Finite Group Databasebeta

← #21434335

Subgroups — #21434335

Order 7552.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838005C211yesmaximal, characteristic, complemented
2#16837876C211yesmaximal, characteristic, complemented
3#16837726C211yesmaximal, characteristic, complemented
4#16837705C211yesmaximal, characteristic, complemented
5#16837701C211yesmaximal, characteristic, complemented
6#16837596C211yesmaximal, characteristic, complemented
7#16837596C211yesmaximal, characteristic, complemented
8#16837538C211yesmaximal, characteristic, complemented
9#16837535C211yesmaximal, characteristic, complemented
10#16837513C211yesmaximal, characteristic, complemented
11#16837511C211yesmaximal, characteristic, complemented
12#16837484C211yesmaximal, characteristic, complemented
13#16837482C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#482C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×D472C2211yescharacteristic
18C2×D472C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21#14273723C2211yescharacteristic, complemented
22#14273718C2211yescharacteristic, complemented
23#14273711—21no—
24#14273709—21no—
25#14273701C2211yescharacteristic
26#14273699—21no—
27#14273698—21no—
28C4×D236—21no—
29C4×D236—21no—
30D4×Dic59C2211yescharacteristic, complemented
31#14273689C2211yescharacteristic
32#14273689C2211yescharacteristic
33#14273689C2211yescharacteristic
34#14273689C2211yescharacteristic
35#14273689C2211yescharacteristic, complemented
36#14273686C2211yescharacteristic
37C22⋊C4×D59—21no—
38C22⋊C4×D59—21no—
39#14273660C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52#121×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59—21no—
60C2×D4×C59—21no—
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C22×Dic59—21no—
67C2×D236—21no—
68C2×D236—22no—
69C2×D236—22no—
70C2×D236C2311yescharacteristic
71C2×D236C2311yescharacteristic
72C2×D236C2311yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C42×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59D411yescharacteristic
88C22⋊Dic59D411yescharacteristic
89#11745669—22no—
90#11745669—22no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59D411yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102C4×Dic59C2311yescharacteristic
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106D472—22no—
107D472—22no—
108C23×C59—21no—
109C23×C59C2×D411yescharacteristic
110C22×D59—21no—
111C22×D59—21no—
112C22×D59—24no—
113C22×D59—21no—
114C22×D59—81no—
115C22×D59—81no—
116D4×C59—21no—
117D4×C59—21no—
118D4×C59—81no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2411yescharacteristic
126C22⋊D59—81no—
127C22⋊D59—81no—
128C22⋊D59—81no—
129C2×Dic59—21no—
130C2×Dic59—81no—
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135D236—24no—
136D236—21no—
137D236—21no—
138D236—21no—
139D236—21no—
140D236#4112yes—
141D236#4112yes—
142C4×D59—81no—
143C4×D59—81no—
144C4×D59—81no—
145C4×D59—81no—
146C4×D59—81no—
147C8×C59—21no—
148C8×C59—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59C22×D411yescharacteristic
158C2×D59—22no—
159C2×D59—22no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—84no—
168C4×C59—21no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59C2×#4111yescharacteristic
173C4×C59C2×#4111yescharacteristic
174Dic59—21no—
175Dic59—21no—
176Dic59—21no—
177Dic59—21no—
178Dic59—41no—
179#3122—591nomaximal, Sylow
180C2×C59—41no—
181C2×C59—81no—
182C2×C59#52511yescharacteristic
183C2×C59#57611yescharacteristic
184C2×C59#57611yescharacteristic
185D59—42no—
186D59—42no—
187D59—81no—
188#540—591no—
189#518—591no—
190#482—591no—
191#482D5911yescharacteristic, complemented
192#478—591no—
193#478—591no—
194#459—591no—
195#459—591no—
196#447—591no—
197#447—591no—
198#442—591no—
199#442—591no—
200C4×D8—591no—
201C4×D8—591no—
202#433—591no—
203C59#312211yescharacteristic, complemented, Sylow
