Finite Group Databasebeta

← #28495239

Subgroups — #28495239

Order 15104.

1334 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273725C211yesmaximal, characteristic
2C2×#16837411C211yesmaximal, characteristic
3C22×#14273645C211yesmaximal, characteristic
4#21426680C211yesmaximal, characteristic
5C2×#16837163C211yesmaximal, characteristic
6C2×#16837161C211yesmaximal, characteristic
7C2×C59×#419C211yesmaximal, characteristic
8C23×Dic118C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C2×#14273725—22no—
11C2×#14273725—22no—
12C2×#14273725—22no—
13C2×#14273725—22no—
14C2×#14273725—22no—
15C2×#14273725C414yescomplemented
16C2×#14273686C2211yescharacteristic
17C22×Dic59⋊C4—22no—
18C22×C4×Dic59C2211yescharacteristic
19#16837411—22no—
20#16837411—22no—
21C2×#14273651—22no—
22C2×#14273645—22no—
23C2×#14273645—22no—
24C2×#14273645—22no—
25#16837308—22no—
26#16837307—22no—
27#16837263—22no—
28#16837163—22no—
29#16837161—22no—
30C23×Q8×C59C2211yescharacteristic
31C22×M16×C59C2211yescharacteristic
32C2×#117×C59C2211yescharacteristic
33C59×#419—22no—
34C59×#419—22no—
35C2×#103×C59—22no—
36C22×Dic118—21no—
37C22×Dic118—21no—
38C22×Dic118—21no—
39C22×Dic118—21no—
40C22×Dic118—21no—
41C22×Dic118—21no—
42C22×Dic118—21no—
43C22×Dic118—21no—
44C22×Dic118—21no—
45C22×Dic118—21no—
46C22×Dic118—21no—
47C22×Dic118—21no—
48C22×Dic118C2×C412yes—
49C22×Dic118D412yes—
50C23×Dic59—21no—
51C23×Dic59D412yes—
52C2×#11745664—21no—
53C2×#11745664—21no—
54C2×#11745664—21no—
55C2×#11745664—21no—
56C2×#11745664—21no—
57C2×#11745664D412yes—
58C22×C59⋊C8—21no—
59#14273725—28no—
60#14273725—28no—
61#14273725—28no—
62#14273725—28no—
63#14273686—21no—
64#14273686—21no—
65#14273686—21no—
66#14273686—21no—
67C2×C4⋊Dic59D412yes—
68C2×Dic59⋊C4—28no—
69C2×Dic59⋊C4—28no—
70C2×Dic59⋊C4—28no—
71C2×C22⋊Dic59—21no—
72C2×C4×Dic59—21no—
73C2×C4×Dic59—21no—
74C2×C4×Dic59—21no—
75C2×C4×Dic59—21no—
76C2×C4×Dic59C2×C412yes—
77C2×C4×Dic59D412yes—
78C2×C4×Dic59D412yes—
79#14273651—28no—
80#14273645—28no—
81C59⋊#95—28no—
82C22×Q8×C59—21no—
83C22×Q8×C59—21no—
84C22×Q8×C59—21no—
85C22×Q8×C59—21no—
86C22×Q8×C59—21no—
87C22×Q8×C59—21no—
88C22×Q8×C59—21no—
89C22×Q8×C59—21no—
90C22×Q8×C59—21no—
91C22×Q8×C59—21no—
92C22×Q8×C59—21no—
93C22×Q8×C59C2×C412yes—
94C22×Q8×C59D412yes—
95C22×Q8×C59D412yes—
96C23×C4×C59—21no—
97C23×C4×C59C2311yescharacteristic
98C2×M16×C59—21no—
99C2×M16×C59—21no—
100C2×M16×C59—21no—
101C2×M16×C59—21no—
102C2×M16×C59—21no—
103C2×M16×C59D412yes—
104C22×C8×C59—21no—
105#117×C59—21no—
106#117×C59—21no—
107#117×C59—21no—
108#117×C59—21no—
109C2×C4⋊C4×C59D412yes—
110C2×C22⋊C4×C59—21no—
111C2×C42×C59—21no—
112#103×C59—28no—
113C24×C59C2×D411yescharacteristic
114C2×Q8×C59—22no—
115C2×Q8×C59—22no—
116C2×Q8×C59—22no—
117C2×Q8×C59—22no—
118C2×Q8×C59—22no—
119C2×Q8×C59—22no—
120C2×Q8×C59—22no—
121C2×Q8×C59—22no—
122C2×Q8×C59—22no—
123C2×Q8×C59—22no—
124C2×Q8×C59—22no—
125C2×Q8×C59—22no—
126C2×Q8×C59—22no—
127C2×Q8×C59—22no—
128C2×Q8×C59—22no—
