Finite Group Databasebeta

← #17949924

Subgroups — #17949924

Order 4352.

862 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 862 conjugacy classes of subgroups — too many to draw. Only its 128 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#14544640C212yesmaximal, complemented
2#14543600C214yesmaximal, complemented
3C2×#11762712C211yesmaximal, characteristic
4C2×#10587544—22no—
5C2×C22⋊#3624—22no—
6#11763675C2214yescomplemented
7C22×C4⋊Dic17C411yescharacteristic
8C22×C22⋊Dic17—22no—
9C22×C4×Dic17C2211yescharacteristic
10#11762712—22no—
11#11762712C412yes—
12#11762712C2212yes—
13C23×D4×C17C411yescharacteristic
14C25×C17—21no—
15C22×D4×C17—24no—
16C22×D4×C17—21no—
17C22×D4×C17—42no—
18C22×D4×C17—42no—
19C22×D4×C17C2×C412yes—
20C23×C4×C17C2×C411yescharacteristic
21C23×Dic17—21no—
22C23×Dic17D412yes—
23C22×#3624—24no—
24C2×C22⋊Dic17—24no—
25C2×C22⋊Dic17—24no—
26C2×C22⋊Dic17—44no—
27C2×C22⋊Dic17—44no—
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17—42no—
30C2×C4⋊Dic17C2×C412yes—
31C2×C4×Dic17—42no—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34C2×C4×Dic17C2311yescharacteristic
35C22⋊#3624—44no—
36#10587544—44no—
37C24×C17—24no—
38C24×C17—22no—
39C24×C17—42no—
40C24×C17—44no—
41C24×C17—42no—
42C24×C17—44no—
43C24×C17C22⋊C411yescharacteristic
44C2×D4×C17—24no—
45C2×D4×C17—22no—
46C2×D4×C17—42no—
47C2×D4×C17—42no—
48C2×D4×C17—416no—
49C2×D4×C17—42no—
50C2×D4×C17—42no—
51C2×D4×C17M1614yes—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17—22no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×Dic17—22no—
58C22×Dic17—42no—
59C22×Dic17—42no—
60C22×Dic17—42no—
61C22×Dic17—44no—
62C22×Dic17C22⋊C412yes—
63C22×Dic17D814yes—
64C22×Dic17SD1614yes—
65C22×Dic17C2×D412yes—
66C2×#3624—44no—
67C2×#3624—44no—
68C2×#3624—44no—
69C22⋊Dic17—48no—
70C22⋊Dic17—44no—
71C22⋊Dic17—44no—
72C4⋊Dic17—42no—
73C4⋊Dic17—42no—
74C4×Dic17—24no—
75C4×Dic17—41no—
76C4×Dic17—41no—
77#7640—171nomaximal, Sylow
78C23×C17—21no—
79C23×C17—21no—
80C23×C17—22no—
81C23×C17—24no—
82C23×C17—48no—
83C23×C17—416no—
84C23×C17—42no—
85C23×C17—42no—
86C23×C17—44no—
87C23×C17—44no—
88C23×C17—88no—
89C23×C17—84no—
90C23×C17—84no—
91C23×C17#10012yes—
92C23×C17#10214yes—
93C23×C17C2×C22⋊C411yescharacteristic
94D4×C17—44no—
95D4×C17—48no—
96D4×C17—44no—
97C2×C4×C17—28no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17#9912yes—
103C2×C4×C17C2×M1612yes—
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—44no—
109C2×Dic17—44no—
110C2×Dic17—42no—
111C2×Dic17—44no—
112C2×Dic17—84no—
113C2×Dic17#10214yes—
114C2×Dic17C2×D812yes—
115C2×Dic17C2×SD1612yes—
116#3624—84no—
117C2×#390—171no—
118#1797—172no—
119#1270—174no—
120C22×C17—22no—
121C22×C17—24no—
122C22×C17—24no—
123C22×C17—22no—
124C22×C17—44no—
125C22×C17—48no—
126C22×C17—816no—
127C22×C17—82no—
128C22×C17—84no—
129C22×C17—82no—
130C22×C17#33114yes—
131C22×C17#40711yescharacteristic
132C22×C17C2×#9911yescharacteristic
133C22×C17C2×#10011yescharacteristic
134C22×C17C2×#10212yes—
135C22×C17#42112yes—
136C4×C17—22no—
137C4×C17—22no—
138Dic17—22no—
139Dic17—24no—
140Dic17—22no—
141Dic17—82no—
