Finite Group Databasebeta

← #21436294

Subgroups — #21436294

Order 7552.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838105C211yesmaximal, characteristic, complemented
2#16838047C211yesmaximal, characteristic, complemented
3#16837759C211yesmaximal, characteristic, complemented
4#16837746C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837656C211yesmaximal, characteristic, complemented
7#16837649C211yesmaximal, characteristic, complemented
8#16837618C211yesmaximal, characteristic, complemented
9#16837548C211yesmaximal, characteristic, complemented
10#16837537C211yesmaximal, characteristic, complemented
11C4×#11745669C211yesmaximal, characteristic, complemented
12#16837479C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#16837400C211yesmaximal, characteristic, complemented
15C59×#478C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745660C2211yescharacteristic, complemented
19C2×D472C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22C2×#11745659C2211yescharacteristic, complemented
23#14273722—21no—
24#14273715C2211yescharacteristic
25#14273712—21no—
26#14273711—21no—
27#14273707C2211yescharacteristic
28#14273702—21no—
29#14273702C2211yescharacteristic
30#14273702C2211yescharacteristic
31#14273702C2211yescharacteristic, complemented
32#14273701—21no—
33#14273697—21no—
34C4×D236C2211yescharacteristic
35C4×D236C2211yescharacteristic, complemented
36#14273689—21no—
37#14273685C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic, complemented
39C2×(C2×D59)⋊C4—21no—
40#14273660C2211yescharacteristic, complemented
41#14273652C2211yescharacteristic, complemented
42#14273650C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic, complemented
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C4×C59⋊C8C2211yescharacteristic, complemented
52#125×C59C2211yescharacteristic, complemented
53C4×D4×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65#11745687—22no—
66#11745687—41no—
67D4×D59—22no—
68D4×D59—41no—
69C2×D236—21no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236D411yescharacteristic
73C2×D236C2311yescharacteristic
74C2×D236C2311yescharacteristic
75C2×C4×D59—21no—
76C2×C4×D59—21no—
77C2×C4×D59C2311yescharacteristic
78C2×C4×D59C2311yescharacteristic
79C2×Dic118C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C42×C59C2311yescharacteristic
89#11745669—22no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4D411yescharacteristic
99(C2×D59)⋊C4D411yescharacteristic
100C4⋊Dic59—21no—
101C4⋊Dic59D411yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C2×C59⋊C8C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107D472—41no—
108#11745660—41no—
109#11745659—41no—
110#11745659—41no—
111C23×C59—21no—
112C22×D59—21no—
113C22×D59—21no—
114C22×D59—42no—
115C22×D59—42no—
116C22×D59—81no—
117C22×D59C2×D411yescharacteristic
118C22×D59C2×D411yescharacteristic
119D4×C59—21no—
120D4×C59#4112yes—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—81no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C22⋊D59—42no—
129C22⋊D59—42no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—42no—
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135D236—21no—
136D236—21no—
137D236—21no—
138D236—21no—
139D236—41no—
140D236—42no—
141D236—81no—
142D236—81no—
143C4×D59—21no—
144C4×D59—21no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—81no—
148C4×D59—81no—
149Dic118—21no—
150Dic118—21no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—22no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—84no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59—41no—
177C4×C59C2×#4111yescharacteristic
178C4×C59H(5,𝔽2)11yescharacteristic
179Dic59—21no—
180Dic59—21no—
181Dic59—41no—
182Dic59—41no—
183#3322—591nomaximal, Sylow
184C2×C59—42no—
185C2×C59#54611yescharacteristic
186C2×C59#57511yescharacteristic
187C2×C59#57611yescharacteristic
188D59—41no—
189D59—41no—
190D59—81no—
191D59—81no—
192#553—591no—
193#546—591no—
194#488—591no—
195#485—591no—
196#480—591no—
197#478D5911yescharacteristic, complemented
198#469—591no—
199#468—591no—
