Finite Group Databasebeta

← #21435188

Subgroups — #21435188

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#16838019C211yesmaximal, characteristic, complemented
2#16837966C211yesmaximal, characteristic, complemented
3#16837790C211yesmaximal, characteristic, complemented
4#16837783C211yesmaximal, characteristic, complemented
5#16837763C211yesmaximal, characteristic, complemented
6#16837747C211yesmaximal, characteristic, complemented
7#16837627C211yesmaximal, characteristic, complemented
8#16837619C211yesmaximal, characteristic, complemented
9#16837601C211yesmaximal, characteristic, complemented
10#16837595C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837555C211yesmaximal, characteristic, complemented
13#16837535C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×#11745672C2211yescharacteristic, complemented
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745670C2211yescharacteristic, complemented
21C2×#11745669C2211yescharacteristic
22C2×#11745669C2211yescharacteristic
23#14273726C2211yescharacteristic, complemented
24#14273723C2211yescharacteristic
25#14273723C2211yescharacteristic
26#14273720—21no—
27#14273716C2211yescharacteristic
28#14273716C2211yescharacteristic
29#14273714—21no—
30#14273714C2211yescharacteristic, complemented
31#14273708—21no—
32#14273706C2211yescharacteristic
33#14273704—21no—
34#14273701—21no—
35#14273701—21no—
36#14273695—21no—
37#14273695—21no—
38#14273692C2211yescharacteristic, complemented
39D4×Dic59C2211yescharacteristic, complemented
40#14273686C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C2×#41×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic, complemented
54C2×D8×C59C2211yescharacteristic, complemented
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59—21no—
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C22×C4×C59—21no—
68C22×C4×C59C2311yescharacteristic
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C22×Dic59—21no—
74C2×D236—21no—
75C2×D236—41no—
76C2×D236—41no—
77C2×D236C2311yescharacteristic
78C2×D236C2311yescharacteristic
79C2×Dic118—21no—
80C2×Dic118C2311yescharacteristic
81SD16×C59—41no—
82D8×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59D411yescharacteristic
92C22⋊Dic59D411yescharacteristic
93#11745672—41no—
94#11745670—41no—
95#11745669—41no—
96#11745669—41no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101C4⋊Dic59D411yescharacteristic
102C4⋊Dic59D411yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108C4×Dic59C2311yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745660—41no—
113#11745660—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59C2×D411yescharacteristic
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122Q8×C59—21no—
123Q8×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—42no—
129D4×C59—81no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—42no—
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C22⋊D59—81no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C22⋊D59—81no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—81no—
144C2×Dic59C2×D411yescharacteristic
145C2×Dic59C2×D411yescharacteristic
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148D236—21no—
149D236—21no—
150D236—21no—
151D236—21no—
152D236—42no—
153Dic118—21no—
154Dic118—21no—
155Dic118—81no—
156C8×C59—21no—
157C8×C59—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×C59C22×D411yescharacteristic
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—84no—
177C4×C59—21no—
178C4×C59—41no—
179C4×C59—41no—
180C4×C59H(5,𝔽2)11yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—21no—
183Dic59—21no—
184Dic59—21no—
185Dic59—21no—
186Dic59—41no—
187Dic59—41no—
188#3224—591nomaximal, Sylow
189C2×C59—41no—
190C2×C59—81no—
191C2×C59—81no—
192C2×C59#53511yescharacteristic
193C2×C59#57611yescharacteristic
194C2×C59#57711yescharacteristic
195D59—81no—
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#459—591no—
207#452—591no—
208#450—591no—
209#449D5911yescharacteristic, complemented
210#447—591no—
211#433—591no—
212C59#322411yescharacteristic, complemented, Sylow
213C2×#41C2×D5911yescharacteristic
214C22×D4—591no—
215C2×Q16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×SD16—591no—
219C2×SD16C2×D5911yescharacteristic, complemented
220C2×D8—591no—
221C2×D8—591no—
222C2×D8C2×D5911yescharacteristic, complemented
223C4⋊Q8—591no—
224#127—591no—
225#127—591no—
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—1181no—
235#121—1181no—
236#121C2×D5911yescharacteristic
237#120—1181no—
238#120—1181no—
239C4×Q8—591no—
240C4×D4—591no—
241#117—591no—
242C4⋊C8—591no—
243C4⋊C8—591no—
244#103—591no—
245#103C2×D5911yescharacteristic, complemented
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102C2×D5911yescharacteristic, complemented
252C22⋊C8—591no—
253C22⋊C8C2×D5911yescharacteristic
254#97—591no—
255C4×C8—591no—
256C24—1181no—
257#41—41no—
258#41—41no—
259C2×Q8—591no—
260C2×Q8—1181no—
261C2×Q8C22×D5911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—591no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4—2361no—
272C2×D4—2361no—
273C2×D4C22×D5911yescharacteristic
274C2×D4C22×D5911yescharacteristic
275C22×C4—21no—
276C22×C4—1181no—
277C22×C4C22×D5911yescharacteristic
278Q16—2361no—
279SD16—41no—
280SD16—2361no—
281SD16—2361no—
282SD16—2361no—
283D8—41no—
284D8—2361no—
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—591no—
310C42—1181no—
311C23—21no—
312C23—21no—
313C23—1181no—
314C23—1181no—
315C23—4721no—
316C23—4721no—
317C23—2362no—
318C23D4×D5911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—1181no—
322Q8—1181no—
323Q8—4721no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—81no—
330D4—1181no—
331D4—1181no—
332D4—1181no—
333D4—1181no—
334D4—4721no—
335D4—4721no—
336D4—4721no—
337D4—4721no—
338D4—2362no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—591no—
345C2×C4—591no—
346C2×C4—591no—
347C2×C4—591no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—4721no—
351C2×C4D4×D5911yescharacteristic
352C2×C4C23×D5911yescharacteristic
353C8—21no—
354C8—21no—
355C8—1181no—
356C8—1181no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—4724no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22C2×D4×D5911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—1181no—
378C4—1181no—
379C4—1181no—
380C4—1181no—
381C4—2361no—
382C4—2361no—
383C4#1427377211yescharacteristic
384C4#1427377211yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—4721no—
389C2—4721no—
390C2#1683796711yescharacteristic
391C2#1683820611yescharacteristic
392C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3224
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16838019C2semidirect
2. #16837966C2semidirect
3. #16837790C2semidirect
4. #16837783C2semidirect
5. #16837763C2semidirect
6. #16837747C2semidirect
7. #16837627C2semidirect
8. #16837619C2semidirect
9. #16837601C2semidirect
10. #16837595C2semidirect
11. #16837564C2semidirect
12. #16837555C2semidirect
13. #16837535C2semidirect
14. #16837460C2semidirect
15. C59×#449C2semidirect
17. C2×#11745672C22semidirect
20. C2×#11745670C22semidirect
23. #14273726C22semidirect
30. #14273714C22semidirect
38. #14273692C22semidirect
39. D4×Dic59C22semidirect
41. Dic59⋊C8C22semidirect
42. Dic59⋊C8C22semidirect
43. #14273651C22semidirect
46. #14273648C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
53. C2×SD16×C59C22semidirect
54. C2×D8×C59C22semidirect
56. #103×C59C22semidirect
57. #102×C59C22semidirect
209. #449D59semidirect
212. C59#3224semidirect
219. C2×SD16C2×D59semidirect
222. C2×D8C2×D59semidirect
245. #103C2×D59semidirect
251. #102C2×D59semidirect