Finite Group Databasebeta

← #21427626

Subgroups — #21427626

Order 7552.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273701C211yesmaximal, characteristic, complemented
2C2×#14273699C211yesmaximal, characteristic, complemented
3C2×#14273697C211yesmaximal, characteristic, complemented
4C2×#14273695C211yesmaximal, characteristic, complemented
5C22×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
6#16837324C211yesmaximal, characteristic, complemented
7#16837319C211yesmaximal, characteristic, complemented
8#16837318C211yesmaximal, characteristic, complemented
9#16837311C211yesmaximal, characteristic, complemented
10#16837304C211yesmaximal, characteristic, complemented
11#16837293C211yesmaximal, characteristic, complemented
12#16837281C211yesmaximal, characteristic, complemented
13#16837281C211yesmaximal, characteristic, complemented
14#16837277C211yesmaximal, characteristic, complemented
15C2×C4×D4×C59C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C22×C22⋊D59C2211yescharacteristic
22C22×C22⋊D59C2211yescharacteristic, complemented
23C23×Dic59C2211yescharacteristic
24#14273701—24no—
25#14273699—24no—
26#14273697—24no—
27#14273695—24no—
28C2×C4⋊Dic59C2211yescharacteristic, complemented
29C2×C4⋊Dic59C2211yescharacteristic, complemented
30C2×Dic59⋊C4C2211yescharacteristic, complemented
31C2×C22⋊Dic59C2211yescharacteristic
32C2×C22⋊Dic59C2211yescharacteristic, complemented
33C2×(C2×D59)⋊C4—24no—
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×(C2×D59)⋊C4C2211yescharacteristic
42C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C59⋊#95C2211yescharacteristic, complemented
47C59⋊#95C2211yescharacteristic, complemented
48C59⋊#95C2211yescharacteristic, complemented
49C22×D4×C59C2211yescharacteristic
50C23×C4×C59C2211yescharacteristic
51C23×C4×C59C2211yescharacteristic, complemented
52C4×D4×C59—24no—
53C2×C4⋊C4×C59C2211yescharacteristic, complemented
54C2×C22⋊C4×C59C2211yescharacteristic
55C2×C22⋊C4×C59C2211yescharacteristic, complemented
56C2×C42×C59C2211yescharacteristic, complemented
57C24×C59C2311yescharacteristic
58C24×C59C2311yescharacteristic
59C23×D59—22no—
60C23×D59—22no—
61C23×D59—22no—
62C23×D59—22no—
63C23×D59—22no—
64C23×D59—41no—
65C23×D59—41no—
66C23×D59C2311yescharacteristic
67C23×D59C2311yescharacteristic
68C23×D59C2311yescharacteristic
69C2×D4×C59—22no—
70C2×D4×C59—22no—
71C2×D4×C59D414yescomplemented
72C22×C4×C59—22no—
73C22×C4×C59—22no—
74C22×C4×C59—22no—
75C22×C4×C59—22no—
76C22×C4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59C2311yescharacteristic
79C22×C4×C59C2311yescharacteristic
80C22×C4×C59C2311yescharacteristic
81C22×C4×C59C2311yescharacteristic
82C22×C4×C59C2311yescharacteristic
83C2×C22⋊D59—22no—
84C2×C22⋊D59—22no—
85C2×C22⋊D59—22no—
86C2×C22⋊D59—22no—
87C2×C22⋊D59—22no—
88C2×C22⋊D59—22no—
89C2×C22⋊D59—22no—
90C2×C22⋊D59—22no—
91C2×C22⋊D59—22no—
92C2×C22⋊D59—41no—
93C2×C22⋊D59—41no—
94C2×C22⋊D59—41no—
95C22×Dic59—22no—
96C22×Dic59—22no—
97C22×Dic59—41no—
98C22×Dic59C2311yescharacteristic
99C22×Dic59C2311yescharacteristic
100C22×Dic59C2311yescharacteristic
101C22×Dic59C2311yescharacteristic
102C22×Dic59C2311yescharacteristic
