Finite Group Databasebeta

← #21434280

Subgroups — #21434280

Order 7552.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838023C211yesmaximal, characteristic, complemented
2#16837743C211yesmaximal, characteristic, complemented
3#16837726C211yesmaximal, characteristic, complemented
4#16837692C211yesmaximal, characteristic, complemented
5#16837682C211yesmaximal, characteristic, complemented
6#16837617C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837553C211yesmaximal, characteristic, complemented
9#16837536C211yesmaximal, characteristic
10#16837512C211yesmaximal, characteristic, complemented
11#16837502C211yesmaximal, characteristic, complemented
12C4×#11745670C211yesmaximal, characteristic, complemented
13C4×#11745669C211yesmaximal, characteristic, complemented
14#16837463C211yesmaximal, characteristic, complemented
15C59×#518C211yesmaximal, characteristic, complemented
16C2×#11745670C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745669C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20#14273727C2211yescharacteristic, complemented
21#14273722—21no—
22#14273715C2211yescharacteristic, complemented
23#14273713—21no—
24#14273709—21no—
25#14273706C2211yescharacteristic
26#14273705—21no—
27#14273701C2211yescharacteristic
28C4×Dic118C2211yescharacteristic, complemented
29C4×D236C2211yescharacteristic, complemented
30#14273660C2211yescharacteristic, complemented
31#14273660C2211yescharacteristic, complemented
32#14273658C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35C4⋊(C59⋊C8)C2211yescharacteristic, complemented
36#14273650C2211yescharacteristic, complemented
37#14273650C2211yescharacteristic, complemented
38#14273648C2211yescharacteristic
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273647C2211yescharacteristic, complemented
43#14273647C2211yescharacteristic, complemented
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46#14273638C2211yescharacteristic, complemented
47C4×C59⋊C8C2211yescharacteristic, complemented
48C22×D4×C59C2211yescharacteristic
49C4×D4×C59—21no—
50C4×D4×C59—21no—
51C4×D4×C59C2211yescharacteristic
52C4×D4×C59C2211yescharacteristic
53C4×D4×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55#117×C59C2211yescharacteristic
56#117×C59C2211yescharacteristic
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C24×C59—21no—
60C2×D4×C59—22no—
61C2×D4×C59—22no—
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59C2311yescharacteristic
70C2×C22⋊D59—21no—
71C2×D236C2311yescharacteristic
72C2×C4×D59—21no—
73C2×Dic118—21no—
74C2×Dic118C2311yescharacteristic
75C4⋊C4×C59D411yescharacteristic
76C4⋊C4×C59D411yescharacteristic
77C4⋊C4×C59C2311yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59D411yescharacteristic
85C22⋊C4×C59D411yescharacteristic
86C42×C59—21no—
87C42×C59C2311yescharacteristic
88C42×C59C2311yescharacteristic
89C22⋊Dic59—21no—
90#11745670—22no—
91#11745670—22no—
92#11745669—22no—
93#11745669—22no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—21no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C23×C59—24no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59—81no—
112C23×C59—81no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115D4×C59—24no—
116D4×C59—21no—
117D4×C59—21no—
118D4×C59#4112yes—
119D4×C59#4112yes—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—81no—
125C2×C4×C59—81no—
126C2×C4×C59—81no—
127C2×C4×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—81no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138D236—21no—
139D236—21no—
140C4×D59—81no—
141Dic118—21no—
142Dic118—21no—
143Dic118—81no—
144C59⋊C8—21no—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—21no—
149C22×C59—22no—
150C22×C59—22no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—84no—
158C22×C59C22×D411yescharacteristic
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—41no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59C2×#4111yescharacteristic
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#3118—591nomaximal, Sylow
