Finite Group Databasebeta

← #21435643

Subgroups — #21435643

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×#14273755C211yesmaximal, characteristic, complemented
2C2×#14273748C211yesmaximal, characteristic, complemented
3#16838070C211yesmaximal, characteristic, complemented
4#16838043C211yesmaximal, characteristic, complemented
5#16837788C211yesmaximal, characteristic, complemented
6#16837639C211yesmaximal, characteristic, complemented
7#16837627C211yesmaximal, characteristic, complemented
8#16837596C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837550C211yesmaximal, characteristic, complemented
11#16837548C211yesmaximal, characteristic, complemented
12#16837535C211yesmaximal, characteristic, complemented
13#16837501C211yesmaximal, characteristic, complemented
14#16837471C211yesmaximal, characteristic, complemented
15C59×#468C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18C2×#11745687C2211yescharacteristic, complemented
19C22×D236C2211yescharacteristic
20#14273755—24no—
21#14273748—24no—
22C2×#11745672C2211yescharacteristic, complemented
23C2×#11745660C2211yescharacteristic
24C2×#11745660C2211yescharacteristic
25C2×#11745671C2211yescharacteristic, complemented
26C2×D472C2211yescharacteristic
27C2×D472C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745669C2211yescharacteristic
30C2×C8×D59C2211yescharacteristic, complemented
31#14273723—21no—
32#14273723C2211yescharacteristic, complemented
33#14273716C2211yescharacteristic
34#14273712—21no—
35#14273702—21no—
36#14273702C2211yescharacteristic
37#14273702C2211yescharacteristic, complemented
38#14273700—21no—
39#14273699—21no—
40#14273697—21no—
41#14273692C2211yescharacteristic, complemented
42#14273689C2211yescharacteristic
43C4×C22⋊D59C2211yescharacteristic
44(C22⋊D59)⋊C4—21no—
45C22⋊C4×D59—21no—
46Dic59⋊C8C2211yescharacteristic, complemented
47#14273650C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic
50#14273647C2211yescharacteristic, complemented
51C22⋊(C59⋊C8)C2211yescharacteristic
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53#14273637C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic, complemented
55C2×M16×C59C2211yescharacteristic
56C22⋊Q8×C59C2211yescharacteristic
57#121×C59C2211yescharacteristic
58#107×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59D411yescharacteristic
71C22×Dic59—21no—
72#11745689—22no—
73#11745689—41no—
74#11745687—22no—
75#11745687—41no—
76#11745685—22no—
77#11745685—41no—
78C2×D236—22no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236—21no—
82C2×D236—21no—
83C2×D236—41no—
84C2×D236C2311yescharacteristic
85C2×D236C2311yescharacteristic
86C2×D236C2311yescharacteristic
87C2×C4×D59—21no—
88C2×C4×D59—21no—
89C2×C4×D59—21no—
90C2×C4×D59C2311yescharacteristic
91C2×Dic118C2311yescharacteristic
92SD16×C59—22no—
93M16×C59—22no—
94C2×C8×C59C2311yescharacteristic
95C2×C8×C59C2311yescharacteristic
96C4⋊C4×C59—21no—
97C4⋊C4×C59C2311yescharacteristic
98C4⋊C4×C59C2311yescharacteristic
99C22⋊C4×C59—21no—
100C22⋊C4×C59—21no—
101C22⋊Dic59D411yescharacteristic
102#11745672—22no—
103#11745671—41no—
104#11745669—22no—
105#11745669—41no—
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
112Dic59⋊C4—21no—
113Dic59⋊C4D411yescharacteristic
114C4×Dic59—21no—
115C4×Dic59C2311yescharacteristic
116C2×C59⋊C8C2311yescharacteristic
117C2×C59⋊C8C2311yescharacteristic
118D472—22no—
119D472—22no—
120#11745660—22no—
121#11745660D414yescomplemented
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—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—81no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2411yescharacteristic
144C22⋊D59—41no—
145C22⋊D59—42no—
146C22⋊D59—42no—
147C22⋊D59—42no—
148C22⋊D59—81no—
149C2×Dic59—21no—
150C2×Dic59—42no—
151C2×Dic59C2×D411yescharacteristic
152C2×Dic59C2×D411yescharacteristic
153C2×Dic59C2×D411yescharacteristic
154D236—21no—
155D236—21no—
156D236—21no—
157D236—21no—
158D236—21no—
159D236—42no—
160D236—42no—
161D236—81no—
162D236—81no—
163D236C2×D412yes—
164C4×D59—21no—
165C4×D59—21no—
166C4×D59—42no—
167C4×D59—42no—
