Finite Group Databasebeta

← #20279271

Subgroups — #20279271

Order 6784.

482 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53⋊#401C211yesmaximal, characteristic, complemented
2#16810562C211yesmaximal, characteristic, complemented
3#16810550C211yesmaximal, characteristic, complemented
4#16810549C211yesmaximal, characteristic, complemented
5#16810515C211yesmaximal, characteristic, complemented
6#16810513C211yesmaximal, characteristic, complemented
7#16810509C211yesmaximal, characteristic, complemented
8#16810502C211yesmaximal, characteristic
9#16810500C211yesmaximal, characteristic
10#16810500C211yesmaximal, characteristic
11#16810498C211yesmaximal, characteristic, complemented
12#16810490C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
14C2×#13133124C211yesmaximal, characteristic, complemented
15C53×#380C211yesmaximal, characteristic, complemented
16C22×C22⋊D53C2211yescharacteristic
17C23×Dic53C2211yescharacteristic
18C23×Dic53C2211yescharacteristic
19C2×C4⋊Dic53C2211yescharacteristic
20C2×C4⋊Dic53C2211yescharacteristic
21C2×C22⋊Dic53C2211yescharacteristic
22C2×#11719921C2211yescharacteristic
23C2×#11719921C2211yescharacteristic
24C2×#11719921C2211yescharacteristic
25C2×#11719921C2211yescharacteristic
26C2×#11719921C2211yescharacteristic
27C2×#11719921C2211yescharacteristic
28C2×C4×Dic53C2211yescharacteristic
29C2×C4×Dic53C2211yescharacteristic
30#13133124C2211yescharacteristic
31#13133124C2211yescharacteristic
32#13133124C2211yescharacteristic
33#13133124C2211yescharacteristic
34#13133124C2211yescharacteristic
35#13133124C2211yescharacteristic
36#13133124C2211yescharacteristic
37#13133124C2211yescharacteristic
38#13133124C2211yescharacteristic
39#13133124C2211yescharacteristic
40#13133124C2211yescharacteristic
41#13133124C2211yescharacteristic
42#13133124C2211yescharacteristic
43#13133124C2211yescharacteristic
44C23×C4×C53C2211yescharacteristic
45C2×C4⋊C4×C53C2211yescharacteristic
46C2×C4⋊C4×C53C2211yescharacteristic
47C2×C22⋊C4×C53C2211yescharacteristic
48C2×C22⋊C4×C53C2211yescharacteristic
49#95×C53C2211yescharacteristic
50#95×C53C2211yescharacteristic
51C24×C53C2311yescharacteristic
52C23×D53C2311yescharacteristic
53C22×C4×C53—22no—
54C22×C4×C53—22no—
55C22×C4×C53—41no—
56C22×C4×C53C2311yescharacteristic
57C22×C4×C53C2311yescharacteristic
58C22×C4×C53C2311yescharacteristic
59C22×C4×C53C2311yescharacteristic
60C22×C4×C53C2311yescharacteristic
61C22×C4×C53C2311yescharacteristic
62C2×C22⋊D53—22no—
63C2×C22⋊D53—22no—
64C2×C22⋊D53—22no—
65C22×Dic53—22no—
66C22×Dic53—22no—
67C22×Dic53—22no—
68C22×Dic53—41no—
69C22×Dic53—41no—
70C22×Dic53—41no—
71C22×Dic53C2311yescharacteristic
72C22×Dic53C2311yescharacteristic
73C22×Dic53C2311yescharacteristic
74C22×Dic53C2311yescharacteristic
75C22×Dic53C2311yescharacteristic
76C22×Dic53C2311yescharacteristic
77C22×Dic53C2311yescharacteristic
78C4⋊C4×C53—22no—
79C4⋊C4×C53—41no—
80C22⋊C4×C53—22no—
81C22⋊C4×C53—22no—
82C22⋊Dic53—22no—
83#11719921—22no—
84#11719921—22no—
85#11719921—41no—
86#11719921—41no—
87#11719921—41no—
88#11719921—41no—
