Finite Group Databasebeta

← #21435190

Subgroups — #21435190

Order 7552.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838023C211yesmaximal, characteristic, complemented
2#16837789C211yesmaximal, characteristic, complemented
3#16837784C211yesmaximal, characteristic, complemented
4#16837761C211yesmaximal, characteristic, complemented
5#16837748C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837599C211yesmaximal, characteristic, complemented
9#16837594C211yesmaximal, characteristic, complemented
10#16837564C211yesmaximal, characteristic, complemented
11#16837553C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837536C211yesmaximal, characteristic, complemented
14#16837463C211yesmaximal, characteristic, complemented
15C59×#535C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic, complemented
17C2×#11745670C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745670C2211yescharacteristic, complemented
20C2×#11745671C2211yescharacteristic, complemented
21C2×#11745669C2211yescharacteristic
22C2×#11745669C2211yescharacteristic
23C2×#11745669C2211yescharacteristic, complemented
24#14273727C2211yescharacteristic, complemented
25#14273722—21no—
26#14273715C2211yescharacteristic, complemented
27#14273713—21no—
28#14273709—21no—
29#14273706C2211yescharacteristic
30#14273705—21no—
31#14273701C2211yescharacteristic
32C4×Dic118C2211yescharacteristic, complemented
33C4×D236C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35C4⋊(C59⋊C8)C2211yescharacteristic, complemented
36#14273651C2211yescharacteristic, complemented
37#14273651C2211yescharacteristic, complemented
38#14273648C2211yescharacteristic
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic, complemented
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46#14273638C2211yescharacteristic, complemented
47C4×C59⋊C8C2211yescharacteristic, complemented
48C2×#41×C59C2211yescharacteristic
49C22×D4×C59C2211yescharacteristic
50#127×C59C2211yescharacteristic
51#127×C59C2211yescharacteristic
52#124×C59C2211yescharacteristic
53#124×C59C2211yescharacteristic
54#121×C59—21no—
55#121×C59—21no—
56#120×C59—21no—
57#120×C59—21no—
58#117×C59C2211yescharacteristic
59C24×C59—21no—
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
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×C59C2311yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C2×D4×C59C2311yescharacteristic
74C22×C4×C59—21no—
75C22×C4×C59C2311yescharacteristic
76C2×C22⋊D59—21no—
77C2×D236C2311yescharacteristic
78C2×C4×D59—21no—
79C2×Dic118—21no—
80C2×Dic118C2311yescharacteristic
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59D411yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59C2311yescharacteristic
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92#11745672—41no—
93#11745671—41no—
94#11745670—41no—
95#11745670—41no—
96#11745670—41no—
97#11745669—41no—
98#11745669—41no—
99#11745669—41no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104C4⋊Dic59—21no—
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59—42no—
118C23×C59—81no—
119C23×C59—81no—
120C23×C59C2×D411yescharacteristic
121C22×D59—21no—
122Q8×C59—21no—
123Q8×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—21no—
130D4×C59—42no—
131D4×C59—42no—
132D4×C59—81no—
133D4×C59—81no—
134D4×C59—81no—
135D4×C59—81no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—42no—
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2×D411yescharacteristic
144C2×C4×C59C2×D411yescharacteristic
145C2×C4×C59C2411yescharacteristic
146C22⋊D59—81no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150D236—21no—
151D236—21no—
152C4×D59—81no—
153Dic118—21no—
154Dic118—21no—
155Dic118—81no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—41no—
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×C59C22×D411yescharacteristic
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—41no—
183C4×C59H(5,𝔽2)11yescharacteristic
184C4×C59H(5,𝔽2)11yescharacteristic
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188#3224—591nomaximal, Sylow
