Finite Group Databasebeta

← #28617564

Subgroups — #28617564

Order 15104.

1166 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
1C2×#16837445C211yesmaximal, characteristic, complemented
2C2×#16837366C211yesmaximal, characteristic
3C2×#16837262C211yesmaximal, characteristic
4#21425533C212yesmaximal, complemented
5#21425532C212yesmaximal, complemented
6#21425527C212yesmaximal, complemented
7#21425522C212yesmaximal, complemented
8#21423817C211yesmaximal, characteristic, complemented
9#21423817C211yesmaximal, characteristic, complemented
10#21423817C211yesmaximal, characteristic, complemented
11C59×#2280C211yesmaximal, characteristic
12C22×#11745664C2211yescharacteristic
13C22×#11745664C2211yescharacteristic
14C22×C4⋊Dic59C2211yescharacteristic
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C22⋊Dic59—21no—
17#16837445—24no—
18C2×#14273660C2212yescomplemented
19C2×#14273658C2212yescomplemented
20#16837366—24no—
21C2×C22⋊(C59⋊C8)C2212yes—
22C2×C22⋊(C59⋊C8)C2212yes—
23#16837262—21no—
24#16837262—21no—
25#16837262C2212yes—
26#16837262C2212yes—
27C2×C59⋊#95—21no—
28#16837164C2212yescomplemented
29#16837164C2212yescomplemented
30#16837164C2212yescomplemented
31#16837164C2212yescomplemented
32#16837164C2212yescomplemented
33#16837164C2212yescomplemented
34C24×C4×C59C2211yescharacteristic
35C2×#117×C59C2211yescharacteristic
36C2×#117×C59C2211yescharacteristic
37C59×#381—21no—
38C59×#380C2211yescharacteristic
39C59×#380C2211yescharacteristic
40C59×#380C2211yescharacteristic
41C59×#380C2211yescharacteristic
42C59×#379—21no—
43C4×C22⋊C4×C59—21no—
44C4×C22⋊C4×C59—21no—
45C23×Dic59—21no—
46C23×Dic59—21no—
47C2×#11745664—22no—
48C2×#11745664—22no—
49C2×#11745664—22no—
50C2×#11745664—22no—
51C2×#11745664—22no—
52C2×#11745664D414yes—
53C22×C59⋊C8C2312yes—
54C22×C59⋊C8C2312yes—
55C2×C4⋊Dic59—22no—
56C2×C4⋊Dic59—22no—
57C2×C4⋊Dic59—22no—
58C2×C4⋊Dic59—22no—
59C2×C4⋊Dic59—21no—
60C2×C4⋊Dic59—21no—
61C2×C4⋊Dic59C2312yes—
62C2×C4⋊Dic59C2312yes—
63C2×C22⋊Dic59—22no—
64C2×C22⋊Dic59—22no—
65C2×C22⋊Dic59—44no—
66#14273660—24no—
67#14273658—24no—
68C22⋊(C59⋊C8)—24no—
69C22⋊(C59⋊C8)—24no—
70C59⋊#95—22no—
71C59⋊#95—22no—
72C25×C59D411yescharacteristic
73C23×C4×C59—22no—
74C23×C4×C59—22no—
75C23×C4×C59—22no—
76C23×C4×C59—22no—
77C23×C4×C59—22no—
78C23×C4×C59—22no—
79C23×C4×C59D411yescharacteristic
80C23×C4×C59D411yescharacteristic
81C23×C4×C59D411yescharacteristic
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C23×C4×C59C2311yescharacteristic
85#117×C59—22no—
86#117×C59—22no—
87#117×C59—22no—
88#117×C59—22no—
89C2×C4⋊C4×C59C2311yescharacteristic
90C2×C4⋊C4×C59C2311yescharacteristic
91C2×C4⋊C4×C59C2311yescharacteristic
92C2×C4⋊C4×C59C2311yescharacteristic
93C2×C22⋊C4×C59—21no—
94C2×C22⋊C4×C59—21no—
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59—21no—
97C2×C22⋊C4×C59—21no—
98C2×C22⋊C4×C59—21no—
99C2×C42×C59—21no—
100C2×C42×C59—21no—
101#95×C59—21no—
102#95×C59—21no—
103#95×C59—21no—
104#95×C59—21no—
105C24×C59—22no—
106C24×C59—22no—
107C24×C59—22no—
108C24×C59—22no—
109C24×C59—22no—
110C24×C59—41no—
111C24×C59—41no—
112C24×C59C2×D411yescharacteristic
113C24×C59C2×D411yescharacteristic
114C24×C59C2×D411yescharacteristic
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
