Finite Group Databasebeta

← #21435184

Subgroups — #21435184

Order 7552.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837971C211yesmaximal, characteristic, complemented
2#16837792C211yesmaximal, characteristic, complemented
3#16837784C211yesmaximal, characteristic, complemented
4#16837764C211yesmaximal, characteristic, complemented
5#16837750C211yesmaximal, characteristic, complemented
6#16837624C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837602C211yesmaximal, characteristic, complemented
9#16837597C211yesmaximal, characteristic, complemented
10#16837562C211yesmaximal, characteristic, complemented
11#16837552C211yesmaximal, characteristic, complemented
12#16837545C211yesmaximal, characteristic, complemented
13#16837535C211yesmaximal, characteristic, complemented
14#16837463C211yesmaximal, characteristic, complemented
15C59×#542C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745670C2211yescharacteristic, complemented
20C2×#11745671C2211yescharacteristic
21C2×#11745671C2211yescharacteristic
22C2×#11745671C2211yescharacteristic, complemented
23C2×#11745669C2211yescharacteristic
24C2×#11745669C2211yescharacteristic
25C2×#11745669C2211yescharacteristic, complemented
26#14273724C2211yescharacteristic
27#14273724C2211yescharacteristic
28#14273715C2211yescharacteristic
29#14273715C2211yescharacteristic
30#14273702—21no—
31#14273702—21no—
32#14273697—21no—
33#14273697—21no—
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35C4⋊(C59⋊C8)C2211yescharacteristic, complemented
36#14273650C2211yescharacteristic, complemented
37#14273650C2211yescharacteristic, complemented
38#14273647C2211yescharacteristic
39#14273647C2211yescharacteristic
40#14273647C2211yescharacteristic
41#14273647C2211yescharacteristic
42#14273647C2211yescharacteristic, complemented
43#14273647C2211yescharacteristic, complemented
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46#14273638C2211yescharacteristic, complemented
47C4×C59⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C59C2211yescharacteristic, complemented
49#126×C59—21no—
50#124×C59—21no—
51#124×C59C2211yescharacteristic, complemented
52#123×C59—21no—
53C22⋊Q8×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic, complemented
58#117×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59—21no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67#11745685—41no—
68#11745685—41no—
69C2×D236—21no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236—41no—
75C2×D236—41no—
76C2×D236C2311yescharacteristic
77C2×D236C2311yescharacteristic
78C2×D236C2311yescharacteristic
79C2×C4×D59—21no—
80C2×Dic118C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59D411yescharacteristic
85C4⋊C4×C59D411yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C22⋊C4×C59—21no—
93C22⋊C4×C59D411yescharacteristic
94C22⋊C4×C59D411yescharacteristic
95C42×C59—21no—
96C42×C59C2311yescharacteristic
97C42×C59C2311yescharacteristic
98#11745672—41no—
99#11745671—41no—
100#11745671—41no—
101#11745671—41no—
102#11745670—41no—
103#11745669—41no—
104#11745669—41no—
105#11745669—41no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122Q8×C59—21no—
123Q8×C59—21no—
124Q8×C59—81no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—81no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—81no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—42no—
141C2×Dic59—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—21no—
146D236—21no—
147D236—21no—
148D236—42no—
149D236—81no—
150D236—81no—
151D236—81no—
152D236—81no—
153C4×D59—42no—
154Dic118—21no—
155Dic118—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59C22×D411yescharacteristic
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—84no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—41no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59H(5,𝔽2)11yescharacteristic
186C4×C59H(5,𝔽2)11yescharacteristic
187Dic59—41no—
188#3224—591nomaximal, Sylow
189C2×C59—41no—
190C2×C59—81no—
191C2×C59#53511yescharacteristic
192C2×C59#57611yescharacteristic
193C2×C59#57711yescharacteristic
194D59—81no—
195D59—81no—
196D59—81no—
197#542D5911yescharacteristic, complemented
198#535—591no—
199#496—591no—
200#495—591no—
201#489—591no—
202#486—591no—
