Finite Group Databasebeta

← #21435902

Subgroups — #21435902

Order 7552.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838052C211yesmaximal, characteristic, complemented
2D4×C22⋊D59C211yesmaximal, characteristic, complemented
3#16837747C211yesmaximal, characteristic, complemented
4#16837716C211yesmaximal, characteristic, complemented
5#16837714C211yesmaximal, characteristic, complemented
6#16837680C211yesmaximal, characteristic, complemented
7#16837636C211yesmaximal, characteristic, complemented
8#16837635C211yesmaximal, characteristic, complemented
9#16837595C211yesmaximal, characteristic, complemented
10#16837534C211yesmaximal, characteristic, complemented
11D8×Dic59C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14273648C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#447C211yesmaximal, characteristic, complemented
16C2×#11745687—21no—
17C22×C22⋊D59—21no—
18C2×D4×D59C2211yescharacteristic
19C2×#11745669C2211yescharacteristic, complemented
20C22×C59⋊C8C2211yescharacteristic, complemented
21C2×C8×D59C2211yescharacteristic, complemented
22#14273726C2211yescharacteristic, complemented
23#14273723C2211yescharacteristic
24#14273709—21no—
25#14273708—21no—
26#14273704—21no—
27#14273701C2211yescharacteristic
28#14273699—21no—
29#14273698C2211yescharacteristic
30#14273698C2211yescharacteristic, complemented
31#14273696—21no—
32#14273695—21no—
33D4×Dic59C2211yescharacteristic
34D4×Dic59C2211yescharacteristic, complemented
35C4×C22⋊D59C2211yescharacteristic
36C2×C4⋊Dic59C2211yescharacteristic, complemented
37C4⋊C4×D59C2211yescharacteristic, complemented
38#14273661C2211yescharacteristic, complemented
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273649C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C22×D4×C59C2211yescharacteristic
53C2×D8×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic, complemented
55#121×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C24×C59—21no—
60C23×D59—21no—
61C2×D4×C59—22no—
62C2×D4×C59—21no—
63C2×D4×C59—21no—
64C2×D4×C59—41no—
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C2×D4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C2×C22⋊D59—21no—
75C2×C22⋊D59—44no—
76C2×C22⋊D59D411yescharacteristic
77C22×Dic59—21no—
78C22×Dic59—21no—
79C22×Dic59—21no—
80#11745687—44no—
81D4×D59—22no—
82D4×D59—41no—
83C2×D236C2311yescharacteristic
84C2×C4×D59—21no—
85C2×C4×D59C2311yescharacteristic
86C2×Dic118—21no—
87D8×C59—22no—
88D8×C59—41no—
89C2×C8×C59C2311yescharacteristic
90C2×C8×C59C2311yescharacteristic
91C4⋊C4×C59C2311yescharacteristic
92C22⋊C4×C59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59D411yescharacteristic
98#11745669—41no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4D411yescharacteristic
101C4⋊Dic59—21no—
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4D411yescharacteristic
108C4×Dic59C2311yescharacteristic
109C2×C59⋊C8—41no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C8×D59—41no—
113C23×C59—21no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—42no—
117C23×C59—42no—
118C23×C59—81no—
119C23×C59C2×D411yescharacteristic
120C22×D59—21no—
121C22×D59—42no—
122C22×D59—42no—
123C22×D59—81no—
124C22×D59C2×D411yescharacteristic
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—21no—
130D4×C59—42no—
131D4×C59—42no—
132D4×C59#4112yescomplemented
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2411yescharacteristic
138C22⋊D59—42no—
139C22⋊D59—42no—
140C22⋊D59—42no—
141C22⋊D59—42no—
142C22⋊D59—42no—
143C22⋊D59—81no—
144C22⋊D59D814yescomplemented
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—42no—
149C2×Dic59—42no—
150C2×Dic59—42no—
151C2×Dic59C2×D411yescharacteristic
152C2×Dic59C2×D411yescharacteristic
153C2×Dic59C2×D411yescharacteristic
154D236—21no—
155D236—21no—
156C4×D59—21no—
157C4×D59—21no—
158C4×D59—42no—
159Dic118—42no—
160C8×C59—21no—
161C8×C59—21no—
162C59⋊C8—21no—
163C59⋊C8—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—22no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—84no—
176C22×C59C2×D812yes—
177C22×C59C22×D411yescharacteristic
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—84no—
184C2×D59C2×D812yes—
185C4×C59—21no—
186C4×C59—41no—
187C4×C59C2×#4111yescharacteristic
188C4×C59H(5,𝔽2)11yescharacteristic
189Dic59—21no—
190Dic59—21no—
191Dic59—41no—
192Dic59—41no—
193Dic59—41no—
194Dic59C2×D812yes—
195#3294—591nomaximal, Sylow
196C2×C59—22no—
197C2×C59—42no—
198C2×C59—81no—
199C2×C59—81no—
200C2×C59#54611yescharacteristic
201C2×C59C22×D811yescharacteristic
202C2×C59#57711yescharacteristic
203D59—22no—
204D59—81no—
205#547—591no—
206D42—591no—
207#486—591no—
208#480—591no—
