Finite Group Databasebeta

← #17953638

Subgroups — #17953638

Order 4352.

418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 72 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#14544685C211yesmaximal, characteristic
2#14544681C211yesmaximal, characteristic
3#14543632C212yesmaximal
4#14543632C212yesmaximal
5#14531277C211yesmaximal, characteristic
6#11763781C2212yes—
7#11763752C2212yes—
8#11763689—21no—
9#11763689—21no—
10#11763687—21no—
11#11763687—21no—
12C2×#10587558C2211yescharacteristic
13#11762701—21no—
14#11762699—21no—
15#11762696—21no—
16#11762690—21no—
17C4×C4⋊Dic17C411yescharacteristic, complemented
18C4×#63227C2211yescharacteristic
19C4×#63227C2211yescharacteristic
20#11762655C411yescharacteristic, complemented
21C42×Dic17C411yescharacteristic, complemented
22C4×C4⋊C4×C17C411yescharacteristic, complemented
23C22×C4×D17C2311yescharacteristic
24C2×C22⋊#595—22no—
25C2×#63247—22no—
26C2×C4⋊C4×C17—21no—
27C2×C42×C17C2×C411yescharacteristic
28C2×C42×C17C2×C411yescharacteristic
29C2×C42×C17C2×C411yescharacteristic
30C2×#63227—21no—
31C2×#63227—21no—
32C2×#63227D411yescharacteristic
33C2×#63227D411yescharacteristic
34C2×C4⋊Dic17—21no—
35C2×#63225D411yescharacteristic
36C2×#63225D411yescharacteristic
37C2×C4×Dic17—21no—
38C2×C4×Dic17—21no—
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17C2×C411yescharacteristic
41C2×C4×Dic17C2×C411yescharacteristic
42#10587558—24no—
43(C2×#595)⋊C4—24no—
44#10587543—24no—
45C17×#95—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51C23×D17C2×D411yescharacteristic
52C22×#595—42no—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C22×Dic17—21no—
59C22×Dic17—21no—
60C22×Dic17C22⋊C411yescharacteristic
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C2×D411yescharacteristic
63C2×C4×D17—41no—
64C2×C4×D17—41no—
65C2×C4×D17#4114yes—
66C22⋊#595—42no—
67C22⋊#595—42no—
68#63247—42no—
69#63247—42no—
70C2×#3624—42no—
71C4⋊C4×C17—42no—
72C42×C17—22no—
73C42×C17—41no—
74C42×C17—41no—
75#63227—22no—
76#63227—22no—
77#63227—42no—
78#63227—42no—
79C4⋊Dic17—42no—
80#63225—22no—
81#63225—22no—
82C4×Dic17—22no—
83C4×Dic17—42no—
84C4×Dic17—42no—
85C4×Dic17—41no—
86C4×Dic17—41no—
87#8740—171nomaximal, Sylow
88C23×C17C2×C22⋊C411yescharacteristic
89C22×D17—21no—
90C22×D17—21no—
91C22×D17—41no—
92C22×D17—41no—
93C22×D17#12312yes—
94C2×#595—82no—
95C2×#595—82no—
96C2×#595—82no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17#11712yes—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—22no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17#12312yes—
123C4×D17—44no—
124#3624—82no—
125#2298—171no—
126#1822—171no—
127#1820—171no—
128#1284—172no—
129#1284—172no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17#38111yescharacteristic
133C22×C17#41011yescharacteristic
134C22×C17#41011yescharacteristic
135C2×D17—22no—
136C2×D17—22no—
137C2×D17—22no—
138C2×D17—81no—
139C2×D17—81no—
140#595—162no—
141C4×C17—22no—
142C4×C17—42no—
143C4×C17—41no—
144C4×C17—41no—
145C4×C17—81no—
146Dic17—22no—
147Dic17—42no—
148Dic17—41no—
149Dic17—41no—
150Dic17—81no—
151C2×#117—171no—
152#407—172no—
