Finite Group Databasebeta

← #21436120

Subgroups — #21436120

Order 7552.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838091C211yesmaximal, characteristic, complemented
2#16838036C211yesmaximal, characteristic
3#16837765C211yesmaximal, characteristic, complemented
4#16837717C211yesmaximal, characteristic, complemented
5#16837701C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837632C211yesmaximal, characteristic, complemented
8#16837601C211yesmaximal, characteristic, complemented
9#16837555C211yesmaximal, characteristic, complemented
10#16837554C211yesmaximal, characteristic, complemented
11#16837501C211yesmaximal, characteristic, complemented
12#16837476C211yesmaximal, characteristic, complemented
13#16837406C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#482C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×D4×D59—21no—
18C2×D4×D59C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745664C2211yescharacteristic, complemented
23C2×C8×D59C2211yescharacteristic, complemented
24#14273723C2211yescharacteristic
25#14273720—21no—
26#14273719—21no—
27#14273718C2211yescharacteristic, complemented
28#14273709—21no—
29#14273707C2211yescharacteristic, complemented
30#14273706C2211yescharacteristic, complemented
31#14273702C2211yescharacteristic
32#14273700—21no—
33#14273697—21no—
34#14273695—21no—
35#14273692C2211yescharacteristic, complemented
36#14273689C2211yescharacteristic
37C4×C22⋊D59C2211yescharacteristic
38#14273684—21no—
39C4⋊C4×D59C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273650C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic, complemented
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51#14273637C2211yescharacteristic, complemented
52#121×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic, complemented
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59D411yescharacteristic
68D4×D59—22no—
69D4×D59—41no—
70D4×D59—44no—
71C2×D236—22no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236—41no—
75C2×D236C2311yescharacteristic
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59C2311yescharacteristic
80C2×Dic118C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C42×C59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59D411yescharacteristic
91#11745670—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59C2311yescharacteristic
106#11745664—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745660—22no—
110#11745660—41no—
111C8×D59—41no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122C22×D59C2×D411yescharacteristic
123D4×C59—21no—
124D4×C59—21no—
125D4×C59—42no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—22no—
134C22⋊D59—42no—
135C22⋊D59—42no—
136C22⋊D59—81no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142D236—21no—
143D236—21no—
144D236—21no—
145D236—42no—
146D236—42no—
147D236#4112yes—
148C4×D59—21no—
149C4×D59—21no—
150C4×D59—42no—
151C4×D59—42no—
152Dic118—21no—
153Dic118—21no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—22no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—84no—
174C2×D59—84no—
175C2×D59AGL(1,ℤ/8)12yes—
176C4×C59—21no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59—41no—
180C4×C59C2×#4111yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—21no—
183Dic59—21no—
184Dic59—21no—
185Dic59—41no—
186Dic59—41no—
187#3310—591nomaximal, Sylow
188C2×C59—41no—
189C2×C59—81no—
190C2×C59#54611yescharacteristic
191C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C59#57711yescharacteristic
193D59—22no—
194D59—42no—
195D59—81no—
196#552—591no—
197D42—591no—
198#490—591no—
199#482D5911yescharacteristic, complemented
200#480—591no—
201#478—591no—
202#468—591no—
203#465—591no—
204#460—591no—
205#450—591no—
206#450—591no—
207#440—591no—
208#435—591no—
209#418—591no—
210C2×#102—591no—
211C59#331011yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C22×D4—591no—
214C22×D4—1181no—
215C2×SD16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×M16—591no—
219C22×C8—591no—
220#127—591no—
221#126—1181no—
222#125—591no—
