Finite Group Databasebeta

← #21435701

Subgroups — #21435701

Order 7552.

520 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×#14273751C211yesmaximal, characteristic, complemented
2#16838046C211yesmaximal, characteristic, complemented
3#16838040C211yesmaximal, characteristic, complemented
4#16837783C211yesmaximal, characteristic, complemented
5#16837648C211yesmaximal, characteristic, complemented
6#16837645C211yesmaximal, characteristic, complemented
7#16837619C211yesmaximal, characteristic, complemented
8#16837615C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11#16837536C211yesmaximal, characteristic, complemented
12#16837534C211yesmaximal, characteristic, complemented
13D8×Dic59C211yesmaximal, characteristic, complemented
14#16837478C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C59C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic, complemented
18#14273751—24no—
19C2×#11745672C2211yescharacteristic, complemented
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745669C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24C2×#11745659C2211yescharacteristic, complemented
25#14273716C2211yescharacteristic, complemented
26#14273714C2211yescharacteristic, complemented
27#14273710—21no—
28#14273708—21no—
29#14273706C2211yescharacteristic, complemented
30#14273703C2211yescharacteristic, complemented
31#14273701C2211yescharacteristic
32#14273699—21no—
33#14273699—21no—
34#14273698C2211yescharacteristic
35#14273696—21no—
36#14273695—21no—
37D4×Dic59C2211yescharacteristic, complemented
38D4×Dic59C2211yescharacteristic, complemented
39C4×C22⋊D59C2211yescharacteristic
40C2×C22⋊Dic59—21no—
41C2×(C2×D59)⋊C4—21no—
42#14273661C2211yescharacteristic, complemented
43Dic59⋊C8C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273651C2211yescharacteristic, complemented
46#14273649C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49#14273648C2211yescharacteristic, complemented
50C22⋊(C59⋊C8)C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C8×Dic59C2211yescharacteristic, complemented
53C2×#41×C59C2211yescharacteristic
54C22×D4×C59C2211yescharacteristic, complemented
55AGL(1,ℤ/8)×C59—24no—
56C2×SD16×C59C2211yescharacteristic, complemented
57C2×SD16×C59C2211yescharacteristic, complemented
58C2×D8×C59C2211yescharacteristic
59C2×D8×C59C2211yescharacteristic
60C2×M16×C59C2211yescharacteristic, complemented
61C24×C59—21no—
62C23×D59—21no—
63#41×C59—22no—
64#41×C59—41no—
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—22no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—41no—
70C2×D4×C59C2311yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C22×C4×C59—21no—
74C22×C4×C59C2311yescharacteristic
75C2×C22⋊D59—21no—
76C2×C22⋊D59—21no—
77C2×C22⋊D59—21no—
78C2×C22⋊D59—21no—
79C2×C22⋊D59D411yescharacteristic
80C22×Dic59—21no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83#11745687—22no—
84#11745687—41no—
85D4×D59—22no—
86D4×D59—41no—
87C2×D236C2311yescharacteristic
88C2×C4×D59C2311yescharacteristic
89C2×Dic118C2311yescharacteristic
90SD16×C59—22no—
91SD16×C59—22no—
92D8×C59—22no—
93D8×C59D414yescomplemented
94M16×C59—22no—
95C2×C8×C59C2311yescharacteristic
96C2×C8×C59C2311yescharacteristic
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101C22⋊Dic59—21no—
102C22⋊Dic59—21no—
103C22⋊Dic59D411yescharacteristic
104#11745672—41no—
105#11745670—22no—
106#11745669—22no—