129C2×Q8×C59—41no—
130C2×Q8×C59—41no—
131C2×Q8×C59—41no—
132C2×Q8×C59—41no—
133C2×Q8×C59—41no—
134C2×Q8×C59—41no—
135C2×Q8×C59—41no—
136C2×Q8×C59—41no—
137C2×Q8×C59—41no—
138C2×Q8×C59—41no—
139C2×Q8×C59—41no—
140C2×Q8×C59—41no—
141C2×Q8×C59C22⋊C414yes—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—41no—
147C22×C4×C59—41no—
148C22×C4×C59—41no—
149C22×C4×C59—41no—
150C22×C4×C59C22×C411yescharacteristic
151C22×C4×C59C2×D411yescharacteristic
152C22×C4×C59C2×D411yescharacteristic
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59#4111yescharacteristic
161C22×C4×C59#4111yescharacteristic
162C22×C4×C59#4111yescharacteristic
163C22×C4×C59#4111yescharacteristic
164C22×Dic59—28no—
165C22×Dic59—22no—
166C22×Dic59—22no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—22no—
171C22×Dic59—22no—
172C22×Dic59—22no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59C22⋊C414yes—
176C2×Dic118—22no—
177C2×Dic118—22no—
178C2×Dic118—22no—
179C2×Dic118—22no—
180C2×Dic118—22no—
181C2×Dic118—22no—
182C2×Dic118—22no—
183C2×Dic118—22no—
184C2×Dic118—22no—
185C2×Dic118—22no—
186C2×Dic118—22no—
187C2×Dic118—22no—
188C2×Dic118—41no—
189C2×Dic118—41no—
190C2×Dic118—41no—
191C2×Dic118—41no—
192C2×Dic118—41no—
193C2×Dic118—41no—
194C2×Dic118—41no—
195C2×Dic118—41no—
196C2×Dic118—41no—
197C2×Dic118—41no—
198C2×Dic118—41no—
199C2×Dic118—41no—
200C2×Dic118—41no—
201C2×Dic118—41no—
202C2×Dic118—41no—
203C2×Dic118—41no—
204M16×C59—22no—
205M16×C59—22no—
206M16×C59—41no—
207M16×C59—41no—
208C2×C8×C59—22no—
209C2×C8×C59—41no—
210C2×C8×C59—41no—
211C4⋊C4×C59—22no—
212C4⋊C4×C59—22no—
213C22⋊C4×C59—41no—
214C22⋊C4×C59—41no—
215C42×C59—41no—
216C42×C59—41no—
217C22⋊Dic59—41no—
218C22⋊Dic59—41no—
219C4⋊Dic59—22no—
220C4⋊Dic59—22no—
221Dic59⋊C4—232no—
222C4×Dic59—22no—
223C4×Dic59—22no—
224C4×Dic59—22no—
225C4×Dic59—41no—
226C4×Dic59—41no—
227C4×Dic59C22⋊C414yes—
228#11745664—22no—
229#11745664—22no—
230#11745664—41no—
231#11745664—41no—
232C2×C59⋊C8—22no—
233C2×C59⋊C8—41no—
234C2×C59⋊C8—41no—
235C23×C59—24no—
236C23×C59C2×C22⋊C411yescharacteristic
237C23×C59#12011yescharacteristic
238C23×C59#12011yescharacteristic
239C23×C59#12011yescharacteristic
240C23×C59#12111yescharacteristic
241C23×C59#12111yescharacteristic
242C23×C59#12311yescharacteristic
243Q8×C59—24no—
244Q8×C59—24no—
245Q8×C59—42no—
246Q8×C59—42no—
247Q8×C59—42no—
248Q8×C59—42no—
249Q8×C59—42no—
250Q8×C59—42no—
251C2×C4×C59—24no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—42no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—42no—
258C2×C4×C59—42no—
259C2×C4×C59—44no—
260C2×C4×C59C2×C22⋊C411yescharacteristic
261C2×C4×C59C2×C22⋊C411yescharacteristic
262C2×C4×C59C4×D411yescharacteristic
263C2×C4×C59C4×D411yescharacteristic
264C2×C4×C59C4×D411yescharacteristic
265C2×C4×C59C4×D411yescharacteristic
266C2×C4×C59#12011yescharacteristic
267C2×C4×C59#12011yescharacteristic
268C2×C4×C59#12011yescharacteristic
269C2×C4×C59#12011yescharacteristic
