Finite Group Databasebeta

← #21433594

Subgroups — #21433594

Order 7552.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273751C211yesmaximal, characteristic, complemented
2C2×D8×D59C211yesmaximal, characteristic, complemented
3#16837965C211yesmaximal, characteristic, complemented
4#16837874C211yesmaximal, characteristic, complemented
5#16837618C211yesmaximal, characteristic, complemented
6#16837617C211yesmaximal, characteristic, complemented
7#16837616C211yesmaximal, characteristic, complemented
8#16837615C211yesmaximal, characteristic, complemented
9#16837596C211yesmaximal, characteristic, complemented
10#16837595C211yesmaximal, characteristic, complemented
11#16837594C211yesmaximal, characteristic, complemented
12#16837427C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#16837395C211yesmaximal, characteristic, complemented
15C59×#459C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19#14273751—24no—
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×D472C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24C2×#11745669C2211yescharacteristic
25C2×#11745669C2211yescharacteristic, complemented
26D8×D59—24no—
27C2×#11745659C2211yescharacteristic
28C2×C8×D59C2211yescharacteristic
29#14273723C2211yescharacteristic, complemented
30#14273715C2211yescharacteristic, complemented
31#14273714C2211yescharacteristic, complemented
32#14273699—21no—
33#14273699—21no—
34#14273695—21no—
35#14273695—21no—
36C4×D236C2211yescharacteristic, complemented
37D4×Dic59C2211yescharacteristic, complemented
38#14273689C2211yescharacteristic, complemented
39C4×C22⋊D59—21no—
40(C22⋊D59)⋊C4—21no—
41#14273685C2211yescharacteristic
42#14273684C2211yescharacteristic
43C2×(C2×D59)⋊C4—21no—
44C22⋊C4×D59—21no—
45C4⋊(C59⋊C8)C2211yescharacteristic, complemented
46Dic59⋊C8C2211yescharacteristic, complemented
47Dic59⋊C8C2211yescharacteristic, complemented
48#14273652C2211yescharacteristic, complemented
49#14273650C2211yescharacteristic, complemented
50#14273649C2211yescharacteristic, complemented
51#14273648C2211yescharacteristic, complemented
52#14273648C2211yescharacteristic, complemented
53#14273647C2211yescharacteristic, complemented
54C2×D8×C59C2211yescharacteristic
55C2×D8×C59C2211yescharacteristic, complemented
56#127×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic, complemented
58C4⋊C8×C59C2211yescharacteristic, complemented
59#102×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C23×D59—21no—
63C2×D4×C59—21no—
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C2×D4×C59C2311yescharacteristic
68C22×C4×C59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76#11745687—22no—
77#11745687—22no—
78D4×D59—22no—
79D4×D59—22no—
80D4×D59—22no—
81D4×D59D414yescomplemented
82C2×D236C2311yescharacteristic
83C2×D236C2311yescharacteristic
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×C4×D59C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88D8×C59—22no—
89D8×C59—22no—
90C2×C8×C59C2311yescharacteristic
91C2×C8×C59C2311yescharacteristic
92C4⋊C4×C59C2311yescharacteristic
93C22⋊C4×C59—21no—
94C42×C59C2311yescharacteristic
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98#11745670—22no—
99#11745669—22no—
100#11745669—22no—
101#11745669—22no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4D411yescharacteristic
108(C2×D59)⋊C4D411yescharacteristic
109C4⋊Dic59C2311yescharacteristic
110Dic59⋊C4D411yescharacteristic
111Dic59⋊C4D411yescharacteristic
