Finite Group Databasebeta

← #21436112

Subgroups — #21436112

Order 7552.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838086C211yesmaximal, characteristic, complemented
2#16838036C211yesmaximal, characteristic
3#16837765C211yesmaximal, characteristic, complemented
4#16837723C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837705C211yesmaximal, characteristic, complemented
7#16837634C211yesmaximal, characteristic, complemented
8#16837600C211yesmaximal, characteristic, complemented
9#16837552C211yesmaximal, characteristic, complemented
10#16837551C211yesmaximal, characteristic, complemented
11#16837505C211yesmaximal, characteristic, complemented
12#16837471C211yesmaximal, characteristic, complemented
13#16837408C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#468C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×D4×D59—21no—
18C2×D4×D59C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic, complemented
21C2×C8×D59C2211yescharacteristic, complemented
22#14273723C2211yescharacteristic
23#14273720—21no—
24#14273718C2211yescharacteristic, complemented
25#14273717—21no—
26#14273709—21no—
27#14273703C2211yescharacteristic, complemented
28#14273702C2211yescharacteristic
29#14273700—21no—
30#14273697—21no—
31#14273695—21no—
32Q8×Dic59C2211yescharacteristic, complemented
33#14273689C2211yescharacteristic
34C4×C22⋊D59C2211yescharacteristic
35#14273686C2211yescharacteristic, complemented
36#14273685—21no—
37C4⋊C4×D59C2211yescharacteristic, complemented
38#14273660C2211yescharacteristic, complemented
39#14273658C2211yescharacteristic, complemented
40Dic59⋊C8C2211yescharacteristic, complemented
41#14273649C2211yescharacteristic
42#14273649C2211yescharacteristic
43#14273649C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51#14273637C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic, complemented
53C2×M16×C59C2211yescharacteristic, complemented
54C22⋊Q8×C59C2211yescharacteristic, complemented
55#121×C59C2211yescharacteristic
56#107×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
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
81SD16×C59—41no—
82M16×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59D411yescharacteristic
92#11745671—22no—
93#11745671—41no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4D411yescharacteristic
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59—21no—
107C4×Dic59—21no—
108C4×Dic59C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
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
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—42no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—22no—
136C22⋊D59—42no—
137C22⋊D59—42no—
138C22⋊D59—81no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—21no—
145D236—21no—
146D236—21no—
147D236—42no—
148D236—42no—
149D236#4112yes—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—42no—
153C4×D59—42no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—22no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—84no—
174C2×D59—84no—
175C2×D59AGL(1,ℤ/8)12yes—
176C4×C59—21no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59—41no—
180C4×C59C2×#4111yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—21no—
183Dic59—21no—
184Dic59—21no—
185Dic59—41no—
186Dic59—41no—
187#3310—591nomaximal, Sylow
188C2×C59—41no—
189C2×C59—81no—
190C2×C59#54611yescharacteristic
191C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C59#57711yescharacteristic
193D59—22no—
194D59—42no—
195D59—81no—
196#552—591no—
197D42—591no—
198#490—591no—
199#482—591no—
200#480—591no—
201#478—591no—
202#468D5911yescharacteristic, complemented
203#465—591no—
204#460—591no—
205#450—591no—
206#450—591no—
207#440—591no—
208#435—591no—
209#418—591no—
210C2×#102—591no—
211C59#331011yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C22×D4—591no—
214C22×D4—1181no—
215C2×SD16—591no—
216C2×SD16—591no—
217C2×SD16C2×D5911yescharacteristic, complemented
218C2×M16C2×D5911yescharacteristic, complemented
