Finite Group Databasebeta

← #21430487

Subgroups — #21430487

Order 7552.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273720C211yesmaximal, characteristic, complemented
2C2×#14273696C211yesmaximal, characteristic
3#16837338C211yesmaximal, characteristic, complemented
4#16837325C211yesmaximal, characteristic, complemented
5#16837318C211yesmaximal, characteristic, complemented
6#16837318C211yesmaximal, characteristic, complemented
7#16837317C211yesmaximal, characteristic, complemented
8#16837317C211yesmaximal, characteristic, complemented
9#16837302C211yesmaximal, characteristic, complemented
10#16837302C211yesmaximal, characteristic, complemented
11#16837296C211yesmaximal, characteristic, complemented
12#16837295C211yesmaximal, characteristic, complemented
13#16837290C211yesmaximal, characteristic, complemented
14#16837258C211yesmaximal, characteristic, complemented
15C59×#379C211yesmaximal, characteristic, complemented
16C22×C22⋊D59C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19#14273720—24no—
20#14273696—24no—
21C2×C4⋊Dic59C2211yescharacteristic, complemented
22C2×C4⋊Dic59C2211yescharacteristic, complemented
23C2×Dic59⋊C4C2211yescharacteristic, complemented
24C2×Dic59⋊C4C2211yescharacteristic, complemented
25C2×Dic59⋊C4C2211yescharacteristic, complemented
26C2×Dic59⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic59C2211yescharacteristic
28C2×C22⋊Dic59C2211yescharacteristic
29C2×C22⋊Dic59C2211yescharacteristic
30C2×C22⋊Dic59C2211yescharacteristic
31C2×C22⋊Dic59C2211yescharacteristic
32C2×C22⋊Dic59C2211yescharacteristic
33C2×C22⋊Dic59C2211yescharacteristic
34C2×C22⋊Dic59C2211yescharacteristic
35C2×C22⋊Dic59C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic59C2211yescharacteristic, complemented
41C2×C4×Dic59C2211yescharacteristic, complemented
42C59⋊#95C2211yescharacteristic, complemented
43C59⋊#95C2211yescharacteristic, complemented
44C59⋊#95C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C25×C59C2211yescharacteristic
47C2×C22⋊C4×C59C2211yescharacteristic
48C2×C22⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50C2×C22⋊C4×C59C2211yescharacteristic
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C22⋊C4×C59C2211yescharacteristic
53C24×C59—22no—
54C24×C59—22no—
55C24×C59—22no—
56C24×C59—41no—
57C24×C59—41no—
58C24×C59—41no—
59C24×C59—41no—
60C24×C59C2311yescharacteristic
61C24×C59C2311yescharacteristic
62C24×C59C2311yescharacteristic
63C23×D59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—22no—
69C2×C22⋊D59—22no—
70C2×C22⋊D59—22no—
71C2×C22⋊D59—22no—
72C2×C22⋊D59—22no—
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—22no—
86C22⋊C4×C59—41no—
87C22⋊C4×C59—41no—
88C22⋊C4×C59—41no—
89C22⋊C4×C59—41no—
90C22⋊Dic59—22no—
91C22⋊Dic59—22no—
92C22⋊Dic59—22no—
93C22⋊Dic59—22no—
94C22⋊Dic59—41no—
95C22⋊Dic59—41no—
96C22⋊Dic59—41no—
97C22⋊Dic59—41no—
98C22⋊Dic59D414yes—
99(C2×D59)⋊C4—41no—
100(C2×D59)⋊C4—41no—
101(C2×D59)⋊C4—41no—
102(C2×D59)⋊C4—41no—
103C4⋊Dic59—22no—
104C4⋊Dic59—41no—
105Dic59⋊C4—22no—
106Dic59⋊C4—22no—
107Dic59⋊C4—41no—
108Dic59⋊C4—41no—
109C4×Dic59—22no—
110C4×Dic59—41no—
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×C59—21no—
127C23×C59—21no—
128C23×C59—21no—
129C23×C59—44no—
130C23×C59—44no—
131C23×C59—44no—
132C23×C59—44no—
133C23×C59—44no—
134C23×C59—44no—
135C23×C59—44no—