107#11745669—41no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110(C2×D59)⋊C4—21no—
111(C2×D59)⋊C4—21no—
112(C2×D59)⋊C4D411yescharacteristic
113C4⋊Dic59C2311yescharacteristic
114C4⋊Dic59C2311yescharacteristic
115Dic59⋊C4—21no—
116Dic59⋊C4—21no—
117Dic59⋊C4D411yescharacteristic
118C4×Dic59C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121#11745660—22no—
122#11745659—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—42no—
127C23×C59—42no—
128C23×C59—81no—
129C23×C59C2×D411yescharacteristic
130C22×D59—21no—
131C22×D59—42no—
132C22×D59—42no—
133C22×D59—81no—
134C22×D59C2×D411yescharacteristic
135Q8×C59—21no—
136Q8×C59—21no—
137D4×C59—21no—
138D4×C59—21no—
139D4×C59—21no—
140D4×C59—21no—
141D4×C59—42no—
142D4×C59—42no—
143D4×C59C2×D412yes—
144D4×C59C2×D412yes—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—42no—
149C2×C4×C59C2×D411yescharacteristic
150C2×C4×C59C2411yescharacteristic
151C22⋊D59—41no—
152C22⋊D59—42no—
153C22⋊D59—42no—
154C22⋊D59—81no—
155C22⋊D59—81no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159C2×Dic59—42no—
160C2×Dic59—81no—
161C2×Dic59—81no—
162C2×Dic59C2×D411yescharacteristic
163C2×Dic59C2×D411yescharacteristic
164C2×Dic59C2×D411yescharacteristic
165D236—21no—
166D236—21no—
167C4×D59—21no—
168C4×D59—21no—
169Dic118—21no—
170Dic118—21no—
171C8×C59—21no—
172C8×C59C2×D412yes—
173C59⋊C8—21no—
174C59⋊C8—21no—
175C22×C59—22no—
176C22×C59—22no—
177C22×C59—21no—
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—41no—
187C22×C59—84no—
188C22×C59C22×D411yescharacteristic
189C2×D59—21no—
190C2×D59—21no—
191C2×D59—21no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—41no—
195C2×D59—84no—
196C4×C59—21no—
197C4×C59—41no—
198C4×C59C22×D411yescharacteristic
199C4×C59H(5,𝔽2)11yescharacteristic
200Dic59—21no—
201Dic59—21no—
202Dic59—21no—
203Dic59—41no—
204Dic59—41no—
205Dic59—41no—
206#3273—591nomaximal, Sylow
207C2×C59—42no—
208C2×C59—41no—
209C2×C59—42no—
210C2×C59—81no—
211C2×C59D4211yescharacteristic
212C2×C59#57511yescharacteristic
213C2×C59#57611yescharacteristic
214D59—41no—
215D59—81no—
216C2×AGL(1,ℤ/8)—591no—
217C2×AGL(1,ℤ/8)D5911yescharacteristic, complemented
218#546—591no—
219#546—591no—
220#495—591no—
221#468—591no—
222#468—591no—
223#463—591no—
224#463—591no—
225#452—591no—
226#452—591no—
227#447—591no—
228#447—591no—
229C4×D8—591no—
230#436—591no—
231C59#327311yescharacteristic, complemented, Sylow
232C2×#41—591no—
233C2×#41C2×D5911yescharacteristic
234C22×D4—591no—
235C22×D4C2×D5911yescharacteristic, complemented
236AGL(1,ℤ/8)—24no—
237AGL(1,ℤ/8)—1184no—
238C2×Q16—591no—
239C2×SD16—591no—
240C2×SD16—591no—
241C2×SD16C2×D5911yescharacteristic, complemented
242C2×SD16C2×D5911yescharacteristic, complemented
243C2×D8—591no—
244C2×D8—591no—
245C2×D8C2×D5911yescharacteristic
246C2×D8C2×D5911yescharacteristic
247C2×M16—591no—
248C2×M16C2×D5911yescharacteristic, complemented
249#124—591no—
250#124—591no—
251#123—1181no—
252#123—1181no—
253C22⋊Q8—591no—
254C22⋊Q8—591no—
255#121—591no—
256#121—591no—
257#121—1181no—
258#121—1181no—
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#103—591no—
270#102—591no—
271#102—591no—
272#102—591no—
273#102—591no—
274C22⋊C8—591no—
275C22⋊C8—591no—
276C4×C8—591no—
277C24—21no—
278C24—1181no—
279#41—22no—
280#41—41no—
281#41—1182no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8C22×D5911yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—591no—
