Finite Group Databasebeta

← #21435592

Subgroups — #21435592

Order 7552.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273752C211yesmaximal, characteristic, complemented
2C22×#11745671C211yesmaximal, characteristic, complemented
3D4×D236C211yesmaximal, characteristic, complemented
4#16837792C211yesmaximal, characteristic, complemented
5#16837650C211yesmaximal, characteristic, complemented
6#16837636C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837602C211yesmaximal, characteristic, complemented
9#16837552C211yesmaximal, characteristic, complemented
10#16837547C211yesmaximal, characteristic, complemented
11#16837541C211yesmaximal, characteristic, complemented
12#16837535C211yesmaximal, characteristic, complemented
13#16837500C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15C59×#548C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×D4×D59—21no—
19#14273752—24no—
20C2×#11745671—24no—
21C2×#11745671C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic, complemented
24C2×#11745671C2211yescharacteristic, complemented
25C2×#11745671C2211yescharacteristic, complemented
26C2×#11745671C2211yescharacteristic, complemented
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic, complemented
29C2×#11745669C2211yescharacteristic, complemented
30C2×#11745664C2211yescharacteristic, complemented
31C22×C59⋊C8C2211yescharacteristic, complemented
32#14273724C2211yescharacteristic
33#14273702—21no—
34#14273701C2211yescharacteristic
35#14273701C2211yescharacteristic
36#14273697—21no—
37#14273697—21no—
38C4×D236C2211yescharacteristic
39#14273660C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic, complemented
44#14273647C2211yescharacteristic
45#14273647C2211yescharacteristic, complemented
46#14273647C2211yescharacteristic, complemented
47C22⋊(C59⋊C8)C2211yescharacteristic, complemented
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49#14273638C2211yescharacteristic, complemented
50C2×#41×C59C2211yescharacteristic, complemented
51C22×Q8×C59C2211yescharacteristic, complemented
52#124×C59—21no—
53#124×C59C2211yescharacteristic, complemented
54C22⋊Q8×C59—21no—
55C22⋊Q8×C59C2211yescharacteristic, complemented
56#121×C59—21no—
57#121×C59C2211yescharacteristic, complemented
58C4×Q8×C59C2211yescharacteristic, complemented
59C4×D4×C59—21no—
60C4×D4×C59C2211yescharacteristic
61C23×D59—21no—
62C23×D59—21no—
63#41×C59—22no—
64#41×C59—41no—
65C2×Q8×C59—21no—
66C2×Q8×C59—22no—
67C2×Q8×C59—41no—
68C2×Q8×C59C2311yescharacteristic
69C2×Q8×C59C2311yescharacteristic
70C2×D4×C59—21no—
71C2×D4×C59—21no—
72C2×D4×C59D411yescharacteristic
73C2×D4×C59C2311yescharacteristic
74C22×C4×C59—21no—
75C22×C4×C59—21no—
76C22×C4×C59C2311yescharacteristic
77C22×C4×C59C2311yescharacteristic
78C2×C22⋊D59—21no—
79C2×C22⋊D59—21no—
80D4×D59—44no—
81C2×D236—22no—
82C2×D236—22no—
83C2×D236—21no—
84C2×D236—21no—
85C2×D236—21no—
86C2×D236—21no—
87C2×D236—41no—
88C2×D236—41no—
89C2×D236C2311yescharacteristic
90C2×D236C2311yescharacteristic
91C2×D236C2311yescharacteristic
92C2×C4×D59—21no—
93C4⋊C4×C59—21no—
94C4⋊C4×C59—21no—
95C4⋊C4×C59D411yescharacteristic
96C4⋊C4×C59C2311yescharacteristic
97C22⋊C4×C59—21no—
98C22⋊C4×C59—21no—
99C22⋊C4×C59—21no—
100C22⋊C4×C59—21no—
101C22⋊C4×C59D411yescharacteristic
102C22⋊C4×C59D411yescharacteristic
103C42×C59—21no—
104C42×C59C2311yescharacteristic
105#11745671—22no—
106#11745671—22no—
107#11745671—22no—
108#11745671—22no—
109#11745671—41no—
110#11745671D414yescomplemented
111#11745669—22no—
112#11745669—22no—
113#11745669—41no—
114(C2×D59)⋊C4—21no—
115(C2×D59)⋊C4—21no—
116(C2×D59)⋊C4—21no—
117C4⋊Dic59C2311yescharacteristic
