Finite Group Databasebeta

← #17952461

Subgroups — #17952461

Order 4352.

1174 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 136 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#14544607C212yesmaximal
2C2×#11763655C214yesmaximal, complemented
3C22×#10587632C211yesmaximal, characteristic
4C2×#10587543—24no—
5C2×C22⋊#3624C2214yes—
6#11763655—28no—
7C23×C4×D17C2211yescharacteristic
8C2×#10587632—28no—
9C2×#10587632—24no—
10C22×C4⋊Dic17C411yescharacteristic
11C22×#63225C2212yes—
12C22×#63227C412yes—
13C23×Q8×C17C411yescharacteristic
14C24×D17C2×C411yescharacteristic
15C22×Q8×C17—24no—
16C22×Q8×C17—22no—
17C22×Q8×C17—44no—
18C23×C4×C17C2×C411yescharacteristic
19C23×C4×C17C2×C412yes—
20C23×Dic17C2×C412yes—
21C23×Dic17C2311yescharacteristic
22C22×C4×D17—24no—
23C22×C4×D17—44no—
24C22×C4×D17D414yes—
25C22×#3624—24no—
26#10587632—232no—
27C2×#63227—24no—
28C2×#63227—24no—
29C2×#63227—24no—
30C2×C4⋊Dic17—22no—
31C2×C4⋊Dic17—24no—
32C2×#63225—24no—
33C2×#63225—24no—
34C2×#63225D418yes—
35C22⋊#3624—28no—
36#10587543—48no—
37C24×C17C22×C411yescharacteristic
38C23×D17—22no—
39C23×D17—24no—
40C23×D17—24no—
41C23×D17—42no—
42C23×D17C22⋊C412yes—
43C2×Q8×C17—28no—
44C2×Q8×C17—416no—
45C2×Q8×C17—44no—
46C2×Q8×C17—44no—
47C22×C4×C17—22no—
48C22×C4×C17—24no—
49C22×C4×C17—22no—
50C22×C4×C17—22no—
51C22×C4×C17—44no—
52C22×C4×C17C22⋊C412yes—
53C22×C4×C17C22⋊C414yes—
54C22×Dic17—22no—
55C22×Dic17—22no—
56C22×Dic17—28no—
57C22×Dic17—42no—
58C22×Dic17C22⋊C414yes—
59C22×Dic17C2×D412yes—
60C22×Dic17C2×D414yes—
61C2×C4×D17—28no—
62C2×C4×D17—28no—
63C2×C4×D17—44no—
64C2×C4×D17—416no—
65C2×#3624—48no—
66C2×#3624—44no—
67#63227—216no—
68C4⋊Dic17—28no—
69#63225—216no—
70#8308—171nomaximal, Sylow
71C23×C17—22no—
72C23×C17—22no—
73C23×C17C2×C22⋊C412yes—
74C23×C17C2×C22⋊C411yescharacteristic
75C23×C17#13114yes—
76C22×D17—28no—
77C22×D17—22no—
78C22×D17—24no—
79C22×D17—24no—
80C22×D17—22no—
81C22×D17—416no—
82C22×D17—44no—
83C22×D17—44no—
84C22×D17#10114yes—
85Q8×C17—416no—
86C2×C4×C17—28no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—24no—
90C2×C4×C17—44no—
91C2×C4×C17—44no—
92C2×C4×C17—44no—
93C2×C4×C17#9914yes—
94C2×Dic17—24no—
95C2×Dic17—24no—
96C2×Dic17—28no—
97C2×Dic17—44no—
98C2×Dic17—44no—
99C2×Dic17—44no—
100C2×Dic17#12014yes—
101C4×D17—416no—
102#3624—84no—
103C22×C22⋊Q8—171no—
104#1779—172no—
105C2×#324—174no—
106C22×C17—28no—
107C22×C17—22no—
108C22×C17—22no—
109C22×C17#37911yescharacteristic
110C22×C17#40814yes—
111C22×C17#40812yes—
112C22×C17C2×#9912yes—
113C22×C17C2×#10112yes—
114C2×D17—28no—
115C2×D17—24no—
116C2×D17—416no—
117C2×D17—44no—
118C2×D17—42no—
119C2×D17—42no—
120C4×C17—24no—
121C4×C17—44no—
122Dic17—24no—
123Dic17—44no—
