Finite Group Databasebeta

← #21430320

Subgroups — #21430320

Order 7552.

796 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273715C211yesmaximal, characteristic, complemented
2C2×#14273713C211yesmaximal, characteristic, complemented
3C2×#14273697C211yesmaximal, characteristic, complemented
4C2×#14273697C211yesmaximal, characteristic, complemented
5#16837319C211yesmaximal, characteristic, complemented
6#16837318C211yesmaximal, characteristic, complemented
7#16837315C211yesmaximal, characteristic, complemented
8#16837312C211yesmaximal, characteristic, complemented
9#16837312C211yesmaximal, characteristic, complemented
10#16837311C211yesmaximal, characteristic, complemented
11#16837304C211yesmaximal, characteristic, complemented
12#16837303C211yesmaximal, characteristic, complemented
13#16837294C211yesmaximal, characteristic, complemented
14#16837257C211yesmaximal, characteristic, complemented
15C59×#388C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×Dic118C2211yescharacteristic, complemented
18C22×D236C2211yescharacteristic
19C22×D236C2211yescharacteristic
20C22×D236C2211yescharacteristic
21C22×D236C2211yescharacteristic
22C22×D236C2211yescharacteristic, complemented
23C22×C22⋊D59C2211yescharacteristic
24C22×C22⋊D59C2211yescharacteristic
25#14273715—24no—
26#14273713—24no—
27#14273697—24no—
28#14273697—24no—
29C2×C4⋊Dic59C2211yescharacteristic, complemented
30C2×C22⋊Dic59C2211yescharacteristic
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, complemented
40C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic59C2211yescharacteristic, complemented
46C59⋊#95C2211yescharacteristic, complemented
47C59⋊#95C2211yescharacteristic, complemented
48C2×C4⋊C4×C59C2211yescharacteristic, complemented
49C2×C22⋊C4×C59C2211yescharacteristic
50C2×C22⋊C4×C59C2211yescharacteristic
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C42×C59C2211yescharacteristic, complemented
53#95×C59C2211yescharacteristic, complemented
54#95×C59C2211yescharacteristic, complemented
55C24×C59C2311yescharacteristic
56C23×D59—22no—
57C23×D59—22no—
58C23×D59—22no—
59C23×D59—41no—
60C23×D59—41no—
61C23×D59—41no—
62C23×D59—41no—
63C23×D59C2311yescharacteristic
64C23×D59C2311yescharacteristic
65C23×D59C2311yescharacteristic
66C23×D59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C22×C4×C59C2311yescharacteristic
71C22×C4×C59C2311yescharacteristic
72C22×C4×C59C2311yescharacteristic
73C2×C22⋊D59—22no—
74C2×C22⋊D59—22no—
75C2×C22⋊D59—22no—
76C2×C22⋊D59—41no—
77C2×C22⋊D59—41no—
78C2×C22⋊D59—41no—
79C22×Dic59C2311yescharacteristic
80C22×Dic59C2311yescharacteristic
81C22×Dic59C2311yescharacteristic
82C22×Dic59C2311yescharacteristic
83C2×D236—22no—
84C2×D236—22no—
85C2×D236—22no—
86C2×D236—22no—
87C2×D236—22no—
88C2×D236—22no—
89C2×D236—22no—
90C2×D236—41no—
91C2×D236—41no—
92C2×D236—41no—
93C2×D236—41no—
94C2×D236—41no—
95C2×D236—41no—
96C2×D236—41no—
97C2×D236—41no—
98C2×Dic118—22no—
99C2×Dic118—22no—
100C2×Dic118—41no—
