Finite Group Databasebeta

← #21436291

Subgroups — #21436291

Order 7552.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838048C211yesmaximal, characteristic, complemented
2#16837759C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837715C211yesmaximal, characteristic, complemented
5#16837699C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837646C211yesmaximal, characteristic, complemented
8#16837617C211yesmaximal, characteristic, complemented
9#16837545C211yesmaximal, characteristic, complemented
10#16837535C211yesmaximal, characteristic, complemented
11C4×#11745669C211yesmaximal, characteristic, complemented
12#16837480C211yesmaximal, characteristic, complemented
13#16837406C211yesmaximal, characteristic, complemented
14#16837401C211yesmaximal, characteristic, complemented
15C59×#553C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745670C2211yescharacteristic, complemented
19C2×#11745669C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C2×#11745664C2211yescharacteristic, complemented
23#14273715C2211yescharacteristic
24#14273712—21no—
25#14273706C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273700—21no—
28#14273695—21no—
29C4×D236C2211yescharacteristic
30C22⋊C4×D59—21no—
31#14273660C2211yescharacteristic, complemented
32#14273660C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273650C2211yescharacteristic, complemented
36#14273650C2211yescharacteristic, complemented
37#14273650C2211yescharacteristic, complemented
38#14273648C2211yescharacteristic, complemented
39#14273647C2211yescharacteristic
40#14273647C2211yescharacteristic
41#14273647C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47C4×C59⋊C8C2211yescharacteristic, complemented
48#126×C59—21no—
49#125×C59C2211yescharacteristic, complemented
50#123×C59—21no—
51#121×C59—21no—
52#121×C59C2211yescharacteristic
53#121×C59C2211yescharacteristic, complemented
54C4×D4×C59—21no—
55C4×D4×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic, complemented
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59D411yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70#11745685—22no—
71#11745685—41no—
72C2×D236—22no—
73C2×D236—21no—
74C2×D236—41no—
75C2×D236C2311yescharacteristic
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×Dic118C2311yescharacteristic
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59D411yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59D411yescharacteristic
92C22⋊C4×C59D411yescharacteristic
93C42×C59—21no—
94C42×C59C2311yescharacteristic
95C22⋊Dic59—21no—
96#11745670—41no—
97#11745669—22no—
98#11745669—41no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105#11745664—41no—
106#11745664—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—81no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—41no—
122D4×C59—42no—
123D4×C59—81no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
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×C59—81no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2411yescharacteristic
138C22⋊D59—42no—
139C22⋊D59—81no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—42no—
146D236#4112yes—
147C4×D59—42no—
148C4×D59—81no—
149Dic118—21no—
150Dic118—21no—
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—22no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—84no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—21no—
175C4×C59—21no—
176C4×C59—41no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59C2×#4111yescharacteristic
180C4×C59H(5,𝔽2)11yescharacteristic
181Dic59—41no—
182Dic59—41no—
183#3322—591nomaximal, Sylow
184C2×C59—41no—
185C2×C59—41no—
186C2×C59—81no—
187C2×C59#54611yescharacteristic
188C2×C59#57511yescharacteristic
189C2×C59#57611yescharacteristic
190D59—42no—
191D59—81no—
192#553D5911yescharacteristic, complemented
193#546—591no—
194#488—591no—
195#485—591no—
196#480—591no—
197#478—591no—
198#469—591no—
199#468—591no—
200#463—591no—
201#449—591no—
202#447—591no—
203C4×D8—591no—
204#436—591no—
205#418—591no—
206#417—591no—
