Finite Group Databasebeta

← #21435724

Subgroups — #21435724

Order 7552.

498 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×#14273759C211yesmaximal, characteristic, complemented
2C2×#14273755C211yesmaximal, characteristic, complemented
3#16838062C211yesmaximal, characteristic, complemented
4#16838043C211yesmaximal, characteristic, complemented
5#16837787C211yesmaximal, characteristic, complemented
6#16837656C211yesmaximal, characteristic, complemented
7#16837627C211yesmaximal, characteristic, complemented
8#16837620C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837552C211yesmaximal, characteristic, complemented
11#16837550C211yesmaximal, characteristic, complemented
12#16837542C211yesmaximal, characteristic, complemented
13#16837489C211yesmaximal, characteristic, complemented
14#16837478C211yesmaximal, characteristic, complemented
15C59×#470C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18C2×Q8×D59C2211yescharacteristic, complemented
19C22×D236C2211yescharacteristic
20#14273759—24no—
21#14273755—24no—
22C2×#11745672C2211yescharacteristic, complemented
23C2×#11745660C2211yescharacteristic
24C2×#11745660C2211yescharacteristic
25C2×#11745671C2211yescharacteristic
26C2×#11745671C2211yescharacteristic
27C2×#11745671C2211yescharacteristic, complemented
28C2×D472C2211yescharacteristic
29C2×D472C2211yescharacteristic
30C2×#11745659C2211yescharacteristic, complemented
31#14273716C2211yescharacteristic
32#14273716C2211yescharacteristic, complemented
33#14273713—21no—
34#14273712—21no—
35#14273705—21no—
36#14273702—21no—
37#14273702C2211yescharacteristic
38#14273702C2211yescharacteristic, complemented
39#14273700—21no—
40#14273697—21no—
41#14273692C2211yescharacteristic, complemented
42#14273689—21no—
43#14273689C2211yescharacteristic
44C4×C22⋊D59C2211yescharacteristic
45C22⋊C4×D59—21no—
46Dic59⋊C8C2211yescharacteristic, complemented
47#14273650C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic
50#14273647C2211yescharacteristic, complemented
51C22⋊(C59⋊C8)C2211yescharacteristic
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53C8×Dic59C2211yescharacteristic, complemented
54C2×Q16×C59C2211yescharacteristic, complemented
55C2×M16×C59C2211yescharacteristic
56C22⋊Q8×C59C2211yescharacteristic
57C22⋊Q8×C59C2211yescharacteristic
58#106×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#103×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59D411yescharacteristic
67#11745689—22no—
68#11745689—41no—
69Q8×D59—22no—
70Q8×D59—41no—
71#11745685—22no—
72#11745685—41no—
73C2×D236—22no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236—21no—
77C2×D236—21no—
78C2×D236—41no—
79C2×D236C2311yescharacteristic
80C2×D236C2311yescharacteristic
81C2×D236C2311yescharacteristic
82C2×C4×D59—21no—
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×C4×D59C2311yescharacteristic
87C2×Dic118—21no—
88C2×Dic118C2311yescharacteristic
89Q16×C59—22no—
90M16×C59—22no—
91C2×C8×C59C2311yescharacteristic
92C2×C8×C59C2311yescharacteristic
93C4⋊C4×C59—21no—
94C4⋊C4×C59—21no—
95C4⋊C4×C59C2311yescharacteristic
96C4⋊C4×C59C2311yescharacteristic
97C22⋊C4×C59—21no—
98C22⋊C4×C59—21no—
99C22⋊Dic59D411yescharacteristic
100#11745672—22no—
101#11745671—22no—
102#11745671—41no—
103#11745671—41no—
104(C2×D59)⋊C4—21no—
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)⋊C4—21no—
111(C2×D59)⋊C4D411yescharacteristic
112Dic59⋊C4—21no—
113Dic59⋊C4D411yescharacteristic
114C4×Dic59—21no—
115C4×Dic59C2311yescharacteristic
116C2×C59⋊C8C2311yescharacteristic
117C2×C59⋊C8C2311yescharacteristic
118D472—22no—
119D472—22no—
120#11745660—22no—
121#11745660D414yescomplemented
122#11745659—22no—
123C23×C59C2×D411yescharacteristic
124C22×D59—21no—
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—42no—
128C22×D59—42no—
129C22×D59—81no—
130C22×D59C2×D411yescharacteristic
131Q8×C59—21no—
132Q8×C59—21no—
133Q8×C59—21no—
134Q8×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2411yescharacteristic
143C22⋊D59—41no—
144C22⋊D59—42no—
145C2×Dic59—21no—
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148C2×Dic59C2×D411yescharacteristic
149D236—21no—
150D236—21no—
151D236—21no—
152D236—21no—
153D236—21no—
154D236—42no—
155D236—42no—
156D236—42no—
157D236—81no—
158D236C2×D412yes—
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—42no—
162C4×D59—42no—
163C4×D59—42no—
164C4×D59—81no—
165Dic118—21no—
166Dic118—42no—
167Dic118C2×D412yes—
168C8×C59—21no—
169C8×C59C2×D412yes—
170C59⋊C8—21no—
171C59⋊C8—21no—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59C22×D411yescharacteristic
176C2×D59—21no—
177C2×D59—22no—
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C4×C59—21no—
190C4×C59—41no—
191C4×C59—41no—
192C4×C59—41no—
193C4×C59—41no—
194C4×C59C22×D411yescharacteristic
195C4×C59H(5,𝔽2)11yescharacteristic
196Dic59—22no—
197Dic59—21no—
198Dic59—21no—
199Dic59—21no—