101C4⋊C4×C59—41no—
102C22⋊C4×C59—22no—
103C22⋊C4×C59—41no—
104C22⋊C4×C59D414yescomplemented
105C42×C59—22no—
106C22⋊Dic59—22no—
107(C2×D59)⋊C4—22no—
108(C2×D59)⋊C4—22no—
109(C2×D59)⋊C4—22no—
110(C2×D59)⋊C4—22no—
111(C2×D59)⋊C4—22no—
112(C2×D59)⋊C4—22no—
113(C2×D59)⋊C4—22no—
114(C2×D59)⋊C4—22no—
115(C2×D59)⋊C4—41no—
116(C2×D59)⋊C4—41no—
117(C2×D59)⋊C4—41no—
118(C2×D59)⋊C4—41no—
119(C2×D59)⋊C4—41no—
120(C2×D59)⋊C4D414yescomplemented
121C4⋊Dic59—41no—
122C4×Dic59—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—21no—
127C23×C59—21no—
128C23×C59—21no—
129C23×C59C2×D412yes—
130C23×C59C2411yescharacteristic
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134C22×D59—21no—
135C22×D59—21no—
136C22×D59—21no—
137C22×D59—21no—
138C22×D59—21no—
139C22×D59—21no—
140C22×D59—21no—
141C22×D59—21no—
142C22×D59—21no—
143C22×D59—21no—
144C22×D59—21no—
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—44no—
158C22×D59—44no—
159C22×D59—44no—
160C22×D59—44no—
161C22×D59—44no—
162C22×D59—44no—
163C22×D59—44no—
164C22×D59C2×D412yes—
165C22×D59#4112yes—
166C2×C4×C59—21no—
167C2×C4×C59—21no—
168C2×C4×C59—21no—
169C2×C4×C59—21no—
170C2×C4×C59—21no—
171C2×C4×C59—21no—
172C2×C4×C59—21no—
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×C59C2×D412yes—
182C2×C4×C59C2×D412yes—
183C2×C4×C59C2×D412yes—
184C22⋊D59—44no—
185C22⋊D59—44no—
186C2×Dic59—21no—
187C2×Dic59—21no—
188C2×Dic59—21no—
189C2×Dic59—21no—
190C2×Dic59—21no—
191C2×Dic59—21no—
192C2×Dic59—21no—
193C2×Dic59—21no—
194C2×Dic59—21no—
195C2×Dic59—21no—
196C2×Dic59—21no—
197C2×Dic59C2×D412yes—
198D236—44no—
199D236—44no—
200D236—44no—
201D236—44no—
202D236—44no—
203Dic118—44no—
204C22×C59—22no—
205C22×C59—22no—
206C22×C59—22no—
207C22×C59—41no—
208C22×C59—41no—
209C22×C59—41no—
210C22×C59—41no—
211C22×C59C22×D411yescharacteristic
212C22×C59C22×D411yescharacteristic
213C22×C59C2×#4111yescharacteristic
214C22×C59H(5,𝔽2)11yescharacteristic
215C22×C59H(5,𝔽2)11yescharacteristic
216C22×C59H(5,𝔽2)11yescharacteristic
217C22×C59H(5,𝔽2)11yescharacteristic
218C2×D59—22no—
219C2×D59—22no—
220C2×D59—22no—
221C2×D59—22no—
222C2×D59—22no—
223C2×D59—22no—
224C2×D59—416no—
225C2×D59—41no—
226C2×D59—41no—
227C2×D59—41no—
228C2×D59—41no—
229C2×D59—41no—
230C2×D59—41no—
231C2×D59—41no—
232C2×D59—41no—
233C2×D59—41no—
234C2×D59—41no—
235C2×D59—41no—
236C2×D59—41no—
237C2×D59—41no—
238C2×D59—41no—
239C2×D59—41no—
240C2×D59—41no—
241C2×D59—41no—
242C2×D59—41no—
243C2×D59—41no—
244C2×D59—41no—
245C2×D59—41no—
246C2×D59—41no—
247C4×C59—22no—
248C4×C59—22no—
249C4×C59—22no—
250C4×C59—41no—
251C4×C59—41no—
252C4×C59—41no—
253Dic59—22no—
254Dic59—41no—
255Dic59—41no—
256Dic59—41no—
257#2670—591nomaximal, Sylow
258C2×C59—42no—
259C2×C59#53511yescharacteristic
260C2×C59#53511yescharacteristic
261C2×C59#53811yescharacteristic
262C2×C59D4211yescharacteristic
263C2×C59#54611yescharacteristic
264C2×C59#54611yescharacteristic
265C2×C59H(3,𝔽4)11yescharacteristic
266D59—42no—