118#11745664—22no—
119C2×C59⋊C8—22no—
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C2×C59⋊C8C2311yescharacteristic
124C23×C59—21no—
125C23×C59C2×D411yescharacteristic
126C23×C59C2×D411yescharacteristic
127C22×D59—21no—
128C22×D59—21no—
129C22×D59—21no—
130C22×D59—42no—
131C22×D59—42no—
132C22×D59—42no—
133C22×D59—42no—
134C22×D59—81no—
135C22×D59—81no—
136Q8×C59—21no—
137Q8×C59—21no—
138Q8×C59—21no—
139Q8×C59—42no—
140Q8×C59C2×D412yescomplemented
141D4×C59—22no—
142D4×C59—21no—
143D4×C59—21no—
144D4×C59—42no—
145D4×C59—42no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—42no—
154C2×C4×C59—42no—
155C2×C4×C59C2×D411yescharacteristic
156C2×C4×C59C2×D411yescharacteristic
157C2×C4×C59C2×D411yescharacteristic
158C2×C4×C59C2×D411yescharacteristic
159C2×C4×C59C2411yescharacteristic
160C22⋊D59—42no—
161C22⋊D59—42no—
162C2×Dic59—21no—
163D236—21no—
164D236—21no—
165D236—21no—
166D236—21no—
167D236—21no—
168D236—42no—
169D236—42no—
170D236—42no—
171D236—81no—
172D236C2×D412yes—
173C4×D59—42no—
174C59⋊C8—21no—
175C59⋊C8—21no—
176C59⋊C8—21no—
177C59⋊C8C2×D412yescomplemented
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59AGL(1,ℤ/8)12yescomplemented
187C22×C59C22×D411yescharacteristic
188C2×D59—22no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—41no—
195C2×D59—41no—
196C2×D59—41no—
197C2×D59—84no—
198C2×D59—84no—
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—22no—
202C4×C59—21no—
203C4×C59—21no—
204C4×C59—41no—
205C4×C59—41no—
206C4×C59C22×D411yescharacteristic
207C4×C59H(5,𝔽2)11yescharacteristic
208Dic59—41no—
209#3265—591nomaximal, Sylow
210C2×C59—22no—
211C2×C59—41no—
212C2×C59—81no—
213C2×C59D4211yescharacteristic
214C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C59#57711yescharacteristic
216D59—42no—
217D59—81no—
218D59—81no—
219C2×AGL(1,ℤ/8)—591no—
220C22×SD16—591no—
221#548D5911yescharacteristic, complemented
222D42—591no—
223#496—591no—
224#468—591no—
225#466—591no—
226#463—591no—
227#460—591no—
228#450—591no—
229#449—591no—
230#448—591no—
231#447—591no—
232#440—591no—
233#435—591no—
234C59#326511yescharacteristic, complemented, Sylow
235C2×#41C2×D5911yescharacteristic, complemented
236C22×Q8C2×D5911yescharacteristic, complemented
237C22×D4—591no—
238C22×D4—591no—
239C22×D4—1181no—
240AGL(1,ℤ/8)—1184no—
241C2×SD16—591no—
242C2×SD16—591no—
243C2×SD16—591no—
244C2×SD16—591no—
245C2×SD16—591no—
246C2×SD16—591no—
247C2×SD16—1184no—
248C2×D8—591no—
249C2×D8—591no—
250C2×D8—591no—
251C2×M16—591no—
252C22×C8—591no—
253#127—591no—
254#124—21no—
255#124C2×D5911yescharacteristic, complemented
256C22⋊Q8—21no—
257C22⋊Q8C2×D5911yescharacteristic, complemented
258#121—21no—
259#121—591no—
260#121—591no—
261#121—1181no—
262#121C2×D5911yescharacteristic, complemented
263#120—1181no—
264#120—1181no—
265C4×Q8C2×D5911yescharacteristic, complemented
266C4×D4—21no—
267C4×D4—591no—
268C4×D4C2×D5911yescharacteristic
269#107—591no—
270C4⋊C8—591no—
271#103—591no—
272#103—591no—
273#102—591no—
274#102—591no—
275#102—591no—
276#102—591no—
277C22⋊C8—591no—
278C22⋊C8—591no—
279#97—591no—
280C24—1181no—
281C24—1181no—
282#41—22no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D5911yescharacteristic
288C2×Q8C22×D5911yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—591no—
292C2×D4—591no—
293C2×D4—591no—
294C2×D4—1182no—
295C2×D4—1182no—
296C2×D4—1181no—
297C2×D4—1181no—
298C2×D4—1181no—
299C2×D4—1181no—
300C2×D4—1181no—
301C2×D4—1181no—
302C2×D4—2361no—
303C2×D4—2361no—
304C2×D4—2364no—
305C2×D4C22⋊D5911yescharacteristic
306C2×D4C22×D5911yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—1181no—
