Finite Group Databasebeta

← #21435639

Subgroups — #21435639

Order 7552.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273752C211yesmaximal, characteristic, complemented
2C2×#14273750C211yesmaximal, characteristic, complemented
3#16838071C211yesmaximal, characteristic, complemented
4#16838043C211yesmaximal, characteristic, complemented
5#16837788C211yesmaximal, characteristic, complemented
6#16837650C211yesmaximal, characteristic, complemented
7#16837637C211yesmaximal, characteristic, complemented
8#16837626C211yesmaximal, characteristic, complemented
9#16837596C211yesmaximal, characteristic, complemented
10#16837550C211yesmaximal, characteristic, complemented
11#16837546C211yesmaximal, characteristic, complemented
12#16837538C211yesmaximal, characteristic, complemented
13#16837505C211yesmaximal, characteristic, complemented
14#16837476C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745689C2211yescharacteristic, complemented
18C22×D236C2211yescharacteristic
19#14273752—24no—
20#14273750—24no—
21C2×#11745671C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic, complemented
24C2×D472C2211yescharacteristic
25C2×D472C2211yescharacteristic
26C2×#11745669C2211yescharacteristic
27C2×#11745669C2211yescharacteristic
28C2×#11745664C2211yescharacteristic
29C2×C8×D59C2211yescharacteristic, complemented
30#14273723—21no—
31#14273723C2211yescharacteristic, complemented
32#14273716C2211yescharacteristic
33#14273712—21no—
34#14273702—21no—
35#14273702C2211yescharacteristic
36#14273701—21no—
37#14273701C2211yescharacteristic
38#14273698—21no—
39#14273698C2211yescharacteristic, complemented
40#14273697—21no—
41Q8×Dic59C2211yescharacteristic, complemented
42#14273689C2211yescharacteristic
43C4×C22⋊D59—21no—
44C4×C22⋊D59C2211yescharacteristic
45C22⋊C4×D59—21no—
46#14273660C2211yescharacteristic, complemented
47Dic59⋊C8C2211yescharacteristic, complemented
48#14273651C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273647C2211yescharacteristic, complemented
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53#14273637C2211yescharacteristic, complemented
54C2×#41×C59C2211yescharacteristic
55C2×Q16×C59C2211yescharacteristic, complemented
56C2×SD16×C59C2211yescharacteristic, complemented
57C22⋊Q8×C59C2211yescharacteristic
58#103×C59C2211yescharacteristic, complemented
59#102×C59C2211yescharacteristic, complemented
60C22⋊C8×C59C2211yescharacteristic
61C23×D59—21no—
62#41×C59—22no—
63#41×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—21no—
67C2×D4×C59C2311yescharacteristic
68C22×C4×C59—21no—
69C22×C4×C59C2311yescharacteristic
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C2×C22⋊D59D411yescharacteristic
75#11745689—22no—
76#11745689—22no—
77#11745689—41no—
78#11745689—41no—
79C2×D236—22no—
80C2×D236—21no—
81C2×D236—21no—
82C2×D236—21no—
83C2×D236—21no—
84C2×D236—41no—
85C2×D236C2311yescharacteristic
86C2×D236C2311yescharacteristic
87C2×D236C2311yescharacteristic
88C2×C4×D59—21no—
89C2×C4×D59—21no—
90C2×C4×D59—21no—
91C2×C4×D59C2311yescharacteristic
92Q16×C59—22no—
93SD16×C59—41no—
94C2×C8×C59C2311yescharacteristic
95C2×C8×C59C2311yescharacteristic
96C4⋊C4×C59—21no—
97C4⋊C4×C59C2311yescharacteristic
98C22⋊C4×C59—21no—
99C22⋊Dic59—21no—
100C22⋊Dic59D411yescharacteristic
101#11745671—22no—
102#11745671—22no—
103#11745671D414yescomplemented
104#11745669—22no—
105#11745669—22no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110(C2×D59)⋊C4—21no—
