Finite Group Databasebeta

← #21434937

Subgroups — #21434937

Order 7552.

418 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#16837915C211yesmaximal, characteristic, complemented
2#16837909C211yesmaximal, characteristic, complemented
3#16837742C211yesmaximal, characteristic, complemented
4#16837740C211yesmaximal, characteristic, complemented
5#16837727C211yesmaximal, characteristic, complemented
6#16837725C211yesmaximal, characteristic, complemented
7#16837657C211yesmaximal, characteristic, complemented
8#16837654C211yesmaximal, characteristic, complemented
9#16837651C211yesmaximal, characteristic, complemented
10#16837645C211yesmaximal, characteristic, complemented
11#16837563C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837546C211yesmaximal, characteristic, complemented
14#16837364C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C22×C4×D59C2211yescharacteristic
18C2×#11745671C2211yescharacteristic, complemented
19C2×#11745669C2211yescharacteristic, complemented
20C2×#11745659C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22#14273712—21no—
23#14273708—21no—
24#14273703C2211yescharacteristic
25#14273703C2211yescharacteristic
26#14273703C2211yescharacteristic
27#14273702C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273698C2211yescharacteristic
30#14273698C2211yescharacteristic
31#14273697—21no—
32#14273695—21no—
33#14273689—21no—
34C4×C22⋊D59—21no—
35C4×C22⋊D59—21no—
36(C22⋊D59)⋊C4—21no—
37#14273686C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273651C2211yescharacteristic, complemented
45#14273651C2211yescharacteristic, complemented
46#14273649C2211yescharacteristic, complemented
47#14273649C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic, complemented
55C22⋊Q8×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59D411yescharacteristic
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C22×Dic59D411yescharacteristic
72#11745689—41no—
73#11745689—41no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59—41no—
79C2×C4×D59—41no—
80C2×C4×D59D411yescharacteristic
81C2×C4×D59D411yescharacteristic
82C2×C4×D59C2311yescharacteristic
83C2×C4×D59C2311yescharacteristic
84Q16×C59—41no—
85SD16×C59—41no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59—21no—
89C4⋊C4×C59C2311yescharacteristic
90C22⋊C4×C59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94#11745671—41no—
95#11745669—41no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C4×Dic59—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745659—41no—
113#11745659—41no—
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—21no—
117C22×D59—41no—
118C22×D59—41no—
119C22×D59—41no—
120C22×D59C2×D411yescharacteristic
121C22×D59C2×D411yescharacteristic
122Q8×C59—21no—
123Q8×C59—21no—
124Q8×C59—21no—
125Q8×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—42no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—42no—
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C22⋊D59—42no—
138C22⋊D59—42no—
139C22⋊D59—42no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—41no—
144C2×Dic59C2×D411yescharacteristic
145C2×Dic59C2×D411yescharacteristic
146D236—21no—
147D236—21no—
148D236—42no—
149D236—42no—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—41no—
155C4×D59—41no—
156C4×D59—42no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59C22×D411yescharacteristic
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—44no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59—41no—
182C4×C59H(5,𝔽2)11yescharacteristic
183C4×C59H(5,𝔽2)11yescharacteristic
184Dic59—21no—
185Dic59—21no—
186Dic59—41no—
187Dic59—41no—
188Dic59—41no—
189#3197—591nomaximal, Sylow
190C2×C59—41no—
191C2×C59—81no—
192C2×C59#53411yescharacteristic
193C2×C59#57511yescharacteristic
194C2×C59#57511yescharacteristic
195D59—41no—
196D59—41no—
197D59—81no—
198#525—591no—
199#525—591no—
200#485—591no—
201#485—591no—
202#482—591no—
203#482—591no—
204#470—591no—
205#469—591no—
206#468—591no—
207#468—591no—
208#452—591no—
209#452D5911yescharacteristic, complemented