103C2×D236—22no—
104C2×D236—22no—
105C2×D236—22no—
106C2×D236—22no—
107C2×D236—41no—
108C2×D236—41no—
109C4⋊C4×C59—22no—
110C22⋊C4×C59—22no—
111C22⋊C4×C59D414yescomplemented
112C42×C59—22no—
113C22⋊Dic59—22no—
114C22⋊Dic59—22no—
115(C2×D59)⋊C4—22no—
116(C2×D59)⋊C4—22no—
117(C2×D59)⋊C4—22no—
118(C2×D59)⋊C4—22no—
119(C2×D59)⋊C4—22no—
120(C2×D59)⋊C4—22no—
121(C2×D59)⋊C4—22no—
122(C2×D59)⋊C4—22no—
123(C2×D59)⋊C4—22no—
124(C2×D59)⋊C4—41no—
125(C2×D59)⋊C4D414yescomplemented
126C4⋊Dic59—22no—
127C4⋊Dic59—41no—
128Dic59⋊C4—22no—
129C23×C59—21no—
130C23×C59—21no—
131C23×C59—21no—
132C23×C59—21no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59—21no—
137C23×C59—21no—
138C23×C59—21no—
139C23×C59C2×D412yes—
140C23×C59C2×D412yes—
141C23×C59C2×D412yes—
142C23×C59#4112yes—
143C23×C59C2411yescharacteristic
144C22×D59—28no—
145C22×D59—21no—
146C22×D59—21no—
147C22×D59—21no—
148C22×D59—21no—
149C22×D59—21no—
150C22×D59—21no—
151C22×D59—21no—
152C22×D59—21no—
153C22×D59—21no—
154C22×D59—21no—
155C22×D59—21no—
156C22×D59—21no—
157C22×D59—21no—
158C22×D59—21no—
159C22×D59—21no—
160C22×D59—21no—
161C22×D59—21no—
162C22×D59—21no—
163C22×D59—21no—
164C22×D59—44no—
165C22×D59—44no—
166C22×D59—44no—
167C22×D59—44no—
168C22×D59—44no—
169C22×D59—44no—
170C22×D59C2×D412yes—
171C22×D59#4112yes—
172D4×C59—28no—
173C2×C4×C59—21no—
174C2×C4×C59—21no—
175C2×C4×C59—21no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—21no—
180C2×C4×C59—21no—
181C2×C4×C59—21no—
182C2×C4×C59—21no—
183C2×C4×C59—21no—
184C2×C4×C59—44no—
185C2×C4×C59—44no—
186C2×C4×C59C2×D412yes—
187C2×C4×C59C2×D412yes—
188C2×C4×C59C2×D412yes—
189C2×C4×C59C2×D412yes—
190C22⋊D59—44no—
191C22⋊D59—44no—
192C22⋊D59—44no—
193C22⋊D59—44no—
194C2×Dic59—21no—
195C2×Dic59—21no—
196C2×Dic59—21no—
197C2×Dic59—21no—
198C2×Dic59—21no—
199C2×Dic59—21no—
200C2×Dic59—21no—
201C2×Dic59—21no—
202C2×Dic59—21no—
203C2×Dic59—21no—
204C2×Dic59—21no—
205C2×Dic59—21no—
206C2×Dic59—21no—
207C2×Dic59—21no—
208C2×Dic59—44no—
209C2×Dic59C2×D412yes—
210D236—44no—
211D236—44no—
212C22×C59—22no—
213C22×C59—22no—
214C22×C59—22no—
215C22×C59—22no—
216C22×C59—22no—
217C22×C59—22no—
218C22×C59—22no—
219C22×C59—22no—
220C22×C59—22no—
221C22×C59—41no—
222C22×C59—41no—
223C22×C59—41no—
224C22×C59—41no—
225C22×C59#12114yescomplemented
226C22×C59C22×D411yescharacteristic
227C22×C59C22×D411yescharacteristic
228C22×C59C22×D411yescharacteristic
229C22×C59C2×#4111yescharacteristic
230C22×C59C2×#4111yescharacteristic
231C22×C59H(5,𝔽2)11yescharacteristic
232C22×C59H(5,𝔽2)11yescharacteristic
233C2×D59—22no—
234C2×D59—22no—
235C2×D59—22no—
236C2×D59—22no—
237C2×D59—22no—
238C2×D59—22no—
239C2×D59—416no—
240C2×D59—41no—
241C2×D59—41no—
242C2×D59—41no—
243C2×D59—41no—
244C2×D59—41no—
245C2×D59—41no—
246C2×D59—41no—
247C2×D59—41no—
248C2×D59—41no—
249C2×D59—41no—
250C2×D59—41no—
251C2×D59—41no—
252C2×D59—41no—
253C2×D59—41no—
254C2×D59—41no—
255C4×C59—22no—
256C4×C59—22no—
257C4×C59—22no—
258C4×C59—22no—
259C4×C59—41no—
260Dic59—22no—
261Dic59—41no—
262Dic59—41no—
263Dic59—41no—
264Dic59—41no—
265#2424—591nomaximal, Sylow
266C2×C59—24no—
267C2×C59—42no—
268C2×C59C2×#12111yescharacteristic
