Finite Group Databasebeta

← #29683764

Subgroups — #29683764

Order 15616.

1858 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840320C211yesmaximal, characteristic
2C2×#99×D61C214yesmaximal, complemented
3#21448432C211yesmaximal, characteristic, complemented
4#21448171C211yesmaximal, characteristic, complemented
5#21446656C211yesmaximal, characteristic, complemented
6#21446655C211yesmaximal, characteristic, complemented
7#21446654C211yesmaximal, characteristic, complemented
8#21446653C214yesmaximal, complemented
9C61×#1964C211yesmaximal, characteristic, complemented
10C22×D4×D61C2212yes—
11#16840320—22no—
12#16840320—22no—
13#16840320—22no—
14#16840320—22no—
15C2×#14519762C412yescomplemented
16C2×#14519759C412yescomplemented
17C2×#14519751C2211yescharacteristic
18C2×#14519749C2212yes—
19C2×#14519747C412yescomplemented
20C2×#14519745C412yescomplemented
21C22×#11758198C2211yescharacteristic
22C2×C22⋊C4×D61C2212yes—
23C2×C22⋊C4×D61C2212yes—
24C2×#14519692C2214yescomplemented
25C2×#14519691C2214yescomplemented
26C2×#14519691C2214yescomplemented
27#99×D61—216no—
28#16839636—22no—
29#16839633—22no—
30#16839622C2211yescharacteristic, complemented
31#16839620C2212yescomplemented
32C22⋊C4×Dic61C2212yescomplemented
33C4×#11758198—22no—
34C4×C22⋊Dic61C2211yescharacteristic, complemented
35#16839609—22no—
36C2×#121×C61C2211yescharacteristic
37C2×#99×C61C2214yescomplemented
38C61×#380C2211yescharacteristic, complemented
39C4×C22⋊C4×C61C2211yescharacteristic, complemented
40C24×D61C2×C412yes—
41C24×D61C2311yescharacteristic
42C22×D244C2×C412yes—
43C22×D244C2×C411yescharacteristic, complemented
44C22×C22⋊D61C2×C412yes—
45C22×C22⋊D61C2×C412yescomplemented
46C22×C22⋊D61C2312yes—
47C2×D4×D61—28no—
48C2×D4×D61—24no—
49C2×D4×D61—24no—
50C2×D4×D61—28no—
51C23×Dic61C2311yescharacteristic
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61C2×C412yes—
55#14519762—24no—
56#14519762—24no—
57#14519759—24no—
58#14519759—24no—
59#14519751—21no—
60#14519751—21no—
61#14519751—21no—
62#14519751—21no—
63#14519749—24no—
64#14519749—24no—
65#14519747—24no—
66#14519747—24no—
67#14519745—24no—
68#14519745—24no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2×C411yescharacteristic, complemented
71C2×#11758196—22no—
72C2×#11758196C2×C412yescomplemented
73C2×C22⋊Dic61C2×C412yescomplemented
74C2×C22⋊Dic61C2312yes—
75C2×C22⋊Dic61C2312yes—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198C2×C412yes—
79C2×#11758198C2×C412yes—
80C2×#11758198C2×C412yescomplemented
81C2×#11758198C2×C412yescomplemented
82C2×#11758198D412yes—
83C2×#11758198D412yes—
84C2×#11758198D412yes—
85C2×#11758198D412yes—
86C22⋊C4×D61—24no—
87C22⋊C4×D61—28no—
88C22⋊C4×D61D418yescomplemented
89C2×C4×Dic61—21no—
90C2×C4×Dic61—22no—
91#14519692—28no—
92#14519691—28no—
93#14519691—28no—
94#14519684—21no—
95#14519684—21no—
96#14519684—22no—
97#14519684—22no—
98C22×D4×C61C2×C411yescharacteristic, complemented
99C22×D4×C61C2312yes—
100C23×C4×C61C2311yescharacteristic
101#121×C61—21no—
102#121×C61—21no—
103#121×C61—21no—
104#121×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
107C2×C22⋊C4×C61C2×C412yescomplemented
108C2×C22⋊C4×C61C2312yes—
109C2×C22⋊C4×C61C2312yes—
110C2×C42×C61—21no—
111#99×C61—28no—
112#95×C61—21no—
113#95×C61—21no—
114C24×C61C22×C412yes—
115C24×C61C2411yescharacteristic
116C23×D61—24no—
117C23×D61—28no—
118C23×D61—81no—
119C23×D61—81no—
120C23×D61—82no—
121C23×D61—82no—
122C23×D61C22×C412yes—
123C23×D61C22×C412yes—
124C23×D61C2×D412yes—
125C23×D61C2×D412yes—
126C23×D61C2×D414yes—
127C23×D61#4114yes—
128C2×D4×C61—24no—