200#3275—591nomaximal, Sylow
201C2×C59—41no—
202C2×C59D4211yescharacteristic
203C2×C59#57511yescharacteristic
204C2×C59#57711yescharacteristic
205D59—41no—
206D59—42no—
207D59—81no—
208D59—81no—
209C2×#137—591no—
210C2×AGL(1,ℤ/8)—591no—
211#548—591no—
212#546—591no—
213#495—591no—
214#470D5911yescharacteristic, complemented
215#469—591no—
216#464—591no—
217#463—591no—
218#452—591no—
219#450—591no—
220#449—591no—
221#448—591no—
222C4×SD16—591no—
223#436—591no—
224C59#327511yescharacteristic, complemented, Sylow
225C2×#41—591no—
226C2×#41—591no—
227C22×Q8—591no—
228C22×D4—591no—
229#137—1184no—
230AGL(1,ℤ/8)—1184no—
231C2×Q16—591no—
232C2×Q16C2×D5911yescharacteristic, complemented
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16—591no—
237C2×SD16—591no—
238C2×D8—591no—
239C2×D8—591no—
240C2×M16—591no—
241C2×M16C2×D5911yescharacteristic
242#124—591no—
243#124—591no—
244#124—1181no—
245#123—1181no—
246C22⋊Q8—1181no—
247C22⋊Q8C2×D5911yescharacteristic
248C22⋊Q8C2×D5911yescharacteristic
249#121—591no—
250#121—591no—
251#121—1181no—
252#121—1181no—
253#120—1181no—
254C4×Q8—591no—
255C4×D4—591no—
256C4×D4—591no—
257C4×D4—1181no—
258C2×C22⋊C4—1181no—
259#106C2×D5911yescharacteristic, complemented
260C4⋊C8—591no—
261#103—591no—
262#103C2×D5911yescharacteristic, complemented
263#103C2×D5911yescharacteristic, complemented
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8—591no—
268C22⋊C8—591no—
269C4×C8—591no—
270C24—1181no—
271#41—1182no—
272#41—1182no—
273#41—2361no—
274#41—2361no—
275C2×Q8—591no—
276C2×Q8—1181no—
277C2×Q8—1182no—
278C2×Q8—2361no—
279C2×Q8C22×D5911yescharacteristic
280C2×Q8C22×D5911yescharacteristic
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—591no—
284C2×D4—591no—
285C2×D4—1182no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4—2361no—
292C22×C4—591no—
293C22×C4—1181no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4C22×D5911yescharacteristic
298Q16—22no—
299Q16—1182no—
300SD16—594no—
301SD16—1182no—
302SD16—1182no—
303SD16—2361no—
304SD16—2361no—
305D8—1182no—
306D8—1182no—
307M16—22no—
308M16—1182no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—591no—
316C4⋊C4—1181no—
317C4⋊C4C22×D5911yescharacteristic
318C4⋊C4C22×D5911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—591no—
322C22⋊C4—591no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C22⋊C4—1181no—
330C42—591no—
331C42—1181no—
332C23—591no—
333C23—1181no—
334C23—1181no—
335C23—1181no—
336C23—4721no—
337C23—2362no—
338C23—2362no—
339C23D4×D5911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—592no—
345Q8—1181no—
346Q8—2362no—
347D4—592no—
348D4—1181no—
349D4—1181no—
350D4—1181no—
351D4—1181no—
352D4—1181no—
353D4—4721no—
354D4—2362no—
355D4—2362no—
356D4—2362no—
357D4—2361no—
358D4—2362no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—591no—
366C2×C4—591no—
367C2×C4—591no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—4721no—
372C2×C4—2362no—
373C2×C4—2362no—
374C2×C4—2362no—
375C2×C4D4×D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—21no—
378C8—1181no—
379C8—1181no—
380C8D4×D5912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—1181no—
385C22—1181no—
386C22—1181no—
387C22—1182no—
388C22—4724no—
389C22—2361no—
390C22—2361no—
391C22—2361no—
392C22—2361no—
393C22—2361no—
394C22—2361no—
395C22—2361no—
396C22—2361no—
397C22C2×D4×D5911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—1181no—
404C4—1181no—
405C4—1181no—
406C4—1182no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377311yescharacteristic
409C2—41no—
410C2—4721no—
411C2—4721no—
412C2—2361no—
413C2—2362no—
414C2#1683803611yescharacteristic
415C2#1683820111yescharacteristic
416C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#470C2
socleC22×C59C22×D4
hypercenter#470D59
hypocenterC59#3275
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#14273759C2semidirect
2. C2×#14273755C2semidirect
3. #16838062C2semidirect
4. #16838043C2semidirect
5. #16837787C2semidirect
6. #16837656C2semidirect
7. #16837627C2semidirect
8. #16837620C2semidirect
9. #16837562C2semidirect
10. #16837552C2semidirect
11. #16837550C2semidirect
12. #16837542C2semidirect
13. #16837489C2semidirect
14. #16837478C2semidirect
15. C59×#470C2semidirect
18. C2×Q8×D59C22semidirect
22. C2×#11745672C22semidirect
27. C2×#11745671C22semidirect
30. C2×#11745659C22semidirect
32. #14273716C22semidirect
38. #14273702C22semidirect
41. #14273692C22semidirect
46. Dic59⋊C8C22semidirect
47. #14273650C22semidirect
50. #14273647C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. C8×Dic59C22semidirect
54. C2×Q16×C59C22semidirect
58. #106×C59C22semidirect
59. #103×C59C22semidirect
60. #103×C59C22semidirect
121. #11745660D4semidirect
214. #470D59semidirect
224. C59#3275semidirect
232. C2×Q16C2×D59semidirect
259. #106C2×D59semidirect
262. #103C2×D59semidirect
263. #103C2×D59semidirect