Finite Group Databasebeta

← #17959386

Subgroups — #17959386

Order 4352.

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

normal subgroups only

This group has 460 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
1C4×#10587539C211yesmaximal, characteristic
2#14544041C211yesmaximal, characteristic
3#14543778C214yesmaximal, complemented
4#14533953C211yesmaximal, characteristic
5C2×#10587539—21no—
6#11763780—21no—
7C4×C22⋊#595—21no—
8#11763687C2212yes—
9#11763654—21no—
10#11763653C2212yes—
11C2×#10587555C411yescharacteristic, complemented
12C2×C4×D68C2211yescharacteristic
13#11762722C412yescomplemented
14#11762722C2212yes—
15#11762711—21no—
16#11762675—21no—
17#11762666—21no—
18#11762666—21no—
19C4×C4⋊C4×C17C411yescharacteristic, complemented
20C22×D68D411yescharacteristic
21C22×C4×D17D411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×Dic34C2×C412yes—
24C2×C22⋊#595—22no—
25C2×C4×#595—41no—
26C2×#63243—41no—
27C2×C4⋊C4×C17—21no—
28C2×C42×C17—21no—
29C2×C42×C17C2×C411yescharacteristic
30C2×#63227—22no—
31C2×#63227—22no—
32C2×#63227C2×C411yescharacteristic
33C2×#63227C2311yescharacteristic
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17D411yescharacteristic
37C4×D68—41no—
38C4×D68—41no—
39#10587555—41no—
40#10587555—41no—
41C22⋊#3624—22no—
42(C2×#595)⋊C4—41no—
43#10587543—41no—
44#10587539—24no—
45C17×#95C2×C412yes—
46#10587502—22no—
47#10587502—22no—
48C23×D17C22⋊C411yescharacteristic
49C23×D17C2×D411yescharacteristic
50C22×#595—42no—
51C22×C4×C17—22no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—22no—
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C2×D68—22no—
59C2×D68—22no—
60C2×D68—41no—
61C2×C4×D17—21no—
62C2×C4×D17—21no—
63C2×C4×D17—21no—
64C2×C4×D17—21no—
65C2×C4×D17—42no—
66C2×C4×D17—42no—
67C2×Dic34—42no—
68C2×Dic34—82no—
69C22⋊#595—24no—
70C22⋊#595—42no—
71C2×#3624—42no—
72C4×#595—82no—
73#63243—82no—
74C4⋊C4×C17—42no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—42no—
78#63227—41no—
79#63227—41no—
80#63227—82no—
81#63227—82no—
82C4⋊Dic17—41no—
83C4⋊Dic17—42no—
84C4⋊Dic17—41no—
85C4⋊Dic17—41no—
86#11787—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—21no—
89C22×D17—21no—
90C22×D17—21no—
91C22×D17—21no—
92C22×D17—21no—
93C22×D17—41no—
94C22×D17—41no—
95C22×D17—41no—
96C22×D17—41no—
97C22×D17#13712yes—
98C2×#595—44no—
99C2×#595—82no—
100C2×#595—82no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17#9911yescharacteristic
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17#10412yes—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119D68—44no—
120C4×D17—42no—
121C4×D17—42no—
122C4×D17—81no—
123C4×D17—81no—
124Dic34—84no—
125#3624—82no—
126#2563—171no—
127C4×#99—171no—
128#1465—171no—
129#1351—174no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17C2×#9911yescharacteristic
133C22×C17#41911yescharacteristic
134C22×C17C2×#10411yescharacteristic
135C2×D17—22no—
136C2×D17—41no—
137C2×D17—41no—
138C2×D17—42no—
139C2×D17—42no—
140C2×D17—41no—
141C2×D17—41no—
142C2×D17—41no—
143C2×D17—81no—
144C2×D17—81no—
145#595—84no—
146C4×C17—21no—
147C4×C17—22no—
148C4×C17—41no—
149C4×C17—82no—
150C4×C17#35412yes—
151Dic17—41no—
152Dic17—41no—
153Dic17—82no—
154C2×C4⋊Q8—171no—
155C2×C4×D4—171no—
156C2×#99—341no—
