Finite Group Databasebeta

← #21435187

Subgroups — #21435187

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#16838017C211yesmaximal, characteristic, complemented
2#16837965C211yesmaximal, characteristic, complemented
3#16837790C211yesmaximal, characteristic, complemented
4#16837785C211yesmaximal, characteristic, complemented
5#16837760C211yesmaximal, characteristic, complemented
6#16837747C211yesmaximal, characteristic, complemented
7#16837625C211yesmaximal, characteristic, complemented
8#16837617C211yesmaximal, characteristic, complemented
9#16837599C211yesmaximal, characteristic, complemented
10#16837565C211yesmaximal, characteristic, complemented
11#16837554C211yesmaximal, characteristic, complemented
12#16837544C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837462C211yesmaximal, characteristic, complemented
15C59×#459C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×Dic236C2211yescharacteristic, complemented
19C2×#11745660C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic, complemented
23C2×#11745669C2211yescharacteristic
24#14273726C2211yescharacteristic, complemented
25#14273723C2211yescharacteristic
26#14273720—21no—
27#14273715C2211yescharacteristic
28#14273714C2211yescharacteristic
29#14273714C2211yescharacteristic, complemented
30#14273713—21no—
31#14273710—21no—
32#14273707C2211yescharacteristic
33#14273706—21no—
34#14273699—21no—
35#14273699—21no—
36#14273698C2211yescharacteristic
37#14273695—21no—
38#14273695—21no—
39C4×Dic118C2211yescharacteristic, complemented
40#14273684C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C2×D8×C59C2211yescharacteristic
53C2×D8×C59C2211yescharacteristic, complemented
54#127×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C22×Dic59—21no—
72#11745687—41no—
73#11745687—41no—
74D4×D59—41no—
75D4×D59—41no—
76C2×D236C2311yescharacteristic
77C2×C4×D59C2311yescharacteristic
78C2×Dic118—21no—
79C2×Dic118C2311yescharacteristic
80C2×Dic118C2311yescharacteristic
81D8×C59—41no—
82D8×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93#11745670—41no—
94#11745670—41no—
95#11745670—41no—
96#11745669—41no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4D411yescharacteristic
101(C2×D59)⋊C4D411yescharacteristic
102C4⋊Dic59—21no—
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4D411yescharacteristic
107Dic59⋊C4D411yescharacteristic
108C4×Dic59—21no—
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112Dic236—41no—
113#11745660—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C22×D59—21no—
118C22×D59—42no—
119C22×D59—81no—
120C22×D59—81no—
121C22×D59C2×D411yescharacteristic
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—81no—
129D4×C59—81no—
130C2×C4×C59—21no—
131C2×C4×C59—81no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—42no—
136C22⋊D59—42no—
137C22⋊D59—81no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—42no—
144C2×Dic59C2×D411yescharacteristic
145C2×Dic59C2×D411yescharacteristic
146C2×Dic59C2×D411yescharacteristic
147D236—21no—
148D236—21no—
149C4×D59—21no—
150C4×D59—21no—
151Dic118—21no—
152Dic118—21no—
153Dic118—21no—
154Dic118—21no—
155Dic118—81no—
156C8×C59—21no—
157C8×C59—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59C22×D411yescharacteristic
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—84no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59H(5,𝔽2)11yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—21no—
183Dic59—21no—
184Dic59—21no—
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188#3224—591nomaximal, Sylow
189C2×C59—81no—
190C2×C59—81no—
191C2×C59—81no—
192C2×C59#53511yescharacteristic
193C2×C59#57611yescharacteristic
194C2×C59#57711yescharacteristic
195D59—41no—
196D59—81no—
197#542—591no—
198#535—591no—
199#496—591no—
200#495—591no—
201#489—591no—
202#486—591no—
203#464—591no—
204#463—591no—
205#460—591no—
206#459D5911yescharacteristic, complemented
207#452—591no—
208#450—591no—
209#449—591no—
210#447—591no—
211#433—591no—