175C2×C59—41no—
176C2×C59—42no—
177C2×C59—42no—
178C2×C59#52511yescharacteristic
179C2×C59#57611yescharacteristic
180C2×C59#57711yescharacteristic
181D59—81no—
182#542—591no—
183#518D5911yescharacteristic, complemented
184#485—591no—
185#482—591no—
186#476—591no—
187#474—591no—
188#463—591no—
189#463—591no—
190#450—591no—
191#447—591no—
192#442—591no—
193#440—591no—
194C4×SD16—591no—
195C4×D8—591no—
196#433—591no—
197C59#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D5911yescharacteristic
199C2×SD16—591no—
200C2×SD16—591no—
201C2×D8—591no—
202C2×D8—591no—
203C4⋊Q8—591no—
204#126—1181no—
205#124—591no—
206#124—1181no—
207#123—1181no—
208C22⋊Q8—591no—
209C22⋊Q8—1181no—
210#121—591no—
211C4×Q8—591no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—591no—
215C4×D4C2×D5911yescharacteristic
216C4×D4C2×D5911yescharacteristic
217C4×D4C2×D5911yescharacteristic
218C4×D4C2×D5911yescharacteristic
219#117C2×D5911yescharacteristic
220#117C2×D5911yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—591no—
224#107—591no—
225#106—591no—
226#106—591no—
227C4⋊C8—591no—
228C4⋊C8—591no—
229#103—591no—
230#103—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235#102—591no—
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97—591no—
240C4×C8—591no—
241C24—21no—
242C2×Q8—591no—
243C2×Q8—1181no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—591no—
248C2×D4—1181no—
249C2×D4C22×D5911yescharacteristic
250C2×D4C22×D5911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1181no—
256C22×C4C22×D5911yescharacteristic
257SD16—1182no—
258SD16—1182no—
259D8—1182no—
260D8—1182no—
261C2×C8—591no—
262C2×C8—591no—
263C2×C8—591no—
264C2×C8—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4C22⋊D5911yescharacteristic
271C4⋊C4C22⋊D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C4⋊C4C22×D5911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4C22⋊D5911yescharacteristic
285C22⋊C4C22⋊D5911yescharacteristic
286C42—21no—
287C42—1181no—
288C42C22×D5911yescharacteristic
289C42C22×D5911yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—1181no—
296C23C2×C22⋊D5911yescharacteristic
297Q8—1181no—
298Q8—1181no—
299Q8—4721no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—1181no—
304D4—1181no—
305D4—4721no—
306D4#1174568512yes—
307D4#1174568512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—4721no—
320C2×C4C2×C22⋊D5911yescharacteristic
321C2×C4C2×C22⋊D5911yescharacteristic
322C2×C4C2×C22⋊D5911yescharacteristic
323C2×C4C2×C22⋊D5911yescharacteristic
324C2×C4C2×C22⋊D5911yescharacteristic
325C2×C4C23×D5911yescharacteristic
326C8—1181no—
327C8—1181no—
328C8—1181no—
329C8—1181no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—2361no—
341C22—2361no—
342C22—2361no—
343C22C22×C22⋊D5911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—2361no—
352C4—2361no—
353C4—2361no—
354C4C2×#1174568511yescharacteristic
355C4C2×#1174568511yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—4721no—
360C2#1683791311yescharacteristic
361C2#1683820511yescharacteristic
362C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#518C2
socleC22×C59C22×D4
hypercenter#518D59
hypocenterC59#3118
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837743C2semidirect
3. #16837726C2semidirect
4. #16837692C2semidirect
5. #16837682C2semidirect
6. #16837617C2semidirect
7. #16837617C2semidirect
8. #16837553C2semidirect
10. #16837512C2semidirect
11. #16837502C2semidirect
12. C4×#11745670C2semidirect
13. C4×#11745669C2semidirect
14. #16837463C2semidirect
15. C59×#518C2semidirect
20. #14273727C22semidirect
22. #14273715C22semidirect
28. C4×Dic118C22semidirect
29. C4×D236C22semidirect
30. #14273660C22semidirect
31. #14273660C22semidirect
32. #14273658C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. C4⋊(C59⋊C8)C22semidirect
36. #14273650C22semidirect
37. #14273650C22semidirect
42. #14273647C22semidirect
43. #14273647C22semidirect
46. #14273638C22semidirect
47. C4×C59⋊C8C22semidirect
183. #518D59semidirect
197. C59#3118semidirect