Finite Group Databasebeta

← #28618723

Subgroups — #28618723

Order 15104.

836 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426494C211yesmaximal, characteristic, complemented
2#21425664C211yesmaximal, characteristic, complemented
3#21425617C211yesmaximal, characteristic, complemented
4#21425577C211yesmaximal, characteristic, complemented
5#21425533C211yesmaximal, characteristic, complemented
6#21425527C211yesmaximal, characteristic, complemented
7#21425509C211yesmaximal, characteristic, complemented
8#21425282C211yesmaximal, characteristic
9#21425275C211yesmaximal, characteristic
10C4×#14273660C211yesmaximal, characteristic, complemented
11C4×#14273658C211yesmaximal, characteristic, complemented
12C4×#14273648C211yesmaximal, characteristic, complemented
13C4×#14273648C211yesmaximal, characteristic, complemented
14C4×C22⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
15C4×#121×C59C211yesmaximal, characteristic
16C2×#14273660C2211yescharacteristic
17C2×#14273660C2211yescharacteristic
18C2×#14273658C2211yescharacteristic
19C2×#14273658C2211yescharacteristic
20C2×#14273648C2211yescharacteristic
21C2×#14273648C2211yescharacteristic
22C2×#14273648C2211yescharacteristic
23C2×#14273648C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25C2×C22⋊(C59⋊C8)C2211yescharacteristic
26C2×C4×C59⋊C8C2211yescharacteristic
27C2×C4×C59⋊C8C2211yescharacteristic
28#16837270—21no—
29#16837268C2211yescharacteristic
30#16837268C2211yescharacteristic
31#16837265—21no—
32#16837262C2211yescharacteristic
33#16837262C2211yescharacteristic
34C4×C4⋊Dic59C2211yescharacteristic
35C4×C4⋊Dic59C2211yescharacteristic
36C4×C22⋊Dic59—21no—
37#16837248—21no—
38#16837164C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48C2×#121×C59C2211yescharacteristic
49C2×C4×D4×C59—21no—
50C2×C4×D4×C59C2211yescharacteristic
51C22×C42×C59C2211yescharacteristic
52C59×#390C2211yescharacteristic
53C59×#389C2211yescharacteristic
54C59×#388—21no—
55C59×#386—21no—
56C59×#380C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C22⋊C4×C59—21no—
59C22×C59⋊C8C2311yescharacteristic
60C22×C59⋊C8C2311yescharacteristic
61C22×C59⋊C8C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63C2×C4⋊Dic59C2311yescharacteristic
64C2×C4⋊Dic59C2311yescharacteristic
65C2×C4⋊Dic59C2311yescharacteristic
66C2×C4⋊Dic59C2311yescharacteristic
67C2×C22⋊Dic59—21no—
68C2×C22⋊Dic59—21no—
69C2×C4×Dic59—21no—
70C2×C4×Dic59—21no—
71#14273660—22no—
72#14273660—22no—
73#14273658—22no—
74#14273658—22no—
75#14273648—22no—
76#14273648—22no—
77#14273648—22no—
78#14273648—22no—
79C22⋊(C59⋊C8)—22no—
80C22⋊(C59⋊C8)—22no—
81C4×C59⋊C8—22no—
82C4×C59⋊C8—22no—
83C59⋊#95—21no—
84C59⋊#95—21no—
85C59⋊#95—21no—
86C59⋊#95—21no—
87C59⋊#95—21no—
88C59⋊#95—21no—
89C59⋊#95—21no—
90C59⋊#95—21no—
91C22×D4×C59—21no—
92C22×D4×C59C2311yescharacteristic
93C23×C4×C59—21no—
94C23×C4×C59D411yescharacteristic
95C23×C4×C59D411yescharacteristic
96C23×C4×C59C2311yescharacteristic
97#121×C59—22no—
98#121×C59—22no—
99C4×D4×C59—22no—
100C4×D4×C59—22no—
101C4×D4×C59—44no—
102C2×C4⋊C4×C59—21no—
103C2×C4⋊C4×C59C2311yescharacteristic
104C2×C4⋊C4×C59C2311yescharacteristic
105C2×C4⋊C4×C59C2311yescharacteristic
106C2×C22⋊C4×C59—21no—
107C2×C22⋊C4×C59—21no—
108C2×C22⋊C4×C59—21no—
109C2×C22⋊C4×C59—21no—
110C2×C22⋊C4×C59—21no—
111C2×C42×C59—22no—
112C2×C42×C59—22no—
