Finite Group Databasebeta

← #21436242

Subgroups — #21436242

Order 7552.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838102C211yesmaximal, characteristic, complemented
2D4×D236C211yesmaximal, characteristic, complemented
3#16837767C211yesmaximal, characteristic, complemented
4#16837728C211yesmaximal, characteristic, complemented
5#16837722C211yesmaximal, characteristic, complemented
6#16837702C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837637C211yesmaximal, characteristic, complemented
9#16837597C211yesmaximal, characteristic, complemented
10#16837534C211yesmaximal, characteristic, complemented
11#16837534C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#442C211yesmaximal, characteristic, complemented
16C22×D236—21no—
17C2×D4×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745669C2211yescharacteristic, complemented
20C2×#11745669C2211yescharacteristic, complemented
21C2×#11745659C2211yescharacteristic, complemented
22C2×C8×D59C2211yescharacteristic, complemented
23#14273724C2211yescharacteristic
24#14273720—21no—
25#14273719C2211yescharacteristic, complemented
26#14273710—21no—
27#14273702C2211yescharacteristic
28#14273702C2211yescharacteristic
29#14273701—21no—
30#14273700—21no—
31#14273698C2211yescharacteristic, complemented
32#14273698C2211yescharacteristic, complemented
33#14273697—21no—
34#14273697—21no—
35C4×D236C2211yescharacteristic
36C4×C22⋊D59—21no—
37#14273685C2211yescharacteristic, complemented
38C4⋊C4×D59C2211yescharacteristic, complemented
39#14273660C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273649C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C2×D8×C59C2211yescharacteristic
53C4×D4×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic, complemented
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×D4×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69D4×D59—22no—
70D4×D59—22no—
71D4×D59—41no—
72D4×D59—41no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236—21no—
77C2×D236—44no—
78C2×D236D411yescharacteristic
79C2×D236C2311yescharacteristic
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×C4×D59C2311yescharacteristic
84D8×C59—22no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C42×C59C2311yescharacteristic
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94#11745669—41no—
95#11745669—41no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4D411yescharacteristic
100(C2×D59)⋊C4D411yescharacteristic
101C4⋊Dic59D411yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C8×D59—41no—
112C23×C59—21no—
113C23×C59—21no—
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
123C22×D59C2×D411yescharacteristic
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59#4112yes—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—42no—
131C2×C4×C59—81no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—42no—
136C22⋊D59—42no—
137C22⋊D59—42no—
138C22⋊D59—81no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143D236—22no—
144D236—21no—
145D236—21no—
146D236—21no—
147D236—21no—
148D236—42no—
149D236—42no—
150D236—42no—
151D236—81no—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—21no—
155C4×D59—21no—
156C4×D59—81no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—22no—
162C22×C59—41no—
163C22×C59—41no—
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—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—84no—
180C2×D59—84no—
181C2×D59AGL(1,ℤ/8)12yes—
182C4×C59—21no—
183C4×C59—21no—
184C4×C59—41no—
185C4×C59—41no—
186C4×C59C2×#4111yescharacteristic
187C4×C59H(5,𝔽2)11yescharacteristic
188Dic59—21no—
189Dic59—21no—
190Dic59—41no—
191Dic59—41no—
192#3318—591nomaximal, Sylow
193C2×C59—42no—
194C2×C59—81no—
195C2×C59#54611yescharacteristic
196C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C59#57611yescharacteristic
198D59—22no—
199D59—41no—
200D59—81no—
201D59—81no—
202#553—591no—
203D42—591no—
204#490—591no—
205#482—591no—
206#481—591no—
207#478—591no—
208#469—591no—
209#466—591no—
210#459—591no—
211#447—591no—
212#447—591no—
213#442D5911yescharacteristic, complemented
214#435—591no—
215#418—591no—
216C2×#102—591no—
217C59#331811yescharacteristic, complemented, Sylow
218C22×D4—591no—
219C22×D4—591no—
220C22×D4—1181no—
221C2×D8—591no—
