Finite Group Databasebeta

← #28618681

Subgroups — #28618681

Order 15104.

880 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
1C4×#14273698C211yesmaximal, characteristic
2#21426500C211yesmaximal, characteristic, complemented
3#21425656C211yesmaximal, characteristic, complemented
4#21425622C211yesmaximal, characteristic, complemented
5#21425571C211yesmaximal, characteristic, complemented
6#21425523C211yesmaximal, characteristic, complemented
7#21425521C211yesmaximal, characteristic, complemented
8#21425502C211yesmaximal, characteristic, complemented
9#21425277C211yesmaximal, characteristic
10#21425276C211yesmaximal, characteristic
11C4×#14273660C211yesmaximal, characteristic, complemented
12C4×#14273661C211yesmaximal, characteristic, complemented
13C4×#14273648C211yesmaximal, characteristic, complemented
14C4×(C2×D59)⋊C8C211yesmaximal, characteristic, complemented
15C4×#102×C59C211yesmaximal, characteristic, complemented
16C2×#14273698C2211yescharacteristic
17C2×C4×C22⋊D59—21no—
18C2×#14273684—21no—
19C2×C42×D59C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273661C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273660C2211yescharacteristic
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×(C2×D59)⋊C8C2211yescharacteristic
27C2×(C2×D59)⋊C8C2211yescharacteristic
28C2×C4×C59⋊C8C2211yescharacteristic
29#16837305C2211yescharacteristic
30#16837298C2211yescharacteristic
31#16837290—21no—
32#16837278—21no—
33#16837271C2211yescharacteristic
34#16837271C2211yescharacteristic
35#16837266—21no—
36#16837261—21no—
37#16837259C2211yescharacteristic
38#16837259C2211yescharacteristic
39#16837259C2211yescharacteristic
40C4×Dic59⋊C4—21no—
41C4×C4⋊Dic59C2211yescharacteristic
42C4×C4⋊Dic59C2211yescharacteristic
43C4×C22⋊Dic59—21no—
44#16837165C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×#102×C59C2211yescharacteristic
54C2×#102×C59C2211yescharacteristic
55C2×C4×C8×C59C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C22×C22⋊D59—21no—
60C22×C4×D59D411yescharacteristic
61C22×C4×D59D411yescharacteristic
62C22×C4×D59C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65#14273698—22no—
66#14273698—22no—
67C4×C22⋊D59—44no—
68#14273684—44no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×C22⋊Dic59—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×C4×Dic59—21no—
85C2×C4×Dic59—21no—
86C2×C4×Dic59D411yescharacteristic
87C2×C4×Dic59D411yescharacteristic
88C2×C4×Dic59C2311yescharacteristic
89C42×D59—22no—
90C42×D59—22no—
91#14273661—22no—
92#14273661—22no—
93#14273660—22no—
94#14273660—22no—
95#14273648—22no—
96#14273648—22no—
97(C2×D59)⋊C8—22no—
98(C2×D59)⋊C8—22no—
99C4×C59⋊C8—22no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C22×D4×C59C2311yescharacteristic
107C23×C4×C59—21no—
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C4×D4×C59—22no—
111C4×D4×C59—22no—
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C4⋊C4×C59C2311yescharacteristic
115C2×C22⋊C4×C59—21no—
116C2×C42×C59—21no—
117C2×C42×C59C2311yescharacteristic
118#102×C59—22no—
119#102×C59—22no—
120C4×C8×C59—22no—
121#95×C59—21no—
122C24×C59—21no—
123C23×D59C2×D411yescharacteristic
124C2×D4×C59—21no—
125C2×D4×C59—21no—
126C2×D4×C59—21no—
127C2×D4×C59—21no—
128C2×D4×C59—21no—
129C2×D4×C59#4112yes—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—42no—
134C22×C4×C59—42no—
135C22×C4×C59—42no—
136C22×C4×C59C2×D411yescharacteristic
