Finite Group Databasebeta

← #28633029

Subgroups — #28633029

Order 15104.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21428398C211yesmaximal, characteristic
2C4⋊C4×C22⋊D59C211yesmaximal, characteristic
3#21425656C211yesmaximal, characteristic, complemented
4#21425571C211yesmaximal, characteristic, complemented
5#21425523C211yesmaximal, characteristic, complemented
6#21425521C211yesmaximal, characteristic, complemented
7#21424666C211yesmaximal, characteristic, complemented
8#21424665C211yesmaximal, characteristic, complemented
9#21424388C211yesmaximal, characteristic
10#21424285C211yesmaximal, characteristic, complemented
11#21424284C211yesmaximal, characteristic, complemented
12#21424182C211yesmaximal, characteristic, complemented
13#21424181C211yesmaximal, characteristic, complemented
14#21424125C211yesmaximal, characteristic, complemented
15C2×C59×#340C211yesmaximal, characteristic, complemented
16C2×#14273710—21no—
17C2×C4×C22⋊D59—21no—
18C2×C4×C22⋊D59C2211yescharacteristic
19C2×C4⋊C4×D59C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273661C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273660C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25C2×(C2×D59)⋊C8C2211yescharacteristic
26C2×(C2×D59)⋊C8C2211yescharacteristic
27#16837333—21no—
28#16837328—21no—
29#16837298C2211yescharacteristic
30#16837298C2211yescharacteristic
31#16837297—21no—
32#16837275—21no—
33#16837273—21no—
34#16837271C2211yescharacteristic
35#16837265—21no—
36#16837262C2211yescharacteristic
37#16837262C2211yescharacteristic
38#16837259C2211yescharacteristic
39#16837259C2211yescharacteristic
40#16837259C2211yescharacteristic
41C4⋊C4×Dic59C2211yescharacteristic
42#16837165C2211yescharacteristic
43#16837165C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C23×C8×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#340C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C22×C22⋊D59D411yescharacteristic
60C22×C4×D59—21no—
61C22×C4×D59C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64#14273710—44no—
65C4×C22⋊D59—22no—
66C4×C22⋊D59—22no—
67C4×C22⋊D59—44no—
68C2×C4⋊Dic59C2311yescharacteristic
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×Dic59⋊C4—21no—
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4D411yescharacteristic
78C4⋊C4×D59—22no—
79C4⋊C4×D59—41no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59D411yescharacteristic
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4D411yescharacteristic
87C2×C4×Dic59—21no—
88C2×C4×Dic59C2311yescharacteristic
89#14273661—22no—
90#14273661—41no—
91#14273660—22no—
92#14273660—41no—
93C22⋊(C59⋊C8)—22no—
94(C2×D59)⋊C8—22no—
95(C2×D59)⋊C8—41no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C23×C4×C59—21no—
105C23×C4×C59—21no—
106C23×C4×C59C2311yescharacteristic
107C22×C8×C59—22no—
108C22×C8×C59—22no—
109C22×C8×C59—41no—
110C22×C8×C59C2311yescharacteristic
111C22×C8×C59C2311yescharacteristic
112C2×C4⋊C4×C59—22no—
113C2×C4⋊C4×C59—22no—
114C2×C4⋊C4×C59—22no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—41no—
118C2×C4⋊C4×C59C2311yescharacteristic
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C24×C59C2×D411yescharacteristic
123C23×D59C2×D411yescharacteristic
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—42no—
133C22×C4×C59—42no—
134C22×C4×C59—42no—
135C22×C4×C59—42no—
136C22×C4×C59—42no—
137C22×C4×C59—81no—
138C22×C4×C59C2×D411yescharacteristic