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—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—44no—
141C22×C4×C59—44no—
142C22×C4×C59—44no—
143C22×C4×C59—44no—
144C22×C4×C59C2×D411yescharacteristic
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×D412yes—
148C22×C4×C59#4112yes—
149C22×C4×C59#4112yes—
150C22×C4×C59#4112yes—
151C22×C4×C59#4112yes—
152C22×C4×C59#4112yes—
153C22×C4×C59C2411yescharacteristic
154C22×Dic59—22no—
155C22×Dic59—22no—
156C22×Dic59—42no—
157C22×Dic59—42no—
158C22×Dic59—42no—
159C22×Dic59—42no—
160C22×Dic59—42no—
161C22×Dic59—42no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59—21no—
167C4⋊C4×C59—21no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C22⋊C4×C59—42no—
171C22⋊C4×C59—42no—
172C22⋊C4×C59—42no—
173C22⋊C4×C59—42no—
174C22⋊C4×C59—42no—
175C22⋊C4×C59—42no—
176C42×C59—42no—
177C42×C59—42no—
178C22⋊Dic59—44no—
179C22⋊Dic59—44no—
180C4⋊Dic59—22no—
181C4⋊Dic59—22no—
182C4⋊Dic59—22no—
183C4⋊Dic59—22no—
184C4⋊Dic59—42no—
185C4⋊Dic59—42no—
186#11745664—28no—
187#11745664—44no—
188C2×C59⋊C8—22no—
189C2×C59⋊C8—22no—
190C2×C59⋊C8—22no—
191C2×C59⋊C8—22no—
192C2×C59⋊C8—22no—
193C2×C59⋊C8C2×D414yes—
194C23×C59—21no—
195C23×C59—21no—
196C23×C59—21no—
197C23×C59—21no—
198C23×C59—28no—
199C23×C59—21no—
200C23×C59—21no—
201C23×C59—21no—
202C23×C59—21no—
203C23×C59—21no—
204C23×C59—21no—
205C23×C59—21no—
206C23×C59—21no—
207C23×C59—21no—
208C23×C59—21no—
209C23×C59—21no—
210C23×C59—21no—
211C23×C59—44no—
212C23×C59—44no—
213C23×C59—44no—
214C23×C59—44no—
215C23×C59—44no—
216C23×C59—44no—
217C23×C59#12112yes—
218C23×C59#12312yes—
219C23×C59#12312yes—
220C23×C59AGL(1,ℤ/8)12yes—
221C23×C59#13712yes—
222C23×C59C22×D411yescharacteristic
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—44no—
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—44no—
239C2×C4×C59—44no—
240C2×C4×C59—41no—
241C2×C4×C59—41no—
242C2×C4×C59—41no—
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—41no—
250C2×C4×C59—41no—
251C2×C4×C59—41no—
252C2×C4×C59#12112yes—
253C2×C4×C59#12312yes—
254C2×C4×C59#12314yes—
255C2×C4×C59#12312yes—
256C2×C4×C59#12414yes—
257C2×C4×C59#12614yes—
258C2×C4×C59#12614yes—
259C2×C4×C59C22×D411yescharacteristic
260C2×C4×C59C2×#4111yescharacteristic
261C2×C4×C59C2×#4111yescharacteristic
262C2×C4×C59C2×#4111yescharacteristic
263C2×C4×C59C2×#4111yescharacteristic
264C2×C4×C59C2×#4111yescharacteristic
265C2×Dic59—42no—
266C2×Dic59—42no—
267C2×Dic59—42no—
268C2×Dic59—42no—
269C2×Dic59—42no—
270C2×Dic59—42no—
271C2×Dic59—84no—
272C2×Dic59—84no—
273C59⋊C8—24no—
274C59⋊C8—42no—
275#23642—591nomaximal, Sylow
276C22×C59—22no—
277C22×C59—22no—
278C22×C59—22no—
279C22×C59—22no—
280C22×C59—22no—
281C22×C59—22no—
282C22×C59—22no—
283C22×C59—22no—
284C22×C59—22no—
285C22×C59—22no—
286C22×C59—22no—
287C22×C59—22no—
288C22×C59—416no—
289C22×C59—41no—
290C22×C59—41no—
291C22×C59—41no—
292C22×C59—41no—
293C22×C59—41no—
294C22×C59—41no—
295C22×C59—41no—
296C22×C59—41no—
297C22×C59#39714yes—
298C22×C59C2×#12111yescharacteristic
299C22×C59C2×#12311yescharacteristic
300C22×C59C2×#12311yescharacteristic
301C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C59C2×#13711yescharacteristic
303C22×C59#57511yescharacteristic
304C22×C59#57511yescharacteristic
