Finite Group Databasebeta

← #21436051

Subgroups — #21436051

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#16838048C211yesmaximal, characteristic, complemented
2#16837764C211yesmaximal, characteristic, complemented
3#16837732C211yesmaximal, characteristic, complemented
4#16837720C211yesmaximal, characteristic, complemented
5#16837689C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837617C211yesmaximal, characteristic, complemented
9#16837545C211yesmaximal, characteristic, complemented
10#16837535C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837401C211yesmaximal, characteristic, complemented
14C2×#14273647C211yesmaximal, characteristic, complemented
15C59×#547C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745670C2211yescharacteristic, complemented
19C2×#11745669C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21C2×#11745664C2211yescharacteristic, complemented
22C22×C59⋊C8C2211yescharacteristic
23#14273715C2211yescharacteristic
24#14273712—21no—
25#14273706C2211yescharacteristic
26#14273701C2211yescharacteristic
27#14273700—21no—
28#14273695—21no—
29C4×D236C2211yescharacteristic
30C22⋊C4×D59—21no—
31#14273658C2211yescharacteristic, complemented
32#14273658C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273650C2211yescharacteristic, complemented
36#14273650C2211yescharacteristic, complemented
37#14273650C2211yescharacteristic, complemented
38#14273648C2211yescharacteristic, complemented
39#14273647C2211yescharacteristic
40#14273647C2211yescharacteristic
41#14273647C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47#14273638C2211yescharacteristic, complemented
48C2×#41×C59—21no—
49C4⋊Q8×C59C2211yescharacteristic, complemented
50#123×C59—21no—
51#123×C59—21no—
52C22⋊Q8×C59—21no—
53#121×C59C2211yescharacteristic
54#121×C59C2211yescharacteristic, complemented
55C4×D4×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic, complemented
57C2×C4⋊C4×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60#41×C59—44no—
61C2×Q8×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59—21no—
64C2×D4×C59D411yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59C2311yescharacteristic
70C22×C4×C59C2311yescharacteristic
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73#11745685—22no—
74#11745685—41no—
75C2×D236—22no—
76C2×D236—21no—
77C2×D236—41no—
78C2×D236C2311yescharacteristic
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×Dic118C2311yescharacteristic
83C4⋊C4×C59—21no—
84C4⋊C4×C59—21no—
85C4⋊C4×C59—21no—
86C4⋊C4×C59D411yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C4⋊C4×C59C2311yescharacteristic
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C22⋊C4×C59—21no—
93C22⋊C4×C59D411yescharacteristic
94C22⋊C4×C59D411yescharacteristic
95C42×C59C2311yescharacteristic
96C22⋊Dic59—21no—
97#11745670—41no—
98#11745669—22no—
99#11745669—41no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106#11745664—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—81no—
120Q8×C59—42no—
121D4×C59—22no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—42no—
125D4×C59—42no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—42no—
134C2×C4×C59—42no—
135C2×C4×C59—42no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2411yescharacteristic
141C22⋊D59—42no—
142C22⋊D59—81no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145D236—21no—
146D236—21no—
147D236—21no—
148D236—42no—
149D236#4112yescomplemented
150C4×D59—42no—
151C4×D59—81no—
152Dic118—21no—
153Dic118—21no—
154C59⋊C8—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59AGL(1,ℤ/8)12yes—
167C22×C59C22×D411yescharacteristic
168C2×D59—22no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—84no—
175C4×C59—21no—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59—41no—
182C4×C59C2×#4111yescharacteristic
183C4×C59H(5,𝔽2)11yescharacteristic
