Finite Group Databasebeta

← #21430482

Subgroups — #21430482

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×#14273722C211yesmaximal, characteristic, complemented
2C2×#14273695C211yesmaximal, characteristic
3#16837337C211yesmaximal, characteristic, complemented
4#16837325C211yesmaximal, characteristic, complemented
5#16837318C211yesmaximal, characteristic, complemented
6#16837317C211yesmaximal, characteristic, complemented
7#16837317C211yesmaximal, characteristic, complemented
8#16837316C211yesmaximal, characteristic, complemented
9#16837302C211yesmaximal, characteristic, complemented
10#16837296C211yesmaximal, characteristic, complemented
11#16837293C211yesmaximal, characteristic, complemented
12#16837293C211yesmaximal, characteristic, complemented
13#16837257C211yesmaximal, characteristic, complemented
14#16837257C211yesmaximal, characteristic, complemented
15C59×#390C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19#14273722—24no—
20#14273695—24no—
21C2×C4⋊Dic59C2211yescharacteristic, complemented
22C2×Dic59⋊C4C2211yescharacteristic, complemented
23C2×Dic59⋊C4C2211yescharacteristic, complemented
24C2×Dic59⋊C4C2211yescharacteristic, complemented
25C2×Dic59⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic59C2211yescharacteristic
27C2×C22⋊Dic59C2211yescharacteristic
28C2×C22⋊Dic59C2211yescharacteristic
29C2×C22⋊Dic59C2211yescharacteristic, complemented
30C2×C22⋊Dic59C2211yescharacteristic, complemented
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×(C2×D59)⋊C4C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic
40C2×(C2×D59)⋊C4C2211yescharacteristic
41C2×C4×Dic59C2211yescharacteristic, complemented
42C59⋊#95C2211yescharacteristic, complemented
43C59⋊#95C2211yescharacteristic, complemented
44C59⋊#95C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C22×D4×C59C2211yescharacteristic
47C2×C4⋊C4×C59C2211yescharacteristic, complemented
48C2×C22⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50C2×C22⋊C4×C59C2211yescharacteristic, complemented
51C2×C22⋊C4×C59C2211yescharacteristic, complemented
52C2×C42×C59C2211yescharacteristic, complemented
53C24×C59C2311yescharacteristic
54C24×C59C2311yescharacteristic
55C23×D59—22no—
56C23×D59—22no—
57C23×D59—22no—
58C23×D59—41no—
59C23×D59—41no—
60C23×D59—41no—
61C23×D59—41no—
62C23×D59C2311yescharacteristic
63C23×D59C2311yescharacteristic
64C2×D4×C59—22no—
65C2×D4×C59—22no—
66C2×D4×C59—41no—
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C22×C4×C59C2311yescharacteristic
71C22×C4×C59C2311yescharacteristic
72C2×C22⋊D59—22no—
73C2×C22⋊D59—22no—
74C2×C22⋊D59—22no—
75C2×C22⋊D59—41no—
76C2×C22⋊D59—41no—
77C2×C22⋊D59—41no—
78C22×Dic59C2311yescharacteristic
79C22×Dic59C2311yescharacteristic
80C22×Dic59C2311yescharacteristic
81C22×Dic59C2311yescharacteristic
82C22×Dic59C2311yescharacteristic
83C22×Dic59C2311yescharacteristic
84C4⋊C4×C59—22no—
85C22⋊C4×C59—41no—
86C22⋊C4×C59—41no—
87C22⋊C4×C59—41no—
88C22⋊C4×C59—41no—
89C42×C59—41no—
90C22⋊Dic59—22no—
91C22⋊Dic59—22no—
92C22⋊Dic59—41no—
93C22⋊Dic59—41no—
94C22⋊Dic59—41no—
95(C2×D59)⋊C4—22no—
96(C2×D59)⋊C4—22no—
97(C2×D59)⋊C4—22no—
98(C2×D59)⋊C4—22no—
99(C2×D59)⋊C4—41no—
