Finite Group Databasebeta

← #21434350

Subgroups — #21434350

Order 7552.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838015C211yesmaximal, characteristic, complemented
2#16837874C211yesmaximal, characteristic
3#16837746C211yesmaximal, characteristic, complemented
4#16837745C211yesmaximal, characteristic, complemented
5#16837699C211yesmaximal, characteristic, complemented
6#16837608C211yesmaximal, characteristic, complemented
7#16837607C211yesmaximal, characteristic, complemented
8#16837554C211yesmaximal, characteristic
9#16837554C211yesmaximal, characteristic
10#16837501C211yesmaximal, characteristic, complemented
11#16837499C211yesmaximal, characteristic, complemented
12#16837493C211yesmaximal, characteristic, complemented
13#16837489C211yesmaximal, characteristic, complemented
14#16837462C211yesmaximal, characteristic, complemented
15C59×#478C211yesmaximal, characteristic, complemented
16C2×D4×D59C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21#14273727C2211yescharacteristic, complemented
22#14273722—21no—
23#14273722—21no—
24#14273718—21no—
25#14273718—21no—
26#14273707C2211yescharacteristic
27#14273707C2211yescharacteristic
28#14273692C2211yescharacteristic, complemented
29#14273692C2211yescharacteristic, complemented
30C4×D236C2211yescharacteristic
31D4×Dic59C2211yescharacteristic
32#14273689C2211yescharacteristic
33C4×C22⋊D59—21no—
34(C22⋊D59)⋊C4—21no—
35#14273685C2211yescharacteristic
36#14273684C2211yescharacteristic
37C2×(C2×D59)⋊C4—21no—
38C22⋊C4×D59—21no—
39#14273660C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273650C2211yescharacteristic, complemented
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52#125×C59C2211yescharacteristic, complemented
53C4×D4×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C2×C22⋊D59—21no—
63C22×Dic59—21no—
64D4×D59—22no—
65D4×D59—22no—
66C2×D236C2311yescharacteristic
67C2×C4×D59—21no—
68C2×C4×D59—21no—
69C2×C4×D59C2311yescharacteristic
70C2×Dic118C2311yescharacteristic
71C2×Dic118C2311yescharacteristic
72C2×C8×C59C2311yescharacteristic
73C2×C8×C59C2311yescharacteristic
74C4⋊C4×C59—21no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59C2311yescharacteristic
77C4⋊C4×C59C2311yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C42×C59C2311yescharacteristic
81C22⋊Dic59—21no—
82#11745670—22no—
83#11745670—22no—
84(C2×D59)⋊C4—21no—
85(C2×D59)⋊C4—21no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4D411yescharacteristic
90(C2×D59)⋊C4D411yescharacteristic
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59C2311yescharacteristic
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98Dic59⋊C4D411yescharacteristic
99Dic59⋊C4D411yescharacteristic
100C4×Dic59—21no—
101C4×Dic59—21no—
102C4×Dic59—21no—
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106#11745660—22no—
107#11745660—22no—
108C23×C59—21no—
109C22×D59—21no—
110C22×D59—24no—
111C22×D59—81no—
112C22×D59—81no—
113C22×D59C2×D411yescharacteristic
114D4×C59—21no—
115D4×C59#4112yes—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—81no—
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2411yescharacteristic
123C22⋊D59—24no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—81no—
128C2×Dic59C2×D411yescharacteristic
129C2×Dic59C2×D411yescharacteristic
130C2×Dic59C2×D411yescharacteristic
131D236—21no—
132D236#4112yes—
133C4×D59—21no—
134C4×D59—21no—
135C4×D59—81no—
136C4×D59—81no—
137Dic118—21no—
138Dic118—21no—
139Dic118—21no—
140Dic118—21no—
141C8×C59—21no—
142C8×C59—21no—
143C59⋊C8—21no—
144C59⋊C8—21no—
145C22×C59—22no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59C22×D411yescharacteristic
149C2×D59—21no—
150C2×D59—22no—
151C2×D59—21no—
152C2×D59—21no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—84no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—41no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59C2×#4111yescharacteristic
162C4×C59C2×#4111yescharacteristic
163Dic59—21no—
164Dic59—21no—
165Dic59—21no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169#3123—591nomaximal, Sylow
170C2×C59—42no—
171C2×C59#52511yescharacteristic
172C2×C59#57711yescharacteristic
173C2×C59#57711yescharacteristic
