Finite Group Databasebeta

← #21436236

Subgroups — #21436236

Order 7552.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838105C211yesmaximal, characteristic, complemented
2#16838037C211yesmaximal, characteristic, complemented
3#16837725C211yesmaximal, characteristic, complemented
4#16837719C211yesmaximal, characteristic, complemented
5#16837699C211yesmaximal, characteristic, complemented
6#16837654C211yesmaximal, characteristic, complemented
7#16837637C211yesmaximal, characteristic, complemented
8#16837594C211yesmaximal, characteristic, complemented
9#16837537C211yesmaximal, characteristic, complemented
10#16837537C211yesmaximal, characteristic, complemented
11#16837515C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#490C211yesmaximal, characteristic, complemented
16C2×D4×D59—21no—
17C2×D4×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×#11745669C2211yescharacteristic, complemented
21C2×#11745669C2211yescharacteristic, complemented
22C2×#11745659C2211yescharacteristic, complemented
23C2×C8×D59C2211yescharacteristic, complemented
24#14273722—21no—
25#14273712—21no—
26#14273702—21no—
27#14273702C2211yescharacteristic, complemented
28#14273702C2211yescharacteristic, complemented
29#14273698—21no—
30#14273698C2211yescharacteristic
31#14273698C2211yescharacteristic
32#14273695—21no—
33#14273695—21no—
34C4×D236C2211yescharacteristic
35C4×D236C2211yescharacteristic
36C4×D236C2211yescharacteristic, complemented
37#14273689—21no—
38#14273685C2211yescharacteristic, complemented
39C4⋊C4×D59C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43C4⋊(C59⋊C8)C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52#127×C59C2211yescharacteristic
53#125×C59C2211yescharacteristic, complemented
54#102×C59C2211yescharacteristic, complemented
55#102×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69D4×D59—22no—
70D4×D59—22no—
71D4×D59—41no—
72D4×D59—41no—
73D4×D59—44no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236D411yescharacteristic
77C2×D236C2311yescharacteristic
78C2×D236C2311yescharacteristic
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×C4×D59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C4⋊C4×C59—21no—
87C4⋊C4×C59—21no—
88C4⋊C4×C59C2311yescharacteristic
89C4⋊C4×C59C2311yescharacteristic
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93#11745669—41no—
94#11745669—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4D411yescharacteristic
101(C2×D59)⋊C4D411yescharacteristic
102C4⋊Dic59D411yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109D472—22no—
110#11745659—41no—
111C8×D59—41no—
112C23×C59—21no—
113C23×C59—21no—
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
123C22×D59C2×D411yescharacteristic
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×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—42no—
136C22⋊D59—42no—
137C22⋊D59—42no—
138C22⋊D59—42no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143D236—22no—
144D236—21no—
145D236—21no—
146D236—21no—
147D236—42no—
148D236—81no—
149D236#4112yes—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—42no—
155C4×D59—81no—
156C4×D59—81no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59C22×D411yescharacteristic
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—22no—
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—84no—
180C2×D59—84no—
181C2×D59AGL(1,ℤ/8)12yes—
182C4×C59—21no—
183C4×C59—21no—
184C4×C59—41no—
185C4×C59—41no—
186C4×C59C2×#4111yescharacteristic
187C4×C59H(5,𝔽2)11yescharacteristic
188Dic59—21no—
189Dic59—21no—
190Dic59—41no—
191Dic59—41no—
192#3318—591nomaximal, Sylow
193C2×C59—81no—
194C2×C59—81no—
195C2×C59#54611yescharacteristic
196C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C59#57611yescharacteristic
198D59—22no—
199D59—41no—
200D59—42no—
201D59—81no—
202#553—591no—
203D42—591no—
204#490D5911yescharacteristic, complemented
205#482—591no—
206#481—591no—
207#478—591no—
208#469—591no—
209#466—591no—
210#459—591no—
211#447—591no—
212#447—591no—
213#442—591no—
214#435—591no—
215#418—591no—
216C2×#102—591no—
217C59#331811yescharacteristic, complemented, Sylow
218C22×D4—591no—
219C22×D4—591no—
220C22×D4—1181no—
221C2×D8—591no—
222C2×D8—591no—
223C2×D8—591no—
224C2×M16—591no—
225C22×C8—591no—
226#127C2×D5911yescharacteristic
227#126—1181no—
