Finite Group Databasebeta

← #21435155

Subgroups — #21435155

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838005C211yesmaximal, characteristic, complemented
2#16837973C211yesmaximal, characteristic, complemented
3#16837790C211yesmaximal, characteristic, complemented
4#16837773C211yesmaximal, characteristic, complemented
5#16837769C211yesmaximal, characteristic, complemented
6#16837755C211yesmaximal, characteristic, complemented
7#16837616C211yesmaximal, characteristic, complemented
8#16837615C211yesmaximal, characteristic, complemented
9#16837606C211yesmaximal, characteristic, complemented
10#16837605C211yesmaximal, characteristic, complemented
11#16837547C211yesmaximal, characteristic, complemented
12#16837543C211yesmaximal, characteristic, complemented
13#16837540C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C22×Dic118C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745671C2211yescharacteristic
22C2×#11745669C2211yescharacteristic
23#14273725C2211yescharacteristic
24#14273725C2211yescharacteristic
25#14273723C2211yescharacteristic
26#14273718C2211yescharacteristic
27#14273714C2211yescharacteristic
28#14273714C2211yescharacteristic
29#14273711—21no—
30#14273709—21no—
31#14273708—21no—
32#14273708—21no—
33#14273706—21no—
34#14273706—21no—
35#14273701C2211yescharacteristic
36#14273699—21no—
37#14273698—21no—
38D4×Dic59C2211yescharacteristic
39#14273689C2211yescharacteristic
40#14273686C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273650C2211yescharacteristic
48#14273648C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50#14273637C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59#41×C59—41no—
60#41×C59—41no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C22×Dic59—21no—
72C22×Dic59—21no—
73C2×D236C2311yescharacteristic
74C2×C4×D59—21no—
75C2×Dic118—21no—
76C2×Dic118—41no—
77C2×Dic118—41no—
78C2×Dic118C2311yescharacteristic
79C2×Dic118C2311yescharacteristic
80SD16×C59—41no—
81D8×C59—41no—
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59D411yescharacteristic
92C22⋊Dic59D411yescharacteristic
93#11745671—41no—
94#11745670—41no—
95#11745670—41no—
96#11745669—41no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59D411yescharacteristic
101C4⋊Dic59D411yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C4×Dic59C2311yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745660—41no—
113#11745660—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59C2×D411yescharacteristic
117C22×D59—21no—
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—42no—
125D4×C59—81no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—42no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—81no—
134C22⋊D59—81no—
135C22⋊D59—81no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—42no—
140C2×Dic59—81no—
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144C2×Dic59C2×D411yescharacteristic
145D236—21no—
146D236—21no—
147C4×D59—81no—
148Dic118—21no—
149Dic118—21no—
150Dic118—21no—
151Dic118—21no—
152Dic118—42no—
153C8×C59—21no—
154C8×C59—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59C22×D411yescharacteristic
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C4×C59—21no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59H(5,𝔽2)11yescharacteristic
174C4×C59H(5,𝔽2)11yescharacteristic
175Dic59—21no—
176Dic59—21no—
177Dic59—21no—
178Dic59—21no—
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182#3221—591nomaximal, Sylow
183C2×C59—41no—
184C2×C59—81no—
185C2×C59—81no—
186C2×C59#53511yescharacteristic
187C2×C59#57711yescharacteristic
188C2×C59#57711yescharacteristic
189D59—81no—
190#540—591no—
191#536—591no—
192#496—591no—
193#492—591no—
194#491—591no—
195#488—591no—
196#463—591no—
197#463—591no—
198#461—591no—
199#461—591no—
200#449—591no—
201#449D5911yescharacteristic, complemented
202#448—591no—
203#448—591no—
204#433—591no—
205C59#322111yescharacteristic, complemented, Sylow
206C2×#41C2×D5911yescharacteristic
207C22×Q8—591no—
208C2×SD16—591no—
209C2×SD16—591no—
210C2×SD16—591no—
211C2×SD16—591no—
212C2×SD16—591no—
213C2×SD16C2×D5911yescharacteristic
214C2×D8—591no—
215C2×D8C2×D5911yescharacteristic
216C4⋊Q8—591no—
217C4⋊Q8—591no—
218#127—591no—
219#125—591no—
220#124—591no—
221#124—591no—
222#123—1181no—
223#123—1181no—
224#123—1181no—
225#123—1181no—
226C22⋊Q8—1181no—
227C22⋊Q8—1181no—
228#121—591no—
229#121—1181no—
230#121—1181no—
231#121C2×D5911yescharacteristic
232C4×D4—591no—
233C4×D4—591no—
234#117—591no—
235C4⋊C8—591no—
236C4⋊C8—591no—
237#103—591no—
238#103—591no—
239#103—591no—
240#103—591no—
241#103—591no—
242#103C2×D5911yescharacteristic
243#102—591no—
244#102C2×D5911yescharacteristic
245C22⋊C8—591no—
246C22⋊C8C2×D5911yescharacteristic
247#97—591no—
248C4×C8—591no—
249#41—41no—
250#41—41no—
251C2×Q8—591no—
252C2×Q8—591no—
253C2×Q8—1181no—
254C2×Q8—2361no—
255C2×Q8—2361no—
256C2×Q8C22×D5911yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—591no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4C22×D5911yescharacteristic
264C2×D4C22×D5911yescharacteristic
265C22×C4—21no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4C22×D5911yescharacteristic
270SD16—41no—
271SD16—2361no—
272SD16—2361no—
273SD16—2361no—
274SD16—2361no—
275SD16—2361no—
276D8—41no—
277D8—2361no—
278C2×C8—591no—
279C2×C8—591no—
280C2×C8C22×D5911yescharacteristic
281C2×C8C22×D5911yescharacteristic
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4C22×D5911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—591no—
294C22⋊C4—591no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C42—591no—
303C42—591no—
304C23—21no—
305C23—21no—
306C23—1181no—
307C23D4×D5911yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—1181no—
311Q8—1181no—
312Q8—1181no—
313Q8—1181no—
314Q8—2362no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—81no—
321D4—1181no—
322D4—1181no—
323D4—4721no—
324D4—4721no—
325D4—4721no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—591no—
332C2×C4—591no—
333C2×C4—591no—
334C2×C4—591no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—4721no—
339C2×C4—4721no—
340C2×C4—2362no—
341C2×C4D4×D5911yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1181no—
346C8—1181no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—2361no—
357C22—2361no—
358C22—2361no—
359C22C2×D4×D5911yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—1181no—
364C4—1181no—
365C4—1181no—
366C4—1181no—
367C4—2361no—
368C4—2361no—
369C4—2361no—
370C4#1427377211yescharacteristic
371C4#1427377211yescharacteristic
372C2—41no—
373C2—81no—
374C2—81no—
375C2—4721no—
376C2#1683796711yescharacteristic
377C2#1683820911yescharacteristic
378C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3221
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16838005C2semidirect
2. #16837973C2semidirect
3. #16837790C2semidirect
4. #16837773C2semidirect
5. #16837769C2semidirect
6. #16837755C2semidirect
7. #16837616C2semidirect
8. #16837615C2semidirect
9. #16837606C2semidirect
10. #16837605C2semidirect
11. #16837547C2semidirect
12. #16837543C2semidirect
13. #16837540C2semidirect
14. #16837460C2semidirect
15. C59×#449C2semidirect
201. #449D59semidirect
205. C59#3221semidirect