Finite Group Databasebeta

← #21434905

Subgroups — #21434905

Order 7552.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837912C211yesmaximal, characteristic, complemented
2#121×D59C211yesmaximal, characteristic, complemented
3#16837734C211yesmaximal, characteristic, complemented
4#16837728C211yesmaximal, characteristic, complemented
5#16837724C211yesmaximal, characteristic, complemented
6#16837714C211yesmaximal, characteristic, complemented
7#16837653C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837646C211yesmaximal, characteristic, complemented
10#16837554C211yesmaximal, characteristic, complemented
11#16837548C211yesmaximal, characteristic, complemented
12#16837544C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837365C211yesmaximal, characteristic, complemented
15C59×#469C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic, complemented
17C2×D4×D59—21no—
18C2×D4×D59C2211yescharacteristic
19C22×C4×D59C2211yescharacteristic
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745669C2211yescharacteristic, complemented
23C2×#11745664C2211yescharacteristic, complemented
24#14273709—21no—
25#14273707C2211yescharacteristic
26#14273706C2211yescharacteristic, complemented
27#14273702C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273700—21no—
30#14273699—21no—
31#14273698C2211yescharacteristic
32#14273698C2211yescharacteristic
33#14273695—21no—
34D4×Dic59—21no—
35(C22⋊D59)⋊C4—21no—
36#14273685C2211yescharacteristic, complemented
37C4⋊C4×D59C2211yescharacteristic
38C22⋊C4×D59—21no—
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic, complemented
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C2×D8×C59C2211yescharacteristic, complemented
53C2×M16×C59C2211yescharacteristic, complemented
54#121×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic, complemented
56#106×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59D411yescharacteristic
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C22×Dic59—21no—
72C22×Dic59D411yescharacteristic
73#11745687—41no—
74#11745687—41no—
75D4×D59—41no—
76D4×D59—41no—
77D4×D59—44no—
78C2×D236—21no—
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83C2×C4×D59D411yescharacteristic
84C2×C4×D59D411yescharacteristic
85C2×C4×D59C2311yescharacteristic
86C2×C4×D59C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88D8×C59—41no—
89M16×C59—41no—
90C2×C8×C59C2311yescharacteristic
91C2×C8×C59C2311yescharacteristic
92C4⋊C4×C59C2311yescharacteristic
93C4⋊C4×C59C2311yescharacteristic
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99#11745670—41no—
100#11745669—41no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105C4⋊Dic59—21no—
106C4⋊Dic59C2311yescharacteristic
107C4⋊Dic59C2311yescharacteristic
108Dic59⋊C4—21no—
109Dic59⋊C4—21no—
110C4×Dic59—21no—
111#11745664—41no—
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114#11745660—41no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59C2×D411yescharacteristic
118C22×D59—22no—
119C22×D59—21no—
120C22×D59—41no—
121C22×D59—41no—
122C22×D59—42no—
123C22×D59—42no—
124C22×D59—42no—
125C22×D59C2×D411yescharacteristic
126C22×D59C2×D411yescharacteristic
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—21no—
130D4×C59—21no—
131D4×C59—42no—
132D4×C59—42no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2411yescharacteristic
139C22⋊D59—42no—
140C22⋊D59—42no—
141C22⋊D59—42no—
142C22⋊D59—42no—
143C22⋊D59—42no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—41no—
148C2×Dic59—42no—
149C2×Dic59C2×D411yescharacteristic
150C2×Dic59C2×D411yescharacteristic
151D236—21no—
152D236—21no—
153D236—42no—
154C4×D59—21no—
155C4×D59—21no—
156C4×D59—21no—
157C4×D59—21no—
158C4×D59—41no—
159C4×D59—41no—
160C4×D59—42no—
161Dic118—21no—
162Dic118—21no—
163C8×C59—21no—
164C8×C59—21no—
165C59⋊C8—21no—
166C59⋊C8—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
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—44no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—84no—
187C2×D59AGL(1,ℤ/8)12yes—
188C4×C59—21no—
189C4×C59—41no—
190C4×C59—41no—
191C4×C59H(5,𝔽2)11yescharacteristic
192C4×C59H(5,𝔽2)11yescharacteristic
193Dic59—21no—
194Dic59—21no—
195Dic59—41no—
196Dic59—41no—
197Dic59—41no—
198#3194—591nomaximal, Sylow
199C2×C59—41no—
200C2×C59—81no—
201C2×C59—81no—
202C2×C59#53411yescharacteristic
203C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
204C2×C59#57511yescharacteristic
205D59—22no—
206D59—41no—
207D59—81no—
208#525—591no—
209C2×#121—591no—
210#483—591no—
211#482—591no—
212#482—591no—
213#480—591no—
214#469—591no—
215#469D5911yescharacteristic, complemented
216#468—591no—
217#468—591no—
218#450—591no—
219#449—591no—
220#449—591no—
