Finite Group Databasebeta

← #21435201

Subgroups — #21435201

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838019C211yesmaximal, characteristic, complemented
2#16837973C211yesmaximal, characteristic, complemented
3#16837793C211yesmaximal, characteristic, complemented
4#16837785C211yesmaximal, characteristic, complemented
5#16837760C211yesmaximal, characteristic, complemented
6#16837751C211yesmaximal, characteristic, complemented
7#16837623C211yesmaximal, characteristic, complemented
8#16837615C211yesmaximal, characteristic, complemented
9#16837611C211yesmaximal, characteristic, complemented
10#16837605C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837560C211yesmaximal, characteristic, complemented
13#16837540C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C2×Dic236C2211yescharacteristic
18C2×Dic236C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745670C2211yescharacteristic
22C2×#11745670C2211yescharacteristic
23#14273726C2211yescharacteristic
24#14273725C2211yescharacteristic
25#14273725C2211yescharacteristic
26#14273720—21no—
27#14273714—21no—
28#14273714C2211yescharacteristic
29#14273714C2211yescharacteristic
30#14273714C2211yescharacteristic
31#14273708—21no—
32#14273708—21no—
33#14273708—21no—
34#14273706—21no—
35#14273706—21no—
36#14273706C2211yescharacteristic
37#14273704—21no—
38#14273692C2211yescharacteristic
39D4×Dic59C2211yescharacteristic
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
68C22×Dic59—21no—
69C22×Dic59—21no—
70C2×Dic118—21no—
71C2×Dic118—21no—
72C2×Dic118—41no—
73C2×Dic118—41no—
74C2×Dic118C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77SD16×C59—41no—
78D8×C59—41no—
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C22⋊Dic59—21no—
84C22⋊Dic59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59D411yescharacteristic
92C22⋊Dic59D411yescharacteristic
93#11745672—41no—
94#11745670—41no—
95#11745670—41no—
96#11745670—41no—
97C4⋊Dic59D411yescharacteristic
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108C4×Dic59C2311yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112Dic236—41no—
113Dic236—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59C2×D411yescharacteristic
117Q8×C59—21no—
118Q8×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—42no—
124D4×C59—81no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—42no—
137C2×Dic59—81no—
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142Dic118—21no—
143Dic118—21no—
144Dic118—21no—
145Dic118—21no—
146Dic118—21no—
147Dic118—21no—
148Dic118—42no—
149Dic118—81no—
150C8×C59—21no—
151C8×C59—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59C22×D411yescharacteristic
164C4×C59—21no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59H(5,𝔽2)11yescharacteristic
168C4×C59H(5,𝔽2)11yescharacteristic
169Dic59—21no—
170Dic59—21no—
171Dic59—21no—
172Dic59—21no—
173Dic59—41no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3225—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—81no—
180C2×C59—81no—
181C2×C59#53511yescharacteristic
182C2×C59#57711yescharacteristic
183C2×C59#57811yescharacteristic
184#542—591no—
185#536—591no—
186#497—591no—
187#495—591no—
188#489—591no—
189#487—591no—
190#464—591no—
191#463—591no—
192#462—591no—
193#461—591no—
194#452—591no—
195#451—591no—
196#449D5911yescharacteristic
197#448—591no—
198#433—591no—
199C59#322511yescharacteristic, complemented, Sylow
200C2×#41C2×D5911yescharacteristic
201C22×Q8—591no—
202C2×Q16—591no—
203C2×Q16—591no—
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C2×SD16—591no—
208C2×SD16C2×D5911yescharacteristic
209C2×D8C2×D5911yescharacteristic
210C4⋊Q8—591no—
211C4⋊Q8—591no—
212C4⋊Q8—591no—
213#126—1181no—
214#124—591no—
215#124—591no—
216#124—591no—
217#124—1181no—
218#123—1181no—
219#123—1181no—
220#123—1181no—
221C22⋊Q8—591no—
222C22⋊Q8—1181no—
223C22⋊Q8—1181no—
224C22⋊Q8—1181no—
225#121C2×D5911yescharacteristic
226C4×Q8—591no—
227C4×D4—591no—
228#117—591no—
229C4⋊C8—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103C2×D5911yescharacteristic
237#102—591no—
238#102C2×D5911yescharacteristic
239C22⋊C8—591no—
240C22⋊C8C2×D5911yescharacteristic
241#97—591no—
242C4×C8—591no—
243#41—41no—
244#41—41no—
245C2×Q8—591no—
246C2×Q8—591no—
247C2×Q8—591no—
248C2×Q8—1181no—
249C2×Q8—1181no—
250C2×Q8—2361no—
251C2×Q8—2361no—
252C2×Q8C22×D5911yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C22×D5911yescharacteristic
256C2×D4C22×D5911yescharacteristic
257C22×C4—21no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4C22×D5911yescharacteristic
261Q16—2361no—
262Q16—2361no—
263Q16—2361no—
264SD16—41no—
265SD16—2361no—
266SD16—2361no—
267SD16—2361no—
268D8—41no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
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⋊C4—1181no—
283C4⋊C4C22×D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—591no—
286C22⋊C4—591no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C42—591no—
296C42—591no—
297C42—1181no—
298C23—21no—
299C23—21no—
300C23D4×D5911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—1181no—
304Q8—1181no—
305Q8—1181no—
306Q8—1181no—
307Q8—1181no—
308Q8—1181no—
309Q8—4721no—
310Q8—2362no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—591no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—591no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—4721no—
331C2×C4—2362no—
332C2×C4D4×D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C2×D4×D5911yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—1181no—
352C4—1181no—
353C4—1181no—
354C4—1181no—
355C4—2361no—
356C4—2361no—
357C4—2361no—
358C4—2361no—
359C4#1427377211yescharacteristic
360C4#1427377211yescharacteristic
361C2—41no—
362C2—81no—
363C2—81no—
364C2#1683796711yescharacteristic
365C2#1683821211yescharacteristic
366C2#1683821611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3225
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. #16838019C2semidirect
2. #16837973C2semidirect
3. #16837793C2semidirect
4. #16837785C2semidirect
5. #16837760C2semidirect
6. #16837751C2semidirect
7. #16837623C2semidirect
8. #16837615C2semidirect
9. #16837611C2semidirect
10. #16837605C2semidirect
11. #16837564C2semidirect
12. #16837560C2semidirect
13. #16837540C2semidirect
14. #16837460C2semidirect
199. C59#3225semidirect