Finite Group Databasebeta

← #16922639

Subgroups — #16922639

Order 4352.

468 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 119 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#14528927C212yesmaximal, complemented
2#14526610C212yesmaximal, complemented
3#14526605C212yesmaximal
4C4×C17×#124C211yesmaximal, characteristic
5#11762564—22no—
6#11762564—22no—
7#11762564C2214yes—
8C2×C17×#124C411yescharacteristic
9C2×C4×Q8×C17C411yescharacteristic
10C2×C4×D4×C17C411yescharacteristic
11C17×#391C2211yescharacteristic
12C17×#390C2211yescharacteristic
13C17×#388—22no—
14C17×#382C411yescharacteristic
15C4×C22⋊C4×C17—22no—
16C43×C17C2211yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×D4×C17C2×C411yescharacteristic
19C23×C4×C17—21no—
20C17×#124—22no—
21C17×#124—22no—
22C4×Q8×C17—42no—
23C4×D4×C17—42no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17C2×C411yescharacteristic
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C22⋊C4×C17—22no—
28C2×C22⋊C4×C17—21no—
29C2×C22⋊C4×C17—22no—
30C2×C42×C17—21no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17C2×C411yescharacteristic
33C2×C42×C17D412yes—
34C2×C42×C17D412yes—
35C2×C42×C17C2311yescharacteristic
36C22×#3622—24no—
37C17×#95—22no—
38C17×#95—22no—
39C24×C17—21no—
40C2×Q8×C17—21no—
41C2×Q8×C17—41no—
42C2×Q8×C17—41no—
43C2×Q8×C17M1612yes—
44C2×D4×C17—21no—
45C2×D4×C17—41no—
46C2×D4×C17—41no—
47C2×D4×C17M1612yes—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17—21no—
51C22×C4×C17—44no—
52C22×C4×C17—42no—
53C22×C4×C17C22⋊C412yes—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×C4×C17C2×D412yes—
58C4⋊C4×C17—41no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—42no—
61C22⋊C4×C17—28no—
62C22⋊C4×C17—42no—
63C22⋊C4×C17—44no—
64C42×C17—22no—
65C42×C17—21no—
66C42×C17—21no—
67C42×C17—24no—
68C42×C17—42no—
69C42×C17—41no—
70C42×C17—42no—
71C2×#3622—44no—
72C2×#3622—44no—
73C2×#3622—44no—
74#7649—171nomaximal, Sylow
75C23×C17—22no—
76C23×C17—41no—
77C23×C17—41no—
78C23×C17—42no—
79C23×C17—42no—
80C23×C17C2×C22⋊C411yescharacteristic
81Q8×C17—42no—
82Q8×C17—42no—
83D4×C17—42no—
84D4×C17—42no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—22no—
91C2×C4×C17—22no—
92C2×C4×C17—21no—
93C2×C4×C17—22no—
94C2×C4×C17—22no—
95C2×C4×C17—22no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—84no—
103C2×C4×C17#10012yes—
104C2×C4×C17C2×M1611yescharacteristic
105C2×C4×C17C2×M1611yescharacteristic
106C2×C4×C17#13514yes—
107#3622—84no—
108C4×#124D1711yescharacteristic
109#1839—172no—
110#1272—172no—
111#1270—172no—
112C22×C17—42no—
113C22×C17—44no—
114C22×C17—81no—
115C22×C17—82no—
116C22×C17—81no—
117C22×C17#40711yescharacteristic
118C22×C17#41011yescharacteristic
119C22×C17C2×#10011yescharacteristic
120C22×C17#41612yes—
121C22×C17#42112yes—
122C4×C17—21no—
123C4×C17—21no—
124C4×C17—24no—
125C4×C17—22no—
126C4×C17—41no—
127C4×C17—42no—
128C4×C17—42no—
129C4×C17—81no—
130C4×C17—81no—
131C2×#124Dic1711yescharacteristic
132C2×C4×Q8Dic1711yescharacteristic
133C2×C4×D4Dic1711yescharacteristic
134#391C2×D1711yescharacteristic
135#390C2×D1711yescharacteristic
136#388—22no—
137#382Dic1711yescharacteristic
138C4×C22⋊C4—22no—
139C43C2×D1711yescharacteristic
140#336—174no—
141#336—342no—
142#336—342no—
143C2×C17—82no—
144C2×C17#146611yescharacteristic
145C2×C17#148812yes—
146C2×C17#152112yes—
147C2×C17#153311yescharacteristic
148C2×C17#154311yescharacteristic
149C22×Q8C2×Dic1711yescharacteristic
150C22×D4C2×Dic1711yescharacteristic
151C23×C4—21no—
152C22×C8—344no—
153#124—22no—
154#124—22no—
155C4×Q8—42no—
156C4×D4—42no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4C2×Dic1711yescharacteristic
159C2×C4⋊C4C2×Dic1711yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—21no—
162C2×C22⋊C4—22no—
163C2×C42—21no—
164C2×C42C2×Dic1711yescharacteristic
165C2×C42C2×Dic1711yescharacteristic
166C2×C42C22⋊D1712yes—
167C2×C42C22⋊D1712yes—
168C2×C42C22×D1711yescharacteristic
169#95—22no—
170#95—22no—
171C17#764911yescharacteristic, complemented, Sylow
172C24—21no—
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8#6322312yes—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4#6322312yes—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—44no—
185C22×C4—42no—
186C22×C4C22⋊Dic1712yes—
187C22×C4C22⋊Dic1711yescharacteristic
188C22×C4C22⋊Dic1711yescharacteristic
189C22×C4C22×Dic1711yescharacteristic
190C22×C4C2×C22⋊D1712yes—
191C2×C8—684no—
192C2×C8—684no—
193C2×C8—684no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C22⋊C4—28no—
198C22⋊C4—42no—
199C22⋊C4—44no—
200C42—22no—
201C42—21no—
202C42—21no—
203C42—24no—
204C42—42no—
205C42—41no—
206C42—42no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—42no—
211C23—42no—
212C23C2×C22⋊Dic1711yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—42no—
216D4—42no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4#1058750412yes—
236C2×C4C2×#6322311yescharacteristic
237C2×C4C2×#6322311yescharacteristic
238C2×C4#1058763614yes—
239C8—1364no—
240C22—42no—
241C22—44no—
242C22—82no—
243C22—81no—
244C22—81no—
245C22#1176277311yescharacteristic
246C22#1176278311yescharacteristic
247C22C2×#1058750411yescharacteristic
248C22#1176280512yes—
249C22#1176282612yes—
250C4—24no—
251C4—21no—
252C4—21no—
253C4—22no—
254C4—42no—
255C4—41no—
256C4—42no—
257C4—81no—
258C4—81no—
259C2—82no—
260C2#1452712511yescharacteristic
261C2#1452721812yes—
262C2#1452736112yes—
263C2#1452740811yescharacteristic
264C2#1452744611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC4×C17×#124C2
socleC23×C17C2×C22⋊C4
prime radicalC22×D4×C17C2×C4
cosocleC2×C42×C17C23
hypercenterC4×#124D17
hypocenterC17#7649
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #14528927C2semidirect
2. #14526610C2semidirect
171. C17#7649semidirect

Maximal subgroups

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

subgroupindex
#145289272
#145266102
#145266052
C4×C17×#1242
#764917