270C2×C4×C59#12011yescharacteristic
271C2×C4×C59#12111yescharacteristic
272C2×C4×C59#12111yescharacteristic
273C2×C4×C59#12111yescharacteristic
274C2×C4×C59#12111yescharacteristic
275C2×C4×C59#12111yescharacteristic
276C2×C4×C59#12111yescharacteristic
277C2×C4×C59#12111yescharacteristic
278C2×C4×C59#12111yescharacteristic
279C2×C4×C59#12111yescharacteristic
280C2×C4×C59#12111yescharacteristic
281C2×C4×C59#12311yescharacteristic
282C2×C4×C59#12311yescharacteristic
283C2×C4×C59#12311yescharacteristic
284C2×C4×C59#12411yescharacteristic
285C2×C4×C59#12411yescharacteristic
286C2×C4×C59#12711yescharacteristic
287C2×C4×C59#12711yescharacteristic
288C2×Dic59—28no—
289C2×Dic59—28no—
290C2×Dic59—28no—
291C2×Dic59—24no—
292C2×Dic59—24no—
293C2×Dic59—24no—
294C2×Dic59—24no—
295C2×Dic59—42no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59—42no—
299C2×Dic59—42no—
300C2×Dic59—44no—
301Dic118—42no—
302Dic118—42no—
303Dic118—42no—
304Dic118—42no—
305Dic118—42no—
306Dic118—42no—
307Dic118—42no—
308Dic118—42no—
309C8×C59—42no—
310C59⋊C8—42no—
311#10978—591nomaximal, Sylow
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—22no—
318C22×C59#37911yescharacteristic
319C22×C59#38611yescharacteristic
320C22×C59#38611yescharacteristic
321C22×C59#39211yescharacteristic
322C22×C59#39211yescharacteristic
323C22×C59#39411yescharacteristic
324C22×C59#39411yescharacteristic
325C22×C59#45614yes—
326C4×C59—44no—
327C4×C59—82no—
328C4×C59#38611yescharacteristic
329C4×C59#38611yescharacteristic
330C4×C59#39011yescharacteristic
331C4×C59#39011yescharacteristic
332C4×C59#39211yescharacteristic
333C4×C59#39211yescharacteristic
334C4×C59#39411yescharacteristic
335C4×C59#39411yescharacteristic
336Dic59—28no—
337Dic59—44no—
338Dic59—82no—
339C22×C4⋊Q8—591no—
340C2×#419—591no—
341C2×#419D5911yescharacteristic
342C22×#101—591no—
343#2310—591no—
344C2×#339—591no—
345C2×#339—591no—
346C2×C59—21no—
347C2×C59—21no—
348C2×C59—21no—
349C2×C59—21no—
350C2×C59#143811yescharacteristic
351C2×C59#188612yes—
352C2×C59#200512yes—
353C2×C59#200512yes—
354C23×Q8—591no—
355C23×Q8C2×D5911yescharacteristic
356C22×M16—591no—
357C22×M16C2×D5911yescharacteristic
358C2×C4⋊Q8—594no—
359C2×C4⋊Q8—1182no—
360C2×C4⋊Q8—1182no—
361C2×C4⋊Q8—1182no—
362C2×C4⋊Q8—1182no—
363C2×C4⋊Q8—1182no—
364C2×#117—591no—
365C2×#117C2×D5911yescharacteristic
366C22×C4⋊C4—1182no—
367C22×C42—591no—
368#419—22no—
369#419—22no—
370#419—1182no—
371#419—1182no—
372C2×#103—22no—
373C2×#103—1182no—
374C2×#101—1182no—
375C2×#101—1182no—
376C2×#101—1182no—
377#391—1182no—
378#391—1182no—
379#381—1182no—
380#339—1182no—
381#339—1182no—
382C59#1097811yescharacteristic, complemented, Sylow
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—592no—
395C22×Q8—592no—
396C22×Q8—1181no—
397C22×Q8—1181no—
398C22×Q8—1181no—
399C22×Q8—1181no—
400C22×Q8—1181no—
401C22×Q8—1181no—
402C22×Q8—1181no—
403C22×Q8—1181no—
404C22×Q8—1181no—
405C22×Q8—1181no—
406C22×Q8—1181no—
407C22×Q8—1181no—
408C22×Q8C4×D5912yes—