112C4×Dic59—21no—
113C4×Dic59C2311yescharacteristic
114C2×C59⋊C8C2311yescharacteristic
115C2×C59⋊C8C2311yescharacteristic
116D472—22no—
117#11745660—22no—
118#11745659—22no—
119C8×D59—22no—
120C23×C59—21no—
121C23×C59—21no—
122C23×C59—21no—
123C22×D59—21no—
124C22×D59—24no—
125C22×D59—21no—
126C22×D59—42no—
127C22×D59—81no—
128C22×D59—81no—
129C22×D59—81no—
130C22×D59—81no—
131C22×D59C2×D411yescharacteristic
132D4×C59—21no—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—21no—
137D4×C59—81no—
138D4×C59—81no—
139D4×C59C2×D412yes—
140C2×C4×C59—21no—
141C2×C4×C59—81no—
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2×D411yescharacteristic
144C2×C4×C59C2411yescharacteristic
145C22⋊D59—24no—
146C22⋊D59—42no—
147C22⋊D59—42no—
148C22⋊D59—81no—
149C22⋊D59—81no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—42no—
153C2×Dic59—81no—
154C2×Dic59C2×D411yescharacteristic
155C2×Dic59C2×D411yescharacteristic
156C2×Dic59C2×D411yescharacteristic
157D236—21no—
158D236—21no—
159D236—21no—
160D236C2×D412yes—
161C4×D59—81no—
162C4×D59—81no—
163C4×D59C2×D412yes—
164C4×D59#4112yes—
165Dic118—21no—
166Dic118—21no—
167C8×C59—21no—
168C8×C59—21no—
169C59⋊C8—21no—
170C59⋊C8—21no—
171C22×C59—22no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59C22×D411yescharacteristic
181C2×D59—21no—
182C2×D59—21no—
183C2×D59—22no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—41no—
189C2×D59—84no—
190C2×D59—84no—
191C2×D59#12112yes—
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—41no—
195C4×C59C22×D411yescharacteristic
196C4×C59C2×#4111yescharacteristic
197Dic59—21no—
198Dic59—21no—
199Dic59—41no—
200Dic59—41no—
201Dic59#12112yes—
202#3041—591nomaximal, Sylow
203C2×C59—42no—
204C2×C59—81no—
205C2×C59—81no—
206C2×C59C2×#12111yescharacteristic
207C2×C59#57611yescharacteristic
208C2×C59#57611yescharacteristic
209D59—22no—
210D59—42no—
211D59—81no—
212C2×AGL(1,ℤ/8)—591no—
213C22×D8—591no—
214#535—591no—
215#518—591no—
216#463—591no—
217#463—591no—
218#463—591no—
219#463—591no—
220#459—591no—
221#459—591no—
222#459—591no—
223#459D5911yescharacteristic, complemented
224#424—591no—
225#418—591no—
226#416—591no—
227C59#304111yescharacteristic, complemented, Sylow
228C2×#41—591no—
229C22×D4—591no—
230C22×D4—591no—
231AGL(1,ℤ/8)—1184no—
232C2×SD16—591no—
233C2×SD16—591no—
234C2×D8—591no—
235C2×D8—591no—
236C2×D8—591no—
237C2×D8—591no—
238C2×D8—1184no—
239C2×D8C2×D5911yescharacteristic
240C2×D8C2×D5911yescharacteristic, complemented
241C2×M16—591no—
242C22×C8—591no—
243#127—591no—
244#127C2×D5911yescharacteristic, complemented
245#124—591no—
246#124—591no—
247#121—1181no—
248#121—1181no—
249#120—1181no—
250#120—1181no—
251C4×D4—591no—
252C4×D4—591no—
253C4×D4—591no—
254C4×D4—1181no—
255C4×D4—1181no—
256C4×D4C2×D5911yescharacteristic, complemented
257#117—591no—
258#117—591no—
259C2×C22⋊C4—1181no—
260C2×C22⋊C4—1181no—
261C4⋊C8—591no—
262C4⋊C8—591no—
263C4⋊C8—591no—
264C4⋊C8C2×D5911yescharacteristic, complemented
265#103—591no—
266#103—591no—
267#102—591no—
268#102—591no—
269#102—591no—
270#102—591no—
271#102C2×D5911yescharacteristic, complemented
272#102C2×D5911yescharacteristic, complemented
273C24—1181no—
274C24—1181no—
275#41—1182no—
276#41—1182no—
277C2×Q8—591no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—594no—
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—1182no—
284C2×D4—1182no—
285C2×D4—1182no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4C22×D5911yescharacteristic