209#480—591no—
210#474—591no—
211#466—591no—
212#466—591no—
213#459—591no—
214#447—591no—
215#447D5911yescharacteristic, complemented
216C4×D8—591no—
217C8×D4—591no—
218C2×#102—591no—
219C2×#102—591no—
220C59#329411yescharacteristic, complemented, Sylow
221C2×#41—1181no—
222C22×D4—591no—
223C22×D4—1181no—
224C22×D4C2×D5911yescharacteristic
225C2×D8—591no—
226C2×D8C2×D5911yescharacteristic
227C2×D8C2×D5911yescharacteristic, complemented
228C22×C8—591no—
229C22×C8—591no—
230C4⋊Q8—591no—
231#127—591no—
232#123—1181no—
233#123—1181no—
234C22⋊Q8—1181no—
235#121—591no—
236#121—591no—
237#121—591no—
238#121—1181no—
239#121C2×D5911yescharacteristic, complemented
240#120—1181no—
241#120—1181no—
242C4×D4—591no—
243C4×D4—591no—
244C4×D4—591no—
245C2×C4⋊C4—591no—
246C2×C4⋊C4—591no—
247#107—591no—
248#107—591no—
249#107—591no—
250C4⋊C8—591no—
251#102—591no—
252#102—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102—591no—
257#102—591no—
258#102—591no—
259#102C2×D5911yescharacteristic
260#102C2×D5911yescharacteristic, complemented
261C22⋊C8—591no—
262C22⋊C8C2×D5911yescharacteristic, complemented
263C4×C8—591no—
264C24—21no—
265C24—1181no—
266#41—2364no—
267C2×Q8—1181no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—591no—
273C2×D4—591no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1182no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4—2361no—
282C2×D4—2364no—
283C2×D4C22×D5911yescharacteristic
284C2×D4C22×D5911yescharacteristic
285C2×D4C22×D5911yescharacteristic
286C22×C4—591no—
287C22×C4—1181no—
288C22×C4—1181no—
289C22×C4—1181no—
290C22×C4—1181no—
291C22×C4C22×D5911yescharacteristic
292D8—22no—
293D8—41no—
294D8—2361no—
295C2×C8—591no—
296C2×C8—591no—
297C2×C8—2361no—
298C2×C8—2361no—
299C2×C8C22×D5911yescharacteristic
300C2×C8C22×D5911yescharacteristic
301C4⋊C4—591no—
302C4⋊C4—591no—
303C4⋊C4—591no—
304C4⋊C4—591no—
305C4⋊C4—1181no—
306C4⋊C4—1181no—
307C4⋊C4—1181no—
308C4⋊C4C22×D5911yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—591no—
311C22⋊C4—591no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C42—591no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—591no—
325C23—1181no—
326C23—4721no—
327C23—2362no—
328C23—2362no—
329C23D4×D5911yescharacteristic
330Q8—2362no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—594no—
339D4—1181no—
340D4—1181no—
341D4—4721no—
342D4—2362no—
343D4—2362no—
344D4—2362no—
345D4—2362no—
346D4—2362no—
347D4#1174568712yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—591no—
352C2×C4—591no—
353C2×C4—591no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—2362no—
360C2×C4—2362no—
361C2×C4—2362no—
362C2×C4—2362no—
363C2×C4D4×D5911yescharacteristic
364C2×C4C23×D5911yescharacteristic
365C8—21no—
366C8—21no—
367C8—1181no—
368C8—1181no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—592no—
382C22—1181no—
383C22—1181no—
384C22—4724no—
385C22—2361no—
386C22—2361no—
387C22—2361no—
388C22D8×D5912yes—
389C22C2×D4×D5911yescharacteristic
390C4—21no—
391C4—41no—
392C4—592no—
393C4—1181no—
394C4—1181no—
395C4—2361no—
396C4—2361no—
397C4—2361no—
398C4C2×#1174568711yescharacteristic
399C4#1427377211yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—1182no—
405C2—4721no—
406C2#1683803911yescharacteristic
407C2C2×D8×D5911yescharacteristic
408C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#447C2
socleC22×C59C22×D4
hypercenter#447D59
hypocenterC59#3294
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16838052C2semidirect
2. D4×C22⋊D59C2semidirect
3. #16837747C2semidirect
4. #16837716C2semidirect
5. #16837714C2semidirect
6. #16837680C2semidirect
7. #16837636C2semidirect
8. #16837635C2semidirect
9. #16837595C2semidirect
10. #16837534C2semidirect
11. D8×Dic59C2semidirect
12. (C22⋊D59)⋊C8C2semidirect
13. C2×#14273648C2semidirect
14. #102×D59C2semidirect
15. C59×#447C2semidirect
19. C2×#11745669C22semidirect
20. C22×C59⋊C8C22semidirect
21. C2×C8×D59C22semidirect
22. #14273726C22semidirect
30. #14273698C22semidirect
34. D4×Dic59C22semidirect
36. C2×C4⋊Dic59C22semidirect
37. C4⋊C4×D59C22semidirect
38. #14273661C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273649C22semidirect
43. #14273649C22semidirect
46. #14273648C22semidirect
47. #14273648C22semidirect
48. #14273648C22semidirect
49. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
54. C2×D8×C59C22semidirect
55. #121×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
132. D4×C59#41semidirect
144. C22⋊D59D8semidirect
215. #447D59semidirect
220. C59#3294semidirect
227. C2×D8C2×D59semidirect
239. #121C2×D59semidirect
260. #102C2×D59semidirect
262. C22⋊C8C2×D59semidirect
347. D4#11745687semidirect