Finite Group Databasebeta

← #28495014

Subgroups — #28495014

Order 15104.

1066 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837365C211yesmaximal, characteristic
2C2×#16837365C211yesmaximal, characteristic
3#21432514C211yesmaximal, characteristic, complemented
4#21426475C211yesmaximal, characteristic
5C2×#16837172C211yesmaximal, characteristic, complemented
6#21423834C211yesmaximal, characteristic, complemented
7C2×C59×#344C211yesmaximal, characteristic, complemented
8C23×C4×D59C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C22×#11745664C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837365—22no—
13#16837365—22no—
14#16837365C414yescomplemented
15#16837365C414yescomplemented
16C2×(C2×D59)⋊C8—22no—
17C2×(C2×D59)⋊C8—22no—
18#16837360—22no—
19#16837357—22no—
20M16×Dic59—22no—
21#16837263C412yes—
22#16837259—22no—
23#16837257C412yes—
24C4×(C2×D59)⋊C4—22no—
25#16837172—22no—
26#16837170—22no—
27C22×M16×C59C2211yescharacteristic
28C22×M16×C59C2211yescharacteristic
29C2×#117×C59C2211yescharacteristic
30C59×#344—22no—
31C24×D59C2×C411yescharacteristic
32C23×Dic59C2×C411yescharacteristic
33C22×C4×D59—21no—
34C22×C4×D59—21no—
35C22×C4×D59—21no—
36C22×C4×D59—21no—
37C22×C4×D59—21no—
38C22×C4×D59—21no—
39C22×C4×D59—21no—
40C22×C4×D59—21no—
41C22×C4×D59—21no—
42C22×C4×D59—21no—
43C22×C4×D59—21no—
44C22×C4×D59—21no—
45C22×C4×D59C2×C412yes—
46C22×C4×D59C2×C412yes—
47C2×#11745664—21no—
48C2×#11745664—21no—
49C2×#11745664—21no—
50C2×#11745664—21no—
51C2×#11745664—21no—
52C2×#11745664—21no—
53C2×#11745664—21no—
54C2×#11745664—21no—
55C2×#11745664—21no—
56C2×#11745664C2×C412yes—
57C2×#11745664C2×C412yes—
58C2×#11745664D412yes—
59C22×C59⋊C8—21no—
60C22×C59⋊C8D412yes—
61#14273686—21no—
62#14273686—21no—
63#14273686—21no—
64#14273686—21no—
65C2×C4⋊Dic59D412yes—
66C2×C22⋊Dic59C2×C412yes—
67C2×(C2×D59)⋊C4—24no—
68C2×C4×Dic59D412yes—
69(C2×D59)⋊C8—28no—
70(C2×D59)⋊C8—28no—
71#14273637—24no—
72C8×Dic59—24no—
73C59⋊#95—24no—
74C23×C4×C59C2311yescharacteristic
75C2×M16×C59—21no—
76C2×M16×C59—21no—
77C2×M16×C59—21no—
78C2×M16×C59—21no—
79C2×M16×C59—21no—
80C2×M16×C59—21no—
81C2×M16×C59—21no—
82C2×M16×C59—21no—
83C2×M16×C59—21no—
84C2×M16×C59C2×C412yes—
85C2×M16×C59C2×C412yes—
86C2×M16×C59D412yes—
87C22×C8×C59—21no—
88C22×C8×C59D412yes—
89#117×C59—21no—
90#117×C59—21no—
91#117×C59—21no—
92#117×C59—21no—
93C2×C4⋊C4×C59—21no—
94C2×C22⋊C4×C59C2×C412yes—
95C2×C42×C59—21no—
96C24×C59C22×C411yescharacteristic
97C23×D59—21no—
98C23×D59—21no—
99C23×D59—21no—
100C23×D59—21no—
101C23×D59—21no—
102C23×D59—21no—
103C23×D59—44no—
104C23×D59C4212yes—
105C22×C4×C59—22no—
106C22×C4×C59C22×C411yescharacteristic
107C22×C4×C59C22×C411yescharacteristic
108C22×C4×C59C2×D411yescharacteristic
109C22×C4×C59C2×D411yescharacteristic
110C22×C4×C59C2×D411yescharacteristic
111C22×C4×C59C2×D411yescharacteristic
112C22×C4×C59C2×D411yescharacteristic
113C22×C4×C59C2×D411yescharacteristic
114C22×C4×C59#4111yescharacteristic
