Finite Group Databasebeta

← #16944015

Subgroups — #16944015

Order 4352.

424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 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#14527122C211yesmaximal, characteristic
2#14527105C211yesmaximal, characteristic
3#14526732C214yesmaximal, complemented
4C17×#2487C211yesmaximal, characteristic
5#11762862—21no—
6#11762773—21no—
7#11762535—21no—
8#11762533—21no—
9#11762533C2212yes—
10#11762533C2212yes—
11C2×C4×D4×C17C2211yescharacteristic
12C22×C4⋊C4×C17C411yescharacteristic
13C17×#400—21no—
14C17×#399—21no—
15C17×#389—21no—
16C17×#386C412yes—
17C17×#385C2212yes—
18C17×#380—21no—
19C17×#380C411yescharacteristic
20C22×D4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×C4×C17C2×C412yes—
23C23×C4×C17D411yescharacteristic
24C4×D4×C17—41no—
25C4×D4×C17—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17—41no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17C2×C412yes—
35C2×C22⋊C4×C17D411yescharacteristic
36C2×C22⋊C4×C17C2311yescharacteristic
37C2×C42×C17D411yescharacteristic
38C2×#63223—41no—
39C17×#95—21no—
40C17×#95—22no—
41C17×#95—22no—
42C22⋊#3622—22no—
43C22⋊#3622—22no—
44C22⋊#3622—41no—
45C4⋊#3622—41no—
46C4×#3622—41no—
47C24×C17C22⋊C411yescharacteristic
48C24×C17C22×C411yescharacteristic
49C2×D4×C17—22no—
50C2×D4×C17—22no—
51C2×D4×C17—41no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—22no—
57C22×C4×C17—22no—
58C22×C4×C17—42no—
59C22×C4×C17—42no—
60C22×C4×C17—42no—
61C22×C4×C17—82no—
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C4⋊C4×C17—41no—
68C4⋊C4×C17—42no—
69C4⋊C4×C17—42no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—82no—
73C22⋊C4×C17—24no—
74C22⋊C4×C17—41no—
75C22⋊C4×C17—41no—
76C22⋊C4×C17—82no—
77C42×C17—21no—
78C42×C17—21no—
79#63223—82no—
80C2×#3622—42no—
81C2×#3622—42no—
82#11579—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—21no—
86C23×C17—21no—
87C23×C17—21no—
88C23×C17—41no—
89C23×C17—41no—
90C23×C17—41no—
91C23×C17—41no—
92C23×C17C2×C22⋊C411yescharacteristic
93C23×C17#13112yes—
94D4×C17—44no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—42no—
113C2×C4×C17—81no—
114C2×C4×C17—84no—
115C2×C4×C17#9911yescharacteristic
116C2×C4×C17#9911yescharacteristic
117C2×C4×C17#10112yes—
118#3622—82no—
119#3622—82no—
120#2487D1711yescharacteristic
121#1465—171no—
122#1460—171no—
123#1326—174no—
124C22×C17—21no—
125C22×C17—21no—
126C22×C17—22no—
127C22×C17—42no—
128C22×C17—42no—
129C22×C17—42no—
130C22×C17—41no—
131C22×C17—41no—
132C22×C17—41no—
133C22×C17—41no—
134C22×C17—41no—
135C22×C17—81no—
136C22×C17#40811yescharacteristic
137C22×C17C2×#9911yescharacteristic
138C22×C17C2×#10111yescharacteristic
139C4×C17—21no—
140C4×C17—22no—
141C4×C17—41no—
142C4×C17—41no—
143C4×C17—41no—
144C4×C17—82no—
145C4×C17—82no—
146C4×C17#35212yes—
147C2×C4×D4C2×D1711yescharacteristic
148C22×C4⋊C4Dic1711yescharacteristic
149#431—341no—
150#407—341no—
151#400—21no—
152#399—21no—
153#389—21no—
154#386Dic1712yes—
155#385C2×D1712yes—
156#380—21no—
157#380Dic1711yescharacteristic
158#324—341no—
159#323—172no—
160#323—172no—
161#323—341no—
162C2×C17—21no—
163C2×C17—21no—
164C2×C17—42no—
165C2×C17—81no—
166C2×C17#147211yescharacteristic
167C2×C17C2×#35211yescharacteristic
168C2×C17#212211yescharacteristic
169C22×D4C2×Dic1711yescharacteristic
170C23×C4C2×Dic1711yescharacteristic
171C23×C4C2×Dic1712yes—
172C23×C4C22⋊D1711yescharacteristic
173C2×M16—681no—
174C4×D4—41no—
175C4×D4—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4C22⋊D1711yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4C2×Dic1712yes—
185C2×C22⋊C4C22⋊D1711yescharacteristic
186C2×C22⋊C4C22×D1711yescharacteristic
187C2×C42C22⋊D1711yescharacteristic
188C4⋊C8—681no—
189C22⋊C8—342no—
190C22⋊C8—342no—
191C22⋊C8—681no—
192C4×C8—681no—
193#95—21no—
194#95—22no—
195#95—22no—
196C17#1157911yescharacteristic, complemented, Sylow
197C24C22⋊Dic1711yescharacteristic
198C24C22×Dic1711yescharacteristic
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—82no—
212C22×C4C22⋊Dic1711yescharacteristic
213C22×C4C22⋊Dic1711yescharacteristic
214C22×C4C22⋊Dic1711yescharacteristic
215C22×C4C2×C22⋊D1711yescharacteristic
216C22×C4C2×C22⋊D1711yescharacteristic
217M16—1362no—
218C2×C8—682no—
219C2×C8—682no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—82no—
226C22⋊C4—24no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—82no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23#1058763412yes—
242C23C2×C22⋊Dic1711yescharacteristic
243D4—44no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—84no—
264C2×C4#1058750511yescharacteristic
265C2×C4#1058750511yescharacteristic
266C2×C4#1058750712yes—
267C8—1362no—
268C8—1362no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22#1176277611yescharacteristic
282C22C2×#1058750511yescharacteristic
283C22C2×#1058750711yescharacteristic
284C4—21no—
285C4—22no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—82no—
290C4—82no—
291C4#1176259912yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—81no—
296C2#1452714811yescharacteristic
297C2C2×#1176259911yescharacteristic
298C2#1453043411yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC24×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2487C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C22⋊C4×C17C23
hypercenter#2487D17
hypocenterC17#11579
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #14526732C2semidirect
196. C17#11579semidirect

Maximal subgroups

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

subgroupindex
#145271222
#145271052
#145267322
C17×#24872
#1157917