Finite Group Databasebeta

← #21435948

Subgroups — #21435948

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838098C211yesmaximal, characteristic, complemented
2#16838048C211yesmaximal, characteristic, complemented
3#16837757C211yesmaximal, characteristic, complemented
4#16837738C211yesmaximal, characteristic, complemented
5#16837727C211yesmaximal, characteristic, complemented
6#16837703C211yesmaximal, characteristic, complemented
7#16837638C211yesmaximal, characteristic, complemented
8#16837631C211yesmaximal, characteristic, complemented
9#16837618C211yesmaximal, characteristic, complemented
10#16837549C211yesmaximal, characteristic, complemented
11#16837538C211yesmaximal, characteristic, complemented
12C4×D472C211yesmaximal, characteristic, complemented
13#16837399C211yesmaximal, characteristic, complemented
14C2×#14273649C211yesmaximal, characteristic, complemented
15C8×D4×C59C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C2×#11745660C2211yescharacteristic, complemented
19C2×D472C2211yescharacteristic
20C2×D472C2211yescharacteristic
21#14273722—21no—
22#14273719C2211yescharacteristic, complemented
23#14273715C2211yescharacteristic
24#14273712—21no—
25#14273709—21no—
26#14273706C2211yescharacteristic
27#14273701C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273701C2211yescharacteristic, complemented
30#14273700—21no—
31#14273699—21no—
32#14273695—21no—
33C4×D236C2211yescharacteristic
34C4×D236C2211yescharacteristic, complemented
35(C22⋊D59)⋊C4—21no—
36#14273686C2211yescharacteristic, complemented
37C2×C4⋊Dic59C2211yescharacteristic
38C22⋊C4×D59—21no—
39#14273661C2211yescharacteristic, complemented
40#14273661C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic, complemented
52C22×C8×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic, complemented
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic, complemented
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic, complemented
58C4×C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59D411yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C22×Dic59—21no—
68#11745685—22no—
69#11745685—41no—
70C2×D236—22no—
71C2×D236—21no—
72C2×D236—41no—
73C2×D236C2311yescharacteristic
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×Dic118C2311yescharacteristic
80C2×C8×C59—41no—
81C2×C8×C59—41no—
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C4⋊C4×C59D411yescharacteristic
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59C2311yescharacteristic
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108D472—22no—
109D472—41no—
110#11745660—41no—
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—81no—
119D4×C59—22no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2411yescharacteristic
129C22⋊D59—42no—
130C22⋊D59—42no—
131C22⋊D59—81no—
132C22⋊D59—81no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—81no—
139D236—21no—
140D236—21no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—42no—
145D236#4112yes—
146C4×D59—42no—
147C4×D59—81no—
148C4×D59—81no—
149Dic118—21no—
150Dic118—21no—
151C8×C59—21no—
152C8×C59—21no—
153C8×C59—21no—
154C8×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59#13512yes—
161C22×C59C22×D411yescharacteristic
162C2×D59—22no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—84no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—21no—
175C4×C59—21no—
176C4×C59C2×#4111yescharacteristic
177C4×C59H(5,𝔽2)11yescharacteristic
178Dic59—41no—
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3297—591nomaximal, Sylow
184C2×C59—22no—
185C2×C59—41no—
186C2×C59#54611yescharacteristic
187C2×C59C2×#13511yescharacteristic
188C2×C59#57611yescharacteristic
189D59—42no—
190D59—81no—
191D59—81no—
192#553—591no—
193#546—591no—
194#488—591no—
195#484—591no—
196#482—591no—
197#478—591no—
198#466—591no—
199#465—591no—
200#463—591no—
201#449—591no—
202#447—591no—
203C4×D8—591no—
204C8×D4D5911yescharacteristic, complemented
205#416—591no—
