Finite Group Databasebeta

← #21435732

Subgroups — #21435732

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×#14273760C211yesmaximal, characteristic, complemented
2C2×#14273755C211yesmaximal, characteristic, complemented
3#16838061C211yesmaximal, characteristic, complemented
4#16838048C211yesmaximal, characteristic, complemented
5#16837786C211yesmaximal, characteristic, complemented
6#16837660C211yesmaximal, characteristic, complemented
7#16837655C211yesmaximal, characteristic, complemented
8#16837625C211yesmaximal, characteristic, complemented
9#16837618C211yesmaximal, characteristic, complemented
10#16837566C211yesmaximal, characteristic, complemented
11#16837555C211yesmaximal, characteristic, complemented
12#16837549C211yesmaximal, characteristic, complemented
13#16837543C211yesmaximal, characteristic, complemented
14C4×#11745660C211yesmaximal, characteristic, complemented
15C59×#436C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18C22×Dic118C2211yescharacteristic, complemented
19C22×D236C2211yescharacteristic
20#14273760—24no—
21#14273755—24no—
22C2×Dic236C2211yescharacteristic, complemented
23C2×Dic236C2211yescharacteristic, complemented
24C2×#11745660C2211yescharacteristic
25C2×#11745660C2211yescharacteristic
26C2×#11745660C2211yescharacteristic
27C2×#11745660C2211yescharacteristic
28C2×#11745660C2211yescharacteristic, complemented
29C2×D472C2211yescharacteristic
30C2×D472C2211yescharacteristic
31#14273715C2211yescharacteristic
32#14273715C2211yescharacteristic, complemented
33#14273713—21no—
34#14273712—21no—
35#14273706C2211yescharacteristic
36#14273706C2211yescharacteristic
37#14273705—21no—
38#14273701C2211yescharacteristic
39#14273701C2211yescharacteristic, complemented
40#14273700—21no—
41#14273699—21no—
42#14273695—21no—
43C4×Dic118C2211yescharacteristic, complemented
44C4×D236C2211yescharacteristic
45(C22⋊D59)⋊C4—21no—
46C22⋊C4×D59—21no—
47#14273659C2211yescharacteristic, complemented
48#14273652C2211yescharacteristic, complemented
49#14273652C2211yescharacteristic, complemented
50#14273652C2211yescharacteristic, complemented
51#14273649C2211yescharacteristic
52#14273649C2211yescharacteristic
53#14273649C2211yescharacteristic, complemented
54C2×M16×C59C2211yescharacteristic
55C2×M16×C59C2211yescharacteristic, complemented
56C4×D4×C59C2211yescharacteristic
57C4⋊C8×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C22⋊C8×C59C2211yescharacteristic, complemented
60C4×C8×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×D4×C59D411yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C22×Dic59—21no—
70#11745685—22no—
71#11745685—22no—
72#11745685—41no—
73#11745685—41no—
74C2×D236—22no—
75C2×D236—21no—
76C2×D236—41no—
77C2×D236C2311yescharacteristic
78C2×D236C2311yescharacteristic
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59—21no—
83C2×Dic118—22no—
84C2×Dic118—21no—
85C2×Dic118—41no—
86C2×Dic118C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88C2×Dic118C2311yescharacteristic
89M16×C59—22no—
90M16×C59—22no—
91C2×C8×C59C2311yescharacteristic
92C2×C8×C59C2311yescharacteristic
93C2×C8×C59C2311yescharacteristic
94C2×C8×C59C2311yescharacteristic
95C4⋊C4×C59D411yescharacteristic
96C22⋊C4×C59D411yescharacteristic
97C22⋊C4×C59D411yescharacteristic
98C42×C59C2311yescharacteristic
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108C4⋊Dic59C2311yescharacteristic
109C4⋊Dic59C2311yescharacteristic
110Dic59⋊C4—21no—
111Dic59⋊C4—21no—
112Dic59⋊C4—21no—
113C4×Dic59—21no—
114Dic236—22no—
115Dic236—22no—
116D472—22no—
117D472—22no—
118#11745660—22no—
119#11745660—22no—
120#11745660—41no—
121#11745660—41no—
122#11745660D414yescomplemented
123C23×C59C2×D411yescharacteristic
124C23×C59C2×D411yescharacteristic
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—42no—
129C22×D59—42no—
130C22×D59—81no—
131D4×C59—41no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2411yescharacteristic
141C22⋊D59—42no—
142C22⋊D59—42no—
143C22⋊D59—42no—
144C22⋊D59—81no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—42no—
151D236—21no—
152D236—21no—
153D236—21no—
154D236—21no—
155D236—21no—
156D236—42no—
157D236C2×D412yes—
158C4×D59—42no—
159C4×D59—42no—
160C4×D59—81no—
161Dic118—21no—
162Dic118—21no—
163Dic118—21no—
164Dic118—21no—
165Dic118—21no—
166Dic118—42no—
167Dic118C2×D412yes—
168C8×C59—21no—
169C8×C59—21no—
170C8×C59—21no—
171C8×C59C2×D412yes—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—21no—
178C22×C59C22×D411yescharacteristic
179C2×D59—22no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—21no—
192C4×C59—21no—
193C4×C59C22×D411yescharacteristic
194C4×C59H(5,𝔽2)11yescharacteristic
195Dic59—22no—
196Dic59—41no—
197Dic59—41no—
198Dic59—41no—