137C22×C4×C59C2×D411yescharacteristic
138C22×C4×C59C2411yescharacteristic
139C2×C22⋊D59—24no—
140C2×C22⋊D59—42no—
141C2×C22⋊D59—42no—
142C22×Dic59—21no—
143C22×Dic59—21no—
144C22×Dic59—21no—
145C22×Dic59—21no—
146C22×Dic59C2×D411yescharacteristic
147C22×Dic59C2×D411yescharacteristic
148C22×Dic59C2×D411yescharacteristic
149C2×C4×D59—22no—
150C2×C4×D59—22no—
151C2×C4×D59—22no—
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—22no—
159C2×C4×D59—41no—
160C2×C4×D59D814yes—
161C2×C8×C59—21no—
162C2×C8×C59—21no—
163C2×C8×C59—21no—
164C2×C8×C59—21no—
165C2×C8×C59—21no—
166C2×C8×C59#4112yes—
167C4⋊C4×C59—21no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59—21no—
172C4⋊C4×C59—21no—
173C22⋊C4×C59—42no—
174C42×C59—42no—
175C42×C59#4112yes—
176C42×C59#4112yes—
177C22⋊Dic59—24no—
178C22⋊Dic59—42no—
179C22⋊Dic59—42no—
180(C2×D59)⋊C4—42no—
181(C2×D59)⋊C4—42no—
182(C2×D59)⋊C4—42no—
183C4⋊Dic59—21no—
184C4⋊Dic59—21no—
185C4⋊Dic59—21no—
186C4⋊Dic59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59#4112yes—
191Dic59⋊C4—42no—
192Dic59⋊C4—42no—
193Dic59⋊C4—42no—
194Dic59⋊C4—42no—
195Dic59⋊C4—42no—
196C4×Dic59—22no—
197C4×Dic59—22no—
198C4×Dic59—21no—
199C4×Dic59—21no—
200C4×Dic59—42no—
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#4112yes—
208C23×C59—22no—
209C23×C59—41no—
210C23×C59—41no—
211C23×C59—41no—
212C23×C59—41no—
213C23×C59—41no—
214C23×C59—41no—
215C23×C59C22×D411yescharacteristic
216C22×D59—21no—
217C22×D59—21no—
218C22×D59—21no—
219C22×D59—21no—
220C22×D59—21no—
221C22×D59—21no—
222C22×D59C2×D812yes—
223D4×C59—22no—
224D4×C59—22no—
225D4×C59—41no—
226D4×C59—41no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—41no—
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—84no—
239C2×C4×C59#12312yes—
240C2×C4×C59#12312yes—
241C2×C4×C59C2×D812yes—
242C2×C4×C59#13712yes—
243C2×C4×C59C2×#4111yescharacteristic
244C2×C4×C59C2×#4111yescharacteristic
245C2×C4×C59C2×#4111yescharacteristic
246C2×C4×C59C2×#4111yescharacteristic
247C2×C4×C59C2×#4111yescharacteristic
248C2×C4×C59C2×#4111yescharacteristic
249C22⋊D59—48no—
250C2×Dic59—21no—
251C2×Dic59—21no—
252C2×Dic59—21no—
253C2×Dic59—21no—
254C2×Dic59—21no—
255C2×Dic59—22no—
256C2×Dic59—21no—
257C2×Dic59—21no—
258C2×Dic59—41no—
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×Dic59C2×D812yes—
270C2×Dic59#13512yes—
271C4×D59—28no—
272C4×D59—44no—
273C4×D59—41no—
274C4×D59—41no—
275C4×D59—41no—
276C4×D59—41no—
277C8×C59—22no—
278C8×C59—41no—
279C59⋊C8—22no—
280C59⋊C8—41no—
281#23754—591nomaximal, Sylow
282C22×C59—42no—
283C22×C59—42no—
284C22×C59—42no—
285C22×C59—81no—
286C22×C59—81no—
287C22×C59—81no—
288C22×C59—81no—
289C22×C59C2×#12311yescharacteristic
290C22×C59#52511yescharacteristic
291C22×C59#53211yescharacteristic
292C22×C59C22×D811yescharacteristic
293C22×C59C2×#13511yescharacteristic
294C22×C59C2×#13711yescharacteristic
295C22×C59#57511yescharacteristic
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—81no—
305C4×C59—81no—
306C4×C59—81no—
307C4×C59#48014yes—
308C4×C59#52911yescharacteristic
309C4×C59#52911yescharacteristic
310C4×C59#52911yescharacteristic
311C4×C59#52911yescharacteristic
312Dic59—22no—
313Dic59—22no—
314Dic59—42no—
315Dic59—41no—
316Dic59—81no—
317Dic59—81no—
318Dic59—81no—
319C4×#121—591no—
320#2285—591no—
321#2099—591no—
322#2093—591no—
323#2083—591no—
324#2075—591no—
325#2075—591no—
326#2071—591no—
