Finite Group Databasebeta

← #21429835

Subgroups — #21429835

Order 7552.

824 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273700C211yesmaximal, characteristic, complemented
2C2×#14273697C211yesmaximal, characteristic, complemented
3C2×#14273695C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D59C211yesmaximal, characteristic, complemented
5#16837331C211yesmaximal, characteristic, complemented
6#16837330C211yesmaximal, characteristic, complemented
7#16837319C211yesmaximal, characteristic, complemented
8#16837318C211yesmaximal, characteristic, complemented
9#16837318C211yesmaximal, characteristic, complemented
10#16837311C211yesmaximal, characteristic, complemented
11#16837310C211yesmaximal, characteristic, complemented
12#16837280C211yesmaximal, characteristic, complemented
13#16837278C211yesmaximal, characteristic, complemented
14#16837259C211yesmaximal, characteristic, complemented
15C59×#394C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C22×C22⋊D59C2211yescharacteristic
22C22×C22⋊D59C2211yescharacteristic, complemented
23C22×C4×D59C2211yescharacteristic
24C22×C4×D59C2211yescharacteristic
25#14273700—24no—
26#14273697—24no—
27#14273695—24no—
28C2×C4⋊Dic59C2211yescharacteristic, complemented
29C2×Dic59⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic59C2211yescharacteristic
31C2×C22⋊Dic59C2211yescharacteristic
32C2×C22⋊Dic59C2211yescharacteristic, complemented
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
42C22⋊C4×D59—24no—
43C59⋊#95C2211yescharacteristic, complemented
44C59⋊#95C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C59⋊#95C2211yescharacteristic, complemented
47C59⋊#95C2211yescharacteristic, complemented
48C22×D4×C59C2211yescharacteristic
49C2×C4⋊C4×C59C2211yescharacteristic, complemented
50C2×C22⋊C4×C59C2211yescharacteristic
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C22⋊C4×C59C2211yescharacteristic, complemented
53C2×C22⋊C4×C59C2211yescharacteristic, complemented
54#95×C59C2211yescharacteristic, complemented
55C24×C59C2311yescharacteristic
56C24×C59C2311yescharacteristic
57C23×D59—22no—
58C23×D59—22no—
59C23×D59—41no—
60C23×D59—41no—
61C23×D59—41no—
62C23×D59—41no—
63C23×D59D414yescomplemented
64C23×D59C2311yescharacteristic
65C23×D59C2311yescharacteristic
66C23×D59C2311yescharacteristic
67C2×D4×C59—22no—
68C2×D4×C59—41no—
69C2×D4×C59—41no—
70C22×C4×C59C2311yescharacteristic
71C22×C4×C59C2311yescharacteristic
72C22×C4×C59C2311yescharacteristic
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C2×C22⋊D59—22no—
76C2×C22⋊D59—22no—
77C2×C22⋊D59—22no—
78C2×C22⋊D59—22no—
79C2×C22⋊D59—22no—
80C2×C22⋊D59—22no—
81C2×C22⋊D59—41no—
82C2×C22⋊D59—41no—
83C2×C22⋊D59—41no—
84C2×C22⋊D59—41no—
85C2×C22⋊D59—41no—
86C2×C22⋊D59—41no—
87C22×Dic59C2311yescharacteristic
88C22×Dic59C2311yescharacteristic
89C22×Dic59C2311yescharacteristic
90C22×Dic59C2311yescharacteristic
91C22×Dic59C2311yescharacteristic
92C2×D236—22no—
93C2×D236—22no—
94C2×D236—22no—
95C2×D236—22no—
96C2×D236—41no—
97C2×D236—41no—
98C2×C4×D59—22no—
99C2×C4×D59—41no—
100C2×C4×D59—41no—
101C2×C4×D59—41no—
102C2×C4×D59—41no—
103C2×C4×D59D414yescomplemented
104C4⋊C4×C59—41no—
105C22⋊C4×C59—22no—
106C22⋊C4×C59—22no—
107C22⋊C4×C59—22no—
108C22⋊C4×C59—41no—
109C22⋊Dic59—22no—
110C22⋊Dic59—22no—
111C22⋊Dic59—41no—
112(C2×D59)⋊C4—22no—
113(C2×D59)⋊C4—22no—
114(C2×D59)⋊C4—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—41no—
120(C2×D59)⋊C4—41no—
121C4⋊Dic59—41no—
122Dic59⋊C4—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—21no—
