Finite Group Databasebeta

← #21436117

Subgroups — #21436117

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#16838092C211yesmaximal, characteristic, complemented
2#16837766C211yesmaximal, characteristic, complemented
3#16837723C211yesmaximal, characteristic, complemented
4#16837713C211yesmaximal, characteristic, complemented
5#16837702C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837599C211yesmaximal, characteristic, complemented
9#16837553C211yesmaximal, characteristic, complemented
10#16837553C211yesmaximal, characteristic, complemented
11#16837502C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837407C211yesmaximal, characteristic, complemented
14C2×#14273648C211yesmaximal, characteristic, complemented
15D42×C59C211yesmaximal, characteristic
16C2×#11745670C2211yescharacteristic
17C2×#11745670C2211yescharacteristic, complemented
18C2×#11745670C2211yescharacteristic, complemented
19C2×#11745664C2211yescharacteristic, complemented
20C22×C59⋊C8C2211yescharacteristic, complemented
21#14273720—21no—
22#14273719C2211yescharacteristic, complemented
23#14273717—21no—
24#14273708—21no—
25#14273706C2211yescharacteristic, complemented
26#14273706C2211yescharacteristic, complemented
27C4×Dic118C2211yescharacteristic, complemented
28#14273686C2211yescharacteristic, complemented
29#14273683—21no—
30C2×C4⋊Dic59C2211yescharacteristic, complemented
31#14273660C2211yescharacteristic, complemented
32#14273660C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273650C2211yescharacteristic, complemented
36#14273648C2211yescharacteristic
37#14273648C2211yescharacteristic
38#14273648C2211yescharacteristic
39#14273648C2211yescharacteristic, complemented
40#14273648C2211yescharacteristic, complemented
41#14273648C2211yescharacteristic, complemented
42#14273648C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic, complemented
45C22⋊(C59⋊C8)C2211yescharacteristic, complemented
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47#14273638C2211yescharacteristic, complemented
48C22×D4×C59—21no—
49C22×D4×C59C2211yescharacteristic
50C22×D4×C59C2211yescharacteristic
51#127×C59C2211yescharacteristic
52#121×C59—21no—
53#121×C59C2211yescharacteristic
54#121×C59C2211yescharacteristic
55#120×C59—21no—
56#120×C59—21no—
57C4×D4×C59C2211yescharacteristic
58C4×D4×C59C2211yescharacteristic
59C24×C59—21no—
60C24×C59—21no—
61C2×D4×C59—22no—
62C2×D4×C59—22no—
63C2×D4×C59—21no—
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—41no—
70C2×D4×C59—41no—
71C2×D4×C59—44no—
72C2×D4×C59D411yescharacteristic
73C2×D4×C59C2311yescharacteristic
74C2×D4×C59C2311yescharacteristic
75C2×D4×C59C2311yescharacteristic
76C22×C4×C59—21no—
77C22×C4×C59C2311yescharacteristic
78C22×C4×C59C2311yescharacteristic
79C22×Dic59—21no—
80C2×Dic118C2311yescharacteristic
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59D411yescharacteristic
87C22⋊C4×C59D411yescharacteristic
88C42×C59C2311yescharacteristic
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92#11745670—22no—
93#11745670—41no—
94#11745670—41no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106#11745664—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—21no—
115C23×C59—42no—
116C23×C59—42no—
117C23×C59—42no—
118C23×C59—42no—
119C23×C59—81no—
120C23×C59—81no—
121C23×C59C2×D411yescharacteristic
122C23×C59C2×D411yescharacteristic
123D4×C59—22no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—42no—
130D4×C59—42no—
131D4×C59—42no—
132D4×C59—42no—
133D4×C59—42no—
134D4×C59—81no—
135D4×C59#4112yes—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—42no—
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2×D411yescharacteristic
144C2×C4×C59C2×D411yescharacteristic
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2411yescharacteristic
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—42no—
152Dic118—21no—
153Dic118—21no—
154C59⋊C8—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—22no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—84no—
173C22×C59—84no—
174C22×C59AGL(1,ℤ/8)12yes—
175C22×C59C22×D411yescharacteristic