305C4×C59—41no—
306C4×C59—41no—
307C4×C59—81no—
308C4×C59—81no—
309C4×C59—81no—
310C4×C59—81no—
311C4×C59#39714yes—
312C4×C59C2×#12311yescharacteristic
313C4×C59C2×#12411yescharacteristic
314C4×C59C2×#12611yescharacteristic
315C4×C59C2×#12611yescharacteristic
316Dic59—82no—
317Dic59—82no—
318C2×#428—591no—
319C2×#407—591no—
320#2280D5911yescharacteristic
321C2×#380—591no—
322#2077—592no—
323#2077—592no—
324#2076—592no—
325#2075—592no—
326#1736—591no—
327#1736—591no—
328#1736—591no—
329C2×C59—24no—
330C2×C59—42no—
331C2×C59—42no—
332C2×C59C2×#39711yescharacteristic
333C2×C59#305511yescharacteristic
334C2×C59#305611yescharacteristic
335C2×C59#309211yescharacteristic
336C2×C59#309311yescharacteristic
337C2×C59#309411yescharacteristic
338C2×C59#309511yescharacteristic
339C24×C4C2×D5911yescharacteristic
340C22×M16—591no—
341C22×M16—591no—
342C2×#117C2×D5911yescharacteristic
343C2×#117C2×D5911yescharacteristic
344C22×C4⋊C4—591no—
345C22×C4⋊C4—591no—
346C22×C22⋊C4—1181no—
347#428—1184no—
348C2×#107—592no—
349C2×#106—592no—
350#407—1184no—
351C2×C22⋊C8—592no—
352C2×C22⋊C8—592no—
353#381—21no—
354#380—592no—
355#380—592no—
356#380—1181no—
357#380—1181no—
358#380C2×D5911yescharacteristic
359#380C2×D5911yescharacteristic
360#380C2×D5911yescharacteristic
361#380C2×D5911yescharacteristic
362#379—21no—
363C4×C22⋊C4—21no—
364C4×C22⋊C4—21no—
365C2×#95—1181no—
366#340—592no—
367#340—592no—
368#340—592no—
369#340—592no—
370#340—592no—
371#340—592no—
372C59#2364211yescharacteristic, complemented, Sylow
373C25C22⋊D5911yescharacteristic
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—1181no—
381C23×C4—1181no—
382C23×C4C22⋊D5911yescharacteristic
383C23×C4C22⋊D5911yescharacteristic
384C23×C4C22⋊D5911yescharacteristic
385C23×C4C22×D5911yescharacteristic
386C23×C4C22×D5911yescharacteristic
387C23×C4C22×D5911yescharacteristic
388C2×M16—594no—
389C2×M16—1182no—
390C2×M16—1182no—
391C2×M16—1182no—
392C2×M16—1182no—
393C2×M16—1182no—
394C22×C8—592no—
395C22×C8—592no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400C2×C4⋊C4—592no—
401C2×C4⋊C4—592no—
402C2×C4⋊C4—1182no—
403C2×C4⋊C4—1182no—
404C2×C4⋊C4—1182no—
405C2×C4⋊C4—1182no—
406C2×C4⋊C4—1181no—
407C2×C4⋊C4—1181no—
408C2×C4⋊C4C22×D5911yescharacteristic
409C2×C4⋊C4C22×D5911yescharacteristic
410C2×C4⋊C4C22×D5911yescharacteristic
411C2×C4⋊C4C22×D5911yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—1182no—
419C2×C22⋊C4—1182no—
420C2×C22⋊C4—2364no—
421C2×C42—21no—
422C2×C42—21no—
423#107—1184no—
424#106—1184no—
425C22⋊C8—1184no—
426C22⋊C8—1184no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—1182no—
432#95—1182no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—41no—
439C24—41no—
440C24C2×C22⋊D5911yescharacteristic
441C24C2×C22⋊D5911yescharacteristic
442C24C2×C22⋊D5911yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
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—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—1182no—
473C22×C4—1182no—
474C22×C4—2362no—
475C22×C4—2362no—
476C22×C4—2362no—
477C22×C4—2362no—
478C22×C4—2362no—
479C22×C4—2362no—
480C22×C4#1174568512yes—
481C22×C4#1174568512yes—
482C22×C4D4×D5912yes—
483C22×C4#1174568712yes—
484C22×C4#1174568712yes—
485C22×C4#1174568712yes—