115C22×C4×C59#4111yescharacteristic
116C22×C4×C59#4111yescharacteristic
117C22×C4×C59#4111yescharacteristic
118C22×C4×C59#4111yescharacteristic
119C22×C4×C59#4111yescharacteristic
120C22×Dic59—21no—
121C22×Dic59—21no—
122C22×Dic59—21no—
123C22×Dic59—21no—
124C22×Dic59—21no—
125C22×Dic59—21no—
126C22×Dic59C4212yes—
127C22×Dic59C22⋊C414yes—
128C2×C4×D59—22no—
129C2×C4×D59—22no—
130C2×C4×D59—22no—
131C2×C4×D59—22no—
132C2×C4×D59—22no—
133C2×C4×D59—22no—
134C2×C4×D59—22no—
135C2×C4×D59—22no—
136C2×C4×D59—22no—
137C2×C4×D59—22no—
138C2×C4×D59—22no—
139C2×C4×D59—22no—
140C2×C4×D59—41no—
141C2×C4×D59—41no—
142C2×C4×D59—41no—
143C2×C4×D59—41no—
144C2×C4×D59—41no—
145C2×C4×D59—41no—
146C2×C4×D59—41no—
147C2×C4×D59—41no—
148C2×C4×D59—41no—
149C2×C4×D59—41no—
150C2×C4×D59—41no—
151C2×C4×D59—41no—
152C2×C4×D59—41no—
153C2×C4×D59—41no—
154C2×C4×D59—41no—
155C2×C4×D59—41no—
156M16×C59—22no—
157M16×C59—22no—
158M16×C59—22no—
159M16×C59—22no—
160M16×C59—22no—
161M16×C59—22no—
162M16×C59—41no—
163M16×C59—41no—
164C2×C8×C59—22no—
165C2×C8×C59—22no—
166C2×C8×C59—22no—
167C2×C8×C59—41no—
168C2×C8×C59—41no—
169C2×C8×C59C22⋊C414yescomplemented
170C4⋊C4×C59—41no—
171C4⋊C4×C59—41no—
172C22⋊C4×C59—22no—
173C22⋊C4×C59—22no—
174C42×C59—41no—
175C42×C59—41no—
176C22⋊Dic59—22no—
177C22⋊Dic59—22no—
178(C2×D59)⋊C4—48no—
179C4⋊Dic59—22no—
180C4⋊Dic59—22no—
181C4×Dic59—22no—
182C4×Dic59—22no—
183#11745664—22no—
184#11745664—22no—
185#11745664—22no—
186#11745664—22no—
187#11745664—22no—
188#11745664—22no—
189#11745664—41no—
190#11745664—41no—
191C2×C59⋊C8—22no—
192C2×C59⋊C8—22no—
193C2×C59⋊C8—22no—
194C2×C59⋊C8—41no—
195C2×C59⋊C8—41no—
196C2×C59⋊C8C22⋊C414yescomplemented
197C23×C59—42no—
198C23×C59C2×C4211yescharacteristic
199C23×C59C2×C22⋊C411yescharacteristic
200C23×C59#11711yescharacteristic
201C23×C59C4×D411yescharacteristic
202C23×C59C4×D411yescharacteristic
203C23×C59C4×D411yescharacteristic
204C23×C59C4×D411yescharacteristic
205C22×D59—24no—
206C22×D59—24no—
207C22×D59—24no—
208C22×D59—22no—
209C22×D59—22no—
210C22×D59—22no—
211C22×D59—44no—
212C22×D59—44no—
213C22×D59—44no—
214C22×D59—44no—
215C22×D59—42no—
216C22×D59—42no—
217C22×D59—42no—
218C22×D59—41no—
219C22×D59—41no—
220C22×D59—41no—
221C22×D59—41no—
222C2×C4×C59—44no—
223C2×C4×C59—42no—
224C2×C4×C59C2×C22⋊C411yescharacteristic
225C2×C4×C59C2×C22⋊C411yescharacteristic
226C2×C4×C59#11711yescharacteristic
227C2×C4×C59#11711yescharacteristic
228C2×C4×C59C4×D411yescharacteristic
229C2×C4×C59C4×D411yescharacteristic
230C2×C4×C59C4×D411yescharacteristic
231C2×C4×C59C4×D411yescharacteristic
232C2×C4×C59C4×D411yescharacteristic
233C2×C4×C59C4×D411yescharacteristic
234C2×C4×C59C4×D411yescharacteristic
235C2×C4×C59C4×D411yescharacteristic
236C2×C4×C59#12011yescharacteristic
237C2×C4×C59#12111yescharacteristic
238C2×C4×C59#12111yescharacteristic
239C2×C4×C59#12111yescharacteristic
240C2×C4×C59#12111yescharacteristic
241C2×C4×C59#12111yescharacteristic
242C2×C4×C59#12111yescharacteristic