142C23×D4#59511yescharacteristic
143C22×C4⋊C4—171no—
144C22×C22⋊C4—342no—
145C22×C42—171no—
146C2×C4⋊C8—342no—
147C2×C22⋊C8—342no—
148#390—172no—
149#390—172no—
150#390—342no—
151#336—174no—
152C2×C17—24no—
153C2×C17—84no—
154C2×C17#146211yescharacteristic
155C2×C17#148612yes—
156C2×C17#151912yes—
157C2×C17#153311yescharacteristic
158C2×C17C2×#33111yescharacteristic
159C25—21no—
160C22×D4—24no—
161C22×D4—21no—
162C22×D4—42no—
163C22×D4—42no—
164C22×D4C2×#59512yes—
165C23×C4—172no—
166C23×C4—341no—
167C23×C4C2×#59511yescharacteristic
168C22×C8—344no—
169C2×C4⋊C4—172no—
170C2×C4⋊C4—341no—
171C2×C4⋊C4—682no—
172C2×C22⋊C4—344no—
173C2×C22⋊C4—344no—
174C2×C22⋊C4—684no—
175C2×C22⋊C4—684no—
176C2×C42—172no—
177C2×C42—171no—
178C2×C42—171no—
179C2×C42—682no—
180C4⋊C8—684no—
181C22⋊C8—684no—
182C17#764011yescharacteristic, complemented, Sylow
183C24—24no—
184C24—22no—
185C24—42no—
186C24—44no—
187C24—44no—
188C24—42no—
189C24C22⋊#59511yescharacteristic
190C2×D4—24no—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—416no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4#6324714yes—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—172no—
202C22×C4—172no—
203C22×C4—174no—
204C22×C4—174no—
205C22×C4—342no—
206C22×C4—682no—
207C22×C4—682no—
208C22×C4—684no—
209C22×C4—682no—
210C22×C4C22⋊#59511yescharacteristic
211C22×C4C22×#59511yescharacteristic
212C2×C8—684no—
213C2×C8—684no—
214C2×C8—684no—
215C4⋊C4—682no—
216C4⋊C4—682no—
217C22⋊C4—684no—
218C22⋊C4—688no—
219C22⋊C4—684no—
220C42—344no—
221C42—681no—
222C42—681no—
223C23—21no—
224C23—21no—
225C23—22no—
226C23—24no—
227C23—48no—
228C23—416no—
229C23—42no—
230C23—42no—
231C23—44no—
232C23—44no—
233C23—88no—
234C23—84no—
235C23—84no—
236C23#1058754714yes—
237C23#1058755312yes—
238C23C2×C22⋊#59511yescharacteristic
239D4—44no—
240D4—44no—
241D4—48no—
242C2×C4—28no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—172no—
248C2×C4—174no—
249C2×C4—172no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—342no—
253C2×C4—342no—
254C2×C4—684no—
255C2×C4—684no—
256C2×C4—682no—
257C2×C4—684no—
258C2×C4—1364no—
259C2×C4#1058755112yes—
260C2×C4C2×#6324712yes—
261C8—1364no—
262C22—24no—
263C22—22no—
264C22—22no—
265C22—24no—
266C22—44no—
267C22—48no—
268C22—816no—
269C22—84no—
270C22—82no—
271C22—82no—
272C22#1176366714yes—
273C22#1176377911yescharacteristic
274C22C2×#1058755111yescharacteristic
275C22C2×#1058755311yescharacteristic
276C22C2×#1058754712yes—
277C22#1176380712yes—
278C4—22no—
279C4—22no—
280C4—342no—
281C4—344no—
282C4—342no—
283C4—1362no—
284C2—24no—
285C2—84no—
286C2#1454402911yescharacteristic
287C2#1454410912yes—
288C2#1454422012yes—
289C2#1454426311yescharacteristic
290C2C2×#1176366711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC23×D4×C17C4
socleC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC23×D4#595
hypocenterC17#7640
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #14544640C2semidirect
2. #14543600C2semidirect
6. #11763675C22semidirect
182. C17#7640semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145436002
C2×#117627122
#764017