Finite Group Databasebeta

← #30615539

Subgroups — #30615539

Order 15616.

1714 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840829C211yesmaximal, characteristic
2#21462298C212yesmaximal, complemented
3#21462291C211yesmaximal, characteristic
4#21461790C218yesmaximal, complemented
5C2×#16840639C212yesmaximal, complemented
6C2×#99×D61C211yesmaximal, characteristic
7#16840829—24no—
8#16840829—22no—
9#16840829C2214yes—
10C2×D4×#6923—24no—
11C2×#14519856—21no—
12C22×C22⋊#6923—21no—
13C22×C22⋊#6923C2211yescharacteristic
14C22×C22⋊#6923C2211yescharacteristic
15C22×C22⋊#6923C2212yes—
16#16840710—22no—
17#16840710C2214yes—
18#16840709—24no—
19#16840709C2218yescomplemented
20#16840705—21no—
21#16840704—24no—
22#16840703—21no—
23#16840639C2218yescomplemented
24C22×D4×D61C2211yescharacteristic
25C2×C22⋊C4×D61C2212yes—
26C2×#14519692C411yescharacteristic, complemented
27C2×#14519691C412yescomplemented
28#99×D61C414yescomplemented
29#99×D61C2214yes—
30C2×#99×C61C411yescharacteristic, complemented
31C23×#6923—22no—
32C23×#6923—21no—
33C23×#6923D414yes—
34C23×#6923C2312yes—
35D4×#6923—216no—
36D4×#6923—216no—
37#14519856—24no—
38#14519856—24no—
39C2×C4⋊#6923—22no—
40C2×C4⋊#6923—28no—
41C2×C22⋊#6923—22no—
42C2×C22⋊#6923—24no—
43C2×C22⋊#6923—22no—
44C2×C22⋊#6923—24no—
45C2×C22⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C22⋊#6923—22no—
48C2×C22⋊#6923—22no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C22⋊#6923—21no—
52C2×C22⋊#6923—21no—
53C2×C22⋊#6923—22no—
54C2×C22⋊#6923—21no—
55C2×C22⋊#6923—24no—
56C2×C22⋊#6923D414yes—
57C2×C22⋊#6923C2312yes—
58C2×C22⋊#6923C2314yes—
59C2×C4×#6923—22no—
60(C2×#6923)⋊C4—28no—
61(C2×#6923)⋊C4—24no—
62C24×D61D411yescharacteristic
63C24×D61C2311yescharacteristic
64C22×D244Q811yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61Q811yescharacteristic
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61C2×C412yes—
72C2×D4×D61D412yes—
73C2×D4×D61Q812yes—
74C2×D4×D61C2312yes—
75C22×C4×D61—22no—
76C22×C4×D61D411yescharacteristic
77C2×C22⋊Dic61C2×C412yescomplemented
78C2×#11758198—22no—
79C22⋊C4×D61—22no—
80C22⋊C4×D61—22no—
81C22⋊C4×D61C2×C414yescomplemented
82C22⋊C4×D61C2314yes—
83#14519692C2×C414yescomplemented
84#14519691C2×C418yescomplemented
85C22×D4×C61C2×C411yescharacteristic
86C2×C22⋊C4×C61C2×C412yescomplemented
87#99×C61C2×C414yescomplemented
88C24×C61C4⋊C411yescharacteristic, complemented
89C24×C61C22×C411yescharacteristic
90C23×D61—21no—
91C23×D61—21no—
92C23×D61—21no—
93C23×D61—21no—
94C23×D61—82no—
95C23×D61—82no—
96C23×D61C4⋊C412yescomplemented
97C23×D61C4⋊C411yescharacteristic, complemented
98C23×D61C22×C411yescharacteristic
99C23×D61C2×D412yes—
100C23×D61C2×D411yescharacteristic
101C23×D61C2×D411yescharacteristic
102C23×D61C2×D412yes—
103C23×D61C2×D412yes—
104C23×D61C2×Q811yescharacteristic
105C23×D61C2×Q811yescharacteristic
106C23×D61#4112yes—
107C23×D61#4112yes—
108C23×D61C2411yescharacteristic
109C22×#6923—24no—
110C22×#6923—28no—
111C22×#6923—24no—
112C22×#6923—22no—
113C22×#6923—22no—
114C22×#6923—24no—
115C22×#6923—42no—
116C22×#6923—82no—
117C22×#6923—84no—
118C22×#6923—84no—