243C2×C4×C59#12311yescharacteristic
244C2×C4×C59#12311yescharacteristic
245C2×C4×C59#12311yescharacteristic
246C2×C4×C59#12411yescharacteristic
247C2×C4×C59#12411yescharacteristic
248C2×C4×C59#12411yescharacteristic
249C2×C4×C59#12611yescharacteristic
250C2×C4×C59#12611yescharacteristic
251C2×C4×C59#12711yescharacteristic
252C2×Dic59—22no—
253C2×Dic59—22no—
254C2×Dic59—22no—
255C2×Dic59—24no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260C2×Dic59—44no—
261C4×D59—42no—
262C4×D59—42no—
263C4×D59—42no—
264C4×D59—42no—
265C4×D59—42no—
266C4×D59—42no—
267C4×D59—42no—
268C4×D59—42no—
269C8×C59—24no—
270C8×C59—42no—
271C59⋊C8—24no—
272C59⋊C8—42no—
273#10937—591nomaximal, Sylow
274C22×C59—22no—
275C22×C59—22no—
276C22×C59—22no—
277C22×C59—41no—
278C22×C59—41no—
279C22×C59—41no—
280C22×C59—41no—
281C22×C59C4×C22⋊C411yescharacteristic
282C22×C59C4×C22⋊C411yescharacteristic
283C22×C59C4×C22⋊C411yescharacteristic
284C22×C59#38611yescharacteristic
285C22×C59#38811yescharacteristic
286C22×C59#38811yescharacteristic
287C22×C59#39011yescharacteristic
288C2×D59—24no—
289C2×D59—24no—
290C2×D59—24no—
291C2×D59—44no—
292C2×D59—42no—
293C2×D59—42no—
294C2×D59—42no—
295C2×D59—44no—
296C2×D59—44no—
297C2×D59—44no—
298C2×D59—42no—
299C4×C59—82no—
300C4×C59#38611yescharacteristic
301C4×C59#38611yescharacteristic
302C4×C59#38811yescharacteristic
303C4×C59#38811yescharacteristic
304C4×C59#38811yescharacteristic
305C4×C59#38811yescharacteristic
306C4×C59#39011yescharacteristic
307C4×C59#39011yescharacteristic
308Dic59—44no—
309Dic59—42no—
310C2×#407—591no—
311C2×#407—591no—
312#2873—591no—
313#2280—591no—
314C2×#344—591no—
315C2×#344D5911yescharacteristic, complemented
316#1742—591no—
317C2×C59—21no—
318C2×C59—21no—
319C2×C59—21no—
320C2×C59—21no—
321C2×C59—21no—
322C2×C59—21no—
323C2×C59#143711yescharacteristic
324C2×C59#189112yes—
325D59—44no—
326C24×C4—591no—
327C22×M16—591no—
328C22×M16—591no—
329C22×M16C2×D5911yescharacteristic
330C22×M16C2×D5911yescharacteristic
331C2×#117—591no—
332C2×#117C2×D5911yescharacteristic
333#407—594no—
334#407—594no—
335#407—1182no—
336#407—1182no—
337C2×C22⋊C8—1182no—
338C2×C22⋊C8—1182no—
339#405—1182no—
340#405—1182no—
341C4×M16—1182no—
342#381—592no—
343#380—1182no—
344#379—592no—
345C4×C22⋊C4—1182no—
346#344—22no—
347#344—1182no—
348#343—1182no—
349C59#1093711yescharacteristic, complemented, Sylow
350C25—591no—
351C23×C4—591no—
352C23×C4—592no—
353C23×C4—592no—
354C23×C4—1181no—
355C23×C4—1181no—
356C23×C4—1181no—
357C23×C4—1181no—
358C23×C4—1181no—
359C23×C4—1181no—
360C23×C4—1181no—
361C23×C4—1181no—
362C23×C4—1181no—
363C23×C4—1181no—
364C23×C4—1181no—
365C23×C4—1181no—
366C23×C4C22×D5911yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—592no—
377C2×M16—592no—
378C2×M16—592no—
379C2×M16—1181no—
380C2×M16—1181no—
381C2×M16—1181no—
382C2×M16—1181no—
383C2×M16—1181no—
384C2×M16—1181no—
385C2×M16—1181no—
386C2×M16—1181no—
387C2×M16—1181no—