111(C2×D59)⋊C4D411yescharacteristic
112C4⋊Dic59—21no—
113C4⋊Dic59C2311yescharacteristic
114Dic59⋊C4D411yescharacteristic
115C4×Dic59—21no—
116C4×Dic59C2311yescharacteristic
117#11745664—22no—
118C2×C59⋊C8C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120D472—22no—
121D472—41no—
122C8×D59—22no—
123C23×C59—21no—
124C23×C59C2×D411yescharacteristic
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—42no—
129C22×D59—42no—
130C22×D59—81no—
131C22×D59C2×D411yescharacteristic
132Q8×C59—21no—
133Q8×C59—21no—
134Q8×C59—21no—
135Q8×C59C2×D412yes—
136D4×C59—21no—
137D4×C59—21no—
138D4×C59—42no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—42no—
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2411yescharacteristic
147C22⋊D59—41no—
148C22⋊D59—42no—
149C22⋊D59—81no—
150C22⋊D59—81no—
151C22⋊D59—81no—
152C2×Dic59—21no—
153C2×Dic59C2×D411yescharacteristic
154C2×Dic59C2×D411yescharacteristic
155C2×Dic59C2×D411yescharacteristic
156D236—21no—
157D236—21no—
158D236—21no—
159D236—21no—
160D236—21no—
161D236—42no—
162D236—42no—
163D236—42no—
164D236—81no—
165D236C2×D412yes—
166C4×D59—21no—
167C4×D59—21no—
168C4×D59—42no—
169C4×D59—42no—
170C4×D59—81no—
171C8×C59—21no—
172C8×C59—21no—
173C59⋊C8—21no—
174C59⋊C8C2×D412yes—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59C22×D411yescharacteristic
182C2×D59—21no—
183C2×D59—22no—
184C2×D59—21no—
185C2×D59—21no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—41no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—84no—
195C4×C59—22no—
196C4×C59—21no—
197C4×C59—41no—
198C4×C59—41no—
199C4×C59C22×D411yescharacteristic
200C4×C59H(5,𝔽2)11yescharacteristic
201Dic59—21no—
202Dic59—21no—
203Dic59—21no—
204Dic59—41no—
205#3268—591nomaximal, Sylow
206C2×C59—41no—
207C2×C59—81no—
208C2×C59D4211yescharacteristic
209C2×C59#57511yescharacteristic
210C2×C59#57611yescharacteristic
211D59—41no—
212D59—42no—
213D59—81no—
214D59—81no—
215C2×AGL(1,ℤ/8)—591no—
216C2×#135—591no—
217#550—591no—
218#546—591no—
219#496—591no—
220#468—591no—
221#466—591no—
222#464—591no—
223#459—591no—
224#452D5911yescharacteristic, complemented
225#449—591no—
226#449—591no—
227#447—591no—
228#440—591no—
229#435—591no—
230C59#326811yescharacteristic, complemented, Sylow
231C2×#41—591no—
232C2×#41—591no—
233C2×#41C2×D5911yescharacteristic
234C22×D4—591no—
235AGL(1,ℤ/8)—1184no—
236#135—1184no—
237C2×Q16C2×D5911yescharacteristic, complemented
238C2×SD16—591no—
239C2×SD16—591no—
240C2×SD16—591no—
241C2×SD16C2×D5911yescharacteristic, complemented
242C2×D8—591no—
243C2×D8—591no—
244C2×D8—591no—
245C2×D8—591no—
246C2×M16—591no—
247C22×C8—591no—
248#127—591no—
249#127—1181no—
250#124—591no—
251#123—1181no—
252C22⋊Q8C2×D5911yescharacteristic
253#121—591no—
254#121—591no—
255#121—591no—
256#121—1181no—
257#121—1181no—
258#121—1181no—
259#120—1181no—
260C4×Q8—591no—
261C4×D4—591no—
262C4×D4—591no—
263C4×D4—1181no—
264C2×C22⋊C4—1181no—
265#107—591no—
266C4⋊C8—591no—
267#103—591no—
268#103C2×D5911yescharacteristic, complemented
269#102—591no—
270#102—591no—
271#102—591no—
272#102C2×D5911yescharacteristic, complemented
273C22⋊C8—591no—
274C22⋊C8C2×D5911yescharacteristic
275#97—591no—
276C24—1181no—
277#41—22no—
278#41—41no—
279#41—1182no—
280#41—1182no—
281#41—2361no—
282#41—2361no—
283C2×Q8C22×D5911yescharacteristic
284C2×Q8C22×D5911yescharacteristic
285C2×D4—21no—
286C2×D4—591no—
287C2×D4—591no—
288C2×D4—591no—
289C2×D4—591no—