127C23×C59—21no—
128C23×C59—21no—
129C23×C59—21no—
130C23×C59—21no—
131C23×C59—21no—
132C23×C59—21no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59C2×D412yes—
137C23×C59C2411yescharacteristic
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—28no—
149C22×D59—21no—
150C22×D59—21no—
151C22×D59—21no—
152C22×D59—21no—
153C22×D59—21no—
154C22×D59—21no—
155C22×D59—21no—
156C22×D59—44no—
157C22×D59—44no—
158C22×D59—44no—
159C22×D59—44no—
160C22×D59—44no—
161C22×D59—44no—
162C22×D59C2×D412yes—
163C22×D59C2×D412yes—
164C22×D59C2×D412yes—
165C22×D59#4112yes—
166D4×C59—44no—
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—
182C22⋊D59—44no—
183C22⋊D59—44no—
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×Dic59—21no—
198C2×Dic59—21no—
199C2×Dic59—21no—
200C2×Dic59C2×D412yes—
201D236—44no—
202D236—44no—
203C4×D59—44no—
204C4×D59—44no—
205C22×C59—22no—
206C22×C59—22no—
207C22×C59—22no—
208C22×C59—41no—
209C22×C59—41no—
210C22×C59—41no—
211C22×C59—41no—
212C22×C59—41no—
213C22×C59—41no—
214C22×C59—41no—
215C22×C59—41no—
216C22×C59—41no—
217C22×C59—41no—
218C22×C59—41no—
219C22×C59C22×D411yescharacteristic
220C22×C59C22×D411yescharacteristic
221C22×C59C2×#4111yescharacteristic
222C22×C59H(5,𝔽2)11yescharacteristic
223C22×C59H(5,𝔽2)11yescharacteristic
224C22×C59H(5,𝔽2)11yescharacteristic
225C22×C59H(5,𝔽2)11yescharacteristic
226C2×D59—22no—
227C2×D59—22no—
228C2×D59—22no—
229C2×D59—22no—
230C2×D59—22no—
231C2×D59—22no—
232C2×D59—22no—
233C2×D59—22no—
234C2×D59—22no—
235C2×D59—416no—
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—
247C2×D59#12114yes—
248C4×C59—22no—
249C4×C59—41no—
250C4×C59—41no—
251C4×C59—41no—
252C4×C59—41no—
253Dic59—22no—
254Dic59—41no—
255Dic59—41no—
256Dic59—41no—
257Dic59—41no—
258#2617—591nomaximal, Sylow
259C2×C59—42no—
260C2×C59—81no—
261C2×C59C2×#12111yescharacteristic
262C2×C59#53411yescharacteristic
263C2×C59#53411yescharacteristic
264C2×C59#53411yescharacteristic
265C2×C59#53511yescharacteristic
266C2×C59#53811yescharacteristic
267C2×C59#53811yescharacteristic
268D59—24no—
269D59—42no—
270D59—81no—
271C2×#121—591no—
272C2×#120—591no—
273C2×#120—591no—
274C22×C22⋊C4—591no—
275#397—591no—
276#397—591no—
277#394—591no—
278#394—591no—
279#394—591no—
280#394D5911yescharacteristic, complemented
281#392—591no—
282#392—591no—
283#386—591no—
284#386—591no—
285#380—591no—
286C59#261711yescharacteristic, complemented, Sylow
287C25—591no—
288C22×D4—591no—
289C22×D4—591no—
290C22×D4—591no—
291C22×D4—591no—
292C22×D4—591no—
293C22×D4—591no—
294C22×D4C2×D5911yescharacteristic
295C23×C4—591no—
296C23×C4—591no—
297#121—1184no—
298#120—1184no—
299#120—1184no—
300C2×C4⋊C4—591no—
301C2×C4⋊C4—591no—
302C2×C4⋊C4C2×D5911yescharacteristic, complemented
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—1184no—
316C2×C22⋊C4C2×D5911yescharacteristic
317C2×C22⋊C4C2×D5911yescharacteristic
318C2×C22⋊C4C2×D5911yescharacteristic, complemented
319C2×C22⋊C4C2×D5911yescharacteristic, complemented
320#95—591no—
321#95—591no—
322#95—591no—
323#95—591no—
324#95—591no—
325#95C2×D5911yescharacteristic, complemented
326C24—591no—
327C24—591no—
328C24—594no—
329C24—591no—
330C24—1182no—
331C24—1182no—
332C24—2361no—
333C24—2361no—
334C24—2361no—
335C24—2361no—
336C24C22×D5911yescharacteristic
337C24C22×D5911yescharacteristic
338C2×D4—22no—
339C2×D4—41no—
340C2×D4—41no—
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—1182no—
351C2×D4—2361no—
352C2×D4—2361no—
353C2×D4—2361no—
354C2×D4—2361no—
355C2×D4—2361no—
