Finite Group Databasebeta

← #21433771

Subgroups — #21433771

Order 7552.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273754C211yesmaximal, characteristic, complemented
2C2×#14273735C211yesmaximal, characteristic, complemented
3#16837982C211yesmaximal, characteristic, complemented
4#16837968C211yesmaximal, characteristic, complemented
5#16837655C211yesmaximal, characteristic, complemented
6#16837654C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837639C211yesmaximal, characteristic, complemented
9#16837636C211yesmaximal, characteristic, complemented
10#16837633C211yesmaximal, characteristic, complemented
11#16837628C211yesmaximal, characteristic, complemented
12#16837443C211yesmaximal, characteristic, complemented
13#16837397C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#468C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19#14273754—24no—
20C2×#11745671C2211yescharacteristic
21C2×D472C2211yescharacteristic
22C2×#11745669C2211yescharacteristic
23#14273735—24no—
24C2×#11745659C2211yescharacteristic
25C2×#11745659C2211yescharacteristic, complemented
26C22×C59⋊C8C2211yescharacteristic, complemented
27C2×C8×D59C2211yescharacteristic
28C2×C8×D59C2211yescharacteristic, complemented
29#14273723—21no—
30#14273713—21no—
31#14273705—21no—
32#14273703C2211yescharacteristic, complemented
33#14273702—21no—
34#14273702C2211yescharacteristic
35#14273702C2211yescharacteristic, complemented
36#14273701C2211yescharacteristic
37#14273701C2211yescharacteristic, complemented
38#14273700—21no—
39#14273700—21no—
40#14273698C2211yescharacteristic
41#14273697—21no—
42#14273695—21no—
43#14273685C2211yescharacteristic
44C4⋊C4×D59C2211yescharacteristic
45#14273660C2211yescharacteristic, complemented
46#14273659C2211yescharacteristic, complemented
47#14273658C2211yescharacteristic, complemented
48#14273651C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic, complemented
51#14273648C2211yescharacteristic
52#14273647C2211yescharacteristic
53#14273647C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic
55C2×M16×C59C2211yescharacteristic, complemented
56C22⋊Q8×C59C2211yescharacteristic, complemented
57#121×C59C2211yescharacteristic
58#107×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59D411yescharacteristic
71C2×C22⋊D59D411yescharacteristic
72#11745689—22no—
73#11745689—22no—
74D4×D59—22no—
75D4×D59—22no—
76#11745685—22no—
77#11745685—22no—
78C2×D236—21no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236D411yescharacteristic
82C2×D236C2311yescharacteristic
83C2×D236C2311yescharacteristic
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×C4×D59C2311yescharacteristic
87C2×C4×D59C2311yescharacteristic
88C2×Dic118D411yescharacteristic
89SD16×C59—22no—
90M16×C59—22no—
91C2×C8×C59C2311yescharacteristic
92C2×C8×C59C2311yescharacteristic
93C4⋊C4×C59—21no—
94C4⋊C4×C59C2311yescharacteristic
95C4⋊C4×C59C2311yescharacteristic
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊Dic59—21no—
99#11745671—22no—
100#11745669—22no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107C4⋊Dic59C2311yescharacteristic
108C4⋊Dic59C2311yescharacteristic
109Dic59⋊C4—21no—
110Dic59⋊C4—21no—
111C4×Dic59—21no—
112C2×C59⋊C8—22no—
113C2×C59⋊C8C2311yescharacteristic
114C2×C59⋊C8C2311yescharacteristic
115D472—22no—
116#11745659—22no—
117#11745659D414yescomplemented
118C8×D59—22no—
119C8×D59—22no—
120C23×C59—21no—
121C23×C59C2×D411yescharacteristic
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—42no—
125C22×D59—81no—
126C22×D59—81no—
127C22×D59C2×D411yescharacteristic
128C22×D59C2×D411yescharacteristic
129Q8×C59—21no—
130Q8×C59—21no—
131D4×C59—21no—
132D4×C59—21no—
133D4×C59—81no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2411yescharacteristic
141C22⋊D59—22no—
142C22⋊D59—22no—
143C22⋊D59—42no—
144C22⋊D59—81no—
145C22⋊D59—81no—
146C22⋊D59—81no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59C2×D411yescharacteristic
150C2×Dic59C2×D411yescharacteristic
151D236—22no—
152D236—21no—
153D236—21no—
154D236—21no—
155D236—21no—
156D236—42no—
157D236—81no—
158D236—81no—
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—42no—
162C4×D59—81no—
163C4×D59C2×D412yes—
164C4×D59#4112yes—
165Dic118—22no—
166C8×C59—21no—
167C8×C59C2×D412yes—
168C59⋊C8—21no—
169C59⋊C8C2×D412yes—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59C22×D411yescharacteristic
177C2×D59—21no—
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—21no—
181C2×D59—21no—
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C2×D59#12112yes—
190C4×C59—21no—
191C4×C59—41no—
192C4×C59—41no—
193C4×C59—41no—
194C4×C59C22×D411yescharacteristic
195C4×C59C2×#4111yescharacteristic
196Dic59—21no—
197Dic59—41no—
198Dic59—41no—
199Dic59#12112yes—
200#3062—591nomaximal, Sylow
201C2×C59—41no—
202C2×C59—81no—
203C2×C59C2×#12111yescharacteristic