100(C2×D59)⋊C4—41no—
101(C2×D59)⋊C4—41no—
102(C2×D59)⋊C4—41no—
103(C2×D59)⋊C4—41no—
104(C2×D59)⋊C4D414yes—
105C4⋊Dic59—22no—
106Dic59⋊C4—22no—
107Dic59⋊C4—41no—
108Dic59⋊C4—41no—
109Dic59⋊C4—41no—
110C4×Dic59—22no—
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#4112yes—
125C23×C59C2411yescharacteristic
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—21no—
129C22×D59—21no—
130C22×D59—21no—
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134C22×D59—21no—
135C22×D59—21no—
136C22×D59—21no—
137C22×D59—21no—
138C22×D59—44no—
139C22×D59—44no—
140C22×D59—44no—
141C22×D59—44no—
142C22×D59—44no—
143C22×D59—44no—
144C22×D59—44no—
145C22×D59C2×D412yes—
146C22×D59#4112yes—
147D4×C59—44no—
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—
159C2×C4×C59—21no—
160C2×C4×C59—21no—
161C2×C4×C59—21no—
162C2×C4×C59C2×D412yes—
163C22⋊D59—44no—
164C22⋊D59—44no—
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×Dic59—21no—
182C2×Dic59C2×D412yes—
183C22×C59—22no—
184C22×C59—22no—
185C22×C59—22no—
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×C59—41no—
195C22×C59—41no—
196C22×C59—41no—
197C22×C59C22×D411yescharacteristic
198C22×C59C2×#4111yescharacteristic
199C22×C59C2×#4111yescharacteristic
200C22×C59H(5,𝔽2)11yescharacteristic
201C22×C59H(5,𝔽2)11yescharacteristic
202C22×C59H(5,𝔽2)11yescharacteristic
203C22×C59H(5,𝔽2)11yescharacteristic
204C2×D59—22no—
205C2×D59—22no—
206C2×D59—22no—
207C2×D59—22no—
208C2×D59—22no—
209C2×D59—22no—
210C2×D59—416no—
211C2×D59—41no—
212C2×D59—41no—
213C2×D59—41no—
214C2×D59—41no—
215C2×D59—41no—
216C2×D59—41no—
217C2×D59—41no—
218C2×D59—41no—
219C4×C59—22no—
220C4×C59—41no—
221C4×C59—41no—
222C4×C59—41no—
223C4×C59—41no—
224Dic59—22no—
225Dic59—41no—
226Dic59—41no—
227Dic59—41no—
228Dic59—41no—
229Dic59—41no—
230#2685—591nomaximal, Sylow
231C2×C59—42no—
232C2×C59—81no—
233C2×C59#53511yescharacteristic
234C2×C59#53811yescharacteristic
235C2×C59#53811yescharacteristic
236C2×C59#54611yescharacteristic
237C2×C59#54611yescharacteristic
238C2×C59#55111yescharacteristic
239C2×C59#56011yescharacteristic
240D59—42no—
241D59—42no—
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#390D5911yescharacteristic, complemented
252#388—591no—
253#388—591no—
254#388—591no—
255#379—591no—
256#379—591no—
257C59#268511yescharacteristic, complemented, Sylow
258C25—591no—
259C22×D4—591no—
260C22×D4—591no—
261C22×D4C2×D5911yescharacteristic
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⋊C4C2×D5911yescharacteristic, complemented
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⋊C4—591no—
284C2×C22⋊C4—591no—
285C2×C22⋊C4C2×D5911yescharacteristic
286C2×C22⋊C4C2×D5911yescharacteristic
287C2×C22⋊C4C2×D5911yescharacteristic, complemented
288C2×C22⋊C4C2×D5911yescharacteristic, complemented
289C2×C42—591no—
290C2×C42C2×D5911yescharacteristic, complemented
291#95—591no—
292#95—591no—
293#95—591no—
294#95—591no—
295C24—591no—
296C24—591no—
297C24—1182no—
298C24—1182no—
299C24—1182no—
300C24—2361no—
301C24—2361no—
302C24—2361no—
303C24—2361no—
304C24C22×D5911yescharacteristic
305C24C22×D5911yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—1182no—
310C2×D4—1182no—
