Finite Group Databasebeta

← #21435005

Subgroups — #21435005

Order 7552.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837981C211yesmaximal, characteristic, complemented
2#16837980C211yesmaximal, characteristic, complemented
3#16837733C211yesmaximal, characteristic, complemented
4#16837731C211yesmaximal, characteristic, complemented
5#16837719C211yesmaximal, characteristic, complemented
6#16837718C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837652C211yesmaximal, characteristic, complemented
9#16837630C211yesmaximal, characteristic, complemented
10#16837628C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837561C211yesmaximal, characteristic, complemented
13#16837544C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273707C2211yescharacteristic
23#14273706—21no—
24#14273706C2211yescharacteristic
25#14273704—21no—
26#14273703C2211yescharacteristic
27#14273703C2211yescharacteristic
28#14273701—21no—
29#14273700—21no—
30#14273699—21no—
31#14273699—21no—
32#14273699—21no—
33#14273698—21no—
34#14273698C2211yescharacteristic
35#14273698C2211yescharacteristic
36#14273698C2211yescharacteristic
37C2×C4⋊Dic59C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273659C2211yescharacteristic
41#14273658C2211yescharacteristic
42#14273658C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
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—
71C2×C22⋊D59—21no—
72C2×C22⋊D59D411yescharacteristic
73C2×C22⋊D59D411yescharacteristic
74C22×Dic59—21no—
75C22×Dic59—21no—
76#11745687—41no—
77#11745687—41no—
78#11745685—41no—
79#11745685—41no—
80C2×D236D411yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×C4×D59C2311yescharacteristic
84C2×Dic118D411yescharacteristic
85C2×Dic118C2311yescharacteristic
86SD16×C59—41no—
87D8×C59—41no—
88C2×C8×C59C2311yescharacteristic
89C2×C8×C59C2311yescharacteristic
90C4⋊C4×C59C2311yescharacteristic
91C22⋊C4×C59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96#11745672—41no—
97#11745670—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103C4⋊Dic59C2311yescharacteristic
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109Dic59⋊C4—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745659—41no—
113C8×D59—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59C2×D411yescharacteristic
117C22×D59C2×D411yescharacteristic
118C22×D59C2×D411yescharacteristic
119Q8×C59—21no—
120Q8×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—21no—
124D4×C59—21no—
125D4×C59—42no—
126D4×C59—81no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—42no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—41no—
135C22⋊D59—41no—
136C22⋊D59—42no—
137C22⋊D59—81no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—42no—
145C2×Dic59—81no—
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148D236—41no—
149C4×D59—21no—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—21no—
153C4×D59—81no—
154Dic118—21no—
155Dic118—21no—
156Dic118—41no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59C22×D411yescharacteristic
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—21no—
175C2×D59—21no—
176C2×D59—21no—
177C4×C59—21no—
178C4×C59—41no—
179C4×C59—41no—
180C4×C59H(5,𝔽2)11yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—21no—
183Dic59—21no—
184Dic59—41no—
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188#3204—591nomaximal, Sylow
189C2×C59—41no—
190C2×C59—81no—
191C2×C59—81no—
192C2×C59#53411yescharacteristic
193C2×C59#57711yescharacteristic
194C2×C59#57711yescharacteristic
195D59—41no—
196D59—41no—
197#537—591no—
198#537—591no—
199#483—591no—
200#483—591no—