327#2033—591no—
328#2033—591no—
329C4×#107—591no—
330C4×#107—591no—
331C4×#102—591no—
332C4×#102D5911yescharacteristic, complemented
333C4×C22⋊C8—591no—
334C2×C59—82no—
335C2×C59#239511yescharacteristic
336C2×C59C2×#48011yescharacteristic
337C2×C59#309111yescharacteristic
338C2×C59#310011yescharacteristic
339C2×C59#310711yescharacteristic
340C2×C59#316911yescharacteristic
341C2×C59#317211yescharacteristic
342D59—42no—
343C2×#121—591no—
344C2×C4×D4—1181no—
345C2×C4×D4C2×D5911yescharacteristic
346C2×#117—1181no—
347C22×C42—591no—
348C2×#107—591no—
349C2×#107—591no—
350C2×#107—591no—
351C2×#107—591no—
352C2×#102—591no—
353C2×#102—591no—
354C2×#102C2×D5911yescharacteristic
355C2×#102C2×D5911yescharacteristic
356C2×C22⋊C8—591no—
357C2×C22⋊C8—591no—
358C2×C4×C8—591no—
359C2×C4×C8C2×D5911yescharacteristic
360#390—591no—
361#389—591no—
362#388—1181no—
363#386—1181no—
364#384—591no—
365#384—591no—
366#382—1181no—
367#380—591no—
368#380—591no—
369#380—591no—
370#380—1181no—
371C4×C4⋊C4—591no—
372C4×C4⋊C4—591no—
373C4×C4⋊C4—1181no—
374C4×C4⋊C4C2×D5911yescharacteristic
375C4×C22⋊C4—1181no—
376#340—591no—
377#340—591no—
378#340—591no—
379#340—591no—
380#340—591no—
381#340—591no—
382#340C2×D5911yescharacteristic
383#340C2×D5911yescharacteristic
384#336—591no—
385#336—591no—
386C59#2375411yescharacteristic, complemented, Sylow
387C22×D4—1181no—
388C22×D4C22×D5911yescharacteristic
389C23×C4—21no—
390C23×C4—591no—
391C23×C4—591no—
392C23×C4—591no—
393C22×C8—591no—
394C22×C8—591no—
395C22×C8C22×D5911yescharacteristic
396C22×C8C22×D5911yescharacteristic
397#121—1182no—
398#121—1182no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—2364no—
402#117—2364no—
403C2×C4⋊C4—591no—
404C2×C4⋊C4—591no—
405C2×C4⋊C4—591no—
406C2×C4⋊C4—591no—
407C2×C4⋊C4—1181no—
408C2×C4⋊C4—1181no—
409C2×C4⋊C4—1181no—
410C2×C4⋊C4—1181no—
411C2×C4⋊C4—1181no—
412C2×C4⋊C4C22×D5911yescharacteristic
413C2×C4⋊C4C22×D5911yescharacteristic
414C2×C4⋊C4C22×D5911yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—1181no—
417C2×C22⋊C4—1181no—
418C2×C22⋊C4—1181no—
419C2×C22⋊C4—1181no—
420C2×C22⋊C4—1181no—
421C2×C22⋊C4—1181no—
422C2×C42—21no—
423C2×C42—591no—
424C2×C42—591no—
425C2×C42—591no—
426C2×C42—1182no—
427C2×C42—1182no—
428C2×C42—1181no—
429C2×C42—1181no—
430C2×C42C22×D5911yescharacteristic
431#107—1182no—
432#107—1182no—
433#107—1182no—
434#107—1182no—
435#102—22no—
436#102—22no—
437#102—1182no—
438#102—1182no—
439C22⋊C8—1182no—
440C22⋊C8—1182no—
441C4×C8—22no—
442C4×C8—1182no—
443#95—21no—
444#95—1181no—
445#95—1181no—
446#95—1181no—
447#95—1181no—
448#95—1181no—
449#95—1181no—
450C24—21no—
451C24—591no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—1184no—
458C2×D4—2362no—
459C2×D4—2362no—
460C2×D4#1174568512yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—591no—
468C22×C4—591no—
469C22×C4—594no—
470C22×C4—591no—
471C22×C4—1182no—
472C22×C4—1182no—
473C22×C4—1182no—
474C22×C4—1181no—
475C22×C4—1182no—
476C22×C4—1181no—
477C22×C4—1181no—
478C22×C4—1181no—
479C22×C4—1181no—
480C22×C4—1181no—
481C22×C4—1181no—
482C22×C4—1181no—
483C22×C4—1181no—
484C22×C4—1181no—
485C22×C4—2361no—
486C22×C4D4×D5911yescharacteristic
487C22×C4D4×D5911yescharacteristic
488C22×C4C23×D5911yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—592no—
495C2×C8—1181no—
496C2×C8—1181no—
497C2×C8—1181no—
498C2×C8—1181no—
499C2×C8—1181no—
