Finite Group Databasebeta

← #17961149

Subgroups — #17961149

Order 4352.

1018 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 108 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×#11763720C214yesmaximal, complemented
2#14544618C212yesmaximal
3C22×#10587555C211yesmaximal, characteristic
4C2×#10587545—22no—
5C2×#10587545C2214yes—
6#11763779—22no—
7#11763720—28no—
8C23×Dic34C411yescharacteristic
9C23×Dic34C2211yescharacteristic
10C2×#10587555—28no—
11C2×#10587555—22no—
12C2×#10587555C412yes—
13C2×#10587555C2212yes—
14C22×C4⋊Dic17—22no—
15C22×C42×C17C411yescharacteristic
16C23×C4×C17—21no—
17C23×C4×C17C2×C411yescharacteristic
18C23×Dic17—21no—
19C23×Dic17D412yes—
20C22×Dic34—21no—
21C22×Dic34—24no—
22C22×Dic34—24no—
23C22×Dic34—42no—
24C22×Dic34—42no—
25C22×Dic34—42no—
26C22×Dic34—42no—
27C22×Dic34C2×C411yescharacteristic
28C22×Dic34C2×C412yes—
29C22×Dic34D412yes—
30C22×Dic34C2311yescharacteristic
31C2×#63247—24no—
32C2×C42×C17—21no—
33C2×C42×C17—24no—
34C2×C42×C17C2×C412yes—
35C2×C4⋊Dic17—216no—
36C2×C4⋊Dic17—24no—
37C2×C4⋊Dic17—24no—
38#10587555—216no—
39#10587555—24no—
40#10587555—24no—
41#10587555—24no—
42#10587555D418yes—
43C22⋊#3624—44no—
44#10587545—28no—
45#10587545—44no—
46C24×C17C22⋊C411yescharacteristic
47C22×C4×C17—28no—
48C22×C4×C17—24no—
49C22×C4×C17—22no—
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17—22no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—24no—
56C22×Dic17—24no—
57C22×Dic17—22no—
58C22×Dic17—24no—
59C22×Dic17—42no—
60C22×Dic17—42no—
61C22×Dic17—42no—
62C22×Dic17C22⋊C412yes—
63C22×Dic17C2×D412yes—
64C2×Dic34—24no—
65C2×Dic34—24no—
66C2×Dic34—22no—
67C2×Dic34—22no—
68C2×Dic34—24no—
69C2×Dic34—41no—
70C2×Dic34—41no—
71C2×Dic34—42no—
72C2×Dic34—41no—
73C2×Dic34—41no—
74C2×Dic34—416no—
75C2×Dic34—42no—
76C2×Dic34—416no—
77C2×Dic34—42no—
78C2×Dic34—42no—
79C2×Dic34—42no—
80C2×Dic34C22⋊C414yes—
81C2×Dic34C2×D414yes—
82#63247—44no—
83#63247—44no—
84C2×#3624—44no—
85C42×C17—24no—
86C42×C17—22no—
87C42×C17C22⋊C414yes—
88C4⋊Dic17—216no—
89C4⋊Dic17—216no—
90#12700—171nomaximal, Sylow
91C23×C17—24no—
92C23×C17—21no—
93C23×C17—21no—
94C23×C17#9912yes—
95C23×C17C2×C22⋊C411yescharacteristic
96C2×C4×C17—28no—
97C2×C4×C17—216no—
98C2×C4×C17—28no—
99C2×C4×C17—21no—
100C2×C4×C17—24no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17#9912yes—
105C2×C4×C17C2×C22⋊C412yes—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—24no—
110C2×Dic17—22no—
111C2×Dic17—22no—
112C2×Dic17—48no—
113C2×Dic17—48no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116C2×Dic17#12014yes—
117Dic34—44no—
118Dic34—48no—
119Dic34—44no—
120Dic34—48no—
121Dic34—44no—
122Dic34—44no—
123#3624—84no—
124C22×C4⋊Q8—171no—
125C2×#356—174no—
126#1784—172no—
127C22×C17—24no—
128C22×C17—24no—
129C22×C17—22no—
130C22×C17—22no—
131C22×C17—22no—
132C22×C17#35614yescomplemented
133C22×C17#37911yescharacteristic
134C22×C17C2×#9911yescharacteristic
135C22×C17C2×#9911yescharacteristic
136C4×C17—28no—
137C4×C17—22no—
138C4×C17—22no—
139Dic17—24no—
140Dic17—42no—
