Finite Group Databasebeta

← #21436119

Subgroups — #21436119

Order 7552.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838092C211yesmaximal, characteristic, complemented
2D4×D236C211yesmaximal, characteristic
3#16837767C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837716C211yesmaximal, characteristic, complemented
6#16837703C211yesmaximal, characteristic, complemented
7#16837648C211yesmaximal, characteristic, complemented
8#16837631C211yesmaximal, characteristic, complemented
9#16837603C211yesmaximal, characteristic, complemented
10#16837555C211yesmaximal, characteristic, complemented
11#16837555C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13#16837408C211yesmaximal, characteristic, complemented
14C2×#14273649C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×D4×D59—21no—
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745660C2211yescharacteristic, complemented
22#14273724C2211yescharacteristic
23#14273720—21no—
24#14273719C2211yescharacteristic, complemented
25#14273717—21no—
26#14273708—21no—
27#14273706C2211yescharacteristic, complemented
28#14273706C2211yescharacteristic, complemented
29#14273702—21no—
30#14273701C2211yescharacteristic
31#14273701C2211yescharacteristic
32#14273697—21no—
33#14273697—21no—
34C4×Dic118C2211yescharacteristic, complemented
35C4×D236C2211yescharacteristic
36#14273686C2211yescharacteristic, complemented
37#14273683—21no—
38C2×C4⋊Dic59C2211yescharacteristic, complemented
39#14273661C2211yescharacteristic, complemented
40#14273661C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic, complemented
47#14273649C2211yescharacteristic, complemented
48#14273649C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic, complemented
50#14273649C2211yescharacteristic, complemented
51#14273649C2211yescharacteristic, complemented
52C2×M16×C59C2211yescharacteristic, complemented
53C22×C8×C59C2211yescharacteristic, complemented
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic, complemented
56C22⋊C8×C59C2211yescharacteristic, complemented
57C22⋊C8×C59C2211yescharacteristic, complemented
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×D4×C59D411yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C22×Dic59—21no—
67D4×D59—44no—
68C2×D236—22no—
69C2×D236—22no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236—41no—
75C2×D236—41no—
76C2×D236C2311yescharacteristic
77C2×D236C2311yescharacteristic
78C2×D236C2311yescharacteristic
79C2×C4×D59—21no—
80C2×Dic118C2311yescharacteristic
81M16×C59—41no—
82C2×C8×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C4⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C22⋊C4×C59D411yescharacteristic
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108C4×Dic59—21no—
109#11745660—22no—
110#11745660—41no—
111#11745660—41no—
112C23×C59C2×D411yescharacteristic
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—42no—
120C22×D59—42no—
121C22×D59—81no—
122C22×D59—81no—
123D4×C59—22no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—42no—
134C22⋊D59—42no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—42no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—21no—
146D236—42no—
147D236—42no—
148D236—42no—
149D236—81no—
150D236#4112yes—
151C4×D59—42no—
152Dic118—21no—
153Dic118—21no—
154C8×C59—21no—
155C8×C59—21no—
156C8×C59—21no—
157C8×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59AGL(1,ℤ/8)12yes—
164C22×C59C22×D411yescharacteristic
165C2×D59—22no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—84no—
175C2×D59—84no—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59C2×#4111yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—41no—
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186Dic59—41no—
187#3310—591nomaximal, Sylow
188C2×C59—22no—
189C2×C59—41no—
190C2×C59#54611yescharacteristic
191C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C59#57711yescharacteristic
193D59—42no—
194D59—81no—
195D59—81no—
196#552—591no—
197D42—591no—
198#490—591no—
199#482—591no—
200#480—591no—
201#478—591no—
202#468—591no—
203#465—591no—
204#460—591no—
205#450—591no—
206#450—591no—
207#440—591no—
208#435D5911yescharacteristic, complemented
209#418—591no—
210C2×#102—591no—
