Finite Group Databasebeta

← #21435726

Subgroups — #21435726

Order 7552.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273759C211yesmaximal, characteristic, complemented
2C2×#14273751C211yesmaximal, characteristic, complemented
3#16838060C211yesmaximal, characteristic, complemented
4#16838045C211yesmaximal, characteristic, complemented
5#16837657C211yesmaximal, characteristic, complemented
6#16837652C211yesmaximal, characteristic, complemented
7#16837621C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837561C211yesmaximal, characteristic, complemented
10#16837551C211yesmaximal, characteristic, complemented
11#16837546C211yesmaximal, characteristic, complemented
12#16837539C211yesmaximal, characteristic, complemented
13C4×#11745660C211yesmaximal, characteristic, complemented
14#16837481C211yesmaximal, characteristic, complemented
15C59×#495C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×Q8×D59C2211yescharacteristic, complemented
19C2×D4×D59C2211yescharacteristic
20#14273759—24no—
21#14273751—24no—
22C2×#11745672C2211yescharacteristic, complemented
23C2×#11745660C2211yescharacteristic
24C2×#11745670C2211yescharacteristic
25C2×#11745671C2211yescharacteristic
26C2×#11745669C2211yescharacteristic
27C2×#11745659C2211yescharacteristic
28C2×#11745659C2211yescharacteristic, complemented
29#14273713—21no—
30#14273709—21no—
31#14273704—21no—
32#14273703C2211yescharacteristic
33#14273703C2211yescharacteristic
34#14273700—21no—
35#14273700—21no—
36#14273698C2211yescharacteristic
37#14273698C2211yescharacteristic, complemented
38#14273697—21no—
39C4×Dic118C2211yescharacteristic, complemented
40C4×D236C2211yescharacteristic
41C4×D236C2211yescharacteristic
42(C22⋊D59)⋊C4—21no—
43C22⋊C4×D59—21no—
44#14273659C2211yescharacteristic, complemented
45C4⋊(C59⋊C8)C2211yescharacteristic, complemented
46#14273652C2211yescharacteristic, complemented
47#14273651C2211yescharacteristic, complemented
48#14273651C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273648C2211yescharacteristic
51#14273648C2211yescharacteristic, complemented
52(C2×D59)⋊C8C2211yescharacteristic
53(C2×D59)⋊C8C2211yescharacteristic, complemented
54C2×Q16×C59C2211yescharacteristic, complemented
55C2×SD16×C59C2211yescharacteristic
56C2×SD16×C59C2211yescharacteristic, complemented
57C2×D8×C59C2211yescharacteristic
58#124×C59C2211yescharacteristic
59#124×C59C2211yescharacteristic, complemented
60C4×C8×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C22×Dic59—21no—
71#11745689—22no—
72#11745689—41no—
73Q8×D59—22no—
74Q8×D59—41no—
75#11745687—22no—
76#11745687—41no—
77D4×D59—22no—
78D4×D59—41no—
79C2×D236—21no—
80C2×D236D411yescharacteristic
81C2×D236C2311yescharacteristic
82C2×C4×D59—21no—
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C4×D59C2311yescharacteristic
86C2×C4×D59C2311yescharacteristic
87C2×Dic118—21no—
88C2×Dic118C2311yescharacteristic
89Q16×C59—22no—
90SD16×C59—41no—
91SD16×C59—41no—
92D8×C59—22no—
93C2×C8×C59C2311yescharacteristic
94C2×C8×C59C2311yescharacteristic
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊C4×C59—21no—
99C42×C59C2311yescharacteristic
100C22⋊Dic59—21no—
101C22⋊Dic59—21no—
102#11745672—22no—
103#11745671—22no—
104#11745670—22no—
105#11745669—22no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4D411yescharacteristic
