Finite Group Databasebeta

← #17961163

Subgroups — #17961163

Order 4352.

962 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544620C212yesmaximal
3C2×#11763385C211yesmaximal, characteristic
4C2×#10587545C2214yes—
5C2×#10587553—22no—
6#11763781—22no—
7#11763720—28no—
8C22×#63252C2211yescharacteristic
9C23×Dic34C411yescharacteristic
10#11763385—28no—
11C2×#10587555C2212yes—
12C2×#10587561C412yes—
13C2×#10587572—22no—
14C2×#10587583—22no—
15C2×C17×#117C411yescharacteristic
16C23×C4×C17C2×C411yescharacteristic
17C22×C22⋊D17D412yes—
18C23×Dic17—21no—
19C2×#63252—24no—
20C2×#63252—42no—
21C2×#63252—42no—
22C22×D68C2×C411yescharacteristic
23C22×C4×D17D412yes—
24C22×Dic34—21no—
25C22×Dic34—24no—
26C22×Dic34—42no—
27C22×Dic34—42no—
28C22×Dic34C2×C412yes—
29C22×Dic34C2311yescharacteristic
30C2×#63247—24no—
31C17×#117—24no—
32C2×C4⋊C4×C17—21no—
33C2×C22⋊C4×C17—21no—
34C2×C42×C17C2×C412yes—
35C2×#63227—24no—
36C2×C4⋊Dic17—24no—
37#10587583—216no—
38#10587572—216no—
39#10587561—24no—
40#10587561—24no—
41#10587555—24no—
42#10587555D418yes—
43#10587553—44no—
44#10587545—28no—
45#10587543—44no—
46C24×C17C22⋊C411yescharacteristic
47C23×D17C22⋊C412yes—
48C22×C4×C17—22no—
49C22×C4×C17—22no—
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22×C411yescharacteristic
54C2×C22⋊D17—24no—
55C2×C22⋊D17—24no—
56C2×C22⋊D17—42no—
57C22×Dic17—24no—
58C22×Dic17—22no—
59C22×Dic17—42no—
60C22×Dic17—42no—
61C22×Dic17C2×D412yes—
62#63252—416no—
63C2×D68—22no—
64C2×D68—41no—
65C2×D68—41no—
66C2×C4×D17—24no—
67C2×C4×D17—24no—
68C2×C4×D17—42no—
69C2×Dic34—24no—
70C2×Dic34—22no—
71C2×Dic34—41no—
72C2×Dic34—41no—
73C2×Dic34—42no—
74C2×Dic34—416no—
75C2×Dic34—42no—
76C2×Dic34—42no—
77C2×Dic34—42no—
78C2×Dic34C22⋊C414yes—
79C2×Dic34C2×D414yes—
80#63247—44no—
81#63247—44no—
82C2×#3624—44no—
83C4⋊C4×C17—24no—
84C22⋊C4×C17—24no—
85C42×C17—22no—
86C42×C17C22⋊C414yes—
87#63227—216no—
88C4⋊Dic17—216no—
89#12704—171nomaximal, Sylow
90C23×C17—21no—
91C23×C17—21no—
92C23×C17—42no—
93C23×C17#9912yes—
94C23×C17C2×C22⋊C411yescharacteristic
95C22×D17—22no—
96C22×D17—22no—
97C22×D17—22no—
98C22×D17—44no—
99C2×C4×C17—28no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—24no—
105C2×C4×C17—44no—
106C2×C4×C17#9912yes—
107C2×C4×C17C2×C22⋊C412yes—
108C22⋊D17—48no—
109C2×Dic17—22no—
110C2×Dic17—22no—
111C2×Dic17—24no—
112C2×Dic17—48no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17#12014yes—
116D68—44no—
117C4×D17—48no—
118Dic34—44no—
119Dic34—44no—
120Dic34—48no—
121Dic34—44no—
122#3624—84no—
123C2×#536—171no—
124C2×#356—174no—
125#1785—172no—
126C22×C17—22no—
127C22×C17—22no—
128C22×C17—42no—
129C22×C17—42no—
130C22×C17—42no—
131C22×C17#37911yescharacteristic
132C22×C17C2×#9911yescharacteristic
133C22×C17C2×#9911yescharacteristic
134C2×D17—44no—
135C2×D17—44no—
136C2×D17—42no—
137C2×D17—82no—
138C4×C17—22no—