189C2×C59—41no—
190C2×C59—81no—
191C2×C59—81no—
192C2×C59—81no—
193C2×C59#53511yescharacteristic
194C2×C59#57611yescharacteristic
195C2×C59#57711yescharacteristic
196D59—81no—
197#542—591no—
198#535D5911yescharacteristic, complemented
199#496—591no—
200#495—591no—
201#489—591no—
202#486—591no—
203#464—591no—
204#463—591no—
205#460—591no—
206#459—591no—
207#452—591no—
208#450—591no—
209#449—591no—
210#447—591no—
211#433—591no—
212C59#322411yescharacteristic, complemented, Sylow
213C2×#41C2×D5911yescharacteristic
214C22×D4C2×D5911yescharacteristic
215C2×Q16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×SD16—591no—
219C2×SD16—591no—
220C2×D8—591no—
221C2×D8—591no—
222C2×D8—591no—
223C4⋊Q8—591no—
224#127C2×D5911yescharacteristic
225#127C2×D5911yescharacteristic
226#126—1181no—
227#124—591no—
228#124—1181no—
229#124C2×D5911yescharacteristic
230#124C2×D5911yescharacteristic
231#123—1181no—
232C22⋊Q8—591no—
233C22⋊Q8—1181no—
234#121—21no—
235#121—21no—
236#121—591no—
237#120—21no—
238#120—21no—
239C4×Q8—591no—
240C4×D4—591no—
241#117C2×D5911yescharacteristic
242C4⋊C8—591no—
243C4⋊C8—591no—
244#103—591no—
245#103—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—
255C4×C8—591no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—591no—
260C2×Q8—1181no—
261C2×Q8C22×D5911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—591no—
271C2×D4—1181no—
272C2×D4C22×D5911yescharacteristic
273C2×D4C22×D5911yescharacteristic
274C2×D4C22×D5911yescharacteristic
275C22×C4—21no—
276C22×C4—1181no—
277C22×C4C22×D5911yescharacteristic
278Q16—2361no—
279SD16—2361no—
280SD16—2361no—
281SD16—2361no—
282SD16—2361no—
283D8—2361no—
284D8—2361no—
285D8—2361no—
286C2×C8—591no—
287C2×C8—591no—
288C2×C8—591no—
289C2×C8—591no—
290C4⋊C4—591no—
291C4⋊C4—591no—
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—21no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4C22⋊D5911yescharacteristic
307C22⋊C4C22⋊D5911yescharacteristic
308C42—1181no—
309C42C22×D5911yescharacteristic
310C42C22×D5911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1181no—
318C23C2×C22⋊D5911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—1181no—
322Q8—1181no—
323Q8—4721no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—1181no—
337D4—1181no—
338D4—4721no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—4721no—
347C2×C4C2×C22⋊D5911yescharacteristic
348C2×C4C2×C22⋊D5911yescharacteristic
349C2×C4C2×C22⋊D5911yescharacteristic
350C2×C4C2×C22⋊D5911yescharacteristic
351C2×C4C2×C22⋊D5911yescharacteristic
352C2×C4C23×D5911yescharacteristic
353C8—1181no—
354C8—1181no—
355C8—1181no—
356C8—1181no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22C22×C22⋊D5911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—2361no—
381C4—2361no—
382C4—2361no—
383C4#1427377211yescharacteristic
384C4#1427377211yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—4721no—
390C2#1683796911yescharacteristic
391C2#1683820511yescharacteristic
392C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#535C2
socleC22×C59C22×D4
hypercenter#535D59
hypocenterC59#3224
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837789C2semidirect
3. #16837784C2semidirect
4. #16837761C2semidirect
5. #16837748C2semidirect
6. #16837621C2semidirect
7. #16837614C2semidirect
8. #16837599C2semidirect
9. #16837594C2semidirect
10. #16837564C2semidirect
11. #16837553C2semidirect
12. #16837547C2semidirect
13. #16837536C2semidirect
14. #16837463C2semidirect
15. C59×#535C2semidirect
16. C2×#11745672C22semidirect
19. C2×#11745670C22semidirect
20. C2×#11745671C22semidirect
23. C2×#11745669C22semidirect
24. #14273727C22semidirect
26. #14273715C22semidirect
32. C4×Dic118C22semidirect
33. C4×D236C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. C4⋊(C59⋊C8)C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
42. #14273648C22semidirect
43. #14273648C22semidirect
46. #14273638C22semidirect
47. C4×C59⋊C8C22semidirect
198. #535D59semidirect
212. C59#3224semidirect