113C2×C42×C59—21no—
114C2×C42×C59D411yescharacteristic
115C2×C42×C59D411yescharacteristic
116C2×C42×C59C2311yescharacteristic
117C2×C42×C59C2311yescharacteristic
118#95×C59—21no—
119#95×C59—21no—
120#95×C59—21no—
121C24×C59—21no—
122C24×C59C2×D411yescharacteristic
123C2×D4×C59—24no—
124C2×D4×C59—21no—
125C2×D4×C59—21no—
126C2×D4×C59—21no—
127C2×D4×C59—21no—
128C2×D4×C59—21no—
129C2×D4×C59—42no—
130C2×D4×C59—42no—
131C2×D4×C59#4112yes—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—41no—
147C22×C4×C59—42no—
148C22×C4×C59—42no—
149C22×C4×C59—42no—
150C22×C4×C59C2×D411yescharacteristic
151C22×C4×C59C2×D411yescharacteristic
152C22×C4×C59C2×D411yescharacteristic
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2411yescharacteristic
156C22×Dic59—21no—
157C22×Dic59—21no—
158C22×Dic59—21no—
159C22×Dic59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—42no—
166C4⋊C4×C59#4112yes—
167C22⋊C4×C59—24no—
168C22⋊C4×C59—42no—
169C22⋊C4×C59—42no—
170C22⋊C4×C59—42no—
171C22⋊C4×C59—42no—
172C42×C59—22no—
173C42×C59—22no—
174C42×C59—21no—
175C42×C59—21no—
176C42×C59—42no—
177C42×C59#4112yes—
178C42×C59#4112yes—
179C22⋊Dic59—42no—
180C22⋊Dic59—42no—
181C4⋊Dic59—21no—
182C4⋊Dic59—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59—21no—
185C4⋊Dic59—21no—
186C4⋊Dic59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4×Dic59—42no—
190C4×Dic59—42no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—21no—
201C2×C59⋊C8#4112yes—
202C2×C59⋊C8#4112yes—
203C23×C59—21no—
204C23×C59—21no—
205C23×C59—21no—
206C23×C59—21no—
207C23×C59—21no—
208C23×C59—21no—
209C23×C59—22no—
210C23×C59—41no—
211C23×C59—41no—
212C23×C59—41no—
213C23×C59—41no—
214C23×C59—41no—
215C23×C59—41no—
216C23×C59#13512yes—
217C23×C59C22×D411yescharacteristic
218D4×C59—22no—
219D4×C59—22no—
220D4×C59—48no—
221D4×C59—41no—
222D4×C59—41no—
223C2×C4×C59—21no—
224C2×C4×C59—21no—
225C2×C4×C59—21no—
226C2×C4×C59—21no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—22no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—21no—
233C2×C4×C59—21no—
234C2×C4×C59—21no—
235C2×C4×C59—44no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—41no—
239C2×C4×C59—41no—
240C2×C4×C59—41no—
241C2×C4×C59—41no—
242C2×C4×C59—44no—
243C2×C4×C59—41no—
244C2×C4×C59—41no—
245C2×C4×C59—41no—
246C2×C4×C59—41no—
247C2×C4×C59—41no—
248C2×C4×C59—41no—
249C2×C4×C59—84no—
250C2×C4×C59#12312yes—
251C2×C4×C59#12312yes—
252C2×C4×C59#13512yes—
253C2×C4×C59AGL(1,ℤ/8)12yes—
254C2×C4×C59C2×#4111yescharacteristic
255C2×C4×C59C2×#4111yescharacteristic
256C2×C4×C59C2×#4111yescharacteristic
257C2×C4×C59C2×#4111yescharacteristic
258C2×C4×C59C2×#4111yescharacteristic
259C2×C4×C59C2×#4111yescharacteristic
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×Dic59—41no—
272C59⋊C8—22no—
273C59⋊C8—22no—
274C59⋊C8—41no—
275C59⋊C8—41no—
276#23758—591nomaximal, Sylow
277C22×C59—22no—
278C22×C59—22no—
279C22×C59—22no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59—41no—
283C22×C59—41no—
284C22×C59—42no—
285C22×C59—42no—
286C22×C59—42no—
287C22×C59—81no—
288C22×C59—81no—
289C22×C59—81no—
290C22×C59—81no—
291C22×C59C2×#12311yescharacteristic
292C22×C59#52511yescharacteristic
293C22×C59#53211yescharacteristic
294C22×C59C2×#13511yescharacteristic
295C22×C59C2×#13511yescharacteristic
296C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C59#57511yescharacteristic