267D59—42no—
268D59—81no—
269D59—81no—
270C2×#124—591no—
271C2×#124—591no—
272C2×#120—591no—
273C2×#120—591no—
274#394—591no—
275#394—591no—
276#393—591no—
277#392—591no—
278#392—591no—
279#392—591no—
280#390—591no—
281#390—591no—
282#388—591no—
283#388D5911yescharacteristic, complemented
284#379—591no—
285C59#267011yescharacteristic, complemented, Sylow
286C25—591no—
287C22×Q8—591no—
288C22×D4—591no—
289C22×D4—591no—
290C22×D4—591no—
291C22×D4—591no—
292C22×D4—591no—
293C22×D4—591no—
294C22×D4—591no—
295#124—1184no—
296#124—1184no—
297#120—1184no—
298#120—1184no—
299C2×C4⋊C4—591no—
300C2×C4⋊C4C2×D5911yescharacteristic, complemented
301C2×C22⋊C4—591no—
302C2×C22⋊C4—591no—
303C2×C22⋊C4—591no—
304C2×C22⋊C4—591no—
305C2×C22⋊C4—591no—
306C2×C22⋊C4—591no—
307C2×C22⋊C4—591no—
308C2×C22⋊C4—591no—
309C2×C22⋊C4—591no—
310C2×C22⋊C4—591no—
311C2×C22⋊C4—591no—
312C2×C22⋊C4—591no—
313C2×C22⋊C4—591no—
314C2×C22⋊C4—591no—
315C2×C22⋊C4—591no—
316C2×C22⋊C4C2×D5911yescharacteristic
317C2×C22⋊C4C2×D5911yescharacteristic
318C2×C22⋊C4C2×D5911yescharacteristic
319C2×C42—591no—
320C2×C42C2×D5911yescharacteristic, complemented
321#95—591no—
322#95—591no—
323#95C2×D5911yescharacteristic, complemented
324#95C2×D5911yescharacteristic, complemented
325C24—591no—
326C24—591no—
327C24—591no—
328C24—591no—
329C24—1182no—
330C24—1182no—
331C24—1182no—
332C24—2361no—
333C24—2361no—
334C24—2361no—
335C24—2361no—
336C24C22×D5911yescharacteristic
337C2×Q8—1182no—
338C2×Q8—1182no—
339C2×Q8—2361no—
340C2×D4—1182no—
341C2×D4—1182no—
342C2×D4—1182no—
343C2×D4—1182no—
344C2×D4—1182no—
345C2×D4—1182no—
346C2×D4—1182no—
347C2×D4—1182no—
348C2×D4—1182no—
349C2×D4—1182no—
350C2×D4—2361no—
351C2×D4—2361no—
352C2×D4—2361no—
353C2×D4—2361no—
354C2×D4—2361no—
355C2×D4—2361no—
356C2×D4—2361no—
357C2×D4—2361no—
358C2×D4—2361no—
359C2×D4—2361no—
360C2×D4—2361no—
361C22×C4—591no—
362C22×C4—591no—
363C22×C4—591no—
364C22×C4—591no—
365C22×C4C22×D5911yescharacteristic
366C22×C4C22×D5911yescharacteristic
367C22×C4C22×D5911yescharacteristic
368C22×C4C22×D5911yescharacteristic
369C22×C4C22×D5911yescharacteristic
370C22×C4C22×D5911yescharacteristic
371C4⋊C4—41no—
372C4⋊C4—2361no—
373C22⋊C4—22no—
374C22⋊C4—41no—
375C22⋊C4—594no—
376C22⋊C4—1182no—
377C22⋊C4—1182no—
378C22⋊C4—1182no—
379C22⋊C4—1182no—
380C22⋊C4—1182no—
381C22⋊C4—1182no—
382C22⋊C4—1182no—
383C22⋊C4—1182no—
384C22⋊C4—1182no—
385C22⋊C4—2361no—
386C22⋊C4—2361no—
387C22⋊C4—2361no—
388C22⋊C4—2361no—
389C22⋊C4—2361no—
390C22⋊C4D23614yescomplemented
391C42—22no—
392C42—1182no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—592no—
400C23—592no—
401C23—1181no—
402C23—1181no—
403C23—1181no—
404C23—1181no—
405C23—1181no—
406C23—1181no—
407C23—1181no—
408C23—1181no—
409C23—1181no—
410C23—1181no—
411C23—1181no—
412C23—1181no—
413C23—1181no—
414C23—1181no—
415C23—1181no—
416C23—1181no—
417C23—1181no—
418C23—1181no—
419C23—1181no—
420C23—1181no—
421C23—1181no—
422C23—1181no—
423C23—1181no—
424C23—1181no—
