Finite Group Databasebeta

← #21434051

Subgroups — #21434051

Order 7552.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837968C211yesmaximal, characteristic
2#16837882C211yesmaximal, characteristic, complemented
3#16837729C211yesmaximal, characteristic, complemented
4#16837726C211yesmaximal, characteristic, complemented
5#16837724C211yesmaximal, characteristic, complemented
6#16837722C211yesmaximal, characteristic, complemented
7#16837718C211yesmaximal, characteristic, complemented
8#16837716C211yesmaximal, characteristic, complemented
9#16837714C211yesmaximal, characteristic, complemented
10#16837441C211yesmaximal, characteristic, complemented
11#16837439C211yesmaximal, characteristic, complemented
12#16837405C211yesmaximal, characteristic, complemented
13#102×D59C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic, complemented
15C59×#482C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745659C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20#14273723—21no—
21#14273713—21no—
22#14273702C2211yescharacteristic
23#14273701C2211yescharacteristic
24#14273698C2211yescharacteristic
25#14273697—21no—
26#14273695—21no—
27C4×Dic118—21no—
28C4×D236—21no—
29(C22⋊D59)⋊C4—21no—
30(C22⋊D59)⋊C4—21no—
31#14273685C2211yescharacteristic
32#14273685C2211yescharacteristic
33#14273685C2211yescharacteristic, complemented
34C2×C4⋊Dic59C2211yescharacteristic, complemented
35C4⋊C4×D59C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic, complemented
37#14273661C2211yescharacteristic, complemented
38#14273661C2211yescharacteristic, complemented
39#14273660C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52#121×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic, complemented
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59—21no—
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59D411yescharacteristic
67C2×C22⋊D59D411yescharacteristic
68C22×Dic59—21no—
69D4×D59—22no—
70D4×D59—22no—
71#11745685—22no—
72#11745685—22no—
73C2×D236—21no—
74C2×D236D411yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79C2×C4×D59C2311yescharacteristic
80C2×Dic118D411yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C42×C59—21no—
89C22⋊Dic59—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101C4×Dic59—21no—
102C4×Dic59—21no—
103C4×Dic59—21no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106#11745659—22no—
107C8×D59—22no—
108C23×C59—21no—
109C23×C59C2×D411yescharacteristic
110C22×D59—21no—
111C22×D59—42no—
112C22×D59—81no—
113C22×D59—81no—
114C22×D59C2×D411yescharacteristic
115C22×D59C2×D411yescharacteristic
116D4×C59—21no—
117D4×C59—21no—
118D4×C59—81no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2411yescharacteristic
126C22⋊D59—22no—
127C22⋊D59—22no—
128C22⋊D59—42no—
129C22⋊D59—81no—
130C22⋊D59—81no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—81no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137D236—22no—
138D236—21no—
139D236—21no—
140D236—81no—
141C4×D59—21no—
142C4×D59—21no—
143C4×D59—81no—
144C4×D59—81no—
145C4×D59#4112yes—
146C4×D59#4112yes—
147Dic118—22no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—84no—
168C2×D59#12312yes—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59C2×#4111yescharacteristic
174C4×C59C2×#4111yescharacteristic
175Dic59—21no—
176Dic59—41no—
177Dic59—41no—
178Dic59—41no—
179Dic59#12312yes—
180#3096—591nomaximal, Sylow
181C2×C59—41no—
182C2×C59—81no—
183C2×C59C2×#12311yescharacteristic
184C2×C59#57611yescharacteristic
185C2×C59#57711yescharacteristic
186D59—22no—
187D59—41no—
188D59—81no—
189#535—591no—
190#520—591no—
191#482—591no—
192#482—591no—
193#482—591no—
194#482D5911yescharacteristic, complemented
195#481—591no—
196#481—591no—
197#480—591no—
198#480—591no—
199#428—591no—
200#427—591no—
201#418—591no—
202C2×#102—591no—
203#408—591no—
204C59#309611yescharacteristic, complemented, Sylow
205C2×#41—591no—