290C2×D4—591no—
291C2×D4—1181no—
292C2×D4—1182no—
293C2×D4—1181no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—2361no—
297C2×D4C22×D5911yescharacteristic
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—2361no—
307SD16—22no—
308SD16—22no—
309SD16—1182no—
310SD16—1182no—
311D8—22no—
312D8—1182no—
313D8—2361no—
314D8C22⋊D5914yescomplemented
315M16—22no—
316M16—1182no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8C22×D5911yescharacteristic
320C2×C8C22×D5911yescharacteristic
321C4⋊C4—591no—
322C4⋊C4—591no—
323C4⋊C4—591no—
324C4⋊C4—1181no—
325C4⋊C4—1181no—
326C22⋊C4—591no—
327C22⋊C4—591no—
328C22⋊C4—1181no—
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—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—591no—
346C23—1181no—
347C23—4721no—
348C23—2362no—
349C23—2362no—
350C23D4×D5911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1181no—
354Q8—1181no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—42no—
360D4—42no—
361D4—1181no—
362D4—1181no—
363D4—4721no—
364D4—4721no—
365D4—2361no—
366D4—2362no—
367D4—2362no—
368D4C2×C22⋊D5912yes—
369D4C2×C22⋊D5912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—591no—
375C2×C4—591no—
376C2×C4—591no—
377C2×C4—1181no—
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—1181no—
389C8—1181no—
390C8C2×C22⋊D5912yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—1181no—
405C22—1181no—
406C22—1181no—
407C22—4724no—
408C22—2361no—
409C22—2361no—
410C22—2361no—
411C22C2×D4×D5911yescharacteristic
412C4—21no—
413C4—41no—
414C4—1181no—
415C4—1181no—
416C4—1181no—
417C4—2361no—
418C4—2361no—
419C4—2361no—
420C4C22×C22⋊D5911yescharacteristic
421C4#1427377211yescharacteristic
422C2—41no—
423C2—42no—
424C2—42no—
425C2—81no—
426C2—4721no—
427C2—2361no—
428C2D4×C22⋊D5911yescharacteristic
429C2#1683819811yescharacteristic
430C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×AGL(1,ℤ/8)×C59C2
socleC22×C59C22×D4
hypercenterC2×AGL(1,ℤ/8)D59
hypocenterC59#3273
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14273751C2semidirect
2. #16838046C2semidirect
3. #16838040C2semidirect
4. #16837783C2semidirect
5. #16837648C2semidirect
6. #16837645C2semidirect
7. #16837619C2semidirect
8. #16837615C2semidirect
9. #16837564C2semidirect
10. #16837561C2semidirect
11. #16837536C2semidirect
12. #16837534C2semidirect
13. D8×Dic59C2semidirect
14. #16837478C2semidirect
15. C2×AGL(1,ℤ/8)×C59C2semidirect
17. C2×D4×D59C22semidirect
19. C2×#11745672C22semidirect
20. C2×#11745660C22semidirect
21. C2×#11745670C22semidirect
24. C2×#11745659C22semidirect
25. #14273716C22semidirect
26. #14273714C22semidirect
29. #14273706C22semidirect
30. #14273703C22semidirect
37. D4×Dic59C22semidirect
38. D4×Dic59C22semidirect
42. #14273661C22semidirect
43. Dic59⋊C8C22semidirect
44. #14273652C22semidirect
45. #14273651C22semidirect
46. #14273649C22semidirect
47. #14273648C22semidirect
48. #14273648C22semidirect
49. #14273648C22semidirect
50. C22⋊(C59⋊C8)C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. C8×Dic59C22semidirect
54. C22×D4×C59C22semidirect
56. C2×SD16×C59C22semidirect
57. C2×SD16×C59C22semidirect
60. C2×M16×C59C22semidirect
93. D8×C59D4semidirect
217. C2×AGL(1,ℤ/8)D59semidirect
231. C59#3273semidirect
235. C22×D4C2×D59semidirect
241. C2×SD16C2×D59semidirect
242. C2×SD16C2×D59semidirect
248. C2×M16C2×D59semidirect
314. D8C22⋊D59semidirect