Finite Group Databasebeta

← #17958201

Subgroups — #17958201

Order 4352.

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

normal subgroups only

This group has 454 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
1C2×#11763654C212yesmaximal
2#14543726C212yesmaximal, complemented
3#14543724C212yesmaximal, complemented
4#14531407C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6#11763654—22no—
7#11763654C2214yes—
8C2×#10587612C411yescharacteristic
9C22×C4⋊Dic17C2211yescharacteristic
10#11762708—22no—
11#11762684—22no—
12#11762679C411yescharacteristic
13#11762679C2211yescharacteristic
14#11762675C411yescharacteristic
15#11762675C2211yescharacteristic
16C2×C17×#117C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C23×Dic17D412yes—
19C22×#3624—42no—
20C17×#117—22no—
21C17×#117C814yescomplemented
22C2×C4⋊C4×C17—21no—
23C2×C22⋊C4×C17—21no—
24C2×C42×C17C2×C411yescharacteristic
25C2×C42×C17C2×C411yescharacteristic
26C2×C22⋊Dic17—21no—
27#10587612—42no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17—22no—
30C2×C4⋊Dic17—42no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4⋊Dic17D412yes—
35C2×C4⋊Dic17C2311yescharacteristic
36C2×C4×Dic17—21no—
37C22⋊#3624—24no—
38C22⋊#3624—42no—
39#10587502—22no—
40#10587502—22no—
41C24×C17C22⋊C411yescharacteristic
42C22×C4×C17—22no—
43C22×C4×C17—22no—
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C2×C812yes—
48C22×C4×C17M1612yes—
49C22×C4×C17C22×C411yescharacteristic
50C22×Dic17—22no—
51C22×Dic17—22no—
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17—82no—
55C22×Dic17C22⋊C412yes—
56C22×Dic17C2×D412yes—
57C2×#3624—44no—
58C2×#3624—84no—
59C4⋊C4×C17—24no—
60C22⋊C4×C17—24no—
61C42×C17—21no—
62C42×C17—21no—
63C42×C17C2×C812yescomplemented
64C42×C17C2×C812yescomplemented
65C22⋊Dic17—42no—
66C4⋊Dic17—41no—
67C4⋊Dic17—42no—
68C4⋊Dic17—41no—
69C4⋊Dic17—41no—
70C4⋊Dic17—41no—
71C4⋊Dic17—82no—
72C4⋊Dic17—82no—
73C4×Dic17—42no—
74#11448—171nomaximal, Sylow
75C23×C17—41no—
76C23×C17—41no—
77C23×C17C22⋊C812yes—
78C23×C17#9912yes—
79C23×C17#10112yes—
80C23×C17C2×C22⋊C411yescharacteristic
81C2×C4×C17—24no—
82C2×C4×C17—24no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17C22⋊C812yes—
94C2×C4×C17C22×C811yescharacteristic
95C2×C4×C17C2×M1611yescharacteristic
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—44no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17—82no—
106#3624—84no—
107#2317—171no—
108C2×#324—172no—
109#1325—172no—
110#1324—172no—
111C22×C17—21no—
112C22×C17—22no—
113C22×C17—21no—
114C22×C17—22no—
115C22×C17—42no—
116C22×C17—42no—
117C22×C17#32414yes—
118C22×C17C2×C22⋊C811yescharacteristic
119C22×C17C2×#9911yescharacteristic
120C22×C17C2×#10111yescharacteristic
121C4×C17—22no—
122C4×C17—21no—
123C4×C17—21no—
124C4×C17—42no—
125C4×C17—42no—
126Dic17—42no—
127Dic17—42no—
128Dic17—81no—
129Dic17—81no—
130C2×#117—171no—
131C2×#117#59511yescharacteristic
132C22×C4⋊C4—171no—
133C2×C22⋊C8—342no—
134#389—342no—
135#385—342no—
136#384—171no—
137#384—171no—
138#382—171no—
139#382—171no—
140#324—174no—
141#324—342no—
142C2×C17—21no—
143C2×C17—24no—
144C2×C17—21no—
145C2×C17C2×#32411yescharacteristic
146C2×C17#212711yescharacteristic
147C2×C17#213311yescharacteristic
148C23×C4—172no—
149C23×C4C2×#59511yescharacteristic
150C22×C8—682no—
151#117—22no—
152#117—682no—
153#117#362414yescomplemented
154C2×C4⋊C4—21no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4—171no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—171no—
159C2×C4⋊C4—171no—
160C2×C4⋊C4—342no—
161C2×C4⋊C4—342no—
162C2×C4⋊C4—682no—
163C2×C22⋊C4—21no—
164C2×C22⋊C4—341no—
165C2×C42—341no—
166C2×C42C2×#59511yescharacteristic
167C2×C42C2×#59511yescharacteristic
168C22⋊C8—344no—
169C22⋊C8—682no—
170#95—342no—
171#95—342no—
172C17#1144811yescharacteristic, complemented, Sylow
173C24C22⋊#59511yescharacteristic
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—172no—
179C22×C4—172no—
180C22×C4—342no—
181C22×C4—342no—
182C22×C4—341no—
183C22×C4—341no—
184C22×C4—1362no—
185C22×C4C2×#362412yes—
186C22×C4#6324712yes—
187C22×C4C22⋊#59511yescharacteristic
188C22×C4C22×#59511yescharacteristic
189C2×C8—684no—
190C2×C8—1364no—
191C4⋊C4—24no—
192C4⋊C4—682no—
193C4⋊C4—681no—
194C4⋊C4—681no—
195C4⋊C4—681no—
196C4⋊C4—681no—
197C4⋊C4—1362no—
198C4⋊C4—1362no—
199C22⋊C4—24no—
200C22⋊C4—682no—
201C42—21no—
202C42—21no—
203C42—682no—
204C42C2×#362412yescomplemented
205C42C2×#362412yescomplemented
206C23—41no—
207C23—41no—
208C23#1058753912yes—
209C23#1058754512yes—
210C23C22⋊#362412yes—
211C23C2×C22⋊#59511yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—342no—
225C2×C4—342no—
226C2×C4—684no—
227C2×C4—682no—
228C2×C4—682no—
229C2×C4—682no—
230C2×C4—682no—
231C2×C4—681no—
232C2×C4—681no—
233C2×C4—1362no—
234C2×C4C22⋊#362412yes—
235C2×C4C22×#362411yescharacteristic
236C2×C4C2×#6324711yescharacteristic
237C8—1364no—
238C22—21no—
239C22—22no—
240C22—21no—
241C22—22no—
242C22—42no—
243C22—42no—
244C22#1176365414yes—
245C22C2×C22⋊#362411yescharacteristic
246C22C2×#1058753911yescharacteristic
247C22C2×#1058754511yescharacteristic
248C4—21no—
249C4—21no—
250C4—22no—
251C4—42no—
252C4—42no—
253C4—682no—
254C4—682no—
255C4—1361no—
256C4—1361no—
257C2—21no—
258C2—21no—
259C2—24no—
260C2C2×#1176365411yescharacteristic
261C2#1454506111yescharacteristic
262C2#1454508111yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11448
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14543726C2semidirect
3. #14543724C2semidirect
21. C17×#117C8semidirect
63. C42×C17C2×C8semidirect
64. C42×C17C2×C8semidirect
153. #117#3624semidirect
172. C17#11448semidirect
204. C42C2×#3624semidirect
205. C42C2×#3624semidirect

Maximal subgroups

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

subgroupindex
C2×#117636542
#145437262
#145437242
#145314072
#1144817