174D59—41no—
175D59—42no—
176#541—591no—
177#518—591no—
178#485—591no—
179#485—591no—
180#478—591no—
181#478D5911yescharacteristic, complemented
182#461—591no—
183#461—591no—
184#450—591no—
185#450—591no—
186#440—591no—
187#440—591no—
188C4×SD16—591no—
189C4×SD16—591no—
190#433—591no—
191C59#312311yescharacteristic, complemented, Sylow
192C22×D4—591no—
193C2×SD16—591no—
194C2×SD16—591no—
195C2×SD16—591no—
196C2×SD16—591no—
197C4⋊Q8—591no—
198#126—1181no—
199#126—1181no—
200#125—1181no—
201#125—1181no—
202#125C2×D5911yescharacteristic, complemented
203C22⋊Q8—591no—
204C22⋊Q8—591no—
205C4×Q8—591no—
206C4×Q8—591no—
207C4×D4—591no—
208C4×D4—591no—
209C4×D4—591no—
210C4×D4—1181no—
211C4×D4—1181no—
212C4×D4C2×D5911yescharacteristic
213#117—591no—
214#117—591no—
215C2×C22⋊C4—1181no—
216C2×C22⋊C4—1181no—
217#107—591no—
218#107C2×D5911yescharacteristic, complemented
219#106—591no—
220#106C2×D5911yescharacteristic, complemented
221C4⋊C8—591no—
222C4⋊C8C2×D5911yescharacteristic, complemented
223#103—591no—
224#103—591no—
225#103—591no—
226#103—591no—
227#102—591no—
228#102—591no—
229#102C2×D5911yescharacteristic
230#102C2×D5911yescharacteristic
231C22⋊C8—591no—
232C22⋊C8—591no—
233#97—591no—
234C4×C8—591no—
235C24—1181no—
236C2×Q8—591no—
237C2×Q8—591no—
238C2×D4—591no—
239C2×D4—1181no—
240C2×D4—1182no—
241C2×D4—1182no—
242C2×D4C22×D5911yescharacteristic
243C22×C4—21no—
244C22×C4—591no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—1181no—
248SD16—1182no—
249SD16—1182no—
250SD16—1182no—
251SD16—1182no—
252C2×C8—591no—
253C2×C8—591no—
254C2×C8C22×D5911yescharacteristic
255C2×C8C22×D5911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—591no—
259C4⋊C4—591no—
260C4⋊C4—591no—
261C4⋊C4—1181no—
262C4⋊C4—1181no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4C22×D5911yescharacteristic
268C4⋊C4C22×D5911yescharacteristic
269C4⋊C4C22×D5911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—591no—
272C22⋊C4—591no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C42—591no—
280C42—1181no—
281C42—1181no—
282C42—1181no—
283C42C22×D5911yescharacteristic
284C23—21no—
285C23—591no—
286C23—1184no—
287C23—1181no—
288C23—4721no—
289C23—4721no—
290Q8—1181no—
291Q8—1181no—
292Q8—1181no—
293Q8—1181no—
294D4—21no—
295D4—592no—
296D4—1184no—
297D4—1181no—
298D4#1174568912yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—591no—
304C2×C4—591no—
305C2×C4—591no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—4721no—
312C2×C4—4721no—
313C2×C4—4721no—
314C2×C4D4×D5911yescharacteristic
315C2×C4D4×D5911yescharacteristic
316C2×C4C23×D5911yescharacteristic
317C8—21no—
318C8—21no—
319C8—1181no—
320C8—1181no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—1181no—
325C22—1182no—
326C22—1181no—
327C22—1181no—
328C22—4724no—
329C22—2361no—
330C22—2361no—
331C22C2×D4×D5911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1181no—
338C4—1181no—
339C4—1181no—
340C4—2361no—
341C4—2361no—
342C4—2361no—
343C4#41×D5911yescharacteristic
344C4C2×#1174568911yescharacteristic
345C2—42no—
346C2—2361no—
347C2—2362no—
348C2#1683791511yescharacteristic
349C2#1683820911yescharacteristic
350C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#478C2
socleC22×C59C22×D4
hypercenter#478D59
hypocenterC59#3123
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16838015C2semidirect
3. #16837746C2semidirect
4. #16837745C2semidirect
5. #16837699C2semidirect
6. #16837608C2semidirect
7. #16837607C2semidirect
10. #16837501C2semidirect
11. #16837499C2semidirect
12. #16837493C2semidirect
13. #16837489C2semidirect
14. #16837462C2semidirect
15. C59×#478C2semidirect
21. #14273727C22semidirect
28. #14273692C22semidirect
29. #14273692C22semidirect
39. #14273660C22semidirect
40. #14273658C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273652C22semidirect
44. #14273650C22semidirect
45. #14273650C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
52. #125×C59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. C4⋊C8×C59C22semidirect
181. #478D59semidirect
191. C59#3123semidirect
202. #125C2×D59semidirect
218. #107C2×D59semidirect
220. #106C2×D59semidirect
222. C4⋊C8C2×D59semidirect