Finite Group Databasebeta

← #21435165

Subgroups — #21435165

Order 7552.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838010C211yesmaximal, characteristic, complemented
2#16837970C211yesmaximal, characteristic
3#16837795C211yesmaximal, characteristic, complemented
4#16837773C211yesmaximal, characteristic, complemented
5#16837765C211yesmaximal, characteristic, complemented
6#16837758C211yesmaximal, characteristic, complemented
7#16837621C211yesmaximal, characteristic, complemented
8#16837603C211yesmaximal, characteristic, complemented
9#16837602C211yesmaximal, characteristic, complemented
10#16837567C211yesmaximal, characteristic, complemented
11#16837563C211yesmaximal, characteristic, complemented
12#16837554C211yesmaximal, characteristic, complemented
13#16837551C211yesmaximal, characteristic, complemented
14#16837462C211yesmaximal, characteristic, complemented
15C59×#464C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic, complemented
24#14273725C2211yescharacteristic, complemented
25#14273724C2211yescharacteristic
26#14273723C2211yescharacteristic
27#14273722—21no—
28#14273721—21no—
29#14273719—21no—
30#14273718C2211yescharacteristic, complemented
31#14273717—21no—
32#14273716C2211yescharacteristic
33#14273707C2211yescharacteristic
34#14273703C2211yescharacteristic
35#14273700—21no—
36#14273700—21no—
37#14273697—21no—
38#14273697—21no—
39C4×Dic118C2211yescharacteristic, 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×Q16×C59C2211yescharacteristic, complemented
53C2×SD16×C59C2211yescharacteristic
54#124×C59C2211yescharacteristic
55C4×Q8×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66#11745689—41no—
67#11745689—41no—
68D4×D59—41no—
69D4×D59—41no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236C2311yescharacteristic
74C2×D236C2311yescharacteristic
75C2×C4×D59—21no—
76C2×C4×D59C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78Q16×C59—41no—
79SD16×C59—41no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C42×C59—21no—
87C42×C59C2311yescharacteristic
88#11745672—41no—
89#11745671—41no—
90#11745671—41no—
91#11745670—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97(C2×D59)⋊C4D411yescharacteristic
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4D411yescharacteristic
107Dic59⋊C4D411yescharacteristic
108C4×Dic59—21no—
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745660—41no—
113#11745660—41no—
114C23×C59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—42no—
118C22×D59—81no—
119C22×D59—81no—
120C22×D59C2×D411yescharacteristic
121Q8×C59—21no—
122Q8×C59—21no—
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—42no—
134C22⋊D59—81no—
135C22⋊D59—81no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141D236—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—42no—
146D236—81no—
147D236—81no—
148C4×D59—21no—
149C4×D59—21no—
150C4×D59—42no—
151Dic118—21no—
152Dic118—21no—
153C8×C59—21no—
154C8×C59—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59C22×D411yescharacteristic
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—84no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59H(5,𝔽2)11yescharacteristic
177C4×C59H(5,𝔽2)11yescharacteristic
178Dic59—21no—
179Dic59—21no—
180Dic59—21no—
181Dic59—41no—
182Dic59—41no—
183#3222—591nomaximal, Sylow
184C2×C59—81no—
185C2×C59#53511yescharacteristic
186C2×C59#57711yescharacteristic
187C2×C59#57711yescharacteristic
188D59—41no—
189D59—81no—
190D59—81no—
191#541—591no—
192#535—591no—
193#497—591no—
194#492—591no—
195#490—591no—
196#488—591no—
197#464—591no—
198#464D5911yescharacteristic, complemented
199#460—591no—
200#460—591no—
201#452—591no—
202#452—591no—
203#450—591no—
204#450—591no—
205#433—591no—
206C59#322211yescharacteristic, complemented, Sylow
207C2×#41—591no—
208C22×D4—591no—
209C2×Q16—591no—
