Finite Group Databasebeta

← #21435918

Subgroups — #21435918

Order 7552.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838107C211yesmaximal, characteristic, complemented
2#16838036C211yesmaximal, characteristic
3#16837747C211yesmaximal, characteristic, complemented
4#16837722C211yesmaximal, characteristic, complemented
5#16837691C211yesmaximal, characteristic, complemented
6#16837632C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837601C211yesmaximal, characteristic, complemented
9#16837555C211yesmaximal, characteristic, complemented
10#16837554C211yesmaximal, characteristic, complemented
11#16837489C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14273647C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#481C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×D4×D59—21no—
18C2×D4×D59C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C22×C59⋊C8C2211yescharacteristic, complemented
23C2×C8×D59C2211yescharacteristic, complemented
24#14273726C2211yescharacteristic, complemented
25#14273723C2211yescharacteristic
26#14273717—21no—
27#14273707C2211yescharacteristic, complemented
28#14273706—21no—
29#14273706C2211yescharacteristic, complemented
30#14273705—21no—
31#14273702C2211yescharacteristic
32#14273700—21no—
33#14273697—21no—
34#14273695—21no—
35#14273692C2211yescharacteristic, complemented
36#14273689C2211yescharacteristic
37C4×C22⋊D59—21no—
38C4×C22⋊D59C2211yescharacteristic
39C4⋊C4×D59C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273650C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic, complemented
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52#121×C59C2211yescharacteristic
53C2×C4⋊C4×C59C2211yescharacteristic, complemented
54#106×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59D411yescharacteristic
69D4×D59—22no—
70D4×D59—41no—
71D4×D59—44no—
72C2×D236—22no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236—41no—
76C2×D236C2311yescharacteristic
77C2×D236C2311yescharacteristic
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82C2×Dic118C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59D411yescharacteristic
92#11745670—41no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59C2311yescharacteristic
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745660—22no—
110#11745660—41no—
111C8×D59—41no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122C22×D59C2×D411yescharacteristic
123D4×C59—21no—
124D4×C59—21no—
125D4×C59—42no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—81no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—42no—
135C22⋊D59—42no—
136C22⋊D59—81no—
137C22⋊D59SD1614yescomplemented
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143D236—21no—
144D236—21no—
145D236—21no—
146D236—42no—
147D236—42no—
148D236#4112yes—
149C4×D59—21no—
150C4×D59—21no—
151C4×D59—42no—
152C4×D59—81no—
153Dic118—21no—
154Dic118—21no—
155Dic118—81no—
156C8×C59—21no—
157C8×C59—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59C2×SD1612yes—
166C22×C59C22×D411yescharacteristic
167C2×D59—21no—
168C2×D59—21no—
169C2×D59—22no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—84no—
176C2×D59—84no—
177C2×D59C2×SD1612yes—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59—41no—
182C4×C59C2×#4111yescharacteristic
183C4×C59H(5,𝔽2)11yescharacteristic
184Dic59—21no—
185Dic59—21no—
186Dic59—41no—
187Dic59—41no—
188Dic59C2×SD1612yes—
189#3295—591nomaximal, Sylow
190C2×C59—22no—
191C2×C59—81no—
192C2×C59#54611yescharacteristic
193C2×C59C22×SD1611yescharacteristic
194C2×C59#57611yescharacteristic
195D59—22no—
196D59—42no—
197D59—81no—
198#554—591no—
199D42—591no—
200#486—591no—
201#481—591no—
202#481D5911yescharacteristic, complemented
203#476—591no—
204#465—591no—
205#465—591no—
206#460—591no—
207#450—591no—
208#450—591no—
209C4×SD16—591no—
210C8×D4—591no—
211C2×#102—591no—
212C2×#102—591no—
213C59#329511yescharacteristic, complemented, Sylow
214C22×D4—591no—
215C22×D4—591no—
216C22×D4—1181no—
217C2×SD16—591no—
218C2×SD16—591no—
219C2×SD16—591no—
220C22×C8—591no—
221C22×C8—591no—
222C4⋊Q8—591no—
223#127—591no—
224#125—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227C22⋊Q8—1181no—
228C22⋊Q8—1181no—
229#121—591no—
230#121—1181no—