199Dic59—41no—
200#3275—591nomaximal, Sylow
201C2×C59—41no—
202C2×C59—41no—
203C2×C59D4211yescharacteristic
204C2×C59#57511yescharacteristic
205C2×C59#57711yescharacteristic
206D59—42no—
207D59—81no—
208D59—81no—
209C2×#137—591no—
210C2×AGL(1,ℤ/8)—591no—
211#548—591no—
212#546—591no—
213#495—591no—
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#436D5911yescharacteristic, complemented
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×Q16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16—591no—
237C2×SD16—591no—
238C2×D8—591no—
239C2×D8—591no—
240C2×M16C2×D5911yescharacteristic
241C2×M16C2×D5911yescharacteristic, complemented
242#124—591no—
243#124—591no—
244#124—1181no—
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—1181no—
257C4×D4C2×D5911yescharacteristic
258C2×C22⋊C4—1181no—
259#106—591no—
260C4⋊C8C2×D5911yescharacteristic, complemented
261#103—591no—
262#103—591no—
263#103—591no—
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8C2×D5911yescharacteristic
268C22⋊C8C2×D5911yescharacteristic, complemented
269C4×C8C2×D5911yescharacteristic, complemented
270C24—1181no—
271#41—1182no—
272#41—1182no—
273#41—2361no—
274#41—2361no—
275C2×Q8—591no—
276C2×Q8—591no—
277C2×Q8—591no—
278C2×Q8—1182no—
279C2×Q8—1181no—
280C2×Q8—2361no—
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—591no—
284C2×D4—1182no—
285C2×D4—1181no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—1181no—
290C2×D4—2361no—
291C2×D4D23611yescharacteristic
292C22×C4—1181no—
293C22×C4—1181no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4C22×D5911yescharacteristic
297C22×C4C22×D5911yescharacteristic
298Q16—1182no—
299Q16—1182no—
300SD16—594no—
301SD16—1182no—
302SD16—1182no—
303SD16—2361no—
304SD16—2361no—
305D8—1182no—
306D8—1182no—
307M16—22no—
308M16—22no—
309C2×C8C22×D5911yescharacteristic
310C2×C8C22×D5911yescharacteristic
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—591no—
314C4⋊C4—591no—
315C4⋊C4—1181no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C4⋊C4D23611yescharacteristic
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4D23611yescharacteristic
329C22⋊C4D23611yescharacteristic
330C42—1181no—
331C42C22×D5911yescharacteristic
332C23—1181no—
333C23—1181no—
334C23—1181no—
335C23—4721no—
336C23—2362no—
337C23—2362no—
338C23C2×D23611yescharacteristic
339C23C2×D23611yescharacteristic
340Q8—592no—
341Q8—1181no—
342Q8—1181no—
343Q8—1181no—
344Q8—1181no—
345Q8—1181no—
346Q8—2362no—
347D4—41no—
348D4—592no—
349D4—1181no—
350D4—1181no—
351D4—1181no—
352D4—1181no—
353D4—1181no—
354D4—4721no—
355D4—2362no—
356D4—2362no—
357D4—2362no—
358D4—2362no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—1181no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—4721no—
369C2×C4—2362no—
370C2×C4—2362no—
371C2×C4—2362no—
372C2×C4C2×D23611yescharacteristic
373C2×C4C2×D23611yescharacteristic
374C2×C4C2×D23611yescharacteristic
375C2×C4C2×D23611yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D5912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—1182no—
388C22—4724no—
389C22—2361no—
390C22—2361no—
391C22—2361no—
392C22—2361no—
393C22—2361no—
394C22—2361no—
395C22—2361no—
396C22—2361no—
397C22C22×D23611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—1182no—
403C4—2361no—
404C4—2361no—
405C4—2361no—
406C4—2361no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377311yescharacteristic
409C2—41no—
410C2—41no—
411C2—4721no—
412C2—4721no—
413C2—2362no—
414C2D4×D23611yescharacteristic
415C2#1683820211yescharacteristic
416C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#436C2
socleC22×C59C22×D4
hypercenter#436D59
hypocenterC59#3275
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14273760C2semidirect
2. C2×#14273755C2semidirect
3. #16838061C2semidirect
4. #16838048C2semidirect
5. #16837786C2semidirect
6. #16837660C2semidirect
7. #16837655C2semidirect
8. #16837625C2semidirect
9. #16837618C2semidirect
10. #16837566C2semidirect
11. #16837555C2semidirect
12. #16837549C2semidirect
13. #16837543C2semidirect
14. C4×#11745660C2semidirect
15. C59×#436C2semidirect
18. C22×Dic118C22semidirect
22. C2×Dic236C22semidirect
23. C2×Dic236C22semidirect
28. C2×#11745660C22semidirect
32. #14273715C22semidirect
39. #14273701C22semidirect
43. C4×Dic118C22semidirect
47. #14273659C22semidirect
48. #14273652C22semidirect
49. #14273652C22semidirect
50. #14273652C22semidirect
53. #14273649C22semidirect
55. C2×M16×C59C22semidirect
57. C4⋊C8×C59C22semidirect
59. C22⋊C8×C59C22semidirect
60. C4×C8×C59C22semidirect
122. #11745660D4semidirect
223. #436D59semidirect
224. C59#3275semidirect
241. C2×M16C2×D59semidirect
260. C4⋊C8C2×D59semidirect
268. C22⋊C8C2×D59semidirect
269. C4×C8C2×D59semidirect