203#464—591no—
204#463—591no—
205#460—591no—
206#459—591no—
207#452—591no—
208#450—591no—
209#449—591no—
210#447—591no—
211#433—591no—
212C59#322411yescharacteristic, complemented, Sylow
213C2×#41—591no—
214C22×D4—591no—
215C2×Q16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×SD16—591no—
219C2×SD16—591no—
220C2×D8—591no—
221C2×D8—591no—
222C2×D8—591no—
223C4⋊Q8C2×D5911yescharacteristic, complemented
224#127—591no—
225#127—591no—
226#126—21no—
227#124—21no—
228#124—591no—
229#124—591no—
230#124C2×D5911yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D5911yescharacteristic
234#121—1181no—
235#121—1181no—
236#121C2×D5911yescharacteristic
237#120—1181no—
238#120—1181no—
239C4×Q8C2×D5911yescharacteristic, complemented
240C4×D4C2×D5911yescharacteristic, complemented
241#117C2×D5911yescharacteristic
242C4⋊C8—591no—
243C4⋊C8—591no—
244#103—591no—
245#103—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252C22⋊C8—591no—
253C22⋊C8—591no—
254#97—591no—
255C4×C8—591no—
256C24—1181no—
257#41—2361no—
258#41—2361no—
259C2×Q8—21no—
260C2×Q8—591no—
261C2×Q8C22×D5911yescharacteristic
262C2×D4—21no—
263C2×D4—591no—
264C2×D4—591no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—2361no—
273C2×D4—2361no—
274C2×D4C22×D5911yescharacteristic
275C22×C4—21no—
276C22×C4—1181no—
277C22×C4C22×D5911yescharacteristic
278Q16—2361no—
279SD16—2361no—
280SD16—2361no—
281SD16—2361no—
282SD16—2361no—
283D8—2361no—
284D8—2361no—
285D8—2361no—
286C2×C8—591no—
287C2×C8—591no—
288C2×C8—591no—
289C2×C8—591no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D5911yescharacteristic
294C4⋊C4C22⋊D5911yescharacteristic
295C4⋊C4C22×D5911yescharacteristic
296C4⋊C4C22×D5911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4C22⋊D5911yescharacteristic
307C22⋊C4C22⋊D5911yescharacteristic
308C42—21no—
309C42C22×D5911yescharacteristic
310C42C22×D5911yescharacteristic
311C23—21no—
312C23—1181no—
313C23—1181no—
314C23—1181no—
315C23—4721no—
316C23—4721no—
317C23—2362no—
318C23C2×C22⋊D5911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—1181no—
323Q8—1181no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—1181no—
328D4—1181no—
329D4—1181no—
330D4—1181no—
331D4—1181no—
332D4—1181no—
333D4—4721no—
334D4—4721no—
335D4—4721no—
336D4—4721no—
337D4—2362no—
338D4—2362no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—1181no—
346C2×C4—2362no—
347C2×C4C2×C22⋊D5911yescharacteristic
348C2×C4C2×C22⋊D5911yescharacteristic
349C2×C4C2×C22⋊D5911yescharacteristic
350C2×C4C2×C22⋊D5911yescharacteristic
351C2×C4C2×C22⋊D5911yescharacteristic
352C2×C4C23×D5911yescharacteristic
353C8—1181no—
354C8—1181no—
355C8—1181no—
356C8—1181no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—4724no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22C22×C22⋊D5911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2361no—
383C4#1427377311yescharacteristic
384C4#1427377311yescharacteristic
385C2—41no—
386C2—81no—
387C2—4721no—
388C2—4721no—
389C2—4721no—
390C2#1683796611yescharacteristic
391C2#1683820511yescharacteristic
392C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#542C2
socleC22×C59C22×D4
hypercenter#542D59
hypocenterC59#3224
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #16837971C2semidirect
2. #16837792C2semidirect
3. #16837784C2semidirect
4. #16837764C2semidirect
5. #16837750C2semidirect
6. #16837624C2semidirect
7. #16837617C2semidirect
8. #16837602C2semidirect
9. #16837597C2semidirect
10. #16837562C2semidirect
11. #16837552C2semidirect
12. #16837545C2semidirect
13. #16837535C2semidirect
14. #16837463C2semidirect
15. C59×#542C2semidirect
18. C2×#11745672C22semidirect
19. C2×#11745670C22semidirect
22. C2×#11745671C22semidirect
25. C2×#11745669C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. C4⋊(C59⋊C8)C22semidirect
36. #14273650C22semidirect
37. #14273650C22semidirect
42. #14273647C22semidirect
43. #14273647C22semidirect
46. #14273638C22semidirect
47. C4×C59⋊C8C22semidirect
48. C4⋊Q8×C59C22semidirect
51. #124×C59C22semidirect
56. C4×Q8×C59C22semidirect
57. C4×D4×C59C22semidirect
197. #542D59semidirect
212. C59#3224semidirect
223. C4⋊Q8C2×D59semidirect
230. #124C2×D59semidirect
239. C4×Q8C2×D59semidirect
240. C4×D4C2×D59semidirect