Finite Group Databasebeta

← #21434283

Subgroups — #21434283

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#16838025C211yesmaximal, characteristic, complemented
2#16837876C211yesmaximal, characteristic, complemented
3#16837726C211yesmaximal, characteristic, complemented
4#16837691C211yesmaximal, characteristic, complemented
5#16837681C211yesmaximal, characteristic, complemented
6#16837620C211yesmaximal, characteristic, complemented
7#16837620C211yesmaximal, characteristic, complemented
8#16837552C211yesmaximal, characteristic, complemented
9#16837538C211yesmaximal, characteristic
10#16837513C211yesmaximal, characteristic, complemented
11#16837505C211yesmaximal, characteristic, complemented
12#16837487C211yesmaximal, characteristic, complemented
13#16837484C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#485C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×D472C2211yescharacteristic
21#14273726C2211yescharacteristic, complemented
22#14273722—21no—
23#14273716C2211yescharacteristic, complemented
24#14273713—21no—
25#14273709—21no—
26#14273707—21no—
27#14273701C2211yescharacteristic
28Q8×Dic59C2211yescharacteristic, complemented
29C4×D236—21no—
30C4×D236—21no—
31#14273689C2211yescharacteristic
32#14273689C2211yescharacteristic
33#14273689C2211yescharacteristic
34#14273689C2211yescharacteristic
35#14273689C2211yescharacteristic, complemented
36#14273686C2211yescharacteristic
37C22⋊C4×D59—21no—
38C22⋊C4×D59—21no—
39#14273660C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C22⋊Q8×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×D236—21no—
64C2×D236—22no—
65C2×D236—22no—
66C2×D236C2311yescharacteristic
67C2×D236C2311yescharacteristic
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×Dic118—21no—
75C2×C8×C59C2311yescharacteristic
76C2×C8×C59C2311yescharacteristic
77C4⋊C4×C59—21no—
78C4⋊C4×C59C2311yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C42×C59—21no—
84C22⋊Dic59D411yescharacteristic
85C22⋊Dic59D411yescharacteristic
86#11745671—22no—
87#11745671—22no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59D411yescharacteristic
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100Dic59⋊C4—21no—
101C4×Dic59—21no—
102C4×Dic59C2311yescharacteristic
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106D472—22no—
107D472—22no—
108C23×C59C2×D411yescharacteristic
109C22×D59—21no—
110C22×D59—21no—
111C22×D59—24no—
112C22×D59—21no—
113C22×D59—81no—
114C22×D59—81no—
115Q8×C59—21no—
116Q8×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C22⋊D59—81no—
126C2×Dic59—21no—
127C2×Dic59C2×D411yescharacteristic
128C2×Dic59C2×D411yescharacteristic
129C2×Dic59C2×D411yescharacteristic
130C2×Dic59C2×D411yescharacteristic
131D236—24no—
132D236—21no—
133D236—21no—
134D236—21no—
135D236—21no—
136D236#4112yes—
137D236#4112yes—
138C4×D59—81no—
139C4×D59—81no—
140C4×D59—81no—
141C4×D59—81no—
142C4×D59—81no—
143Dic118—81no—
144C8×C59—21no—
145C8×C59—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59C22×D411yescharacteristic
152C2×D59—22no—
153C2×D59—22no—
154C2×D59—41no—
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—84no—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59C2×#4111yescharacteristic
168C4×C59C2×#4111yescharacteristic
169Dic59—21no—
170Dic59—21no—
171Dic59—21no—
172Dic59—21no—
173Dic59—41no—
174#3118—591nomaximal, Sylow
175C2×C59—41no—
176C2×C59#52511yescharacteristic
177C2×C59#57611yescharacteristic
178C2×C59#57711yescharacteristic
179D59—42no—
180D59—42no—
181D59—81no—
182#542—591no—
183#518—591no—
184#485D5911yescharacteristic, complemented
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×D4—591no—
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—1181no—