210C2×Q16C2×D5911yescharacteristic, complemented
211C2×SD16—591no—
212C2×SD16—591no—
213C2×SD16—591no—
214C2×SD16—591no—
215C2×SD16—591no—
216C2×SD16C2×D5911yescharacteristic
217C4⋊Q8—591no—
218#127—591no—
219#127—591no—
220#126—1181no—
221#126—1181no—
222#125—591no—
223#125—1181no—
224#125—1181no—
225#124—591no—
226#124C2×D5911yescharacteristic
227C22⋊Q8—591no—
228C22⋊Q8—591no—
229#121—1181no—
230#121—1181no—
231#120—1181no—
232#120—1181no—
233C4×Q8—591no—
234C4×Q8C2×D5911yescharacteristic, complemented
235#117—591no—
236C4⋊C8—591no—
237C4⋊C8C2×D5911yescharacteristic, complemented
238#103—591no—
239#103C2×D5911yescharacteristic, complemented
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102C2×D5911yescharacteristic
246C22⋊C8—591no—
247C22⋊C8—591no—
248#97—591no—
249C4×C8—591no—
250C24—1181no—
251#41—2361no—
252#41—2361no—
253C2×Q8—591no—
254C2×Q8C22×D5911yescharacteristic
255C2×Q8C22×D5911yescharacteristic
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—1181no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—2361no—
265C2×D4—2361no—
266C2×D4C22×D5911yescharacteristic
267C22×C4—591no—
268C22×C4—1181no—
269Q16—41no—
270Q16—2361no—
271SD16—41no—
272SD16—2361no—
273SD16—2361no—
274SD16—2361no—
275SD16—2361no—
276SD16—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4C22×D5911yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—591no—
296C22⋊C4—591no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C42—21no—
302C42—591no—
303C42—1181no—
304C42C22×D5911yescharacteristic
305C23—21no—
306C23—591no—
307C23—1181no—
308C23—1181no—
309C23—4721no—
310C23—4721no—
311C23—2362no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—1181no—
317Q8—1181no—
318D4—21no—
319D4—21no—
320D4—1181no—
321D4—1181no—
322D4—1181no—
323D4—1181no—
324D4—4721no—
325D4—4721no—
326D4—4721no—
327D4—4721no—
328D4—2362no—
329D4—2362no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—591no—
334C2×C4—591no—
335C2×C4—591no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—2362no—
341C2×C4D4×D5911yescharacteristic
342C2×C4D4×D5911yescharacteristic
343C2×C4C23×D5911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1181no—
347C8—1181no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1181no—
352C22—1181no—
353C22—1181no—
354C22—4724no—
355C22—2361no—
356C22—2361no—
357C22—2361no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C2×D4×D5911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—1181no—
368C4—1181no—
369C4—1181no—
370C4—2361no—
371C4—2361no—
372C4#1427377211yescharacteristic
373C4#1427377311yescharacteristic
374C2—81no—
375C2—4721no—
376C2—4721no—
377C2—2361no—
378C2#1683796811yescharacteristic
379C2#1683820911yescharacteristic
380C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#464C2
socleC22×C59C22×D4
hypercenter#464D59
hypocenterC59#3222
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #16838010C2semidirect
3. #16837795C2semidirect
4. #16837773C2semidirect
5. #16837765C2semidirect
6. #16837758C2semidirect
7. #16837621C2semidirect
8. #16837603C2semidirect
9. #16837602C2semidirect
10. #16837567C2semidirect
11. #16837563C2semidirect
12. #16837554C2semidirect
13. #16837551C2semidirect
14. #16837462C2semidirect
15. C59×#464C2semidirect
18. C2×#11745672C22semidirect
20. C2×#11745660C22semidirect
23. C2×#11745671C22semidirect
24. #14273725C22semidirect
30. #14273718C22semidirect
39. C4×Dic118C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273651C22semidirect
44. #14273649C22semidirect
47. #14273647C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
52. C2×Q16×C59C22semidirect
55. C4×Q8×C59C22semidirect
56. C4⋊C8×C59C22semidirect
57. #103×C59C22semidirect
198. #464D59semidirect
206. C59#3222semidirect
210. C2×Q16C2×D59semidirect
234. C4×Q8C2×D59semidirect
237. C4⋊C8C2×D59semidirect
239. #103C2×D59semidirect