228#125C2×D5911yescharacteristic, complemented
229#123—1181no—
230#121—591no—
231#121—591no—
232#121—591no—
233#121—591no—
234#121—1181no—
235#121—1181no—
236#120—1181no—
237#120—1181no—
238C4×D4—591no—
239C4×D4—591no—
240C4×D4—591no—
241C4×D4—1181no—
242#117—591no—
243C2×C4⋊C4—591no—
244#107—591no—
245#106—591no—
246#106—591no—
247C4⋊C8—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102—591no—
253#102—591no—
254#102C2×D5911yescharacteristic, complemented
255#102C2×D5911yescharacteristic, complemented
256#102C2×D5911yescharacteristic, complemented
257#102C2×D5911yescharacteristic, complemented
258C22⋊C8—591no—
259C22⋊C8—591no—
260#97C2×D5911yescharacteristic, complemented
261C24—1181no—
262C24—1181no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—591no—
266C2×D4—591no—
267C2×D4—591no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1182no—
273C2×D4—1182no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—2361no—
277C2×D4—2361no—
278C2×D4—2364no—
279C2×D4C22×D5911yescharacteristic
280C2×D4C22×D5911yescharacteristic
281C22×C4—591no—
282C22×C4—591no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—1181no—
286D8—1182no—
287D8—2361no—
288D8—2361no—
289M16—2361no—
290C2×C8—591no—
291C2×C8—591no—
292C2×C8—2361no—
293C2×C8C22×D5911yescharacteristic
294C2×C8C22×D5911yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—591no—
298C4⋊C4—591no—
299C4⋊C4—591no—
300C4⋊C4—1181no—
301C4⋊C4C22×D5911yescharacteristic
302C4⋊C4C22×D5911yescharacteristic
303C22⋊C4—591no—
304C22⋊C4—591no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C42—1181no—
313C42C22×D5911yescharacteristic
314C23—21no—
315C23—21no—
316C23—591no—
317C23—591no—
318C23—1181no—
319C23—1181no—
320C23—4721no—
321C23—4721no—
322C23—2362no—
323C23—2362no—
324C23—2362no—
325C23—2362no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—592no—
333D4—1182no—
334D4—1181no—
335D4—1181no—
336D4—1181no—
337D4—4721no—
338D4—2362no—
339D4—2362no—
340D4—2362no—
341D4—2362no—
342D4—2362no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—591no—
346C2×C4—591no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—4721no—
354C2×C4—4721no—
355C2×C4—2362no—
356C2×C4D4×D5911yescharacteristic
357C2×C4D4×D5911yescharacteristic
358C2×C4C23×D5911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1181no—
362C8—1181no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—592no—
370C22—1181no—
371C22—1181no—
372C22—1181no—
373C22—1181no—
374C22—1181no—
375C22—1182no—
376C22—4724no—
377C22—4724no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22C2×D4×D5911yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—1181no—
389C4—1181no—
390C4—2361no—
391C4—2361no—
392C4#41×D5911yescharacteristic
393C4#1427377311yescharacteristic
394C2—81no—
395C2—81no—
396C2—1182no—
397C2—4721no—
398C2—2361no—
399C2—2362no—
400C2#1683804511yescharacteristic
401C2AGL(1,ℤ/8)×D5911yescharacteristic
402C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#490C2
socleC22×C59C22×D4
hypercenter#490D59
hypocenterC59#3318
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #16838105C2semidirect
2. #16838037C2semidirect
3. #16837725C2semidirect
4. #16837719C2semidirect
5. #16837699C2semidirect
6. #16837654C2semidirect
7. #16837637C2semidirect
8. #16837594C2semidirect
9. #16837537C2semidirect
10. #16837537C2semidirect
11. #16837515C2semidirect
12. #16837475C2semidirect
13. #16837405C2semidirect
14. #102×D59C2semidirect
15. C59×#490C2semidirect
20. C2×#11745669C22semidirect
21. C2×#11745669C22semidirect
22. C2×#11745659C22semidirect
23. C2×C8×D59C22semidirect
27. #14273702C22semidirect
28. #14273702C22semidirect
36. C4×D236C22semidirect
38. #14273685C22semidirect
39. C4⋊C4×D59C22semidirect
40. #14273660C22semidirect
41. #14273659C22semidirect
42. #14273658C22semidirect
43. C4⋊(C59⋊C8)C22semidirect
45. #14273649C22semidirect
46. #14273648C22semidirect
47. #14273648C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
53. #125×C59C22semidirect
54. #102×C59C22semidirect
55. #102×C59C22semidirect
56. #102×C59C22semidirect
57. #102×C59C22semidirect
58. #97×C59C22semidirect
204. #490D59semidirect
217. C59#3318semidirect
228. #125C2×D59semidirect
254. #102C2×D59semidirect
255. #102C2×D59semidirect
256. #102C2×D59semidirect
257. #102C2×D59semidirect
260. #97C2×D59semidirect