Finite Group Databasebeta

← #21436256

Subgroups — #21436256

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#16838116C211yesmaximal, characteristic, complemented
2#16838040C211yesmaximal, characteristic, complemented
3#16837763C211yesmaximal, characteristic, complemented
4#16837741C211yesmaximal, characteristic, complemented
5#16837727C211yesmaximal, characteristic, complemented
6#16837680C211yesmaximal, characteristic, complemented
7#16837645C211yesmaximal, characteristic, complemented
8#16837636C211yesmaximal, characteristic, complemented
9#16837619C211yesmaximal, characteristic, complemented
10#16837534C211yesmaximal, characteristic, complemented
11#16837514C211yesmaximal, characteristic, complemented
12#16837470C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#16837398C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C2×D4×D59C2211yescharacteristic
17C2×#11745669C2211yescharacteristic
18C2×#11745659C2211yescharacteristic
19C22×C59⋊C8C2211yescharacteristic, complemented
20#14273726C2211yescharacteristic, complemented
21#14273716C2211yescharacteristic
22#14273714—21no—
23#14273713—21no—
24#14273710—21no—
25#14273703C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273699—21no—
28#14273699—21no—
29#14273698C2211yescharacteristic
30#14273695—21no—
31D4×Dic59C2211yescharacteristic
32D4×Dic59C2211yescharacteristic, complemented
33C4×C22⋊D59C2211yescharacteristic
34#14273686C2211yescharacteristic, complemented
35#14273685C2211yescharacteristic
36#14273683—21no—
37C2×(C2×D59)⋊C4—21no—
38#14273661C2211yescharacteristic, complemented
39#14273660C2211yescharacteristic, complemented
40#14273659C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic, complemented
52C2×#41×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic, complemented
54C2×D8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60#41×C59—22no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C22×C4×C59—21no—
68C22×C4×C59C2311yescharacteristic
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59D411yescharacteristic
73C22×Dic59—21no—
74C22×Dic59—21no—
75D4×D59—22no—
76D4×D59—41no—
77C2×D236C2311yescharacteristic
78C2×C4×D59C2311yescharacteristic
79C2×Dic118—21no—
80SD16×C59—41no—
81D8×C59—22no—
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59D411yescharacteristic
91#11745669—41no—
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)⋊C4D411yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—42no—
116C22×D59—42no—
117C22×D59—81no—
118C22×D59C2×D411yescharacteristic
119Q8×C59—21no—
120Q8×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—42no—
125D4×C59—81no—
126D4×C59#4112yes—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—42no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—41no—
135C22⋊D59—42no—
136C22⋊D59—81no—
137C22⋊D59—81no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—42no—
142C2×Dic59—81no—
143C2×Dic59C2×D411yescharacteristic
144C2×Dic59C2×D411yescharacteristic
145C2×Dic59C2×D411yescharacteristic
146D236—21no—
147D236—21no—
148C4×D59—21no—
149C4×D59—21no—
150Dic118—81no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—22no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—84no—
172C4×C59—21no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59C2×#4111yescharacteristic
176C4×C59H(5,𝔽2)11yescharacteristic
177Dic59—21no—
178Dic59—21no—
179Dic59—21no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3319—591nomaximal, Sylow
184C2×C59—42no—
185C2×C59—41no—
186C2×C59—81no—
187C2×C59#54611yescharacteristic
188C2×C59#57511yescharacteristic
189C2×C59#57611yescharacteristic
190D59—41no—
191D59—81no—
192#555—591no—
193#546—591no—
194#489—591no—
195#485—591no—
196#482—591no—
197#474—591no—
198#468—591no—
199#466—591no—
200#463—591no—
201#449D5911yescharacteristic, complemented
202#447—591no—
203#442—591no—
204#435—591no—
205#418—591no—