219C22×C8—591no—
220#127—591no—
221#126—1181no—
222#125—591no—
223#125—1181no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8C2×D5911yescharacteristic, complemented
227#121—591no—
228#121—1181no—
229#121C2×D5911yescharacteristic
230#120—1181no—
231#120—1181no—
232C4×Q8—591no—
233C4×D4—591no—
234C4×D4—591no—
235#117—591no—
236#117—1181no—
237C2×C4⋊C4—591no—
238#107—591no—
239#107C2×D5911yescharacteristic, complemented
240#106—591no—
241C4⋊C8—591no—
242#103C2×D5911yescharacteristic, complemented
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102C2×D5911yescharacteristic, complemented
252C22⋊C8—591no—
253C22⋊C8—591no—
254#97—591no—
255C24—1181no—
256C24—1181no—
257C2×Q8C22×D5911yescharacteristic
258C2×D4—21no—
259C2×D4—591no—
260C2×D4—591no—
261C2×D4—591no—
262C2×D4—1182no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1182no—
268C2×D4—1181no—
269C2×D4—2361no—
270C2×D4—2361no—
271C2×D4—2364no—
272C2×D4C22×D5911yescharacteristic
273C22×C4—591no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4C22×D5911yescharacteristic
277SD16—41no—
278SD16—1182no—
279SD16—2361no—
280M16—41no—
281C2×C8—591no—
282C2×C8—591no—
283C2×C8—2361no—
284C2×C8C22×D5911yescharacteristic
285C2×C8C22×D5911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4C22×D5911yescharacteristic
296C4⋊C4C22×D5911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—591no—
300C22⋊C4—591no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C42—591no—
306C42—1181no—
307C42—1181no—
308C23—21no—
309C23—591no—
310C23—1181no—
311C23—1181no—
312C23—4721no—
313C23—4721no—
314C23—2362no—
315C23—2362no—
316C23—2362no—
317C23—2362no—
318C23D4×D5911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—592no—
325D4—1182no—
326D4—1181no—
327D4—1181no—
328D4—1181no—
329D4—4721no—
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—591no—
340C2×C4—591no—
341C2×C4—591no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—2362no—
347C2×C4—2362no—
348C2×C4D4×D5911yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1181no—
353C8—1181no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—592no—
361C22—1181no—
362C22—1181no—
363C22—1182no—
364C22—4724no—
365C22—4724no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22C2×D4×D5911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—1181no—
377C4—1181no—
378C4—1181no—
379C4—2361no—
380C4—2361no—
381C4#41×D5911yescharacteristic
382C4#1427377211yescharacteristic
383C2—41no—
384C2—81no—
385C2—1182no—
386C2—4721no—
387C2—2362no—
388C2#1683804111yescharacteristic
389C2AGL(1,ℤ/8)×D5911yescharacteristic
390C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#468C2
socleC22×C59C22×D4
hypercenter#468D59
hypocenterC59#3310
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #16838086C2semidirect
3. #16837765C2semidirect
4. #16837723C2semidirect
5. #16837717C2semidirect
6. #16837705C2semidirect
7. #16837634C2semidirect
8. #16837600C2semidirect
9. #16837552C2semidirect
10. #16837551C2semidirect
11. #16837505C2semidirect
12. #16837471C2semidirect
13. #16837408C2semidirect
14. #102×D59C2semidirect
15. C59×#468C2semidirect
20. C2×#11745671C22semidirect
21. C2×C8×D59C22semidirect
24. #14273718C22semidirect
27. #14273703C22semidirect
32. Q8×Dic59C22semidirect
35. #14273686C22semidirect
37. C4⋊C4×D59C22semidirect
38. #14273660C22semidirect
39. #14273658C22semidirect
40. Dic59⋊C8C22semidirect
43. #14273649C22semidirect
44. #14273649C22semidirect
45. #14273648C22semidirect
46. #14273648C22semidirect
48. #14273647C22semidirect
49. C22⋊(C59⋊C8)C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. #14273637C22semidirect
52. C2×SD16×C59C22semidirect
53. C2×M16×C59C22semidirect
54. C22⋊Q8×C59C22semidirect
56. #107×C59C22semidirect
57. #103×C59C22semidirect
58. #102×C59C22semidirect
202. #468D59semidirect
211. C59#3310semidirect
217. C2×SD16C2×D59semidirect
218. C2×M16C2×D59semidirect
226. C22⋊Q8C2×D59semidirect
239. #107C2×D59semidirect
242. #103C2×D59semidirect
251. #102C2×D59semidirect