298C4×C59—22no—
299C4×C59—41no—
300C4×C59—41no—
301C4×C59—42no—
302C4×C59—41no—
303C4×C59—81no—
304C4×C59—81no—
305C4×C59#48214yes—
306C4×C59#52911yescharacteristic
307C4×C59#52911yescharacteristic
308C4×C59#52911yescharacteristic
309C4×C59#52911yescharacteristic
310Dic59—81no—
311Dic59—81no—
312Dic59—81no—
313Dic59—81no—
314C4×#121D5911yescharacteristic
315#2283—591no—
316#2101—591no—
317#2092—591no—
318#2085—591no—
319#2077—591no—
320#2076—591no—
321#2073—591no—
322#2034—591no—
323#2033—591no—
324C4×#107—591no—
325C4×#106—591no—
326C4×#102—591no—
327C4×#102—591no—
328C4×C22⋊C8—591no—
329C2×C59—42no—
330C2×C59—82no—
331C2×C59#239511yescharacteristic
332C2×C59C2×#48211yescharacteristic
333C2×C59#309111yescharacteristic
334C2×C59#310211yescharacteristic
335C2×C59#310511yescharacteristic
336C2×C59#316811yescharacteristic
337C2×C59#317111yescharacteristic
338C2×#121C2×D5911yescharacteristic
339C2×C4×D4—21no—
340C2×C4×D4C2×D5911yescharacteristic
341C22×C42C2×D5911yescharacteristic
342C2×#107—591no—
343C2×#107—591no—
344C2×#106—591no—
345C2×#106—591no—
346C2×#102—591no—
347C2×#102—591no—
348C2×#102—591no—
349C2×#102—591no—
350C2×C22⋊C8—591no—
351C2×C22⋊C8—591no—
352C2×C4×C8—591no—
353C2×C4×C8—591no—
354#390C2×D5911yescharacteristic
355#389C2×D5911yescharacteristic
356#388—21no—
357#386—21no—
358#383—1181no—
359#382—591no—
360#382—591no—
361#381—1181no—
362#380—591no—
363#380—591no—
364#380C2×D5911yescharacteristic
365C4×C4⋊C4—591no—
366C4×C4⋊C4—591no—
367C4×C4⋊C4C2×D5911yescharacteristic
368C4×C22⋊C4—21no—
369C4×C22⋊C4—1181no—
370#376—1181no—
371#340—591no—
372#340—591no—
373#340—591no—
374#340—591no—
375#340—591no—
376#340—591no—
377#340—591no—
378#340—591no—
379#336—591no—
380#336—591no—
381C59#2375811yescharacteristic, complemented, Sylow
382C22×D4—21no—
383C22×D4C22×D5911yescharacteristic
384C23×C4—21no—
385C23×C4C22⋊D5911yescharacteristic
386C23×C4C22⋊D5911yescharacteristic
387C23×C4C22×D5911yescharacteristic
388C22×C8—591no—
389C22×C8—591no—
390C22×C8—591no—
391C22×C8—591no—
392#121—22no—
393#121—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—44no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—591no—
399C2×C4⋊C4—591no—
400C2×C4⋊C4—591no—
401C2×C4⋊C4—591no—
402C2×C4⋊C4C22×D5911yescharacteristic
403C2×C4⋊C4C22×D5911yescharacteristic
404C2×C4⋊C4C22×D5911yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—1181no—
411C2×C22⋊C4—1181no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—21no—
415C2×C42—1181no—
416C2×C42—1181no—
417C2×C42C22⋊D5911yescharacteristic
418C2×C42C22⋊D5911yescharacteristic
419C2×C42C22×D5911yescharacteristic
420C2×C42C22×D5911yescharacteristic
421#107—1182no—
422#107—1182no—
423#106—1182no—
424#106—1182no—
425#102—1182no—
426#102—1182no—
427#102—1182no—
428#102—1182no—
429C22⋊C8—1182no—
430C22⋊C8—1182no—
431C4×C8—1182no—
432C4×C8—1182no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—1181no—
437#95—1181no—
438#95—1181no—
439#95—1181no—
440#95—1181no—
441#95—1181no—
442#95—1181no—
443#95—1181no—
444C24—21no—
445C24C2×C22⋊D5911yescharacteristic
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4#1174568512yes—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—1181no—
474C22×C4—1181no—
475C22×C4—1181no—
476C22×C4—1181no—
477C22×C4C2×C22⋊D5911yescharacteristic
478C22×C4C2×C22⋊D5911yescharacteristic
