Finite Group Databasebeta

← #21436350

Subgroups — #21436350

Order 7552.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838100C211yesmaximal, characteristic, complemented
2#16838059C211yesmaximal, characteristic, complemented
3#16837755C211yesmaximal, characteristic, complemented
4#16837732C211yesmaximal, characteristic, complemented
5#16837724C211yesmaximal, characteristic, complemented
6#16837711C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837616C211yesmaximal, characteristic, complemented
10#16837547C211yesmaximal, characteristic, complemented
11#16837542C211yesmaximal, characteristic, complemented
12#16837487C211yesmaximal, characteristic, complemented
13#16837478C211yesmaximal, characteristic, complemented
14#16837409C211yesmaximal, characteristic, complemented
15C59×#417C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21#14273722—21no—
22#14273718C2211yescharacteristic
23#14273714—21no—
24#14273714C2211yescharacteristic
25#14273712—21no—
26#14273706—21no—
27#14273706C2211yescharacteristic
28#14273702C2211yescharacteristic
29#14273701—21no—
30#14273701C2211yescharacteristic
31#14273698—21no—
32#14273698C2211yescharacteristic
33Q8×Dic59C2211yescharacteristic
34#14273689C2211yescharacteristic
35C4×C22⋊D59—21no—
36C4×C22⋊D59—21no—
37C4×C22⋊D59C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273658C2211yescharacteristic
41#14273658C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273648C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic
54C2×C4⋊C4×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59D411yescharacteristic
70Q8×D59—22no—
71Q8×D59—41no—
72C2×D236—21no—
73C2×D236C2311yescharacteristic
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×C4×D59C2311yescharacteristic
77C2×Dic118—21no—
78C2×Dic118C2311yescharacteristic
79M16×C59—41no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59D411yescharacteristic
90#11745671—22no—
91#11745669—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745660—41no—
110#11745659—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59#4112yes—
117D4×C59—21no—
118D4×C59—21no—
119D4×C59—42no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—42no—
126C2×C4×C59—81no—
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2411yescharacteristic
129C22⋊D59—41no—
130C22⋊D59—42no—
131C22⋊D59—42no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138D236—21no—
139D236—21no—
140D236—81no—
141C4×D59—21no—
142C4×D59—21no—
143C4×D59—42no—
144C4×D59—81no—
145Dic118—21no—
146Dic118—21no—
147Dic118—42no—
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—41no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—22no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—21no—
172Dic59—21no—
173Dic59—21no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3326—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59#57511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—41no—
184D59—81no—
185#553—591no—
186#548—591no—
187#488—591no—
188#483—591no—
189#482—591no—
190#479—591no—
191#469—591no—
192#468—591no—
193#463—591no—
194#449—591no—
195#448—591no—
196C4×SD16—591no—
197#436—591no—
198#419—591no—
199#417D5911yescharacteristic, complemented
200C59#332611yescharacteristic, complemented, Sylow
201C2×#41C2×D5911yescharacteristic
202C22×Q8—591no—
203C2×SD16—591no—
204C2×SD16—591no—
205C2×D8—591no—
206C2×M16—591no—
207C2×M16C2×D5911yescharacteristic
208#126—1181no—
209#125—591no—
210#124—591no—
211#124—1181no—
212#123—1181no—
213C22⋊Q8—591no—
214C22⋊Q8—1181no—
215#121—591no—
216#121—591no—
217#121—591no—
218#121—1181no—
219#121—1181no—
220C4×Q8—591no—
221C4×D4—591no—
222C4×D4—591no—
223C4×D4—1181no—
224C4×D4—1181no—
225#117—591no—
226C2×C4⋊C4C2×D5911yescharacteristic
227#107—591no—
228#106—591no—
229#106—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103C2×D5911yescharacteristic
236#103C2×D5911yescharacteristic
237#102—591no—
238#102—591no—
239#102C2×D5911yescharacteristic
240#102C2×D5911yescharacteristic
241C22⋊C8—591no—
242C22⋊C8—591no—
243C4×C8—591no—
244#41—22no—
245#41—41no—
246C2×Q8—591no—
247C2×Q8—1181no—
248C2×Q8—1182no—
249C2×Q8—2361no—
250C2×Q8C22×D5911yescharacteristic
251C2×D4—21no—
252C2×D4—591no—
253C2×D4—591no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4C22×D5911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—591no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4C22×D5911yescharacteristic
264SD16—1182no—
265SD16—2361no—
266D8—2361no—
267M16—41no—
268M16—2361no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4C22×D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C22⋊C4—591no—
284C22⋊C4—591no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—591no—
294C42—1181no—
295C42—1181no—
296C23—21no—
297C23—591no—
298C23—1181no—
299C23D4×D5911yescharacteristic
300Q8—21no—
301Q8—1181no—
302Q8—1181no—
303Q8—2362no—
304Q8#1174568512yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—1181no—
309D4—1181no—
310D4—4721no—
311D4—2361no—
312D4—2362no—
313D4—2362no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—81no—
321C2×C4—591no—
322C2×C4—591no—
323C2×C4—591no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—4721no—
330C2×C4—2362no—
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—1181no—
344C22—1181no—
345C22—1181no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—1181no—
355C4—1181no—
356C4—1181no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4C2×#1174568511yescharacteristic
361C4#1427377211yescharacteristic
362C2—41no—
363C2—81no—
364C2—4721no—
365C2—2361no—
366C2#1683804211yescharacteristic
367C2#1683820111yescharacteristic
368C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#417C2
socleC22×C59C22×D4
hypercenter#417D59
hypocenterC59#3326
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #16838100C2semidirect
2. #16838059C2semidirect
3. #16837755C2semidirect
4. #16837732C2semidirect
5. #16837724C2semidirect
6. #16837711C2semidirect
7. #16837654C2semidirect
8. #16837648C2semidirect
9. #16837616C2semidirect
10. #16837547C2semidirect
11. #16837542C2semidirect
12. #16837487C2semidirect
13. #16837478C2semidirect
14. #16837409C2semidirect
15. C59×#417C2semidirect
199. #417D59semidirect
200. C59#3326semidirect