136C23×C59C2×D412yes—
137C23×C59#4112yes—
138C23×C59#4112yes—
139C23×C59C2411yescharacteristic
140C22×D59—21no—
141C22×D59—21no—
142C22×D59—21no—
143C22×D59—21no—
144C22×D59—21no—
145C22×D59—21no—
146C22×D59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—21no—
158C2×C4×C59—21no—
159C22⋊D59—44no—
160C22⋊D59—44no—
161C22⋊D59—44no—
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—
173C2×Dic59—21no—
174C2×Dic59—21no—
175C2×Dic59—21no—
176C2×Dic59—21no—
177C2×Dic59—21no—
178C2×Dic59—21no—
179C2×Dic59—21no—
180C2×Dic59—21no—
181C2×Dic59C2×D412yes—
182C2×Dic59C2×D412yes—
183C22×C59—22no—
184C22×C59—22no—
185C22×C59—22no—
186C22×C59—22no—
187C22×C59—22no—
188C22×C59—22no—
189C22×C59—22no—
190C22×C59—22no—
191C22×C59—22no—
192C22×C59—416no—
193C22×C59—41no—
194C22×C59—41no—
195C22×C59—41no—
196C22×C59—41no—
197C22×C59—41no—
198C22×C59—41no—
199C22×C59—41no—
200C22×C59—41no—
201C22×C59—41no—
202C22×C59—41no—
203C22×C59—41no—
204C22×C59—41no—
205C22×C59C22×D411yescharacteristic
206C22×C59C2×#4111yescharacteristic
207C22×C59C2×#4111yescharacteristic
208C22×C59H(5,𝔽2)11yescharacteristic
209C22×C59H(5,𝔽2)11yescharacteristic
210C22×C59H(5,𝔽2)11yescharacteristic
211C22×C59H(5,𝔽2)11yescharacteristic
212C2×D59—41no—
213C2×D59—41no—
214C2×D59—41no—
215C2×D59—41no—
216C2×D59—41no—
217C2×D59—41no—
218C2×D59—41no—
219C4×C59—41no—
220C4×C59—41no—
221C4×C59—41no—
222C4×C59—41no—
223Dic59—22no—
224Dic59—22no—
225Dic59—41no—
226Dic59—41no—
227Dic59—41no—
228Dic59—41no—
229Dic59—41no—
230#2685—591nomaximal, Sylow
231C2×C59—42no—
232C2×C59—42no—
233C2×C59—42no—
234C2×C59#53511yescharacteristic
235C2×C59#53811yescharacteristic
236C2×C59#53811yescharacteristic
237C2×C59#54611yescharacteristic
238C2×C59#54611yescharacteristic
239C2×C59#55111yescharacteristic
240C2×C59#56011yescharacteristic
241D59—81no—
242C2×#126—591no—
243C2×#120—591no—
244#399—591no—
245#396—591no—
246#394—591no—
247#394—591no—
248#394—591no—
249#394—591no—
250#390—591no—
251#390—591no—
252#388—591no—
253#388—591no—
254#388—591no—
255#379—591no—
256#379D5911yescharacteristic, complemented
257C59#268511yescharacteristic, complemented, Sylow
258C25C2×D5911yescharacteristic
259C22×D4—591no—
260C22×D4—591no—
261C22×D4—591no—
262#126—1184no—
263#120—1184no—
264C2×C4⋊C4—591no—
265C2×C4⋊C4—591no—
266C2×C4⋊C4—591no—
267C2×C4⋊C4—591no—
268C2×C4⋊C4—591no—
269C2×C4⋊C4—591no—
270C2×C22⋊C4—591no—
271C2×C22⋊C4—591no—
272C2×C22⋊C4—591no—
273C2×C22⋊C4—591no—
274C2×C22⋊C4—591no—
275C2×C22⋊C4—591no—
276C2×C22⋊C4—591no—
277C2×C22⋊C4—591no—
278C2×C22⋊C4—591no—
279C2×C22⋊C4—591no—
280C2×C22⋊C4—591no—
281C2×C22⋊C4—591no—
282C2×C22⋊C4—591no—
283C2×C22⋊C4C2×D5911yescharacteristic
284C2×C22⋊C4C2×D5911yescharacteristic
285C2×C22⋊C4C2×D5911yescharacteristic
286C2×C22⋊C4C2×D5911yescharacteristic
287C2×C22⋊C4C2×D5911yescharacteristic
288C2×C22⋊C4C2×D5911yescharacteristic
289C2×C42—591no—
290C2×C42—591no—
291#95—591no—
292#95—591no—
293#95—591no—
294#95—591no—
295C24—22no—
296C24—22no—
297C24—22no—
298C24—41no—
299C24—41no—
300C24—41no—
301C24—41no—
302C24—591no—
303C24C22×D5911yescharacteristic
304C24C22×D5911yescharacteristic
305C24C22×D5911yescharacteristic
306C2×D4—1182no—
307C2×D4—1182no—
308C2×D4—1182no—
309C2×D4—1182no—
310C2×D4—1182no—
311C2×D4—2361no—
312C2×D4—2361no—
313C2×D4—2361no—
314C2×D4—2361no—
315C22×C4—591no—
