Finite Group Databasebeta

← #21435143

Subgroups — #21435143

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838003C211yesmaximal, characteristic, complemented
2#16837970C211yesmaximal, characteristic, complemented
3#16837788C211yesmaximal, characteristic, complemented
4#16837777C211yesmaximal, characteristic, complemented
5#16837765C211yesmaximal, characteristic, complemented
6#16837758C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837598C211yesmaximal, characteristic, complemented
9#16837597C211yesmaximal, characteristic, complemented
10#16837550C211yesmaximal, characteristic, complemented
11#16837546C211yesmaximal, characteristic, complemented
12#16837537C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837462C211yesmaximal, characteristic, complemented
15C59×#463C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745671C2211yescharacteristic, complemented
19C2×D472C2211yescharacteristic
20C2×D472C2211yescharacteristic, complemented
21C2×#11745669C2211yescharacteristic
22C2×#11745669C2211yescharacteristic
23C2×#11745669C2211yescharacteristic, complemented
24#14273724C2211yescharacteristic
25#14273723C2211yescharacteristic
26#14273723C2211yescharacteristic, complemented
27#14273718C2211yescharacteristic, complemented
28#14273716C2211yescharacteristic
29#14273710—21no—
30#14273709—21no—
31#14273702C2211yescharacteristic
32#14273701—21no—
33#14273700—21no—
34#14273700—21no—
35#14273700—21no—
36#14273698C2211yescharacteristic
37#14273697—21no—
38#14273697—21no—
39C4×D236C2211yescharacteristic, complemented
40#14273684C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic, complemented
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic, complemented
53C2×D8×C59C2211yescharacteristic
54#124×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70#11745689—41no—
71#11745689—41no—
72D4×D59—41no—
73D4×D59—41no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236—21no—
77C2×D236—21no—
78C2×D236C2311yescharacteristic
79C2×D236C2311yescharacteristic
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59—21no—
83C2×C4×D59C2311yescharacteristic
84SD16×C59—41no—
85D8×C59—41no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C42×C59C2311yescharacteristic
93C22⋊Dic59—21no—
94#11745671—41no—
95#11745669—41no—
96#11745669—41no—
97#11745669—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4D411yescharacteristic
103(C2×D59)⋊C4D411yescharacteristic
104C4⋊Dic59—21no—
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4D411yescharacteristic
108Dic59⋊C4D411yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112D472—41no—
113D472—41no—
114C23×C59—21no—
115C23×C59—21no—
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122C22×D59C2×D411yescharacteristic
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—81no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—42no—
136C22⋊D59—81no—
137C22⋊D59—81no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C22⋊D59—81no—
141C2×Dic59—21no—
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144C2×Dic59C2×D411yescharacteristic
145D236—21no—
146D236—21no—
147D236—21no—
148D236—21no—
149D236—21no—
150D236—21no—
151D236—42no—
152D236—81no—
153D236—81no—
154D236—81no—
155C4×D59—21no—
156C4×D59—21no—
157C4×D59—42no—
158C4×D59—81no—
159C8×C59—21no—
160C8×C59—21no—
161C59⋊C8—21no—
162C59⋊C8—21no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59C22×D411yescharacteristic
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—84no—
183C4×C59—21no—
184C4×C59—21no—
185C4×C59—41no—
186C4×C59—41no—
187C4×C59H(5,𝔽2)11yescharacteristic
188C4×C59H(5,𝔽2)11yescharacteristic
189Dic59—21no—
190Dic59—21no—
191Dic59—21no—
192Dic59—41no—
193#3220—591nomaximal, Sylow
194C2×C59—81no—
195C2×C59—81no—
196C2×C59#53511yescharacteristic
197C2×C59#57611yescharacteristic
198C2×C59#57611yescharacteristic
199D59—41no—
200D59—81no—
201D59—81no—
202D59—81no—
203#540—591no—
204#535—591no—
205#496—591no—
206#493—591no—
207#490—591no—
208#488—591no—
209#463—591no—
210#463D5911yescharacteristic, complemented
211#459—591no—
212#459—591no—
213#449—591no—
214#449—591no—
215#447—591no—
216#447—591no—
217#433—591no—