204C2×C59#57611yescharacteristic
205C2×C59#57711yescharacteristic
206D59—22no—
207D59—41no—
208D59—81no—
209D59—81no—
210C2×AGL(1,ℤ/8)—591no—
211C2×#131—591no—
212#537—591no—
213#535—591no—
214#469—591no—
215#469—591no—
216#468—591no—
217#468D5911yescharacteristic, complemented
218#466—591no—
219#466—591no—
220#465—591no—
221#465—591no—
222#428—591no—
223#416—591no—
224C2×#102—591no—
225C59#306211yescharacteristic, complemented, Sylow
226C2×#41—591no—
227C2×#41—591no—
228C22×D4—591no—
229AGL(1,ℤ/8)—1184no—
230C2×SD16—591no—
231C2×SD16C2×D5911yescharacteristic
232C2×D8—591no—
233C2×D8—591no—
234#131—1184no—
235C2×M16—591no—
236C2×M16—591no—
237C2×M16C2×D5911yescharacteristic, complemented
238C22×C8—591no—
239C22×C8—591no—
240C22×C8—591no—
241#127—1181no—
242#124—1181no—
243C22⋊Q8—591no—
244C22⋊Q8—1181no—
245C22⋊Q8C2×D5911yescharacteristic, complemented
246#121—591no—
247#121—591no—
248#121—591no—
249#121—591no—
250#121—591no—
251#121—1181no—
252#121—1181no—
253#121—1181no—
254#121C2×D5911yescharacteristic
255#120—1181no—
256#120—1181no—
257#117—591no—
258C2×C4⋊C4—591no—
259#107—591no—
260#107C2×D5911yescharacteristic, complemented
261#106—591no—
262#106—591no—
263#103—591no—
264#103C2×D5911yescharacteristic, complemented
265#102—591no—
266#102—591no—
267#102—591no—
268#102—591no—
269#102—591no—
270#102C2×D5911yescharacteristic
271C24—1181no—
272#41—1182no—
273#41—1182no—
274#41—1182no—
275#41—1182no—
276C2×Q8—591no—
277C2×Q8C22×D5911yescharacteristic
278C2×D4—21no—
279C2×D4—591no—
280C2×D4—591no—
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—591no—
284C2×D4—1181no—
285C2×D4—1181no—
286C2×D4—1181no—
287C2×D4—1182no—
288C2×D4—1182no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4—1181no—
292C2×D4—1181no—
293C2×D4C22×D5911yescharacteristic
294C22×C4—591no—
295C22×C4—591no—
296C22×C4—1181no—
297C22×C4—1181no—
298C22×C4C22×D5911yescharacteristic
299SD16—22no—
300SD16—1182no—
301D8—1182no—
302D8—1182no—
303M16—22no—
304M16—594no—
305M16—1182no—
306C2×C8—591no—
307C2×C8—591no—
308C2×C8—1182no—
309C2×C8—1182no—
310C2×C8—1182no—
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—591no—
315C4⋊C4—591no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C4⋊C4C22×D5911yescharacteristic
319C4⋊C4C22×D5911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C42—1181no—
330C23—21no—
331C23—591no—
332C23—591no—
333C23—1181no—
334C23—1181no—
335C23—4721no—
336C23—4721no—
337C23—2362no—
338C23D4×D5911yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—1182no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—1182no—
346D4—1182no—
347D4—1182no—
348D4—1181no—
349D4—1181no—
350D4—1181no—
351D4—1181no—
352D4—4721no—
353D4—4721no—
354D4—4721no—
355D4—4721no—
356D4—4721no—
357D4—2362no—
358D4—2362no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—591no—
365C2×C4—592no—
366C2×C4—592no—
367C2×C4—591no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—1181no—
372C2×C4—4721no—
373C2×C4—2362no—
374C2×C4D4×D5911yescharacteristic
375C2×C4C23×D5911yescharacteristic
376C8—21no—
377C8—592no—
378C8—1181no—
379C8D4×D5912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—592no—
387C22—1181no—
388C22—1181no—
389C22—1181no—
390C22—1181no—
391C22—1181no—
392C22—4724no—
393C22—2361no—
394C22—2361no—
395C22—2361no—
396C22—2361no—
397C22—2361no—
398C22—2361no—
399C22C2×D4×D5911yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—592no—
405C4—1181no—
406C4—2361no—
407C4—2361no—
408C4C2×D4×D5911yescharacteristic
409C4#41×D5911yescharacteristic
410C2—41no—
411C2—81no—
412C2—1182no—
413C2—4721no—
414C2—4721no—
415C2—2361no—
416C2#121×D5911yescharacteristic
417C2#1683820611yescharacteristic
418C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#468C2
socleC22×C59C22×D4
hypercenter#468D59
hypocenterC59#3062
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14273754C2semidirect
2. C2×#14273735C2semidirect
3. #16837982C2semidirect
4. #16837968C2semidirect
5. #16837655C2semidirect
6. #16837654C2semidirect
7. #16837651C2semidirect
8. #16837639C2semidirect
9. #16837636C2semidirect
10. #16837633C2semidirect
11. #16837628C2semidirect
12. #16837443C2semidirect
13. #16837397C2semidirect
14. #102×D59C2semidirect
15. C59×#468C2semidirect
25. C2×#11745659C22semidirect
26. C22×C59⋊C8C22semidirect
28. C2×C8×D59C22semidirect
32. #14273703C22semidirect
35. #14273702C22semidirect
37. #14273701C22semidirect
45. #14273660C22semidirect
46. #14273659C22semidirect
47. #14273658C22semidirect
48. #14273651C22semidirect
50. #14273649C22semidirect
53. #14273647C22semidirect
55. C2×M16×C59C22semidirect
56. C22⋊Q8×C59C22semidirect
58. #107×C59C22semidirect
59. #103×C59C22semidirect
117. #11745659D4semidirect
217. #468D59semidirect
225. C59#3062semidirect
237. C2×M16C2×D59semidirect
245. C22⋊Q8C2×D59semidirect
260. #107C2×D59semidirect
264. #103C2×D59semidirect