Finite Group Databasebeta

← #21435733

Subgroups — #21435733

Order 7552.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273756C211yesmaximal, characteristic, complemented
2C2×#14273751C211yesmaximal, characteristic, complemented
3#16838060C211yesmaximal, characteristic, complemented
4#16838047C211yesmaximal, characteristic, complemented
5#16837784C211yesmaximal, characteristic, complemented
6#16837659C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837625C211yesmaximal, characteristic, complemented
9#16837565C211yesmaximal, characteristic, complemented
10#16837551C211yesmaximal, characteristic, complemented
11#16837544C211yesmaximal, characteristic, complemented
12#16837542C211yesmaximal, characteristic, complemented
13C4×#11745670C211yesmaximal, characteristic, complemented
14#16837479C211yesmaximal, characteristic, complemented
15C59×#463C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×Q8×D59C2211yescharacteristic, complemented
19C2×D4×D59C2211yescharacteristic
20#14273756—24no—
21#14273751—24no—
22C2×Dic236C2211yescharacteristic, complemented
23C2×#11745672C2211yescharacteristic, complemented
24C2×#11745660C2211yescharacteristic
25C2×#11745670C2211yescharacteristic
26C2×#11745670C2211yescharacteristic, complemented
27C2×#11745671C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745659C2211yescharacteristic
30C2×#11745659C2211yescharacteristic, complemented
31#14273715C2211yescharacteristic
32#14273713—21no—
33#14273711—21no—
34#14273707C2211yescharacteristic
35#14273704—21no—
36#14273703C2211yescharacteristic
37#14273702C2211yescharacteristic
38#14273701—21no—
39#14273700—21no—
40#14273698C2211yescharacteristic, complemented
41#14273697—21no—
42C4×Dic118C2211yescharacteristic, complemented
43C4×D236C2211yescharacteristic
44(C22⋊D59)⋊C4—21no—
45C2×(C2×D59)⋊C4—21no—
46#14273658C2211yescharacteristic, complemented
47#14273652C2211yescharacteristic, complemented
48#14273650C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273648C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53C4×C59⋊C8C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic
55C2×D8×C59C2211yescharacteristic
56#124×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic
58C4⋊C8×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C22×Dic59—21no—
71C22×Dic59—21no—
72Q8×D59—22no—
73Q8×D59—41no—
74#11745687—22no—
75#11745687—22no—
76#11745687—41no—
77#11745687—41no—
78D4×D59—22no—
79D4×D59—41no—
80C2×D236—21no—
81C2×D236D411yescharacteristic
82C2×D236C2311yescharacteristic
83C2×C4×D59—21no—
84C2×C4×D59C2311yescharacteristic
85C2×C4×D59C2311yescharacteristic
86C2×Dic118—21no—
87C2×Dic118C2311yescharacteristic
88C2×Dic118C2311yescharacteristic
89SD16×C59—22no—
90D8×C59—22no—
91C2×C8×C59C2311yescharacteristic
92C2×C8×C59C2311yescharacteristic
93C4⋊C4×C59C2311yescharacteristic
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C42×C59C2311yescharacteristic
98C22⋊Dic59—21no—
99#11745672—22no—
100#11745671—41no—
101#11745670—41no—
102#11745670D414yescomplemented
103#11745669—22no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4D411yescharacteristic
110(C2×D59)⋊C4D411yescharacteristic
111C4⋊Dic59—21no—
112C4⋊Dic59D411yescharacteristic
113C4⋊Dic59C2311yescharacteristic
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116C4×Dic59—21no—
117C2×C59⋊C8C2311yescharacteristic
118C2×C59⋊C8C2311yescharacteristic
119Dic236—22no—
120#11745660—22no—
121#11745659—22no—
122#11745659—22no—
123C23×C59—21no—
124C23×C59—21no—
125C22×D59—21no—
126C22×D59—42no—
127C22×D59—42no—
128C22×D59—81no—
129C22×D59C2×D411yescharacteristic
130C22×D59C2×D411yescharacteristic
131Q8×C59—21no—
132Q8×C59—21no—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59C2×D412yes—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—81no—
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2411yescharacteristic
143C22⋊D59—42no—
144C22⋊D59—42no—
145C22⋊D59—42no—
146C22⋊D59—42no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—42no—
151C2×Dic59—42no—
152C2×Dic59C2×D411yescharacteristic
153C2×Dic59C2×D411yescharacteristic
154D236—21no—
155D236—21no—
156D236—41no—
157D236—81no—
158C4×D59—21no—
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—21no—
162C4×D59—42no—
163Dic118—21no—
164Dic118—21no—
165Dic118—21no—
166Dic118—42no—
167Dic118C2×D412yes—
168C8×C59—21no—
169C8×C59—21no—
170C59⋊C8—21no—
171C59⋊C8C2×D412yes—
172C22×C59—22no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59C22×D411yescharacteristic
179C2×D59—21no—
180C2×D59—21no—
181C2×D59—21no—
182C2×D59—21no—
183C2×D59—21no—
184C2×D59—21no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—41no—
192C4×C59—41no—
193C4×C59C22×D411yescharacteristic
194C4×C59H(5,𝔽2)11yescharacteristic
195Dic59—22no—
196Dic59—21no—
197Dic59—21no—
198Dic59—41no—
199Dic59—41no—
200#3275—591nomaximal, Sylow
201C2×C59—42no—
202C2×C59—81no—