292C2×D4C22×D5911yescharacteristic
293C2×D4C22×D5911yescharacteristic
294C22×C4—21no—
295C22×C4—591no—
296C22×C4—1181no—
297C22×C4—1181no—
298C22×C4—1181no—
299C22×C4—1181no—
300SD16—1182no—
301SD16—1182no—
302D8—22no—
303D8—22no—
304D8—1182no—
305D8—1182no—
306D8—1182no—
307D8—1182no—
308M16—1182no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8—1182no—
312C2×C8C22×D5911yescharacteristic
313C2×C8C22×D5911yescharacteristic
314C4⋊C4—591no—
315C4⋊C4—591no—
316C4⋊C4—591no—
317C4⋊C4C22×D5911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—591no—
320C22⋊C4—591no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C42—591no—
330C42—1181no—
331C42C22×D5911yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—591no—
336C23—1184no—
337C23—1181no—
338C23—1181no—
339C23—4721no—
340C23—4721no—
341C23—4721no—
342C23—4721no—
343C23—2362no—
344Q8—1181no—
345Q8—1181no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—592no—
354D4—1184no—
355D4—1181no—
356D4—1181no—
357D4—1181no—
358D4—4721no—
359D4—4721no—
360D4—2362no—
361D4—2362no—
362D4D4×D5912yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—591no—
366C2×C4—592no—
367C2×C4—592no—
368C2×C4—591no—
369C2×C4—591no—
370C2×C4—1181no—
371C2×C4—1181no—
372C2×C4—4721no—
373C2×C4—4721no—
374C2×C4—4721no—
375C2×C4—2362no—
376C2×C4D4×D5911yescharacteristic
377C2×C4D4×D5911yescharacteristic
378C2×C4C23×D5911yescharacteristic
379C8—21no—
380C8—21no—
381C8—1181no—
382C8—1181no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—592no—
393C22—1181no—
394C22—1181no—
395C22—1182no—
396C22—4724no—
397C22—4724no—
398C22—2361no—
399C22—2361no—
400C22—2361no—
401C22—2361no—
402C22—2361no—
403C22C2×D4×D5911yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—592no—
408C4—1181no—
409C4—1181no—
410C4—2361no—
411C4—2361no—
412C4C2×D4×D5911yescharacteristic
413C4#41×D5911yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—1182no—
418C2—4721no—
419C2—2362no—
420C2#121×D5911yescharacteristic
421C2#1683820311yescharacteristic
422C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3041
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14273751C2semidirect
2. C2×D8×D59C2semidirect
3. #16837965C2semidirect
4. #16837874C2semidirect
5. #16837618C2semidirect
6. #16837617C2semidirect
7. #16837616C2semidirect
8. #16837615C2semidirect
9. #16837596C2semidirect
10. #16837595C2semidirect
11. #16837594C2semidirect
12. #16837427C2semidirect
13. #16837405C2semidirect
14. #16837395C2semidirect
15. C59×#459C2semidirect
20. C2×#11745660C22semidirect
21. C2×#11745670C22semidirect
25. C2×#11745669C22semidirect
29. #14273723C22semidirect
30. #14273715C22semidirect
31. #14273714C22semidirect
36. C4×D236C22semidirect
37. D4×Dic59C22semidirect
38. #14273689C22semidirect
45. C4⋊(C59⋊C8)C22semidirect
46. Dic59⋊C8C22semidirect
47. Dic59⋊C8C22semidirect
48. #14273652C22semidirect
49. #14273650C22semidirect
50. #14273649C22semidirect
51. #14273648C22semidirect
52. #14273648C22semidirect
53. #14273647C22semidirect
55. C2×D8×C59C22semidirect
56. #127×C59C22semidirect
57. C4×D4×C59C22semidirect
58. C4⋊C8×C59C22semidirect
59. #102×C59C22semidirect
60. #102×C59C22semidirect
81. D4×D59D4semidirect
223. #459D59semidirect
227. C59#3041semidirect
240. C2×D8C2×D59semidirect
244. #127C2×D59semidirect
256. C4×D4C2×D59semidirect
264. C4⋊C8C2×D59semidirect
271. #102C2×D59semidirect
272. #102C2×D59semidirect