Finite Group Databasebeta

← #17953530

Subgroups — #17953530

Order 4352.

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

normal subgroups only

This group has 786 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#14544606C212yesmaximal
2#14543622C214yesmaximal, complemented
3C2×#11762670C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5C2×C22⋊#3624—22no—
6C2×C22⋊#3624C2214yes—
7C24×Dic17C2211yescharacteristic
8C22×C22⋊Dic17C411yescharacteristic
9#11762670—22no—
10#11762670—22no—
11C2×#10587502C412yes—
12C2×#10587502C2212yes—
13C22×C22⋊C4×C17C411yescharacteristic
14C25×C17C2×C411yescharacteristic
15C23×C4×C17C2×C412yes—
16C23×Dic17—24no—
17C23×Dic17—42no—
18C23×Dic17—42no—
19C23×Dic17C2×C412yes—
20C23×Dic17C2×C411yescharacteristic
21C23×Dic17D412yes—
22C23×Dic17D412yes—
23C23×Dic17C2311yescharacteristic
24C22×#3624—24no—
25C2×C22⋊C4×C17—21no—
26C2×C22⋊C4×C17—21no—
27C2×C22⋊C4×C17—42no—
28C2×C22⋊Dic17—21no—
29C2×C22⋊Dic17—21no—
30C2×C22⋊Dic17—42no—
31C22⋊#3624—28no—
32C22⋊#3624—44no—
33C22⋊#3624—44no—
34#10587502—24no—
35#10587502—24no—
36C24×C17—22no—
37C24×C17—22no—
38C24×C17—22no—
39C24×C17—24no—
40C24×C17—42no—
41C24×C17C22⋊C411yescharacteristic
42C24×C17C22⋊C411yescharacteristic
43C24×C17C22×C411yescharacteristic
44C22×C4×C17—22no—
45C22×C4×C17—24no—
46C22×C4×C17—42no—
47C22×C4×C17—42no—
48C22×Dic17—24no—
49C22×Dic17—24no—
50C22×Dic17—22no—
51C22×Dic17—24no—
52C22×Dic17—24no—
53C22×Dic17—22no—
54C22×Dic17—24no—
55C22×Dic17—41no—
56C22×Dic17—41no—
57C22×Dic17—42no—
58C22×Dic17—42no—
59C22×Dic17—41no—
60C22×Dic17—41no—
61C22×Dic17—416no—
62C22×Dic17—42no—
63C22×Dic17—42no—
64C22×Dic17C22⋊C412yes—
65C22×Dic17C2×D412yes—
66C22×Dic17#4114yes—
67C2×#3624—44no—
68C2×#3624—44no—
69C2×#3624—44no—
70C22⋊C4×C17—42no—
71C22⋊C4×C17—42no—
72C22⋊Dic17—42no—
73C22⋊Dic17—42no—
74#8702—171nomaximal, Sylow
75C23×C17—21no—
76C23×C17—21no—
77C23×C17—22no—
78C23×C17—28no—
79C23×C17—21no—
80C23×C17—21no—
81C23×C17—22no—
82C23×C17—22no—
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—22no—
86C23×C17—22no—
87C23×C17—48no—
88C23×C17—48no—
89C23×C17—44no—
90C23×C17—44no—
91C23×C17#9912yes—
92C23×C17#9912yes—
93C23×C17C2×C22⋊C411yescharacteristic
94C23×C17#11712yes—
95C23×C17#13114yes—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17—84no—
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—22no—
105C2×Dic17—44no—
106C2×Dic17—48no—
107C2×Dic17—48no—
108C2×Dic17—44no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112C2×Dic17—84no—
113C2×Dic17#12314yes—
114#3624—84no—
115C2×#381—171no—
116#1779—172no—
117#1280—174no—
118C22×C17—22no—
119C22×C17—22no—
120C22×C17—24no—
121C22×C17—24no—
122C22×C17—22no—
123C22×C17—22no—
124C22×C17—24no—
125C22×C17—24no—
126C22×C17—416no—
127C22×C17—41no—
128C22×C17—41no—
129C22×C17—41no—
130C22×C17—41no—
131C22×C17—42no—
132C22×C17—42no—
133C22×C17#38111yescharacteristic
134C22×C17#40812yes—
135C22×C17C2×#9911yescharacteristic
136C22×C17C2×#9911yescharacteristic
137C22×C17#41312yes—
138C22×C17#43314yes—
139C4×C17—82no—
140Dic17—24no—
141Dic17—42no—
142Dic17—82no—