157#407—341no—
158#393—172no—
159#393—172no—
160#390—341no—
161#382—341no—
162#380—341no—
163#380—341no—
164C4×C4⋊C4#59511yescharacteristic, complemented
165C4×C22⋊C4—341no—
166#342—172no—
167#324—341no—
168#323—172no—
169C2×C17—21no—
170C2×C17—21no—
171C2×C17#150811yescharacteristic
172C2×C17#212211yescharacteristic
173C2×C17C2×#35411yescharacteristic
174D17—42no—
175D17—81no—
176C22×Q8—172no—
177C22×D4—171no—
178C23×C4—171no—
179C23×C4—171no—
180C2×M16—681no—
181C4⋊Q8—681no—
182C4⋊Q8—681no—
183C4×D4—681no—
184C4×D4—681no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4—341no—
189C2×C22⋊C4—171no—
190C2×C22⋊C4—171no—
191C2×C22⋊C4—342no—
192C2×C22⋊C4—342no—
193C2×C22⋊C4—342no—
194C2×C42—21no—
195C2×C42—681no—
196C2×C42C2×#59511yescharacteristic
197#99—344no—
198C22⋊C8—342no—
199C22⋊C8—681no—
200#95—342no—
201#95—342no—
202#95—681no—
203#95C2×#59512yes—
204C17#1178711yescharacteristic, complemented, Sylow
205C24—171no—
206C24—171no—
207C2×Q8—682no—
208C2×Q8—1362no—
209C2×D4—342no—
210C2×D4—342no—
211C2×D4—681no—
212C22×C4—22no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—341no—
216C22×C4—341no—
217C22×C4—341no—
218C22×C4—341no—
219C22×C4—342no—
220C22×C4—682no—
221C22×C4—682no—
222C22×C4—682no—
223C22×C4C22⋊#59511yescharacteristic
224C22×C4C22⋊#59511yescharacteristic
225C22×C4C22×#59511yescharacteristic
226M16—1362no—
227C2×C8—682no—
228C4⋊C4—42no—
229C4⋊C4—681no—
230C4⋊C4—682no—
231C4⋊C4—681no—
232C4⋊C4—681no—
233C22⋊C4—344no—
234C22⋊C4—681no—
235C22⋊C4—681no—
236C22⋊C4—682no—
237C22⋊C4—1362no—
238C22⋊C4—1362no—
239C42—21no—
240C42—21no—
241C42—42no—
242C42—1362no—
243C23—172no—
244C23—341no—
245C23—341no—
246C23—341no—
247C23—341no—
248C23—341no—
249C23—681no—
250C23—681no—
251C23—681no—
252C23—681no—
253C23C2×C22⋊#59511yescharacteristic
254Q8—1364no—
255D4—684no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—341no—
265C2×C4—341no—
266C2×C4—682no—
267C2×C4—682no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—682no—
271C2×C4—682no—
272C2×C4—684no—
273C2×C4—682no—
274C2×C4—1361no—
275C2×C4—1361no—
276C2×C4—1362no—
277C2×C4—1362no—
278C2×C4#1058753911yescharacteristic
279C2×C4#1058753911yescharacteristic
280C2×C4#1058754812yes—
281C8—1362no—
282C22—21no—
283C22—21no—
284C22—342no—
285C22—682no—
286C22—682no—
287C22—681no—
288C22—681no—
289C22—681no—
290C22—681no—
291C22—681no—
292C22—1361no—
293C22—1361no—
294C22C2×#1058753911yescharacteristic
295C22#1176380211yescharacteristic
296C22C2×#1058754811yescharacteristic
297C4—22no—
298C4—21no—
299C4—41no—
300C4—82no—
301C4—681no—
302C4—681no—
303C4—1364no—
304C4—1362no—
305C4#1176371612yes—
306C2—21no—
307C2—21no—
308C2—682no—
309C2—1361no—
310C2#1454418311yescharacteristic
311C2#1454504511yescharacteristic
312C2C2×#1176371611yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC22×D68D4
cosocleC2×#63227C23
hypercenterC4×C4⋊C4#595
hypocenterC17#11787
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543778C2semidirect
11. C2×#10587555C4semidirect
13. #11762722C4semidirect
19. C4×C4⋊C4×C17C4semidirect
164. C4×C4⋊C4#595semidirect
204. C17#11787semidirect

Maximal subgroups

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

subgroupindex
C4×#105875392
#145440412
#145437782
#145339532
#1178717