Finite Group Databasebeta

← #20282091

Subgroups — #20282091

Order 6784.

520 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53⋊#401C211yesmaximal, characteristic, complemented
2C53⋊#401C211yesmaximal, characteristic, complemented
3#16810536C211yesmaximal, characteristic, complemented
4#16810535C211yesmaximal, characteristic, complemented
5#16810535C211yesmaximal, characteristic, complemented
6#16810531C211yesmaximal, characteristic
7#16810503C211yesmaximal, characteristic, complemented
8#16810502C211yesmaximal, characteristic, complemented
9#16810500C211yesmaximal, characteristic, complemented
10#16810499C211yesmaximal, characteristic, complemented
11#16810499C211yesmaximal, characteristic, complemented
12#16810486C211yesmaximal, characteristic, complemented
13#16810485C211yesmaximal, characteristic, complemented
14#16810484C211yesmaximal, characteristic, complemented
15C53×#386C211yesmaximal, characteristic, complemented
16C22×Dic106C2211yescharacteristic
17C22×C22⋊D53C2211yescharacteristic
18C22×C22⋊D53C2211yescharacteristic
19C23×Dic53C2211yescharacteristic
20C22×C4×D53C2211yescharacteristic
21C2×C22⋊Dic53C2211yescharacteristic
22C2×C22⋊Dic53C2211yescharacteristic
23C2×C22⋊Dic53C2211yescharacteristic
24C2×C22⋊Dic53C2211yescharacteristic
25C2×C22⋊Dic53C2211yescharacteristic
26C2×#11719921C2211yescharacteristic
27C2×#11719921C2211yescharacteristic
28C2×#11719921C2211yescharacteristic
29C2×#11719921C2211yescharacteristic
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
44C22×D4×C53C2211yescharacteristic
45C23×C4×C53C2211yescharacteristic
46C2×C22⋊C4×C53C2211yescharacteristic
47C2×C22⋊C4×C53C2211yescharacteristic
48C2×C22⋊C4×C53C2211yescharacteristic
49#95×C53C2211yescharacteristic
50#95×C53C2211yescharacteristic
51C24×C53C2311yescharacteristic
52C24×C53C2311yescharacteristic
53C23×D53C2311yescharacteristic
54C2×D4×C53—22no—
55C2×D4×C53—22no—
56C2×D4×C53—41no—
57C22×C4×C53—22no—
58C22×C4×C53—41no—
59C22×C4×C53—41no—
60C22×C4×C53C2311yescharacteristic
61C22×C4×C53C2311yescharacteristic
62C22×C4×C53C2311yescharacteristic
63C22×C4×C53C2311yescharacteristic
64C22×C4×C53C2311yescharacteristic
65C2×C22⋊D53—22no—
66C2×C22⋊D53—22no—
67C2×C22⋊D53—22no—
68C2×C22⋊D53—22no—
69C2×C22⋊D53—41no—
70C2×C22⋊D53—41no—
71C22×Dic53—22no—
72C22×Dic53—41no—
73C22×Dic53—41no—
74C22×Dic53C2311yescharacteristic
75C22×Dic53C2311yescharacteristic
76C22×Dic53C2311yescharacteristic
77C22×Dic53C2311yescharacteristic
78C22×Dic53C2311yescharacteristic
79C22×Dic53C2311yescharacteristic
80C22×Dic53C2311yescharacteristic
81C2×C4×D53—22no—
82C2×C4×D53—41no—
83C2×C4×D53—41no—
84C2×Dic106—41no—
85C2×Dic106—41no—
86C2×Dic106—41no—
87C22⋊C4×C53—41no—
88C22⋊C4×C53—41no—
89C22⋊C4×C53—41no—
90C22⋊Dic53—41no—
91C22⋊Dic53—41no—
92C22⋊Dic53—41no—
93C22⋊Dic53—41no—
94C22⋊Dic53—41no—
95#11719921—41no—
96#11719921—41no—
97#11719921—41no—
98#11719921—41no—
99C23×C53—21no—
100C23×C53—21no—
101C23×C53—21no—
102C23×C53—21no—
103C23×C53—21no—
104C23×C53—21no—
105C23×C53—21no—
106C23×C53—21no—
