Finite Group Databasebeta

← #21435728

Subgroups — #21435728

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×#14273758C211yesmaximal, characteristic, complemented
2C2×#14273752C211yesmaximal, characteristic, complemented
3#16838048C211yesmaximal, characteristic, complemented
4#16837784C211yesmaximal, characteristic, complemented
5#16837658C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837624C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837552C211yesmaximal, characteristic, complemented
11#16837545C211yesmaximal, characteristic, complemented
12#16837541C211yesmaximal, characteristic, complemented
13C4×#11745671C211yesmaximal, characteristic, complemented
14#16837480C211yesmaximal, characteristic, complemented
15C59×#548C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18#14273758—24no—
19#14273752—24no—
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745672C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic, complemented
23C2×#11745671C2211yescharacteristic
24C2×#11745671C2211yescharacteristic
25C2×#11745671C2211yescharacteristic
26C2×#11745671C2211yescharacteristic
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745664C2211yescharacteristic
30C2×#11745664C2211yescharacteristic, complemented
31#14273715C2211yescharacteristic
32#14273712—21no—
33#14273706C2211yescharacteristic
34#14273701C2211yescharacteristic
35#14273700—21no—
36#14273695—21no—
37C4×D236C2211yescharacteristic
38C22⋊C4×D59—21no—
39#14273658C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic, complemented
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49C4×C59⋊C8C2211yescharacteristic, complemented
50C2×#41×C59C2211yescharacteristic
51C22×Q8×C59C2211yescharacteristic, complemented
52#124×C59—21no—
53#124×C59C2211yescharacteristic, complemented
54C22⋊Q8×C59—21no—
55C22⋊Q8×C59C2211yescharacteristic
56#121×C59—21no—
57#121×C59C2211yescharacteristic, complemented
58C4×Q8×C59C2211yescharacteristic, complemented
59C4×D4×C59—21no—
60C4×D4×C59C2211yescharacteristic
61C23×D59—21no—
62#41×C59—22no—
63#41×C59—41no—
64C2×Q8×C59—21no—
65C2×Q8×C59—22no—
66C2×Q8×C59—41no—
67C2×Q8×C59C2311yescharacteristic
68C2×Q8×C59C2311yescharacteristic
69C2×D4×C59—21no—
70C2×D4×C59—21no—
71C2×D4×C59D411yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C2×C22⋊D59—21no—
78C2×C22⋊D59—21no—
79#11745685—22no—
80#11745685—41no—
81C2×D236—22no—
82C2×D236—21no—
83C2×D236—41no—
84C2×D236C2311yescharacteristic
85C2×D236C2311yescharacteristic
86C2×C4×D59—21no—
87C2×C4×D59—21no—
88C2×Dic118C2311yescharacteristic
89C4⋊C4×C59—21no—
90C4⋊C4×C59—21no—
91C4⋊C4×C59D411yescharacteristic
92C4⋊C4×C59C2311yescharacteristic
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59D411yescharacteristic
98C22⋊C4×C59D411yescharacteristic
99C42×C59—21no—
100C42×C59C2311yescharacteristic
101C22⋊Dic59—21no—
102#11745672—22no—
103#11745672—22no—
104#11745671—22no—
105#11745671—22no—
106#11745671—41no—
107#11745671D414yescomplemented
108#11745670—41no—
109#11745669—22no—
110#11745669—22no—
111(C2×D59)⋊C4—21no—
112(C2×D59)⋊C4—21no—
113(C2×D59)⋊C4—21no—
114(C2×D59)⋊C4—21no—
115C4⋊Dic59C2311yescharacteristic
116Dic59⋊C4—21no—
117#11745664—22no—
118#11745664—22no—
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C23×C59—21no—
124C23×C59C2×D411yescharacteristic
125C23×C59C2×D411yescharacteristic
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—42no—
129C22×D59—42no—
130C22×D59—81no—
131Q8×C59—21no—
132Q8×C59—21no—
133Q8×C59—21no—
134Q8×C59—42no—
135Q8×C59C2×D412yes—
136D4×C59—21no—
137D4×C59—21no—
138D4×C59—41no—
139D4×C59—42no—
140D4×C59—42no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—42no—
149C2×C4×C59—42no—
150C2×C4×C59C2×D411yescharacteristic
151C2×C4×C59C2×D411yescharacteristic
152C2×C4×C59C2×D411yescharacteristic
153C2×C4×C59C2×D411yescharacteristic
154C2×C4×C59C2411yescharacteristic
155C22⋊D59—42no—
156C22⋊D59—81no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159D236—21no—
160D236—21no—
161D236—21no—
162D236—42no—
163D236C2×D412yes—
164C4×D59—42no—
165C4×D59—81no—
166Dic118—21no—
167Dic118—21no—
168C59⋊C8—21no—
169C59⋊C8—21no—
170C59⋊C8—21no—
171C59⋊C8C2×D412yes—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59C22×D411yescharacteristic
182C2×D59—22no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—84no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—22no—
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—41no—
195C4×C59—41no—
196C4×C59C22×D411yescharacteristic
197C4×C59H(5,𝔽2)11yescharacteristic