486C22×C4C2×C22⋊D5911yescharacteristic
487C22×C4C2×C22⋊D5911yescharacteristic
488C22×C4C2×C22⋊D5911yescharacteristic
489C22×C4C23×D5911yescharacteristic
490M16—1188no—
491M16—2364no—
492C2×C8—594no—
493C2×C8—1182no—
494C2×C8—1182no—
495C2×C8—1182no—
496C2×C8—1182no—
497C2×C8—1182no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—1182no—
507C4⋊C4—1182no—
508C4⋊C4—1182no—
509C4⋊C4—1182no—
510C4⋊C4—2362no—
511C4⋊C4—2362no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—2364no—
519C22⋊C4—2364no—
520C42—42no—
521C42—42no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—28no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23#1427369912yes—
546C23#1427370812yes—
547C23#1427371012yes—
548C23#1427375212yes—
549C23#1427375712yes—
550C23C22×C22⋊D5911yescharacteristic
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
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—44no—
567C2×C4—44no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—4724no—
581C2×C4—4724no—
582C2×C4—2362no—
583C2×C4—2362no—
584C2×C4—2362no—
585C2×C4—2362no—
586C2×C4—2362no—
587C2×C4—2362no—
588C2×C4#1427369912yes—
589C2×C4#1427370812yes—
590C2×C4#1427370914yes—
591C2×C4#1427371012yes—
592C2×C4#1427371314yes—
593C2×C4#1427372014yes—
594C2×C4#1427372014yes—
595C2×C4C2×D4×D5911yescharacteristic
596C2×C4C2×#1174568711yescharacteristic
597C2×C4C2×#1174568711yescharacteristic
598C2×C4C2×#1174568711yescharacteristic
599C2×C4C2×#1174568511yescharacteristic
600C2×C4C2×#1174568511yescharacteristic
601C8—1184no—
602C8—2362no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22#1683733014yes—
625C22C2×#1427369911yescharacteristic
626C22C2×#1427370811yescharacteristic
627C22C2×#1427371011yescharacteristic
628C22C2×#1427375211yescharacteristic
629C22C2×#1427375711yescharacteristic
630C22#1683820011yescharacteristic
631C22#1683820011yescharacteristic
632C4—41no—
633C4—41no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—4722no—
639C4—4722no—
640C4#1683733014yes—
641C4C2×#1427370911yescharacteristic
642C4C2×#1427371311yescharacteristic
643C4C2×#1427372011yescharacteristic
644C4C2×#1427372011yescharacteristic
645C2—24no—
646C2—42no—
647C2—42no—
648C2C2×#1683733011yescharacteristic
649C2#2143371711yescharacteristic
650C2#2143372811yescharacteristic
651C2#2143401611yescharacteristic
652C2#2143402511yescharacteristic
653C2#2143403611yescharacteristic
654C2#2143404411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2280C2
socleC23×C59C22×D4
prime radicalC25×C59D4
hypercenter#2280D59
hypocenterC59#23642
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. C2×#16837445C2semidirect
4. #21425533C2semidirect
5. #21425532C2semidirect
6. #21425527C2semidirect
7. #21425522C2semidirect
8. #21423817C2semidirect
9. #21423817C2semidirect
10. #21423817C2semidirect
18. C2×#14273660C22semidirect
19. C2×#14273658C22semidirect
28. #16837164C22semidirect
29. #16837164C22semidirect
30. #16837164C22semidirect
31. #16837164C22semidirect
32. #16837164C22semidirect
33. #16837164C22semidirect
372. C59#23642semidirect

Maximal subgroups

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

subgroupindex
C2×#168374452
C2×#168373662
C2×#168372622
#214255332
#214255322
#214255272
#214255222
#214238172
C59×#22802
#2364259