Finite Group Databasebeta

← #21435192

Subgroups — #21435192

Order 7552.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838023C211yesmaximal, characteristic, complemented
2#16837971C211yesmaximal, characteristic, complemented
3#16837791C211yesmaximal, characteristic, complemented
4#16837786C211yesmaximal, characteristic, complemented
5#16837762C211yesmaximal, characteristic, complemented
6#16837749C211yesmaximal, characteristic, complemented
7#16837625C211yesmaximal, characteristic, complemented
8#16837618C211yesmaximal, characteristic, complemented
9#16837603C211yesmaximal, characteristic, complemented
10#16837598C211yesmaximal, characteristic, complemented
11#16837566C211yesmaximal, characteristic, complemented
12#16837555C211yesmaximal, characteristic, complemented
13#16837549C211yesmaximal, characteristic, complemented
14#16837538C211yesmaximal, characteristic, complemented
15C59×#433C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×Dic236C2211yescharacteristic, complemented
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21C2×#11745660C2211yescharacteristic, complemented
22C2×#11745660C2211yescharacteristic, complemented
23C2×D472C2211yescharacteristic
24C2×D472C2211yescharacteristic
25C2×D472C2211yescharacteristic, complemented
26#14273727C2211yescharacteristic, complemented
27#14273724C2211yescharacteristic
28#14273724C2211yescharacteristic
29#14273722—21no—
30#14273715C2211yescharacteristic
31#14273715C2211yescharacteristic
32#14273715C2211yescharacteristic, complemented
33#14273713—21no—
34#14273709—21no—
35#14273706C2211yescharacteristic
36#14273705—21no—
37#14273702—21no—
38#14273702—21no—
39#14273701C2211yescharacteristic
40#14273697—21no—
41#14273697—21no—
42C4×Dic118C2211yescharacteristic, complemented
43C4×D236C2211yescharacteristic, 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×C22⋊D59—21no—
63#11745685—41no—
64#11745685—41no—
65C2×D236—21no—
66C2×D236—21no—
67C2×D236—21no—
68C2×D236—21no—
69C2×D236—21no—
70C2×D236—41no—
71C2×D236—41no—
72C2×D236C2311yescharacteristic
73C2×D236C2311yescharacteristic
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×Dic118—21no—
79C2×Dic118C2311yescharacteristic
80C2×Dic118C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59D411yescharacteristic
86C4⋊C4×C59D411yescharacteristic
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59C2311yescharacteristic
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106Dic236—41no—
107D472—41no—
108D472—41no—
109D472—41no—
110#11745660—41no—
111#11745660—41no—
112#11745660—41no—
113#11745660—41no—
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—42no—
131C22⋊D59—81no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136D236—21no—
137D236—21no—
138D236—21no—
139D236—21no—
140D236—21no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—42no—
145D236—81no—
146D236—81no—
147D236—81no—
148D236—81no—
149C4×D59—42no—
150C4×D59—81no—
151Dic118—21no—
152Dic118—21no—
153Dic118—21no—
154Dic118—21no—
155Dic118—81no—
156C8×C59—21no—
157C8×C59—21no—
158C8×C59—21no—
159C8×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59C22×D411yescharacteristic
164C2×D59—41no—
165C2×D59—41no—
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—41no—
175C2×D59—41no—
176C2×D59—84no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59H(5,𝔽2)11yescharacteristic
183C4×C59H(5,𝔽2)11yescharacteristic
184Dic59—41no—
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188#3224—591nomaximal, Sylow
189C2×C59—41no—
190C2×C59#53511yescharacteristic
191C2×C59#57611yescharacteristic
192C2×C59#57711yescharacteristic
193D59—81no—
194D59—81no—
195D59—81no—
196D59—81no—
197#542—591no—
198#535—591no—
199#496—591no—
200#495—591no—
201#489—591no—
202#486—591no—
203#464—591no—
204#463—591no—
205#460—591no—
206#459—591no—
207#452—591no—
208#450—591no—
209#449—591no—
210#447—591no—
211#433D5911yescharacteristic, complemented
212C59#322411yescharacteristic, complemented, Sylow