221#447—591no—
222#407—591no—
223C59#319411yescharacteristic, complemented, Sylow
224C2×#41—591no—
225C22×D4—591no—
226C22×D4—1181no—
227C23×C4—591no—
228C2×SD16—591no—
229C2×SD16—591no—
230C2×D8—591no—
231C2×D8C2×D5911yescharacteristic, complemented
232C2×M16—591no—
233C2×M16C2×D5911yescharacteristic, complemented
234#123—1181no—
235C22⋊Q8—591no—
236C22⋊Q8—591no—
237#121—591no—
238#121—591no—
239#121—591no—
240#121—591no—
241#121—1181no—
242#121—1181no—
243#121C2×D5911yescharacteristic
244#121C2×D5911yescharacteristic, complemented
245#120—1181no—
246C4×D4—1181no—
247C4×D4—1181no—
248#117—591no—
249C2×C4⋊C4—591no—
250C2×C22⋊C4—1181no—
251#107—591no—
252#107—591no—
253#106—591no—
254#106C2×D5911yescharacteristic, complemented
255#103—591no—
256#103—591no—
257#102—591no—
258#102—591no—
259#102—591no—
260#102—591no—
261#102C2×D5911yescharacteristic, complemented
262#102C2×D5911yescharacteristic, complemented
263C22⋊C8—591no—
264C22⋊C8—591no—
265C22⋊C8—591no—
266C22⋊C8—591no—
267C24—591no—
268C24—1181no—
269#41—2361no—
270#41—2361no—
271C2×Q8—591no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—591no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4—2361no—
282C2×D4—2361no—
283C2×D4—2364no—
284C2×D4C22×D5911yescharacteristic
285C2×D4C22×D5911yescharacteristic
286C22×C4—591no—
287C22×C4—591no—
288C22×C4—591no—
289C22×C4—591no—
290C22×C4—591no—
291C22×C4—1181no—
292C22×C4—1181no—
293C22×C4—2361no—
294C22×C4—2361no—
295C22×C4C22×D5911yescharacteristic
296SD16—2361no—
297SD16—2361no—
298D8—41no—
299D8—2361no—
300M16—41no—
301M16—2361no—
302C2×C8—591no—
303C2×C8—591no—
304C2×C8C22×D5911yescharacteristic
305C2×C8C22×D5911yescharacteristic
306C4⋊C4—591no—
307C4⋊C4—591no—
308C4⋊C4—1181no—
309C4⋊C4—1181no—
310C4⋊C4—1181no—
311C4⋊C4C22×D5911yescharacteristic
312C4⋊C4C22×D5911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C22⋊C4—1181no—
318C22⋊C4—1181no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C42—1181no—
323C23—21no—
324C23—21no—
325C23—591no—
326C23—591no—
327C23—1182no—
328C23—1181no—
329C23—2361no—
330C23—2361no—
331C23—2362no—
332C23—2362no—
333C23—2362no—
334C23D4×D5911yescharacteristic
335Q8—1181no—
336Q8—1181no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—1181no—
344D4—1181no—
345D4—2362no—
346D4—2362no—
347D4—2362no—
348D4—2362no—
349D4—2362no—
350D4—2362no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—591no—
356C2×C4—591no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4—1181no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—1181no—
364C2×C4—2361no—
365C2×C4—2361no—
366C2×C4—2362no—
367C2×C4—2361no—
368C2×C4—2362no—
369C2×C4D4×D5911yescharacteristic
370C2×C4C23×D5911yescharacteristic
371C8—21no—
372C8—21no—
373C8—1181no—
374C8—1181no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—592no—
385C22—1181no—
386C22—1181no—
387C22—1181no—
388C22—1181no—
389C22—1181no—
390C22—4724no—
391C22—2364no—
392C22—2361no—
393C22—2361no—
394C22—2361no—
395C22C2×D4×D5911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—1181no—
400C4—1181no—
401C4—2361no—
402C4—2361no—
403C4—2361no—
404C4#1427377211yescharacteristic
405C4#1427377311yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—1182no—
410C2—4721no—
411C2—2361no—
412C2#1683796011yescharacteristic
413C2AGL(1,ℤ/8)×D5911yescharacteristic
414C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#469C2
socleC22×C59C22×D4
hypercenter#469D59
hypocenterC59#3194
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #16837912C2semidirect
2. #121×D59C2semidirect
3. #16837734C2semidirect
4. #16837728C2semidirect
5. #16837724C2semidirect
6. #16837714C2semidirect
7. #16837653C2semidirect
8. #16837648C2semidirect
9. #16837646C2semidirect
10. #16837554C2semidirect
11. #16837548C2semidirect
12. #16837544C2semidirect
13. #16837534C2semidirect
14. #16837365C2semidirect
15. C59×#469C2semidirect
16. C2×#11745687C22semidirect
20. C2×#11745660C22semidirect
21. C2×#11745670C22semidirect
22. C2×#11745669C22semidirect
23. C2×#11745664C22semidirect
26. #14273706C22semidirect
36. #14273685C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. #14273658C22semidirect
42. #14273652C22semidirect
43. #14273650C22semidirect
44. #14273649C22semidirect
45. #14273648C22semidirect
46. #14273648C22semidirect
47. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. C2×D8×C59C22semidirect
53. C2×M16×C59C22semidirect
55. #121×C59C22semidirect
56. #106×C59C22semidirect
57. #102×C59C22semidirect
58. #102×C59C22semidirect
215. #469D59semidirect
223. C59#3194semidirect
231. C2×D8C2×D59semidirect
233. C2×M16C2×D59semidirect
244. #121C2×D59semidirect
254. #106C2×D59semidirect
261. #102C2×D59semidirect
262. #102C2×D59semidirect