110(C2×D59)⋊C4D411yescharacteristic
111C4⋊Dic59D411yescharacteristic
112C4⋊Dic59C2311yescharacteristic
113C4⋊Dic59C2311yescharacteristic
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116Dic59⋊C4—21no—
117C4×Dic59—21no—
118C2×C59⋊C8C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120#11745660D414yescomplemented
121#11745659—22no—
122#11745659—22no—
123C23×C59—21no—
124C23×C59—21no—
125C22×D59—21no—
126C22×D59—42no—
127C22×D59—42no—
128C22×D59—81no—
129C22×D59C2×D411yescharacteristic
130C22×D59C2×D411yescharacteristic
131Q8×C59—21no—
132Q8×C59—21no—
133Q8×C59—21no—
134Q8×C59—21no—
135D4×C59—21no—
136D4×C59—21no—
137D4×C59—21no—
138D4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2411yescharacteristic
144C22⋊D59—42no—
145C22⋊D59—42no—
146C22⋊D59—42no—
147C22⋊D59—81no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—42no—
152C2×Dic59C2×D411yescharacteristic
153C2×Dic59C2×D411yescharacteristic
154D236—21no—
155D236—41no—
156D236—42no—
157D236C2×D412yes—
158C4×D59—21no—
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—21no—
162C4×D59—42no—
163C4×D59—42no—
164C4×D59—81no—
165Dic118—21no—
166Dic118—42no—
167Dic118C2×D412yes—
168C8×C59—21no—
169C8×C59C2×D412yes—
170C59⋊C8—21no—
171C59⋊C8—21no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59C22×D411yescharacteristic
179C2×D59—21no—
180C2×D59—21no—
181C2×D59—22no—
182C2×D59—21no—
183C2×D59—21no—
184C2×D59—21no—
185C2×D59—21no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—41no—
192C4×C59—41no—
193C4×C59C22×D411yescharacteristic
194C4×C59H(5,𝔽2)11yescharacteristic
195Dic59—22no—
196Dic59—21no—
197Dic59—21no—
198Dic59—41no—
199Dic59—41no—
200#3275—591nomaximal, Sylow
201C2×C59—81no—
202C2×C59—81no—
203C2×C59D4211yescharacteristic
204C2×C59#57511yescharacteristic
205C2×C59#57711yescharacteristic
206D59—41no—
207D59—41no—
208D59—42no—
209C2×#137—591no—
210C2×AGL(1,ℤ/8)—591no—
211#548—591no—
212#546—591no—
213#495D5911yescharacteristic, complemented
214#470—591no—
215#469—591no—
216#464—591no—
217#463—591no—
218#452—591no—
219#450—591no—
220#449—591no—
221#448—591no—
222C4×SD16—591no—
223#436—591no—
224C59#327511yescharacteristic, complemented, Sylow
225C2×#41—591no—
226C2×#41—591no—
227C22×Q8—591no—
228C22×D4—591no—
229#137—1184no—
230AGL(1,ℤ/8)—1184no—
231C2×Q16—591no—
232C2×Q16C2×D5911yescharacteristic, complemented
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16C2×D5911yescharacteristic
237C2×SD16C2×D5911yescharacteristic, complemented
238C2×D8—591no—
239C2×D8C2×D5911yescharacteristic
240C2×M16—591no—
241C2×M16—591no—
242#124—1181no—
243#124C2×D5911yescharacteristic
244#124C2×D5911yescharacteristic, complemented
245#123—1181no—
246C22⋊Q8—591no—
247C22⋊Q8—591no—
248C22⋊Q8—1181no—
249#121—591no—
250#121—591no—
251#121—1181no—
252#121—1181no—
253#120—1181no—
254C4×Q8—591no—
255C4×D4—591no—
256C4×D4—591no—
257C4×D4—1181no—
258C2×C22⋊C4—1181no—
259#106—591no—
260C4⋊C8—591no—
261#103—591no—
262#103—591no—
263#103—591no—
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8—591no—
268C22⋊C8—591no—
269C4×C8C2×D5911yescharacteristic, complemented
270C24—1181no—
271#41—1182no—
272#41—1182no—
273#41—2361no—
274#41—2361no—
275C2×Q8—591no—
276C2×Q8—1181no—
277C2×Q8—1182no—
278C2×Q8—2361no—
279C2×Q8C22×D5911yescharacteristic
280C2×Q8C22×D5911yescharacteristic