107C23×C53—21no—
108C23×C53—21no—
109C23×C53—21no—
110C23×C53—21no—
111C23×C53#4112yes—
112C23×C53#4112yes—
113C23×C53C2411yescharacteristic
114C22×D53—21no—
115C22×D53—21no—
116C22×D53—21no—
117C22×D53—21no—
118C22×D53—21no—
119C22×D53—21no—
120C22×D53#4112yes—
121D4×C53—44no—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—21no—
128C2×C4×C53—21no—
129C2×C4×C53—21no—
130C2×C4×C53—21no—
131C2×C4×C53—21no—
132C2×C4×C53—21no—
133C2×C4×C53—21no—
134C2×C4×C53—21no—
135C2×C4×C53—21no—
136C2×C4×C53—21no—
137C2×C4×C53—44no—
138C22⋊D53—44no—
139C22⋊D53—44no—
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—21no—
149C2×Dic53—21no—
150C2×Dic53—21no—
151C2×Dic53—21no—
152C2×Dic53—21no—
153C2×Dic53—21no—
154C2×Dic53—21no—
155C2×Dic53—21no—
156C2×Dic53—21no—
157C2×Dic53—21no—
158C2×Dic53—21no—
159C2×Dic53—21no—
160C2×Dic53—21no—
161C2×Dic53—44no—
162C4×D53—44no—
163Dic106—44no—
164C22×C53—22no—
165C22×C53—22no—
166C22×C53—22no—
167C22×C53—22no—
168C22×C53—22no—
169C22×C53—22no—
170C22×C53—41no—
171C22×C53—41no—
172C22×C53—41no—
173C22×C53—41no—
174C22×C53—41no—
175C22×C53—41no—
176C22×C53—41no—
177C22×C53—41no—
178C22×C53C2×#4111yescharacteristic
179C22×C53C2×#4111yescharacteristic
180C22×C53C2×#4111yescharacteristic
181C22×C53H(5,𝔽2)11yescharacteristic
182C22×C53H(5,𝔽2)11yescharacteristic
183C22×C53H(5,𝔽2)11yescharacteristic
184C22×C53H(5,𝔽2)11yescharacteristic
185C2×D53—22no—
186C2×D53—22no—
187C2×D53—22no—
188C2×D53—41no—
189C2×D53—41no—
190C2×D53—41no—
191C2×D53—41no—
192C4×C53—41no—
193C4×C53—41no—
194C4×C53—41no—
195C4×C53—41no—
196C4×C53—41no—
197Dic53—41no—
198Dic53—41no—
199Dic53—41no—
200Dic53—41no—
201Dic53—41no—
202Dic53—41no—
203Dic53—41no—
204#2760—531nomaximal, Sylow
205C2×C53—42no—
206C2×C53—42no—
207C2×C53#53811yescharacteristic
208C2×C53#53811yescharacteristic
209C2×C53#53811yescharacteristic
210C2×C53#55111yescharacteristic
211C2×C53#55111yescharacteristic
212C2×C53#55111yescharacteristic
213C2×C53#56011yescharacteristic
214D53—42no—
215#401—531no—
216#401—531no—
217#393—531no—
218#393—531no—
219#393—531no—
220#392—531no—
221#386—531no—
222#386—531no—
223#386—531no—
224#386—531no—
225#386—531no—
226#386D5311yescharacteristic, complemented
227#381—531no—
228#381—531no—
229#381—531no—
230C53#276011yescharacteristic, complemented, Sylow
231C22×Q8—531no—
232C22×D4—531no—
233C22×D4—531no—
234C22×D4C2×D5311yescharacteristic
235C23×C4—531no—
236C23×C4—531no—
237C23×C4C2×D5311yescharacteristic
238C2×C22⋊C4—531no—
239C2×C22⋊C4—531no—
240C2×C22⋊C4—531no—
241C2×C22⋊C4—531no—
242C2×C22⋊C4—531no—
243C2×C22⋊C4—531no—
244C2×C22⋊C4—531no—
245C2×C22⋊C4—531no—
246C2×C22⋊C4—531no—
247C2×C22⋊C4C2×D5311yescharacteristic
248C2×C22⋊C4C2×D5311yescharacteristic
249C2×C22⋊C4C2×D5311yescharacteristic
250#95—531no—
251#95—531no—
252#95—531no—
253#95—531no—
254#95—531no—
255#95—531no—
256#95—531no—
257#95—531no—
258#95—531no—
259#95—531no—
260#95—531no—
261#95—531no—
262#95—531no—
263#95—531no—
264#95C2×D5311yescharacteristic
265#95C2×D5311yescharacteristic
266C24—531no—
