Finite Group Databasebeta

← #17958618

Subgroups — #17958618

Order 4352.

444 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 74 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#14544039C211yesmaximal, characteristic
2#14544023C211yesmaximal, characteristic
3#14543711C214yesmaximal, complemented
4#14533093C211yesmaximal, characteristic
5#11763826—21no—
6#11763780—21no—
7#11763655—21no—
8#11763653—21no—
9#11763652C2212yes—
10#11763652C2212yes—
11C2×#10587572C412yes—
12C2×C4×C22⋊D17C2211yescharacteristic
13C22×C4⋊Dic17C411yescharacteristic
14#11762741—21no—
15#11762736—21no—
16#11762708—21no—
17#11762670C2212yes—
18#11762666—21no—
19C17×#380C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C22×C22⋊D17C2×C411yescharacteristic
22C23×Dic17C2×C412yes—
23C22×C4×D17D411yescharacteristic
24C2×#63243—41no—
25C2×C4⋊C4×C17—21no—
26C2×C22⋊C4×C17C2×C412yes—
27C2×C22⋊Dic17C2311yescharacteristic
28C4×C22⋊D17—41no—
29C4×C22⋊D17—41no—
30C2×#63227—22no—
31C2×#63227D411yescharacteristic
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17—41no—
36C2×C4⋊Dic17—41no—
37C2×#63225D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39#10587572—44no—
40C22⋊#3624—22no—
41C22⋊#3624—22no—
42#10587544—41no—
43#10587543—41no—
44C4×#3624—41no—
45C17×#95—21no—
46#10587502—22no—
47#10587502—22no—
48C24×C17C22×C411yescharacteristic
49C23×D17C22⋊C411yescharacteristic
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—22no—
53C22×C4×C17—42no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C2×C22⋊D17—22no—
57C2×C22⋊D17—22no—
58C2×C22⋊D17—41no—
59C22×Dic17—22no—
60C22×Dic17—24no—
61C22×Dic17—42no—
62C22×Dic17—42no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71#63243—82no—
72C4⋊C4×C17—42no—
73C22⋊C4×C17—42no—
74C22⋊Dic17—41no—
75#63227—41no—
76#63227—44no—
77C4⋊Dic17—42no—
78C4⋊Dic17—41no—
79C4⋊Dic17—41no—
80C4⋊Dic17—44no—
81#63225—41no—
82C4×Dic17—21no—
83C4×Dic17—21no—
84#11562—171nomaximal, Sylow
85C23×C17—21no—
86C23×C17—21no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17C2×C22⋊C411yescharacteristic
90C23×C17#13112yes—
91C22×D17—21no—
92C22×D17—21no—
93C22×D17—21no—
94C22×D17—41no—
95C22×D17—41no—
96C2×C4×C17—22no—
97C2×C4×C17—21no—
98C2×C4×C17—42no—
99C2×C4×C17—42no—
100C2×C4×C17—41no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#9911yescharacteristic
106C22⋊D17—44no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116C2×Dic17—84no—
117C2×Dic17#10012yes—
118C4×D17—42no—
119C4×D17—81no—
120#3624—82no—
121#3624—82no—
122#2486—171no—
123#1465—171no—
124#1460—171no—
125#1317—174no—
126C22×C17—21no—
127C22×C17—21no—
128C22×C17—22no—
129C22×C17—42no—
130C22×C17—42no—
131C22×C17—41no—
132C22×C17—41no—
133C22×C17#40811yescharacteristic
134C22×C17C2×#9911yescharacteristic
135C22×C17C2×#10011yescharacteristic
136C2×D17—42no—
137C2×D17—41no—
138C2×D17—41no—
139C2×D17—41no—
140C2×D17—81no—
141C4×C17—21no—
142C4×C17—41no—
143C4×C17—82no—
144C4×C17#35212yes—
145Dic17—22no—
146Dic17—41no—
147Dic17—41no—
148Dic17—82no—
149C2×#123—172no—
150C2×C4×D4—171no—
151C22×C4⋊C4—171no—
152#431—341no—
153#407—341no—
154#398—341no—
155#397—341no—
156#389—341no—
157#381—172no—
158#380—341no—
159#380#59511yescharacteristic
160#324—341no—
161#323—172no—
162#323—172no—
163#323—341no—
164C2×C17—21no—
165C2×C17—21no—
166C2×C17—42no—
167C2×C17#147111yescharacteristic
168C2×C17C2×#35211yescharacteristic
169C2×C17#212311yescharacteristic
170D17—81no—
171C22×D4—171no—
172C23×C4—171no—
173C23×C4—172no—
174C23×C4C2×#59511yescharacteristic
175C2×M16—681no—
176#123—684no—
177C4×D4—681no—
178C4×D4—681no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—342no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4—341no—
184C2×C4⋊C4—681no—
185C2×C4⋊C4—681no—
186C2×C22⋊C4—171no—
187C2×C22⋊C4—171no—
188C2×C22⋊C4—342no—
189C2×C22⋊C4C2×#59512yes—
190C2×C42—171no—
191C4⋊C8—681no—
192C22⋊C8—342no—
193C22⋊C8—342no—
194C22⋊C8—681no—
195C4×C8—681no—
196#95—21no—
197#95—342no—
198#95—342no—
199C17#1156211yescharacteristic, complemented, Sylow
200C24—171no—
201C24C22×#59511yescharacteristic
202C2×D4—342no—
203C2×D4—342no—
204C2×D4—681no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—171no—
210C22×C4—171no—
211C22×C4—171no—
212C22×C4—341no—
213C22×C4—341no—
214C22×C4—342no—
215C22×C4—344no—
216C22×C4—682no—
217C22×C4—682no—
218C22×C4—682no—
219C22×C4C22⋊#59511yescharacteristic
220C22×C4C22⋊#59511yescharacteristic
221M16—1362no—
222C2×C8—682no—
223C2×C8—682no—
224C4⋊C4—42no—
225C4⋊C4—681no—
226C4⋊C4—682no—
227C4⋊C4—684no—
228C4⋊C4—681no—
229C4⋊C4—681no—
230C22⋊C4—42no—
231C22⋊C4—681no—
232C22⋊C4—684no—
233C22⋊C4—681no—
234C42—341no—
235C42—341no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23—341no—
241C23—341no—
242C23—341no—
243C23—681no—
244C23—681no—
245C23#1058768012yes—
246C23C2×C22⋊#59511yescharacteristic
247D4—684no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—172no—
257C2×C4—341no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—682no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—682no—
265C2×C4—682no—
266C2×C4—682no—
267C2×C4—1361no—
268C2×C4—1364no—
269C2×C4#1058753911yescharacteristic
270C2×C4#1058753911yescharacteristic
271C8—1362no—
272C8—1362no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—682no—
281C22—681no—
282C22—681no—
283C22—681no—
284C22—1361no—
285C22#1176378411yescharacteristic
286C22C2×#1058753911yescharacteristic
287C22D17⋊#10011yescharacteristic
288C4—21no—
289C4—41no—
290C4—82no—
291C4—342no—
292C4—681no—
293C4—681no—
294C4—1362no—
295C4#1176371212yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—1361no—
300C2#1454406111yescharacteristic
301C2C2×#1176371211yescharacteristic
302C2#1454504811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#380C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17C2×C4
cosocleC2×C22⋊Dic17C23
hypercenter#380#595
hypocenterC17#11562
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543711C2semidirect
199. C17#11562semidirect

Maximal subgroups

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

subgroupindex
#145440392
#145440232
#145437112
#145330932
#1156217