Finite Group Databasebeta

← #16932136

Subgroups — #16932136

Order 4352.

610 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 107 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#14533071C211yesmaximal, characteristic
2#14531141C211yesmaximal, characteristic
3#14528881C212yesmaximal
4#14526638C212yesmaximal
5C17×#1463C211yesmaximal, characteristic
6C2×#10587612—21no—
7C2×#10587612C2211yescharacteristic
8#11762748C412yescomplemented
9#11762739C412yescomplemented
10#11762690—22no—
11#11762682—21no—
12#11762672—21no—
13#11762672C2211yescharacteristic
14C4⋊C4×Dic17—24no—
15C4×C22⋊Dic17—21no—
16C4×C22⋊Dic17C2212yes—
17#11762570—24no—
18C22×C4⋊C4×C17C2211yescharacteristic
19C17×#407C2212yes—
20C17×#324—22no—
21C23×C4×C17D411yescharacteristic
22C23×C4×C17D411yescharacteristic
23C23×C4×C17C2311yescharacteristic
24C2×M16×C17—22no—
25C2×C4⋊C4×C17—22no—
26C2×C4⋊C4×C17—22no—
27C2×C4⋊C4×C17C2×C412yes—
28C2×C4⋊C4×C17D412yes—
29C2×C22⋊Dic17—22no—
30C2×C22⋊Dic17—21no—
31C2×C22⋊Dic17—21no—
32#10587612—28no—
33#10587612—22no—
34#10587612—22no—
35C2×C4⋊Dic17—22no—
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×C4⋊Dic17C2×C411yescharacteristic
38C2×#63225—22no—
39C2×C4×Dic17—22no—
40C2×C4×Dic17—22no—
41C2×C4×Dic17—21no—
42C2×C4×Dic17D414yes—
43C17×C22⋊C8—22no—
44C17×C22⋊C8—22no—
45#10587502—22no—
46#10587502—22no—
47#10587502—22no—
48#10587502—22no—
49#10587502—21no—
50#10587502—22no—
51#10587502C2×C412yes—
52C24×C17C2×D411yescharacteristic
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—24no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—42no—
59C22×C4×C17—42no—
60C22×C4×C17C22⋊C412yes—
61C22×C4×C17C22⋊C412yes—
62C22×C4×C17C22×C411yescharacteristic
63C22×C4×C17C2×D412yes—
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17#4112yes—
66C22×Dic17—24no—
67C22×Dic17—22no—
68C22×Dic17—21no—
69C22×Dic17—21no—
70M16×C17—44no—
71C2×C8×C17—42no—
72C4⋊C4×C17—24no—
73C4⋊C4×C17—24no—
74C22⋊Dic17—28no—
75C22⋊Dic17—42no—
76C22⋊Dic17—41no—
77C22⋊Dic17—41no—
78C4⋊Dic17—28no—
79C4⋊Dic17—22no—
80C4⋊Dic17—22no—
81#63225—44no—
82C4×Dic17—28no—
83C4×Dic17—42no—
84C4×Dic17—44no—
85C4×Dic17—82no—
86#9478—171nomaximal, Sylow
87C23×C17—22no—
88C23×C17—22no—
89C23×C17—41no—
90C23×C17C2×C22⋊C411yescharacteristic
91C23×C17#12011yescharacteristic
92C23×C17#12311yescharacteristic
93C2×C4×C17—24no—
94C2×C4×C17—22no—
95C2×C4×C17—22no—
96C2×C4×C17—22no—
97C2×C4×C17—22no—
98C2×C4×C17—24no—
99C2×C4×C17—22no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17—81no—
106C2×C4×C17#10414yes—
107C2×C4×C17C4×D412yes—
108C2×C4×C17#12112yes—
109C2×Dic17—28no—
110C2×Dic17—44no—
111C2×Dic17—44no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C8×C17—82no—
120#2484—171no—
121#2274—171no—
122#1826—172no—
123#1463D1711yescharacteristic
124#1284—172no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—44no—
133C22×C17#38611yescharacteristic
134C22×C17C2×#10412yes—
135C22×C17#45812yes—
136C4×C17—22no—
137C4×C17—22no—