124C23×Q8#59511yescharacteristic
125C24×C4—171no—
126C2×C22⋊Q8—348no—
127C2×C22⋊Q8—344no—
128C22×C4⋊C4—172no—
129C22×C4⋊C4—171no—
130C22×C22⋊C4—172no—
131C2×C22⋊C8—174no—
132C2×C22⋊C8—344no—
133#324—348no—
134C2×C17—24no—
135C2×C17#147214yes—
136C2×C17#178011yescharacteristic
137C2×C17#178111yescharacteristic
138C2×C17#178411yescharacteristic
139D17—44no—
140C25—171no—
141C22×Q8—24no—
142C22×Q8—22no—
143C22×Q8—44no—
144C23×C4—171no—
145C23×C4—172no—
146C23×C4—174no—
147C23×C4—344no—
148C23×C4—684no—
149C23×C4C2×#59512yes—
150C23×C4C2×#59511yescharacteristic
151C22×C8—344no—
152C22⋊Q8—3432no—
153C2×C4⋊C4—178no—
154C2×C4⋊C4—344no—
155C2×C4⋊C4—344no—
156C2×C4⋊C4—344no—
157C2×C4⋊C4—342no—
158C2×C22⋊C4—344no—
159C2×C22⋊C4—344no—
160C2×C22⋊C4—344no—
161C22⋊C8—348no—
162C22⋊C8—688no—
163C17#830811yescharacteristic, complemented, Sylow
164C24—172no—
165C24—344no—
166C24—342no—
167C24—344no—
168C24—682no—
169C24C22×#59511yescharacteristic
170C2×Q8—28no—
171C2×Q8—416no—
172C2×Q8—44no—
173C2×Q8—44no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—44no—
179C22×C4—172no—
180C22×C4—174no—
181C22×C4—174no—
182C22×C4—348no—
183C22×C4—348no—
184C22×C4—342no—
185C22×C4—342no—
186C22×C4—348no—
187C22×C4—684no—
188C22×C4—6816no—
189C22×C4—682no—
190C22×C4C22⋊#59512yes—
191C22×C4C22⋊#59514yes—
192C2×C8—684no—
193C2×C8—688no—
194C4⋊C4—3416no—
195C4⋊C4—348no—
196C22⋊C4—3416no—
197C23—22no—
198C23—22no—
199C23—174no—
200C23—348no—
201C23—342no—
202C23—344no—
203C23—344no—
204C23—342no—
205C23—6816no—
206C23—684no—
207C23—684no—
208C23#1058768014yes—
209C23C2×C22⋊#59512yes—
210C23C2×C22⋊#59511yescharacteristic
211Q8—416no—
212C2×C4—28no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—44no—
219C2×C4—174no—
220C2×C4—344no—
221C2×C4—344no—
222C2×C4—348no—
223C2×C4—6816no—
224C2×C4—684no—
225C2×C4—684no—
226C2×C4—684no—
227C2×C4#1058755114yes—
228C8—1364no—
229C22—28no—
230C22—22no—
231C22—22no—
232C22—348no—
233C22—344no—
234C22—6816no—
235C22—684no—
236C22—682no—
237C22—682no—
238C22#1176375011yescharacteristic
239C22#1176378414yes—
240C22#1176378412yes—
241C22C2×#1058755112yes—
242C22D17⋊#10112yes—
243C4—24no—
244C4—44no—
245C4—344no—
246C4—684no—
247C2—24no—
248C2—684no—
249C2#1454406414yes—
250C2#1454460911yescharacteristic
251C2#1454461011yescharacteristic
252C2#1454461911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC23×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC23×Dic17C23
hypercenterC23×Q8#595
hypocenterC17#8308
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11763655C2semidirect
163. C17#8308semidirect

Maximal subgroups

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

subgroupindex
#145446072
C2×#117636552
C22×#105876322
#830817