Finite Group Databasebeta

← #17958675

Subgroups — #17958675

Order 4352.

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

normal subgroups only

This group has 424 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#14543729C214yesmaximal, complemented
4#14533095C211yesmaximal, characteristic
5#11763826—21no—
6#11763780—21no—
7#11763655—21no—
8#11763653—21no—
9#11763652C2212yes—
10#11763652C2212yes—
11C2×C4×C22⋊D17C2211yescharacteristic
12#11762747—21no—
13#11762744—21no—
14#11762705—21no—
15#11762688C412yes—
16#11762682C2212yes—
17#11762669C411yescharacteristic
18#11762666—21no—
19C22×C4⋊C4×C17C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C412yes—
22C22×C22⋊D17C2×C411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C2×#63243—41no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—41no—
28C2×C4⋊C4×C17—41no—
29C2×C22⋊Dic17C2×C412yes—
30C2×C22⋊Dic17C2311yescharacteristic
31C4×C22⋊D17—41no—
32C4×C22⋊D17—41no—
33C2×#63227—22no—
34C2×#63227D411yescharacteristic
35C2×C4⋊Dic17—21no—
36C2×#63225—22no—
37C2×#63225D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C22⋊#3624—22no—
40C22⋊#3624—22no—
41#10587544—41no—
42#10587543—41no—
43C4×#3624—41no—
44#10587502—21no—
45#10587502—22no—
46#10587502—22no—
47C24×C17C22×C411yescharacteristic
48C23×D17C22⋊C411yescharacteristic
49C22×C4×C17—21no—
50C22×C4×C17—21no—
51C22×C4×C17—22no—
52C22×C4×C17—42no—
53C22×C4×C17—42no—
54C22×C4×C17—82no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C2×C22⋊D17—22no—
58C2×C22⋊D17—22no—
59C2×C22⋊D17—41no—
60C22×Dic17—22no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C2×D411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C2×C4×D17—21no—
65C2×C4×D17—21no—
66C2×C4×D17—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69#63243—82no—
70C4⋊C4×C17—42no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—41no—
73C22⋊Dic17—24no—
74C22⋊Dic17—41no—
75#63227—41no—
76#63227—82no—
77C4⋊Dic17—42no—
78#63225—41no—
79#63225—82no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82#11579—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—41no—
86C23×C17—41no—
87C23×C17C2×C22⋊C411yescharacteristic
88C23×C17#13112yes—
89C22×D17—21no—
90C22×D17—21no—
91C22×D17—21no—
92C22×D17—41no—
93C22×D17—41no—
94C2×C4×C17—22no—
95C2×C4×C17—21no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—41no—
99C2×C4×C17—42no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—84no—
103C2×C4×C17#9911yescharacteristic
104C2×C4×C17#9911yescharacteristic
105C22⋊D17—44no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17#10112yes—
116C4×D17—42no—
117C4×D17—81no—
118#3624—82no—
119#3624—82no—
120#2487—171no—
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—41no—
130C22×C17—41no—
131C22×C17#40811yescharacteristic
132C22×C17C2×#9911yescharacteristic
133C22×C17C2×#10111yescharacteristic
134C2×D17—42no—
135C2×D17—41no—
136C2×D17—41no—
137C2×D17—41no—
138C2×D17—81no—
139C4×C17—21no—
140C4×C17—41no—
141C4×C17—82no—
142C4×C17#35212yes—
143Dic17—22no—
144Dic17—41no—
145Dic17—41no—
146Dic17—82no—
147C2×C4×D4—171no—
148C22×C4⋊C4#59511yescharacteristic
149#431—341no—
150#407—341no—
151#400—341no—
152#399—341no—
153#389—341no—
154#386—172no—
155#385—172no—
156#380—171no—
157#380—341no—
158#324—341no—
159#323—172no—
160#323—172no—
161#323—341no—
162C2×C17—21no—
163C2×C17—21no—
164C2×C17—42no—
165C2×C17#147211yescharacteristic
166C2×C17C2×#35211yescharacteristic
167C2×C17#212211yescharacteristic
168D17—81no—
169C22×D4—171no—
170C23×C4—171no—
171C23×C4C2×#59512yes—
172C23×C4C2×#59511yescharacteristic
173C2×M16—681no—
174C4×D4—681no—
175C4×D4—681no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—342no—
183C2×C22⋊C4—172no—
184C2×C22⋊C4—171no—
185C2×C22⋊C4—171no—
186C2×C22⋊C4—342no—
187C2×C42—171no—
188C4⋊C8—681no—
189C22⋊C8—342no—
190C22⋊C8—342no—
191C22⋊C8—681no—
192C4×C8—681no—
193#95—342no—
194#95—342no—
195#95—341no—
196C17#1157911yescharacteristic, complemented, Sylow
197C24—171no—
198C24C22×#59511yescharacteristic
199C2×D4—342no—
200C2×D4—342no—
201C2×D4—681no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—82no—
208C22×C4—171no—
209C22×C4—171no—
210C22×C4—171no—
211C22×C4—341no—
212C22×C4—341no—
213C22×C4—342no—
214C22×C4—682no—
215C22×C4C22⋊#59511yescharacteristic
216C22×C4C22⋊#59511yescharacteristic
217M16—1362no—
218C2×C8—682no—
219C2×C8—682no—
220C4⋊C4—42no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—681no—
224C4⋊C4—682no—
225C4⋊C4—1362no—
226C22⋊C4—344no—
227C22⋊C4—681no—
228C22⋊C4—681no—
229C22⋊C4—1362no—
230C42—341no—
231C42—341no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—341no—
237C23—341no—
238C23—341no—
239C23—681no—
240C23—681no—
241C23#1058768012yes—
242C23C2×C22⋊#59511yescharacteristic
243D4—684no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—84no—
253C2×C4—172no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—682no—
259C2×C4—681no—
260C2×C4—681no—
261C2×C4—682no—
262C2×C4—682no—
263C2×C4—682no—
264C2×C4—1361no—
265C2×C4#1058755111yescharacteristic
266C2×C4#1058755111yescharacteristic
267C8—1362no—
268C8—1362no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—682no—
277C22—681no—
278C22—681no—
279C22—681no—
280C22—1361no—
281C22#1176378411yescharacteristic
282C22C2×#1058755111yescharacteristic
283C22D17⋊#10111yescharacteristic
284C4—21no—
285C4—41no—
286C4—82no—
287C4—342no—
288C4—681no—
289C4—681no—
290C4—1362no—
291C4#1176371112yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—1361no—
296C2#1454406411yescharacteristic
297C2C2×#1176371111yescharacteristic
298C2#1454504311yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17C2×C4
cosocleC2×C22⋊Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#11579
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543729C2semidirect
196. C17#11579semidirect

Maximal subgroups

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

subgroupindex
#145440392
#145440232
#145437292
#145330952
#1157917