Finite Group Databasebeta

← #17960848

Subgroups — #17960848

Order 4352.

584 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#11763715C212yesmaximal
2#14544529C212yesmaximal
3#14543878C212yesmaximal
4#14531327C211yesmaximal, characteristic
5C2×#10587539C2214yes—
6C4×C22⋊#595—22no—
7#11763715C418yescomplemented
8#11763687—22no—
9C2×#10587633C2211yescharacteristic
10C2×Q8×Dic17C411yescharacteristic, complemented
11C2×#10587579C2211yescharacteristic
12#11762711C2211yescharacteristic
13#11762701—22no—
14#11762674C411yescharacteristic, complemented
15#11762656—22no—
16C42×Dic17C411yescharacteristic, complemented
17C17×#391C411yescharacteristic, complemented
18C22×Q8×C17C2×C411yescharacteristic
19C22×D68C2311yescharacteristic
20C22×C4×D17D412yes—
21C2×C22⋊#595—24no—
22C2×C4×#595—42no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25#10587633—22no—
26#10587633C2×C414yes—
27Q8×Dic17—41no—
28Q8×Dic17—41no—
29C2×#63227—22no—
30C2×#63227—22no—
31C2×#63227D412yes—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4×Dic17—21no—
35C2×C4×Dic17—21no—
36C2×C4×Dic17—21no—
37C2×C4×Dic17C2×C411yescharacteristic
38C2×C4×Dic17C2×C411yescharacteristic
39#10587579—41no—
40#10587579—41no—
41(C2×#595)⋊C4—42no—
42#10587539—24no—
43#10587539C2×C418yes—
44C17×#95—22no—
45#10587502—22no—
46C23×D17C2×D412yes—
47C22×#595—44no—
48C2×Q8×C17—21no—
49C2×Q8×C17—41no—
50C2×Q8×C17—41no—
51C2×Q8×C17C4212yescomplemented
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17C22⋊C412yes—
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—21no—
57C22×Dic17—21no—
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C22⋊C411yescharacteristic
60C2×D68—41no—
61C2×D68—41no—
62C2×D68C22×C412yes—
63C2×D68#4112yes—
64C2×C4×D17—22no—
65C2×C4×D17—22no—
66C2×C4×D17—44no—
67C22⋊#595—28no—
68C22⋊#595—44no—
69C4×#595—84no—
70C4⋊C4×C17—41no—
71C42×C17—41no—
72#63227—28no—
73#63227—42no—
74#63227—44no—
75C4⋊Dic17—42no—
76C4⋊Dic17—41no—
77C4×Dic17—21no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80C4×Dic17—42no—
81C4×Dic17—42no—
82C4×Dic17—41no—
83C4×Dic17—41no—
84C4×Dic17C4212yescomplemented
85C4×#354—171nomaximal, Sylow
86C23×C17C2×C22⋊C411yescharacteristic
87C22×D17—22no—
88C22×D17—22no—
89C22×D17—42no—
90C22×D17—42no—
91C22×D17C4×D414yes—
92C2×#595—48no—
93C2×#595—84no—
94C2×#595—84no—
95Q8×C17—42no—
96Q8×C17—42no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17—22no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—42no—
107C2×C4×C17C2×C4211yescharacteristic
108C2×C4×C17#11711yescharacteristic
109C2×Dic17—22no—
110C2×Dic17—22no—
111C2×Dic17—21no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—42no—
116C2×Dic17—41no—
117C2×Dic17#9911yescharacteristic
118C2×Dic17#9911yescharacteristic
119D68—42no—
120D68—42no—
121C4×D17—44no—
122C4×D17—82no—
123C4×#124—171no—
124C2×#354—172no—
125C4×#99—172no—
126#1393—172no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17C4×C22⋊C411yescharacteristic
130C22×C17C2×#9911yescharacteristic
131C22×C17#41011yescharacteristic
132C2×D17—24no—
133C2×D17—42no—
134C2×D17—42no—
135C2×D17—44no—
136C2×D17—82no—
137#595—88no—
138C4×C17—21no—
139C4×C17—21no—
140C4×C17—42no—
141C4×C17—42no—
142C4×C17—42no—
143Dic17—21no—
144Dic17—42no—
145Dic17—41no—
146Dic17—81no—
147Dic17#35412yescomplemented
148C2×#124—171no—