269C2×C59#52511yescharacteristic
270C2×C59#53811yescharacteristic
271C2×C59D4211yescharacteristic
272C2×C59D4211yescharacteristic
273C2×C59#54611yescharacteristic
274C2×C59#54611yescharacteristic
275D59—42no—
276D59—42no—
277D59—81no—
278C2×#121—591no—
279C2×#121—591no—
280C2×#120—591no—
281C2×#120—591no—
282C2×C4×D4D5911yescharacteristic, complemented
283C22×C22⋊C4—591no—
284#396—591no—
285#394—591no—
286#394—591no—
287#392—591no—
288#390—591no—
289#388—591no—
290#386—591no—
291#386—591no—
292#385—591no—
293C59#242411yescharacteristic, complemented, Sylow
294C25—591no—
295C22×D4—591no—
296C22×D4—591no—
297C22×D4—591no—
298C22×D4—591no—
299C22×D4—591no—
300C22×D4—591no—
301C22×D4C2×D5911yescharacteristic
302C23×C4—591no—
303C23×C4C2×D5911yescharacteristic
304C23×C4C2×D5911yescharacteristic, complemented
305#121—1184no—
306#121—1184no—
307#120—1184no—
308#120—1184no—
309C4×D4—24no—
310C2×C4⋊C4—591no—
311C2×C4⋊C4—591no—
312C2×C4⋊C4—591no—
313C2×C4⋊C4C2×D5911yescharacteristic, complemented
314C2×C22⋊C4—591no—
315C2×C22⋊C4—591no—
316C2×C22⋊C4—591no—
317C2×C22⋊C4—591no—
318C2×C22⋊C4—591no—
319C2×C22⋊C4—591no—
320C2×C22⋊C4—591no—
321C2×C22⋊C4—591no—
322C2×C22⋊C4—591no—
323C2×C22⋊C4—591no—
324C2×C22⋊C4—591no—
325C2×C22⋊C4—591no—
326C2×C22⋊C4—591no—
327C2×C22⋊C4—1184no—
328C2×C22⋊C4C2×D5911yescharacteristic
329C2×C22⋊C4C2×D5911yescharacteristic, complemented
330C2×C42C2×D5911yescharacteristic, complemented
331#95—591no—
332#95—591no—
333#95—591no—
334#95—591no—
335C24—591no—
336C24—591no—
337C24—591no—
338C24—1182no—
339C24—1182no—
340C24—1182no—
341C24—1182no—
342C24—1182no—
343C24—2361no—
344C24—2361no—
345C24C22×D5911yescharacteristic
346C24C22×D5911yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—1182no—
350C2×D4—1182no—
351C2×D4—1182no—
352C2×D4—1182no—
353C2×D4—1182no—
354C2×D4—1182no—
355C2×D4—1182no—
356C2×D4—1182no—
357C2×D4—1182no—
358C2×D4—1182no—
359C2×D4—1182no—
360C2×D4—1182no—
361C2×D4—1182no—
362C2×D4—2361no—
363C2×D4—2361no—
364C2×D4—2361no—
365C2×D4—2361no—
366C2×D4—2361no—
367C2×D4D23614yescomplemented
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—591no—
375C22×C4—591no—
376C22×C4—591no—
377C22×C4—591no—
378C22×C4—591no—
379C22×C4—1182no—
380C22×C4—1182no—
381C22×C4—2361no—
382C22×C4C22×D5911yescharacteristic
383C22×C4C22×D5911yescharacteristic
384C22×C4C22×D5911yescharacteristic
385C22×C4C22×D5911yescharacteristic
386C22×C4C22×D5911yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—1182no—
389C4⋊C4—1182no—
390C4⋊C4—2361no—
391C22⋊C4—22no—
392C22⋊C4—594no—
393C22⋊C4—1182no—
394C22⋊C4—1182no—
395C22⋊C4—1182no—
396C22⋊C4—1182no—
397C22⋊C4—1182no—
398C22⋊C4—1182no—
399C22⋊C4—1182no—
400C22⋊C4—1182no—
401C22⋊C4—1182no—
402C22⋊C4—1182no—
403C22⋊C4—1182no—
404C22⋊C4—2361no—
405C22⋊C4C22⋊D5914yescomplemented
406C42—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—592no—
418C23—592no—
419C23—1188no—
420C23—1181no—
421C23—1181no—
422C23—1181no—
423C23—1181no—
424C23—1181no—
425C23—1181no—
426C23—1181no—
427C23—1181no—
428C23—1181no—
429C23—1181no—
430C23—1181no—
431C23—1181no—
432C23—1181no—
433C23—1181no—
434C23—1181no—
435C23—1181no—
436C23—1181no—
437C23—1181no—