201#481—591no—
202#481—591no—
203#470—591no—
204#469—591no—
205#465—591no—
206#465—591no—
207#452—591no—
208#452—591no—
209#449—591no—
210#449D5911yescharacteristic, complemented
211#408—591no—
212C59#320411yescharacteristic, complemented, Sylow
213C2×#41—591no—
214C2×#41—591no—
215C2×#41C2×D5911yescharacteristic
216C2×Q16—591no—
217C2×SD16—591no—
218C2×SD16C2×D5911yescharacteristic
219C2×D8C2×D5911yescharacteristic
220C2×M16—591no—
221C22×C8—591no—
222C22⋊Q8—591no—
223C22⋊Q8—591no—
224C22⋊Q8—591no—
225C22⋊Q8—591no—
226C22⋊Q8—1181no—
227C22⋊Q8—1181no—
228#121—591no—
229#121—591no—
230#121—591no—
231#121—1181no—
232#121—1181no—
233#121—1181no—
234#121—1181no—
235#121—1181no—
236#121—1181no—
237#121C2×D5911yescharacteristic
238C2×C4⋊C4—591no—
239C2×C4⋊C4—591no—
240#106—591no—
241#106—591no—
242#106—591no—
243#106—591no—
244#103—591no—
245#103—591no—
246#103—591no—
247#103C2×D5911yescharacteristic
248#102—591no—
249#102—591no—
250#102—591no—
251#102C2×D5911yescharacteristic
252C22⋊C8—591no—
253C22⋊C8—591no—
254C22⋊C8—591no—
255C22⋊C8C2×D5911yescharacteristic
256#41—41no—
257#41—41no—
258#41—2361no—
259#41—2361no—
260#41—2361no—
261#41—2361no—
262C2×Q8—591no—
263C2×Q8—591no—
264C2×Q8C22×D5911yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—591no—
268C2×D4—591no—
269C2×D4—591no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4C22×D5911yescharacteristic
275C2×D4C22×D5911yescharacteristic
276C22×C4—21no—
277C22×C4—591no—
278C22×C4—591no—
279C22×C4—1181no—
280C22×C4—1181no—
281C22×C4—1181no—
282C22×C4C22×D5911yescharacteristic
283Q16—2361no—
284SD16—41no—
285SD16—2361no—
286D8—41no—
287M16—2361no—
288C2×C8—591no—
289C2×C8—591no—
290C2×C8—2361no—
291C2×C8C22×D5911yescharacteristic
292C2×C8C22×D5911yescharacteristic
293C4⋊C4—591no—
294C4⋊C4—591no—
295C4⋊C4—591no—
296C4⋊C4—1181no—
297C4⋊C4—1181no—
298C4⋊C4—1181no—
299C4⋊C4—1181no—
300C4⋊C4—1181no—
301C4⋊C4—1181no—
302C4⋊C4C22×D5911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C23—21no—
312C23—21no—
313C23—591no—
314C23—591no—
315C23D4×D5911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—1181no—
319Q8—1181no—
320Q8—2361no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—4721no—
328D4—4721no—
329D4—4721no—
330D4—2361no—
331D4—2361no—
332D4—2361no—
333D4—2362no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—591no—
340C2×C4—591no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—4721no—
350C2×C4—4721no—
351C2×C4—2362no—
352C2×C4D4×D5911yescharacteristic
353C2×C4C23×D5911yescharacteristic
354C8—21no—
355C8—21no—
356C8—1181no—
357C8—1181no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—1181no—
368C22—1181no—
369C22—1181no—
370C22—1181no—
371C22—1181no—
372C22—1181no—
373C22C2×D4×D5911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—1181no—
378C4—1181no—
379C4—2361no—
380C4—2361no—
381C4—2361no—
382C4—2361no—
383C4#1427377211yescharacteristic
384C4#1427377211yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—2361no—
389C2—2361no—
390C2#1683796211yescharacteristic
391C2#1683820911yescharacteristic
392C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3204
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. #16837981C2semidirect
2. #16837980C2semidirect
3. #16837733C2semidirect
4. #16837731C2semidirect
5. #16837719C2semidirect
6. #16837718C2semidirect
7. #16837659C2semidirect
8. #16837652C2semidirect
9. #16837630C2semidirect
10. #16837628C2semidirect
11. #16837564C2semidirect
12. #16837561C2semidirect
13. #16837544C2semidirect
14. #16837367C2semidirect
15. C59×#449C2semidirect
210. #449D59semidirect
212. C59#3204semidirect