212C59#322411yescharacteristic, complemented, Sylow
213C2×#41—591no—
214C22×D4—591no—
215C2×Q16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×SD16—591no—
219C2×SD16—591no—
220C2×D8—591no—
221C2×D8C2×D5911yescharacteristic
222C2×D8C2×D5911yescharacteristic, complemented
223C4⋊Q8—591no—
224#127—591no—
225#127C2×D5911yescharacteristic
226#126—1181no—
227#124—591no—
228#124—591no—
229#124—591no—
230#124—1181no—
231#123—1181no—
232C22⋊Q8—591no—
233C22⋊Q8—1181no—
234#121—591no—
235#121—1181no—
236#121—1181no—
237#120—1181no—
238#120—1181no—
239C4×Q8—591no—
240C4×D4C2×D5911yescharacteristic, complemented
241#117—591no—
242C4⋊C8—591no—
243C4⋊C8C2×D5911yescharacteristic, complemented
244#103—591no—
245#103—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102C2×D5911yescharacteristic
251#102C2×D5911yescharacteristic, complemented
252C22⋊C8—591no—
253C22⋊C8—591no—
254#97—591no—
255C4×C8—591no—
256C24—1181no—
257#41—2361no—
258#41—2361no—
259C2×Q8—591no—
260C2×Q8—591no—
261C2×Q8—1181no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—591no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—2361no—
271C2×D4—2361no—
272C2×D4C22×D5911yescharacteristic
273C2×D4C22×D5911yescharacteristic
274C2×D4C22×D5911yescharacteristic
275C22×C4—21no—
276C22×C4—591no—
277C22×C4—1181no—
278Q16—2361no—
279SD16—2361no—
280SD16—2361no—
281SD16—2361no—
282SD16—2361no—
283D8—41no—
284D8—41no—
285D8—2361no—
286C2×C8—591no—
287C2×C8—591no—
288C2×C8C22×D5911yescharacteristic
289C2×C8C22×D5911yescharacteristic
290C4⋊C4—591no—
291C4⋊C4—591no—
292C4⋊C4—591no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4—1181no—
296C4⋊C4C22×D5911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—591no—
299C22⋊C4—591no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C42—591no—
309C42—1181no—
310C42C22×D5911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—591no—
315C23—1181no—
316C23—4721no—
317C23—4721no—
318C23—2362no—
319Q8—1181no—
320Q8—1181no—
321Q8—1181no—
322Q8—1181no—
323Q8—4721no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—1181no—
333D4—1181no—
334D4—4721no—
335D4—4721no—
336D4—4721no—
337D4—2362no—
338D4—2362no—
339C2×C4—21no—
340C2×C4—81no—
341C2×C4—591no—
342C2×C4—591no—
343C2×C4—591no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—2362no—
350C2×C4D4×D5911yescharacteristic
351C2×C4D4×D5911yescharacteristic
352C2×C4C23×D5911yescharacteristic
353C8—21no—
354C8—21no—
355C8—1181no—
356C8—1181no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—1181no—
367C22—1181no—
368C22—1181no—
369C22—4724no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22C2×D4×D5911yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—1181no—
378C4—1181no—
379C4—1181no—
380C4—2361no—
381C4—2361no—
382C4—2361no—
383C4#1427377211yescharacteristic
384C4#1427377311yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—4721no—
389C2—2361no—
390C2#1683796811yescharacteristic
391C2#1683820311yescharacteristic
392C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3224
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16838017C2semidirect
2. #16837965C2semidirect
3. #16837790C2semidirect
4. #16837785C2semidirect
5. #16837760C2semidirect
6. #16837747C2semidirect
7. #16837625C2semidirect
8. #16837617C2semidirect
9. #16837599C2semidirect
10. #16837565C2semidirect
11. #16837554C2semidirect
12. #16837544C2semidirect
13. #16837534C2semidirect
14. #16837462C2semidirect
15. C59×#459C2semidirect
18. C2×Dic236C22semidirect
21. C2×#11745670C22semidirect
22. C2×#11745670C22semidirect
24. #14273726C22semidirect
29. #14273714C22semidirect
39. C4×Dic118C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273650C22semidirect
46. #14273648C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
53. C2×D8×C59C22semidirect
55. C4×D4×C59C22semidirect
56. C4⋊C8×C59C22semidirect
58. #102×C59C22semidirect
206. #459D59semidirect
212. C59#3224semidirect
222. C2×D8C2×D59semidirect
240. C4×D4C2×D59semidirect
243. C4⋊C8C2×D59semidirect
251. #102C2×D59semidirect