218C59#322011yescharacteristic, complemented, Sylow
219C2×#41—591no—
220C22×D4—591no—
221C2×SD16—591no—
222C2×SD16C2×D5911yescharacteristic, complemented
223C2×D8—591no—
224C2×D8—591no—
225C2×D8—591no—
226C2×D8—591no—
227C2×D8—591no—
228C2×D8C2×D5911yescharacteristic
229#127—591no—
230#127—591no—
231#127—591no—
232#125—591no—
233#124—591no—
234#124C2×D5911yescharacteristic
235#123—1181no—
236#123—1181no—
237#121—591no—
238#121—591no—
239#121—1181no—
240#121—1181no—
241#121—1181no—
242#121—1181no—
243#120—1181no—
244#120—1181no—
245C4×D4—591no—
246C4×D4C2×D5911yescharacteristic, complemented
247#117—591no—
248C4⋊C8—591no—
249C4⋊C8C2×D5911yescharacteristic, complemented
250#103—591no—
251#103C2×D5911yescharacteristic, complemented
252#102—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102—591no—
257#102C2×D5911yescharacteristic
258C22⋊C8—591no—
259C22⋊C8—591no—
260#97—591no—
261C4×C8—591no—
262C24—1181no—
263#41—2361no—
264#41—2361no—
265C2×Q8C22×D5911yescharacteristic
266C2×D4—591no—
267C2×D4—591no—
268C2×D4—591no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—1181no—
279C2×D4—2361no—
280C2×D4—2361no—
281C2×D4C22×D5911yescharacteristic
282C2×D4C22×D5911yescharacteristic
283C22×C4—21no—
284C22×C4—591no—
285C22×C4—1181no—
286C22×C4—1181no—
287SD16—41no—
288SD16—2361no—
289D8—41no—
290D8—2361no—
291D8—2361no—
292D8—2361no—
293D8—2361no—
294D8—2361no—
295C2×C8—591no—
296C2×C8—591no—
297C2×C8C22×D5911yescharacteristic
298C2×C8C22×D5911yescharacteristic
299C4⋊C4—591no—
300C4⋊C4—591no—
301C4⋊C4—591no—
302C4⋊C4—1181no—
303C4⋊C4—1181no—
304C4⋊C4C22×D5911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—591no—
309C22⋊C4—591no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C42—591no—
316C42C22×D5911yescharacteristic
317C23—21no—
318C23—21no—
319C23—591no—
320C23—1181no—
321C23—1181no—
322C23—1181no—
323C23—4721no—
324C23—4721no—
325C23—2362no—
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—1181no—
333D4—1181no—
334D4—1181no—
335D4—1181no—
336D4—1181no—
337D4—1181no—
338D4—4721no—
339D4—4721no—
340D4—4721no—
341D4—4721no—
342D4—4721no—
343D4—4721no—
344D4—4721no—
345D4—4721no—
346D4—2362no—
347D4—2362no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—591no—
352C2×C4—591no—
353C2×C4—591no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—4721no—
358C2×C4—2362no—
359C2×C4D4×D5911yescharacteristic
360C2×C4D4×D5911yescharacteristic
361C2×C4C23×D5911yescharacteristic
362C8—21no—
363C8—21no—
364C8—1181no—
365C8—1181no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—1181no—
373C22—1181no—
374C22—1181no—
375C22—4724no—
376C22—2361no—
377C22—2361no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22—2361no—
384C22—2361no—
385C22C2×D4×D5911yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—1181no—
391C4—1181no—
392C4—1181no—
393C4—2361no—
394C4#1427377211yescharacteristic
395C4#1427377311yescharacteristic
396C2—81no—
397C2—81no—
398C2—4721no—
399C2—4721no—
400C2—4721no—
401C2—2361no—
402C2#1683796811yescharacteristic
403C2#1683820411yescharacteristic
404C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#463C2
socleC22×C59C22×D4
hypercenter#463D59
hypocenterC59#3220
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16838003C2semidirect
2. #16837970C2semidirect
3. #16837788C2semidirect
4. #16837777C2semidirect
5. #16837765C2semidirect
6. #16837758C2semidirect
7. #16837614C2semidirect
8. #16837598C2semidirect
9. #16837597C2semidirect
10. #16837550C2semidirect
11. #16837546C2semidirect
12. #16837537C2semidirect
13. #16837534C2semidirect
14. #16837462C2semidirect
15. C59×#463C2semidirect
18. C2×#11745671C22semidirect
20. C2×D472C22semidirect
23. C2×#11745669C22semidirect
26. #14273723C22semidirect
27. #14273718C22semidirect
39. C4×D236C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273651C22semidirect
44. #14273649C22semidirect
47. #14273647C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
52. C2×SD16×C59C22semidirect
55. C4×D4×C59C22semidirect
56. C4⋊C8×C59C22semidirect
57. #103×C59C22semidirect
210. #463D59semidirect
218. C59#3220semidirect
222. C2×SD16C2×D59semidirect
246. C4×D4C2×D59semidirect
249. C4⋊C8C2×D59semidirect
251. #103C2×D59semidirect