Finite Group Databasebeta

← #21436313

Subgroups — #21436313

Order 7552.

402 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#16838087C211yesmaximal, characteristic, complemented
2#16838040C211yesmaximal, characteristic
3#16837758C211yesmaximal, characteristic, complemented
4#16837742C211yesmaximal, characteristic, complemented
5#16837720C211yesmaximal, characteristic, complemented
6#16837700C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837627C211yesmaximal, characteristic, complemented
10#16837564C211yesmaximal, characteristic, complemented
11#16837554C211yesmaximal, characteristic, complemented
12#16837493C211yesmaximal, characteristic, complemented
13#16837478C211yesmaximal, characteristic, complemented
14#16837405C211yesmaximal, characteristic, complemented
15C59×#417C211yesmaximal, characteristic, complemented
16C2×D4×D59C2211yescharacteristic
17C2×#11745672C2211yescharacteristic, complemented
18C2×#11745660C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21#14273722—21no—
22#14273718C2211yescharacteristic, complemented
23#14273717—21no—
24#14273716C2211yescharacteristic
25#14273710—21no—
26#14273710—21no—
27#14273707C2211yescharacteristic
28#14273706C2211yescharacteristic, complemented
29#14273703C2211yescharacteristic
30#14273701C2211yescharacteristic
31#14273699—21no—
32#14273695—21no—
33#14273692C2211yescharacteristic, complemented
34D4×Dic59C2211yescharacteristic
35C4×C22⋊D59C2211yescharacteristic
36#14273686—21no—
37#14273685C2211yescharacteristic
38C2×(C2×D59)⋊C4—21no—
39#14273661C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273651C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic, complemented
52C2×#41×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic, complemented
54C2×C4⋊C4×C59C2211yescharacteristic, complemented
55#103×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60#41×C59—22no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59D411yescharacteristic
71C22×Dic59—21no—
72D4×D59—22no—
73D4×D59—41no—
74C2×D236C2311yescharacteristic
75C2×C4×D59C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77M16×C59—41no—
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C4⋊C4×C59—21no—
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊Dic59—21no—
84C22⋊Dic59—21no—
85C22⋊Dic59D411yescharacteristic
86#11745672—41no—
87#11745670—22no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
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×D59—42no—
115C22×D59—42no—
116C22×D59—81no—
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—21no—
121D4×C59—42no—
122D4×C59#4112yes—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—42no—
129C2×C4×C59—42no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—41no—
133C22⋊D59—42no—
134C22⋊D59—81no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—81no—
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142D236—21no—
143D236—21no—
144C4×D59—21no—
145C4×D59—21no—
146Dic118—21no—
147Dic118—21no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—22no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
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—
165C2×D59—84no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59C2×#4111yescharacteristic
171C4×C59H(5,𝔽2)11yescharacteristic
172Dic59—21no—
173Dic59—21no—
174Dic59—21no—
175Dic59—41no—
176Dic59—41no—
177Dic59—41no—
178#3323—591nomaximal, Sylow
179C2×C59—42no—
180C2×C59—41no—
181C2×C59#54611yescharacteristic
182C2×C59#57511yescharacteristic
183C2×C59#57711yescharacteristic
184D59—41no—
185D59—81no—
186#552—591no—
187#546—591no—
188#488—591no—
189#485—591no—
190#481—591no—
191#478—591no—
192#470—591no—
193#468—591no—
194#464—591no—
195#452—591no—
196#450—591no—
197C4×SD16—591no—
198#436—591no—
199#418—591no—
200#417D5911yescharacteristic, complemented
201C59#332311yescharacteristic, complemented, Sylow
202C2×#41C2×D5911yescharacteristic
203C22×D4—591no—
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C2×M16—591no—
208C2×M16C2×D5911yescharacteristic, complemented
209#126—1181no—
210#125—591no—
211#125—1181no—
212#124—591no—
213#123—1181no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8—591no—
218#121—591no—
219#121—1181no—
220#120—1181no—
221C4×Q8—591no—
222C4×D4—591no—
223C4×D4—591no—
224#117—591no—
225#117—1181no—
226C2×C4⋊C4C2×D5911yescharacteristic, complemented
227C2×C22⋊C4—1181no—
228#107—591no—
229#106—591no—
230#106—591no—
231C4⋊C8—591no—
232#103—591no—
233#103—591no—
234#103C2×D5911yescharacteristic, complemented
235#103C2×D5911yescharacteristic, complemented
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102C2×D5911yescharacteristic
241#102C2×D5911yescharacteristic
242C22⋊C8—591no—
243C22⋊C8—591no—
244C4×C8—591no—
245C24—1181no—
246#41—22no—
247#41—41no—
248C2×Q8—591no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—21no—
251C2×D4—591no—
252C2×D4—591no—
253C2×D4—1181no—
254C2×D4—1182no—
255C2×D4—1181no—
256C2×D4—2361no—
257C2×D4C22×D5911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—591no—
261C22×C4—1181no—
262C22×C4C22×D5911yescharacteristic
263Q16—2361no—
264SD16—1182no—
265SD16—2361no—
266M16—41no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8C22×D5911yescharacteristic
271C2×C8C22×D5911yescharacteristic
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—591no—
285C22⋊C4—591no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C42—591no—
295C42—1181no—
296C42—1181no—
297C23—21no—
298C23—591no—
299C23—1181no—
300C23—4721no—
301C23—2362no—
302C23—2362no—
303C23D4×D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1181no—
307Q8—1181no—
308D4—21no—
309D4—42no—
310D4—1181no—
311D4—1181no—
312D4—4721no—
313D4—2361no—
314D4—2362no—
315D4#1174568512yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—591no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—4721no—
332C2×C4D4×D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—1181no—
345C22—1181no—
346C22—1181no—
347C22—4724no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22C2×D4×D5911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1181no—
357C4—1181no—
358C4—1181no—
359C4—2361no—
360C4—2361no—
361C4—2361no—
362C4C2×#1174568511yescharacteristic
363C4#1427377211yescharacteristic
364C2—41no—
365C2—42no—
366C2—4721no—
367C2—2361no—
368C2#1683804211yescharacteristic
369C2#1683819811yescharacteristic
370C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#417C2
socleC22×C59C22×D4
hypercenter#417D59
hypocenterC59#3323
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. #16838087C2semidirect
3. #16837758C2semidirect
4. #16837742C2semidirect
5. #16837720C2semidirect
6. #16837700C2semidirect
7. #16837659C2semidirect
8. #16837648C2semidirect
9. #16837627C2semidirect
10. #16837564C2semidirect
11. #16837554C2semidirect
12. #16837493C2semidirect
13. #16837478C2semidirect
14. #16837405C2semidirect
15. C59×#417C2semidirect
17. C2×#11745672C22semidirect
22. #14273718C22semidirect
28. #14273706C22semidirect
33. #14273692C22semidirect
39. #14273661C22semidirect
40. #14273658C22semidirect
41. #14273658C22semidirect
42. Dic59⋊C8C22semidirect
43. #14273652C22semidirect
44. #14273651C22semidirect
49. C22⋊(C59⋊C8)C22semidirect
51. C8×Dic59C22semidirect
53. C2×M16×C59C22semidirect
54. C2×C4⋊C4×C59C22semidirect
55. #103×C59C22semidirect
56. #103×C59C22semidirect
200. #417D59semidirect
201. C59#3323semidirect
208. C2×M16C2×D59semidirect
226. C2×C4⋊C4C2×D59semidirect
234. #103C2×D59semidirect
235. #103C2×D59semidirect