209C22⋊Q8C2×D5911yescharacteristic
210#121—591no—
211C4×Q8—591no—
212C4×D4—591no—
213C4×D4—591no—
214C4×D4—591no—
215C4×D4—591no—
216C4×D4—591no—
217C4×D4—1181no—
218C4×D4—1181no—
219#117—591no—
220#117C2×D5911yescharacteristic
221C2×C22⋊C4—1181no—
222C2×C22⋊C4—1181no—
223#107—591no—
224#107C2×D5911yescharacteristic, complemented
225#106—591no—
226#106C2×D5911yescharacteristic, complemented
227C4⋊C8—591no—
228C4⋊C8—591no—
229#103C2×D5911yescharacteristic, complemented
230#103C2×D5911yescharacteristic, complemented
231#102—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235#102—591no—
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8C2×D5911yescharacteristic
239#97—591no—
240C4×C8—591no—
241C24—1181no—
242C2×Q8—1181no—
243C2×Q8C22×D5911yescharacteristic
244C2×D4—591no—
245C2×D4—591no—
246C2×D4—591no—
247C2×D4—1182no—
248C2×D4—1182no—
249C2×D4—1181no—
250C2×D4—1181no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4C22×D5911yescharacteristic
257SD16—1182no—
258SD16—1182no—
259D8—1182no—
260D8—1182no—
261C2×C8—591no—
262C2×C8—591no—
263C2×C8C22×D5911yescharacteristic
264C2×C8C22×D5911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—591no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4C22×D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C4⋊C4C22×D5911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—591no—
277C22⋊C4—591no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C42—21no—
287C42—591no—
288C42—591no—
289C42—1181no—
290C23—1184no—
291C23—1181no—
292C23—1181no—
293C23—1181no—
294C23—4721no—
295C23—4721no—
296C23D4×D5911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—4721no—
300D4—592no—
301D4—592no—
302D4—1184no—
303D4—1181no—
304D4—1181no—
305D4—1181no—
306D4—1181no—
307D4—4721no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—591no—
315C2×C4—591no—
316C2×C4—591no—
317C2×C4—591no—
318C2×C4—1181no—
319C2×C4—4721no—
320C2×C4—4721no—
321C2×C4—4721no—
322C2×C4—4721no—
323C2×C4—4721no—
324C2×C4D4×D5911yescharacteristic
325C2×C4C23×D5911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1181no—
329C8—1181no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—1182no—
334C22—1182no—
335C22—4724no—
336C22—2361no—
337C22—2361no—
338C22—2361no—
339C22—2361no—
340C22—2361no—
341C22—2361no—
342C22—2361no—
343C22C2×D4×D5911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1181no—
350C4—1181no—
351C4—1181no—
352C4—1181no—
353C4—2361no—
354C4#41×D5911yescharacteristic
355C4#41×D5911yescharacteristic
356C2—41no—
357C2—4721no—
358C2—2362no—
359C2—2362no—
360C2#1683791011yescharacteristic
361C2#1683820411yescharacteristic
362C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#485C2
socleC22×C59C22×D4
hypercenter#485D59
hypocenterC59#3118
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16838025C2semidirect
2. #16837876C2semidirect
3. #16837726C2semidirect
4. #16837691C2semidirect
5. #16837681C2semidirect
6. #16837620C2semidirect
7. #16837620C2semidirect
8. #16837552C2semidirect
10. #16837513C2semidirect
11. #16837505C2semidirect
12. #16837487C2semidirect
13. #16837484C2semidirect
14. #16837460C2semidirect
15. C59×#485C2semidirect
21. #14273726C22semidirect
23. #14273716C22semidirect
28. Q8×Dic59C22semidirect
35. #14273689C22semidirect
39. #14273660C22semidirect
40. #14273658C22semidirect
41. Dic59⋊C8C22semidirect
42. Dic59⋊C8C22semidirect
47. #14273647C22semidirect
48. #14273647C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. #103×C59C22semidirect
57. #103×C59C22semidirect
184. #485D59semidirect
197. C59#3118semidirect
224. #107C2×D59semidirect
226. #106C2×D59semidirect
229. #103C2×D59semidirect
230. #103C2×D59semidirect