184Dic59—41no—
185Dic59—41no—
186#3306—591nomaximal, Sylow
187C2×C59—22no—
188C2×C59—41no—
189C2×C59—81no—
190C2×C59#54611yescharacteristic
191C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C59#57711yescharacteristic
193D59—42no—
194D59—81no—
195#547D5911yescharacteristic, complemented
196#546—591no—
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—21no—
212C2×#41—591no—
213C22×D4—591no—
214C2×SD16—591no—
215C2×D8—591no—
216C2×D8—591no—
217C2×M16—591no—
218C22×C8—591no—
219C4⋊Q8C2×D5911yescharacteristic, complemented
220#124—591no—
221#123—21no—
222#123—21no—
223#123—1181no—
224C22⋊Q8—21no—
225C22⋊Q8—591no—
226#121—591no—
227#121—1181no—
228#121C2×D5911yescharacteristic
229#121C2×D5911yescharacteristic, complemented
230#120—1181no—
231C4×D4—591no—
232C4×D4C2×D5911yescharacteristic
233C4×D4C2×D5911yescharacteristic, complemented
234C2×C4⋊C4C2×D5911yescharacteristic
235C2×C4⋊C4C2×D5911yescharacteristic, complemented
236C2×C22⋊C4—1181no—
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—1181no—
255#41—44no—
256#41—1182no—
257#41—2361no—
258C2×Q8—21no—
259C2×Q8—591no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—591no—
263C2×D4—591no—
264C2×D4—1182no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—2361no—
269C2×D4C22⋊D5911yescharacteristic
270C2×D4C22×D5911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
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—21no—
289C4⋊C4—21no—
290C4⋊C4—591no—
291C4⋊C4—1181no—
292C4⋊C4C22⋊D5911yescharacteristic
293C4⋊C4C22×D5911yescharacteristic
294C4⋊C4C22×D5911yescharacteristic
295C4⋊C4C22×D5911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4C22⋊D5911yescharacteristic
305C22⋊C4C22⋊D5911yescharacteristic
306C42C22×D5911yescharacteristic
307C23—21no—
308C23—1181no—
309C23—1181no—
310C23—4721no—
311C23—2362no—
312C23—2362no—
313C23C2×C22⋊D5911yescharacteristic
314C23C2×C22⋊D5911yescharacteristic
315Q8—42no—
316Q8—1181no—
317Q8—1181no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—592no—
324D4—1181no—
325D4—1181no—
326D4—1181no—
327D4—4721no—
328D4—2362no—
329D4—2362no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—4721no—
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—41no—
359C22—41no—
360C22—41no—
361C22—1182no—
362C22—4724no—
363C22—2361no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22#1427375312yes—
369C22C22×C22⋊D5911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—2361no—
378C4—2361no—
379C4#41×D5911yescharacteristic
380C4#1427377311yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—4721no—
385C2—2362no—
386C2#1683804011yescharacteristic
387C2C2×#1427375311yescharacteristic
388C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#547C2
socleC22×C59C22×D4
hypercenter#547D59
hypocenterC59#3306
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #16838048C2semidirect
2. #16837764C2semidirect
3. #16837732C2semidirect
4. #16837720C2semidirect
5. #16837689C2semidirect
6. #16837653C2semidirect
7. #16837629C2semidirect
8. #16837617C2semidirect
9. #16837545C2semidirect
10. #16837535C2semidirect
11. #16837512C2semidirect
12. #16837474C2semidirect
13. #16837401C2semidirect
14. C2×#14273647C2semidirect
15. C59×#547C2semidirect
18. C2×#11745670C22semidirect
21. C2×#11745664C22semidirect
31. #14273658C22semidirect
32. #14273658C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273650C22semidirect
36. #14273650C22semidirect
37. #14273650C22semidirect
38. #14273648C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. #14273638C22semidirect
49. C4⋊Q8×C59C22semidirect
54. #121×C59C22semidirect
56. C4×D4×C59C22semidirect
58. C2×C4⋊C4×C59C22semidirect
149. D236#41semidirect
195. #547D59semidirect
210. C59#3306semidirect
219. C4⋊Q8C2×D59semidirect
229. #121C2×D59semidirect
233. C4×D4C2×D59semidirect
235. C2×C4⋊C4C2×D59semidirect