Finite Group Databasebeta

← #21435931

Subgroups — #21435931

Order 7552.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838092C211yesmaximal, characteristic, complemented
2#16837756C211yesmaximal, characteristic, complemented
3#16837730C211yesmaximal, characteristic, complemented
4#16837723C211yesmaximal, characteristic, complemented
5#16837702C211yesmaximal, characteristic, complemented
6#16837641C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837621C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837553C211yesmaximal, characteristic, complemented
11C4×#11745670C211yesmaximal, characteristic, complemented
12D4×C59⋊C8C211yesmaximal, characteristic, complemented
13#16837398C211yesmaximal, characteristic, complemented
14C2×#14273648C211yesmaximal, characteristic, complemented
15C59×#546C211yesmaximal, characteristic
16C2×#11745672C2211yescharacteristic, complemented
17C2×#11745670C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C22×C59⋊C8C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic, complemented
21#14273720—21no—
22#14273719C2211yescharacteristic, complemented
23#14273717—21no—
24#14273708—21no—
25#14273706C2211yescharacteristic
26#14273706C2211yescharacteristic, complemented
27C4×Dic118C2211yescharacteristic, complemented
28#14273686C2211yescharacteristic, complemented
29#14273683—21no—
30C2×C4⋊Dic59C2211yescharacteristic
31#14273660C2211yescharacteristic, complemented
32#14273658C2211yescharacteristic, complemented
33#14273658C2211yescharacteristic, complemented
34C4⋊(C59⋊C8)C2211yescharacteristic, complemented
35#14273651C2211yescharacteristic, complemented
36#14273651C2211yescharacteristic, complemented
37#14273651C2211yescharacteristic, complemented
38#14273650C2211yescharacteristic, complemented
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic, complemented
47C4×C59⋊C8C2211yescharacteristic, complemented
48C2×#41×C59C2211yescharacteristic
49C22×D4×C59C2211yescharacteristic
50#124×C59C2211yescharacteristic
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53#121×C59—21no—
54#121×C59C2211yescharacteristic
55#120×C59—21no—
56C4×D4×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic
58C2×C22⋊C4×C59—21no—
59C24×C59—21no—
60#41×C59—22no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—22no—
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—41no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C2×D4×C59C2311yescharacteristic
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C22×Dic59—21no—
76C2×Dic118C2311yescharacteristic
77C4⋊C4×C59—21no—
78C4⋊C4×C59D411yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59D411yescharacteristic
86C22⋊C4×C59D411yescharacteristic
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91#11745672—41no—
92#11745670—22no—
93#11745670—41no—
94C4⋊Dic59—21no—
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—21no—
104C4×Dic59—21no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—42no—
114C23×C59—42no—
115C23×C59—81no—
116C23×C59C2×D411yescharacteristic
117C23×C59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—22no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—42no—
125D4×C59—42no—
126D4×C59—81no—
127D4×C59#4112yes—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—42no—
135C2×C4×C59—81no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2411yescharacteristic
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—42no—
146Dic118—21no—
147Dic118—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—22no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—84no—
164C22×C59#13512yes—
165C22×C59C22×D411yescharacteristic
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59C2×#4111yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177Dic59—41no—
178#3296—591nomaximal, Sylow
179C2×C59—22no—
180C2×C59—41no—
181C2×C59—42no—
182C2×C59—81no—
183C2×C59#54611yescharacteristic
184C2×C59C2×#13511yescharacteristic
185C2×C59#57711yescharacteristic
186#552—591no—
187#546D5911yescharacteristic
188#488—591no—
189#483—591no—
190#482—591no—
191#478—591no—
192#467—591no—
193#465—591no—
194#464—591no—
195#452—591no—
196#450—591no—
197C4×SD16—591no—
198C8×D4—591no—
199#416—591no—
200C2×#102—591no—
201C59#329611yescharacteristic, complemented, Sylow
202C2×#41C2×D5911yescharacteristic
203C22×D4C2×D5911yescharacteristic
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C22×C8—591no—
208C22×C8—591no—
209#126—1181no—
210#125—591no—
211#125—1181no—
212#124C2×D5911yescharacteristic
213#123—21no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8C2×D5911yescharacteristic
218#121—21no—
219#121C2×D5911yescharacteristic
220#120—21no—
221C4×Q8—591no—
222C4×D4C2×D5911yescharacteristic
223C4×D4C2×D5911yescharacteristic
224#117—591no—
225#117—1181no—
226C2×C4⋊C4—591no—
227C2×C22⋊C4—21no—
228#107—591no—
229#106—591no—
230#106—591no—
231C4⋊C8—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242C22⋊C8—591no—
243C22⋊C8—591no—
244C4×C8—591no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—591no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D5911yescharacteristic
256C2×D4C22×D5911yescharacteristic
257C2×D4C22×D5911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—1181no—
261C22×C4C22×D5911yescharacteristic
262C22×C4C22×D5911yescharacteristic
263Q16—2361no—
264SD16—1182no—
265SD16—2361no—
266C2×C8—591no—
267C2×C8—591no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—2361no—
271C2×C8—2361no—
272C4⋊C4—21no—
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4C22⋊D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4C22⋊D5911yescharacteristic
293C22⋊C4C22⋊D5911yescharacteristic
294C42—1181no—
295C42—1181no—
296C42C22×D5911yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D5911yescharacteristic
303C23C2×C22⋊D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1181no—
307Q8—1181no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1174568712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—2362no—
329C2×C4C2×C22⋊D5911yescharacteristic
330C2×C4C2×C22⋊D5911yescharacteristic
331C2×C4C2×C22⋊D5911yescharacteristic
332C2×C4C2×C22⋊D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—1181no—
335C8—1181no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1427374712yes—
351C22C22×C22⋊D5911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—2361no—
359C4—2361no—
360C4—2361no—
361C4—2361no—
362C4C2×#1174568711yescharacteristic
363C4#1427377211yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1683804611yescharacteristic
369C2C2×#1427374711yescharacteristic
370C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#546C2
socleC22×C59C22×D4
hypercenter#546D59
hypocenterC59#3296
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #16838092C2semidirect
2. #16837756C2semidirect
3. #16837730C2semidirect
4. #16837723C2semidirect
5. #16837702C2semidirect
6. #16837641C2semidirect
7. #16837629C2semidirect
8. #16837621C2semidirect
9. #16837564C2semidirect
10. #16837553C2semidirect
11. C4×#11745670C2semidirect
12. D4×C59⋊C8C2semidirect
13. #16837398C2semidirect
14. C2×#14273648C2semidirect
16. C2×#11745672C22semidirect
20. C22×C59⋊C8C22semidirect
22. #14273719C22semidirect
26. #14273706C22semidirect
27. C4×Dic118C22semidirect
28. #14273686C22semidirect
31. #14273660C22semidirect
32. #14273658C22semidirect
33. #14273658C22semidirect
34. C4⋊(C59⋊C8)C22semidirect
35. #14273651C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
38. #14273650C22semidirect
46. C22⋊(C59⋊C8)C22semidirect
47. C4×C59⋊C8C22semidirect
201. C59#3296semidirect