Finite Group Databasebeta

← #21434282

Subgroups — #21434282

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#16837876C211yesmaximal, characteristic, complemented
3#16837744C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837693C211yesmaximal, characteristic, complemented
6#16837683C211yesmaximal, characteristic, complemented
7#16837618C211yesmaximal, characteristic, complemented
8#16837618C211yesmaximal, characteristic, complemented
9#16837555C211yesmaximal, characteristic, complemented
10#16837538C211yesmaximal, characteristic
11#16837515C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13C4×#11745660C211yesmaximal, characteristic, complemented
14C4×D472C211yesmaximal, characteristic, complemented
15C59×#433C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×D472C2211yescharacteristic
21#14273727C2211yescharacteristic, complemented
22#14273722—21no—
23#14273715C2211yescharacteristic, complemented
24#14273713—21no—
25#14273709—21no—
26#14273706C2211yescharacteristic
27#14273705—21no—
28#14273701C2211yescharacteristic
29C4×Dic118C2211yescharacteristic, complemented
30C4×D236C2211yescharacteristic
31C4×D236C2211yescharacteristic
32C4×D236C2211yescharacteristic
33C4×D236C2211yescharacteristic
34C4×D236C2211yescharacteristic, complemented
35#14273689—21no—
36#14273689—21no—
37#14273686C2211yescharacteristic
38C22⋊C4×D59—21no—
39C22⋊C4×D59—21no—
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
52#117×C59C2211yescharacteristic
53C4⋊C8×C59C2211yescharacteristic, complemented
54C4⋊C8×C59C2211yescharacteristic, complemented
55C22⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57#97×C59C2211yescharacteristic, complemented
58C4×C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C22×C4×C59C2311yescharacteristic
61C2×C22⋊D59—21no—
62C2×D236—21no—
63C2×D236—22no—
64C2×D236—22no—
65C2×D236C2311yescharacteristic
66C2×D236C2311yescharacteristic
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×Dic118—21no—
74C2×Dic118C2311yescharacteristic
75C2×C8×C59C2311yescharacteristic
76C2×C8×C59C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59D411yescharacteristic
80C4⋊C4×C59D411yescharacteristic
81C22⋊C4×C59D411yescharacteristic
82C22⋊C4×C59D411yescharacteristic
83C42×C59C2311yescharacteristic
84C42×C59C2311yescharacteristic
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87(C2×D59)⋊C4—21no—
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—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102C4×Dic59—21no—
103C4×Dic59—21no—
104D472—22no—
105D472—22no—
106#11745660—22no—
107#11745660—22no—
108C23×C59C2×D411yescharacteristic
109C22×D59—21no—
110C22×D59—21no—
111C22×D59—24no—
112C22×D59—21no—
113C22×D59—81no—
114C22×D59—81no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59C2×D411yescharacteristic
118C2×C4×C59C2×D411yescharacteristic
119C2×C4×C59C2×D411yescharacteristic
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2411yescharacteristic
123C22⋊D59—81no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129D236—24no—
130D236—21no—
131D236—21no—
132D236—21no—
133D236—21no—
134D236#4112yes—
135D236#4112yes—
136C4×D59—81no—
137C4×D59—81no—
138C4×D59—81no—
139C4×D59—81no—
140C4×D59—81no—
141Dic118—21no—
142Dic118—21no—
143Dic118—81no—
144C8×C59—21no—
145C8×C59—21no—
146C8×C59—21no—
147C8×C59—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—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59C2×#4111yescharacteristic
168C4×C59C2×#4111yescharacteristic
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172Dic59—41no—
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#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#433D5911yescharacteristic, complemented
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—591no—
209C22⋊Q8—1181no—
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#107—591no—
225#106—591no—
226#106—591no—
227C4⋊C8C2×D5911yescharacteristic, complemented
228C4⋊C8C2×D5911yescharacteristic, complemented
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⋊C8C2×D5911yescharacteristic
238C22⋊C8C2×D5911yescharacteristic
239#97C2×D5911yescharacteristic, complemented
240C4×C8C2×D5911yescharacteristic, complemented
241C24—1181no—
242C2×Q8—591no—
243C2×Q8—1181no—
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×C8C22×D5911yescharacteristic
262C2×C8C22×D5911yescharacteristic
263C2×C8C22×D5911yescharacteristic
264C2×C8C22×D5911yescharacteristic
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—591no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4D23611yescharacteristic
273C4⋊C4D23611yescharacteristic
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4D23611yescharacteristic
285C22⋊C4D23611yescharacteristic
286C42—1181no—
287C42—1181no—
288C42C22×D5911yescharacteristic
289C42C22×D5911yescharacteristic
290C23—1184no—
291C23—1181no—
292C23—1181no—
293C23—1181no—
294C23—4721no—
295C23—4721no—
296C23C2×D23611yescharacteristic
297Q8—1181no—
298Q8—1181no—
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—1181no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—4721no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4C2×D23611yescharacteristic
321C2×C4C2×D23611yescharacteristic
322C2×C4C2×D23611yescharacteristic
323C2×C4C2×D23611yescharacteristic
324C2×C4C2×D23611yescharacteristic
325C2×C4C23×D5911yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
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—
343C22C22×D23611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—2361no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4—2361no—
354C4#41×D5911yescharacteristic
355C4#41×D5911yescharacteristic
356C2—41no—
357C2—4721no—
358C2—2362no—
359C2—2362no—
360C2#1683791411yescharacteristic
361C2#1683820711yescharacteristic
362C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3118
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837876C2semidirect
3. #16837744C2semidirect
4. #16837727C2semidirect
5. #16837693C2semidirect
6. #16837683C2semidirect
7. #16837618C2semidirect
8. #16837618C2semidirect
9. #16837555C2semidirect
11. #16837515C2semidirect
12. #16837504C2semidirect
13. C4×#11745660C2semidirect
14. C4×D472C2semidirect
15. C59×#433C2semidirect
21. #14273727C22semidirect
23. #14273715C22semidirect
29. C4×Dic118C22semidirect
34. C4×D236C22semidirect
40. #14273661C22semidirect
41. #14273661C22semidirect
42. #14273659C22semidirect
43. #14273659C22semidirect
44. #14273652C22semidirect
45. #14273652C22semidirect
50. #14273649C22semidirect
51. #14273649C22semidirect
53. C4⋊C8×C59C22semidirect
54. C4⋊C8×C59C22semidirect
57. #97×C59C22semidirect
58. C4×C8×C59C22semidirect
196. #433D59semidirect
197. C59#3118semidirect
227. C4⋊C8C2×D59semidirect
228. C4⋊C8C2×D59semidirect
239. #97C2×D59semidirect
240. C4×C8C2×D59semidirect