Finite Group Databasebeta

← #21431986

Subgroups — #21431986

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837331C211yesmaximal, characteristic, complemented
2#16837329C211yesmaximal, characteristic, complemented
3#16837324C211yesmaximal, characteristic, complemented
4#16837324C211yesmaximal, characteristic, complemented
5#16837319C211yesmaximal, characteristic
6#16837319C211yesmaximal, characteristic
7#16837304C211yesmaximal, characteristic
8#16837301C211yesmaximal, characteristic, complemented
9#16837294C211yesmaximal, characteristic, complemented
10#16837292C211yesmaximal, characteristic, complemented
11#16837292C211yesmaximal, characteristic, complemented
12#16837291C211yesmaximal, characteristic, complemented
13#16837288C211yesmaximal, characteristic, complemented
14#16837286C211yesmaximal, characteristic, complemented
15C59×#389C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×C4⋊Dic59C2211yescharacteristic
18C2×C4⋊Dic59C2211yescharacteristic
19C2×C4⋊Dic59C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×(C2×D59)⋊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×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×C4×Dic59C2211yescharacteristic
35C2×C4×Dic59C2211yescharacteristic
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
52C23×D59C2311yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C22×C4×C59C2311yescharacteristic
55C22×C4×C59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C22×Dic59C2311yescharacteristic
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C2×D236—22no—
67C2×D236—41no—
68C2×D236—41no—
69C4⋊C4×C59—22no—
70C4⋊C4×C59—22no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—41no—
73C42×C59—41no—
74(C2×D59)⋊C4—22no—
75(C2×D59)⋊C4—22no—
76(C2×D59)⋊C4—22no—
77(C2×D59)⋊C4—22no—
78(C2×D59)⋊C4—41no—
79(C2×D59)⋊C4—41no—
80(C2×D59)⋊C4—41no—
81(C2×D59)⋊C4—41no—
82(C2×D59)⋊C4—41no—
83(C2×D59)⋊C4—41no—
84(C2×D59)⋊C4—41no—
85(C2×D59)⋊C4—41no—
86C4⋊Dic59—41no—
87C4⋊Dic59—41no—
88C4⋊Dic59—41no—
89Dic59⋊C4—22no—
90Dic59⋊C4—41no—
91C4×Dic59—41no—
92C4×Dic59—41no—
93C23×C59C2411yescharacteristic
94C22×D59—21no—
95C22×D59—21no—
96C22×D59—21no—
97C22×D59—21no—
98C22×D59—21no—
99C22×D59—21no—
100C22×D59—21no—
101C22×D59—21no—
102C22×D59—21no—
103C22×D59—21no—
104C22×D59—21no—
105C22×D59—21no—
106C22×D59—21no—
107C22×D59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59#4112yes—
127C2×C4×C59#4112yes—
128C2×C4×C59#4112yes—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147D236—44no—
148C22×C59C2×#4111yescharacteristic
149C22×C59C2×#4111yescharacteristic
150C22×C59C2×#4111yescharacteristic
151C22×C59H(5,𝔽2)11yescharacteristic
152C22×C59H(5,𝔽2)11yescharacteristic
153C22×C59H(5,𝔽2)11yescharacteristic
154C22×C592−1+411yescharacteristic
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C4×C59—22no—
170C4×C59—22no—
171C4×C59—22no—
172C4×C59—41no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59—41no—
176Dic59—41no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182#2800—591nomaximal, Sylow
183C2×C59#53811yescharacteristic
184C2×C59#54011yescharacteristic
185C2×C59#54211yescharacteristic
186C2×C59#55311yescharacteristic
187C2×C59#55311yescharacteristic
188C2×C59#55611yescharacteristic
189C2×C59#56211yescharacteristic
190D59—81no—
191D59—81no—
192#397—591no—
193#397—591no—
194#396—591no—
195#396—591no—
196#394—591no—
197#394—591no—
198#390—591no—