290C2×D4—1182no—
291C2×D4—1181no—
292C2×D4—1181no—
293C2×D4—1181no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—1181no—
297C2×D4—1181no—
298C2×D4—1181no—
299C2×D4—2361no—
300C2×D4C22×D5911yescharacteristic
301C22×C4—21no—
302C22×C4—591no—
303C22×C4—1181no—
304C22×C4—1181no—
305C22×C4—1181no—
306C22×C4C22×D5911yescharacteristic
307Q16—22no—
308SD16—41no—
309SD16—594no—
310SD16—1182no—
311SD16—1182no—
312D8—1182no—
313D8—1182no—
314D8—1182no—
315D8—2361no—
316M16—1182no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8—1182no—
320C2×C8C22×D5911yescharacteristic
321C2×C8C22×D5911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—591no—
324C4⋊C4—591no—
325C4⋊C4—1181no—
326C4⋊C4C22×D5911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—591no—
329C22⋊C4—591no—
330C22⋊C4—1181no—
331C22⋊C4—1181no—
332C22⋊C4—1181no—
333C22⋊C4—1181no—
334C22⋊C4—1181no—
335C22⋊C4—1181no—
336C42—591no—
337C42—1181no—
338C23—21no—
339C23—591no—
340C23—1181no—
341C23—1181no—
342C23—1181no—
343C23—4721no—
344C23—2362no—
345C23—2362no—
346C23D4×D5911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8D4×D5912yes—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—592no—
355D4—1181no—
356D4—1181no—
357D4—1181no—
358D4—1181no—
359D4—1181no—
360D4—4721no—
361D4—4721no—
362D4—4721no—
363D4—4721no—
364D4—2362no—
365D4—2362no—
366D4—2362no—
367D4—2361no—
368D4—2362no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—591no—
376C2×C4—591no—
377C2×C4—591no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—4721no—
382C2×C4—2362no—
383C2×C4—2362no—
384C2×C4D4×D5911yescharacteristic
385C2×C4C23×D5911yescharacteristic
386C8—21no—
387C8—21no—
388C8—592no—
389C8—1181no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—1181no—
397C22—1181no—
398C22—1181no—
399C22—1182no—
400C22—4724no—
401C22—2361no—
402C22—2361no—
403C22—2361no—
404C22—2361no—
405C22—2361no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22C2×D4×D5911yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—1181no—
415C4—1181no—
416C4—1181no—
417C4—2361no—
418C4C2×D4×D5911yescharacteristic
419C4#1427377211yescharacteristic
420C2—41no—
421C2—81no—
422C2—4721no—
423C2—4721no—
424C2—2361no—
425C2—2362no—
426C2#1683803411yescharacteristic
427C2#1683820111yescharacteristic
428C2#1683820411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3268
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#14273752C2semidirect
2. C2×#14273750C2semidirect
3. #16838071C2semidirect
4. #16838043C2semidirect
5. #16837788C2semidirect
6. #16837650C2semidirect
7. #16837637C2semidirect
8. #16837626C2semidirect
9. #16837596C2semidirect
10. #16837550C2semidirect
11. #16837546C2semidirect
12. #16837538C2semidirect
13. #16837505C2semidirect
14. #16837476C2semidirect
15. C59×#452C2semidirect
17. C2×#11745689C22semidirect
23. C2×#11745671C22semidirect
29. C2×C8×D59C22semidirect
31. #14273723C22semidirect
39. #14273698C22semidirect
41. Q8×Dic59C22semidirect
46. #14273660C22semidirect
47. Dic59⋊C8C22semidirect
48. #14273651C22semidirect
51. #14273647C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. #14273637C22semidirect
55. C2×Q16×C59C22semidirect
56. C2×SD16×C59C22semidirect
58. #103×C59C22semidirect
59. #102×C59C22semidirect
103. #11745671D4semidirect
224. #452D59semidirect
230. C59#3268semidirect
237. C2×Q16C2×D59semidirect
241. C2×SD16C2×D59semidirect
268. #103C2×D59semidirect
272. #102C2×D59semidirect