204C22×D4—591no—
205C2×D8—591no—
206C2×D8—591no—
207C2×D8—591no—
208C2×D8—591no—
209#127—591no—
210#125—591no—
211#123—1181no—
212#123—1181no—
213#121—591no—
214#121—1181no—
215#121—1181no—
216#121C2×D5911yescharacteristic
217C4×D4—591no—
218C4×D4—591no—
219C4×D4—591no—
220C4×D4—591no—
221C4×D4—591no—
222C4×D4—591no—
223C4×D4—1181no—
224C4×D4—1181no—
225#117—591no—
226#117C2×D5911yescharacteristic
227C2×C22⋊C4—1181no—
228C2×C22⋊C4—1181no—
229#107—591no—
230#107C2×D5911yescharacteristic, complemented
231#106—591no—
232#106C2×D5911yescharacteristic, complemented
233C4⋊C8—591no—
234C4⋊C8—591no—
235#102—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241#102C2×D5911yescharacteristic, complemented
242#102C2×D5911yescharacteristic, complemented
243C22⋊C8—591no—
244C22⋊C8C2×D5911yescharacteristic
245#97—591no—
246C4×C8—591no—
247C24—1181no—
248C2×D4—21no—
249C2×D4—591no—
250C2×D4—591no—
251C2×D4—591no—
252C2×D4—1182no—
253C2×D4—1182no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4—1181no—
258C2×D4C22×D5911yescharacteristic
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4C22×D5911yescharacteristic
266D8—1182no—
267D8—1182no—
268D8—1182no—
269D8—1182no—
270C2×C8—591no—
271C2×C8—591no—
272C2×C8C22×D5911yescharacteristic
273C2×C8C22×D5911yescharacteristic
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4C22×D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C4⋊C4C22×D5911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—591no—
285C22⋊C4—591no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—21no—
294C42—591no—
295C42—591no—
296C23—21no—
297C23—1184no—
298C23—1181no—
299C23—1181no—
300C23—1181no—
301C23—4721no—
302C23—4721no—
303C23D4×D5911yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—592no—
308D4—592no—
309D4—1184no—
310D4—1181no—
311D4—1181no—
312D4—1181no—
313D4—1181no—
314D4—4721no—
315D4—4721no—
316D4—4721no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—591no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—591no—
326C2×C4—1181no—
327C2×C4—4721no—
328C2×C4—4721no—
329C2×C4—4721no—
330C2×C4—4721no—
331C2×C4—4721no—
332C2×C4—4721no—
333C2×C4D4×D5911yescharacteristic
334C2×C4C23×D5911yescharacteristic
335C8—21no—
336C8—21no—
337C8—1181no—
338C8—1181no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1182no—
346C22—1182no—
347C22—4724no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22—2361no—
355C22C2×D4×D5911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1181no—
361C4—1181no—
362C4—1181no—
363C4—1181no—
364C4—2361no—
365C4#41×D5911yescharacteristic
366C4#41×D5911yescharacteristic
367C2—41no—
368C2—81no—
369C2—4721no—
370C2—2362no—
371C2—2362no—
372C2#1683791011yescharacteristic
373C2#1683820411yescharacteristic
374C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#482C2
socleC22×C59C22×D4
hypercenter#482D59
hypocenterC59#3122
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16838005C2semidirect
2. #16837876C2semidirect
3. #16837726C2semidirect
4. #16837705C2semidirect
5. #16837701C2semidirect
6. #16837596C2semidirect
7. #16837596C2semidirect
8. #16837538C2semidirect
9. #16837535C2semidirect
10. #16837513C2semidirect
11. #16837511C2semidirect
12. #16837484C2semidirect
13. #16837482C2semidirect
14. #16837460C2semidirect
15. C59×#482C2semidirect
21. #14273723C22semidirect
22. #14273718C22semidirect
30. D4×Dic59C22semidirect
35. #14273689C22semidirect
39. #14273660C22semidirect
40. #14273658C22semidirect
41. Dic59⋊C8C22semidirect
42. Dic59⋊C8C22semidirect
47. #14273647C22semidirect
48. #14273647C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. #102×C59C22semidirect
57. #102×C59C22semidirect
191. #482D59semidirect
203. C59#3122semidirect
230. #107C2×D59semidirect
232. #106C2×D59semidirect
241. #102C2×D59semidirect
242. #102C2×D59semidirect