388C2×M16C4×D5912yes—
389C2×M16C4×D5912yes—
390C2×M16C22⋊D5912yes—
391C22×C8—21no—
392C22×C8—592no—
393C22×C8—1181no—
394C22×C8D23612yes—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—1181no—
400#117—1181no—
401#117—1181no—
402#117—1181no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—592no—
405C2×C22⋊C4—592no—
406C2×C22⋊C4—1184no—
407C2×C22⋊C4C4×D5912yes—
408C2×C42—21no—
409C2×C42—592no—
410C22⋊C8—1188no—
411C22⋊C8—1188no—
412#97—1184no—
413C4×C8—1184no—
414#95—1184no—
415C24—592no—
416C24—1181no—
417C24—1181no—
418C24—1181no—
419C24—1181no—
420C24—1181no—
421C24—1181no—
422C24—2364no—
423C24C2×C4×D5911yescharacteristic
424C22×C4—22no—
425C22×C4—592no—
426C22×C4—594no—
427C22×C4—1181no—
428C22×C4—1181no—
429C22×C4—1181no—
430C22×C4—1181no—
431C22×C4—1181no—
432C22×C4—1181no—
433C22×C4—1182no—
434C22×C4—1182no—
435C22×C4—1182no—
436C22×C4—1182no—
437C22×C4—1182no—
438C22×C4—1182no—
439C22×C4—1182no—
440C22×C4—1182no—
441C22×C4—1182no—
442C22×C4—1182no—
443C22×C4—1182no—
444C22×C4—1182no—
445C22×C4—2361no—
446C22×C4—2361no—
447C22×C4—2361no—
448C22×C4—2361no—
449C22×C4—2361no—
450C22×C4—2361no—
451C22×C4—2361no—
452C22×C4—2361no—
453C22×C4—2361no—
454C22×C4—2361no—
455C22×C4—2361no—
456C22×C4—2361no—
457C22×C4—2361no—
458C22×C4—2361no—
459C22×C4—2361no—
460C22×C4—2361no—
461C22×C4C2×C4×D5911yescharacteristic
462C22×C4C2×C4×D5911yescharacteristic
463C22×C4C2×D23611yescharacteristic
464C22×C4#1174568511yescharacteristic
465C22×C4#1174568511yescharacteristic
466C22×C4D4×D5911yescharacteristic
467C22×C4D4×D5911yescharacteristic
468C22×C4D4×D5911yescharacteristic
469C22×C4D4×D5911yescharacteristic
470C22×C4#1174568711yescharacteristic
471C22×C4#1174568711yescharacteristic
472C22×C4#1174568911yescharacteristic
473C22×C4#1174568911yescharacteristic
474C22×C4C2×C22⋊D5911yescharacteristic
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—1182no—
484M16—1182no—
485M16—1182no—
486M16—1182no—
487M16—1182no—
488M16—1182no—
489M16—2361no—
490M16—2361no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—594no—
497C2×C8—1182no—
498C2×C8—1182no—
499C2×C8—1182no—
500C2×C8—2361no—
501C2×C8—2361no—
502C2×C8(C2×D59)⋊C414yescomplemented
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—1182no—
506C4⋊C4—1182no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—1182no—
510C22⋊C4—1182no—
511C22⋊C4—2368no—
512C42—41no—
513C42—41no—
514C42—1182no—
515C42—1182no—
516C23—42no—
517C23—1184no—
518C23—1184no—
519C23—1184no—
520C23—1182no—
521C23—1182no—
522C23—1182no—
523C23—2362no—
524C23—2362no—
525C23—2362no—
526C23—2364no—
527C23—2364no—
528C23—2364no—
529C23—2364no—
530C23—2361no—
531C23—2361no—
532C23—2361no—
533C23—2361no—
534C23C42×D5911yescharacteristic
535C23C22⋊C4×D5911yescharacteristic
536C23#1427368511yescharacteristic
537C23(C22⋊D59)⋊C411yescharacteristic
538C23C4×C22⋊D5911yescharacteristic
539C23#1427368911yescharacteristic
540C23C4×D23611yescharacteristic
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—1182no—
