Finite Group Databasebeta

← #21431639

Subgroups — #21431639

Order 7552.

378 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837341C211yesmaximal, characteristic, complemented
2#16837339C211yesmaximal, characteristic
3#16837337C211yesmaximal, characteristic
4#16837335C211yesmaximal, characteristic, complemented
5#16837329C211yesmaximal, characteristic
6#16837328C211yesmaximal, characteristic
7#16837298C211yesmaximal, characteristic, complemented
8#16837293C211yesmaximal, characteristic
9#16837292C211yesmaximal, characteristic
10#16837292C211yesmaximal, characteristic
11#16837288C211yesmaximal, characteristic, complemented
12#16837287C211yesmaximal, characteristic, complemented
13#16837285C211yesmaximal, characteristic, complemented
14#16837268C211yesmaximal, characteristic, complemented
15C59×#389C211yesmaximal, characteristic, complemented
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2211yescharacteristic
18C2×C4⋊Dic59C2211yescharacteristic
19C2×C4⋊Dic59C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2211yescharacteristic
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2211yescharacteristic
27C2×(C2×D59)⋊C4C2211yescharacteristic
28C2×(C2×D59)⋊C4C2211yescharacteristic
29C2×(C2×D59)⋊C4C2211yescharacteristic
30C2×C4×Dic59C2211yescharacteristic
31C2×C4×Dic59C2211yescharacteristic
32C59⋊#95C2211yescharacteristic
33C59⋊#95C2211yescharacteristic
34C59⋊#95C2211yescharacteristic
35C59⋊#95C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C2×C4⋊C4×C59C2211yescharacteristic
45C2×C4⋊C4×C59C2211yescharacteristic
46C2×C4⋊C4×C59C2211yescharacteristic
47C2×C4⋊C4×C59C2211yescharacteristic
48C2×C42×C59C2211yescharacteristic
49#95×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51C23×D59C2311yescharacteristic
52C22×C4×C59C2311yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C22×C4×C59C2311yescharacteristic
55C22×C4×C59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×Dic59C2311yescharacteristic
60C22×Dic59C2311yescharacteristic
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C4⋊C4×C59—22no—
67C4⋊C4×C59—22no—
68C4⋊C4×C59—41no—
69C4⋊C4×C59—41no—
70C42×C59—22no—
71(C2×D59)⋊C4—22no—
72(C2×D59)⋊C4—22no—
73(C2×D59)⋊C4—22no—
74(C2×D59)⋊C4—41no—
75(C2×D59)⋊C4—41no—
76(C2×D59)⋊C4—41no—
77(C2×D59)⋊C4—41no—
78C4⋊Dic59—22no—
79C4⋊Dic59—22no—
80C4⋊Dic59—22no—
81C4⋊Dic59—41no—
82Dic59⋊C4—41no—
83Dic59⋊C4—41no—
84Dic59⋊C4—41no—
85C4×Dic59—41no—
86C4×Dic59—41no—
87C23×C59C2411yescharacteristic
88C22×D59—21no—
89C22×D59—21no—
90C22×D59—21no—
91C22×D59—21no—
92C22×D59—21no—
93C22×D59—21no—
94C22×D59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59#4112yes—
114C2×C4×C59#4112yes—
115C2×C4×C59#4112yes—
116C2×Dic59—21no—
117C2×Dic59—21no—
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—21no—
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C22×C59C2×#4111yescharacteristic
138C22×C59C2×#4111yescharacteristic
139C22×C59C2×#4111yescharacteristic
140C22×C59H(5,𝔽2)11yescharacteristic
141C22×C59H(5,𝔽2)11yescharacteristic
142C22×C592−1+411yescharacteristic
143C22×C592−1+411yescharacteristic
144C2×D59—41no—
145C2×D59—41no—
146C2×D59—41no—
147C2×D59—41no—
148C2×D59—41no—
149C2×D59—41no—
150C2×D59—41no—
151C4×C59—22no—
152C4×C59—22no—
153C4×C59—22no—
154C4×C59—41no—
155C4×C59—41no—
156C4×C59—41no—
157C4×C59—41no—
158Dic59—41no—
159Dic59—41no—
160Dic59—41no—
161Dic59—41no—
162Dic59—41no—
163Dic59—41no—
164Dic59—41no—
165#2773—591nomaximal, Sylow
166C2×C59#53911yescharacteristic
167C2×C59#54011yescharacteristic
168C2×C59#54211yescharacteristic