89C4⋊Dic53—41no—
90C4⋊Dic53—41no—
91C4×Dic53—22no—
92C4×Dic53—41no—
93C23×C53—21no—
94C23×C53—21no—
95C23×C53—21no—
96C23×C53—21no—
97C23×C53#4112yes—
98C23×C53#4112yes—
99C23×C53#4112yes—
100C23×C53C2411yescharacteristic
101C22×D53—21no—
102C22×D53—21no—
103C22×D53—21no—
104C22×D53—21no—
105C22×D53—21no—
106C22×D53—21no—
107C22×D53—21no—
108C2×C4×C53—21no—
109C2×C4×C53—21no—
110C2×C4×C53—21no—
111C2×C4×C53—21no—
112C2×C4×C53—21no—
113C2×C4×C53—21no—
114C2×C4×C53—21no—
115C2×C4×C53—21no—
116C2×C4×C53—21no—
117C2×C4×C53—21no—
118C2×C4×C53—21no—
119C2×C4×C53—21no—
120C2×C4×C53—21no—
121C2×C4×C53—21no—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—44no—
126C2×C4×C53#4112yes—
127C22⋊D53—44no—
128C2×Dic53—21no—
129C2×Dic53—21no—
130C2×Dic53—21no—
131C2×Dic53—21no—
132C2×Dic53—21no—
133C2×Dic53—21no—
134C2×Dic53—21no—
135C2×Dic53—21no—
136C2×Dic53—21no—
137C2×Dic53—21no—
138C2×Dic53—21no—
139C2×Dic53—21no—
140C2×Dic53—21no—
141C2×Dic53—21no—
142C2×Dic53—21no—
143C2×Dic53—21no—
144C2×Dic53—21no—
145C2×Dic53—21no—
146C2×Dic53—21no—
147C2×Dic53—21no—
148C2×Dic53—44no—
149C2×Dic53—44no—
150C2×Dic53#4112yes—
151C22×C53—22no—
152C22×C53—22no—
153C22×C53—22no—
154C22×C53—22no—
155C22×C53—22no—
156C22×C53—22no—
157C22×C53#12614yes—
158C22×C53C2×#4111yescharacteristic
159C22×C53C2×#4111yescharacteristic
160C22×C53C2×#4111yescharacteristic
161C22×C53C2×#4111yescharacteristic
162C22×C53C2×#4111yescharacteristic
163C22×C53H(5,𝔽2)11yescharacteristic
164C22×C53H(5,𝔽2)11yescharacteristic
165C2×D53—41no—
166C2×D53—41no—
167C2×D53—41no—
168C2×D53—41no—
169C2×D53—41no—
170C2×D53—41no—
171C2×D53—41no—
172C4×C53—22no—
173C4×C53—41no—
174C4×C53—41no—
175C4×C53—41no—
176C4×C53—41no—
177C4×C53—41no—
178Dic53—22no—
179Dic53—41no—
180Dic53—41no—
181Dic53—41no—
182Dic53—41no—
183Dic53—41no—
184Dic53—41no—
185#2510—531nomaximal, Sylow
186C2×C53—24no—
187C2×C53C2×#12611yescharacteristic
188C2×C53#52911yescharacteristic
189C2×C53#53811yescharacteristic
190C2×C53#55111yescharacteristic
191C2×C53#55111yescharacteristic
192C2×C53#55311yescharacteristic
193C2×C53#55311yescharacteristic
194D53—81no—
195#401—531no—
196#400—531no—
197#397—531no—
198#397—531no—
199#388—531no—
200#388—531no—
201#387—531no—
202#386—531no—
203#386—531no—
204#386—531no—
205#385—531no—
206#383—531no—
207#380D5311yescharacteristic, complemented
208C4×C22⋊C4—531no—
209C2×#95—531no—
210C53#251011yescharacteristic, complemented, Sylow
211C22×D4—531no—
212C23×C4—531no—
213C23×C4—531no—
214C23×C4C2×D5311yescharacteristic
215C2×C4⋊C4—531no—
216C2×C4⋊C4—531no—
217C2×C4⋊C4C2×D5311yescharacteristic
218C2×C4⋊C4C2×D5311yescharacteristic
219C2×C22⋊C4—531no—
220C2×C22⋊C4—531no—
221C2×C22⋊C4—531no—
222C2×C22⋊C4—531no—
223C2×C22⋊C4—531no—
224C2×C22⋊C4—531no—
225C2×C22⋊C4—531no—
226C2×C22⋊C4C2×D5311yescharacteristic
227C2×C22⋊C4C2×D5311yescharacteristic
228C2×C42—531no—
229C2×C42—531no—
230#95—531no—
231#95—531no—
232#95—531no—
233#95—531no—
234#95—531no—
235#95—531no—
236#95—531no—
237#95—531no—
238#95—531no—
239#95—531no—
240#95—531no—