211C59#331011yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C22×D4—591no—
214C22×D4—1181no—
215C2×SD16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×M16C2×D5911yescharacteristic, complemented
219C22×C8C2×D5911yescharacteristic, complemented
220#127—591no—
221#126—1181no—
222#125—591no—
223#125—1181no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227#121—591no—
228#121—591no—
229#121—1181no—
230#120—1181no—
231#120—1181no—
232C4×Q8—591no—
233C4×D4—591no—
234C4×D4C2×D5911yescharacteristic
235#117—591no—
236#117—1181no—
237C2×C4⋊C4—591no—
238#107—591no—
239#107—591no—
240#106—591no—
241C4⋊C8C2×D5911yescharacteristic, complemented
242#103—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252C22⋊C8C2×D5911yescharacteristic, complemented
253C22⋊C8C2×D5911yescharacteristic, complemented
254#97C2×D5911yescharacteristic, complemented
255C24—1181no—
256C24—1181no—
257C2×Q8—591no—
258C2×D4—591no—
259C2×D4—591no—
260C2×D4—591no—
261C2×D4—1182no—
262C2×D4—1182no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—2361no—
270C2×D4—2361no—
271C2×D4—2364no—
272C2×D4D23611yescharacteristic
273C22×C4—1181no—
274C22×C4—1181no—
275C22×C4C22×D5911yescharacteristic
276C22×C4C22×D5911yescharacteristic
277SD16—1182no—
278SD16—2361no—
279SD16—2361no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D5911yescharacteristic
283C2×C8C22×D5911yescharacteristic
284C2×C8C22×D5911yescharacteristic
285C2×C8C22×D5911yescharacteristic
286C4⋊C4—591no—
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4—1181no—
296C4⋊C4D23611yescharacteristic
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4D23611yescharacteristic
304C22⋊C4D23611yescharacteristic
305C42—1181no—
306C42—1181no—
307C42C22×D5911yescharacteristic
308C23—1181no—
309C23—1181no—
310C23—1181no—
311C23—4721no—
312C23—4721no—
313C23—2362no—
314C23—2362no—
315C23—2362no—
316C23—2362no—
317C23C2×D23611yescharacteristic
318C23C2×D23611yescharacteristic
319Q8—1181no—
320Q8—1181no—
321D4—22no—
322D4—592no—
323D4—1181no—
324D4—1181no—
325D4—1181no—
326D4—1181no—
327D4—1181no—
328D4—4721no—
329D4—2362no—
330D4—2362no—
331D4—2362no—
332D4—2362no—
333D4—2362no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—2362no—
344C2×C4—2362no—
345C2×C4C2×D23611yescharacteristic
346C2×C4C2×D23611yescharacteristic
347C2×C4C2×D23611yescharacteristic
348C2×C4C2×D23611yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—1182no—
360C22—4724no—
361C22—4724no—
362C22—2361no—
363C22—2361no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22#1427375512yes—
371C22C22×D23611yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—2361no—
377C4—2361no—
378C4—2361no—
379C4—2361no—
380C4—2361no—
381C4#41×D5911yescharacteristic
382C4#1427377211yescharacteristic
383C2—22no—
384C2—41no—
385C2—4721no—
386C2—4721no—
387C2—2362no—
388C2#1683804711yescharacteristic
389C2C2×#1427375511yescharacteristic
390C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3310
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16838092C2semidirect
3. #16837767C2semidirect
4. #16837727C2semidirect
5. #16837716C2semidirect
6. #16837703C2semidirect
7. #16837648C2semidirect
8. #16837631C2semidirect
9. #16837603C2semidirect
10. #16837555C2semidirect
11. #16837555C2semidirect
12. #16837504C2semidirect
13. #16837408C2semidirect
14. C2×#14273649C2semidirect
15. C59×#435C2semidirect
20. C2×#11745660C22semidirect
21. C2×#11745660C22semidirect
24. #14273719C22semidirect
27. #14273706C22semidirect
28. #14273706C22semidirect
34. C4×Dic118C22semidirect
36. #14273686C22semidirect
38. C2×C4⋊Dic59C22semidirect
39. #14273661C22semidirect
40. #14273661C22semidirect
41. #14273659C22semidirect
42. #14273652C22semidirect
46. #14273649C22semidirect
47. #14273649C22semidirect
48. #14273649C22semidirect
49. #14273649C22semidirect
50. #14273649C22semidirect
51. #14273649C22semidirect
52. C2×M16×C59C22semidirect
53. C22×C8×C59C22semidirect
55. C4⋊C8×C59C22semidirect
56. C22⋊C8×C59C22semidirect
57. C22⋊C8×C59C22semidirect
58. #97×C59C22semidirect
208. #435D59semidirect
211. C59#3310semidirect
218. C2×M16C2×D59semidirect
219. C22×C8C2×D59semidirect
241. C4⋊C8C2×D59semidirect
252. C22⋊C8C2×D59semidirect
253. C22⋊C8C2×D59semidirect
254. #97C2×D59semidirect