Finite Group Databasebeta

← #21436062

Subgroups — #21436062

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#16838057C211yesmaximal, characteristic, complemented
2#16838047C211yesmaximal, characteristic, complemented
3#16837762C211yesmaximal, characteristic, complemented
4#16837734C211yesmaximal, characteristic, complemented
5#16837722C211yesmaximal, characteristic, complemented
6#16837692C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837630C211yesmaximal, characteristic, complemented
9#16837617C211yesmaximal, characteristic, complemented
10#16837544C211yesmaximal, characteristic, complemented
11#16837534C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837400C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#442C211yesmaximal, characteristic, complemented
16C2×#11745685—21no—
17C2×#11745687C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745670C2211yescharacteristic, complemented
20C2×#11745669C2211yescharacteristic
21C2×#11745659C2211yescharacteristic, complemented
22C2×C8×D59C2211yescharacteristic
23#14273727C2211yescharacteristic, complemented
24#14273715C2211yescharacteristic
25#14273711—21no—
26#14273709—21no—
27#14273709—21no—
28#14273707C2211yescharacteristic
29#14273706—21no—
30#14273702C2211yescharacteristic
31#14273701—21no—
32#14273698C2211yescharacteristic
33#14273698C2211yescharacteristic, complemented
34#14273697—21no—
35C4×D236C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic, complemented
38C2×(C2×D59)⋊C4—21no—
39#14273658C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C2×D8×C59C2211yescharacteristic
53C4×D4×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic, complemented
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C22×Dic59—21no—
69#11745687—22no—
70#11745687—41no—
71D4×D59—22no—
72D4×D59—41no—
73#11745685—44no—
74C2×D236—21no—
75C2×D236D411yescharacteristic
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59C2311yescharacteristic
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82C2×Dic118C2311yescharacteristic
83D8×C59—22no—
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93#11745670—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)⋊C4D411yescharacteristic
100(C2×D59)⋊C4D411yescharacteristic
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59D411yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C8×D59—41no—
112C23×C59—21no—
113C23×C59—21no—
114C22×D59—21no—
115C22×D59—42no—
116C22×D59—42no—
117C22×D59—81no—
118C22×D59C2×D411yescharacteristic
119C22×D59C2×D411yescharacteristic
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59#4112yescomplemented
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—42no—
127C2×C4×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C22⋊D59—42no—
133C22⋊D59—42no—
134C22⋊D59—42no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—42no—
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141D236—22no—
142D236—21no—
143D236—21no—
144D236—81no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—21no—
149C4×D59—42no—
150C4×D59—42no—
151Dic118—21no—
152Dic118—21no—
153Dic118—42no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—22no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—84no—
174C2×D59AGL(1,ℤ/8)12yes—
175C4×C59—21no—
176C4×C59—21no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59C2×#4111yescharacteristic
180C4×C59H(5,𝔽2)11yescharacteristic
181Dic59—21no—
182Dic59—21no—
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186#3306—591nomaximal, Sylow
187C2×C59—42no—
188C2×C59—81no—
189C2×C59#54611yescharacteristic
190C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C59#57711yescharacteristic
192D59—22no—
193D59—41no—
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#442D5911yescharacteristic, complemented
207#435—591no—
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×D8C2×D5911yescharacteristic
217C2×M16—591no—
218C22×C8—591no—
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×D4C2×D5911yescharacteristic
233C4×D4C2×D5911yescharacteristic, complemented
234C2×C4⋊C4—591no—
235C2×C4⋊C4—591no—
236C2×C22⋊C4—1181no—
237#106—591no—
238#106—591no—
239#106C2×D5911yescharacteristic, complemented
240C4⋊C8—591no—
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#102C2×D5911yescharacteristic
250#102C2×D5911yescharacteristic, complemented
251C22⋊C8—591no—
252C22⋊C8—591no—
253#97C2×D5911yescharacteristic, complemented
254C24—1181no—
255#41—1182no—
256#41—2364no—
257#41—2361no—
258C2×Q8—591no—
259C2×Q8—1181no—
260C2×D4—591no—
261C2×D4—591no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—1182no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—2361no—
269C2×D4C22×D5911yescharacteristic
270C2×D4C22×D5911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—591no—
274C22×C4—591no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4—1181no—
278SD16—2361no—
279D8—22no—
280D8—2361no—
281M16—2361no—
282C2×C8—591no—
283C2×C8—591no—
284C2×C8—2361no—
285C2×C8C22×D5911yescharacteristic
286C2×C8C22×D5911yescharacteristic
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4C22×D5911yescharacteristic
295C4⋊C4C22×D5911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—591no—
299C22⋊C4—591no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C42C22×D5911yescharacteristic
307C23—21no—
308C23—21no—
309C23—591no—
310C23—591no—
311C23—1181no—
312C23—4721no—
313C23—2362no—
314C23—2362no—
315Q8—1181no—
316Q8—1181no—
317Q8—2362no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—1182no—
322D4—1181no—
323D4—1181no—
324D4—4721no—
325D4—2362no—
326D4—2362no—
327D4—2362no—
328D4—2362no—
329D4#1174568512yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—591no—
335C2×C4—591no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—2362no—
344C2×C4—2362no—
345C2×C4—2362no—
346C2×C4D4×D5911yescharacteristic
347C2×C4D4×D5911yescharacteristic
348C2×C4C23×D5911yescharacteristic
349C8—21no—
350C8—21no—
351C8—1181no—
352C8—1181no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—592no—
360C22—1181no—
361C22—1181no—
362C22—1181no—
363C22—1181no—
364C22—1181no—
365C22—4724no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22C2×D4×D5911yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—1181no—
375C4—1181no—
376C4—2361no—
377C4—2361no—
378C4—2361no—
379C4C2×#1174568511yescharacteristic
380C4#1427377311yescharacteristic
381C2—42no—
382C2—81no—
383C2—1182no—
384C2—4721no—
385C2—2361no—
386C2#1683804811yescharacteristic
387C2AGL(1,ℤ/8)×D5911yescharacteristic
388C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#442C2
socleC22×C59C22×D4
hypercenter#442D59
hypocenterC59#3306
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16838057C2semidirect
2. #16838047C2semidirect
3. #16837762C2semidirect
4. #16837734C2semidirect
5. #16837722C2semidirect
6. #16837692C2semidirect
7. #16837654C2semidirect
8. #16837630C2semidirect
9. #16837617C2semidirect
10. #16837544C2semidirect
11. #16837534C2semidirect
12. #16837475C2semidirect
13. #16837400C2semidirect
14. #102×D59C2semidirect
15. C59×#442C2semidirect
19. C2×#11745670C22semidirect
21. C2×#11745659C22semidirect
23. #14273727C22semidirect
33. #14273698C22semidirect
37. C4⋊C4×D59C22semidirect
39. #14273658C22semidirect
40. #14273658C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273652C22semidirect
44. #14273650C22semidirect
51. (C2×D59)⋊C8C22semidirect
54. C4×D4×C59C22semidirect
55. #106×C59C22semidirect
57. #102×C59C22semidirect
58. #97×C59C22semidirect
123. D4×C59#41semidirect
206. #442D59semidirect
210. C59#3306semidirect
233. C4×D4C2×D59semidirect
239. #106C2×D59semidirect
250. #102C2×D59semidirect
253. #97C2×D59semidirect
329. D4#11745685semidirect