Finite Group Databasebeta

← #21435779

Subgroups — #21435779

Order 7552.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273747C211yesmaximal, characteristic, complemented
2C2×D8×D59C211yesmaximal, characteristic, complemented
3#16838049C211yesmaximal, characteristic, complemented
4#16838040C211yesmaximal, characteristic, complemented
5#16837783C211yesmaximal, characteristic, complemented
6#16837642C211yesmaximal, characteristic, complemented
7#16837636C211yesmaximal, characteristic, complemented
8#16837620C211yesmaximal, characteristic, complemented
9#16837615C211yesmaximal, characteristic, complemented
10#16837554C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837549C211yesmaximal, characteristic, complemented
13#16837482C211yesmaximal, characteristic, complemented
14(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic, complemented
17C2×D4×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19#14273747—24no—
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745660C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic, complemented
23C2×#11745671C2211yescharacteristic, complemented
24C2×D472C2211yescharacteristic
25C2×#11745669C2211yescharacteristic
26C2×#11745669C2211yescharacteristic
27D8×D59—24no—
28C22×C59⋊C8C2211yescharacteristic, complemented
29C2×C8×D59C2211yescharacteristic
30#14273716C2211yescharacteristic, complemented
31#14273714C2211yescharacteristic, complemented
32#14273710—21no—
33#14273709—21no—
34#14273707C2211yescharacteristic
35#14273703C2211yescharacteristic
36#14273701C2211yescharacteristic, complemented
37#14273699—21no—
38#14273698—21no—
39#14273695—21no—
40#14273695—21no—
41D4×Dic59C2211yescharacteristic, complemented
42#14273689C2211yescharacteristic, complemented
43C4×C22⋊D59C2211yescharacteristic
44C2×(C2×D59)⋊C4—21no—
45C22⋊C4×D59—21no—
46#14273660C2211yescharacteristic, complemented
47Dic59⋊C8C2211yescharacteristic, complemented
48#14273652C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic, complemented
50#14273648C2211yescharacteristic, complemented
51#14273647C2211yescharacteristic, complemented
52(C2×D59)⋊C8C2211yescharacteristic
53C8×Dic59C2211yescharacteristic, complemented
54C2×#41×C59C2211yescharacteristic, complemented
55C2×SD16×C59C2211yescharacteristic, complemented
56C2×D8×C59C2211yescharacteristic
57#121×C59C2211yescharacteristic, complemented
58#103×C59C2211yescharacteristic, complemented
59#102×C59C2211yescharacteristic, complemented
60C22⋊C8×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C23×D59—21no—
63#41×C59—22no—
64#41×C59—41no—
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59C2311yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C22×C4×C59—21no—
71C22×C4×C59C2311yescharacteristic
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C2×C22⋊D59D411yescharacteristic
77C22×Dic59—21no—
78D4×D59—22no—
79D4×D59—22no—
80D4×D59—41no—
81D4×D59—41no—
82#11745685—22no—
83#11745685—41no—
84C2×D236C2311yescharacteristic
85C2×D236C2311yescharacteristic
86C2×C4×D59—21no—
87C2×C4×D59—21no—
88C2×C4×D59C2311yescharacteristic
89C2×Dic118C2311yescharacteristic
90SD16×C59—41no—
91D8×C59—22no—
92C2×C8×C59C2311yescharacteristic
93C2×C8×C59C2311yescharacteristic
94C4⋊C4×C59C2311yescharacteristic
95C22⋊C4×C59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99C22⋊Dic59D411yescharacteristic
100#11745672—22no—
101#11745671—22no—
102#11745670—22no—
103#11745669—22no—
104#11745669D414yescomplemented
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110(C2×D59)⋊C4—21no—
111(C2×D59)⋊C4D411yescharacteristic
112C4⋊Dic59—21no—
