Finite Group Databasebeta

← #21434950

Subgroups — #21434950

Order 7552.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837980C211yesmaximal, characteristic, complemented
2#16837966C211yesmaximal, characteristic, complemented
3#16837744C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837721C211yesmaximal, characteristic, complemented
6#16837716C211yesmaximal, characteristic, complemented
7#16837655C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837638C211yesmaximal, characteristic, complemented
10#16837631C211yesmaximal, characteristic, complemented
11#16837555C211yesmaximal, characteristic, complemented
12#16837549C211yesmaximal, characteristic, complemented
13#16837549C211yesmaximal, characteristic, complemented
14#16837538C211yesmaximal, characteristic, complemented
15C59×#408C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic, complemented
17C22×D236C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×D472C2211yescharacteristic
21C2×D472C2211yescharacteristic
22#14273723—21no—
23#14273716—21no—
24#14273706C2211yescharacteristic
25#14273706C2211yescharacteristic, complemented
26#14273703—21no—
27#14273701C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273701C2211yescharacteristic
30#14273701C2211yescharacteristic
31#14273701C2211yescharacteristic
32#14273701C2211yescharacteristic, complemented
33#14273699—21no—
34#14273699—21no—
35#14273698—21no—
36#14273695—21no—
37#14273695—21no—
38#14273686C2211yescharacteristic
39C2×C4⋊Dic59C2211yescharacteristic, complemented
40#14273661C2211yescharacteristic, complemented
41#14273661C2211yescharacteristic, complemented
42#14273659C2211yescharacteristic, complemented
43#14273659C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273652C2211yescharacteristic, complemented
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic, complemented
51#14273649C2211yescharacteristic, complemented
52C2×#41×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic, complemented
54C22×C8×C59C2211yescharacteristic, complemented
55C22⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59D411yescharacteristic
63C2×D4×C59D411yescharacteristic
64C2×D4×C59D411yescharacteristic
65C2×D4×C59D411yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C22×Dic59—21no—
77#11745685—41no—
78#11745685—41no—
79C2×D236—21no—
80C2×D236—41no—
81C2×D236—41no—
82C2×D236C2311yescharacteristic
83C2×D236C2311yescharacteristic
84C2×D236C2311yescharacteristic
85C2×C4×D59—21no—
86C2×Dic118C2311yescharacteristic
87M16×C59—41no—
88C2×C8×C59—41no—
89C2×C8×C59C2311yescharacteristic
90C2×C8×C59C2311yescharacteristic
91C2×C8×C59C2311yescharacteristic
92C2×C8×C59C2311yescharacteristic
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109C4×Dic59—21no—
110D472—41no—
111D472—41no—
112#11745660—41no—
113#11745660—41no—
114C23×C59C2×D411yescharacteristic
115C23×C59C2×D411yescharacteristic
116C23×C59C2×D411yescharacteristic
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—21no—
120C22×D59—42no—
121C22×D59—81no—
122C22×D59—81no—
123Q8×C59—41no—
124D4×C59—41no—
125D4×C59—41no—
126D4×C59—41no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C22⋊D59—42no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C22⋊D59—81no—
141C22⋊D59—81no—
142C22⋊D59—81no—
143C22⋊D59—81no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—81no—
150D236—21no—
151D236—21no—
152D236—21no—
153D236—21no—
154D236—21no—
155D236—21no—
156D236—42no—
157C4×D59—42no—
158Dic118—21no—
159Dic118—21no—
160C8×C59—21no—
161C8×C59—21no—
162C8×C59—21no—
163C8×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59C22×D411yescharacteristic
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—41no—
183C2×D59—84no—
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59H(5,𝔽2)11yescharacteristic
188C4×C59H(5,𝔽2)11yescharacteristic
189Dic59—41no—
190Dic59—41no—
191Dic59—41no—
192Dic59—41no—
193Dic59—41no—
194#3198—591nomaximal, Sylow
195C2×C59—41no—
196C2×C59—41no—
197C2×C59—41no—
198C2×C59#53411yescharacteristic
199C2×C59#57611yescharacteristic
200C2×C59#57711yescharacteristic
201D59—81no—
202D59—81no—
203D59—81no—
204#537—591no—
205#535—591no—
206#485—591no—
207#482—591no—
208#481—591no—
209#480—591no—
210#469—591no—
211#468—591no—
212#466—591no—
213#465—591no—
214#450—591no—
