Finite Group Databasebeta

← #17958320

Subgroups — #17958320

Order 4352.

440 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 98 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#14544027C212yesmaximal, complemented
2#14543726C212yesmaximal, complemented
3#14543712C212yesmaximal
4#14531497C211yesmaximal, characteristic
5#11763825—22no—
6#11763654—22no—
7#11763654C2214yes—
8C2×Q8×Dic17C2211yescharacteristic
9C2×D4×Dic17C411yescharacteristic
10#11762716C411yescharacteristic
11#11762712C2211yescharacteristic
12#11762702—22no—
13#11762684—22no—
14#11762679C2211yescharacteristic
15#11762655C411yescharacteristic
16C2×C17×#124C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×D4×C17C2×C411yescharacteristic
19C23×Dic17—21no—
20C17×#124—22no—
21C17×#124C814yescomplemented
22C2×C22⋊C4×C17—22no—
23C2×C42×C17C2×C411yescharacteristic
24C2×C22⋊Dic17—21no—
25C2×C22⋊Dic17—22no—
26Q8×Dic17—42no—
27D4×Dic17—42no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17C2×C411yescharacteristic
30C2×C4⋊Dic17D412yes—
31C2×C4⋊Dic17C2311yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17D412yes—
35C22⋊#3624—24no—
36C4⋊#3624—42no—
37C4×#3624—42no—
38#10587502—22no—
39#10587502—21no—
40#10587502—21no—
41C24×C17—21no—
42C2×Q8×C17—41no—
43C2×Q8×C17—41no—
44C2×Q8×C17C2×C812yes—
45C2×Q8×C17M1612yes—
46C2×D4×C17—21no—
47C2×D4×C17—41no—
48C2×D4×C17—41no—
49C2×D4×C17C2×C812yes—
50C22×C4×C17—21no—
51C22×C4×C17C22⋊C412yes—
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—21no—
54C22×Dic17—21no—
55C22×Dic17—42no—
56C22×Dic17—82no—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C2×D412yes—
60C2×#3624—44no—
61C22⋊C4×C17—28no—
62C42×C17—21no—
63C42×C17C2×C812yes—
64C22⋊Dic17—42no—
65C22⋊Dic17—82no—
66C4⋊Dic17—42no—
67C4⋊Dic17—41no—
68C4⋊Dic17—41no—
69C4⋊Dic17—82no—
70C4×Dic17—22no—
71C4×Dic17—22no—
72C4×Dic17—22no—
73C4×Dic17—41no—
74#11480—171nomaximal, Sylow
75C23×C17—22no—
76C23×C17—42no—
77C23×C17—42no—
78C23×C17—41no—
79C23×C17—41no—
80C23×C17C2×C22⋊C411yescharacteristic
81Q8×C17—42no—
82Q8×C17—42no—
83D4×C17—42no—
84D4×C17—42no—
85C2×C4×C17—22no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17C22⋊C814yes—
93C2×C4×C17C22×C811yescharacteristic
94C2×C4×C17C2×M1611yescharacteristic
95C2×Dic17—22no—
96C2×Dic17—21no—
97C2×Dic17—41no—
98C2×Dic17—42no—
99C2×Dic17—41no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—42no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17—84no—
106C2×Dic17#9912yes—
107#3624—84no—
108#2326—171no—
109#1461—172no—
110#1325—172no—
111#1318—172no—
112C22×C17—21no—
113C22×C17—21no—
114C22×C17—44no—
115C22×C17—42no—
116C22×C17—82no—
117C22×C17—81no—
118C22×C17—81no—
119C22×C17C2×C22⋊C811yescharacteristic
120C22×C17C2×#9911yescharacteristic
121C22×C17#41311yescharacteristic
122C4×C17—24no—
123C4×C17—21no—
124C4×C17—21no—
125C4×C17—42no—
126Dic17—22no—
127Dic17—42no—
128Dic17—41no—
129Dic17—81no—
130Dic17—81no—
131C2×#124#59511yescharacteristic
132C2×C4×Q8—171no—
133C2×C4×D4—171no—
134#431—342no—
135#391—171no—
136#390—171no—
137#388—342no—
138#385—342no—
139#384—171no—
140#376—171no—
141#324—174no—
142#324—342no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17—82no—
146C2×C17#145911yescharacteristic
147C2×C17#212811yescharacteristic
148C2×C17#213311yescharacteristic
149C22×Q8C2×#59511yescharacteristic
150C22×D4C2×#59511yescharacteristic
151C23×C4—341no—
152#124—22no—
153#124#362414yescomplemented
154C4×Q8—682no—
155C4×D4—682no—
156C2×C4⋊C4—172no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—171no—
159C2×C4⋊C4—342no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—341no—
162C2×C22⋊C4—342no—
163C2×C42—172no—
164C2×C42—171no—
165C2×C42—171no—
166C2×C42C2×#59511yescharacteristic
167C4⋊C8—682no—
168C22⋊C8—344no—
169C4×C8—682no—
170#95—341no—
171#95—341no—
172#95—342no—
173C17#1148011yescharacteristic, complemented, Sylow
174C24—21no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8C2×#362412yes—
178C2×Q8#6324712yes—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4C2×#362412yes—
183C22×C4—21no—
184C22×C4—171no—
185C22×C4—171no—
186C22×C4—172no—
187C22×C4—341no—
188C22×C4—341no—
189C22×C4—682no—
190C22×C4—1362no—
191C22×C4C22⋊#59512yes—
192C22×C4C22×#59511yescharacteristic
193C2×C8—684no—
194C4⋊C4—681no—
195C4⋊C4—682no—
196C4⋊C4—681no—
197C4⋊C4—1362no—
198C22⋊C4—28no—
199C22⋊C4—682no—
200C22⋊C4—1362no—
201C42—21no—
202C42—342no—
203C42—342no—
204C42—342no—
205C42—681no—
206C42C2×#362412yes—
207C23—22no—
208C23—42no—
209C23—42no—
210C23—41no—
211C23—41no—
212C23C2×C22⋊#59511yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—172no—
225C2×C4—342no—
226C2×C4—341no—
227C2×C4—681no—
228C2×C4—682no—
229C2×C4—681no—
230C2×C4—681no—
231C2×C4—682no—
232C2×C4—681no—
233C2×C4—681no—
234C2×C4—681no—
235C2×C4—1364no—
236C2×C4C22⋊#362414yes—
237C2×C4C22×#362411yescharacteristic
238C2×C4C2×#6324711yescharacteristic
239C8—1364no—
240C22—21no—
241C22—21no—
242C22—44no—
243C22—42no—
244C22—82no—
245C22—81no—
246C22—81no—
247C22C2×C22⋊#362411yescharacteristic
248C22D17⋊#9911yescharacteristic
249C22#1176379611yescharacteristic
250C4—21no—
251C4—21no—
252C4—24no—
253C4—42no—
254C4—342no—
255C4—682no—
256C4—681no—
257C4—1361no—
258C4—1361no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2#1454402011yescharacteristic
263C2#1454506411yescharacteristic
264C2#1454508011yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#124C4
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊Dic17C23
hypercenterC2×#124#595
hypocenterC17#11480
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #14544027C2semidirect
2. #14543726C2semidirect
21. C17×#124C8semidirect
153. #124#3624semidirect
173. C17#11480semidirect

Maximal subgroups

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

subgroupindex
#145440272
#145437262
#145437122
#145314972
#1148017