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61—24no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—81no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—81no—
138C22×C4×C61C22×C412yes—
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C2×C22⋊D61—24no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—24no—
149C2×C22⋊D61—24no—
150C2×C22⋊D61—28no—
151C2×C22⋊D61—24no—
152C2×C22⋊D61—82no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—81no—
156C22×Dic61C22×C412yes—
157C22×Dic61C22×C412yes—
158C22×Dic61C2×D412yes—
159C22×Dic61C2×D412yes—
160D4×D61—48no—
161D4×D61—48no—
162D4×D61—48no—
163D4×D61—48no—
164C2×D244—24no—
165C2×D244—28no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—81no—
169C2×C4×D61—24no—
170C2×C4×D61—28no—
171C2×C4×D61—28no—
172C2×C4×D61—44no—
173C2×C4×D61—82no—
174C2×C4×D61—82no—
175C2×C4×D61—82no—
176C2×C4×D61—82no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—81no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—24no—
184C22⋊C4×C61C2×D414yes—
185C42×C61—81no—
186C22⋊Dic61—22no—
187C22⋊Dic61—24no—
188C22⋊Dic61—24no—
189C22⋊Dic61C2×D414yes—
190#11758198—28no—
191#11758198—22no—
192#11758198—22no—
193#11758198—24no—
194#11758198—44no—
195#11758198C22⋊C414yes—
196#11758198C22⋊C414yes—
197#11758198C22⋊C414yes—
198#11758198C22⋊C414yes—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—81no—
202#11758196—24no—
203#11758196—82no—
204C4×Dic61—82no—
205C4×Dic61—81no—
206C23×C61—22no—
207C23×C61—24no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61C23×C411yescharacteristic
213C23×C61C22×D411yescharacteristic
214C23×C61C22×D411yescharacteristic
215C23×C61C22×D412yes—
216C23×C61C2×#4112yes—
217C22×D61—22no—
218C22×D61—24no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61—48no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61—84no—
229C22×D61—84no—
230C22×D61—84no—
231C22×D61—84no—
232C22×D61—816no—
233C22×D61C2×C22⋊C414yes—
234C22×D61C4×D418yes—
235C22×D61#12114yes—
236C22×D61#12114yes—
237C22×D61#12414yes—
238C22×D61#12714yes—
239D4×C61—44no—
240D4×C61—42no—
241D4×C61—42no—
242D4×C61—81no—
243D4×C61—81no—
244C2×C4×C61—22no—
245C2×C4×C61—24no—
246C2×C4×C61—24no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C22⋊D61—44no—
263C22⋊D61—42no—
264C22⋊D61—42no—
265C22⋊D61—48no—
266C22⋊D61—84no—
267C2×Dic61—22no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—42no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61C2×C22⋊C414yes—
279D244—48no—
280D244—81no—
281D244—81no—
282C4×D61—48no—
283C4×D61—88no—
284C4×D61—88no—
285#21213—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—84no—
298C22×C61C22×C22⋊C411yescharacteristic
299C22×C61C2×C4×D412yes—
300C22×C61C2×#12112yes—
301C22×C61C2×#12411yescharacteristic
302C22×C61C2×#12711yescharacteristic
303C2×D61—24no—
304C2×D61—24no—
305C2×D61—44no—
306C2×D61—44no—
307C2×D61—48no—
308C2×D61—44no—
309C2×D61—44no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—816no—
314C2×D61—84no—
315C2×D61#39018yes—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—44no—
321C4×C61—42no—
322C4×C61—82no—
323Dic61—24no—
324Dic61—44no—
325Dic61—42no—
326Dic61—82no—
327C2×#534—611no—
328C22×#99—614no—
329#2315—611no—
330#2273—611no—
331#1964—614no—
332#1964—611no—
333#1964—611no—
334#1964—611no—
335#1964D6111yescharacteristic, complemented
336C2×C61—22no—
337C2×C61—21no—
338C2×C61—22no—
339C2×C61—21no—
340C2×C61—82no—
341C2×C61C2×#39011yescharacteristic
342C2×C61#288311yescharacteristic
343C2×C61#288311yescharacteristic
344D61—28no—
345D61—82no—
346C23×D4—612no—
347#534—1222no—