241#95—531no—
242#95—531no—
243#95—531no—
244#95C2×D5311yescharacteristic
245#95C2×D5311yescharacteristic
246C24—531no—
247C24C22×D5311yescharacteristic
248C2×D4—1062no—
249C2×D4—1062no—
250C2×D4—1062no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—531no—
255C22×C4—531no—
256C22×C4—531no—
257C22×C4—531no—
258C22×C4—531no—
259C22×C4—531no—
260C22×C4—531no—
261C22×C4—1062no—
262C22×C4—1062no—
263C22×C4—1062no—
264C22×C4—2121no—
265C22×C4—2121no—
266C22×C4—2121no—
267C22×C4C22×D5311yescharacteristic
268C22×C4C22×D5311yescharacteristic
269C22×C4C22×D5311yescharacteristic
270C22×C4C22×D5311yescharacteristic
271C22×C4C22×D5311yescharacteristic
272C22×C4C22×D5311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—2121no—
276C4⋊C4—2121no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—1062no—
280C22⋊C4—1062no—
281C22⋊C4—1062no—
282C22⋊C4—2121no—
283C22⋊C4—2121no—
284C22⋊C4—2121no—
285C22⋊C4—2121no—
286C42—1062no—
287C42—2121no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—1061no—
293C23—1061no—
294C23—1061no—
295C23—1061no—
296C23—1061no—
297C23—1061no—
298C23—1061no—
299C23#1171994512yes—
300C23#1171994712yes—
301C23#1171994912yes—
302C23C23×D5311yescharacteristic
303D4—2124no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—532no—
323C2×C4—1061no—
324C2×C4—1061no—
325C2×C4—1061no—
326C2×C4—1061no—
327C2×C4—1061no—
328C2×C4—1061no—
329C2×C4—1061no—
330C2×C4—1061no—
331C2×C4—1061no—
332C2×C4—1061no—
333C2×C4—1061no—
334C2×C4—1061no—
335C2×C4—1061no—
336C2×C4—1061no—
337C2×C4—1061no—
338C2×C4—1061no—
339C2×C4—1061no—
340C2×C4—1061no—
341C2×C4—1061no—
342C2×C4—1061no—
343C2×C4—2124no—
344C2×C4—2124no—
345C2×C4#1171994712yes—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—2121no—
353C22—2121no—
354C22—2121no—
355C22—2121no—
356C22—2121no—
357C22—2121no—
358C22—2121no—
359C22#1313321214yes—
360C22#41×D5311yescharacteristic
361C22C2×#1171994711yescharacteristic
362C22C2×#1171994711yescharacteristic
363C22C2×#1171994511yescharacteristic
364C22C2×#1171994911yescharacteristic
365C22#1313326211yescharacteristic
366C22#1313326311yescharacteristic
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—1062no—
374C4—2121no—
375C4—2121no—
376C4—2121no—
377C4—2121no—
378C4—2121no—
379C4—2121no—
380C2—24no—
381C2—4241no—
382C2C2×#1313321211yescharacteristic
383C2#1681115911yescharacteristic
384C2#1681121311yescharacteristic
385C2#1681129711yescharacteristic
386C2#1681129911yescharacteristic
387C2#1681131611yescharacteristic
388C2#1681132511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D53
commutator, socleC23×C53C24
FittingC53×#380C2
hypercenter#380D53
hypocenterC53#2510
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C53⋊#401C2semidirect
2. #16810562C2semidirect
3. #16810550C2semidirect
4. #16810549C2semidirect
5. #16810515C2semidirect
6. #16810513C2semidirect
7. #16810509C2semidirect
11. #16810498C2semidirect
12. #16810490C2semidirect
13. C22⋊C4×Dic53C2semidirect
14. C2×#13133124C2semidirect
15. C53×#380C2semidirect
207. #380D53semidirect
210. C53#2510semidirect