210#449—591no—
211#449—591no—
212#407—591no—
213C59#319711yescharacteristic, complemented, Sylow
214C2×#41—591no—
215C2×#41C2×D5911yescharacteristic
216C23×C4—591no—
217C2×Q16C2×D5911yescharacteristic, complemented
218C2×SD16—591no—
219C2×SD16C2×D5911yescharacteristic, complemented
220C2×D8—591no—
221C2×M16—591no—
222C2×M16—591no—
223#123—1181no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227C22⋊Q8—591no—
228C22⋊Q8C2×D5911yescharacteristic
229#121—591no—
230#121—591no—
231#121—591no—
232#121—591no—
233#120—1181no—
234#120—1181no—
235C4×D4—1181no—
236C4×D4—1181no—
237C4×D4—1181no—
238C4×D4—1181no—
239#117—591no—
240#117—591no—
241#107—591no—
242#107—591no—
243#106—591no—
244#106—591no—
245#103—591no—
246#103—591no—
247#103—591no—
248#103C2×D5911yescharacteristic, complemented
249#102—591no—
250#102—591no—
251#102—591no—
252#102C2×D5911yescharacteristic, complemented
253C22⋊C8—591no—
254C22⋊C8—591no—
255C22⋊C8—591no—
256C22⋊C8C2×D5911yescharacteristic
257C24—591no—
258#41—41no—
259#41—41no—
260#41—2361no—
261#41—2361no—
262C2×Q8C22×D5911yescharacteristic
263C2×Q8C22×D5911yescharacteristic
264C2×D4—21no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4C22×D5911yescharacteristic
272C22×C4—21no—
273C22×C4—591no—
274C22×C4—591no—
275C22×C4—591no—
276C22×C4—591no—
277C22×C4—591no—
278C22×C4—1181no—
279C22×C4—2361no—
280C22×C4—2361no—
281C22×C4C22×D5911yescharacteristic
282Q16—41no—
283SD16—41no—
284SD16—2361no—
285D8—2361no—
286M16—2361no—
287M16—2361no—
288C2×C8—591no—
289C2×C8—591no—
290C2×C8C22×D5911yescharacteristic
291C2×C8C22×D5911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—591no—
294C4⋊C4—591no—
295C4⋊C4—591no—
296C4⋊C4—1181no—
297C4⋊C4—1181no—
298C4⋊C4—1181no—
299C4⋊C4C22×D5911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C42—1181no—
311C42—1181no—
312C23—21no—
313C23—591no—
314C23—591no—
315C23—1181no—
316C23—2361no—
317C23—2361no—
318C23—2361no—
319C23D4×D5911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—1181no—
328D4—1181no—
329D4—2362no—
330D4—2362no—
331D4—2362no—
332D4—2362no—
333D4—2362no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—591no—
341C2×C4—591no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—2361no—
350C2×C4—2361no—
351C2×C4—2362no—
352C2×C4—2361no—
353C2×C4D4×D5911yescharacteristic
354C2×C4C23×D5911yescharacteristic
355C8—21no—
356C8—21no—
357C8—1181no—
358C8—1181no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—1181no—
366C22—1181no—
367C22—1181no—
368C22—1181no—
369C22—1181no—
370C22—1181no—
371C22—2364no—
372C22—2361no—
373C22—2361no—
374C22—2361no—
375C22C2×D4×D5911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1181no—
381C4—1181no—
382C4—2361no—
383C4—2361no—
384C4—2361no—
385C4#1427377211yescharacteristic
386C4#1427377211yescharacteristic
387C2—41no—
388C2—81no—
389C2—4721no—
390C2—2361no—
391C2—2361no—
392C2#1683796211yescharacteristic
393C2#1683819911yescharacteristic
394C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3197
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16837915C2semidirect
2. #16837909C2semidirect
3. #16837742C2semidirect
4. #16837740C2semidirect
5. #16837727C2semidirect
6. #16837725C2semidirect
7. #16837657C2semidirect
8. #16837654C2semidirect
9. #16837651C2semidirect
10. #16837645C2semidirect
11. #16837563C2semidirect
12. #16837547C2semidirect
13. #16837546C2semidirect
14. #16837364C2semidirect
15. C59×#452C2semidirect
18. C2×#11745671C22semidirect
19. C2×#11745669C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. #14273659C22semidirect
42. #14273658C22semidirect
43. #14273651C22semidirect
44. #14273651C22semidirect
45. #14273651C22semidirect
46. #14273649C22semidirect
47. #14273649C22semidirect
48. #14273648C22semidirect
53. C2×Q16×C59C22semidirect
54. C2×SD16×C59C22semidirect
56. #103×C59C22semidirect
57. #102×C59C22semidirect
209. #452D59semidirect
213. C59#3197semidirect
217. C2×Q16C2×D59semidirect
219. C2×SD16C2×D59semidirect
248. #103C2×D59semidirect
252. #102C2×D59semidirect