215#449—591no—
216#449—591no—
217#447—591no—
218#408D5911yescharacteristic, complemented
219C59#319811yescharacteristic, complemented, Sylow
220C2×#41—591no—
221C2×#41C2×D5911yescharacteristic
222C22×D4—591no—
223C2×SD16—591no—
224C2×SD16—591no—
225C2×D8—591no—
226C2×D8—591no—
227C2×M16C2×D5911yescharacteristic, complemented
228C22×C8C2×D5911yescharacteristic, complemented
229#127—1181no—
230#124—1181no—
231C22⋊Q8—591no—
232C22⋊Q8—591no—
233C22⋊Q8—1181no—
234#121—591no—
235#121—591no—
236#121—591no—
237#121—591no—
238#121—591no—
239#121—591no—
240#121—1181no—
241#121—1181no—
242#121—1181no—
243#120—1181no—
244#120—1181no—
245#117—591no—
246C2×C4⋊C4—591no—
247#107—591no—
248#107—591no—
249#106—591no—
250#106—591no—
251#103—591no—
252#103—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102—591no—
257#102—591no—
258#102—591no—
259C22⋊C8C2×D5911yescharacteristic
260C22⋊C8C2×D5911yescharacteristic
261C22⋊C8C2×D5911yescharacteristic, complemented
262C22⋊C8C2×D5911yescharacteristic, complemented
263C24—1181no—
264#41—41no—
265#41—41no—
266#41—2361no—
267#41—2361no—
268C2×Q8—591no—
269C2×Q8D23611yescharacteristic
270C2×D4—591no—
271C2×D4—591no—
272C2×D4—591no—
273C2×D4—1181no—
274C2×D4—1181no—
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×D4D23611yescharacteristic
284C2×D4D23611yescharacteristic
285C2×D4D23611yescharacteristic
286C22×C4—1181no—
287C22×C4—1181no—
288C22×C4C22×D5911yescharacteristic
289C22×C4C22×D5911yescharacteristic
290C22×C4C22×D5911yescharacteristic
291SD16—2361no—
292SD16—2361no—
293D8—2361no—
294D8—2361no—
295M16—41no—
296C2×C8—41no—
297C2×C8C22×D5911yescharacteristic
298C2×C8C22×D5911yescharacteristic
299C2×C8C22×D5911yescharacteristic
300C2×C8C22×D5911yescharacteristic
301C4⋊C4—591no—
302C4⋊C4—591no—
303C4⋊C4—591no—
304C4⋊C4—591no—
305C4⋊C4—1181no—
306C4⋊C4—1181no—
307C4⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C42—1181no—
318C23—1181no—
319C23—1181no—
320C23—1181no—
321C23—4721no—
322C23—4721no—
323C23—2362no—
324C23C2×D23611yescharacteristic
325C23C2×D23611yescharacteristic
326C23C2×D23611yescharacteristic
327Q8—41no—
328Q8—1181no—
329Q8—1181no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—1181no—
334D4—1181no—
335D4—1181no—
336D4—1181no—
337D4—1181no—
338D4—1181no—
339D4—4721no—
340D4—4721no—
341D4—4721no—
342D4—4721no—
343D4—4721no—
344D4—4721no—
345D4—2362no—
346D4—2362no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—1181no—
358C2×C4—4721no—
359C2×C4—2362no—
360C2×C4C2×D23611yescharacteristic
361C2×C4C2×D23611yescharacteristic
362C2×C4C2×D23611yescharacteristic
363C2×C4C23×D5911yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—4724no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22—2361no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22C22×D23611yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—2361no—
392C4—2361no—
393C4—2361no—
394C4—2361no—
395C4—2361no—
396C4#1427377211yescharacteristic
397C4#1427377211yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—4721no—
402C2—4721no—
403C2—4721no—
404C2#1683796411yescharacteristic
405C2#1683820711yescharacteristic
406C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#408C2
socleC22×C59C22×D4
hypercenter#408D59
hypocenterC59#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16837980C2semidirect
2. #16837966C2semidirect
3. #16837744C2semidirect
4. #16837727C2semidirect
5. #16837721C2semidirect
6. #16837716C2semidirect
7. #16837655C2semidirect
8. #16837648C2semidirect
9. #16837638C2semidirect
10. #16837631C2semidirect
11. #16837555C2semidirect
12. #16837549C2semidirect
13. #16837549C2semidirect
14. #16837538C2semidirect
15. C59×#408C2semidirect
16. C2×#11745685C22semidirect
25. #14273706C22semidirect
32. #14273701C22semidirect
39. C2×C4⋊Dic59C22semidirect
40. #14273661C22semidirect
41. #14273661C22semidirect
42. #14273659C22semidirect
43. #14273659C22semidirect
44. #14273652C22semidirect
45. #14273652C22semidirect
50. #14273649C22semidirect
51. #14273649C22semidirect
53. C2×M16×C59C22semidirect
54. C22×C8×C59C22semidirect
57. C22⋊C8×C59C22semidirect
58. C22⋊C8×C59C22semidirect
218. #408D59semidirect
219. C59#3198semidirect
227. C2×M16C2×D59semidirect
228. C22×C8C2×D59semidirect
261. C22⋊C8C2×D59semidirect
262. C22⋊C8C2×D59semidirect