113C4⋊Dic59C2311yescharacteristic
114Dic59⋊C4—21no—
115Dic59⋊C4D411yescharacteristic
116C4×Dic59C2311yescharacteristic
117C2×C59⋊C8—22no—
118C2×C59⋊C8C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120D472—22no—
121#11745660—41no—
122C8×D59—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59C2×D411yescharacteristic
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—42no—
129C22×D59—42no—
130C22×D59—42no—
131C22×D59—42no—
132C22×D59—81no—
133C22×D59—81no—
134C22×D59C2×D411yescharacteristic
135Q8×C59—21no—
136Q8×C59—21no—
137D4×C59—21no—
138D4×C59—21no—
139D4×C59—21no—
140D4×C59—42no—
141D4×C59—81no—
142D4×C59C2×D412yes—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—42no—
148C2×C4×C59C2×D411yescharacteristic
149C2×C4×C59C2411yescharacteristic
150C22⋊D59—22no—
151C22⋊D59—42no—
152C22⋊D59—42no—
153C22⋊D59—42no—
154C22⋊D59—81no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—81no—
158C2×Dic59C2×D411yescharacteristic
159C2×Dic59C2×D411yescharacteristic
160C2×Dic59C2×D411yescharacteristic
161D236—21no—
162D236—21no—
163D236—21no—
164D236C2×D412yes—
165C4×D59—21no—
166C4×D59—21no—
167C4×D59—42no—
168C4×D59—81no—
169Dic118—21no—
170Dic118—21no—
171C8×C59—21no—
172C8×C59—21no—
173C59⋊C8—21no—
174C59⋊C8C2×D412yes—
175C22×C59—21no—
176C22×C59—22no—
177C22×C59—21no—
178C22×C59—21no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59C22×D411yescharacteristic
185C2×D59—21no—
186C2×D59—21no—
187C2×D59—22no—
188C2×D59—41no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—84no—
194C2×D59—84no—
195C2×D59#13512yescomplemented
196C4×C59—21no—
197C4×C59—41no—
198C4×C59—41no—
199C4×C59C22×D411yescharacteristic
200C4×C59H(5,𝔽2)11yescharacteristic
201Dic59—21no—
202Dic59—21no—
203Dic59—21no—
204Dic59—41no—
205Dic59—41no—
206#3280—591nomaximal, Sylow
207C2×C59—42no—
208C2×C59—41no—
209C2×C59—81no—
210C2×C59D4211yescharacteristic
211C2×C59C2×#13511yescharacteristic
212C2×C59#57611yescharacteristic
213D59—22no—
214D59—42no—
215D59—81no—
216C2×#135—591no—
217C22×D8—591no—
218#546—591no—
219#546—591no—
220#495—591no—
221#467—591no—
222#466—591no—
223#463—591no—
224#463—591no—
225#450—591no—
226#450—591no—
227#449—591no—
228#449D5911yescharacteristic, complemented
229C4×D8—591no—
230C8×D4—591no—
231C59#328011yescharacteristic, complemented, Sylow
232C2×#41—591no—
233C2×#41C2×D5911yescharacteristic, complemented
234C22×D4—591no—
235C22×D4—591no—
236#135—1184no—
237C2×Q16—591no—
238C2×SD16—591no—
239C2×SD16—591no—
240C2×SD16—591no—
241C2×SD16C2×D5911yescharacteristic, complemented
242C2×D8—591no—
243C2×D8—591no—
244C2×D8—591no—
245C2×D8—1184no—
246C2×D8C2×D5911yescharacteristic
247C22×C8—591no—
248C22×C8—591no—
249#124—591no—
250#124—591no—
251#123—1181no—
252#123—1181no—
253C22⋊Q8—591no—
254C22⋊Q8—591no—
255#121—591no—
256#121—1181no—
257#121—1181no—
258#121C2×D5911yescharacteristic, complemented
259#120—1181no—
260#120—1181no—
261C4×D4—591no—
262C4×D4—591no—
263C4×D4—591no—
264C2×C22⋊C4—1181no—
265C2×C22⋊C4—1181no—
266#107—591no—
267C4⋊C8—591no—
268#103—591no—
269#103C2×D5911yescharacteristic, complemented
270#102—591no—
271#102—591no—
272#102—591no—
273#102C2×D5911yescharacteristic, complemented
274C22⋊C8—591no—
275C22⋊C8C2×D5911yescharacteristic, complemented
276C4×C8—591no—
277C24—1181no—
278C24—1181no—
279#41—22no—
280#41—41no—
281#41—1182no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8C22×D5911yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—591no—
288C2×D4—591no—
289C2×D4—591no—
290C2×D4—1181no—
291C2×D4—1181no—
292C2×D4—1182no—
293C2×D4—1182no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—2361no—