169C2×C59#55211yescharacteristic
170C2×C59#55211yescharacteristic
171C2×C59#55911yescharacteristic
172C2×C59#56311yescharacteristic
173D59—81no—
174#400—591no—
175#399—591no—
176#399—591no—
177#398—591no—
178#397—591no—
179#397—591no—
180#389—591no—
181#389D5911yescharacteristic, complemented
182#388—591no—
183#388—591no—
184#388—591no—
185#387—591no—
186#387—591no—
187#387—591no—
188#382—591no—
189C59#277311yescharacteristic, complemented, Sylow
190C2×C4⋊C4—591no—
191C2×C4⋊C4—591no—
192C2×C4⋊C4—591no—
193C2×C4⋊C4—591no—
194C2×C4⋊C4—591no—
195C2×C4⋊C4—591no—
196C2×C4⋊C4—591no—
197C2×C4⋊C4C2×D5911yescharacteristic
198C2×C4⋊C4C2×D5911yescharacteristic
199C2×C4⋊C4C2×D5911yescharacteristic
200C2×C4⋊C4C2×D5911yescharacteristic
201C2×C22⋊C4—591no—
202C2×C22⋊C4—591no—
203C2×C22⋊C4—591no—
204C2×C22⋊C4—591no—
205C2×C22⋊C4—591no—
206C2×C22⋊C4—591no—
207C2×C22⋊C4—591no—
208C2×C42—591no—
209C2×C42—591no—
210C2×C42C2×D5911yescharacteristic
211#95—591no—
212#95—591no—
213#95—591no—
214#95—591no—
215#95—591no—
216#95—591no—
217#95—591no—
218#95—591no—
219#95—591no—
220#95—591no—
221#95—591no—
222#95—591no—
223#95C2×D5911yescharacteristic
224#95C2×D5911yescharacteristic
225C24—591no—
226C22×C4—591no—
227C22×C4—591no—
228C22×C4—591no—
229C22×C4—591no—
230C22×C4—591no—
231C22×C4—591no—
232C22×C4—591no—
233C22×C4C22×D5911yescharacteristic
234C22×C4C22×D5911yescharacteristic
235C22×C4C22×D5911yescharacteristic
236C22×C4C22×D5911yescharacteristic
237C22×C4C22×D5911yescharacteristic
238C22×C4C22×D5911yescharacteristic
239C22×C4C22×D5911yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—1182no—
245C4⋊C4—1182no—
246C4⋊C4—1182no—
247C4⋊C4—2361no—
248C4⋊C4—2361no—
249C4⋊C4—2361no—
250C4⋊C4—2361no—
251C22⋊C4—1182no—
252C22⋊C4—1182no—
253C22⋊C4—1182no—
254C22⋊C4—2361no—
255C22⋊C4—2361no—
256C22⋊C4—2361no—
257C22⋊C4—2361no—
258C42—22no—
259C42—2361no—
260C42—2361no—
261C23—1181no—
262C23—1181no—
263C23—1181no—
264C23—1181no—
265C23—1181no—
266C23—1181no—
267C23—1181no—
268C23C23×D5911yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—1181no—
288C2×C4—1181no—
289C2×C4—1181no—
290C2×C4—1181no—
291C2×C4—1181no—
292C2×C4—1181no—
293C2×C4—1181no—
294C2×C4—1181no—
295C2×C4—1181no—
296C2×C4—1181no—
297C2×C4—1181no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—1181no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4#1174568512yes—
309C2×C4#1174568712yes—
310C2×C4#1174568912yes—
311C22—2361no—
312C22—2361no—
313C22—2361no—
314C22—2361no—
315C22—2361no—
316C22—2361no—
317C22—2361no—
318C22C2×#1174568711yescharacteristic
319C22C2×#1174568511yescharacteristic
320C22C2×#1174568911yescharacteristic
321C22#1427377211yescharacteristic
322C22#1427377311yescharacteristic
323C22#1427377411yescharacteristic
324C22#1427377511yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—2361no—
333C4—2361no—
334C4—2361no—
335C4—2361no—
336C4—2361no—
337C4—2361no—
338C4—2361no—
339C2—4721no—
340C2#1683799411yescharacteristic
341C2#1683800511yescharacteristic
342C2#1683802611yescharacteristic
343C2#1683808711yescharacteristic
344C2#1683809411yescharacteristic
345C2#1683813711yescharacteristic
346C2#1683815611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#389C2
hypercenter#389D59
hypocenterC59#2773
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #16837341C2semidirect
4. #16837335C2semidirect
7. #16837298C2semidirect
11. #16837288C2semidirect
12. #16837287C2semidirect
13. #16837285C2semidirect
14. #16837268C2semidirect
15. C59×#389C2semidirect
181. #389D59semidirect
189. C59#2773semidirect