425C23—1181no—
426C23—1181no—
427C23—2364no—
428C23—2364no—
429C23—2364no—
430C23—2364no—
431C23—2364no—
432C23—2364no—
433C23—2364no—
434C23C2×D23612yes—
435C23C23×D5911yescharacteristic
436Q8—2364no—
437D4—2364no—
438D4—2364no—
439D4—2364no—
440D4—2364no—
441D4—2364no—
442D4—2364no—
443D4—2364no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—592no—
460C2×C4—1181no—
461C2×C4—1181no—
462C2×C4—1181no—
463C2×C4—1181no—
464C2×C4—1181no—
465C2×C4—1181no—
466C2×C4—1181no—
467C2×C4—1181no—
468C2×C4—1181no—
469C2×C4—1181no—
470C2×C4—1181no—
471C2×C4C2×D23612yes—
472C2×C4C2×D23612yes—
473C2×C4D4×D5912yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—1182no—
482C22—1182no—
483C22—1182no—
484C22—1182no—
485C22—1182no—
486C22—1182no—
487C22—23616no—
488C22—2361no—
489C22—2361no—
490C22—2361no—
491C22—2361no—
492C22—2361no—
493C22—2361no—
494C22—2361no—
495C22—2361no—
496C22—2361no—
497C22—2361no—
498C22—2361no—
499C22—2361no—
500C22—2361no—
501C22—2361no—
502C22—2361no—
503C22—2361no—
504C22—2361no—
505C22—2361no—
506C22—2361no—
507C22—2361no—
508C22—2361no—
509C22—2361no—
510C22C2×D4×D5911yescharacteristic
511C22C22×D23611yescharacteristic
512C22#41×D5911yescharacteristic
513C22#1427377211yescharacteristic
514C22#1427377311yescharacteristic
515C22#1427377311yescharacteristic
516C22#1427377311yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—1182no—
524C4—2361no—
525C4—2361no—
526C4—2361no—
527C2—42no—
528C2—4721no—
529C2—4721no—
530C2—2362no—
531C2—2362no—
532C2#1683796811yescharacteristic
533C2#1683797111yescharacteristic
534C2#1683799111yescharacteristic
535C2D4×D23611yescharacteristic
536C2#1683804411yescharacteristic
537C2#1683804711yescharacteristic
538C2#1683814411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#388C2
hypercenter#388D59
hypocenterC59#2670
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14273715C2semidirect
2. C2×#14273713C2semidirect
3. C2×#14273697C2semidirect
4. C2×#14273697C2semidirect
5. #16837319C2semidirect
6. #16837318C2semidirect
7. #16837315C2semidirect
8. #16837312C2semidirect
9. #16837312C2semidirect
10. #16837311C2semidirect
11. #16837304C2semidirect
12. #16837303C2semidirect
13. #16837294C2semidirect
14. #16837257C2semidirect
15. C59×#388C2semidirect
17. C22×Dic118C22semidirect
22. C22×D236C22semidirect
29. C2×C4⋊Dic59C22semidirect
39. C2×(C2×D59)⋊C4C22semidirect
40. C2×(C2×D59)⋊C4C22semidirect
41. C2×(C2×D59)⋊C4C22semidirect
42. C2×(C2×D59)⋊C4C22semidirect
43. C2×(C2×D59)⋊C4C22semidirect
44. C2×(C2×D59)⋊C4C22semidirect
45. C2×C4×Dic59C22semidirect
46. C59⋊#95C22semidirect
47. C59⋊#95C22semidirect
48. C2×C4⋊C4×C59C22semidirect
52. C2×C42×C59C22semidirect
53. #95×C59C22semidirect
54. #95×C59C22semidirect
104. C22⋊C4×C59D4semidirect
120. (C2×D59)⋊C4D4semidirect
283. #388D59semidirect
285. C59#2670semidirect
300. C2×C4⋊C4C2×D59semidirect
320. C2×C42C2×D59semidirect
323. #95C2×D59semidirect
324. #95C2×D59semidirect
390. C22⋊C4D236semidirect