213C2×#41—591no—
214C22×D4—591no—
215C2×Q16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×SD16—591no—
219C2×SD16—591no—
220C2×D8—591no—
221C2×D8—591no—
222C2×D8—591no—
223C4⋊Q8—591no—
224#127—591no—
225#127—591no—
226#126—1181no—
227#124—591no—
228#124—591no—
229#124—591no—
230#124—1181no—
231#123—1181no—
232C22⋊Q8—591no—
233C22⋊Q8—1181no—
234#121—591no—
235#121—1181no—
236#121—1181no—
237#120—1181no—
238#120—1181no—
239C4×Q8—591no—
240C4×D4—591no—
241#117C2×D5911yescharacteristic
242C4⋊C8C2×D5911yescharacteristic, complemented
243C4⋊C8C2×D5911yescharacteristic, complemented
244#103—591no—
245#103—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252C22⋊C8C2×D5911yescharacteristic
253C22⋊C8C2×D5911yescharacteristic
254#97C2×D5911yescharacteristic, complemented
255C4×C8C2×D5911yescharacteristic, complemented
256C24—1181no—
257#41—2361no—
258#41—2361no—
259C2×Q8—591no—
260C2×Q8—591no—
261C2×Q8—1181no—
262C2×D4—591no—
263C2×D4—591no—
264C2×D4—591no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—2361no—
274C2×D4—2361no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4C22×D5911yescharacteristic
278Q16—2361no—
279SD16—2361no—
280SD16—2361no—
281SD16—2361no—
282SD16—2361no—
283D8—2361no—
284D8—2361no—
285D8—2361no—
286C2×C8C22×D5911yescharacteristic
287C2×C8C22×D5911yescharacteristic
288C2×C8C22×D5911yescharacteristic
289C2×C8C22×D5911yescharacteristic
290C4⋊C4—591no—
291C4⋊C4—591no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4D23611yescharacteristic
296C4⋊C4D23611yescharacteristic
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4D23611yescharacteristic
307C22⋊C4D23611yescharacteristic
308C42—1181no—
309C42C22×D5911yescharacteristic
310C42C22×D5911yescharacteristic
311C23—1181no—
312C23—1181no—
313C23—1181no—
314C23—1181no—
315C23—4721no—
316C23—4721no—
317C23—2362no—
318C23C2×D23611yescharacteristic
319Q8—1181no—
320Q8—1181no—
321Q8—1181no—
322Q8—1181no—
323Q8—4721no—
324D4—1181no—
325D4—1181no—
326D4—1181no—
327D4—1181no—
328D4—1181no—
329D4—1181no—
330D4—1181no—
331D4—1181no—
332D4—4721no—
333D4—4721no—
334D4—4721no—
335D4—4721no—
336D4—4721no—
337D4—2362no—
338D4—2362no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—4721no—
346C2×C4—2362no—
347C2×C4C2×D23611yescharacteristic
348C2×C4C2×D23611yescharacteristic
349C2×C4C2×D23611yescharacteristic
350C2×C4C2×D23611yescharacteristic
351C2×C4C2×D23611yescharacteristic
352C2×C4C23×D5911yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—4724no—
361C22—2361no—
362C22—2361no—
363C22—2361no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22C22×D23611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—2361no—
380C4—2361no—
381C4—2361no—
382C4—2361no—
383C4#1427377311yescharacteristic
384C4#1427377311yescharacteristic
385C2—41no—
386C2—4721no—
387C2—4721no—
388C2—4721no—
389C2—4721no—
390C2#1683797111yescharacteristic
391C2#1683820711yescharacteristic
392C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3224
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. #16837971C2semidirect
3. #16837791C2semidirect
4. #16837786C2semidirect
5. #16837762C2semidirect
6. #16837749C2semidirect
7. #16837625C2semidirect
8. #16837618C2semidirect
9. #16837603C2semidirect
10. #16837598C2semidirect
11. #16837566C2semidirect
12. #16837555C2semidirect
13. #16837549C2semidirect
14. #16837538C2semidirect
15. C59×#433C2semidirect
18. C2×Dic236C22semidirect
21. C2×#11745660C22semidirect
22. C2×#11745660C22semidirect
25. C2×D472C22semidirect
26. #14273727C22semidirect
32. #14273715C22semidirect
42. C4×Dic118C22semidirect
43. C4×D236C22semidirect
44. #14273652C22semidirect
45. #14273652C22semidirect
50. #14273649C22semidirect
51. #14273649C22semidirect
53. C4⋊C8×C59C22semidirect
54. C4⋊C8×C59C22semidirect
57. #97×C59C22semidirect
58. C4×C8×C59C22semidirect
211. #433D59semidirect
212. C59#3224semidirect
242. C4⋊C8C2×D59semidirect
243. C4⋊C8C2×D59semidirect
254. #97C2×D59semidirect
255. C4×C8C2×D59semidirect