203C2×C59D4211yescharacteristic
204C2×C59#57511yescharacteristic
205C2×C59#57711yescharacteristic
206D59—41no—
207D59—41no—
208D59—81no—
209C2×#137—591no—
210C2×AGL(1,ℤ/8)—591no—
211#548—591no—
212#546—591no—
213#495—591no—
214#470—591no—
215#469—591no—
216#464—591no—
217#463D5911yescharacteristic, complemented
218#452—591no—
219#450—591no—
220#449—591no—
221#448—591no—
222C4×SD16—591no—
223#436—591no—
224C59#327511yescharacteristic, complemented, Sylow
225C2×#41—591no—
226C2×#41—591no—
227C22×Q8—591no—
228C22×D4—591no—
229#137—1184no—
230AGL(1,ℤ/8)—1184no—
231C2×Q16—591no—
232C2×Q16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16—591no—
237C2×SD16C2×D5911yescharacteristic
238C2×D8—591no—
239C2×D8C2×D5911yescharacteristic
240C2×M16—591no—
241C2×M16—591no—
242#124—591no—
243#124—1181no—
244#124C2×D5911yescharacteristic, complemented
245#123—1181no—
246C22⋊Q8—591no—
247C22⋊Q8—591no—
248C22⋊Q8—1181no—
249#121—591no—
250#121—591no—
251#121—1181no—
252#121—1181no—
253#120—1181no—
254C4×Q8—591no—
255C4×D4—591no—
256C4×D4—1181no—
257C4×D4C2×D5911yescharacteristic
258C2×C22⋊C4—1181no—
259#106—591no—
260C4⋊C8C2×D5911yescharacteristic, complemented
261#103—591no—
262#103—591no—
263#103C2×D5911yescharacteristic, complemented
264#102—591no—
265#102—591no—
266#102C2×D5911yescharacteristic, complemented
267C22⋊C8—591no—
268C22⋊C8—591no—
269C4×C8—591no—
270C24—1181no—
271#41—1182no—
272#41—1182no—
273#41—2361no—
274#41—2361no—
275C2×Q8—591no—
276C2×Q8—591no—
277C2×Q8—1181no—
278C2×Q8—1182no—
279C2×Q8—2361no—
280C2×Q8C22×D5911yescharacteristic
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4—1182no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—2361no—
290C2×D4C22×D5911yescharacteristic
291C2×D4C22×D5911yescharacteristic
292C22×C4—21no—
293C22×C4—591no—
294C22×C4—591no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4—1181no—
298Q16—1182no—
299Q16—1182no—
300SD16—22no—
301SD16—594no—
302SD16—1182no—
303SD16—2361no—
304SD16—2361no—
305D8—22no—
306D8—1182no—
307M16—1182no—
308M16—1182no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—591no—
314C4⋊C4—591no—
315C4⋊C4—1181no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C4⋊C4C22×D5911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—591no—
323C22⋊C4—591no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C22⋊C4—1181no—
330C42—1181no—
331C42C22×D5911yescharacteristic
332C23—21no—
333C23—21no—
334C23—591no—
335C23—591no—
336C23—1181no—
337C23—4721no—
338C23—2362no—
339C23—2362no—
340Q8—21no—
341Q8—21no—
342Q8—592no—
343Q8—1181no—
344Q8—1181no—
345Q8—1181no—
346Q8—2362no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—1181no—
351D4—1181no—
352D4—4721no—
353D4—2361no—
354D4—2362no—
355D4—2362no—
356D4—2362no—
357D4—2362no—
358D4D4×D5912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—81no—
362C2×C4—591no—
363C2×C4—591no—
364C2×C4—1181no—
365C2×C4—1181no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—2362no—
372C2×C4—2362no—
373C2×C4—2362no—
374C2×C4D4×D5911yescharacteristic
375C2×C4D4×D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—21no—
378C8—21no—
379C8—592no—
380C8—1181no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—1181no—
388C22—1181no—
389C22—1181no—
390C22—1181no—
391C22—1181no—
392C22—1181no—
393C22—4724no—
394C22—2361no—
395C22—2361no—
396C22—2361no—
397C22C2×D4×D5911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1181no—
403C4—1181no—
404C4—1182no—
405C4—2361no—
406C4—2361no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377311yescharacteristic
409C2—42no—
410C2—81no—
411C2—4721no—
412C2—2361no—
413C2—2361no—
414C2#1683803611yescharacteristic
415C2#1683819911yescharacteristic
416C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#463C2
socleC22×C59C22×D4
hypercenter#463D59
hypocenterC59#3275
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×#14273756C2semidirect
2. C2×#14273751C2semidirect
3. #16838060C2semidirect
4. #16838047C2semidirect
5. #16837784C2semidirect
6. #16837659C2semidirect
7. #16837654C2semidirect
8. #16837625C2semidirect
9. #16837565C2semidirect
10. #16837551C2semidirect
11. #16837544C2semidirect
12. #16837542C2semidirect
13. C4×#11745670C2semidirect
14. #16837479C2semidirect
15. C59×#463C2semidirect
18. C2×Q8×D59C22semidirect
22. C2×Dic236C22semidirect
23. C2×#11745672C22semidirect
26. C2×#11745670C22semidirect
30. C2×#11745659C22semidirect
40. #14273698C22semidirect
42. C4×Dic118C22semidirect
46. #14273658C22semidirect
47. #14273652C22semidirect
48. #14273650C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. C4×C59⋊C8C22semidirect
56. #124×C59C22semidirect
58. C4⋊C8×C59C22semidirect
59. #103×C59C22semidirect
60. #102×C59C22semidirect
102. #11745670D4semidirect
217. #463D59semidirect
224. C59#3275semidirect
244. #124C2×D59semidirect
260. C4⋊C8C2×D59semidirect
263. #103C2×D59semidirect
266. #102C2×D59semidirect