207C59#332211yescharacteristic, complemented, Sylow
208C2×#41—591no—
209C22×D4—591no—
210C2×SD16—591no—
211C2×D8—591no—
212C2×D8—591no—
213C2×M16—591no—
214C2×M16—591no—
215#126—21no—
216#125C2×D5911yescharacteristic, complemented
217#124—591no—
218#123—21no—
219#123—1181no—
220C22⋊Q8—591no—
221#121—21no—
222#121—591no—
223#121—1181no—
224#121C2×D5911yescharacteristic
225#121C2×D5911yescharacteristic, complemented
226#120—1181no—
227C4×D4—21no—
228C4×D4—591no—
229C4×D4C2×D5911yescharacteristic
230C4×D4C2×D5911yescharacteristic, complemented
231#117C2×D5911yescharacteristic
232C2×C4⋊C4C2×D5911yescharacteristic, complemented
233C2×C22⋊C4—1181no—
234#107—591no—
235#107—591no—
236#106—591no—
237C4⋊C8—591no—
238#103—591no—
239#103—591no—
240#103—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248C22⋊C8—591no—
249C22⋊C8—591no—
250C4×C8—591no—
251C24—1181no—
252#41—1182no—
253#41—2361no—
254C2×Q8—591no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—591no—
258C2×D4—591no—
259C2×D4—1182no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—2361no—
264C2×D4C22⋊D5911yescharacteristic
265C2×D4C22×D5911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—1181no—
269C22×C4—1181no—
270C22×C4C22×D5911yescharacteristic
271C22×C4C22×D5911yescharacteristic
272SD16—2361no—
273D8—1182no—
274D8—2361no—
275M16—2361no—
276M16—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8—591no—
280C2×C8—591no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4C22⋊D5911yescharacteristic
287C4⋊C4C22×D5911yescharacteristic
288C4⋊C4C22×D5911yescharacteristic
289C4⋊C4C22×D5911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4C22⋊D5911yescharacteristic
300C22⋊C4C22⋊D5911yescharacteristic
301C42—21no—
302C42C22×D5911yescharacteristic
303C23—21no—
304C23—1181no—
305C23—1181no—
306C23—4721no—
307C23—2362no—
308C23—2362no—
309C23C2×C22⋊D5911yescharacteristic
310C23C2×C22⋊D5911yescharacteristic
311Q8—1181no—
312Q8—1181no—
313D4—21no—
314D4—21no—
315D4—41no—
316D4—42no—
317D4—81no—
318D4—592no—
319D4—1181no—
320D4—1181no—
321D4—1181no—
322D4—4721no—
323D4—2362no—
324D4—2362no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—4721no—
337C2×C4—2362no—
338C2×C4C2×C22⋊D5911yescharacteristic
339C2×C4C2×C22⋊D5911yescharacteristic
340C2×C4C2×C22⋊D5911yescharacteristic
341C2×C4C2×C22⋊D5911yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—1181no—
344C8—1181no—
345C8—1181no—
346C8—1181no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—1182no—
357C22—4724no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22—2361no—
362C22—2361no—
363C22C22×C22⋊D5911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—2361no—
372C4—2361no—
373C4#41×D5911yescharacteristic
374C4#1427377311yescharacteristic
375C2—41no—
376C2—41no—
377C2—81no—
378C2—4721no—
379C2—2362no—
380C2#1683804011yescharacteristic
381C2#1683820011yescharacteristic
382C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#553C2
socleC22×C59C22×D4
hypercenter#553D59
hypocenterC59#3322
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #16838048C2semidirect
2. #16837759C2semidirect
3. #16837743C2semidirect
4. #16837715C2semidirect
5. #16837699C2semidirect
6. #16837653C2semidirect
7. #16837646C2semidirect
8. #16837617C2semidirect
9. #16837545C2semidirect
10. #16837535C2semidirect
11. C4×#11745669C2semidirect
12. #16837480C2semidirect
13. #16837406C2semidirect
14. #16837401C2semidirect
15. C59×#553C2semidirect
18. C2×#11745670C22semidirect
22. C2×#11745664C22semidirect
31. #14273660C22semidirect
32. #14273660C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273650C22semidirect
36. #14273650C22semidirect
37. #14273650C22semidirect
38. #14273648C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. C4×C59⋊C8C22semidirect
49. #125×C59C22semidirect
53. #121×C59C22semidirect
56. C4×D4×C59C22semidirect
58. C2×C4⋊C4×C59C22semidirect
192. #553D59semidirect
207. C59#3322semidirect
216. #125C2×D59semidirect
225. #121C2×D59semidirect
230. C4×D4C2×D59semidirect
232. C2×C4⋊C4C2×D59semidirect