Finite Group Databasebeta

← #21435702

Subgroups — #21435702

Order 7552.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273754C211yesmaximal, characteristic, complemented
2C2×#14273751C211yesmaximal, characteristic, complemented
3#16838047C211yesmaximal, characteristic, complemented
4#16838045C211yesmaximal, characteristic, complemented
5#16837784C211yesmaximal, characteristic, complemented
6#16837651C211yesmaximal, characteristic, complemented
7#16837647C211yesmaximal, characteristic, complemented
8#16837618C211yesmaximal, characteristic, complemented
9#16837567C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11#16837537C211yesmaximal, characteristic, complemented
12#16837534C211yesmaximal, characteristic, complemented
13C4×#11745669C211yesmaximal, characteristic, complemented
14#16837479C211yesmaximal, characteristic, complemented
15C59×#463C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic, complemented
19C2×D4×D59C2211yescharacteristic, complemented
20#14273754—24no—
21#14273751—24no—
22C2×#11745672C2211yescharacteristic, complemented
23C2×#11745660C2211yescharacteristic, complemented
24C2×#11745670C2211yescharacteristic, complemented
25C2×#11745671C2211yescharacteristic, complemented
26C2×D472C2211yescharacteristic
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745659C2211yescharacteristic, complemented
30C2×#11745659C2211yescharacteristic, complemented
31#14273715C2211yescharacteristic, complemented
32#14273711—21no—
33#14273709—21no—
34#14273707C2211yescharacteristic, complemented
35#14273703C2211yescharacteristic, complemented
36#14273702C2211yescharacteristic
37#14273701—21no—
38#14273700—21no—
39#14273698C2211yescharacteristic
40#14273697—21no—
41#14273697—21no—
42C4×D236C2211yescharacteristic
43C4×D236C2211yescharacteristic, complemented
44C2×(C2×D59)⋊C4—21no—
45C22⋊C4×D59—21no—
46#14273660C2211yescharacteristic, complemented
47#14273652C2211yescharacteristic, complemented
48#14273649C2211yescharacteristic, complemented
49#14273648C2211yescharacteristic, complemented
50#14273647C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53C4×C59⋊C8C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic, complemented
55C2×D8×C59C2211yescharacteristic
56#124×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic, complemented
58C4⋊C8×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C23×D59—21no—
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C22×Dic59—21no—
72#11745689—22no—
73#11745689—41no—
74#11745687—22no—
75#11745687—41no—
76D4×D59—22no—
77D4×D59—22no—
78D4×D59—41no—
79D4×D59—41no—
80C2×D236—21no—
81C2×D236—21no—
82C2×D236D411yescharacteristic
83C2×D236C2311yescharacteristic
84C2×D236C2311yescharacteristic
85C2×C4×D59—21no—
86C2×C4×D59—21no—
87C2×C4×D59C2311yescharacteristic
88C2×C4×D59C2311yescharacteristic
89C2×Dic118C2311yescharacteristic
90SD16×C59—22no—
91D8×C59—22no—
92C2×C8×C59C2311yescharacteristic
93C2×C8×C59C2311yescharacteristic
94C4⋊C4×C59C2311yescharacteristic
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C42×C59C2311yescharacteristic
99C22⋊Dic59—21no—
100#11745672—41no—
101#11745671—22no—
102#11745670—22no—
103#11745669—41no—
104#11745669D414yescomplemented
105(C2×D59)⋊C4—21no—
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
112(C2×D59)⋊C4D411yescharacteristic
113C4⋊Dic59—21no—
114C4⋊Dic59D411yescharacteristic
115C4⋊Dic59C2311yescharacteristic
116Dic59⋊C4—21no—
117C2×C59⋊C8C2311yescharacteristic
118C2×C59⋊C8C2311yescharacteristic
119D472—22no—
120#11745660—22no—
