Finite Group Databasebeta

← #21435620

Subgroups — #21435620

Order 7552.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273754C211yesmaximal, characteristic, complemented
2C2×#14273750C211yesmaximal, characteristic, complemented
3#16838055C211yesmaximal, characteristic, complemented
4#16838045C211yesmaximal, characteristic, complemented
5#16837657C211yesmaximal, characteristic, complemented
6#16837628C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837604C211yesmaximal, characteristic, complemented
9#16837563C211yesmaximal, characteristic, complemented
10#16837563C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837546C211yesmaximal, characteristic, complemented
13#16837515C211yesmaximal, characteristic, complemented
14#16837475C211yesmaximal, characteristic, complemented
15C59×#497C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745689C2211yescharacteristic
18C2×#11745689C2211yescharacteristic, complemented
19C2×D4×D59C2211yescharacteristic
20#14273754—24no—
21#14273750—24no—
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic
24C2×#11745671C2211yescharacteristic, complemented
25C2×D472C2211yescharacteristic
26C2×#11745669C2211yescharacteristic
27C2×#11745659C2211yescharacteristic
28C2×C8×D59C2211yescharacteristic, complemented
29#14273712—21no—
30#14273712—21no—
31#14273709—21no—
32#14273703C2211yescharacteristic
33#14273703C2211yescharacteristic
34#14273703C2211yescharacteristic, complemented
35#14273702—21no—
36#14273700—21no—
37#14273698C2211yescharacteristic
38#14273697—21no—
39C4×D236C2211yescharacteristic
40C4×D236C2211yescharacteristic
41C4×D236C2211yescharacteristic, complemented
42C4⋊C4×D59—21no—
43C22⋊C4×D59—21no—
44#14273659C2211yescharacteristic, complemented
45C4⋊(C59⋊C8)C2211yescharacteristic, complemented
46#14273651C2211yescharacteristic, complemented
47#14273651C2211yescharacteristic, complemented
48#14273651C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic, complemented
51#14273648C2211yescharacteristic
52(C2×D59)⋊C8C2211yescharacteristic
53(C2×D59)⋊C8C2211yescharacteristic, complemented
54C2×Q16×C59C2211yescharacteristic, complemented
55C2×Q16×C59C2211yescharacteristic, complemented
56C2×SD16×C59C2211yescharacteristic
57C2×SD16×C59C2211yescharacteristic
58C4⋊Q8×C59C2211yescharacteristic, complemented
59#124×C59C2211yescharacteristic
60#97×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×Q8×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68#11745689—22no—
69#11745689—22no—
70#11745689—22no—
71#11745689—41no—
72#11745689—41no—
73#11745689—41no—
74D4×D59—22no—
75D4×D59—41no—
76C2×D236—21no—
77C2×D236—21no—
78C2×D236—21no—
79C2×D236D411yescharacteristic
80C2×D236C2311yescharacteristic
81C2×D236C2311yescharacteristic
82C2×C4×D59—21no—
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×C4×D59—21no—
87C2×C4×D59C2311yescharacteristic
88C2×C4×D59C2311yescharacteristic
89Q16×C59—22no—
90Q16×C59—41no—
91SD16×C59—22no—
92SD16×C59—41no—
93C2×C8×C59C2311yescharacteristic
94C2×C8×C59C2311yescharacteristic
95C4⋊C4×C59—21no—
96C4⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊C4×C59—21no—
99C42×C59C2311yescharacteristic
100C22⋊Dic59—21no—
101#11745671—22no—
102#11745671—22no—
103#11745671—22no—
104#11745669—22no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110(C2×D59)⋊C4D411yescharacteristic
