Finite Group Databasebeta

← #21434924

Subgroups — #21434924

Order 7552.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837909C211yesmaximal, characteristic
2C22⋊Q8×D59C211yesmaximal, characteristic, complemented
3#16837744C211yesmaximal, characteristic, complemented
4#16837740C211yesmaximal, characteristic, complemented
5#16837736C211yesmaximal, characteristic, complemented
6#16837719C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837657C211yesmaximal, characteristic, complemented
9#16837647C211yesmaximal, characteristic, complemented
10#16837645C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837556C211yesmaximal, characteristic, complemented
13#16837539C211yesmaximal, characteristic, complemented
14#16837364C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C22×C4×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745670C2211yescharacteristic, complemented
20C2×#11745659C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22#14273708—21no—
23#14273707C2211yescharacteristic
24#14273706C2211yescharacteristic
25#14273705—21no—
26#14273704—21no—
27#14273703C2211yescharacteristic
28#14273703C2211yescharacteristic
29#14273703C2211yescharacteristic
30#14273698C2211yescharacteristic
31#14273698C2211yescharacteristic
32#14273695—21no—
33C4×C22⋊D59—21no—
34C4×C22⋊D59—21no—
35#14273686C2211yescharacteristic
36C4⋊C4×D59—21no—
37C4⋊C4×D59C2211yescharacteristic
38C22⋊C4×D59—21no—
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273651C2211yescharacteristic, complemented
46#14273651C2211yescharacteristic, complemented
47#14273651C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic, complemented
55C22⋊Q8×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C23×D59D411yescharacteristic
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C22×Dic59D411yescharacteristic
71Q8×D59—41no—
72Q8×D59—41no—
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59—41no—
76C2×C4×D59—41no—
77C2×C4×D59D411yescharacteristic
78C2×C4×D59D411yescharacteristic
79C2×C4×D59C2311yescharacteristic
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82C2×Dic118C2311yescharacteristic
83Q16×C59—41no—
84SD16×C59—41no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C4⋊C4×C59—21no—
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94#11745672—41no—
95#11745670—41no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745659—41no—
113#11745659—41no—
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—22no—
117C22×D59—41no—
118C22×D59—41no—
119C22×D59C2×D411yescharacteristic
120C22×D59C2×D411yescharacteristic
121Q8×C59—21no—
122Q8×C59—21no—
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—42no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—42no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2411yescharacteristic
136C22⋊D59—42no—
137C22⋊D59—42no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—41no—
143C2×Dic59C2×D411yescharacteristic
144C2×Dic59C2×D411yescharacteristic
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—21no—
149C4×D59—41no—
150C4×D59—41no—
151C4×D59—42no—
152C4×D59—42no—
153Dic118—21no—
154Dic118—21no—
155Dic118—42no—
156C8×C59—21no—
157C8×C59—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59C22×D411yescharacteristic
167C2×D59—21no—
168C2×D59—21no—
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—44no—
173C2×D59#13712yes—
174C4×C59—21no—
175C4×C59—41no—
176C4×C59—41no—
177C4×C59—41no—
178C4×C59H(5,𝔽2)11yescharacteristic
179C4×C59H(5,𝔽2)11yescharacteristic
180Dic59—21no—
181Dic59—21no—
182Dic59—41no—
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186#3196—591nomaximal, Sylow
187C2×C59—41no—
188C2×C59—81no—
189C2×C59#53411yescharacteristic
190C2×C59C2×#13711yescharacteristic
191C2×C59#57511yescharacteristic
192D59—22no—
193D59—41no—
194#525—591no—
195C2×C22⋊Q8—591no—
196#485—591no—
197#485—591no—
198#484—591no—
199#481—591no—
200#470—591no—
201#470—591no—
202#468—591no—
203#468—591no—
204#452—591no—
205#452D5911yescharacteristic, complemented