121#11745659—22no—
122#11745659—22no—
123C23×C59—21no—
124C23×C59—21no—
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—42no—
128C22×D59—42no—
129C22×D59—42no—
130C22×D59—42no—
131C22×D59—81no—
132C22×D59—81no—
133C22×D59C2×D411yescharacteristic
134C22×D59C2×D411yescharacteristic
135Q8×C59—21no—
136Q8×C59—21no—
137D4×C59—21no—
138D4×C59—21no—
139D4×C59—21no—
140D4×C59C2×D412yes—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—81no—
144C2×C4×C59C2×D411yescharacteristic
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2411yescharacteristic
147C22⋊D59—42no—
148C22⋊D59—42no—
149C22⋊D59—42no—
150C22⋊D59—81no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—42no—
154C2×Dic59C2×D411yescharacteristic
155C2×Dic59C2×D411yescharacteristic
156D236—21no—
157D236—21no—
158D236—21no—
159D236—41no—
160D236—42no—
161D236—81no—
162D236C2×D412yes—
163C4×D59—21no—
164C4×D59—21no—
165C4×D59—21no—
166C4×D59—21no—
167C4×D59—42no—
168C4×D59—81no—
169Dic118—21no—
170Dic118—21no—
171C8×C59—21no—
172C8×C59—21no—
173C59⋊C8—21no—
174C59⋊C8C2×D412yes—
175C22×C59—22no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59C22×D411yescharacteristic
182C2×D59—21no—
183C2×D59—21no—
184C2×D59—22no—
185C2×D59—21no—
186C2×D59—21no—
187C2×D59—21no—
188C2×D59—21no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—84no—
195C2×D59—84no—
196C4×C59—21no—
197C4×C59—21no—
198C4×C59—41no—
199C4×C59—41no—
200C4×C59C22×D411yescharacteristic
201C4×C59H(5,𝔽2)11yescharacteristic
202Dic59—21no—
203Dic59—21no—
204Dic59—41no—
205Dic59—41no—
206#3273—591nomaximal, Sylow
207C2×C59—42no—
208C2×C59—81no—
209C2×C59D4211yescharacteristic
210C2×C59#57511yescharacteristic
211C2×C59#57611yescharacteristic
212D59—41no—
213D59—41no—
214D59—42no—
215D59—81no—
216C2×AGL(1,ℤ/8)—591no—
217C2×AGL(1,ℤ/8)—591no—
218#546—591no—
219#546—591no—
220#495—591no—
221#468—591no—
222#468—591no—
223#463—591no—
224#463D5911yescharacteristic, complemented
225#452—591no—
226#452—591no—
227#447—591no—
228#447—591no—
229C4×D8—591no—
230#436—591no—
231C59#327311yescharacteristic, complemented, Sylow
232C2×#41—591no—
233C2×#41—591no—
234C22×D4—591no—
235C22×D4—591no—
236AGL(1,ℤ/8)—1184no—
237AGL(1,ℤ/8)—1184no—
238C2×Q16—591no—
239C2×SD16—591no—
240C2×SD16—591no—
241C2×SD16—591no—
242C2×SD16C2×D5911yescharacteristic, complemented
243C2×D8—591no—
244C2×D8—591no—
245C2×D8—591no—
246C2×D8C2×D5911yescharacteristic
247C2×M16—591no—
248C2×M16—591no—
249#124—591no—
250#124C2×D5911yescharacteristic, complemented
251#123—1181no—
252#123—1181no—
253C22⋊Q8—591no—
254C22⋊Q8—591no—
255#121—591no—
256#121—591no—
257#121—1181no—
258#121—1181no—
259#120—1181no—
260#120—1181no—
261C4×D4—591no—
262C4×D4—591no—
263C4×D4C2×D5911yescharacteristic, complemented
264C2×C22⋊C4—1181no—
265C2×C22⋊C4—1181no—
266#107—591no—
267C4⋊C8C2×D5911yescharacteristic, complemented
268#103—591no—
269#103C2×D5911yescharacteristic, complemented
270#102—591no—
271#102—591no—
272#102—591no—
273#102C2×D5911yescharacteristic, complemented
274C22⋊C8—591no—
275C22⋊C8—591no—
276C4×C8—591no—
277C24—1181no—
278C24—1181no—
279#41—1182no—
280#41—1182no—
281#41—2361no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8C22×D5911yescharacteristic
285C2×D4—591no—
286C2×D4—591no—
287C2×D4—591no—
288C2×D4—1181no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4—1181no—
292C2×D4—1182no—
293C2×D4—1182no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—2361no—
297C2×D4—2361no—
298C2×D4C22×D5911yescharacteristic
299C2×D4C22×D5911yescharacteristic