348#534—1222no—
349#534—1222no—
350#534—1222no—
351C2×#123—612no—
352C2×#123—612no—
353C2×#121—612no—
354C2×#121—611no—
355C2×#121C2×D6111yescharacteristic
356C2×#120—612no—
357C2×#120—612no—
358C22×C22⋊C4—611no—
359C22×C22⋊C4—612no—
360C22×C22⋊C4—612no—
361C2×#99—614no—
362C2×#99—614no—
363C2×#99—614no—
364C2×#99—12216no—
365C2×#99C2×D6114yescomplemented
366#385—1222no—
367#385—1222no—
368#380—611no—
369#380—612no—
370#380C2×D6111yescharacteristic, complemented
371C4×C22⋊C4—611no—
372C4×C22⋊C4—612no—
373C4×C22⋊C4—1222no—
374C4×C22⋊C4—1222no—
375C4×C22⋊C4C2×D6111yescharacteristic, complemented
376C61#2121311yescharacteristic, complemented, Sylow
377C25—611no—
378C25—612no—
379C22×D4—612no—
380C22×D4—612no—
381C22×D4—612no—
382C22×D4—612no—
383C22×D4—611no—
384C22×D4—1224no—
385C22×D4—1224no—
386C22×D4—1228no—
387C22×D4—1228no—
388C22×D4C4×D6111yescharacteristic, complemented
389C22×D4C22×D6112yes—
390C23×C4—611no—
391C23×C4—612no—
392C23×C4—1222no—
393C23×C4—1222no—
394C23×C4C22×D6111yescharacteristic
395#123—1224no—
396#123—1224no—
397#123—1224no—
398#123—1224no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—1224no—
404#121—1224no—
405#121—1221no—
406#121—1221no—
407#121—1221no—
408#121—1221no—
409#120—1224no—
410#120—1224no—
411#120—1224no—
412#120—1224no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—612no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—1222no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4C4×D6111yescharacteristic, complemented
419C2×C22⋊C4—612no—
420C2×C22⋊C4—612no—
421C2×C22⋊C4—612no—
422C2×C22⋊C4—612no—
423C2×C22⋊C4—612no—
424C2×C22⋊C4—612no—
425C2×C22⋊C4—612no—
426C2×C22⋊C4—618no—
427C2×C22⋊C4—612no—
428C2×C22⋊C4—612no—
429C2×C22⋊C4—612no—
430C2×C22⋊C4—612no—
431C2×C22⋊C4—1224no—
432C2×C22⋊C4—1228no—
433C2×C22⋊C4—1222no—
434C2×C22⋊C4—1222no—
435C2×C22⋊C4C4×D6112yescomplemented
436C2×C22⋊C4C22×D6112yes—
437C2×C22⋊C4C22×D6112yes—
438C2×C42—21no—
439C2×C42—1222no—
440C2×C42—1221no—
441#99—28no—
442#99—1228no—
443#99—1228no—
444#99—1228no—
445#95—21no—
446#95—21no—
447#95—1222no—
448#95—1222no—
449#95—1221no—
450#95—1221no—
451C24—614no—
452C24—614no—
453C24—612no—
454C24—612no—
455C24—612no—
456C24—612no—
457C24—1224no—
458C24—1228no—
459C24—4882no—
460C24—4882no—
461C24—4881no—
462C24—4881no—
463C24C2×C4×D6112yes—
464C24C23×D6111yescharacteristic
465C2×D4—24no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—81no—
472C2×D4—1224no—
473C2×D4—1228no—
474C2×D4—1224no—
475C2×D4—1224no—
476C2×D4—1228no—
477C2×D4—1224no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1224no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—4881no—
484C2×D4—4882no—
485C2×D4—2448no—
486C2×D4—2448no—
487C2×D4—2448no—
488C2×D4—2448no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—81no—
492C22×C4—612no—
493C22×C4—612no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—1228no—
497C22×C4—1224no—
498C22×C4—1228no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—4882no—
502C22×C4—4882no—
503C22×C4—4882no—
504C22×C4—4882no—
505C22×C4—4881no—
506C22×C4—2444no—
507C22×C4C2×C4×D6112yes—
508C22×C4C2×C4×D6111yescharacteristic
509C22×C4C2×C4×D6111yescharacteristic
510C22×C4D4×D6111yescharacteristic
511C22×C4D4×D6111yescharacteristic
512C22×C4D4×D6111yescharacteristic
513C22×C4D4×D6111yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—81no—
517C4⋊C4—1224no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—4882no—
521C4⋊C4—4881no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—24no—
526C22⋊C4—614no—
527C22⋊C4—614no—
528C22⋊C4—614no—