111(C2×D59)⋊C4D411yescharacteristic
112C4⋊Dic59D411yescharacteristic
113C4⋊Dic59C2311yescharacteristic
114C4⋊Dic59C2311yescharacteristic
115Dic59⋊C4—21no—
116Dic59⋊C4—21no—
117Dic59⋊C4—21no—
118C2×C59⋊C8C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120D472D414yescomplemented
121#11745659—22no—
122C8×D59—22no—
123C23×C59—21no—
124C22×D59—21no—
125C22×D59—21no—
126C22×D59—42no—
127C22×D59—42no—
128C22×D59—81no—
129C22×D59C2×D411yescharacteristic
130C22×D59C2×D411yescharacteristic
131Q8×C59—21no—
132Q8×C59—21no—
133Q8×C59—21no—
134Q8×C59—21no—
135Q8×C59—21no—
136Q8×C59—21no—
137D4×C59—21no—
138D4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2×D411yescharacteristic
144C2×C4×C59C2411yescharacteristic
145C22⋊D59—42no—
146C22⋊D59—81no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59C2×D411yescharacteristic
150C2×Dic59C2×D411yescharacteristic
151D236—21no—
152D236—21no—
153D236—41no—
154D236—42no—
155D236—42no—
156D236—42no—
157D236C2×D412yes—
158D236C2×D412yes—
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—21no—
162C4×D59—21no—
163C4×D59—42no—
164C4×D59—42no—
165C4×D59—42no—
166C4×D59—42no—
167C4×D59—81no—
168C8×C59—21no—
169C8×C59C2×D412yes—
170C59⋊C8—21no—
171C59⋊C8—21no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59C22×D411yescharacteristic
176C2×D59—21no—
177C2×D59—21no—
178C2×D59—22no—
179C2×D59—22no—
180C2×D59—21no—
181C2×D59—21no—
182C2×D59—21no—
183C2×D59—21no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—41no—
192C4×C59—41no—
193C4×C59—41no—
194C4×C59C22×D411yescharacteristic
195C4×C59H(5,𝔽2)11yescharacteristic
196Dic59—21no—
197Dic59—21no—
198Dic59—41no—
199Dic59—41no—
200#3267—591nomaximal, Sylow
201C2×C59—81no—
202C2×C59D4211yescharacteristic
203C2×C59#57511yescharacteristic
204C2×C59#57711yescharacteristic
205D59—41no—
206D59—41no—
207D59—42no—
208D59—42no—
209C2×AGL(1,ℤ/8)—591no—
210C2×#135—591no—
211#547—591no—
212#546—591no—
213#497D5911yescharacteristic, complemented
214#470—591no—
215#465—591no—
216#463—591no—
217#461—591no—
218#452—591no—
219#452—591no—
220#450—591no—
221#449—591no—
222#442—591no—
223#435—591no—
224C59#326711yescharacteristic, complemented, Sylow
225C2×#41—591no—
226C2×#41—591no—
227C2×#41—591no—
228C22×D4—591no—
229AGL(1,ℤ/8)—1184no—
230#135—1184no—
231C2×Q16C2×D5911yescharacteristic, complemented
232C2×Q16C2×D5911yescharacteristic, complemented
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16C2×D5911yescharacteristic
237C2×SD16C2×D5911yescharacteristic
238C2×D8—591no—
239C2×D8—591no—
240C2×M16—591no—
241C22×C8—591no—
242C4⋊Q8C2×D5911yescharacteristic, complemented
243#124C2×D5911yescharacteristic
244#123—1181no—
245#123—1181no—
246#123—1181no—
247C22⋊Q8—591no—
248C22⋊Q8—591no—
249C22⋊Q8—591no—
250#121—591no—
251#121—1181no—
252#121—1181no—
253#120—1181no—
254C4×D4—591no—
255C4×D4—591no—
256C4×D4—591no—
257C2×C4⋊C4—1181no—
258C2×C22⋊C4—1181no—
259#106—591no—
260C4⋊C8—591no—
261#103—591no—
262#103—591no—
263#103—591no—
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8—591no—
268C22⋊C8—591no—
269#97C2×D5911yescharacteristic, complemented
270C24—1181no—
271#41—1182no—
272#41—1182no—
273#41—1182no—
274#41—2361no—
275#41—2361no—
276#41—2361no—
277C2×Q8C22×D5911yescharacteristic
278C2×Q8C22×D5911yescharacteristic
279C2×Q8C22×D5911yescharacteristic
280C2×D4—591no—