300C22×C4—21no—
301C22×C4—591no—
302C22×C4—591no—
303C22×C4—1181no—
304C22×C4—1181no—
305C22×C4—1181no—
306Q16—2361no—
307SD16—22no—
308SD16—1182no—
309SD16—1182no—
310SD16—1182no—
311D8—22no—
312D8—594no—
313D8—1182no—
314D8—2361no—
315M16—1182no—
316M16—1182no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8C22×D5911yescharacteristic
320C2×C8C22×D5911yescharacteristic
321C4⋊C4—591no—
322C4⋊C4—591no—
323C4⋊C4—1181no—
324C4⋊C4—1181no—
325C4⋊C4C22×D5911yescharacteristic
326C22⋊C4—21no—
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—
336C22⋊C4—1181no—
337C22⋊C4—1181no—
338C42C22×D5911yescharacteristic
339C23—21no—
340C23—21no—
341C23—591no—
342C23—591no—
343C23—1181no—
344C23—1181no—
345C23—4721no—
346C23—4721no—
347C23—2362no—
348C23—2362no—
349C23—2362no—
350C23—2362no—
351Q8—21no—
352Q8—21no—
353Q8—1181no—
354Q8—1181no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—592no—
359D4—1181no—
360D4—1181no—
361D4—1181no—
362D4—4721no—
363D4—4721no—
364D4—2361no—
365D4—2362no—
366D4—2362no—
367D4—2362no—
368D4—2362no—
369D4D4×D5912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—591no—
374C2×C4—591no—
375C2×C4—1181no—
376C2×C4—1181no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—4721no—
382C2×C4—2362no—
383C2×C4—2362no—
384C2×C4D4×D5911yescharacteristic
385C2×C4D4×D5911yescharacteristic
386C2×C4C23×D5911yescharacteristic
387C8—21no—
388C8—21no—
389C8—592no—
390C8—1181no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—1181no—
398C22—1181no—
399C22—1181no—
400C22—1181no—
401C22—1181no—
402C22—1181no—
403C22—1182no—
404C22—4724no—
405C22—4724no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22—2361no—
410C22—2361no—
411C22C2×D4×D5911yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—1181no—
417C4—1181no—
418C4—2361no—
419C4—2361no—
420C4C2×D4×D5911yescharacteristic
421C4#1427377311yescharacteristic
422C2—42no—
423C2—81no—
424C2—4721no—
425C2—2361no—
426C2—2361no—
427C2—2362no—
428C2#1683803611yescharacteristic
429C2#1683819911yescharacteristic
430C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#463C2
socleC22×C59C22×D4
hypercenter#463D59
hypocenterC59#3273
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14273754C2semidirect
2. C2×#14273751C2semidirect
3. #16838047C2semidirect
4. #16838045C2semidirect
5. #16837784C2semidirect
6. #16837651C2semidirect
7. #16837647C2semidirect
8. #16837618C2semidirect
9. #16837567C2semidirect
10. #16837561C2semidirect
11. #16837537C2semidirect
12. #16837534C2semidirect
13. C4×#11745669C2semidirect
14. #16837479C2semidirect
15. C59×#463C2semidirect
18. C2×D4×D59C22semidirect
19. C2×D4×D59C22semidirect
22. C2×#11745672C22semidirect
23. C2×#11745660C22semidirect
24. C2×#11745670C22semidirect
25. C2×#11745671C22semidirect
29. C2×#11745659C22semidirect
30. C2×#11745659C22semidirect
31. #14273715C22semidirect
34. #14273707C22semidirect
35. #14273703C22semidirect
43. C4×D236C22semidirect
46. #14273660C22semidirect
47. #14273652C22semidirect
48. #14273649C22semidirect
49. #14273648C22semidirect
50. #14273647C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. C4×C59⋊C8C22semidirect
54. C2×SD16×C59C22semidirect
56. #124×C59C22semidirect
57. C4×D4×C59C22semidirect
58. C4⋊C8×C59C22semidirect
59. #103×C59C22semidirect
60. #102×C59C22semidirect
104. #11745669D4semidirect
224. #463D59semidirect
231. C59#3273semidirect
242. C2×SD16C2×D59semidirect
250. #124C2×D59semidirect
263. C4×D4C2×D59semidirect
267. C4⋊C8C2×D59semidirect
269. #103C2×D59semidirect
273. #102C2×D59semidirect