143C24×C4—171no—
144C22×C22⋊C4—171no—
145C22×C22⋊C4#59511yescharacteristic
146C2×C22⋊C8—174no—
147C2×C22⋊C8—342no—
148C2×C22⋊C8—342no—
149#381—342no—
150#381—342no—
151C2×#95—172no—
152C2×#95—172no—
153C2×C17—24no—
154C2×C17—42no—
155C2×C17—42no—
156C2×C17#146812yes—
157C2×C17#146812yes—
158C2×C17#181811yescharacteristic
159C2×C17#181911yescharacteristic
160C2×C17#182211yescharacteristic
161C25C2×#59511yescharacteristic
162C23×C4—171no—
163C23×C4—172no—
164C23×C4—172no—
165C23×C4—171no—
166C23×C4—172no—
167C23×C4—344no—
168C23×C4—682no—
169C23×C4—682no—
170C23×C4C2×#59512yes—
171C22×C8—344no—
172C2×C22⋊C4—21no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—42no—
175C2×C22⋊C4—341no—
176C2×C22⋊C4—341no—
177C2×C22⋊C4—682no—
178C22⋊C8—348no—
179C22⋊C8—684no—
180C22⋊C8—684no—
181#95—344no—
182#95—344no—
183C17#870211yescharacteristic, complemented, Sylow
184C24—22no—
185C24—22no—
186C24—22no—
187C24—24no—
188C24—42no—
189C24C22⋊#59511yescharacteristic
190C24C22⋊#59511yescharacteristic
191C24C22×#59511yescharacteristic
192C22×C4—22no—
193C22×C4—24no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—172no—
197C22×C4—174no—
198C22×C4—172no—
199C22×C4—344no—
200C22×C4—344no—
201C22×C4—342no—
202C22×C4—344no—
203C22×C4—344no—
204C22×C4—342no—
205C22×C4—344no—
206C22×C4—681no—
207C22×C4—682no—
208C22×C4—681no—
209C22×C4—682no—
210C22×C4—681no—
211C22×C4—681no—
212C22×C4—6816no—
213C22×C4—682no—
214C22×C4—682no—
215C2×C8—684no—
216C2×C8—684no—
217C2×C8—684no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—682no—
221C22⋊C4—682no—
222C23—21no—
223C23—21no—
224C23—22no—
225C23—28no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—22no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—48no—
235C23—48no—
236C23—44no—
237C23—44no—
238C23#1058753912yes—
239C23#1058755112yes—
240C23#1058767712yes—
241C23#1058767814yes—
242C23C2×C22⋊#59511yescharacteristic
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—174no—
248C2×C4—342no—
249C2×C4—342no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—342no—
253C2×C4—684no—
254C2×C4—688no—
255C2×C4—688no—
256C2×C4—684no—
257C2×C4—682no—
258C2×C4—682no—
259C2×C4—682no—
260C2×C4—1364no—
261C8—1364no—
262C22—22no—
263C22—22no—
264C22—24no—
265C22—24no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—416no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—42no—
276C22—42no—
277C22#1176375211yescharacteristic
278C22#1176378212yes—
279C22C2×#1058755111yescharacteristic
280C22C2×#1058753911yescharacteristic
281C22#1176379612yes—
282C22#1176383314yes—
283C4—82no—
284C4—344no—
285C4—682no—
286C4—1362no—
287C2—24no—
288C2—42no—
289C2—42no—
290C2#1454404912yes—
291C2#1454405112yes—
292C2#1454467711yescharacteristic
293C2#1454467911yescharacteristic
294C2#1454468611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17#8702
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14543622C2semidirect
183. C17#8702semidirect

Maximal subgroups

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

subgroupindex
#145446062
#145436222
C2×#117626702
#870217