500C2×C8#1174568512yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—592no—
508C4⋊C4—1181no—
509C4⋊C4—1181no—
510C4⋊C4—1181no—
511C4⋊C4—1181no—
512C4⋊C4—1181no—
513C4⋊C4—1181no—
514C4⋊C4—1181no—
515C4⋊C4—2362no—
516C4⋊C4—2362no—
517C4⋊C4—2362no—
518C4⋊C4—2362no—
519C4⋊C4—2362no—
520C22⋊C4—42no—
521C22⋊C4—1184no—
522C22⋊C4—2362no—
523C22⋊C4—2362no—
524C22⋊C4—2362no—
525C22⋊C4—2362no—
526C22⋊C4—2362no—
527C42—42no—
528C42—1182no—
529C42—1182no—
530C42—1181no—
531C42—1181no—
532C42—2362no—
533C42—2362no—
534C42#1174568512yes—
535C42#1174568712yes—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—592no—
544C23—1181no—
545C23—1181no—
546C23—1181no—
547C23—1181no—
548C23—1181no—
549C23—1181no—
550C23C2×D4×D5911yescharacteristic
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—2368no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
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—84no—
568C2×C4—592no—
569C2×C4—592no—
570C2×C4—1181no—
571C2×C4—1181no—
572C2×C4—1181no—
573C2×C4—1181no—
574C2×C4—1188no—
575C2×C4—1181no—
576C2×C4—1181no—
577C2×C4—1182no—
578C2×C4—1181no—
579C2×C4—2364no—
580C2×C4—2361no—
581C2×C4—2361no—
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#1427370912yes—
596C2×C4#1427370912yes—
597C2×C4D8×D5912yes—
598C2×C4#1427375612yes—
599C2×C4#41×D5911yescharacteristic
600C2×C4#41×D5911yescharacteristic
601C2×C4C2×#1174568711yescharacteristic
602C2×C4C2×#1174568511yescharacteristic
603C2×C4C2×#1174568511yescharacteristic
604C2×C4C2×#1174568511yescharacteristic
605C8—22no—
606C8—41no—
607C8—1182no—
608C8—2361no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—1182no—
617C22—1182no—
618C22—1182no—
619C22—2361no—
620C22—2361no—
621C22—2361no—
622C22—2361no—
623C22C2×#1427370911yescharacteristic
624C22#1683791111yescharacteristic
625C22#1683794911yescharacteristic
626C22C2×D8×D5911yescharacteristic
627C22#135×D5911yescharacteristic
628C22C2×#1427375611yescharacteristic
629C22#1683819911yescharacteristic
630C4—22no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—1182no—
635C4—1182no—
636C4—4721no—
637C4—4721no—
638C4—4721no—
639C4—2361no—
640C4—2362no—
641C4#1683771414yes—
642C4#1683793011yescharacteristic
643C4#1683793211yescharacteristic
644C4#1683793211yescharacteristic
645C4#1683793611yescharacteristic
646C2—82no—
647C2—2362no—
648C2#2142735711yescharacteristic
649C2C2×#1683771411yescharacteristic
650C2#2143400711yescharacteristic
651C2#2143409411yescharacteristic
652C2#2143416311yescharacteristic
653C2#2143467211yescharacteristic
654C2#2143469811yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC4×#102×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273698C22
hypercenterC4×#102D59
hypocenterC59#23754
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #21426500C2semidirect
3. #21425656C2semidirect
4. #21425622C2semidirect
5. #21425571C2semidirect
6. #21425523C2semidirect
7. #21425521C2semidirect
8. #21425502C2semidirect
11. C4×#14273660C2semidirect
12. C4×#14273661C2semidirect
13. C4×#14273648C2semidirect
14. C4×(C2×D59)⋊C8C2semidirect
15. C4×#102×C59C2semidirect
332. C4×#102D59semidirect
386. C59#23754semidirect

Maximal subgroups

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

subgroupindex
C4×#142736982
#214265002
#214256562
#214256222
#214255712
#214255232
#214255212
#214255022
#214252772
#214252762
C4×#142736602
C4×#142736612
C4×#142736482
C4×(C2×D59)⋊C82
C4×#102×C592
#2375459