438C23—1181no—
439C23—2364no—
440C23—2364no—
441C23—2364no—
442C23—2364no—
443C23—2364no—
444C23—2364no—
445C23C2×D23612yes—
446C23C2×D23612yes—
447C23#1174568512yes—
448C23C2×C22⋊D5912yes—
449C23C23×D5911yescharacteristic
450D4—28no—
451D4—2364no—
452D4—2364no—
453D4—2364no—
454D4—2364no—
455D4—2364no—
456D4—2364no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—592no—
471C2×C4—1181no—
472C2×C4—1181no—
473C2×C4—1181no—
474C2×C4—1181no—
475C2×C4—1181no—
476C2×C4—1181no—
477C2×C4—1181no—
478C2×C4—1181no—
479C2×C4—1181no—
480C2×C4—1181no—
481C2×C4—1181no—
482C2×C4—1181no—
483C2×C4—1181no—
484C2×C4—1181no—
485C2×C4—2364no—
486C2×C4C2×D23612yes—
487C2×C4D4×D5912yes—
488C2×C4C2×C22⋊D5912yes—
489C2×C4C2×C22⋊D5912yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—1182no—
504C22—1182no—
505C22—1182no—
506C22—1182no—
507C22—1182no—
508C22—1182no—
509C22—23616no—
510C22—2361no—
511C22—2361no—
512C22—2361no—
513C22—2361no—
514C22—2361no—
515C22—2361no—
516C22—2361no—
517C22—2361no—
518C22—2361no—
519C22—2361no—
520C22—2361no—
521C22—2361no—
522C22—2361no—
523C22—2361no—
524C22—2361no—
525C22#1427370114yescomplemented
526C22C2×D4×D5911yescharacteristic
527C22C22×C22⋊D5911yescharacteristic
528C22C22×D23611yescharacteristic
529C22#41×D5911yescharacteristic
530C22C2×#1174568511yescharacteristic
531C22#1427377211yescharacteristic
532C22#1427377311yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—1182no—
539C4—2361no—
540C4—2361no—
541C4—2361no—
542C4—2361no—
543C2—24no—
544C2—42no—
545C2—4721no—
546C2—2362no—
547C2—2362no—
548C2C2×#1427370111yescharacteristic
549C2#1683791111yescharacteristic
550C2#1683798511yescharacteristic
551C2D4×C22⋊D5911yescharacteristic
552C2D4×D23611yescharacteristic
553C2#1683804011yescharacteristic
554C2#1683804711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×C4×D4×C59C2
hypercenterC2×C4×D4D59
hypocenterC59#2424
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14273701C2semidirect
2. C2×#14273699C2semidirect
3. C2×#14273697C2semidirect
4. C2×#14273695C2semidirect
5. C22×(C2×D59)⋊C4C2semidirect
6. #16837324C2semidirect
7. #16837319C2semidirect
8. #16837318C2semidirect
9. #16837311C2semidirect
10. #16837304C2semidirect
11. #16837293C2semidirect
12. #16837281C2semidirect
13. #16837281C2semidirect
14. #16837277C2semidirect
15. C2×C4×D4×C59C2semidirect
22. C22×C22⋊D59C22semidirect
28. C2×C4⋊Dic59C22semidirect
29. C2×C4⋊Dic59C22semidirect
30. C2×Dic59⋊C4C22semidirect
32. C2×C22⋊Dic59C22semidirect
42. C2×(C2×D59)⋊C4C22semidirect
43. C2×(C2×D59)⋊C4C22semidirect
44. C2×(C2×D59)⋊C4C22semidirect
45. C59⋊#95C22semidirect
46. C59⋊#95C22semidirect
47. C59⋊#95C22semidirect
48. C59⋊#95C22semidirect
51. C23×C4×C59C22semidirect
53. C2×C4⋊C4×C59C22semidirect
55. C2×C22⋊C4×C59C22semidirect
56. C2×C42×C59C22semidirect
71. C2×D4×C59D4semidirect
111. C22⋊C4×C59D4semidirect
125. (C2×D59)⋊C4D4semidirect
225. C22×C59#121semidirect
282. C2×C4×D4D59semidirect
293. C59#2424semidirect
304. C23×C4C2×D59semidirect
313. C2×C4⋊C4C2×D59semidirect
329. C2×C22⋊C4C2×D59semidirect
330. C2×C42C2×D59semidirect
367. C2×D4D236semidirect
405. C22⋊C4C22⋊D59semidirect
525. C22#14273701semidirect