199#389—591no—
200#389D5911yescharacteristic, complemented
201#388—591no—
202#388—591no—
203#388—591no—
204#388—591no—
205#387—591no—
206#387—591no—
207C59#280011yescharacteristic, complemented, Sylow
208C22×D4—591no—
209C2×C4⋊C4—591no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—591no—
213C2×C4⋊C4—591no—
214C2×C4⋊C4C2×D5911yescharacteristic
215C2×C4⋊C4C2×D5911yescharacteristic
216C2×C4⋊C4C2×D5911yescharacteristic
217C2×C4⋊C4C2×D5911yescharacteristic
218C2×C22⋊C4—591no—
219C2×C22⋊C4—591no—
220C2×C22⋊C4—591no—
221C2×C22⋊C4—591no—
222C2×C22⋊C4—591no—
223C2×C22⋊C4—591no—
224C2×C22⋊C4—591no—
225C2×C22⋊C4—591no—
226C2×C22⋊C4—591no—
227C2×C22⋊C4—591no—
228C2×C22⋊C4—591no—
229C2×C22⋊C4—591no—
230C2×C42—591no—
231C2×C42—591no—
232C2×C42C2×D5911yescharacteristic
233#95—591no—
234#95—591no—
235#95—591no—
236#95—591no—
237#95—591no—
238#95—591no—
239#95—591no—
240#95—591no—
241#95C2×D5911yescharacteristic
242#95C2×D5911yescharacteristic
243C24—591no—
244C24—591no—
245C2×D4—1182no—
246C2×D4—2361no—
247C2×D4—2361no—
248C22×C4—591no—
249C22×C4—591no—
250C22×C4—591no—
251C22×C4—591no—
252C22×C4—591no—
253C22×C4—591no—
254C22×C4C22×D5911yescharacteristic
255C22×C4C22×D5911yescharacteristic
256C22×C4C22×D5911yescharacteristic
257C22×C4C22×D5911yescharacteristic
258C22×C4C22×D5911yescharacteristic
259C22×C4C22×D5911yescharacteristic
260C22×C4C22×D5911yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—1182no—
266C4⋊C4—2361no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C4⋊C4—2361no—
270C22⋊C4—1182no—
271C22⋊C4—1182no—
272C22⋊C4—1182no—
273C22⋊C4—1182no—
274C22⋊C4—2361no—
275C22⋊C4—2361no—
276C22⋊C4—2361no—
277C22⋊C4—2361no—
278C22⋊C4—2361no—
279C22⋊C4—2361no—
280C22⋊C4—2361no—
281C22⋊C4—2361no—
282C42—41no—
283C42—2361no—
284C42—2361no—
285C23—1181no—
286C23—1181no—
287C23—1181no—
288C23—1181no—
289C23—1181no—
290C23—1181no—
291C23—1181no—
292C23—1181no—
293C23—1181no—
294C23—1181no—
295C23—1181no—
296C23—1181no—
297C23—1181no—
298C23—1181no—
299C23C23×D5911yescharacteristic
300D4—2364no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4#1174568512yes—
338C2×C4#1174568712yes—
339C2×C4#1174568912yes—
340C22—2361no—
341C22—2361no—
342C22—2361no—
343C22—2361no—
344C22—2361no—
345C22—2361no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22C2×#1174568711yescharacteristic
355C22C2×#1174568511yescharacteristic
356C22C2×#1174568911yescharacteristic
357C22#1427377211yescharacteristic
358C22#1427377311yescharacteristic
359C22#1427377311yescharacteristic
360C22#1427377511yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4—2361no—
372C4—2361no—
373C4—2361no—
374C2—4721no—
375C2—4721no—
376C2#1683798911yescharacteristic
377C2#1683800811yescharacteristic
378C2#1683802411yescharacteristic
379C2#1683809811yescharacteristic
380C2#1683810011yescharacteristic
381C2#1683812611yescharacteristic
382C2#1683814811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#389C2
hypercenter#389D59
hypocenterC59#2800
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #16837331C2semidirect
2. #16837329C2semidirect
3. #16837324C2semidirect
4. #16837324C2semidirect
8. #16837301C2semidirect
9. #16837294C2semidirect
10. #16837292C2semidirect
11. #16837292C2semidirect
12. #16837291C2semidirect
13. #16837288C2semidirect
14. #16837286C2semidirect
15. C59×#389C2semidirect
200. #389D59semidirect
207. C59#2800semidirect