Finite Group Databasebeta

← #21436310

Subgroups — #21436310

Order 7552.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838091C211yesmaximal, characteristic, complemented
2#16838043C211yesmaximal, characteristic
3#16837758C211yesmaximal, characteristic, complemented
4#16837722C211yesmaximal, characteristic, complemented
5#16837705C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837649C211yesmaximal, characteristic, complemented
8#16837627C211yesmaximal, characteristic, complemented
9#16837567C211yesmaximal, characteristic, complemented
10#16837555C211yesmaximal, characteristic, complemented
11#16837489C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837406C211yesmaximal, characteristic, complemented
14#16837402C211yesmaximal, characteristic, complemented
15C59×#485C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C2×#11745659C2211yescharacteristic, complemented
23#14273720—21no—
24#14273719—21no—
25#14273718C2211yescharacteristic, complemented
26#14273716C2211yescharacteristic
27#14273712—21no—
28#14273709—21no—
29#14273707C2211yescharacteristic, complemented
30#14273706C2211yescharacteristic
31#14273702—21no—
32#14273702C2211yescharacteristic
33#14273697—21no—
34#14273692C2211yescharacteristic, complemented
35#14273689C2211yescharacteristic
36C4×C22⋊D59C2211yescharacteristic
37#14273684—21no—
38C4⋊C4×D59C2211yescharacteristic, complemented
39C22⋊C4×D59—21no—
40#14273658C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, 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⋊D59D411yescharacteristic
63#11745689—22no—
64#11745689—41no—
65C2×D236—22no—
66C2×D236—21no—
67C2×D236—21no—
68C2×D236—21no—
69C2×D236—41no—
70C2×D236C2311yescharacteristic
71C2×D236C2311yescharacteristic
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C42×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59D411yescharacteristic
88#11745672—41no—
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)⋊C4D411yescharacteristic
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59C2311yescharacteristic
105#11745664—41no—
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108#11745660—22no—
109#11745660—41no—
110#11745659—41no—
111C23×C59C2×D411yescharacteristic
112C22×D59—21no—
113C22×D59—21no—
114C22×D59—42no—
115C22×D59—42no—
116C22×D59—81no—
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C22⋊D59—41no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133C2×Dic59C2×D411yescharacteristic
134D236—21no—
135D236—21no—
136D236—21no—
137D236—42no—
138D236—42no—
139D236—81no—
140D236#4112yes—
141C4×D59—21no—
142C4×D59—21no—
143C4×D59—42no—
144C4×D59—42no—
145C4×D59—81no—
146Dic118—21no—
147Dic118—21no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59C22×D411yescharacteristic
156C2×D59—21no—
157C2×D59—22no—
158C2×D59—21no—
159C2×D59—21no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—84no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59C2×#4111yescharacteristic
172C4×C59H(5,𝔽2)11yescharacteristic
173Dic59—21no—
174Dic59—21no—
175Dic59—21no—
176Dic59—41no—
177Dic59—41no—
178#3323—591nomaximal, Sylow
179C2×C59—41no—
180C2×C59#54611yescharacteristic
181C2×C59#57511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—41no—
184D59—42no—
185D59—81no—
186#552—591no—
187#546—591no—
188#488—591no—
189#485D5911yescharacteristic, complemented
190#481—591no—
191#478—591no—
192#470—591no—
193#468—591no—
194#464—591no—
195#452—591no—
196#450—591no—
197C4×SD16—591no—
198#436—591no—
199#418—591no—
200#417—591no—
201C59#332311yescharacteristic, complemented, Sylow
202C2×#41—591no—
203C22×D4—591no—
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C2×M16—591no—
208C2×M16—591no—
209#126—1181no—
210#125—591no—
211#125—1181no—
212#124—591no—
213#123—1181no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8C2×D5911yescharacteristic
218#121—591no—
219#121—1181no—
220#120—1181no—
221C4×Q8—591no—
222C4×D4—591no—
223C4×D4—591no—
224#117—1181no—
225#117C2×D5911yescharacteristic
226C2×C4⋊C4—591no—
227C2×C22⋊C4—1181no—
228#107C2×D5911yescharacteristic, complemented
229#106—591no—
230#106C2×D5911yescharacteristic, complemented
231C4⋊C8—591no—
232#103—591no—
233#103—591no—
234#103C2×D5911yescharacteristic, complemented
235#103C2×D5911yescharacteristic, complemented
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242C22⋊C8—591no—
243C22⋊C8C2×D5911yescharacteristic
244C4×C8—591no—
245C24—1181no—
246#41—1182no—
247#41—2361no—
248C2×Q8—591no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—591no—
251C2×D4—591no—
252C2×D4—591no—
253C2×D4—1182no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4—2361no—
258C22×C4—591no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4C22×D5911yescharacteristic
263Q16—2361no—
264SD16—1182no—
265SD16—2361no—
266M16—2361no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8C22×D5911yescharacteristic
271C2×C8C22×D5911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4C22×D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—591no—
287C22⋊C4—591no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C42—21no—
295C42—591no—
296C42—1181no—
297C23—591no—
298C23—1181no—
299C23—1181no—
300C23—4721no—
301C23—2362no—
302C23—2362no—
303C23D4×D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1181no—
307Q8—1181no—
308D4—592no—
309D4—1181no—
310D4—1181no—
311D4—1181no—
312D4—4721no—
313D4—2362no—
314D4—2362no—
315D4—2361no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—591no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—4721no—
330C2×C4—2362no—
331C2×C4—2362no—
332C2×C4D4×D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—1181no—
342C22—1181no—
343C22—1181no—
344C22—1182no—
345C22—4724no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22C2×D4×D5911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1181no—
358C4—1181no—
359C4—1181no—
360C4—2361no—
361C4—2361no—
362C4#41×D5911yescharacteristic
363C4#1427377311yescharacteristic
364C2—41no—
365C2—4721no—
366C2—2361no—
367C2—2362no—
368C2#1683804411yescharacteristic
369C2#1683820111yescharacteristic
370C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#485C2
socleC22×C59C22×D4
hypercenter#485D59
hypocenterC59#3323
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. #16838091C2semidirect
3. #16837758C2semidirect
4. #16837722C2semidirect
5. #16837705C2semidirect
6. #16837658C2semidirect
7. #16837649C2semidirect
8. #16837627C2semidirect
9. #16837567C2semidirect
10. #16837555C2semidirect
11. #16837489C2semidirect
12. #16837477C2semidirect
13. #16837406C2semidirect
14. #16837402C2semidirect
15. C59×#485C2semidirect
18. C2×#11745672C22semidirect
22. C2×#11745659C22semidirect
25. #14273718C22semidirect
29. #14273707C22semidirect
34. #14273692C22semidirect
38. C4⋊C4×D59C22semidirect
40. #14273658C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273651C22semidirect
43. #14273650C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. #103×C59C22semidirect
57. #103×C59C22semidirect
189. #485D59semidirect
201. C59#3323semidirect
228. #107C2×D59semidirect
230. #106C2×D59semidirect
234. #103C2×D59semidirect
235. #103C2×D59semidirect