—
81C2×C4×C17#9914yes—
82C2×Dic17—28no—
83C2×Dic17—28no—
84C2×Dic17—24no—
85C2×Dic17—24no—
86C2×Dic17—24no—
87C2×Dic17—22no—
88C2×Dic17—24no—
89C2×Dic17—44no—
90C2×Dic17—44no—
91C2×Dic17#10118yescomplemented
92C2×Dic17#12014yes—
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—44no—
107Dic17—24no—
108Dic17—28no—
109Dic17—42no—
110C23×Q8—171no—
111C23×Q8#59511yescharacteristic
112C2×C4⋊Q8—348no—
113C2×C4⋊Q8—344no—
114C22×C4⋊C4—172no—
115C22×C4⋊C4—172no—
116C22×C42—171no—
117C2×#101—344no—
118#407—174no—
119#324—348no—
120C2×C17—22no—
121C2×C17—24no—
122C2×C17#178111yescharacteristic
123C2×C17#178412yes—
124C22×Q8—24no—
125C22×Q8—22no—
126C22×Q8—44no—
127C22×Q8—174no—
128C22×Q8—344no—
129C22×Q8—684no—
130C23×C4—171no—
131C23×C4—172no—
132C23×C4—171no—
133C23×C4C2×#59511yescharacteristic
134C23×C4C2×#59512yes—
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—344no—
144C2×C42—342no—
145#101—688no—
146C22⋊C8—348no—
147C17#855111yescharacteristic, complemented, Sylow
148C24C22×#59511yescharacteristic
149C2×Q8—28no—
150C2×Q8—416no—
151C2×Q8—44no—
152C2×Q8—44no—
153C2×Q8—348no—
154C2×Q8—348no—
155C2×Q8—684no—
156C2×Q8—6816no—
157C22×C4—22no—
158C22×C4—24no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—44no—
162C22×C4—174no—
163C22×C4—172no—
164C22×C4—174no—
165C22×C4—172no—
166C22×C4—348no—
167C22×C4—342no—
168C22×C4—342no—
169C22×C4—342no—
170C22×C4—682no—
171C22×C4—682no—
172C22×C4C22⋊#59512yes—
173C22×C4C22⋊#59514yes—
174M16—688no—
175C2×C8—684no—
176C4⋊C4—3416no—
177C4⋊C4—3416no—
178C42—348no—
179C23—22no—
180C23—24no—
181C23C2×C22⋊#59511yescharacteristic
182C23C2×C22⋊#59512yes—
183Q8—416no—
184Q8—6816no—
185C2×C4—28no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—44no—
192C2×C4—174no—
193C2×C4—178no—
194C2×C4—348no—
195C2×C4—348no—
196C2×C4—344no—
197C2×C4—344no—
198C2×C4—344no—
199C2×C4—342no—
200C2×C4—344no—
201C2×C4—684no—
202C2×C4—684no—
203C2×C4#1058755114yes—
204C8—1364no—
205C22—28no—
206C22—22no—
207C22—22no—
208C22—22no—
209C22#1176375011yescharacteristic
210C22C2×#1058755112yes—
211C22D17⋊#10114yes—
212C4—24no—
213C4—44no—
214C4—344no—
215C4—348no—
216C4—682no—
217C2—22no—
218C2—24no—
219C2#1454461011yescharacteristic
220C2#1454461912yes—
subgroupG/H
centerC22#11763750
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC23×Q8×C17C4
socleC22×C17#379
cosocleC23×Dic17C23
hypercenterC23×Q8#595
hypocenterC17#8551
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
91. C2×Dic17#101semidirect
147. C17#8551semidirect

Maximal subgroups

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

subgroupindex
#145446182
#145440342
C22×#105876302
#855117