Finite Group Databasebeta

← #21433603

Subgroups — #21433603

Order 7552.

494 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273754C211yesmaximal, characteristic
2C2×SD16×D59C211yesmaximal, characteristic, complemented
3#16837977C211yesmaximal, characteristic, complemented
4#16837874C211yesmaximal, characteristic, complemented
5#16837620C211yesmaximal, characteristic, complemented
6#16837619C211yesmaximal, characteristic, complemented
7#16837618C211yesmaximal, characteristic, complemented
8#16837617C211yesmaximal, characteristic, complemented
9#16837606C211yesmaximal, characteristic, complemented
10#16837605C211yesmaximal, characteristic, complemented
11#16837604C211yesmaximal, characteristic, complemented
12#16837427C211yesmaximal, characteristic, complemented
13#16837409C211yesmaximal, characteristic, complemented
14#16837397C211yesmaximal, characteristic, complemented
15C59×#461C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19#14273754—24no—
20C2×#11745660C2211yescharacteristic
21C2×#11745670C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic
24SD16×D59—24no—
25C2×D472C2211yescharacteristic
26C2×#11745669C2211yescharacteristic
27C2×#11745659C2211yescharacteristic
28C2×C8×D59C2211yescharacteristic
29#14273725C2211yescharacteristic, complemented
30#14273716C2211yescharacteristic, complemented
31#14273715C2211yescharacteristic, complemented
32#14273712—21no—
33#14273712—21no—
34#14273705—21no—
35#14273705—21no—
36C4×D236C2211yescharacteristic
37D4×Dic59C2211yescharacteristic
38#14273689C2211yescharacteristic
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#14273651C2211yescharacteristic, complemented
50#14273651C2211yescharacteristic, complemented
51#14273650C2211yescharacteristic, complemented
52#14273649C2211yescharacteristic, complemented
53#14273647C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic
55C2×SD16×C59C2211yescharacteristic
56C4⋊Q8×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic
58C4⋊C8×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#103×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C2×C22⋊D59—21no—
67C22×Dic59—21no—
68#11745689—22no—
69#11745689—22no—
70Q8×D59—22no—
71Q8×D59—22no—
72D4×D59—22no—
73D4×D59D414yes—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59C2311yescharacteristic
82C2×Dic118—21no—
83C2×Dic118C2311yescharacteristic
84SD16×C59—22no—
85SD16×C59—22no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59—21no—
89C4⋊C4×C59—21no—
90C4⋊C4×C59C2311yescharacteristic
91C22⋊C4×C59—21no—
92C42×C59C2311yescharacteristic
93C22⋊Dic59—21no—
94#11745671—22no—
95#11745671—22no—
96#11745670—22no—
97#11745669—22no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4D411yescharacteristic
106(C2×D59)⋊C4D411yescharacteristic
107C4⋊Dic59C2311yescharacteristic
108Dic59⋊C4—21no—
109Dic59⋊C4—21no—
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—
121C22×D59—21no—
122C22×D59—24no—
123C22×D59—21no—
124C22×D59—81no—
125C22×D59—81no—
126C22×D59C2×D411yescharacteristic
127Q8×C59—21no—
128Q8×C59—21no—
129Q8×C59—21no—
130Q8×C59—21no—
131D4×C59—21no—
132D4×C59C2×D412yes—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—81no—
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—24no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—81no—
144C2×Dic59C2×D411yescharacteristic
145C2×Dic59C2×D411yescharacteristic
146C2×Dic59C2×D411yescharacteristic
147D236—21no—
148D236—21no—
149D236—21no—
150D236—42no—
151D236C2×D412yes—
152C4×D59—42no—
153C4×D59—42no—
154C4×D59—81no—
155C4×D59—81no—
156C4×D59C2×D412yes—
157C4×D59#4112yes—
158Dic118—21no—
159Dic118—21no—
160Dic118—42no—
161C8×C59—21no—
162C8×C59—21no—
163C59⋊C8—21no—
164C59⋊C8—21no—
165C22×C59—22no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59C22×D411yescharacteristic
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—22no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—84no—
178C2×D59#12112yes—
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—41no—
182C4×C59—41no—
183C4×C59—41no—
184C4×C59C22×D411yescharacteristic
185C4×C59C2×#4111yescharacteristic
186Dic59—21no—
187Dic59—21no—
188Dic59—41no—
189Dic59—41no—
190Dic59#12112yes—
191#3042—591nomaximal, Sylow
192C2×C59—42no—
193C2×C59C2×#12111yescharacteristic
194C2×C59#57711yescharacteristic
195C2×C59#57711yescharacteristic
196D59—22no—
197D59—42no—
198D59—81no—
199C2×AGL(1,ℤ/8)—591no—
200C22×SD16—591no—
201#536—591no—
202#518—591no—
203#463—591no—
204#463—591no—