297C2×D4—2361no—
298C2×D4C22×D5911yescharacteristic
299C2×D4C22×D5911yescharacteristic
300C22×C4—21no—
301C22×C4—591no—
302C22×C4—1181no—
303C22×C4—1181no—
304C22×C4—1181no—
305C22×C4C22×D5911yescharacteristic
306Q16—1182no—
307SD16—41no—
308SD16—1182no—
309SD16—1182no—
310SD16—2361no—
311D8—22no—
312D8—594no—
313D8—1182no—
314D8—1182no—
315C2×C8—591no—
316C2×C8—591no—
317C2×C8—1182no—
318C2×C8—1182no—
319C2×C8C22×D5911yescharacteristic
320C2×C8C22×D5911yescharacteristic
321C4⋊C4—591no—
322C4⋊C4—591no—
323C4⋊C4—1181no—
324C4⋊C4—1181no—
325C4⋊C4C22×D5911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—591no—
328C22⋊C4—591no—
329C22⋊C4—1181no—
330C22⋊C4—1181no—
331C22⋊C4—1181no—
332C22⋊C4—1181no—
333C22⋊C4—1181no—
334C22⋊C4—1181no—
335C22⋊C4—1181no—
336C22⋊C4—1181no—
337C22⋊C4—1181no—
338C42—591no—
339C23—21no—
340C23—21no—
341C23—591no—
342C23—1181no—
343C23—1181no—
344C23—4721no—
345C23—4721no—
346C23—2362no—
347C23—2362no—
348C23—2362no—
349C23—2362no—
350C23D4×D5911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1181no—
354Q8—1181no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—81no—
360D4—592no—
361D4—1182no—
362D4—1181no—
363D4—1181no—
364D4—1181no—
365D4—4721no—
366D4—2362no—
367D4—2362no—
368D4—2362no—
369D4D4×D5912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—591no—
376C2×C4—591no—
377C2×C4—591no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—1181no—
382C2×C4—4721no—
383C2×C4—4721no—
384C2×C4—2362no—
385C2×C4D4×D5911yescharacteristic
386C2×C4C23×D5911yescharacteristic
387C8—21no—
388C8—21no—
389C8—592no—
390C8—1181no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—592no—
401C22—1181no—
402C22—1181no—
403C22—1182no—
404C22—4724no—
405C22—4724no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22—2361no—
410C22—2361no—
411C22C2×D4×D5911yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—1181no—
416C4—1181no—
417C4—1181no—
418C4—2361no—
419C4—2361no—
420C4C2×D4×D5911yescharacteristic
421C4#1427377211yescharacteristic
422C2—41no—
423C2—42no—
424C2—81no—
425C2—1182no—
426C2—4721no—
427C2—2362no—
428C2#1683803411yescharacteristic
429C2#135×D5911yescharacteristic
430C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3280
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. C2×#14273747C2semidirect
2. C2×D8×D59C2semidirect
3. #16838049C2semidirect
4. #16838040C2semidirect
5. #16837783C2semidirect
6. #16837642C2semidirect
7. #16837636C2semidirect
8. #16837620C2semidirect
9. #16837615C2semidirect
10. #16837554C2semidirect
11. #16837551C2semidirect
12. #16837549C2semidirect
13. #16837482C2semidirect
14. (C22⋊D59)⋊C8C2semidirect
15. C59×#449C2semidirect
16. C2×#11745685C22semidirect
20. C2×#11745672C22semidirect
21. C2×#11745660C22semidirect
22. C2×#11745670C22semidirect
23. C2×#11745671C22semidirect
28. C22×C59⋊C8C22semidirect
30. #14273716C22semidirect
31. #14273714C22semidirect
36. #14273701C22semidirect
41. D4×Dic59C22semidirect
42. #14273689C22semidirect
46. #14273660C22semidirect
47. Dic59⋊C8C22semidirect
48. #14273652C22semidirect
49. #14273649C22semidirect
50. #14273648C22semidirect
51. #14273647C22semidirect
53. C8×Dic59C22semidirect
54. C2×#41×C59C22semidirect
55. C2×SD16×C59C22semidirect
57. #121×C59C22semidirect
58. #103×C59C22semidirect
59. #102×C59C22semidirect
60. C22⋊C8×C59C22semidirect
104. #11745669D4semidirect
195. C2×D59#135semidirect
228. #449D59semidirect
231. C59#3280semidirect
233. C2×#41C2×D59semidirect
241. C2×SD16C2×D59semidirect
258. #121C2×D59semidirect
269. #103C2×D59semidirect
273. #102C2×D59semidirect
275. C22⋊C8C2×D59semidirect