138C4×C17—24no—
139C4×C17—42no—
140Dic17—48no—
141Dic17—82no—
142Dic17—81no—
143Dic17—81no—
144C2×#117—171no—
145C2×#117—341no—
146C22×C4⋊C4C2×D1711yescharacteristic
147#407C2×D1712yes—
148#400—172no—
149#398—172no—
150#387—342no—
151#385—341no—
152#381—171no—
153#381—341no—
154C4×C4⋊C4—344no—
155C4×C22⋊C4—172no—
156C4×C22⋊C4—341no—
157#339—344no—
158#324—22no—
159C2×C17—22no—
160C2×C17—22no—
161C2×C17—41no—
162C2×C17#189011yescharacteristic
163C2×C17#189611yescharacteristic
164C2×C17#191211yescharacteristic
165C23×C4D6811yescharacteristic
166C23×C4D6811yescharacteristic
167C23×C4C22×D1711yescharacteristic
168C2×M16—22no—
169#117—348no—
170#117—342no—
171#117—342no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—171no—
175C2×C4⋊C4—171no—
176C2×C4⋊C4—342no—
177C2×C4⋊C4—342no—
178C2×C4⋊C4C4×D1712yes—
179C2×C4⋊C4C22⋊D1712yes—
180C2×C22⋊C4—342no—
181C2×C22⋊C4—341no—
182C2×C22⋊C4—341no—
183C2×C42—174no—
184C2×C42—342no—
185C2×C42—341no—
186C2×C42—342no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189#95—172no—
190#95—342no—
191#95—342no—
192#95—341no—
193#95—342no—
194#95—342no—
195#95—342no—
196C17#947811yescharacteristic, complemented, Sylow
197C24C2×D6811yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—344no—
206C22×C4—342no—
207C22×C4—341no—
208C22×C4—341no—
209C22×C4#6322712yes—
210C22×C4#6322712yes—
211C22×C4C2×C4×D1711yescharacteristic
212C22×C4D4×D1712yes—
213C22×C4#6325412yes—
214C22×C4C2×C22⋊D1711yescharacteristic
215M16—44no—
216C2×C8—42no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—348no—
220C4⋊C4—342no—
221C4⋊C4—342no—
222C4⋊C4—684no—
223C22⋊C4—348no—
224C22⋊C4—682no—
225C22⋊C4—681no—
226C22⋊C4—681no—
227C42—348no—
228C42—684no—
229C42—682no—
230C42—1362no—
231C23—22no—
232C23—22no—
233C23—41no—
234C23#1058756811yescharacteristic
235C23#1058757211yescharacteristic
236C23C2×#6322711yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—348no—
251C2×C4—684no—
252C2×C4—684no—
253C2×C4—682no—
254C2×C4—682no—
255C2×C4—682no—
256C2×C4—682no—
257C2×C4—682no—
258C2×C4—681no—
259C2×C4—681no—
260C2×C4#1058749614yes—
261C2×C4#1058756712yes—
262C2×C4#1058762512yes—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22#1176268611yescharacteristic
273C22C2×#1058749612yes—
274C22#1176300012yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—42no—
279C4—688no—
280C4—1362no—
281C4—1361no—
282C4—1361no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2#1452919511yescharacteristic
287C2#1452922511yescharacteristic
288C2#1452931911yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1463C2
socleC22×C17#386
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenter#1463D17
hypocenterC17#9478
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
8. #11762748C4semidirect
9. #11762739C4semidirect
196. C17#9478semidirect

Maximal subgroups

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

subgroupindex
#145330712
#145311412
#145288812
#145266382
C17×#14632
#947817