409C22×Q8D23612yes—
410C22×Q8C22⋊D5912yes—
411C23×C4—21no—
412C23×C4—592no—
413C23×C4—1181no—
414C23×C4C22×D5911yescharacteristic
415C2×M16—21no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—21no—
420C2×M16—592no—
421C2×M16—1181no—
422C2×M16—1181no—
423C2×M16—1181no—
424C2×M16—1181no—
425C2×M16—1181no—
426C2×M16C22⋊D5912yes—
427C22×C8—21no—
428C22×C8—1181no—
429C4⋊Q8—1188no—
430C4⋊Q8—1188no—
431C4⋊Q8—1188no—
432C4⋊Q8—1188no—
433#117—21no—
434#117—21no—
435#117—21no—
436#117—21no—
437#117—1181no—
438#117—1181no—
439#117—1181no—
440#117—1181no—
441C2×C4⋊C4—592no—
442C2×C4⋊C4—1188no—
443C2×C4⋊C4—1188no—
444C2×C4⋊C4—1188no—
445C2×C4⋊C4C22⋊D5912yes—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—1181no—
448C2×C42—21no—
449C2×C42—592no—
450C2×C42—592no—
451C2×C42—592no—
452C2×C42—1181no—
453C2×C42—1181no—
454C2×C42—1181no—
455C2×C42—1181no—
456#103—28no—
457#103—1188no—
458#101—1188no—
459#95—1188no—
460C24D4×D5911yescharacteristic
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—1182no—
489C2×Q8—1182no—
490C2×Q8—1182no—
491C2×Q8—1182no—
492C2×Q8—1182no—
493C2×Q8—1182no—
494C2×Q8—1182no—
495C2×Q8—1182no—
496C2×Q8—1182no—
497C2×Q8—1182no—
498C2×Q8—1182no—
499C2×Q8—1182no—
500C2×Q8—2361no—
501C2×Q8—2361no—
502C2×Q8—2361no—
503C2×Q8—2361no—
504C2×Q8—2361no—
505C2×Q8—2361no—
506C2×Q8—2361no—
507C2×Q8—2361no—
508C2×Q8—2361no—
509C2×Q8—2361no—
510C2×Q8—2361no—
511C2×Q8—2361no—
512C2×Q8—2361no—
513C2×Q8—2361no—
514C2×Q8—2361no—
515C2×Q8—2361no—
516C2×Q8(C2×D59)⋊C414yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—594no—
526C22×C4—1188no—
527C22×C4—1182no—
528C22×C4—1182no—
529C22×C4—1182no—
530C22×C4—1182no—
531C22×C4—1182no—
532C22×C4—1182no—
533C22×C4—1182no—
534C22×C4—1182no—
535C22×C4—1182no—
536C22×C4—1182no—
537C22×C4C2×C4×D5911yescharacteristic
538C22×C4C2×D23611yescharacteristic
539C22×C4#1174568511yescharacteristic
540C22×C4#1174568511yescharacteristic
541C22×C4D4×D5911yescharacteristic
542C22×C4D4×D5911yescharacteristic
543C22×C4D4×D5911yescharacteristic
544C22×C4D4×D5911yescharacteristic
545C22×C4D4×D5911yescharacteristic
546C22×C4#1174568711yescharacteristic
547C22×C4#1174568711yescharacteristic
548C22×C4C2×C22⋊D5911yescharacteristic
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C2×C22⋊D5911yescharacteristic
551M16—22no—
552M16—22no—
553M16—41no—
554M16—41no—
555M16—1182no—
556M16—1182no—
557M16—2361no—
558M16—2361no—
559C2×C8—22no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—1182no—
563C2×C8—2361no—
564C2×C8—2361no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—11832no—
568C4⋊C4—1182no—
569C4⋊C4—1182no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—2361no—
573C22⋊C4—2361no—
574C42—41no—
575C42—41no—
576C42—594no—
577C42—1182no—
578C42—1182no—
579C42—1182no—
580C42—2361no—
581C42—2361no—
582C23—24no—
583C23C22⋊C4×D5911yescharacteristic
584C23#1427369511yescharacteristic
585C23#1427369511yescharacteristic
586C23#1427369711yescharacteristic