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4—1181no—
286C2×D4—1181no—
287C2×D4—1182no—
288C2×D4—1181no—
289C2×D4—2361no—
290C2×D4C22×D5911yescharacteristic
291C22×C4—591no—
292C22×C4—591no—
293C22×C4—1181no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4—1181no—
298Q16—22no—
299Q16—41no—
300SD16—22no—
301SD16—41no—
302SD16—1182no—
303SD16—1182no—
304SD16—1182no—
305D8—594no—
306D8—1182no—
307M16—1182no—
308C2×C8—591no—
309C2×C8—591no—
310C2×C8—1182no—
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—591no—
316C4⋊C4—591no—
317C4⋊C4—591no—
318C4⋊C4—1181no—
319C4⋊C4—1181no—
320C4⋊C4—1181no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—591no—
324C22⋊C4—591no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C22⋊C4—1181no—
330C22⋊C4—1181no—
331C42C22×D5911yescharacteristic
332C23—21no—
333C23—591no—
334C23—591no—
335C23—1181no—
336C23—1181no—
337C23—4721no—
338C23—2362no—
339C23—2362no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—21no—
346D4—21no—
347D4—21no—
348D4—592no—
349D4—592no—
350D4—1181no—
351D4—1181no—
352D4—4721no—
353D4—2361no—
354D4—2362no—
355D4—2362no—
356D4—2362no—
357D4—2362no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—591no—
362C2×C4—591no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—1181no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—4721no—
370C2×C4—2362no—
371C2×C4—2362no—
372C2×C4—2362no—
373C2×C4—2362no—
374C2×C4D4×D5911yescharacteristic
375C2×C4D4×D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—21no—
378C8—1181no—
379C8—1181no—
380C8D4×D5912yes—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—1181no—
385C22—1181no—
386C22—1181no—
387C22—1181no—
388C22—1181no—
389C22—1181no—
390C22—1182no—
391C22—1182no—
392C22—4724no—
393C22—2361no—
394C22—2361no—
395C22—2361no—
396C22—2361no—
397C22C2×D4×D5911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—1181no—
404C4—1181no—
405C4—2361no—
406C4—2361no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377211yescharacteristic
409C2—81no—
410C2—2361no—
411C2—2361no—
412C2—2362no—
413C2—2362no—
414C2#1683803711yescharacteristic
415C2#1683820111yescharacteristic
416C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#497C2
socleC22×C59C22×D4
hypercenter#497D59
hypocenterC59#3267
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#14273754C2semidirect
2. C2×#14273750C2semidirect
3. #16838055C2semidirect
4. #16838045C2semidirect
5. #16837657C2semidirect
6. #16837628C2semidirect
7. #16837614C2semidirect
8. #16837604C2semidirect
9. #16837563C2semidirect
10. #16837563C2semidirect
11. #16837551C2semidirect
12. #16837546C2semidirect
13. #16837515C2semidirect
14. #16837475C2semidirect
15. C59×#497C2semidirect
18. C2×#11745689C22semidirect
24. C2×#11745671C22semidirect
28. C2×C8×D59C22semidirect
34. #14273703C22semidirect
41. C4×D236C22semidirect
44. #14273659C22semidirect
45. C4⋊(C59⋊C8)C22semidirect
46. #14273651C22semidirect
47. #14273651C22semidirect
48. #14273651C22semidirect
50. #14273649C22semidirect
53. (C2×D59)⋊C8C22semidirect
54. C2×Q16×C59C22semidirect
55. C2×Q16×C59C22semidirect
58. C4⋊Q8×C59C22semidirect
60. #97×C59C22semidirect
120. D472D4semidirect
213. #497D59semidirect
224. C59#3267semidirect
231. C2×Q16C2×D59semidirect
232. C2×Q16C2×D59semidirect
242. C4⋊Q8C2×D59semidirect
269. #97C2×D59semidirect