139C22×C4×C59#4112yes—
140C22×C4×C59#4112yes—
141C22×C4×C59C2411yescharacteristic
142C2×C22⋊D59—22no—
143C2×C22⋊D59—22no—
144C2×C22⋊D59D814yes—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59C2×D411yescharacteristic
150C22×Dic59C2×D411yescharacteristic
151C22×Dic59C2×D411yescharacteristic
152C2×C4×D59—21no—
153C2×C4×D59—21no—
154C2×C4×D59—21no—
155C2×C4×D59—21no—
156C2×C4×D59—21no—
157C2×C4×D59—21no—
158C2×C4×D59—42no—
159C2×C4×D59—42no—
160C2×C4×D59—81no—
161C2×C8×C59—21no—
162C2×C8×C59—21no—
163C2×C8×C59—21no—
164C2×C8×C59—21no—
165C2×C8×C59—21no—
166C2×C8×C59—44no—
167C2×C8×C59#4112yes—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59—21no—
172C4⋊C4×C59—21no—
173C4⋊C4×C59—21no—
174C4⋊C4×C59—21no—
175C4⋊C4×C59—42no—
176C4⋊C4×C59—42no—
177C4⋊C4×C59#4112yes—
178C22⋊Dic59—22no—
179C22⋊Dic59—42no—
180C22⋊Dic59—42no—
181(C2×D59)⋊C4—22no—
182(C2×D59)⋊C4—42no—
183(C2×D59)⋊C4—42no—
184(C2×D59)⋊C4—42no—
185C4⋊Dic59—21no—
186C4⋊Dic59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59—21no—
191C4⋊Dic59—21no—
192C4⋊Dic59—21no—
193Dic59⋊C4—22no—
194Dic59⋊C4—42no—
195Dic59⋊C4—42no—
196Dic59⋊C4—42no—
197Dic59⋊C4—42no—
198Dic59⋊C4—81no—
199C4×Dic59—21no—
200C4×Dic59—21no—
201C4×Dic59—42no—
202C2×C59⋊C8—21no—
203C2×C59⋊C8—21no—
204C2×C59⋊C8—21no—
205C2×C59⋊C8—21no—
206C2×C59⋊C8—21no—
207C2×C59⋊C8—21no—
208C23×C59—21no—
209C23×C59—21no—
210C23×C59—21no—
211C23×C59—21no—
212C23×C59#12312yes—
213C23×C59C2×D812yes—
214C23×C59#13712yes—
215C23×C59C22×D411yescharacteristic
216C22×D59—21no—
217C22×D59—21no—
218C22×D59—21no—
219C22×D59—21no—
220C22×D59—21no—
221C22×D59—21no—
222C22×D59C2×D812yes—
223C2×C4×C59—21no—
224C2×C4×C59—21no—
225C2×C4×C59—22no—
226C2×C4×C59—22no—
227C2×C4×C59—22no—
228C2×C4×C59—22no—
229C2×C4×C59—22no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—41no—
239C2×C4×C59—41no—
240C2×C4×C59—41no—
241C2×C4×C59—84no—
242C2×C4×C59—84no—
243C2×C4×C59#12312yes—
244C2×C4×C59C2×#4111yescharacteristic
245C2×C4×C59C2×#4111yescharacteristic
246C2×C4×C59C2×#4111yescharacteristic
247C2×C4×C59C2×#4111yescharacteristic
248C2×C4×C59H(5,𝔽2)11yescharacteristic
249C2×C4×C592−1+411yescharacteristic
250C22⋊D59—28no—
251C2×Dic59—21no—
252C2×Dic59—21no—
253C2×Dic59—21no—
254C2×Dic59—21no—
255C2×Dic59—21no—
256C2×Dic59—21no—
257C2×Dic59—21no—
258C2×Dic59—21no—
259C2×Dic59—41no—
260C2×Dic59—41no—
261C2×Dic59—41no—
262C2×Dic59—41no—
263C2×Dic59—41no—
264C2×Dic59—41no—
265C2×Dic59—41no—
266C2×Dic59—41no—
267C2×Dic59—41no—
268C2×Dic59—41no—
269C2×Dic59—41no—
270C2×Dic59—41no—
271C2×Dic59C2×D812yes—
272C4×D59—41no—
273C4×D59—41no—
274C4×D59—41no—
275C4×D59—41no—
276C4×D59—84no—
277C8×C59—22no—
278C8×C59—41no—
279C59⋊C8—41no—
280C59⋊C8—41no—
281#24933—591nomaximal, Sylow
282C22×C59—22no—
283C22×C59—22no—
284C22×C59—22no—
285C22×C59—22no—
286C22×C59—22no—
287C22×C59—22no—
288C22×C59#48014yes—
289C22×C59C2×#12311yescharacteristic
290C22×C59#54611yescharacteristic
291C22×C59#54711yescharacteristic
292C22×C59C22×D811yescharacteristic
293C22×C59C2×#13711yescharacteristic
294C22×C59#57711yescharacteristic
295C22×C59#57811yescharacteristic
296C2×D59—22no—
297C2×D59—22no—
298C2×D59—22no—
299C2×D59—41no—
300C2×D59—41no—
301C2×D59—41no—
302C2×D59—41no—
303C4×C59—22no—
304C4×C59—42no—
305C4×C59—81no—
306C4×C59—81no—
307C4×C59—81no—
308C4×C59#52911yescharacteristic
309C4×C59#53911yescharacteristic
310C4×C59#55111yescharacteristic