231#121C2×D5911yescharacteristic
232#120—1181no—
233#120—1181no—
234C4×Q8—591no—
235C4×D4—591no—
236C4×D4—591no—
237C4×D4—1181no—
238C2×C4⋊C4—591no—
239C2×C4⋊C4C2×D5911yescharacteristic, complemented
240#106—591no—
241#106C2×D5911yescharacteristic, complemented
242#106C2×D5911yescharacteristic, complemented
243C4⋊C8—591no—
244#103—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102C2×D5911yescharacteristic, complemented
253#102C2×D5911yescharacteristic, complemented
254C22⋊C8—591no—
255C22⋊C8C2×D5911yescharacteristic, complemented
256C4×C8—591no—
257C24—1181no—
258C24—1181no—
259C2×Q8—591no—
260C2×Q8—1181no—
261C2×D4—21no—
262C2×D4—591no—
263C2×D4—591no—
264C2×D4—591no—
265C2×D4—1182no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1182no—
271C2×D4—1181no—
272C2×D4—2361no—
273C2×D4—2361no—
274C2×D4—2364no—
275C2×D4C22×D5911yescharacteristic
276C22×C4—21no—
277C22×C4—591no—
278C22×C4—1181no—
279C22×C4—1181no—
280C22×C4C22×D5911yescharacteristic
281SD16—1182no—
282SD16—2361no—
283SD16—2361no—
284C2×C8—591no—
285C2×C8—591no—
286C2×C8—2361no—
287C2×C8—2361no—
288C2×C8C22×D5911yescharacteristic
289C2×C8C22×D5911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—591no—
292C4⋊C4—591no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4—1181no—
296C4⋊C4—1181no—
297C4⋊C4—1181no—
298C4⋊C4C22×D5911yescharacteristic
299C4⋊C4C22×D5911yescharacteristic
300C4⋊C4C22×D5911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—591no—
303C22⋊C4—591no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C42—591no—
309C42—1181no—
310C23—21no—
311C23—591no—
312C23—1181no—
313C23—1181no—
314C23—4721no—
315C23—4721no—
316C23—2362no—
317C23—2362no—
318C23—2362no—
319C23—2362no—
320C23D4×D5911yescharacteristic
321Q8—1181no—
322Q8—1181no—
323Q8—4721no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—594no—
328D4—592no—
329D4—1181no—
330D4—1181no—
331D4—1181no—
332D4—4721no—
333D4—2362no—
334D4—2362no—
335D4—2362no—
336D4—2362no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—81no—
343C2×C4—591no—
344C2×C4—591no—
345C2×C4—591no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—4721no—
351C2×C4—2362no—
352C2×C4D4×D5911yescharacteristic
353C2×C4C23×D5911yescharacteristic
354C8—21no—
355C8—21no—
356C8—1181no—
357C8—1181no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—592no—
364C22—1181no—
365C22—1181no—
366C22—1182no—
367C22—4724no—
368C22—4724no—
369C22—2361no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22—2361no—
374C22SD16×D5912yes—
375C22C2×D4×D5911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—592no—
381C4—1181no—
382C4—1181no—
383C4—2361no—
384C4—2361no—
385C4#41×D5911yescharacteristic
386C4#1427377311yescharacteristic
387C2—22no—
388C2—81no—
389C2—1182no—
390C2—4721no—
391C2—2362no—
392C2#1683804411yescharacteristic
393C2C2×SD16×D5911yescharacteristic
394C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#481C2
socleC22×C59C22×D4
hypercenter#481D59
hypocenterC59#3295
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #16838107C2semidirect
3. #16837747C2semidirect
4. #16837722C2semidirect
5. #16837691C2semidirect
6. #16837632C2semidirect
7. #16837629C2semidirect
8. #16837601C2semidirect
9. #16837555C2semidirect
10. #16837554C2semidirect
11. #16837489C2semidirect
12. (C22⋊D59)⋊C8C2semidirect
13. C2×#14273647C2semidirect
14. #102×D59C2semidirect
15. C59×#481C2semidirect
20. C2×#11745660C22semidirect
21. C2×#11745670C22semidirect
22. C22×C59⋊C8C22semidirect
23. C2×C8×D59C22semidirect
24. #14273726C22semidirect
27. #14273707C22semidirect
29. #14273706C22semidirect
35. #14273692C22semidirect
39. C4⋊C4×D59C22semidirect
40. #14273658C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273650C22semidirect
44. #14273649C22semidirect
45. #14273648C22semidirect
48. #14273647C22semidirect
49. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
53. C2×C4⋊C4×C59C22semidirect
54. #106×C59C22semidirect
55. #106×C59C22semidirect
56. #102×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
137. C22⋊D59SD16semidirect
202. #481D59semidirect
213. C59#3295semidirect
239. C2×C4⋊C4C2×D59semidirect
241. #106C2×D59semidirect
242. #106C2×D59semidirect
252. #102C2×D59semidirect
253. #102C2×D59semidirect
255. C22⋊C8C2×D59semidirect