479C22×C4C2×C22⋊D5911yescharacteristic
480C22×C4C2×C22⋊D5911yescharacteristic
481C22×C4C2×C22⋊D5911yescharacteristic
482C22×C4C23×D5911yescharacteristic
483C2×C8—592no—
484C2×C8—592no—
485C2×C8—1181no—
486C2×C8—1181no—
487C2×C8—1181no—
488C2×C8—1181no—
489C2×C8—1181no—
490C2×C8—1181no—
491C2×C8—1181no—
492C2×C8—1181no—
493C2×C8—1181no—
494C2×C8—1181no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—1181no—
502C4⋊C4—1181no—
503C4⋊C4—1181no—
504C4⋊C4—1181no—
505C4⋊C4—1181no—
506C4⋊C4—1181no—
507C4⋊C4—1181no—
508C4⋊C4—1181no—
509C4⋊C4#1174568512yes—
510C22⋊C4—24no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—2362no—
516C22⋊C4—2362no—
517C42—22no—
518C42—22no—
519C42—21no—
520C42—21no—
521C42—42no—
522C42—2362no—
523C42—2362no—
524C42#1174568712yes—
525C42#1174568712yes—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—22no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23#1427374712yes—
540C23C22×C22⋊D5911yescharacteristic
541D4—22no—
542D4—22no—
543D4—48no—
544D4—41no—
545D4—41no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—44no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—2361no—
574C2×C4—2361no—
575C2×C4—2361no—
576C2×C4—2361no—
577C2×C4—2361no—
578C2×C4—2361no—
579C2×C4—2361no—
580C2×C4—2361no—
581C2×C4—2361no—
582C2×C4—2361no—
583C2×C4—2361no—
584C2×C4—2361no—
585C2×C4#1427370812yes—
586C2×C4#1427370812yes—
587C2×C4#1427374712yes—
588C2×C4#1427375312yes—
589C2×C4#41×D5911yescharacteristic
590C2×C4#41×D5911yescharacteristic
591C2×C4C2×#1174568711yescharacteristic
592C2×C4C2×#1174568711yescharacteristic
593C2×C4C2×#1174568511yescharacteristic
594C2×C4C2×#1174568511yescharacteristic
595C8—1182no—
596C8—1182no—
597C8—2361no—
598C8—2361no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22C2×#1427370811yescharacteristic
614C22#1683791311yescharacteristic
615C22#1683794811yescharacteristic
616C22C2×#1427374711yescharacteristic
617C22C2×#1427374711yescharacteristic
618C22C2×#1427375311yescharacteristic
619C22#1683820011yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—4721no—
628C4—4721no—
629C4—4721no—
630C4—4721no—
631C4#1683772314yes—
632C4#1683793211yescharacteristic
633C4#1683793211yescharacteristic
634C4#1683793411yescharacteristic
635C4#1683793411yescharacteristic
636C2—42no—
637C2—82no—
638C2#2142735511yescharacteristic
639C2C2×#1683772311yescharacteristic
640C2#2143400511yescharacteristic
641C2#2143411411yescharacteristic
642C2#2143414311yescharacteristic
643C2#2143466011yescharacteristic
644C2#2143468511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC4×#121×C59C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
hypercenterC4×#121D59
hypocenterC59#23758
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #21426494C2semidirect
2. #21425664C2semidirect
3. #21425617C2semidirect
4. #21425577C2semidirect
5. #21425533C2semidirect
6. #21425527C2semidirect
7. #21425509C2semidirect
10. C4×#14273660C2semidirect
11. C4×#14273658C2semidirect
12. C4×#14273648C2semidirect
13. C4×#14273648C2semidirect
14. C4×C22⋊(C59⋊C8)C2semidirect
381. C59#23758semidirect

Maximal subgroups

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

subgroupindex
#214264942
#214256642
#214256172
#214255772
#214255332
#214255272
#214255092
#214252822
#214252752
C4×#142736602
C4×#142736582
C4×#142736482
C4×C22⋊(C59⋊C8)2
C4×#121×C592
#2375859