311C4×C59#55211yescharacteristic
312Dic59—22no—
313Dic59—41no—
314Dic59—41no—
315Dic59—81no—
316Dic59—81no—
317Dic59—81no—
318Dic59—81no—
319#2486—591no—
320D4×C4⋊C4—591no—
321#2099—591no—
322#2083—591no—
323#2075—591no—
324#2075—591no—
325#1918—591no—
326#1918—591no—
327#1869—591no—
328#1852—591no—
329#1852—591no—
330#1823—591no—
331#1823—591no—
332#1808—591no—
333C2×#340D5911yescharacteristic, complemented
334C2×C59—24no—
335C2×C59#241911yescharacteristic
336C2×C59C2×#48011yescharacteristic
337C2×C59#309711yescharacteristic
338C2×C59#329411yescharacteristic
339C2×C59#331211yescharacteristic
340C2×C59#333411yescharacteristic
341C2×C59#334411yescharacteristic
342D59—42no—
343C23×C8C2×D5911yescharacteristic
344C2×#123—1181no—
345C2×C4×D4—591no—
346C2×C4×D4—1181no—
347C22×C4⋊C4—591no—
348C22×C4⋊C4C2×D5911yescharacteristic
349C22×C4⋊C4C2×D5911yescharacteristic
350C2×#107—591no—
351C2×#107—591no—
352C2×#107—591no—
353C2×#107—591no—
354C2×C22⋊C8—591no—
355C2×C22⋊C8—591no—
356C2×C22⋊C8—591no—
357#398—1181no—
358#397—1181no—
359#389—591no—
360#389—591no—
361#389—1181no—
362#385—1181no—
363#385—1181no—
364#384—591no—
365#381—1181no—
366#380—591no—
367#380—591no—
368#380—591no—
369#380—591no—
370#380—591no—
371C4×C4⋊C4—591no—
372#340—591no—
373#340—591no—
374#340—591no—
375#340—591no—
376#340—591no—
377#340—591no—
378#340—591no—
379#340—591no—
380#340C2×D5911yescharacteristic
381#340C2×D5911yescharacteristic
382#340C2×D5911yescharacteristic
383#340C2×D5911yescharacteristic
384#336—591no—
385#336—591no—
386C59#2493311yescharacteristic, complemented, Sylow
387C22×D4—591no—
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—591no—
391C23×C4—1181no—
392C23×C4C22×D5911yescharacteristic
393C22×C8—22no—
394C22×C8—22no—
395C22×C8—41no—
396C22×C8—591no—
397C22×C8—591no—
398C22×C8C22×D5911yescharacteristic
399C22×C8C22×D5911yescharacteristic
400#123—2364no—
401C4×D4—1182no—
402C4×D4—1182no—
403C4×D4—2364no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—591no—
411C2×C4⋊C4—591no—
412C2×C4⋊C4—591no—
413C2×C4⋊C4—591no—
414C2×C4⋊C4—591no—
415C2×C4⋊C4—1182no—
416C2×C4⋊C4—1181no—
417C2×C4⋊C4—1181no—
418C2×C4⋊C4—1181no—
419C2×C4⋊C4—1181no—
420C2×C4⋊C4—1181no—
421C2×C4⋊C4—2361no—
422C2×C4⋊C4C22×D5911yescharacteristic
423C2×C4⋊C4C22×D5911yescharacteristic
424C2×C4⋊C4C22×D5911yescharacteristic
425C2×C4⋊C4C22×D5911yescharacteristic
426C2×C22⋊C4—591no—
427C2×C22⋊C4—591no—
428C2×C22⋊C4—1181no—
429C2×C22⋊C4—1181no—
430C2×C22⋊C4—1181no—
431C2×C22⋊C4—1181no—
432C2×C22⋊C4—1181no—
433C2×C42—591no—
434C2×C42—1181no—
435#107—1182no—
436#107—1182no—
437#107—2361no—
438#107—2361no—
439C22⋊C8—1182no—
440C22⋊C8—1182no—
441C22⋊C8—2361no—
442#95—1181no—
443#95—1181no—
444#95—1181no—
445#95—1181no—
446#95—1181no—
447#95—1181no—
448#95—1181no—
449#95—1181no—
450C24—591no—
451C24D4×D5911yescharacteristic
452C2×D4—594no—
453C2×D4—1182no—
454C2×D4—1182no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—591no—
470C22×C4—591no—
471C22×C4—591no—
472C22×C4—1181no—
473C22×C4—1181no—
474C22×C4—1181no—
475C22×C4—1181no—
476C22×C4—1181no—
477C22×C4—1181no—
478C22×C4—1181no—
479C22×C4—1181no—
480C22×C4—1181no—
481C22×C4—1181no—
482C22×C4—4721no—
483C22×C4—2362no—
484C22×C4—2362no—
485C22×C4#1174568512yes—
486C22×C4D4×D5911yescharacteristic
487C22×C4#1174568712yes—
488C22×C4C23×D5911yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—44no—
495C2×C8—1181no—
496C2×C8—1181no—