205#463—591no—
206#463—591no—
207#461—591no—
208#461—591no—
209#461—591no—
210#461D5911yescharacteristic, complemented
211#424—591no—
212#419—591no—
213#416—591no—
214C59#304211yescharacteristic, complemented, Sylow
215C2×#41—591no—
216C22×Q8—591no—
217C22×D4—591no—
218AGL(1,ℤ/8)—1184no—
219C2×SD16—591no—
220C2×SD16—591no—
221C2×SD16—591no—
222C2×SD16—591no—
223C2×SD16—1184no—
224C2×SD16C2×D5911yescharacteristic
225C2×SD16C2×D5911yescharacteristic
226C2×D8—591no—
227C2×D8—591no—
228C2×M16—591no—
229C22×C8—591no—
230C4⋊Q8—591no—
231C4⋊Q8C2×D5911yescharacteristic, complemented
232#124—591no—
233#124—591no—
234#123—1181no—
235#123—1181no—
236C22⋊Q8—1181no—
237C22⋊Q8—1181no—
238C4×D4—591no—
239C4×D4—591no—
240C4×D4—591no—
241C4×D4—1181no—
242C4×D4—1181no—
243C4×D4C2×D5911yescharacteristic
244#117—591no—
245#117—591no—
246C2×C22⋊C4—1181no—
247C2×C22⋊C4—1181no—
248C4⋊C8—591no—
249C4⋊C8—591no—
250C4⋊C8—591no—
251C4⋊C8C2×D5911yescharacteristic, complemented
252#103—591no—
253#103—591no—
254#103—591no—
255#103—591no—
256#103C2×D5911yescharacteristic, complemented
257#103C2×D5911yescharacteristic, complemented
258#102—591no—
259#102—591no—
260C24—1181no—
261#41—1182no—
262#41—1182no—
263C2×Q8—591no—
264C2×Q8—1181no—
265C2×Q8—1182no—
266C2×Q8—1182no—
267C2×Q8C22×D5911yescharacteristic
268C2×Q8C22×D5911yescharacteristic
269C2×D4—594no—
270C2×D4—591no—
271C2×D4—591no—
272C2×D4—1181no—
273C2×D4—1182no—
274C2×D4—1181no—
275C2×D4C22×D5911yescharacteristic
276C22×C4—21no—
277C22×C4—591no—
278C22×C4—1181no—
279C22×C4—1181no—
280C22×C4—1181no—
281C22×C4—1181no—
282C22×C4—1181no—
283SD16—22no—
284SD16—22no—
285SD16—1182no—
286SD16—1182no—
287SD16—1182no—
288SD16—1182no—
289D8—1182no—
290D8—1182no—
291M16—1182no—
292C2×C8—591no—
293C2×C8—591no—
294C2×C8—1182no—
295C2×C8C22×D5911yescharacteristic
296C2×C8C22×D5911yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—591no—
300C4⋊C4—591no—
301C4⋊C4—591no—
302C4⋊C4—1181no—
303C4⋊C4—1181no—
304C4⋊C4C22×D5911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—591no—
307C22⋊C4—591no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C42—591no—
317C42—1181no—
318C42C22×D5911yescharacteristic
319C23—21no—
320C23—591no—
321C23—1184no—
322C23—1181no—
323C23—1181no—
324C23—4721no—
325C23—4721no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—1181no—
331Q8—1181no—
332Q8—2362no—
333D4—21no—
334D4—592no—
335D4—1184no—
336D4—1181no—
337D4—1181no—
338D4—1181no—
339D4—2362no—
340D4D4×D5912yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—591no—
346C2×C4—592no—
347C2×C4—592no—
348C2×C4—591no—
349C2×C4—591no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—4721no—
353C2×C4—4721no—
354C2×C4—4721no—
355C2×C4—2362no—
356C2×C4—2362no—
357C2×C4D4×D5911yescharacteristic
358C2×C4D4×D5911yescharacteristic
359C2×C4C23×D5911yescharacteristic
360C8—21no—
361C8—21no—
362C8—1181no—
363C8—1181no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—592no—
368C22—1181no—
369C22—1181no—
370C22—1182no—
371C22—4724no—
372C22—2361no—
373C22—2361no—
374C22—2361no—
375C22—2361no—
376C22—2361no—
377C22C2×D4×D5911yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—592no—
384C4—1181no—
385C4—1181no—
386C4—2361no—
387C4—2361no—
388C4C2×D4×D5911yescharacteristic
389C4#41×D5911yescharacteristic
390C2—42no—
391C2—1182no—
392C2—4721no—
393C2—2362no—
394C2#121×D5911yescharacteristic
395C2#1683820811yescharacteristic
396C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59#3042
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D59C2semidirect
3. #16837977C2semidirect
4. #16837874C2semidirect
5. #16837620C2semidirect
6. #16837619C2semidirect
7. #16837618C2semidirect
8. #16837617C2semidirect
9. #16837606C2semidirect
10. #16837605C2semidirect
11. #16837604C2semidirect
12. #16837427C2semidirect
13. #16837409C2semidirect
14. #16837397C2semidirect
15. C59×#461C2semidirect
29. #14273725C22semidirect
30. #14273716C22semidirect
31. #14273715C22semidirect
45. C4⋊(C59⋊C8)C22semidirect
46. Dic59⋊C8C22semidirect
47. Dic59⋊C8C22semidirect
48. #14273652C22semidirect
49. #14273651C22semidirect
50. #14273651C22semidirect
51. #14273650C22semidirect
52. #14273649C22semidirect
53. #14273647C22semidirect
56. C4⋊Q8×C59C22semidirect
58. C4⋊C8×C59C22semidirect
59. #103×C59C22semidirect
60. #103×C59C22semidirect
210. #461D59semidirect
214. C59#3042semidirect
231. C4⋊Q8C2×D59semidirect
251. C4⋊C8C2×D59semidirect
256. #103C2×D59semidirect
257. #103C2×D59semidirect