544C2×C4—1182no—
545C2×C4—1182no—
546C2×C4—1184no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4—2361no—
551C2×C4—2362no—
552C2×C4—2362no—
553C2×C4—2362no—
554C2×C4—2362no—
555C2×C4—2362no—
556C2×C4—2362no—
557C2×C4—2362no—
558C2×C4—2362no—
559C2×C4—2364no—
560C2×C4C22⋊C4×D5911yescharacteristic
561C2×C4C2×(C2×D59)⋊C411yescharacteristic
562C2×C4#1427368411yescharacteristic
563C2×C4#1427368511yescharacteristic
564C2×C4(C22⋊D59)⋊C411yescharacteristic
565C2×C4(C22⋊D59)⋊C411yescharacteristic
566C2×C4(C22⋊D59)⋊C411yescharacteristic
567C2×C4C4×C22⋊D5911yescharacteristic
568C2×C4#1427368911yescharacteristic
569C2×C4#1427368911yescharacteristic
570C2×C4#1427368911yescharacteristic
571C2×C4C4×D23611yescharacteristic
572C2×C4#1427369711yescharacteristic
573C2×C4#1427369911yescharacteristic
574C2×C4#1427369911yescharacteristic
575C2×C4#1427370011yescharacteristic
576C2×C4#1427370011yescharacteristic
577C2×C4#1427370211yescharacteristic
578C2×C4#1427370211yescharacteristic
579C2×C4#1427371111yescharacteristic
580C2×C4#1427371211yescharacteristic
581C2×C4#1427371211yescharacteristic
582C2×C4#1427371311yescharacteristic
583C2×C4#1427371311yescharacteristic
584C2×C4#1427371611yescharacteristic
585C2×C4#1427372211yescharacteristic
586C2×C4#1427372211yescharacteristic
587C2×C4#1427372311yescharacteristic
588C8—24no—
589C8—42no—
590C8—1184no—
591C8—2362no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—1184no—
600C22—1184no—
601C22—1184no—
602C22—2364no—
603C22—2362no—
604C22—2362no—
605C22—2362no—
606C22—2364no—
607C22—2364no—
608C22—2364no—
609C22—2362no—
610C22#1683724911yescharacteristic
611C22#1683724911yescharacteristic
612C22C4×(C2×D59)⋊C411yescharacteristic
613C22#1683728011yescharacteristic
614C22#1683729211yescharacteristic
615C22#1683729411yescharacteristic
616C22#1683730211yescharacteristic
617C4—82no—
618C4—2364no—
619C4—2362no—
620C4#1683727911yescharacteristic
621C4#1683728011yescharacteristic
622C4#1683729111yescharacteristic
623C4#1683729111yescharacteristic
624C4#1683729211yescharacteristic
625C4#1683729411yescharacteristic
626C4#1683730211yescharacteristic
627C4#1683730311yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—2364no—
635C2#2142233211yescharacteristic
636C2#2142451312yes—
subgroupG/H
centerC2×C4#14273697
commutatorC23×C59C2×C42
FrattiniC23×C4C22×D59
FittingC2×C59×#344C2
socleC22×C59#386
prime radicalC24×D59C2×C4
cosocleC23×C4×C59C23
hypercenterC2×#344D59
hypocenterC59#10937
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
3. #21432514C2semidirect
5. C2×#16837172C2semidirect
6. #21423834C2semidirect
7. C2×C59×#344C2semidirect
14. #16837365C4semidirect
15. #16837365C4semidirect
169. C2×C8×C59C22⋊C4semidirect
196. C2×C59⋊C8C22⋊C4semidirect
315. C2×#344D59semidirect
349. C59#10937semidirect
502. C2×C8(C2×D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168373652
#214325142
#214264752
C2×#168371722
#214238342
C2×C59×#3442
#1093759