223#125—1181no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227#121—591no—
228#121—1181no—
229#121C2×D5911yescharacteristic
230#120—1181no—
231#120—1181no—
232C4×Q8—591no—
233C4×D4—591no—
234C4×D4—591no—
235#117—1181no—
236#117C2×D5911yescharacteristic, complemented
237C2×C4⋊C4—591no—
238#107—591no—
239#107C2×D5911yescharacteristic, complemented
240#106C2×D5911yescharacteristic, complemented
241C4⋊C8—591no—
242#103—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102C2×D5911yescharacteristic, complemented
251#102C2×D5911yescharacteristic, complemented
252C22⋊C8—591no—
253C22⋊C8C2×D5911yescharacteristic, complemented
254#97—591no—
255C24—1181no—
256C24—1181no—
257C2×Q8—591no—
258C2×D4—21no—
259C2×D4—591no—
260C2×D4—591no—
261C2×D4—591no—
262C2×D4—1182no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1182no—
268C2×D4—1181no—
269C2×D4—2361no—
270C2×D4—2361no—
271C2×D4—2364no—
272C2×D4C22×D5911yescharacteristic
273C22×C4—591no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4C22×D5911yescharacteristic
277SD16—1182no—
278SD16—2361no—
279SD16—2361no—
280M16—2361no—
281C2×C8—591no—
282C2×C8—591no—
283C2×C8—2361no—
284C2×C8C22×D5911yescharacteristic
285C2×C8C22×D5911yescharacteristic
286C4⋊C4—591no—
287C4⋊C4—591no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4C22×D5911yescharacteristic
295C4⋊C4C22×D5911yescharacteristic
296C4⋊C4C22×D5911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—591no—
300C22⋊C4—591no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C42—21no—
306C42—591no—
307C42—1181no—
308C23—21no—
309C23—591no—
310C23—1181no—
311C23—1181no—
312C23—4721no—
313C23—4721no—
314C23—2362no—
315C23—2362no—
316C23—2362no—
317C23—2362no—
318C23D4×D5911yescharacteristic
319Q8—1181no—
320Q8—1181no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—592no—
325D4—1182no—
326D4—1181no—
327D4—1181no—
328D4—1181no—
329D4—4721no—
330D4—2362no—
331D4—2362no—
332D4—2362no—
333D4—2362no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—591no—
340C2×C4—591no—
341C2×C4—591no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—2362no—
347C2×C4—2362no—
348C2×C4D4×D5911yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1181no—
353C8—1181no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—592no—
361C22—1181no—
362C22—1181no—
363C22—1182no—
364C22—4724no—
365C22—4724no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22C2×D4×D5911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—1181no—
377C4—1181no—
378C4—1181no—
379C4—2361no—
380C4—2361no—
381C4#41×D5911yescharacteristic
382C4#1427377311yescharacteristic
383C2—41no—
384C2—81no—
385C2—1182no—
386C2—4721no—
387C2—2362no—
388C2#1683804411yescharacteristic
389C2AGL(1,ℤ/8)×D5911yescharacteristic
390C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#482C2
socleC22×C59C22×D4
hypercenter#482D59
hypocenterC59#3310
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. #16838091C2semidirect
3. #16837765C2semidirect
4. #16837717C2semidirect
5. #16837701C2semidirect
6. #16837646C2semidirect
7. #16837632C2semidirect
8. #16837601C2semidirect
9. #16837555C2semidirect
10. #16837554C2semidirect
11. #16837501C2semidirect
12. #16837476C2semidirect
13. #16837406C2semidirect
14. #102×D59C2semidirect
15. C59×#482C2semidirect
20. C2×#11745660C22semidirect
21. C2×#11745670C22semidirect
22. C2×#11745664C22semidirect
23. C2×C8×D59C22semidirect
27. #14273718C22semidirect
29. #14273707C22semidirect
30. #14273706C22semidirect
35. #14273692C22semidirect
39. C4⋊C4×D59C22semidirect
40. #14273660C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273650C22semidirect
44. #14273649C22semidirect
45. #14273648C22semidirect
48. #14273647C22semidirect
49. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. #14273637C22semidirect
53. #117×C59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. #102×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
199. #482D59semidirect
211. C59#3310semidirect
236. #117C2×D59semidirect
239. #107C2×D59semidirect
240. #106C2×D59semidirect
250. #102C2×D59semidirect
251. #102C2×D59semidirect
253. C22⋊C8C2×D59semidirect