311C2×D4—1182no—
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×C4C22×D5911yescharacteristic
322C22×C4C22×D5911yescharacteristic
323C22×C4C22×D5911yescharacteristic
324C22×C4C22×D5911yescharacteristic
325C22×C4C22×D5911yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—1182no—
328C4⋊C4—1182no—
329C4⋊C4—2361no—
330C4⋊C4—2361no—
331C4⋊C4—2361no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—594no—
337C22⋊C4—1182no—
338C22⋊C4—1182no—
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—41no—
352C42—1182no—
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—592no—
367C23—592no—
368C23—1181no—
369C23—1181no—
370C23—1181no—
371C23—1181no—
372C23—1181no—
373C23—1181no—
374C23—1181no—
375C23—1181no—
376C23—1181no—
377C23—1181no—
378C23—1181no—
379C23—1181no—
380C23—2364no—
381C23—2364no—
382C23—2364no—
383C23—2364no—
384C23—2364no—
385C23—2364no—
386C23—2364no—
387C23#1174568512yes—
388C23C23×D5911yescharacteristic
389D4—44no—
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—21no—
405C2×C4—21no—
406C2×C4—592no—
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×C4D4×D5912yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—1182no—
440C22—1182no—
441C22—1182no—
442C22—1182no—
443C22—1182no—
444C22—1182no—
445C22—23616no—
446C22—2361no—
447C22—2361no—
448C22—2361no—
449C22—2361no—
450C22—2361no—
451C22—2361no—
452C22—2361no—
453C22—2361no—
454C22C2×D4×D5911yescharacteristic
455C22#41×D5911yescharacteristic
456C22C2×#1174568511yescharacteristic
457C22#1427377211yescharacteristic
458C22#1427377211yescharacteristic
459C22#1427377211yescharacteristic
460C22#1427377311yescharacteristic
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—1182no—
467C4—2361no—
468C4—2361no—
469C4—2361no—
470C4—2361no—
471C4—2361no—
472C2—42no—
473C2—81no—
474C2—2362no—
475C2—2362no—
476C2#1683796511yescharacteristic
477C2#1683798411yescharacteristic
478C2#1683798511yescharacteristic
479C2#1683804211yescharacteristic
480C2#1683804511yescharacteristic
481C2#1683808111yescharacteristic
482C2#1683814011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#390C2
hypercenter#390D59
hypocenterC59#2685
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14273722C2semidirect
3. #16837337C2semidirect
4. #16837325C2semidirect
5. #16837318C2semidirect
6. #16837317C2semidirect
7. #16837317C2semidirect
8. #16837316C2semidirect
9. #16837302C2semidirect
10. #16837296C2semidirect
11. #16837293C2semidirect
12. #16837293C2semidirect
13. #16837257C2semidirect
14. #16837257C2semidirect
15. C59×#390C2semidirect
21. C2×C4⋊Dic59C22semidirect
22. C2×Dic59⋊C4C22semidirect
23. C2×Dic59⋊C4C22semidirect
24. C2×Dic59⋊C4C22semidirect
25. C2×Dic59⋊C4C22semidirect
29. C2×C22⋊Dic59C22semidirect
30. C2×C22⋊Dic59C22semidirect
41. C2×C4×Dic59C22semidirect
42. C59⋊#95C22semidirect
43. C59⋊#95C22semidirect
44. C59⋊#95C22semidirect
45. C59⋊#95C22semidirect
47. C2×C4⋊C4×C59C22semidirect
50. C2×C22⋊C4×C59C22semidirect
51. C2×C22⋊C4×C59C22semidirect
52. C2×C42×C59C22semidirect
251. #390D59semidirect
257. C59#2685semidirect
269. C2×C4⋊C4C2×D59semidirect
287. C2×C22⋊C4C2×D59semidirect
288. C2×C22⋊C4C2×D59semidirect
290. C2×C42C2×D59semidirect