Finite Group Databasebeta

← #21432218

Subgroups — #21432218

Order 7552.

508 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837344C211yesmaximal, characteristic, complemented
2#16837330C211yesmaximal, characteristic, complemented
3#16837327C211yesmaximal, characteristic, complemented
4#16837318C211yesmaximal, characteristic, complemented
5#16837318C211yesmaximal, characteristic, complemented
6#16837317C211yesmaximal, characteristic, complemented
7#16837316C211yesmaximal, characteristic, complemented
8#16837316C211yesmaximal, characteristic, complemented
9#16837310C211yesmaximal, characteristic, complemented
10#16837310C211yesmaximal, characteristic, complemented
11#16837310C211yesmaximal, characteristic, complemented
12#16837305C211yesmaximal, characteristic, complemented
13#16837295C211yesmaximal, characteristic, complemented
14#16837291C211yesmaximal, characteristic, complemented
15C59×#392C211yesmaximal, characteristic, complemented
16C22×C22⋊D59C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19C2×C4⋊Dic59C2211yescharacteristic
20C2×C4⋊Dic59C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×C22⋊Dic59C2211yescharacteristic
24C2×C22⋊Dic59C2211yescharacteristic
25C2×C22⋊Dic59C2211yescharacteristic
26C2×C22⋊Dic59C2211yescharacteristic
27C2×C22⋊Dic59C2211yescharacteristic
28C2×C22⋊Dic59C2211yescharacteristic
29C2×C22⋊Dic59C2211yescharacteristic
30C2×C22⋊Dic59C2211yescharacteristic
31C2×C22⋊Dic59C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×(C2×D59)⋊C4C2211yescharacteristic
36C2×C4×Dic59C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C22×D4×C59C2211yescharacteristic
45C22×D4×C59C2211yescharacteristic
46C22×D4×C59C2211yescharacteristic
47C2×C22⋊C4×C59C2211yescharacteristic
48C2×C22⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51C24×C59C2311yescharacteristic
52C24×C59C2311yescharacteristic
53C24×C59C2311yescharacteristic
54C23×D59C2311yescharacteristic
55C2×D4×C59—22no—
56C2×D4×C59—41no—
57C2×D4×C59—41no—
58C2×D4×C59—41no—
59C2×D4×C59—41no—
60C2×D4×C59—41no—
61C2×D4×C59—41no—
62C2×D4×C59—41no—
63C2×D4×C59—41no—
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—41no—
69C2×C22⋊D59—41no—
70C2×C22⋊D59—41no—
71C2×C22⋊D59—41no—
72C2×C22⋊D59—41no—
73C2×C22⋊D59—41no—
74C2×C22⋊D59—41no—
75C2×C22⋊D59—41no—
76C2×C22⋊D59—41no—
77C22×Dic59C2311yescharacteristic
78C22×Dic59C2311yescharacteristic
79C22×Dic59C2311yescharacteristic
80C22×Dic59C2311yescharacteristic
81C22×Dic59C2311yescharacteristic
82C22×Dic59C2311yescharacteristic
83C22×Dic59C2311yescharacteristic
84C22⋊C4×C59—22no—
85C22⋊C4×C59—41no—
86C22⋊C4×C59—41no—
87C22⋊Dic59—41no—
88C22⋊Dic59—41no—
89C22⋊Dic59—41no—
90C22⋊Dic59—41no—
91C22⋊Dic59—41no—
92C22⋊Dic59—41no—
93C22⋊Dic59—41no—
94C22⋊Dic59—41no—
95C22⋊Dic59—41no—
96(C2×D59)⋊C4—22no—
97(C2×D59)⋊C4—41no—
98(C2×D59)⋊C4—41no—
99(C2×D59)⋊C4—41no—
100C4⋊Dic59—41no—
101C4⋊Dic59—41no—
102Dic59⋊C4—41no—
103Dic59⋊C4—41no—
104C4×Dic59—41no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59—21no—