529C22⋊C4—614no—
530C22⋊C4—614no—
531C22⋊C4—1224no—
532C22⋊C4—1228no—
533C22⋊C4—1224no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1224no—
538C22⋊C4—2444no—
539C22⋊C4D4×D6114yes—
540C42—81no—
541C42—4881no—
542C42—4882no—
543C23—22no—
544C23—24no—
545C23—41no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—614no—
550C23—618no—
551C23—614no—
552C23—614no—
553C23—614no—
554C23—614no—
555C23—1224no—
556C23—1222no—
557C23—4884no—
558C23—4884no—
559C23—4884no—
560C23—4884no—
561C23—48816no—
562C23—2442no—
563C23—2442no—
564C23—2442no—
565C23—2442no—
566C23—2442no—
567C23—2442no—
568C23—2442no—
569C23—2442no—
570C23—2448no—
571C23C22×C4×D6111yescharacteristic
572C23C2×D4×D6111yescharacteristic
573C23C2×D4×D6111yescharacteristic
574C23C2×D4×D6112yes—
575C23#41×D6112yes—
576D4—44no—
577D4—42no—
578D4—42no—
579D4—81no—
580D4—81no—
581D4—4881no—
582D4—4881no—
583D4—4884no—
584D4—2448no—
585D4—2448no—
586D4—2444no—
587D4—2442no—
588D4—2442no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—614no—
604C2×C4—1222no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—4888no—
608C2×C4—4888no—
609C2×C4—2448no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4C22⋊C4×D6111yescharacteristic
619C2×C4C22⋊C4×D6111yescharacteristic
620C2×C4C22⋊C4×D6111yescharacteristic
621C2×C4C22⋊C4×D6111yescharacteristic
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—84no—
634C22—618no—
635C22—1224no—
636C22—1224no—
637C22—4884no—
638C22—48816no—
639C22—2444no—
640C22—2444no—
641C22—2448no—
642C22—2444no—
643C22—2444no—
644C22—2442no—
645C22—2442no—
646C22—2442no—
647C22C2×C22⋊C4×D6111yescharacteristic
648C22C4×D4×D6112yes—
649C22#121×D6112yes—
650C22#124×D6111yescharacteristic
651C22#127×D6111yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—44no—
657C4—42no—
658C4—82no—
659C4—1224no—
660C4—4882no—
661C4—2444no—
662C4—2442no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—21no—
667C2—82no—
668C2—1228no—
669C2—4882no—
670C2#390×D6111yescharacteristic
671C2#2145427711yescharacteristic
672C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1964C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840320C2
cosocleC24×C61C24
hypercenter#1964D61
hypocenterC61#21213
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. C2×#99×D61C2semidirect
3. #21448432C2semidirect
4. #21448171C2semidirect
5. #21446656C2semidirect
6. #21446655C2semidirect
7. #21446654C2semidirect
8. #21446653C2semidirect
9. C61×#1964C2semidirect
15. C2×#14519762C4semidirect
16. C2×#14519759C4semidirect
19. C2×#14519747C4semidirect
20. C2×#14519745C4semidirect
24. C2×#14519692C22semidirect
25. C2×#14519691C22semidirect
26. C2×#14519691C22semidirect
30. #16839622C22semidirect
31. #16839620C22semidirect
32. C22⋊C4×Dic61C22semidirect
34. C4×C22⋊Dic61C22semidirect
37. C2×#99×C61C22semidirect
38. C61×#380C22semidirect
39. C4×C22⋊C4×C61C22semidirect
43. C22×D244C2×C4semidirect
45. C22×C22⋊D61C2×C4semidirect
70. C2×C4⋊Dic61C2×C4semidirect
72. C2×#11758196C2×C4semidirect
73. C2×C22⋊Dic61C2×C4semidirect
80. C2×#11758198C2×C4semidirect
81. C2×#11758198C2×C4semidirect
88. C22⋊C4×D61D4semidirect
98. C22×D4×C61C2×C4semidirect
106. C2×C4⋊C4×C61C2×C4semidirect
107. C2×C22⋊C4×C61C2×C4semidirect
335. #1964D61semidirect
365. C2×#99C2×D61semidirect
370. #380C2×D61semidirect
375. C4×C22⋊C4C2×D61semidirect
376. C61#21213semidirect
388. C22×D4C4×D61semidirect
418. C2×C4⋊C4C4×D61semidirect
435. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403202
C2×#99×D612
#214484322
#214481712
#214466562
#214466552
#214466542
#214466532
C61×#19642
#2121361