356C2×D4—2361no—
357C2×D4—2361no—
358C2×D4—2361no—
359C22×C4—591no—
360C22×C4—594no—
361C22×C4—591no—
362C22×C4—591no—
363C22×C4—591no—
364C22×C4—591no—
365C22×C4—1182no—
366C22×C4—2361no—
367C22×C4—2361no—
368C22×C4—2361no—
369C22×C4—2361no—
370C22×C4C22×D5911yescharacteristic
371C22×C4C22×D5911yescharacteristic
372C22×C4C22×D5911yescharacteristic
373C22×C4C22×D5911yescharacteristic
374C22×C4C22×D5911yescharacteristic
375C4⋊C4—41no—
376C4⋊C4—1182no—
377C4⋊C4—2361no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C22⋊C4—1182no—
383C22⋊C4—1182no—
384C22⋊C4—1182no—
385C22⋊C4—1182no—
386C22⋊C4—1182no—
387C22⋊C4—1182no—
388C22⋊C4—1182no—
389C22⋊C4—1182no—
390C22⋊C4—1182no—
391C22⋊C4—2361no—
392C22⋊C4—2361no—
393C22⋊C4—2361no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—592no—
408C23—592no—
409C23—592no—
410C23—592no—
411C23—1188no—
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—1181no—
428C23—1181no—
429C23—2364no—
430C23—2364no—
431C23—2364no—
432C23—2364no—
433C23—2364no—
434C23—2364no—
435C23D4×D5912yes—
436C23C23×D5911yescharacteristic
437D4—44no—
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—592no—
459C2×C4—1181no—
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×C4—1181no—
472C2×C4—1181no—
473C2×C4—2364no—
474C2×C4—2364no—
475C2×C4D4×D5912yes—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—594no—
491C22—1182no—
492C22—1182no—
493C22—1182no—
494C22—1182no—
495C22—1182no—
496C22—1182no—
497C22—1182no—
498C22—1182no—
499C22—1182no—
500C22—23616no—
501C22—2361no—
502C22—2361no—
503C22—2361no—
504C22—2361no—
505C22—2361no—
506C22—2361no—
507C22—2361no—
508C22—2361no—
509C22—2361no—
510C22—2361no—
511C22—2361no—
512C22C2×D4×D5911yescharacteristic
513C22C2×D4×D5911yescharacteristic
514C22#41×D5911yescharacteristic
515C22#1427377211yescharacteristic
516C22#1427377211yescharacteristic
517C22#1427377311yescharacteristic
518C22#1427377311yescharacteristic
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—1182no—
525C4—2361no—
526C4—2361no—
527C4—2361no—
528C4—2361no—
529C2—42no—
530C2—81no—
531C2—1184no—
532C2—4721no—
533C2—2362no—
534C2#121×D5911yescharacteristic
535C2#1683796011yescharacteristic
536C2#1683796211yescharacteristic
537C2#1683796311yescharacteristic
538C2#1683796811yescharacteristic
539C2#1683798611yescharacteristic
540C2#1683798811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2617
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14273700C2semidirect
2. C2×#14273697C2semidirect
3. C2×#14273695C2semidirect
4. C2×C22⋊C4×D59C2semidirect
5. #16837331C2semidirect
6. #16837330C2semidirect
7. #16837319C2semidirect
8. #16837318C2semidirect
9. #16837318C2semidirect
10. #16837311C2semidirect
11. #16837310C2semidirect
12. #16837280C2semidirect
13. #16837278C2semidirect
14. #16837259C2semidirect
15. C59×#394C2semidirect
22. C22×C22⋊D59C22semidirect
28. C2×C4⋊Dic59C22semidirect
29. C2×Dic59⋊C4C22semidirect
32. C2×C22⋊Dic59C22semidirect
39. C2×(C2×D59)⋊C4C22semidirect
40. C2×(C2×D59)⋊C4C22semidirect
41. C2×(C2×D59)⋊C4C22semidirect
43. C59⋊#95C22semidirect
44. C59⋊#95C22semidirect
45. C59⋊#95C22semidirect
46. C59⋊#95C22semidirect
47. C59⋊#95C22semidirect
49. C2×C4⋊C4×C59C22semidirect
52. C2×C22⋊C4×C59C22semidirect
53. C2×C22⋊C4×C59C22semidirect
54. #95×C59C22semidirect
63. C23×D59D4semidirect
103. C2×C4×D59D4semidirect
280. #394D59semidirect
286. C59#2617semidirect
302. C2×C4⋊C4C2×D59semidirect
318. C2×C22⋊C4C2×D59semidirect
319. C2×C22⋊C4C2×D59semidirect
325. #95C2×D59semidirect