310C22×C4C22×D5911yescharacteristic
311C22×C4C22×D5911yescharacteristic
312SD16—594no—
313SD16—1182no—
314SD16—1182no—
315SD16—1182no—
316SD16—1182no—
317SD16—2361no—
318D8—1182no—
319D8—1182no—
320D8—2361no—
321M16—1182no—
322C2×C8—591no—
323C2×C8—591no—
324C2×C8—591no—
325C2×C8—591no—
326C2×C8—1182no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—591no—
330C4⋊C4C22⋊D5911yescharacteristic
331C4⋊C4C22×D5911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—1181no—
337C22⋊C4—1181no—
338C22⋊C4—1181no—
339C22⋊C4C22⋊D5911yescharacteristic
340C22⋊C4C22⋊D5911yescharacteristic
341C42—21no—
342C42C22×D5911yescharacteristic
343C23—21no—
344C23—1181no—
345C23—1181no—
346C23—1181no—
347C23—4721no—
348C23—4721no—
349C23—2362no—
350C23—2362no—
351C23—2362no—
352C23—2362no—
353C23C2×C22⋊D5911yescharacteristic
354C23C2×C22⋊D5911yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D5912yescomplemented
360D4—22no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—592no—
366D4—1181no—
367D4—1181no—
368D4—1181no—
369D4—1181no—
370D4—1181no—
371D4—4721no—
372D4—2362no—
373D4—2362no—
374D4—2362no—
375D4—2362no—
376D4—2362no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—1181no—
387C2×C4—2362no—
388C2×C4C2×C22⋊D5911yescharacteristic
389C2×C4C2×C22⋊D5911yescharacteristic
390C2×C4C2×C22⋊D5911yescharacteristic
391C2×C4C2×C22⋊D5911yescharacteristic
392C2×C4C23×D5911yescharacteristic
393C8—592no—
394C8—1181no—
395C8—1181no—
396C8—1181no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—1182no—
406C22—4724no—
407C22—4724no—
408C22—2361no—
409C22—2361no—
410C22—2361no—
411C22—2361no—
412C22—2361no—
413C22—2361no—
414C22—2361no—
415C22—2361no—
416C22#1427375212yescomplemented
417C22C22×C22⋊D5911yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—22no—
423C4—41no—
424C4—41no—
425C4—2361no—
426C4C2×D4×D5911yescharacteristic
427C4#1427377211yescharacteristic
428C2—22no—
429C2—41no—
430C2—81no—
431C2—4721no—
432C2—4721no—
433C2—2362no—
434C2D4×C22⋊D5911yescharacteristic
435C2C2×#1427375211yescharacteristic
436C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3265
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14273752C2semidirect
2. C22×#11745671C2semidirect
3. D4×D236C2semidirect
4. #16837792C2semidirect
5. #16837650C2semidirect
6. #16837636C2semidirect
7. #16837614C2semidirect
8. #16837602C2semidirect
9. #16837552C2semidirect
10. #16837547C2semidirect
11. #16837541C2semidirect
12. #16837535C2semidirect
13. #16837500C2semidirect
14. #16837474C2semidirect
15. C59×#548C2semidirect
23. C2×#11745671C22semidirect
24. C2×#11745671C22semidirect
25. C2×#11745671C22semidirect
26. C2×#11745671C22semidirect
28. C2×#11745669C22semidirect
29. C2×#11745669C22semidirect
30. C2×#11745664C22semidirect
31. C22×C59⋊C8C22semidirect
39. #14273660C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273651C22semidirect
42. #14273651C22semidirect
43. #14273648C22semidirect
45. #14273647C22semidirect
46. #14273647C22semidirect
47. C22⋊(C59⋊C8)C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. #14273638C22semidirect
50. C2×#41×C59C22semidirect
51. C22×Q8×C59C22semidirect
53. #124×C59C22semidirect
55. C22⋊Q8×C59C22semidirect
57. #121×C59C22semidirect
58. C4×Q8×C59C22semidirect
110. #11745671D4semidirect
140. Q8×C59C2×D4semidirect
177. C59⋊C8C2×D4semidirect
186. C22×C59AGL(1,ℤ/8)semidirect
221. #548D59semidirect
234. C59#3265semidirect
235. C2×#41C2×D59semidirect
236. C22×Q8C2×D59semidirect
255. #124C2×D59semidirect
257. C22⋊Q8C2×D59semidirect
262. #121C2×D59semidirect
265. C4×Q8C2×D59semidirect
359. Q8D4×D59semidirect
416. C22#14273752semidirect