Finite Group Databasebeta

← #21436059

Subgroups — #21436059

Order 7552.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838056C211yesmaximal, characteristic, complemented
2#16838048C211yesmaximal, characteristic, complemented
3#16837762C211yesmaximal, characteristic, complemented
4#16837733C211yesmaximal, characteristic, complemented
5#16837721C211yesmaximal, characteristic, complemented
6#16837693C211yesmaximal, characteristic, complemented
7#16837655C211yesmaximal, characteristic, complemented
8#16837631C211yesmaximal, characteristic, complemented
9#16837618C211yesmaximal, characteristic, complemented
10#16837549C211yesmaximal, characteristic, complemented
11#16837538C211yesmaximal, characteristic, complemented
12#16837515C211yesmaximal, characteristic, complemented
13#16837404C211yesmaximal, characteristic, complemented
14C2×#14273649C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745687—21no—
18C22×D236C2211yescharacteristic
19C2×#11745660C2211yescharacteristic, complemented
20C2×D472C2211yescharacteristic
21C2×D472C2211yescharacteristic
22#14273727C2211yescharacteristic, complemented
23#14273715C2211yescharacteristic
24#14273712—21no—
25#14273711—21no—
26#14273711—21no—
27#14273707—21no—
28#14273706C2211yescharacteristic
29#14273701C2211yescharacteristic
30#14273701C2211yescharacteristic
31#14273701C2211yescharacteristic, complemented
32#14273700—21no—
33#14273695—21no—
34C4×D236C2211yescharacteristic
35C4×D236C2211yescharacteristic, complemented
36C2×C4⋊Dic59C2211yescharacteristic
37C2×C4⋊Dic59C2211yescharacteristic, complemented
38C22⋊C4×D59—21no—
39#14273659C2211yescharacteristic, complemented
40#14273659C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic, complemented
52C2×M16×C59C2211yescharacteristic, complemented
53C22×C8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic, complemented
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic, complemented
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59D411yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69#11745687—44no—
70#11745685—22no—
71#11745685—41no—
72C2×D236—22no—
73C2×D236—21no—
74C2×D236—41no—
75C2×D236C2311yescharacteristic
76C2×D236C2311yescharacteristic
77C2×D236C2311yescharacteristic
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×Dic118—21no—
82C2×Dic118C2311yescharacteristic
83M16×C59—41no—
84C2×C8×C59—41no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C2×C8×C59C2311yescharacteristic
89C4⋊C4×C59D411yescharacteristic
90C22⋊C4×C59D411yescharacteristic
91C22⋊C4×C59D411yescharacteristic
92C42×C59C2311yescharacteristic
93C22⋊Dic59—21no—
94(C2×D59)⋊C4—21no—
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)⋊C4—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59—21no—
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107C4⋊Dic59C2311yescharacteristic
108Dic59⋊C4—21no—
109D472—22no—
110D472—41no—
111#11745660—41no—
112C23×C59C2×D411yescharacteristic
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—81no—
120D4×C59—22no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—42no—
131C22⋊D59—42no—
132C22⋊D59—42no—
133C22⋊D59—81no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—42no—
140C2×Dic59—42no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—21no—
146D236—42no—
147D236#4112yescomplemented
148C4×D59—42no—
149C4×D59—42no—
150C4×D59—81no—
151Dic118—21no—
152Dic118—21no—
153Dic118—42no—
154C8×C59—21no—
155C8×C59—21no—
156C8×C59—21no—
157C8×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59AGL(1,ℤ/8)12yes—
164C22×C59C22×D411yescharacteristic
165C2×D59—22no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—84no—
175C4×C59—21no—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59C2×#4111yescharacteristic
180C4×C59H(5,𝔽2)11yescharacteristic
181Dic59—41no—
182Dic59—41no—
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186#3306—591nomaximal, Sylow
187C2×C59—22no—
188C2×C59—41no—
189C2×C59#54611yescharacteristic
190C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C59#57711yescharacteristic
192D59—42no—
193D59—81no—
194D59—81no—
195#547—591no—
196#546—591no—
197#489—591no—
198#483—591no—
199#481—591no—
200#476—591no—
201#469—591no—
202#465—591no—
203#463—591no—
204#449—591no—
