Finite Group Databasebeta

← #21436057

Subgroups — #21436057

Order 7552.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838056C211yesmaximal, characteristic, complemented
2#16837761C211yesmaximal, characteristic, complemented
3#16837730C211yesmaximal, characteristic, complemented
4#16837718C211yesmaximal, characteristic, complemented
5#16837692C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837633C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837547C211yesmaximal, characteristic, complemented
10#16837536C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14C2×#14273648C211yesmaximal, characteristic, complemented
15C59×#546C211yesmaximal, characteristic, complemented
16C2×#11745687—21no—
17C2×#11745671C2211yescharacteristic, complemented
18C2×#11745669C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745664C2211yescharacteristic, complemented
21C22×C59⋊C8C2211yescharacteristic
22#14273727C2211yescharacteristic, complemented
23#14273711—21no—
24#14273711—21no—
25#14273707—21no—
26#14273701C2211yescharacteristic
27#14273701C2211yescharacteristic, complemented
28C4×D236C2211yescharacteristic, complemented
29C2×C4⋊Dic59C2211yescharacteristic
30C2×C4⋊Dic59C2211yescharacteristic, complemented
31#14273658C2211yescharacteristic, complemented
32#14273658C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273651C2211yescharacteristic, complemented
36#14273651C2211yescharacteristic, complemented
37#14273651C2211yescharacteristic, complemented
38#14273648C2211yescharacteristic
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273647C2211yescharacteristic, complemented
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47#14273638C2211yescharacteristic, complemented
48C2×#41×C59C2211yescharacteristic
49C22×D4×C59C2211yescharacteristic
50#124×C59C2211yescharacteristic
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53#121×C59—21no—
54#121×C59C2211yescharacteristic
55#120×C59—21no—
56C4×D4×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic
58C2×C22⋊C4×C59—21no—
59C24×C59—21no—
60#41×C59—22no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—22no—
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—41no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C2×D4×C59C2311yescharacteristic
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C2×C22⋊D59—21no—
76C2×C22⋊D59—21no—
77C22×Dic59—21no—
78C22×Dic59—21no—
79#11745687—44no—
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×Dic118—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59D411yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59D411yescharacteristic
92C22⋊C4×C59D411yescharacteristic
93C42×C59C2311yescharacteristic
94#11745671—41no—
95#11745669—22no—
96#11745669—41no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106#11745664—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—42no—
115C23×C59—42no—
116C23×C59—81no—
117C23×C59C2×D411yescharacteristic
118C23×C59C2×D411yescharacteristic
119C22×D59—21no—
120Q8×C59—21no—
121Q8×C59—21no—
122D4×C59—22no—
123D4×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—42no—
127D4×C59—42no—
128D4×C59—81no—
129D4×C59#4112yescomplemented
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—42no—
137C2×C4×C59—81no—
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2411yescharacteristic
143C22⋊D59—42no—
144C22⋊D59—42no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—42no—
149C2×Dic59—42no—
150D236—21no—
151D236—21no—
152C4×D59—42no—
153Dic118—42no—
154C59⋊C8—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—22no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—84no—
170C22×C59AGL(1,ℤ/8)12yes—
171C22×C59C22×D411yescharacteristic
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C4×C59—21no—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59C2×#4111yescharacteristic
182C4×C59H(5,𝔽2)11yescharacteristic
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186#3306—591nomaximal, Sylow
187C2×C59—22no—
188C2×C59—41no—
189C2×C59—42no—
190C2×C59—81no—
191C2×C59#54611yescharacteristic