497C2×C8—1181no—
498C2×C8—1181no—
499C2×C8—1181no—
500C2×C8—1181no—
501C2×C8#1174568512yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—1182no—
512C4⋊C4—1181no—
513C4⋊C4—1181no—
514C4⋊C4—1181no—
515C4⋊C4—1181no—
516C4⋊C4—1181no—
517C4⋊C4—1181no—
518C4⋊C4—1181no—
519C4⋊C4—1181no—
520C4⋊C4—4721no—
521C4⋊C4—2362no—
522C4⋊C4—2362no—
523C4⋊C4—2362no—
524C4⋊C4—2362no—
525C4⋊C4#1174568512yes—
526C22⋊C4—1182no—
527C22⋊C4—1182no—
528C22⋊C4—2362no—
529C22⋊C4—2362no—
530C22⋊C4—2362no—
531C22⋊C4—2362no—
532C22⋊C4—2362no—
533C42—1181no—
534C42—1181no—
535C42—2362no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—592no—
541C23—1181no—
542C23—1181no—
543C23—1181no—
544C23—1181no—
545C23—1181no—
546C23—1181no—
547C23#1427370912yes—
548C23D8×D5912yes—
549C23#1427375612yes—
550C23C2×D4×D5911yescharacteristic
551D4—1188no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4—84no—
572C2×C4—592no—
573C2×C4—1181no—
574C2×C4—1181no—
575C2×C4—1181no—
576C2×C4—1181no—
577C2×C4—1181no—
578C2×C4—1181no—
579C2×C4—1181no—
580C2×C4—1181no—
581C2×C4—4724no—
582C2×C4—2361no—
583C2×C4—2361no—
584C2×C4—2361no—
585C2×C4—2361no—
586C2×C4—2361no—
587C2×C4—2361no—
588C2×C4—2361no—
589C2×C4—2361no—
590C2×C4—2361no—
591C2×C4—2361no—
592C2×C4—2361no—
593C2×C4—2361no—
594C2×C4—2361no—
595C2×C4—2361no—
596C2×C4—2361no—
597C2×C4—2361no—
598C2×C4#1427370912yes—
599C2×C4C2×#1174568711yescharacteristic
600C2×C4C2×#1174568511yescharacteristic
601C2×C4C2×#1174568511yescharacteristic
602C2×C4C2×#1174568511yescharacteristic
603C2×C4#1427377211yescharacteristic
604C2×C4#1427377511yescharacteristic
605C8—22no—
606C8—41no—
607C8—2361no—
608C8—2361no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—1182no—
616C22—1182no—
617C22—1182no—
618C22—2361no—
619C22—2361no—
620C22—2361no—
621C22—2361no—
622C22#1683771414yes—
623C22C2×#1427370911yescharacteristic
624C22#1683804211yescharacteristic
625C22#1683805311yescharacteristic
626C22C2×D8×D5911yescharacteristic
627C22C2×#1427375611yescharacteristic
628C22#1683820811yescharacteristic
629C22#1683821511yescharacteristic
630C4—22no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—1182no—
636C4—4721no—
637C4—4721no—
638C4—4721no—
639C4—4721no—
640C4—2361no—
641C4—2361no—
642C4#1683793611yescharacteristic
643C4#1683799911yescharacteristic
644C4#1683807811yescharacteristic
645C4#1683808711yescharacteristic
646C2—24no—
647C2—2362no—
648C2#2142757311yescharacteristic
649C2C2×#1683771411yescharacteristic
650C2#2143406111yescharacteristic
651C2#2143590511yescharacteristic
652C2#2143614311yescharacteristic
653C2#2143644111yescharacteristic
654C2#2143654711yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#340C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#340D59
hypocenterC59#24933
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #21425656C2semidirect
4. #21425571C2semidirect
5. #21425523C2semidirect
6. #21425521C2semidirect
7. #21424666C2semidirect
8. #21424665C2semidirect
10. #21424285C2semidirect
11. #21424284C2semidirect
12. #21424182C2semidirect
13. #21424181C2semidirect
14. #21424125C2semidirect
15. C2×C59×#340C2semidirect
333. C2×#340D59semidirect
386. C59#24933semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214283982
C4⋊C4×C22⋊D592
#214256562
#214255712
#214255232
#214255212
#214246662
#214246652
#214243882
#214242852
#214242842
#214241822
#214241812
#214241252
C2×C59×#3402
#2493359