153#388—341no—
154#388—341no—
155#387—341no—
156#387—341no—
157#381—172no—
158C4×C4⋊C4—171no—
159C4×C4⋊C4#59511yescharacteristic, complemented
160C4×C22⋊C4—171no—
161C4×C22⋊C4—171no—
162#376—171no—
163C43—171no—
164#343—341no—
165#343—341no—
166#342—341no—
167#342—341no—
168C2×C17—21no—
169C2×C17—21no—
170C2×C17#182011yescharacteristic
171C2×C17#182711yescharacteristic
172C2×C17#182711yescharacteristic
173D17—42no—
174C23×C4—171no—
175C2×M16—342no—
176#117—344no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—171no—
179C2×C4⋊C4—171no—
180C2×C4⋊C4—341no—
181C2×C22⋊C4—171no—
182C2×C22⋊C4—171no—
183C2×C22⋊C4—341no—
184C2×C22⋊C4—341no—
185C2×C22⋊C4—342no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42—171no—
189C2×C42—341no—
190C2×C42—341no—
191C2×C42C2×#59511yescharacteristic
192C2×C42C2×#59511yescharacteristic
193C2×C42C2×#59511yescharacteristic
194C22⋊C8—344no—
195#95—21no—
196#95—341no—
197#95—341no—
198#95—341no—
199#95—341no—
200#95—344no—
201#95—341no—
202C17#874011yescharacteristic, complemented, Sylow
203C24—171no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—171no—
207C22×C4—174no—
208C22×C4—171no—
209C22×C4—171no—
210C22×C4—341no—
211C22×C4—341no—
212C22×C4—681no—
213C22×C4—681no—
214C22×C4—682no—
215C22×C4C22⋊#59511yescharacteristic
216C22×C4C22⋊#59511yescharacteristic
217C22×C4C22×#59511yescharacteristic
218M16—682no—
219M16—682no—
220C2×C8—682no—
221C4⋊C4—42no—
222C4⋊C4—342no—
223C4⋊C4—342no—
224C4⋊C4—682no—
225C22⋊C4—342no—
226C22⋊C4—342no—
227C22⋊C4—682no—
228C22⋊C4—682no—
229C22⋊C4—682no—
230C22⋊C4—682no—
231C42—22no—
232C42—41no—
233C42—41no—
234C42—342no—
235C42—681no—
236C42—681no—
237C42—682no—
238C42—682no—
239C23—172no—
240C23—341no—
241C23—341no—
242C23—681no—
243C23—681no—
244C23C2×C22⋊#59511yescharacteristic
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—172no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—342no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—684no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—681no—
271C2×C4—1362no—
272C2×C4—1362no—
273C2×C4—1362no—
274C2×C4#1058767712yes—
275C8—1362no—
276C22—21no—
277C22—21no—
278C22—342no—
279C22—342no—
280C22—342no—
281C22—1361no—
282C22—1361no—
283C22#1176375211yescharacteristic
284C22#1176378911yescharacteristic
285C22#1176379011yescharacteristic
286C4—22no—
287C4—42no—
288C4—41no—
289C4—41no—
290C4—81no—
291C4—2722no—
292C4—342no—
293C4—682no—
294C4—681no—
295C4—681no—
296C4—1361no—
297C2—21no—
298C2—21no—
299C2—682no—
300C2#1454468211yescharacteristic
301C2#1454469311yescharacteristic
302C2#1454469411yescharacteristic
subgroupG/H
centerC22#11763752
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17#381
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#8740
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
17. C4×C4⋊Dic17C4semidirect
20. #11762655C4semidirect
21. C42×Dic17C4semidirect
22. C4×C4⋊C4×C17C4semidirect
159. C4×C4⋊C4#595semidirect
202. C17#8740semidirect

Maximal subgroups

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

subgroupindex
#145446852
#145446812
#145436322
#145312772
#874017