206#416—591no—
207C59#331911yescharacteristic, complemented, Sylow
208C2×#41C2×D5911yescharacteristic
209C22×D4—591no—
210C2×SD16C2×D5911yescharacteristic, complemented
211C2×D8—591no—
212C2×D8C2×D5911yescharacteristic
213C2×M16—591no—
214C22×C8—591no—
215C4⋊Q8—591no—
216#124—591no—
217#124—1181no—
218#124—1181no—
219#123—1181no—
220C22⋊Q8—591no—
221#121—591no—
222#121—591no—
223#121—1181no—
224#121—1181no—
225#121C2×D5911yescharacteristic, complemented
226#120—1181no—
227C4×D4—591no—
228C4×D4—591no—
229C4×D4—591no—
230#117—591no—
231#117—591no—
232#117—1181no—
233C2×C22⋊C4—1181no—
234#107—591no—
235#107—591no—
236#106—591no—
237C4⋊C8—591no—
238#103—591no—
239#103—591no—
240#103C2×D5911yescharacteristic, complemented
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102C2×D5911yescharacteristic
248C22⋊C8—591no—
249C22⋊C8C2×D5911yescharacteristic, complemented
250#97—591no—
251C24—1181no—
252#41—22no—
253#41—41no—
254C2×Q8—1181no—
255C2×Q8C22×D5911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—591no—
259C2×D4—591no—
260C2×D4—1181no—
261C2×D4—1182no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—2361no—
265C2×D4C22×D5911yescharacteristic
266C2×D4C22×D5911yescharacteristic
267C22×C4—21no—
268C22×C4—591no—
269C22×C4—1181no—
270C22×C4—1181no—
271C22×C4C22×D5911yescharacteristic
272SD16—41no—
273D8—22no—
274D8—2361no—
275M16—2361no—
276C2×C8—591no—
277C2×C8—591no—
278C2×C8—2361no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22×D5911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—591no—
290C22⋊C4—591no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C42—591no—
301C42—1181no—
302C42—1181no—
303C23—21no—
304C23—21no—
305C23—591no—
306C23—1181no—
307C23—4721no—
308C23—2362no—
309C23—2362no—
310C23D4×D5911yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—4721no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—81no—
319D4—1181no—
320D4—1181no—
321D4—4721no—
322D4—4721no—
323D4—2361no—
324D4—2362no—
325D4#1174568712yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—591no—
332C2×C4—591no—
333C2×C4—591no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—4721no—
340C2×C4—2362no—
341C2×C4D4×D5911yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1181no—
346C8—1181no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—1181no—
357C22—1181no—
358C22—1181no—
359C22—4724no—
360C22—2361no—
361C22—2361no—
362C22—2361no—
363C22C2×D4×D5911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—1181no—
368C4—1181no—
369C4—1181no—
370C4—2361no—
371C4—2361no—
372C4—2361no—
373C4C2×#1174568711yescharacteristic
374C4#1427377211yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—4721no—
379C2—2361no—
380C2#1683803911yescharacteristic
381C2#1683819911yescharacteristic
382C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3319
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16838116C2semidirect
2. #16838040C2semidirect
3. #16837763C2semidirect
4. #16837741C2semidirect
5. #16837727C2semidirect
6. #16837680C2semidirect
7. #16837645C2semidirect
8. #16837636C2semidirect
9. #16837619C2semidirect
10. #16837534C2semidirect
11. #16837514C2semidirect
12. #16837470C2semidirect
13. #16837405C2semidirect
14. #16837398C2semidirect
15. C59×#449C2semidirect
19. C22×C59⋊C8C22semidirect
20. #14273726C22semidirect
32. D4×Dic59C22semidirect
34. #14273686C22semidirect
38. #14273661C22semidirect
39. #14273660C22semidirect
40. #14273659C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273651C22semidirect
43. #14273651C22semidirect
48. #14273648C22semidirect
51. #14273637C22semidirect
53. C2×SD16×C59C22semidirect
55. #121×C59C22semidirect
56. #103×C59C22semidirect
58. C22⋊C8×C59C22semidirect
201. #449D59semidirect
207. C59#3319semidirect
210. C2×SD16C2×D59semidirect
225. #121C2×D59semidirect
240. #103C2×D59semidirect
249. C22⋊C8C2×D59semidirect