267C24C22×D5311yescharacteristic
268C24C22×D5311yescharacteristic
269C2×Q8—2121no—
270C2×Q8—2121no—
271C2×Q8—2121no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—1062no—
276C2×D4—1062no—
277C2×D4—1062no—
278C2×D4—1062no—
279C2×D4—2121no—
280C2×D4—2121no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—531no—
285C22×C4—531no—
286C22×C4—531no—
287C22×C4—531no—
288C22×C4—531no—
289C22×C4—531no—
290C22×C4—531no—
291C22×C4—1062no—
292C22×C4—1062no—
293C22×C4—2121no—
294C22×C4—2121no—
295C22×C4—2121no—
296C22×C4—2121no—
297C22×C4C22×D5311yescharacteristic
298C22×C4C22×D5311yescharacteristic
299C22×C4C22×D5311yescharacteristic
300C22×C4C22×D5311yescharacteristic
301C22×C4C22×D5311yescharacteristic
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—2121no—
306C22⋊C4—2121no—
307C22⋊C4—2121no—
308C22⋊C4—2121no—
309C22⋊C4—2121no—
310C22⋊C4—2121no—
311C22⋊C4—2121no—
312C22⋊C4—2121no—
313C22⋊C4—2121no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—532no—
327C23—1061no—
328C23—1061no—
329C23—1061no—
330C23—1061no—
331C23—1061no—
332C23—1061no—
333C23#1171994512yes—
334C23#1171994712yes—
335C23C23×D5311yescharacteristic
336Q8—2124no—
337D4—44no—
338D4—2124no—
339D4—2124no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—1061no—
357C2×C4—1061no—
358C2×C4—1061no—
359C2×C4—1061no—
360C2×C4—1061no—
361C2×C4—1061no—
362C2×C4—1061no—
363C2×C4—1061no—
364C2×C4—1061no—
365C2×C4—1061no—
366C2×C4—1061no—
367C2×C4—1061no—
368C2×C4—1061no—
369C2×C4—1061no—
370C2×C4—1061no—
371C2×C4—1061no—
372C2×C4—1061no—
373C2×C4—1061no—
374C2×C4—1061no—
375C2×C4—1061no—
376C2×C4—1061no—
377C2×C4—2124no—
378C2×C4—2124no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—1062no—
394C22—1062no—
395C22—1062no—
396C22—2121no—
397C22—2121no—
398C22—2121no—
399C22—2121no—
400C22#41×D5311yescharacteristic
401C22C2×#1171994711yescharacteristic
402C22C2×#1171994511yescharacteristic
403C22#1313326211yescharacteristic
404C22#1313326211yescharacteristic
405C22#1313326211yescharacteristic
406C22#1313326311yescharacteristic
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—2121no—
413C4—2121no—
414C4—2121no—
415C4—2121no—
416C4—2121no—
417C4—2121no—
418C4—2121no—
419C2—42no—
420C2—42no—
421C2—2122no—
422C2#1681120511yescharacteristic
423C2#1681120611yescharacteristic
424C2#1681120811yescharacteristic
425C2#1681129611yescharacteristic
426C2#1681129911yescharacteristic
427C2#1681130211yescharacteristic
428C2#1681136111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D53
commutator, socleC23×C53C24
FittingC53×#386C2
hypercenter#386D53
hypocenterC53#2760
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C53⋊#401C2semidirect
2. C53⋊#401C2semidirect
3. #16810536C2semidirect
4. #16810535C2semidirect
5. #16810535C2semidirect
7. #16810503C2semidirect
8. #16810502C2semidirect
9. #16810500C2semidirect
10. #16810499C2semidirect
11. #16810499C2semidirect
12. #16810486C2semidirect
13. #16810485C2semidirect
14. #16810484C2semidirect
15. C53×#386C2semidirect
226. #386D53semidirect
230. C53#2760semidirect