Finite Group Databasebeta

← #17958214

Subgroups — #17958214

Order 4352.

462 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 112 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#14544015C212yesmaximal
2#14543728C214yesmaximal
3#14531268C211yesmaximal, characteristic
4#11763825—22no—
5#11763654—22no—
6#11763652C2214yes—
7C2×#10587612C2211yescharacteristic
8C22×C4×Dic17C411yescharacteristic
9#11762708—22no—
10#11762684C412yes—
11#11762684C2212yes—
12C4×C4⋊Dic17—22no—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17C2×C412yes—
16C17×#117—22no—
17C17×#117C814yescomplemented
18C2×C4⋊C4×C17—21no—
19C2×C22⋊C4×C17C2×C412yes—
20C2×C42×C17—21no—
21C2×C22⋊Dic17C2×C411yescharacteristic
22C2×C22⋊Dic17C2311yescharacteristic
23#10587612—41no—
24#10587612—41no—
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17—22no—
27C2×C4⋊Dic17D412yes—
28C2×C4×Dic17—21no—
29C2×C4×Dic17—21no—
30C2×C4×Dic17—41no—
31C2×C4×Dic17—41no—
32C2×C4×Dic17D412yes—
33C22⋊#3624—24no—
34C4⋊#3624—42no—
35C4×#3624—42no—
36#10587502—22no—
37#10587502—22no—
38C24×C17C22×C411yescharacteristic
39C22×C4×C17—21no—
40C22×C4×C17—21no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17C22⋊C411yescharacteristic
44C22×C4×C17C22⋊C411yescharacteristic
45C22×C4×C17C2×C812yes—
46C22×C4×C17M1612yes—
47C22×Dic17—22no—
48C22×Dic17—44no—
49C22×Dic17—42no—
50C22×Dic17C22⋊C412yes—
51C22×Dic17C2×D412yes—
52C2×#3624—44no—
53C4⋊C4×C17—24no—
54C22⋊C4×C17—22no—
55C22⋊C4×C17C2×C814yes—
56C42×C17—24no—
57C22⋊Dic17—41no—
58C22⋊Dic17—41no—
59C4⋊Dic17—42no—
60C4⋊Dic17—44no—
61C4⋊Dic17—44no—
62C4×Dic17—22no—
63C4×Dic17—22no—
64C4×Dic17—42no—
65C4×Dic17—41no—
66C4×Dic17—41no—
67#11452—171nomaximal, Sylow
68C23×C17—21no—
69C23×C17—21no—
70C23×C17—42no—
71C23×C17C2×C22⋊C411yescharacteristic
72C23×C17C22×C811yescharacteristic
73C23×C17C2×M1611yescharacteristic
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—22no—
77C2×C4×C17—22no—
78C2×C4×C17—22no—
79C2×C4×C17—22no—
80C2×C4×C17—24no—
81C2×C4×C17—42no—
82C2×C4×C17—42no—
83C2×C4×C17C22⋊C812yes—
84C2×C4×C17C22⋊C812yes—
85C2×C4×C17#9911yescharacteristic
86C2×C4×C17#9911yescharacteristic
87C2×C4×C17#10112yes—
88C2×Dic17—24no—
89C2×Dic17—22no—
90C2×Dic17—22no—
91C2×Dic17—42no—
92C2×Dic17—44no—
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96C2×Dic17—44no—
97#3624—84no—
98#2296—171no—
99#1458—172no—
100#1326—174no—
101C22×C17—22no—
102C22×C17—21no—
103C22×C17—21no—
104C22×C17—41no—
105C22×C17—41no—
106C22×C17—42no—
107C22×C17—42no—
108C22×C17C2×C22⋊C811yescharacteristic
109C22×C17C2×#9911yescharacteristic
110C22×C17C2×#10111yescharacteristic
111C4×C17—22no—
112C4×C17—44no—
113C4×C17#32412yes—
114C4×C17#32412yes—
115Dic17—42no—
116Dic17—42no—
117Dic17—44no—
118C2×#117—171no—
119C2×#117#59511yescharacteristic
120C22×C42—171no—
121#431—342no—
122#389—342no—
123#385—172no—
124#385—172no—
125C4×C4⋊C4—342no—
126#324—342no—
127#323—174no—
128C2×C17—21no—
129C2×C17—21no—
130C2×C17—41no—
131C2×C17—41no—
132C2×C17C2×#32411yescharacteristic
133C2×C17#212012yes—
134C23×C4—172no—
135C23×C4C2×#59511yescharacteristic
136#117—22no—
137#117—681no—
138#117—681no—
139#117#362414yescomplemented
140C2×C4⋊C4—21no—
141C2×C4⋊C4—172no—
142C2×C4⋊C4—342no—
143C2×C4⋊C4—342no—
144C2×C22⋊C4—171no—
145C2×C22⋊C4—171no—
146C2×C22⋊C4C2×#59512yes—
147C2×C42—21no—
148C2×C42—172no—
149C2×C42—341no—
150C2×C42—341no—
151C2×C42—681no—
152C2×C42—681no—
153C4⋊C8—682no—
154C22⋊C8—344no—
155C4×C8—682no—
156#95—342no—
157#95—342no—
158C17#1145211yescharacteristic, complemented, Sylow
159C24C22×#59511yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—172no—
165C22×C4—172no—
166C22×C4—342no—
167C22×C4—684no—
168C22×C4—682no—
169C22×C4C2×#362412yes—
170C22×C4#6324712yes—
171C22×C4C22⋊#59511yescharacteristic
172C22×C4C22⋊#59511yescharacteristic
173C2×C8—684no—
174C4⋊C4—24no—
175C4⋊C4—682no—
176C4⋊C4—684no—
177C4⋊C4—684no—
178C22⋊C4—22no—
179C22⋊C4—681no—
180C22⋊C4—681no—
181C22⋊C4C2×#362414yes—
182C42—24no—
183C42—342no—
184C42—342no—
185C42—682no—
186C42—681no—
187C42—681no—
188C23—21no—
189C23—21no—
190C23—42no—
191C23C22×#362411yescharacteristic
192C23C2×#6324711yescharacteristic
193C23C2×C22⋊#59511yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—344no—
204C2×C4—342no—
205C2×C4—342no—
206C2×C4—682no—
207C2×C4—684no—
208C2×C4—682no—
209C2×C4—682no—
210C2×C4—682no—
211C2×C4—684no—
212C2×C4#1058753911yescharacteristic
213C2×C4#1058753911yescharacteristic
214C2×C4#1058754512yes—
215C2×C4C22⋊#362412yes—
216C2×C4C22⋊#362412yes—
217C8—1364no—
218C22—22no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22C2×C22⋊#362411yescharacteristic
226C22C2×#1058753911yescharacteristic
227C22C2×#1058754511yescharacteristic
228C4—22no—
229C4—44no—
230C4—682no—
231C4—684no—
232C4—682no—
233C4#1176365412yes—
234C4#1176365412yes—
235C2—21no—
236C2—21no—
237C2—41no—
238C2—41no—
239C2C2×#1176365411yescharacteristic
240C2#1454503712yes—
subgroupG/H
centerC2×C4#10587539
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC24×C17C22×C4
cosocleC2×C22⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11452
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
17. C17×#117C8semidirect
139. #117#3624semidirect
158. C17#11452semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437282
#145312682
#1145217