192C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C59#57711yescharacteristic
194D59—81no—
195#547—591no—
196#546D5911yescharacteristic, complemented
197#489—591no—
198#483—591no—
199#481—591no—
200#476—591no—
201#469—591no—
202#465—591no—
203#463—591no—
204#449—591no—
205#447—591no—
206#442—591no—
207#435—591no—
208#417—591no—
209C2×#102—591no—
210C59#330611yescharacteristic, complemented, Sylow
211C2×#41—1181no—
212C2×#41C2×D5911yescharacteristic
213C22×D4C2×D5911yescharacteristic
214C2×SD16—591no—
215C2×D8—591no—
216C2×D8—591no—
217C2×M16—591no—
218C22×C8—591no—
219C4⋊Q8—591no—
220#124C2×D5911yescharacteristic
221#123—21no—
222#123—1181no—
223#123—1181no—
224C22⋊Q8—1181no—
225C22⋊Q8C2×D5911yescharacteristic
226#121—21no—
227#121—591no—
228#121—591no—
229#121C2×D5911yescharacteristic
230#120—21no—
231C4×D4—591no—
232C4×D4C2×D5911yescharacteristic
233C4×D4C2×D5911yescharacteristic
234C2×C4⋊C4—591no—
235C2×C4⋊C4—591no—
236C2×C22⋊C4—21no—
237#106—591no—
238#106—591no—
239#106—591no—
240C4⋊C8—591no—
241#103—591no—
242#103—591no—
243#103—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251C22⋊C8—591no—
252C22⋊C8—591no—
253#97—591no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—2364no—
258C2×Q8—1181no—
259C2×Q8C22×D5911yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4C22⋊D5911yescharacteristic
269C2×D4C22×D5911yescharacteristic
270C2×D4C22×D5911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—1181no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4C22×D5911yescharacteristic
277C22×C4C22×D5911yescharacteristic
278SD16—2361no—
279D8—1182no—
280D8—2361no—
281M16—2361no—
282C2×C8—591no—
283C2×C8—591no—
284C2×C8—591no—
285C2×C8—591no—
286C2×C8—2361no—
287C4⋊C4—21no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—591no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4C22⋊D5911yescharacteristic
295C4⋊C4C22×D5911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4C22⋊D5911yescharacteristic
305C22⋊C4C22⋊D5911yescharacteristic
306C42C22×D5911yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—1181no—
313C23C2×C22⋊D5911yescharacteristic
314C23C2×C22⋊D5911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—2362no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—1181no—
326D4—1181no—
327D4—2362no—
328D4—2362no—
329D4#1174568712yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—2362no—
342C2×C4—2362no—
343C2×C4—2362no—
344C2×C4C2×C22⋊D5911yescharacteristic
345C2×C4C2×C22⋊D5911yescharacteristic
346C2×C4C2×C22⋊D5911yescharacteristic
347C2×C4C2×C22⋊D5911yescharacteristic
348C2×C4C23×D5911yescharacteristic
349C8—1181no—
350C8—1181no—
351C8—1181no—
352C8—1181no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22#1427375212yes—
369C22C22×C22⋊D5911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—2361no—
377C4—2361no—
378C4—2361no—
379C4C2×#1174568711yescharacteristic
380C4#1427377211yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—4721no—
386C2#1683804611yescharacteristic
387C2C2×#1427375211yescharacteristic
388C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#546C2
socleC22×C59C22×D4
hypercenter#546D59
hypocenterC59#3306
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #16838056C2semidirect
2. #16837761C2semidirect
3. #16837730C2semidirect
4. #16837718C2semidirect
5. #16837692C2semidirect
6. #16837653C2semidirect
7. #16837633C2semidirect
8. #16837614C2semidirect
9. #16837547C2semidirect
10. #16837536C2semidirect
11. #16837512C2semidirect
12. #16837474C2semidirect
13. #16837403C2semidirect
14. C2×#14273648C2semidirect
15. C59×#546C2semidirect
17. C2×#11745671C22semidirect
20. C2×#11745664C22semidirect
22. #14273727C22semidirect
27. #14273701C22semidirect
28. C4×D236C22semidirect
30. C2×C4⋊Dic59C22semidirect
31. #14273658C22semidirect
32. #14273658C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273651C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
44. #14273647C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. #14273638C22semidirect
129. D4×C59#41semidirect
196. #546D59semidirect
210. C59#3306semidirect
329. D4#11745687semidirect