168C4×D59—81no—
169Dic118—21no—
170Dic118C2×D412yes—
171C8×C59—21no—
172C8×C59C2×D412yes—
173C59⋊C8—21no—
174C59⋊C8—21no—
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—21no—
196C4×C59—41no—
197C4×C59—41no—
198C4×C59—41no—
199C4×C59C22×D411yescharacteristic
200C4×C59H(5,𝔽2)11yescharacteristic
201Dic59—22no—
202Dic59—21no—
203Dic59—21no—
204Dic59—21no—
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#468D5911yescharacteristic, complemented
221#466—591no—
222#464—591no—
223#459—591no—
224#452—591no—
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×#41—591no—
234C22×D4—591no—
235AGL(1,ℤ/8)—1184no—
236#135—1184no—
237C2×Q16—591no—
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×M16C2×D5911yescharacteristic
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—1181no—
256#121—1181no—
257#121—1181no—
258#121C2×D5911yescharacteristic
259#120—1181no—
260C4×Q8—591no—
261C4×D4—591no—
262C4×D4—591no—
263C4×D4—1181no—
264C2×C22⋊C4—1181no—
265#107C2×D5911yescharacteristic, complemented
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⋊C8—591no—
275#97—591no—
276C24—1181no—
277#41—1182no—
278#41—1182no—
279#41—1182no—
280#41—2361no—
281#41—2361no—
282#41—2361no—
283C2×Q8—591no—
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—591no—
302C22×C4—1181no—
303C22×C4—1181no—
304C22×C4—1181no—
305C22×C4—1181no—
306C22×C4C22×D5911yescharacteristic
307Q16—1182no—
308SD16—22no—
309SD16—594no—
310SD16—1182no—
311SD16—2361no—
312D8—1182no—
313D8—1182no—
314D8—1182no—
315D8—2361no—
316M16—22no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8—1182no—
320C2×C8C22×D5911yescharacteristic
321C2×C8C22×D5911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—591no—
324C4⋊C4—1181no—
325C4⋊C4C22×D5911yescharacteristic
326C4⋊C4C22×D5911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—591no—
330C22⋊C4—591no—
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—592no—
350Q8—1181no—
351D4—21no—
352D4—21no—
353D4—81no—
354D4—592no—
355D4—1181no—
356D4—1181no—
357D4—1181no—
358D4—1181no—
359D4—1181no—
360D4—4721no—
361D4—4721no—
362D4—4721no—
363D4—2362no—
364D4—2362no—
365D4—2361no—
366D4—2362no—
367D4—2362no—
368D4—2362no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—591no—
375C2×C4—591no—
376C2×C4—591no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—4721no—
381C2×C4—2362no—
382C2×C4—2362no—
383C2×C4—2362no—
384C2×C4D4×D5911yescharacteristic
385C2×C4C23×D5911yescharacteristic
386C8—21no—
387C8—1181no—
388C8—1181no—
389C8D4×D5912yes—
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—41no—
412C4—41no—
413C4—41no—
414C4—1181no—
415C4—1181no—
416C4—1181no—
417C4—1182no—
418C4C2×D4×D5911yescharacteristic
419C4#1427377311yescharacteristic
420C2—41no—
421C2—81no—
422C2—4721no—
423C2—4721no—
424C2—2361no—
425C2—2362no—
426C2#1683803611yescharacteristic
427C2#1683820111yescharacteristic
428C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#468C2
socleC22×C59C22×D4
hypercenter#468D59
hypocenterC59#3268
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14273755C2semidirect
2. C2×#14273748C2semidirect
3. #16838070C2semidirect
4. #16838043C2semidirect
5. #16837788C2semidirect
6. #16837639C2semidirect
7. #16837627C2semidirect
8. #16837596C2semidirect
9. #16837562C2semidirect
10. #16837550C2semidirect
11. #16837548C2semidirect
12. #16837535C2semidirect
13. #16837501C2semidirect
14. #16837471C2semidirect
15. C59×#468C2semidirect
18. C2×#11745687C22semidirect
22. C2×#11745672C22semidirect
25. C2×#11745671C22semidirect
30. C2×C8×D59C22semidirect
32. #14273723C22semidirect
37. #14273702C22semidirect
41. #14273692C22semidirect
46. Dic59⋊C8C22semidirect
47. #14273650C22semidirect
50. #14273647C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. #14273637C22semidirect
54. C2×SD16×C59C22semidirect
58. #107×C59C22semidirect
59. #103×C59C22semidirect
60. #102×C59C22semidirect
121. #11745660D4semidirect
220. #468D59semidirect
230. C59#3268semidirect
241. C2×SD16C2×D59semidirect
265. #107C2×D59semidirect
268. #103C2×D59semidirect
272. #102C2×D59semidirect