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4—1182no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—2361no—
290C2×D4C22×D5911yescharacteristic
291C2×D4C22×D5911yescharacteristic
292C22×C4—591no—
293C22×C4—591no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4—1181no—
298Q16—22no—
299Q16—1182no—
300SD16—41no—
301SD16—41no—
302SD16—594no—
303SD16—1182no—
304SD16—1182no—
305D8—22no—
306D8—1182no—
307M16—1182no—
308M16—1182no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—591no—
314C4⋊C4—591no—
315C4⋊C4—591no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C4⋊C4—1181no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—591no—
324C22⋊C4—591no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C22⋊C4—1181no—
330C42—1181no—
331C42C22×D5911yescharacteristic
332C23—21no—
333C23—21no—
334C23—591no—
335C23—591no—
336C23—1181no—
337C23—4721no—
338C23—2362no—
339C23—2362no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—592no—
345Q8—1181no—
346Q8—2362no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—592no—
352D4—1181no—
353D4—4721no—
354D4—2361no—
355D4—2362no—
356D4—2362no—
357D4—2362no—
358D4—2362no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—591no—
362C2×C4—591no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—1181no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—4721no—
371C2×C4—2362no—
372C2×C4—2362no—
373C2×C4—2362no—
374C2×C4D4×D5911yescharacteristic
375C2×C4D4×D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—21no—
378C8—1181no—
379C8—1181no—
380C8D4×D5912yes—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—1181no—
388C22—1181no—
389C22—1181no—
390C22—1181no—
391C22—1181no—
392C22—1181no—
393C22—1182no—
394C22—4724no—
395C22—2361no—
396C22—2361no—
397C22C2×D4×D5911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1181no—
403C4—1181no—
404C4—1182no—
405C4—2361no—
406C4—2361no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377211yescharacteristic
409C2—81no—
410C2—81no—
411C2—2361no—
412C2—2361no—
413C2—2362no—
414C2#1683803711yescharacteristic
415C2#1683819911yescharacteristic
416C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#495C2
socleC22×C59C22×D4
hypercenter#495D59
hypocenterC59#3275
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#14273759C2semidirect
2. C2×#14273751C2semidirect
3. #16838060C2semidirect
4. #16838045C2semidirect
5. #16837657C2semidirect
6. #16837652C2semidirect
7. #16837621C2semidirect
8. #16837614C2semidirect
9. #16837561C2semidirect
10. #16837551C2semidirect
11. #16837546C2semidirect
12. #16837539C2semidirect
13. C4×#11745660C2semidirect
14. #16837481C2semidirect
15. C59×#495C2semidirect
18. C2×Q8×D59C22semidirect
22. C2×#11745672C22semidirect
28. C2×#11745659C22semidirect
37. #14273698C22semidirect
39. C4×Dic118C22semidirect
44. #14273659C22semidirect
45. C4⋊(C59⋊C8)C22semidirect
46. #14273652C22semidirect
47. #14273651C22semidirect
48. #14273651C22semidirect
51. #14273648C22semidirect
53. (C2×D59)⋊C8C22semidirect
54. C2×Q16×C59C22semidirect
56. C2×SD16×C59C22semidirect
59. #124×C59C22semidirect
60. C4×C8×C59C22semidirect
120. #11745660D4semidirect
213. #495D59semidirect
224. C59#3275semidirect
232. C2×Q16C2×D59semidirect
237. C2×SD16C2×D59semidirect
244. #124C2×D59semidirect
269. C4×C8C2×D59semidirect