587C23#1427369811yescharacteristic
588C23#1427370011yescharacteristic
589C23#1427370911yescharacteristic
590Q8—24no—
591Q8—24no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596Q8—42no—
597Q8—42no—
598Q8—2362no—
599Q8—2362no—
600Q8—2362no—
601Q8—2362no—
602Q8—2362no—
603Q8—2362no—
604Q8—2362no—
605Q8—2362no—
606C2×C4—24no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—1188no—
616C2×C4—1188no—
617C2×C4—1188no—
618C2×C4—1184no—
619C2×C4—1184no—
620C2×C4—1184no—
621C2×C4—1184no—
622C2×C4—2362no—
623C2×C4—2364no—
624C2×C4—2362no—
625C2×C4—2362no—
626C2×C4—2362no—
627C2×C4—2362no—
628C2×C4C22⋊C4×D5911yescharacteristic
629C2×C4C2×(C2×D59)⋊C411yescharacteristic
630C2×C4(C22⋊D59)⋊C411yescharacteristic
631C2×C4(C22⋊D59)⋊C411yescharacteristic
632C2×C4C4×C22⋊D5911yescharacteristic
633C2×C4C4×C22⋊D5911yescharacteristic
634C2×C4#1427369511yescharacteristic
635C2×C4#1427369511yescharacteristic
636C2×C4#1427369611yescharacteristic
637C2×C4#1427369711yescharacteristic
638C2×C4#1427369711yescharacteristic
639C2×C4#1427369811yescharacteristic
640C2×C4#1427369911yescharacteristic
641C2×C4#1427369911yescharacteristic
642C2×C4#1427369911yescharacteristic
643C2×C4#1427369911yescharacteristic
644C2×C4#1427370011yescharacteristic
645C2×C4#1427370011yescharacteristic
646C2×C4#1427370011yescharacteristic
647C2×C4#1427370111yescharacteristic
648C2×C4#1427370111yescharacteristic
649C2×C4#1427370911yescharacteristic
650C2×C4#1427371011yescharacteristic
651C2×C4#1427371111yescharacteristic
652C2×C4#1427371311yescharacteristic
653C2×C4#1427371311yescharacteristic
654C2×C4#1427372311yescharacteristic
655C2×C4#1427372311yescharacteristic
656C8—42no—
657C8—2362no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22#1683725711yescharacteristic
665C22#1683727811yescharacteristic
666C22#1683727811yescharacteristic
667C22#1683731011yescharacteristic
668C22#1683731111yescharacteristic
669C22#1683731711yescharacteristic
670C22#1683731811yescharacteristic
671C22#1683758314yes—
672C4—44no—
673C4—82no—
674C4—1188no—
675C4—4722no—
676C4—2364no—
677C4#1683727911yescharacteristic
678C4#1683728111yescharacteristic
679C4#1683730211yescharacteristic
680C4#1683730211yescharacteristic
681C4#1683731011yescharacteristic
682C4#1683731111yescharacteristic
683C4#1683731711yescharacteristic
684C4#1683731811yescharacteristic
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2#2142233511yescharacteristic
690C2#2142448612yes—
691C2#2142512912yes—
692C2#2142513312yes—
subgroupG/H
centerC23#14273695
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#419C2
socleC23×C59#120
prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenterC2×#419D59
hypocenterC59#10978
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
15. C2×#14273725C4semidirect
382. C59#10978semidirect

Maximal subgroups

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

subgroupindex
C22×#142737252
C2×#168374112
C22×#142736452
#214266802
C2×#168371632
C2×#168371612
C2×C59×#4192
#1097859