206C2×#102—591no—
207C59#329711yescharacteristic, complemented, Sylow
208C2×#41—591no—
209C22×D4—591no—
210C2×SD16—591no—
211C2×D8—591no—
212C2×D8—591no—
213C22×C8C2×D5911yescharacteristic
214C22×C8C2×D5911yescharacteristic, complemented
215#126—1181no—
216#125—591no—
217#124—591no—
218#123—1181no—
219#123—1181no—
220C22⋊Q8—591no—
221#121—591no—
222#121—591no—
223#121—591no—
224#121—1181no—
225#121—1181no—
226#120—1181no—
227C4×D4—591no—
228C4×D4—591no—
229C4×D4—1181no—
230C4×D4C2×D5911yescharacteristic
231#117—591no—
232C2×C4⋊C4—591no—
233C2×C22⋊C4—1181no—
234#107—591no—
235#107—591no—
236#106—591no—
237C4⋊C8C2×D5911yescharacteristic, complemented
238#103—591no—
239#103—591no—
240#103—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248C22⋊C8C2×D5911yescharacteristic
249C22⋊C8C2×D5911yescharacteristic, complemented
250C4×C8C2×D5911yescharacteristic, complemented
251C24—1181no—
252#41—1182no—
253#41—2361no—
254C2×Q8—591no—
255C2×D4—591no—
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—1182no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—2361no—
265C2×D4D23611yescharacteristic
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4—1181no—
270C22×C4C22×D5911yescharacteristic
271C22×C4C22×D5911yescharacteristic
272SD16—2361no—
273D8—1182no—
274D8—2361no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D5911yescharacteristic
278C2×C8C22×D5911yescharacteristic
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4—1181no—
289C4⋊C4D23611yescharacteristic
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4D23611yescharacteristic
300C22⋊C4D23611yescharacteristic
301C42—1181no—
302C42C22×D5911yescharacteristic
303C23—1181no—
304C23—1181no—
305C23—1181no—
306C23—4721no—
307C23—2362no—
308C23—2362no—
309C23C2×D23611yescharacteristic
310C23C2×D23611yescharacteristic
311Q8—1181no—
312Q8—1181no—
313D4—22no—
314D4—592no—
315D4—1181no—
316D4—1181no—
317D4—1181no—
318D4—1181no—
319D4—1181no—
320D4—4721no—
321D4—4721no—
322D4—2362no—
323D4—2362no—
324D4—2362no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—4721no—
335C2×C4—4721no—
336C2×C4—4721no—
337C2×C4—2362no—
338C2×C4C2×D23611yescharacteristic
339C2×C4C2×D23611yescharacteristic
340C2×C4C2×D23611yescharacteristic
341C2×C4C2×D23611yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—1182no—
353C22—4724no—
354C22—2361no—
355C22—2361no—
356C22—2361no—
357C22—2361no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22—2361no—
362C22#1427374912yes—
363C22C22×D23611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4—2361no—
372C4—2361no—
373C4#41×D5911yescharacteristic
374C4#1427377211yescharacteristic
375C2—22no—
376C2—41no—
377C2—4721no—
378C2—4721no—
379C2—2362no—
380C2#1683804711yescharacteristic
381C2C2×#1427374911yescharacteristic
382C2#1683820711yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC8×D4×C59C2
socleC22×C59C22×D4
hypercenterC8×D4D59
hypocenterC59#3297
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #16838098C2semidirect
2. #16838048C2semidirect
3. #16837757C2semidirect
4. #16837738C2semidirect
5. #16837727C2semidirect
6. #16837703C2semidirect
7. #16837638C2semidirect
8. #16837631C2semidirect
9. #16837618C2semidirect
10. #16837549C2semidirect
11. #16837538C2semidirect
12. C4×D472C2semidirect
13. #16837399C2semidirect
14. C2×#14273649C2semidirect
15. C8×D4×C59C2semidirect
18. C2×#11745660C22semidirect
22. #14273719C22semidirect
29. #14273701C22semidirect
34. C4×D236C22semidirect
36. #14273686C22semidirect
39. #14273661C22semidirect
40. #14273661C22semidirect
41. #14273659C22semidirect
42. #14273652C22semidirect
43. #14273652C22semidirect
44. #14273652C22semidirect
51. #14273649C22semidirect
53. C22×C8×C59C22semidirect
55. C4⋊C8×C59C22semidirect
57. C22⋊C8×C59C22semidirect
58. C4×C8×C59C22semidirect
204. C8×D4D59semidirect
207. C59#3297semidirect
214. C22×C8C2×D59semidirect
237. C4⋊C8C2×D59semidirect
249. C22⋊C8C2×D59semidirect
250. C4×C8C2×D59semidirect