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—41no—
181C4×C59C2×#4111yescharacteristic
182C4×C59H(5,𝔽2)11yescharacteristic
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186Dic59—41no—
187#3310—591nomaximal, Sylow
188C2×C59—22no—
189C2×C59—41no—
190C2×C59—42no—
191C2×C59—81no—
192C2×C59—81no—
193C2×C59#54611yescharacteristic
194C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C59#57711yescharacteristic
196#552—591no—
197D42D5911yescharacteristic
198#490—591no—
199#482—591no—
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—21no—
213C22×D4C2×D5911yescharacteristic
214C22×D4C2×D5911yescharacteristic
215C2×SD16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×M16—591no—
219C22×C8—591no—
220#127C2×D5911yescharacteristic
221#126—1181no—
222#125—591no—
223#125—1181no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227#121—21no—
228#121C2×D5911yescharacteristic
229#121C2×D5911yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—591no—
233C4×D4C2×D5911yescharacteristic
234C4×D4C2×D5911yescharacteristic
235#117—591no—
236#117—1181no—
237C2×C4⋊C4—591no—
238#107—591no—
239#107—591no—
240#106—591no—
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#102—591no—
251#102—591no—
252C22⋊C8—591no—
253C22⋊C8—591no—
254#97—591no—
255C24—21no—
256C24—21no—
257C2×Q8—591no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D5911yescharacteristic
270C2×D4C22×D5911yescharacteristic
271C2×D4C22×D5911yescharacteristic
272C2×D4C22×D5911yescharacteristic
273C22×C4—21no—
274C22×C4—1181no—
275C22×C4C22×D5911yescharacteristic
276C22×C4C22×D5911yescharacteristic
277SD16—1182no—
278SD16—2361no—
279SD16—2361no—
280M16—2361no—
281C2×C8—591no—
282C2×C8—591no—
283C2×C8—591no—
284C2×C8—591no—
285C2×C8—2361no—
286C4⋊C4—591no—
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4C22⋊D5911yescharacteristic
296C4⋊C4C22×D5911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4C22⋊D5911yescharacteristic
304C22⋊C4C22⋊D5911yescharacteristic
305C42—1181no—
306C42—1181no—
307C42C22×D5911yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D5911yescharacteristic
318C23C2×C22⋊D5911yescharacteristic
319Q8—1181no—
320Q8—1181no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1174568712yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—2362no—
345C2×C4C2×C22⋊D5911yescharacteristic
346C2×C4C2×C22⋊D5911yescharacteristic
347C2×C4C2×C22⋊D5911yescharacteristic
348C2×C4C2×C22⋊D5911yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—1181no—
351C8—1181no—
352C8—1181no—
353C8—1181no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1427375312yes—
371C22C22×C22⋊D5911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—2361no—
378C4—2361no—
379C4—2361no—
380C4—2361no—
381C4C2×#1174568711yescharacteristic
382C4#1427377211yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1683804611yescharacteristic
389C2C2×#1427375311yescharacteristic
390C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD42×C59C2
socleC22×C59C22×D4
hypercenterD42D59
hypocenterC59#3310
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #16838092C2semidirect
2. #16837766C2semidirect
3. #16837723C2semidirect
4. #16837713C2semidirect
5. #16837702C2semidirect
6. #16837646C2semidirect
7. #16837629C2semidirect
8. #16837599C2semidirect
9. #16837553C2semidirect
10. #16837553C2semidirect
11. #16837502C2semidirect
12. #16837474C2semidirect
13. #16837407C2semidirect
14. C2×#14273648C2semidirect
17. C2×#11745670C22semidirect
18. C2×#11745670C22semidirect
19. C2×#11745664C22semidirect
20. C22×C59⋊C8C22semidirect
22. #14273719C22semidirect
25. #14273706C22semidirect
26. #14273706C22semidirect
27. C4×Dic118C22semidirect
28. #14273686C22semidirect
30. C2×C4⋊Dic59C22semidirect
31. #14273660C22semidirect
32. #14273660C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273650C22semidirect
39. #14273648C22semidirect
40. #14273648C22semidirect
41. #14273648C22semidirect
42. #14273648C22semidirect
43. #14273648C22semidirect
44. #14273648C22semidirect
45. C22⋊(C59⋊C8)C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. #14273638C22semidirect
211. C59#3310semidirect