200#463—591no—
201#449—591no—
202#447—591no—
203C4×D8—591no—
204#436—591no—
205#418—591no—
206#417—591no—
207C59#332211yescharacteristic, complemented, Sylow
208C2×#41—591no—
209C22×D4—591no—
210C2×SD16—591no—
211C2×D8—591no—
212C2×D8—591no—
213C2×M16—591no—
214C2×M16—591no—
215#126—1181no—
216#125C2×D5911yescharacteristic, complemented
217#124—591no—
218#123—1181no—
219#123—1181no—
220C22⋊Q8—591no—
221#121—591no—
222#121—591no—
223#121—591no—
224#121—1181no—
225#121—1181no—
226#120—1181no—
227C4×D4—591no—
228C4×D4—591no—
229C4×D4—1181no—
230C4×D4C2×D5911yescharacteristic
231#117—591no—
232C2×C4⋊C4—591no—
233C2×C22⋊C4—1181no—
234#107—591no—
235#107C2×D5911yescharacteristic, complemented
236#106C2×D5911yescharacteristic, complemented
237C4⋊C8C2×D5911yescharacteristic, complemented
238#103—591no—
239#103—591no—
240#103—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102C2×D5911yescharacteristic
247#102C2×D5911yescharacteristic
248C22⋊C8—591no—
249C22⋊C8—591no—
250C4×C8—591no—
251C24—1181no—
252#41—1182no—
253#41—2361no—
254C2×Q8—591no—
255C2×D4—591no—
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—1181no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1182no—
263C2×D4—1181no—
264C2×D4—2361no—
265C2×D4C22×D5911yescharacteristic
266C22×C4—21no—
267C22×C4—591no—
268C22×C4—591no—
269C22×C4—1181no—
270C22×C4—1181no—
271C22×C4—1181no—
272SD16—2361no—
273D8—1182no—
274D8—2361no—
275M16—2361no—
276M16—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22×D5911yescharacteristic
288C4⋊C4C22×D5911yescharacteristic
289C4⋊C4C22×D5911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—591no—
292C22⋊C4—591no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C42—1181no—
302C42C22×D5911yescharacteristic
303C23—21no—
304C23—591no—
305C23—591no—
306C23—1181no—
307C23—1181no—
308C23—4721no—
309C23—2362no—
310C23—2362no—
311Q8—1181no—
312Q8—1181no—
313D4—21no—
314D4—1181no—
315D4—1181no—
316D4—1181no—
317D4—1181no—
318D4—4721no—
319D4—4721no—
320D4—2361no—
321D4—2362no—
322D4—2362no—
323D4—2362no—
324D4#1174568912yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—591no—
330C2×C4—591no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—4721no—
338C2×C4—4721no—
339C2×C4—2362no—
340C2×C4D4×D5911yescharacteristic
341C2×C4D4×D5911yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1181no—
346C8—1181no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—1181no—
351C22—1181no—
352C22—1181no—
353C22—1181no—
354C22—1181no—
355C22—1181no—
356C22—4724no—
357C22—2361no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22—2361no—
362C22—2361no—
363C22C2×D4×D5911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—1181no—
370C4—1181no—
371C4—2361no—
372C4—2361no—
373C4C2×#1174568911yescharacteristic
374C4#1427377311yescharacteristic
375C2—42no—
376C2—4721no—
377C2—4721no—
378C2—2361no—
379C2—2361no—
380C2#1683804311yescharacteristic
381C2#1683819911yescharacteristic
382C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#478C2
socleC22×C59C22×D4
hypercenter#478D59
hypocenterC59#3322
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16838105C2semidirect
2. #16838047C2semidirect
3. #16837759C2semidirect
4. #16837746C2semidirect
5. #16837717C2semidirect
6. #16837656C2semidirect
7. #16837649C2semidirect
8. #16837618C2semidirect
9. #16837548C2semidirect
10. #16837537C2semidirect
11. C4×#11745669C2semidirect
12. #16837479C2semidirect
13. #16837405C2semidirect
14. #16837400C2semidirect
15. C59×#478C2semidirect
18. C2×#11745660C22semidirect
22. C2×#11745659C22semidirect
31. #14273702C22semidirect
35. C4×D236C22semidirect
38. C4⋊C4×D59C22semidirect
40. #14273660C22semidirect
41. #14273652C22semidirect
42. #14273650C22semidirect
43. #14273650C22semidirect
48. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C4×C59⋊C8C22semidirect
52. #125×C59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. C4⋊C8×C59C22semidirect
197. #478D59semidirect
207. C59#3322semidirect
216. #125C2×D59semidirect
235. #107C2×D59semidirect
236. #106C2×D59semidirect
237. C4⋊C8C2×D59semidirect