222C2×D8—591no—
223C2×D8C2×D5911yescharacteristic
224C2×M16—591no—
225C22×C8—591no—
226#127—591no—
227#126—1181no—
228#125—591no—
229#123—1181no—
230#121—591no—
231#121—591no—
232#121—591no—
233#121—591no—
234#121—1181no—
235#121—1181no—
236#120—1181no—
237#120—1181no—
238C4×D4—591no—
239C4×D4—1181no—
240C4×D4C2×D5911yescharacteristic
241C4×D4C2×D5911yescharacteristic, complemented
242#117—591no—
243C2×C4⋊C4—591no—
244#107—591no—
245#106—591no—
246#106C2×D5911yescharacteristic, complemented
247C4⋊C8—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102C2×D5911yescharacteristic
257#102C2×D5911yescharacteristic, complemented
258C22⋊C8—591no—
259C22⋊C8—591no—
260#97C2×D5911yescharacteristic, complemented
261C24—1181no—
262C24—1181no—
263C2×D4—591no—
264C2×D4—591no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1182no—
271C2×D4—1182no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—2364no—
277C2×D4—2361no—
278C2×D4—2361no—
279C2×D4C22×D5911yescharacteristic
280C2×D4C22×D5911yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—591no—
284C22×C4—591no—
285C22×C4—1181no—
286D8—22no—
287D8—2361no—
288D8—2361no—
289M16—2361no—
290C2×C8—591no—
291C2×C8—591no—
292C2×C8—2361no—
293C2×C8C22×D5911yescharacteristic
294C2×C8C22×D5911yescharacteristic
295C4⋊C4—591no—
296C4⋊C4—591no—
297C4⋊C4—591no—
298C4⋊C4—1181no—
299C4⋊C4—1181no—
300C4⋊C4—1181no—
301C4⋊C4C22×D5911yescharacteristic
302C4⋊C4C22×D5911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—591no—
306C22⋊C4—591no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C42—1181no—
313C42C22×D5911yescharacteristic
314C23—21no—
315C23—21no—
316C23—591no—
317C23—591no—
318C23—1181no—
319C23—1181no—
320C23—4721no—
321C23—4721no—
322C23—2362no—
323C23—2362no—
324C23—2362no—
325C23—2362no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—1182no—
330D4—1181no—
331D4—1181no—
332D4—1181no—
333D4—1181no—
334D4—4721no—
335D4—4721no—
336D4—2362no—
337D4—2362no—
338D4—2362no—
339D4—2362no—
340D4—2362no—
341D4—2362no—
342D4#1174568512yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—591no—
348C2×C4—591no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—4721no—
356C2×C4D4×D5911yescharacteristic
357C2×C4D4×D5911yescharacteristic
358C2×C4C23×D5911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1181no—
362C8—1181no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—592no—
370C22—1181no—
371C22—1181no—
372C22—1181no—
373C22—1181no—
374C22—1181no—
375C22—4724no—
376C22—4724no—
377C22—2361no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22C2×D4×D5911yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—1181no—
389C4—1181no—
390C4—2361no—
391C4—2361no—
392C4C2×#1174568511yescharacteristic
393C4#1427377311yescharacteristic
394C2—42no—
395C2—81no—
396C2—1182no—
397C2—4721no—
398C2—4721no—
399C2—2361no—
400C2#1683804811yescharacteristic
401C2AGL(1,ℤ/8)×D5911yescharacteristic
402C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#442C2
socleC22×C59C22×D4
hypercenter#442D59
hypocenterC59#3318
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16838102C2semidirect
2. D4×D236C2semidirect
3. #16837767C2semidirect
4. #16837728C2semidirect
5. #16837722C2semidirect
6. #16837702C2semidirect
7. #16837654C2semidirect
8. #16837637C2semidirect
9. #16837597C2semidirect
10. #16837534C2semidirect
11. #16837534C2semidirect
12. #16837475C2semidirect
13. #16837405C2semidirect
14. #102×D59C2semidirect
15. C59×#442C2semidirect
19. C2×#11745669C22semidirect
20. C2×#11745669C22semidirect
21. C2×#11745659C22semidirect
22. C2×C8×D59C22semidirect
25. #14273719C22semidirect
31. #14273698C22semidirect
32. #14273698C22semidirect
37. #14273685C22semidirect
38. C4⋊C4×D59C22semidirect
39. #14273660C22semidirect
40. #14273658C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273649C22semidirect
43. #14273649C22semidirect
44. #14273649C22semidirect
45. #14273649C22semidirect
48. #14273647C22semidirect
49. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
54. C4×D4×C59C22semidirect
55. #106×C59C22semidirect
57. #102×C59C22semidirect
58. #97×C59C22semidirect
213. #442D59semidirect
217. C59#3318semidirect
241. C4×D4C2×D59semidirect
246. #106C2×D59semidirect
257. #102C2×D59semidirect
260. #97C2×D59semidirect