206#451—591no—
207#448—591no—
208#407—591no—
209C59#319611yescharacteristic, complemented, Sylow
210C2×#41C2×D5911yescharacteristic
211C22×Q8—591no—
212C23×C4—591no—
213C2×Q16—591no—
214C2×Q16C2×D5911yescharacteristic, complemented
215C2×SD16—591no—
216C2×SD16C2×D5911yescharacteristic, complemented
217C2×M16—591no—
218C2×M16—591no—
219#123—1181no—
220C22⋊Q8—591no—
221C22⋊Q8—591no—
222C22⋊Q8—591no—
223C22⋊Q8—591no—
224C22⋊Q8—591no—
225C22⋊Q8—1181no—
226C22⋊Q8—1181no—
227C22⋊Q8C2×D5911yescharacteristic
228#121—591no—
229#121—591no—
230#120—1181no—
231C4×D4—1181no—
232C4×D4—1181no—
233#117—591no—
234C2×C4⋊C4—591no—
235C2×C4⋊C4—1181no—
236C2×C22⋊C4—1181no—
237#107—591no—
238#107—591no—
239#106—591no—
240#106—591no—
241#103—591no—
242#103—591no—
243#103—591no—
244#103—591no—
245#103—591no—
246#103C2×D5911yescharacteristic, complemented
247#102—591no—
248#102C2×D5911yescharacteristic, complemented
249C22⋊C8—591no—
250C22⋊C8—591no—
251C22⋊C8—591no—
252C22⋊C8C2×D5911yescharacteristic
253C24—591no—
254#41—41no—
255#41—41no—
256C2×Q8—591no—
257C2×Q8—1181no—
258C2×Q8—2361no—
259C2×Q8—2361no—
260C2×Q8C22×D5911yescharacteristic
261C2×Q8C22×D5911yescharacteristic
262C2×D4—21no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4C22×D5911yescharacteristic
266C22×C4—21no—
267C22×C4—591no—
268C22×C4—591no—
269C22×C4—591no—
270C22×C4—591no—
271C22×C4—591no—
272C22×C4—1181no—
273C22×C4—1181no—
274C22×C4—2361no—
275C22×C4—2361no—
276C22×C4C22×D5911yescharacteristic
277Q16—41no—
278Q16—2361no—
279SD16—41no—
280SD16—2361no—
281M16—2361no—
282M16—2361no—
283C2×C8—591no—
284C2×C8—591no—
285C2×C8C22×D5911yescharacteristic
286C2×C8C22×D5911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—591no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4—1181no—
296C4⋊C4—1181no—
297C4⋊C4C22×D5911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C42—1181no—
308C23—21no—
309C23—591no—
310C23—591no—
311C23—1182no—
312C23—2361no—
313C23—2361no—
314C23D4×D5911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—1181no—
320Q8—1181no—
321Q8—2362no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—2362no—
326D4—2362no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—591no—
334C2×C4—591no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—2361no—
344C2×C4—2361no—
345C2×C4—2362no—
346C2×C4—2362no—
347C2×C4—2361no—
348C2×C4D4×D5911yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1181no—
353C8—1181no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—592no—
361C22—1181no—
362C22—1181no—
363C22—1181no—
364C22—1181no—
365C22—1181no—
366C22—2364no—
367C22C2×D4×D5911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—1181no—
373C4—1181no—
374C4—2361no—
375C4—2361no—
376C4—2361no—
377C4—2361no—
378C4#1427377211yescharacteristic
379C4#1427377211yescharacteristic
380C2—41no—
381C2—81no—
382C2—1182no—
383C2—2361no—
384C2#1683796211yescharacteristic
385C2#137×D5911yescharacteristic
386C2#1683819911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3196
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D59C2semidirect
3. #16837744C2semidirect
4. #16837740C2semidirect
5. #16837736C2semidirect
6. #16837719C2semidirect
7. #16837659C2semidirect
8. #16837657C2semidirect
9. #16837647C2semidirect
10. #16837645C2semidirect
11. #16837564C2semidirect
12. #16837556C2semidirect
13. #16837539C2semidirect
14. #16837364C2semidirect
15. C59×#452C2semidirect
18. C2×#11745672C22semidirect
19. C2×#11745670C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. #14273659C22semidirect
42. #14273658C22semidirect
43. #14273652C22semidirect
44. #14273652C22semidirect
45. #14273651C22semidirect
46. #14273651C22semidirect
47. #14273651C22semidirect
48. #14273648C22semidirect
53. C2×Q16×C59C22semidirect
54. C2×SD16×C59C22semidirect
56. #103×C59C22semidirect
57. #102×C59C22semidirect
205. #452D59semidirect
209. C59#3196semidirect
214. C2×Q16C2×D59semidirect
216. C2×SD16C2×D59semidirect
246. #103C2×D59semidirect
248. #102C2×D59semidirect