Finite Group Databasebeta

← #21436056

Subgroups — #21436056

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#16838055C211yesmaximal, characteristic, complemented
2#16838045C211yesmaximal, characteristic, complemented
3#16837731C211yesmaximal, characteristic, complemented
4#16837719C211yesmaximal, characteristic, complemented
5#16837689C211yesmaximal, characteristic, complemented
6#16837654C211yesmaximal, characteristic, complemented
7#16837634C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837550C211yesmaximal, characteristic, complemented
10#16837537C211yesmaximal, characteristic, complemented
11#16837515C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837402C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#489C211yesmaximal, characteristic, complemented
16C2×#11745689—21no—
17C2×#11745689C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745671C2211yescharacteristic, complemented
20C2×D472C2211yescharacteristic
21C2×#11745669C2211yescharacteristic
22C2×#11745659C2211yescharacteristic, complemented
23C2×C8×D59C2211yescharacteristic
24#14273712—21no—
25#14273712—21no—
26#14273709—21no—
27#14273703—21no—
28#14273703C2211yescharacteristic
29#14273702C2211yescharacteristic
30#14273702C2211yescharacteristic, complemented
31#14273700—21no—
32#14273698C2211yescharacteristic
33#14273697—21no—
34C4×D236C2211yescharacteristic
35C4×D236C2211yescharacteristic
36C4×D236C2211yescharacteristic, complemented
37C4⋊C4×D59C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic, complemented
39C22⋊C4×D59—21no—
40#14273659C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43C4⋊(C59⋊C8)C2211yescharacteristic, complemented
44#14273651C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C4⋊Q8×C59C2211yescharacteristic, complemented
53#124×C59C2211yescharacteristic
54#103×C59C2211yescharacteristic, complemented
55#103×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×Q8×C59—21no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65#11745689—22no—
66#11745689—41no—
67#11745689—44no—
68D4×D59—22no—
69D4×D59—41no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236D411yescharacteristic
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59C2311yescharacteristic
82C2×C4×D59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92#11745671—41no—
93#11745669—41no—
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)⋊C4D411yescharacteristic
100(C2×D59)⋊C4D411yescharacteristic
101C4⋊Dic59D411yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109D472—22no—
110#11745659—41no—
111C8×D59—41no—
112C23×C59—21no—
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—42no—
116C22×D59—42no—
117C22×D59—81no—
118C22×D59C2×D411yescharacteristic
119C22×D59C2×D411yescharacteristic
120Q8×C59—21no—
121Q8×C59—21no—
122Q8×C59—42no—
123D4×C59—21no—
124D4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C22⋊D59—81no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137D236—22no—
138D236—21no—
139D236—21no—
140D236—21no—
141D236—42no—
142D236—42no—
143D236—42no—
144D236#4112yescomplemented
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—21no—
149C4×D59—42no—
150C4×D59—42no—
151C4×D59—42no—
152C4×D59—42no—
153C4×D59—81no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59C22×D411yescharacteristic
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—22no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—41no—
169C2×D59—41no—
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×C59—41no—
180C4×C59C2×#4111yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—21no—
183Dic59—21no—
184Dic59—41no—
185Dic59—41no—
186#3306—591nomaximal, Sylow
187C2×C59—81no—
188C2×C59#54611yescharacteristic
189C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C59#57711yescharacteristic
191D59—22no—
192D59—41no—
193D59—42no—
194D59—81no—
195#547—591no—
196#546—591no—
197#489D5911yescharacteristic, complemented
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#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×D8—591no—
217C2×M16—591no—
218C22×C8—591no—
219C4⋊Q8C2×D5911yescharacteristic, complemented
220#124C2×D5911yescharacteristic
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×D4—591no—
234C2×C4⋊C4—591no—
235C2×C4⋊C4—591no—
236C2×C22⋊C4—1181no—
237#106—591no—
238#106—591no—
239#106—591no—
240C4⋊C8—591no—
241#103—591no—
242#103C2×D5911yescharacteristic, complemented
243#103C2×D5911yescharacteristic, complemented
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102C2×D5911yescharacteristic
250#102C2×D5911yescharacteristic
251C22⋊C8—591no—
252C22⋊C8—591no—
253#97C2×D5911yescharacteristic, complemented
254C24—1181no—
255#41—1182no—
256#41—2361no—
257#41—2364no—
258C2×Q8—21no—
259C2×Q8C22×D5911yescharacteristic
260C2×D4—591no—
261C2×D4—591no—
262C2×D4—591no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1182no—
268C2×D4—1181no—
269C2×D4—2361no—
270C2×D4C22×D5911yescharacteristic
271C22×C4—591no—
272C22×C4—591no—
273C22×C4—1181no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4—1181no—
278SD16—2361no—
279D8—1182no—
280D8—2361no—
281M16—2361no—
282C2×C8—591no—
283C2×C8—591no—
284C2×C8—2361no—
285C2×C8C22×D5911yescharacteristic
286C2×C8C22×D5911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—591no—
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—591no—
309C23—591no—
310C23—1181no—
311C23—1181no—
312C23—4721no—
313C23—2362no—
314C23—2362no—
315Q8—21no—
316Q8—21no—
317Q8—42no—
318D4—21no—
319D4—21no—
320D4—592no—
321D4—1182no—
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—591no—
334C2×C4—591no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—4721no—
342C2×C4—2362no—
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—41no—
354C22—41no—
355C22—41no—
356C22—592no—
357C22—1181no—
358C22—1181no—
359C22—1181no—
360C22—1181no—
361C22—1181no—
362C22—1182no—
363C22—4724no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22C2×D4×D5911yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—1181no—
376C4—1181no—
377C4—2361no—
378C4—2361no—
379C4#41×D5911yescharacteristic
380C4#1427377311yescharacteristic
381C2—81no—
382C2—1182no—
383C2—4721no—
384C2—2361no—
385C2—2362no—
386C2#1683804511yescharacteristic
387C2AGL(1,ℤ/8)×D5911yescharacteristic
388C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#489C2
socleC22×C59C22×D4
hypercenter#489D59
hypocenterC59#3306
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16838055C2semidirect
2. #16838045C2semidirect
3. #16837731C2semidirect
4. #16837719C2semidirect
5. #16837689C2semidirect
6. #16837654C2semidirect
7. #16837634C2semidirect
8. #16837614C2semidirect
9. #16837550C2semidirect
10. #16837537C2semidirect
11. #16837515C2semidirect
12. #16837475C2semidirect
13. #16837402C2semidirect
14. #102×D59C2semidirect
15. C59×#489C2semidirect
19. C2×#11745671C22semidirect
22. C2×#11745659C22semidirect
30. #14273702C22semidirect
36. C4×D236C22semidirect
38. C4⋊C4×D59C22semidirect
40. #14273659C22semidirect
41. #14273658C22semidirect
42. #14273658C22semidirect
43. C4⋊(C59⋊C8)C22semidirect
44. #14273651C22semidirect
46. #14273649C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. C4⋊Q8×C59C22semidirect
54. #103×C59C22semidirect
55. #103×C59C22semidirect
58. #97×C59C22semidirect
144. D236#41semidirect
197. #489D59semidirect
210. C59#3306semidirect
219. C4⋊Q8C2×D59semidirect
242. #103C2×D59semidirect
243. #103C2×D59semidirect
253. #97C2×D59semidirect