316C22×C4—591no—
317C22×C4—591no—
318C22×C4—591no—
319C22×C4—591no—
320C22×C4—591no—
321C22×C4—591no—
322C22×C4C22×D5911yescharacteristic
323C22×C4C22×D5911yescharacteristic
324C22×C4C22×D5911yescharacteristic
325C22×C4C22×D5911yescharacteristic
326C4⋊C4—1182no—
327C4⋊C4—1182no—
328C4⋊C4—1182no—
329C4⋊C4—2361no—
330C4⋊C4—2361no—
331C4⋊C4—2361no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—594no—
339C22⋊C4—1182no—
340C22⋊C4—1182no—
341C22⋊C4—1182no—
342C22⋊C4—1182no—
343C22⋊C4—2361no—
344C22⋊C4—2361no—
345C22⋊C4—2361no—
346C22⋊C4—2361no—
347C22⋊C4—2361no—
348C22⋊C4—2361no—
349C22⋊C4—2361no—
350C22⋊C4—2361no—
351C42—1182no—
352C42—2361no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—44no—
372C23—44no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—1181no—
379C23—1181no—
380C23—1181no—
381C23—1181no—
382C23—1181no—
383C23—1181no—
384C23—1181no—
385C23#1174568512yes—
386C23D4×D5912yes—
387C23#1174568712yes—
388C23C23×D5911yescharacteristic
389D4—2364no—
390D4—2364no—
391D4—2364no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—592no—
405C2×C4—592no—
406C2×C4—1181no—
407C2×C4—1181no—
408C2×C4—1181no—
409C2×C4—1181no—
410C2×C4—1181no—
411C2×C4—1181no—
412C2×C4—1181no—
413C2×C4—1181no—
414C2×C4—1181no—
415C2×C4—1181no—
416C2×C4—1181no—
417C2×C4—1181no—
418C2×C4—1181no—
419C2×C4—1181no—
420C2×C4—1181no—
421C2×C4—1181no—
422C2×C4—1181no—
423C2×C4—1181no—
424C2×C4—1181no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—416no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—2361no—
448C22—2361no—
449C22—2361no—
450C22—2361no—
451C22—2361no—
452C22—2361no—
453C22—2361no—
454C22C2×D4×D5911yescharacteristic
455C22C2×#1174568711yescharacteristic
456C22C2×#1174568511yescharacteristic
457C22#1427377211yescharacteristic
458C22#1427377211yescharacteristic
459C22#1427377211yescharacteristic
460C22#1427377211yescharacteristic
461C4—41no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—1182no—
466C4—1182no—
467C4—2361no—
468C4—2361no—
469C4—2361no—
470C4—2361no—
471C4—2361no—
472C2—42no—
473C2—42no—
474C2—42no—
475C2—4721no—
476C2#1683796711yescharacteristic
477C2#1683798711yescharacteristic
478C2#1683799011yescharacteristic
479C2#1683803911yescharacteristic
480C2#1683804211yescharacteristic
481C2#1683807811yescharacteristic
482C2#1683814111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#379C2
hypercenter#379D59
hypocenterC59#2685
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14273720C2semidirect
3. #16837338C2semidirect
4. #16837325C2semidirect
5. #16837318C2semidirect
6. #16837318C2semidirect
7. #16837317C2semidirect
8. #16837317C2semidirect
9. #16837302C2semidirect
10. #16837302C2semidirect
11. #16837296C2semidirect
12. #16837295C2semidirect
13. #16837290C2semidirect
14. #16837258C2semidirect
15. C59×#379C2semidirect
21. C2×C4⋊Dic59C22semidirect
22. C2×C4⋊Dic59C22semidirect
23. C2×Dic59⋊C4C22semidirect
24. C2×Dic59⋊C4C22semidirect
25. C2×Dic59⋊C4C22semidirect
26. C2×Dic59⋊C4C22semidirect
36. C2×(C2×D59)⋊C4C22semidirect
37. C2×(C2×D59)⋊C4C22semidirect
38. C2×(C2×D59)⋊C4C22semidirect
39. C2×(C2×D59)⋊C4C22semidirect
40. C2×C4×Dic59C22semidirect
41. C2×C4×Dic59C22semidirect
42. C59⋊#95C22semidirect
43. C59⋊#95C22semidirect
44. C59⋊#95C22semidirect
45. C59⋊#95C22semidirect
256. #379D59semidirect
257. C59#2685semidirect