141Dic17—44no—
142C23×Q8—171no—
143C23×Q8—171no—
144C2×C4⋊Q8—172no—
145C2×C4⋊Q8—172no—
146C2×C4⋊Q8—348no—
147C2×C4⋊Q8—342no—
148C22×C4⋊C4—342no—
149C22×C42#59511yescharacteristic
150C2×#101—174no—
151C2×#101—342no—
152#407—342no—
153#356—348no—
154C2×C17—21no—
155C2×C17—24no—
156C2×C17—21no—
157C2×C17#178111yescharacteristic
158C2×C17C2×#35612yes—
159C22×Q8—172no—
160C22×Q8—171no—
161C22×Q8—171no—
162C22×Q8—172no—
163C22×Q8—344no—
164C22×Q8—344no—
165C22×Q8—341no—
166C22×Q8—682no—
167C22×Q8—682no—
168C22×Q8—682no—
169C22×Q8—682no—
170C23×C4—21no—
171C23×C4—172no—
172C23×C4—341no—
173C23×C4C2×#59511yescharacteristic
174C2×M16—344no—
175C4⋊Q8—178no—
176C4⋊Q8—344no—
177C4⋊Q8—344no—
178C4⋊Q8—3416no—
179C4⋊Q8—344no—
180C2×C4⋊C4—344no—
181C2×C4⋊C4—344no—
182C2×C4⋊C4—3416no—
183C2×C42—21no—
184C2×C42—24no—
185C2×C42C2×#59512yes—
186#101—348no—
187#101—684no—
188C22⋊C8—684no—
189C17#1270011yescharacteristic, complemented, Sylow
190C24C22⋊#59511yescharacteristic
191C2×Q8—174no—
192C2×Q8—174no—
193C2×Q8—344no—
194C2×Q8—344no—
195C2×Q8—342no—
196C2×Q8—342no—
197C2×Q8—344no—
198C2×Q8—681no—
199C2×Q8—681no—
200C2×Q8—682no—
201C2×Q8—681no—
202C2×Q8—681no—
203C2×Q8—6816no—
204C2×Q8—6816no—
205C2×Q8—682no—
206C2×Q8—682no—
207C2×Q8—682no—
208C2×Q8—682no—
209C22×C4—24no—
210C22×C4—28no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—172no—
216C22×C4—172no—
217C22×C4—344no—
218C22×C4—344no—
219C22×C4—342no—
220C22×C4—344no—
221C22×C4—682no—
222C22×C4—682no—
223C22×C4—682no—
224C22×C4C22⋊#59511yescharacteristic
225C22×C4C22×#59511yescharacteristic
226M16—684no—
227M16—684no—
228C2×C8—684no—
229C4⋊C4—3416no—
230C4⋊C4—3416no—
231C42—24no—
232C42—22no—
233C42C22⋊#59514yes—
234C23—24no—
235C23—21no—
236C23—21no—
237C23#1058753912yes—
238C23C2×C22⋊#59511yescharacteristic
239Q8—684no—
240Q8—688no—
241Q8—684no—
242Q8—684no—
243Q8—684no—
244Q8—688no—
245C2×C4—28no—
246C2×C4—216no—
247C2×C4—28no—
248C2×C4—21no—
249C2×C4—24no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—174no—
254C2×C4—342no—
255C2×C4—342no—
256C2×C4—342no—
257C2×C4—344no—
258C2×C4—342no—
259C2×C4—342no—
260C2×C4—688no—
261C2×C4—688no—
262C2×C4—682no—
263C2×C4—682no—
264C2×C4#1058753912yes—
265C2×C4C2×C22⋊#59512yes—
266C8—1364no—
267C22—24no—
268C22—24no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22#1176372014yescomplemented
273C22#1176375011yescharacteristic
274C22C2×#1058753911yescharacteristic
275C22C2×#1058753911yescharacteristic
276C4—28no—
277C4—22no—
278C4—22no—
279C4—344no—
280C4—682no—
281C4—684no—
282C2—21no—
283C2—24no—
284C2—21no—
285C2#1454461211yescharacteristic
286C2C2×#1176372012yes—
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC22×Dic34C23
hypercenterC22×C42#595
hypocenterC17#12700
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#11763720C2semidirect
132. C22×C17#356semidirect
189. C17#12700semidirect
272. C22#11763720semidirect

Maximal subgroups

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

subgroupindex
C2×#117637202
#145446182
C22×#105875552
#1270017