149C2×C4×Q8—171no—
150C2×C4×D4—171no—
151C2×#99—174no—
152#391#59511yescharacteristic, complemented
153#390—171no—
154#388—342no—
155#382—171no—
156C4×C22⋊C4—342no—
157C4×C22⋊C4—342no—
158C43—171no—
159#354—178no—
160#342—342no—
161C2×C17—21no—
162C2×C17—21no—
163C2×C17C4×#9911yescharacteristic
164C2×C17C2×#35411yescharacteristic
165C2×C17#212611yescharacteristic
166D17—44no—
167C22×Q8C2×#59511yescharacteristic
168C22×D4—171no—
169C23×C4—172no—
170#124—174no—
171#124—342no—
172C4×Q8—681no—
173C4×Q8—681no—
174C4×D4—681no—
175C4×D4—681no—
176C2×C4⋊C4—171no—
177C2×C4⋊C4—341no—
178C2×C4⋊C4C2×#59511yescharacteristic
179C2×C22⋊C4—172no—
180C2×C22⋊C4—342no—
181C2×C22⋊C4—344no—
182C2×C22⋊C4—342no—
183C2×C42—171no—
184C2×C42—171no—
185C2×C42—341no—
186C2×C42—341no—
187C2×C42—341no—
188C2×C42—682no—
189C2×C42C2×#59511yescharacteristic
190#99—178no—
191#99—344no—
192#95—22no—
193#95—342no—
194#95—682no—
195C17C4×#35411yescharacteristic, complemented, Sylow
196C24—172no—
197C2×Q8—21no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8C4×#59512yescomplemented
201C2×D4—172no—
202C2×D4—172no—
203C2×D4—681no—
204C2×D4—681no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—171no—
208C22×C4—171no—
209C22×C4—342no—
210C22×C4—342no—
211C22×C4—341no—
212C22×C4—341no—
213C22×C4—684no—
214C22×C4—684no—
215C22×C4C22⋊#59512yes—
216C22×C4C22×#59511yescharacteristic
217C4⋊C4—41no—
218C4⋊C4—681no—
219C4⋊C4—682no—
220C22⋊C4—348no—
221C22⋊C4—348no—
222C22⋊C4—682no—
223C22⋊C4—684no—
224C22⋊C4—684no—
225C42—41no—
226C42—172no—
227C42—341no—
228C42—341no—
229C42—341no—
230C42—682no—
231C42—681no—
232C42—681no—
233C42—682no—
234C42—1364no—
235C23—174no—
236C23—342no—
237C23—342no—
238C23—682no—
239C23—682no—
240C23C2×C22⋊#59511yescharacteristic
241Q8—42no—
242Q8—42no—
243D4—682no—
244D4—682no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—171no—
256C2×C4—171no—
257C2×C4—342no—
258C2×C4—342no—
259C2×C4—341no—
260C2×C4—684no—
261C2×C4—681no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—682no—
265C2×C4—688no—
266C2×C4—681no—
267C2×C4—1362no—
268C2×C4—1364no—
269C2×C4—1364no—
270C2×C4C2×C4×#59511yescharacteristic
271C2×C4#1058767711yescharacteristic
272C22—21no—
273C22—21no—
274C22—344no—
275C22—684no—
276C22—682no—
277C22—682no—
278C22—1362no—
279C22C4×C22⋊#59511yescharacteristic
280C22D17⋊#9911yescharacteristic
281C22#1176378911yescharacteristic
282C4—21no—
283C4—21no—
284C4—42no—
285C4—42no—
286C4—42no—
287C4—172no—
288C4—341no—
289C4—682no—
290C4—681no—
291C4—1368no—
292C4—1361no—
293C2—21no—
294C2—21no—
295C2—684no—
296C2#1454453111yescharacteristic
297C2D17⋊#35411yescharacteristic
298C2#1454505811yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radical, cosocleC22×D68C23
hypercenter#391#595
hypocenterC17C4×#354
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #391

Complements

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

NH ≅ G/Ntype
7. #11763715C4semidirect
10. C2×Q8×Dic17C4semidirect
14. #11762674C4semidirect
16. C42×Dic17C4semidirect
17. C17×#391C4semidirect
51. C2×Q8×C17C42semidirect
84. C4×Dic17C42semidirect
147. Dic17#354semidirect
152. #391#595semidirect
195. C17C4×#354semidirect
200. C2×Q8C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637152
#145445292
#145438782
#145313272
C4×#35417