206C22×D4—591no—
207C2×M16—591no—
208C22×C8—591no—
209#127—1181no—
210#124—1181no—
211#121—591no—
212#121—591no—
213#121—591no—
214#121C2×D5911yescharacteristic
215#120—1181no—
216#120—1181no—
217C4×Q8—1181no—
218C4×D4—1181no—
219C4×D4—1181no—
220C4×D4—1181no—
221#117—591no—
222#117—591no—
223#117—591no—
224#117C2×D5911yescharacteristic, complemented
225C2×C4⋊C4—591no—
226C2×C4⋊C4—591no—
227C2×C4⋊C4—591no—
228#107—591no—
229#107—591no—
230#107—591no—
231#107C2×D5911yescharacteristic, complemented
232#106—591no—
233#106—591no—
234#106—591no—
235#106C2×D5911yescharacteristic, complemented
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242#102C2×D5911yescharacteristic
243#102C2×D5911yescharacteristic
244C22⋊C8—591no—
245C22⋊C8—591no—
246C22⋊C8—591no—
247C22⋊C8C2×D5911yescharacteristic, complemented
248C24—1181no—
249#41—1182no—
250#41—1182no—
251C2×Q8—591no—
252C2×D4—21no—
253C2×D4—591no—
254C2×D4—591no—
255C2×D4—591no—
256C2×D4—591no—
257C2×D4—1181no—
258C2×D4—1182no—
259C2×D4—1182no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4C22×D5911yescharacteristic
264C22×C4—591no—
265C22×C4—591no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4C22×D5911yescharacteristic
270M16—1182no—
271C2×C8—591no—
272C2×C8—591no—
273C2×C8—1182no—
274C2×C8C22×D5911yescharacteristic
275C2×C8C22×D5911yescharacteristic
276C4⋊C4—591no—
277C4⋊C4—591no—
278C4⋊C4—591no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4C22×D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C4⋊C4C22×D5911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—21no—
294C42—1181no—
295C42—1181no—
296C42—1181no—
297C23—21no—
298C23—591no—
299C23—591no—
300C23—1181no—
301C23—4721no—
302C23—4721no—
303C23—2362no—
304C23D4×D5911yescharacteristic
305Q8—1182no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—1182no—
310D4—1182no—
311D4—1182no—
312D4—1181no—
313D4—1181no—
314D4—4721no—
315D4—4721no—
316D4—4721no—
317D4—2362no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—591no—
324C2×C4—592no—
325C2×C4—592no—
326C2×C4—591no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—4721no—
333C2×C4—4721no—
334C2×C4—4721no—
335C2×C4D4×D5911yescharacteristic
336C2×C4C23×D5911yescharacteristic
337C8—21no—
338C8—21no—
339C8—1181no—
340C8—1181no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—592no—
348C22—1181no—
349C22—1181no—
350C22—1181no—
351C22—1181no—
352C22—1181no—
353C22—4724no—
354C22—2361no—
355C22—2361no—
356C22—2361no—
357C22C2×D4×D5911yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—592no—
363C4—1181no—
364C4—2361no—
365C4—2361no—
366C4—2361no—
367C4#41×D5911yescharacteristic
368C4#41×D5911yescharacteristic
369C2—41no—
370C2—81no—
371C2—1182no—
372C2—4721no—
373C2—2361no—
374C2#123×D5911yescharacteristic
375C2#1683820411yescharacteristic
376C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#482C2
socleC22×C59C22×D4
hypercenter#482D59
hypocenterC59#3096
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #16837882C2semidirect
3. #16837729C2semidirect
4. #16837726C2semidirect
5. #16837724C2semidirect
6. #16837722C2semidirect
7. #16837718C2semidirect
8. #16837716C2semidirect
9. #16837714C2semidirect
10. #16837441C2semidirect
11. #16837439C2semidirect
12. #16837405C2semidirect
13. #102×D59C2semidirect
14. #16837367C2semidirect
15. C59×#482C2semidirect
33. #14273685C22semidirect
34. C2×C4⋊Dic59C22semidirect
36. C4⋊C4×D59C22semidirect
37. #14273661C22semidirect
38. #14273661C22semidirect
39. #14273660C22semidirect
40. #14273658C22semidirect
41. #14273658C22semidirect
42. #14273658C22semidirect
49. C22⋊(C59⋊C8)C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
53. #117×C59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
58. C22⋊C8×C59C22semidirect
194. #482D59semidirect
204. C59#3096semidirect
224. #117C2×D59semidirect
231. #107C2×D59semidirect
235. #106C2×D59semidirect
247. C22⋊C8C2×D59semidirect