139C4×C17—22no—
140C4×C17—44no—
141Dic17—24no—
142Dic17—44no—
143C22×#41—171no—
144C23×Q8—171no—
145#536—348no—
146C2×C4⋊Q8—172no—
147C2×#124—172no—
148C2×#123—342no—
149C2×C22⋊Q8—342no—
150C2×#117#59511yescharacteristic
151C2×#101—174no—
152C2×#100—342no—
153#407—342no—
154#356—348no—
155C2×C17—21no—
156C2×C17—21no—
157C2×C17—42no—
158C2×C17#178111yescharacteristic
159C2×C17#213512yes—
160D17—82no—
161C2×#41—344no—
162C2×#41—682no—
163C2×#41—682no—
164C22×Q8—171no—
165C22×Q8—172no—
166C22×Q8—344no—
167C22×Q8—341no—
168C22×Q8—682no—
169C22×Q8—682no—
170C22×D4—172no—
171C22×D4—171no—
172C23×C4—172no—
173C23×C4—341no—
174C23×C4C2×#59511yescharacteristic
175C2×M16—344no—
176C4⋊Q8—178no—
177C4⋊Q8—344no—
178#124—344no—
179#124—344no—
180#123—3416no—
181C22⋊Q8—3416no—
182#117—24no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—344no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—344no—
187C2×C42C2×#59512yes—
188#101—348no—
189#100—684no—
190C22⋊C8—684no—
191C17#1270411yescharacteristic, complemented, Sylow
192C24—172no—
193C24C22⋊#59511yescharacteristic
194#41—6816no—
195C2×Q8—174no—
196C2×Q8—174no—
197C2×Q8—344no—
198C2×Q8—342no—
199C2×Q8—681no—
200C2×Q8—681no—
201C2×Q8—6816no—
202C2×Q8—682no—
203C2×Q8—682no—
204C2×Q8—682no—
205C2×Q8—682no—
206C2×D4—344no—
207C2×D4—344no—
208C2×D4—342no—
209C2×D4—681no—
210C2×D4—681no—
211C2×D4—682no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
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—24no—
230C4⋊C4—3416no—
231C22⋊C4—24no—
232C22⋊C4—3416no—
233C42—22no—
234C42C22⋊#59514yes—
235C23—21no—
236C23—21no—
237C23—42no—
238C23—342no—
239C23—342no—
240C23—342no—
241C23—684no—
242C23#1058753912yes—
243C23C2×C22⋊#59511yescharacteristic
244Q8—684no—
245Q8—684no—
246Q8—688no—
247Q8—684no—
248D4—684no—
249D4—688no—
250C2×C4—28no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—44no—
257C2×C4—174no—
258C2×C4—342no—
259C2×C4—342no—
260C2×C4—344no—
261C2×C4—688no—
262C2×C4—688no—
263C2×C4—682no—
264C2×C4—682no—
265C2×C4#1058753912yes—
266C2×C4C2×C22⋊#59512yes—
267C8—1364no—
268C22—22no—
269C22—22no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—684no—
274C22—684no—
275C22—682no—
276C22—1362no—
277C22#1176375011yescharacteristic
278C22C2×#1058753911yescharacteristic
279C22C2×#1058753911yescharacteristic
280C4—22no—
281C4—22no—
282C4—44no—
283C4—344no—
284C4—684no—
285C2—21no—
286C2—21no—
287C2—42no—
288C2—1362no—
289C2#1454461211yescharacteristic
290C2#1454508812yes—
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC22×#63252C22
cosocleC22×Dic34C23
hypercenterC2×#117#595
hypocenterC17#12704
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#11763720C2semidirect
191. C17#12704semidirect

Maximal subgroups

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

subgroupindex
C2×#117637202
#145446202
C2×#117633852
#1270417