118C23×C59—21no—
119C23×C59—21no—
120C23×C59—21no—
121C23×C59—21no—
122C23×C59—21no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59C2411yescharacteristic
127C22×D59—21no—
128C22×D59—21no—
129C22×D59—21no—
130C22×D59—21no—
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134D4×C59—44no—
135D4×C59—44no—
136D4×C59—44no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59#4112yes—
149C22⋊D59—44no—
150C22⋊D59—44no—
151C22⋊D59—44no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159C2×Dic59—21no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162C2×Dic59—21no—
163C2×Dic59—21no—
164C2×Dic59—21no—
165C2×Dic59—21no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—21no—
171C2×Dic59—21no—
172C2×Dic59—21no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—41no—
187C22×C59—41no—
188C22×C59—41no—
189C22×C59—41no—
190C22×C59—41no—
191C22×C59—41no—
192C22×C59—41no—
193C22×C59—41no—
194C22×C59C2×#4111yescharacteristic
195C22×C59H(5,𝔽2)11yescharacteristic
196C22×C59H(5,𝔽2)11yescharacteristic
197C22×C59H(5,𝔽2)11yescharacteristic
198C22×C59H(5,𝔽2)11yescharacteristic
199C22×C59H(5,𝔽2)11yescharacteristic
200C22×C59H(5,𝔽2)11yescharacteristic
201C2×D59—41no—
202C2×D59—41no—
203C2×D59—41no—
204C2×D59—41no—
205C2×D59—41no—
206C2×D59—41no—
207C2×D59—41no—
208C4×C59—22no—
209C4×C59—41no—
210C4×C59—41no—
211C4×C59—41no—
212Dic59—41no—
213Dic59—41no—
214Dic59—41no—
215Dic59—41no—
216Dic59—41no—
217Dic59—41no—
218Dic59—41no—
219#2828—591nomaximal, Sylow
220C2×C59—81no—
221C2×C59—81no—
222C2×C59—81no—
223C2×C59#53811yescharacteristic
224C2×C59#54011yescharacteristic
225C2×C59#54011yescharacteristic
226C2×C59#56011yescharacteristic
227C2×C59#56011yescharacteristic
228C2×C59#56011yescharacteristic
229C2×C59H(3,𝔽4)11yescharacteristic
230D59—81no—
231#400—591no—
232#397—591no—
233#397—591no—
234#394—591no—
235#394—591no—
236#394—591no—
237#394—591no—
238#394—591no—
239#392—591no—
240#392—591no—
241#392—591no—
242#392D5911yescharacteristic, complemented
243#390—591no—
244#388—591no—
245#388—591no—
246C59#282811yescharacteristic, complemented, Sylow
247C22×D4—591no—
248C22×D4—591no—
249C22×D4—591no—
250C22×D4C2×D5911yescharacteristic
251C22×D4C2×D5911yescharacteristic
252C22×D4C2×D5911yescharacteristic
253C2×C4⋊C4—591no—
254C2×C4⋊C4—591no—
255C2×C4⋊C4—591no—
256C2×C4⋊C4—591no—
257C2×C22⋊C4—591no—
258C2×C22⋊C4—591no—
259C2×C22⋊C4—591no—
260C2×C22⋊C4—591no—
261C2×C22⋊C4—591no—
262C2×C22⋊C4—591no—
263C2×C22⋊C4—591no—
264C2×C22⋊C4—591no—
265C2×C22⋊C4—591no—
266C2×C22⋊C4—591no—
267C2×C22⋊C4—591no—
268C2×C22⋊C4—591no—
269C2×C22⋊C4—591no—
270C2×C22⋊C4C2×D5911yescharacteristic
271C2×C22⋊C4C2×D5911yescharacteristic
272C2×C22⋊C4C2×D5911yescharacteristic
273C2×C42—591no—
274#95—591no—
275#95—591no—
276#95—591no—
277#95—591no—
278#95—591no—
279#95—591no—
280#95—591no—
281#95C2×D5911yescharacteristic
282C24—591no—
283C24C22×D5911yescharacteristic
284C24C22×D5911yescharacteristic