205#447—591no—
206#442—591no—
207#435D5911yescharacteristic, complemented
208#417—591no—
209C2×#102—591no—
210C59#330611yescharacteristic, complemented, Sylow
211C2×#41—591no—
212C2×#41—1181no—
213C22×D4—591no—
214C2×SD16—591no—
215C2×D8—591no—
216C2×D8—591no—
217C2×M16C2×D5911yescharacteristic, complemented
218C22×C8C2×D5911yescharacteristic
219C4⋊Q8—591no—
220#124—591no—
221#123—1181no—
222#123—1181no—
223#123—1181no—
224C22⋊Q8—591no—
225C22⋊Q8—1181no—
226#121—591no—
227#121—591no—
228#121—591no—
229#121—1181no—
230#120—1181no—
231C4×D4—591no—
232C4×D4—591no—
233C4×D4C2×D5911yescharacteristic
234C2×C4⋊C4—591no—
235C2×C4⋊C4—591no—
236C2×C22⋊C4—1181no—
237#106—591no—
238#106—591no—
239#106—591no—
240C4⋊C8C2×D5911yescharacteristic, complemented
241#103—591no—
242#103—591no—
243#103—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251C22⋊C8C2×D5911yescharacteristic
252C22⋊C8C2×D5911yescharacteristic, complemented
253#97C2×D5911yescharacteristic, complemented
254C24—1181no—
255#41—1182no—
256#41—2361no—
257#41—2364no—
258C2×Q8—591no—
259C2×Q8—1181no—
260C2×D4—591no—
261C2×D4—591no—
262C2×D4—591no—
263C2×D4—1182no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—2361no—
270C2×D4D23611yescharacteristic
271C22×C4—1181no—
272C22×C4—1181no—
273C22×C4—1181no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4C22×D5911yescharacteristic
277C22×C4C22×D5911yescharacteristic
278SD16—2361no—
279D8—1182no—
280D8—2361no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D5911yescharacteristic
284C2×C8C22×D5911yescharacteristic
285C2×C8C22×D5911yescharacteristic
286C2×C8C22×D5911yescharacteristic
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—591no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4D23611yescharacteristic
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4D23611yescharacteristic
305C22⋊C4D23611yescharacteristic
306C42C22×D5911yescharacteristic
307C23—1181no—
308C23—1181no—
309C23—1181no—
310C23—4721no—
311C23—2362no—
312C23—2362no—
313C23C2×D23611yescharacteristic
314C23C2×D23611yescharacteristic
315Q8—1181no—
316Q8—1181no—
317Q8—2362no—
318D4—22no—
319D4—592no—
320D4—1181no—
321D4—1181no—
322D4—1181no—
323D4—1181no—
324D4—1181no—
325D4—4721no—
326D4—2362no—
327D4—2362no—
328D4—2362no—
329D4—2362no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—4721no—
340C2×C4—2362no—
341C2×C4—2362no—
342C2×C4—2362no—
343C2×C4—2362no—
344C2×C4C2×D23611yescharacteristic
345C2×C4C2×D23611yescharacteristic
346C2×C4C2×D23611yescharacteristic
347C2×C4C2×D23611yescharacteristic
348C2×C4C23×D5911yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—1182no—
359C22—4724no—
360C22—2361no—
361C22—2361no—
362C22—2361no—
363C22—2361no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22#1427375512yes—
369C22C22×D23611yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—2361no—
375C4—2361no—
376C4—2361no—
377C4—2361no—
378C4—2361no—
379C4#41×D5911yescharacteristic
380C4#1427377211yescharacteristic
381C2—22no—
382C2—41no—
383C2—4721no—
384C2—4721no—
385C2—2362no—
386C2#1683804711yescharacteristic
387C2C2×#1427375511yescharacteristic
388C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3306
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16838056C2semidirect
2. #16838048C2semidirect
3. #16837762C2semidirect
4. #16837733C2semidirect
5. #16837721C2semidirect
6. #16837693C2semidirect
7. #16837655C2semidirect
8. #16837631C2semidirect
9. #16837618C2semidirect
10. #16837549C2semidirect
11. #16837538C2semidirect
12. #16837515C2semidirect
13. #16837404C2semidirect
14. C2×#14273649C2semidirect
15. C59×#435C2semidirect
19. C2×#11745660C22semidirect
22. #14273727C22semidirect
31. #14273701C22semidirect
35. C4×D236C22semidirect
37. C2×C4⋊Dic59C22semidirect
39. #14273659C22semidirect
40. #14273659C22semidirect
41. #14273659C22semidirect
42. #14273652C22semidirect
43. #14273652C22semidirect
44. #14273652C22semidirect
51. #14273649C22semidirect
52. C2×M16×C59C22semidirect
55. C4⋊C8×C59C22semidirect
57. C22⋊C8×C59C22semidirect
58. #97×C59C22semidirect
147. D236#41semidirect
207. #435D59semidirect
210. C59#3306semidirect
217. C2×M16C2×D59semidirect
240. C4⋊C8C2×D59semidirect
252. C22⋊C8C2×D59semidirect
253. #97C2×D59semidirect