198Dic59—41no—
199Dic59—41no—
200#3275—591nomaximal, Sylow
201C2×C59—41no—
202C2×C59—41no—
203C2×C59—81no—
204C2×C59D4211yescharacteristic
205C2×C59#57511yescharacteristic
206C2×C59#57711yescharacteristic
207D59—42no—
208D59—81no—
209C2×#137—591no—
210C2×AGL(1,ℤ/8)—591no—
211#548D5911yescharacteristic, complemented
212#546—591no—
213#495—591no—
214#470—591no—
215#469—591no—
216#464—591no—
217#463—591no—
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×#41C2×D5911yescharacteristic
227C22×Q8C2×D5911yescharacteristic, complemented
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×SD16—591no—
238C2×D8—591no—
239C2×D8—591no—
240C2×M16—591no—
241C2×M16—591no—
242#124—21no—
243#124—591no—
244#124C2×D5911yescharacteristic, complemented
245#123—1181no—
246C22⋊Q8—21no—
247C22⋊Q8—591no—
248C22⋊Q8C2×D5911yescharacteristic
249#121—21no—
250#121—591no—
251#121—1181no—
252#121C2×D5911yescharacteristic, complemented
253#120—1181no—
254C4×Q8C2×D5911yescharacteristic, complemented
255C4×D4—21no—
256C4×D4—591no—
257C4×D4C2×D5911yescharacteristic
258C2×C22⋊C4—1181no—
259#106—591no—
260C4⋊C8—591no—
261#103—591no—
262#103—591no—
263#103—591no—
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8—591no—
268C22⋊C8—591no—
269C4×C8—591no—
270C24—1181no—
271#41—22no—
272#41—41no—
273#41—1182no—
274#41—2361no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—591no—
279C2×Q8C22×D5911yescharacteristic
280C2×Q8C22×D5911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—591no—
284C2×D4—591no—
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—21no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4C22×D5911yescharacteristic
297C22×C4C22×D5911yescharacteristic
298Q16—1182no—
299Q16—1182no—
300SD16—594no—
301SD16—1182no—
302SD16—1182no—
303SD16—2361no—
304SD16—2361no—
305D8—1182no—
306D8—1182no—
307M16—1182no—
308M16—1182no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8—591no—
312C2×C8—591no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—591no—
316C4⋊C4—1181no—
317C4⋊C4C22⋊D5911yescharacteristic
318C4⋊C4C22×D5911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4C22⋊D5911yescharacteristic
329C22⋊C4C22⋊D5911yescharacteristic
330C42—21no—
331C42C22×D5911yescharacteristic
332C23—21no—
333C23—1181no—
334C23—1181no—
335C23—4721no—
336C23—2362no—
337C23—2362no—
338C23C2×C22⋊D5911yescharacteristic
339C23C2×C22⋊D5911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—1181no—
345Q8—1181no—
346Q8D4×D5912yes—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—592no—
353D4—1181no—
354D4—1181no—
355D4—1181no—
356D4—4721no—
357D4—2362no—
358D4—2362no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—4721no—
371C2×C4—2362no—
372C2×C4C2×C22⋊D5911yescharacteristic
373C2×C4C2×C22⋊D5911yescharacteristic
374C2×C4C2×C22⋊D5911yescharacteristic
375C2×C4C2×C22⋊D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—592no—
378C8—1181no—
379C8—1181no—
380C8—1181no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—1182no—
391C22—4724no—
392C22—2361no—
393C22—2361no—
394C22—2361no—
395C22—2361no—
396C22—2361no—
397C22C22×C22⋊D5911yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—2361no—
406C4—2361no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377211yescharacteristic
409C2—41no—
410C2—41no—
411C2—81no—
412C2—4721no—
413C2—2362no—
414C2D4×C22⋊D5911yescharacteristic
415C2#1683820011yescharacteristic
416C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3275
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14273758C2semidirect
2. C2×#14273752C2semidirect
3. #16838048C2semidirect
4. #16837784C2semidirect
5. #16837658C2semidirect
6. #16837653C2semidirect
7. #16837624C2semidirect
8. #16837614C2semidirect
9. #16837564C2semidirect
10. #16837552C2semidirect
11. #16837545C2semidirect
12. #16837541C2semidirect
13. C4×#11745671C2semidirect
14. #16837480C2semidirect
15. C59×#548C2semidirect
20. C2×#11745672C22semidirect
21. C2×#11745672C22semidirect
22. C2×#11745670C22semidirect
30. C2×#11745664C22semidirect
39. #14273658C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273651C22semidirect
42. #14273651C22semidirect
43. #14273650C22semidirect
44. #14273648C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. C4×C59⋊C8C22semidirect
51. C22×Q8×C59C22semidirect
53. #124×C59C22semidirect
57. #121×C59C22semidirect
58. C4×Q8×C59C22semidirect
107. #11745671D4semidirect
211. #548D59semidirect
224. C59#3275semidirect
227. C22×Q8C2×D59semidirect
244. #124C2×D59semidirect
252. #121C2×D59semidirect
254. C4×Q8C2×D59semidirect