285C24C22×D5911yescharacteristic
286C2×D4—22no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—2361no—
296C2×D4—2361no—
297C2×D4—2361no—
298C2×D4—2361no—
299C2×D4—2361no—
300C2×D4—2361no—
301C2×D4—2361no—
302C2×D4—2361no—
303C2×D4—2361no—
304C22×C4—591no—
305C22×C4—591no—
306C22×C4—591no—
307C22×C4—591no—
308C22×C4—591no—
309C22×C4—591no—
310C22×C4—591no—
311C22×C4C22×D5911yescharacteristic
312C22×C4C22×D5911yescharacteristic
313C22×C4C22×D5911yescharacteristic
314C22×C4C22×D5911yescharacteristic
315C4⋊C4—2361no—
316C4⋊C4—2361no—
317C4⋊C4—2361no—
318C4⋊C4—2361no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—1182no—
323C22⋊C4—2361no—
324C22⋊C4—2361no—
325C22⋊C4—2361no—
326C22⋊C4—2361no—
327C22⋊C4—2361no—
328C22⋊C4—2361no—
329C22⋊C4—2361no—
330C22⋊C4—2361no—
331C22⋊C4—2361no—
332C22⋊C4—2361no—
333C22⋊C4—2361no—
334C22⋊C4—2361no—
335C42—2361no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—1181no—
358C23—1181no—
359C23—1181no—
360C23—1181no—
361C23—1181no—
362C23—1181no—
363C23—1181no—
364C23C23×D5911yescharacteristic
365D4—44no—
366D4—44no—
367D4—44no—
368D4—2364no—
369D4—2364no—
370D4—2364no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—1181no—
383C2×C4—1181no—
384C2×C4—1181no—
385C2×C4—1181no—
386C2×C4—1181no—
387C2×C4—1181no—
388C2×C4—1181no—
389C2×C4—1181no—
390C2×C4—1181no—
391C2×C4—1181no—
392C2×C4—1181no—
393C2×C4—1181no—
394C2×C4—1181no—
395C2×C4—1181no—
396C2×C4—1181no—
397C2×C4—1181no—
398C2×C4—1181no—
399C2×C4—1181no—
400C2×C4—1181no—
401C2×C4—1181no—
402C2×C4—1181no—
403C2×C4#1174568712yes—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—2361no—
426C22—2361no—
427C22—2361no—
428C22—2361no—
429C22—2361no—
430C22—2361no—
431C22—2361no—
432C22C2×#1174568711yescharacteristic
433C22#1427377211yescharacteristic
434C22#1427377211yescharacteristic
435C22#1427377211yescharacteristic
436C22#1427377211yescharacteristic
437C22#1427377211yescharacteristic
438C22#1427377311yescharacteristic
439C4—22no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—2361no—
444C4—2361no—
445C4—2361no—
446C4—2361no—
447C4—2361no—
448C4—2361no—
449C4—2361no—
450C2—81no—
451C2—81no—
452C2—81no—
453C2—4721no—
454C2#1683798711yescharacteristic
455C2#1683800511yescharacteristic
456C2#1683800611yescharacteristic
457C2#1683814011yescharacteristic
458C2#1683814011yescharacteristic
459C2#1683814111yescharacteristic
460C2#1683814511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#392C2
hypercenter#392D59
hypocenterC59#2828
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #16837344C2semidirect
2. #16837330C2semidirect
3. #16837327C2semidirect
4. #16837318C2semidirect
5. #16837318C2semidirect
6. #16837317C2semidirect
7. #16837316C2semidirect
8. #16837316C2semidirect
9. #16837310C2semidirect
10. #16837310C2semidirect
11. #16837310C2semidirect
12. #16837305C2semidirect
13. #16837295C2semidirect
14. #16837291C2semidirect
15. C59×#392C2semidirect
242. #392D59semidirect
246. C59#2828semidirect