119C22×#6923—82no—
120C22×#6923C2×D418yes—
121C2×D4×C61—22no—
122C2×D4×C61—22no—
123C2×D4×C61C4⋊C412yescomplemented
124C2×D4×C61C22×C412yes—
125C22×C4×C61—22no—
126C22×C4×C61C4⋊C411yescharacteristic, complemented
127C2×C22⋊D61—22no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61C4⋊C412yescomplemented
132C2×C22⋊D61C4⋊C412yescomplemented
133C2×C22⋊D61C22×C412yes—
134C2×C22⋊D61C2×Q812yes—
135C22×Dic61—22no—
136C22×Dic61C4⋊C411yescharacteristic, complemented
137D4×D61—24no—
138D4×D61—24no—
139D4×D61—24no—
140D4×D61—24no—
141D4×D61—24no—
142D4×D61—24no—
143D4×D61—24no—
144D4×D61—24no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244C4⋊C412yescomplemented
148C2×D244C2×Q812yes—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—84no—
156C2×C4×D61C4⋊C412yescomplemented
157C2×C4×D61C2×D412yes—
158C22⋊#6923—28no—
159C22⋊#6923—24no—
160C22⋊#6923—24no—
161C22⋊#6923—24no—
162C22⋊#6923—24no—
163C22⋊#6923—24no—
164C22⋊#6923—41no—
165C22⋊#6923—42no—
166C22⋊#6923—41no—
167C22⋊#6923—41no—
168C22⋊#6923—41no—
169C22⋊#6923—84no—
170C4⋊#6923—28no—
171C4⋊#6923—88no—
172C4×#6923—28no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61C22×C414yescomplemented
175C22⋊Dic61—22no—
176C22⋊Dic61C22×C414yescomplemented
177#11758198—24no—
178#11758198—24no—
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—81no—
182C23×C61—81no—
183C23×C61C2×C4⋊C412yes—
184C23×C61C2×C4⋊C411yescharacteristic
185C23×C61C2×C4⋊C411yescharacteristic
186C23×C61C4×D412yes—
187C23×C61C4×D412yes—
188C23×C61C23×C411yescharacteristic
189C22×D61—21no—
190C22×D61—21no—
191C22×D61—22no—
192C22×D61—22no—
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—44no—
196C22×D61—44no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—44no—
201C22×D61—44no—
202C22×D61—82no—
203C22×D61—81no—
204C22×D61—81no—
205C22×D61—81no—
206C22×D61—82no—
207C22×D61—82no—
208C22×D61—82no—
209C22×D61—81no—
210C22×D61—82no—
211C22×D61—82no—
212C22×D61C2×C4⋊C412yes—
213C22×D61C2×C4⋊C411yescharacteristic
214C22×D61C2×C4⋊C411yescharacteristic
215C22×D61C4×D412yes—
216C22×D61C4×D412yes—
217C22×D61#12011yescharacteristic
218C22×D61#12012yes—
219C22×D61#12011yescharacteristic
220C22×D61C22⋊Q812yes—
221C22×D61C22⋊Q812yes—
222C22×D61C22⋊Q812yes—
223C22×D61C22⋊Q812yes—
224C22×D61#12311yescharacteristic
225C22×D61#12311yescharacteristic
226C22×D61#12312yes—
227C22×D61C22×D412yes—
228C22×D61C22×D411yescharacteristic
229C22×D61C22×Q811yescharacteristic
230C22×D61C2×#4112yes—
231C2×#6923—28no—
232C2×#6923—48no—
233C2×#6923—48no—
234C2×#6923—48no—
235C2×#6923—44no—
236C2×#6923—44no—
237C2×#6923—42no—
238C2×#6923—42no—
239C2×#6923—84no—
240C2×#6923—88no—
241C2×#6923—84no—
242D4×C61—24no—
243D4×C61—24no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—24no—
247C2×C4×C61—82no—
248C2×C4×C61C2×C4⋊C412yes—
249C22⋊D61—24no—
250C22⋊D61—24no—
251C22⋊D61—24no—
252C22⋊D61—24no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—24no—
256C2×Dic61—82no—
257C2×Dic61C2×C4⋊C412yes—
258D244—24no—
259D244—24no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—48no—
265C4×D61—84no—
266#20889—611nomaximal, Sylow
267C22×C61—22no—
268C22×C61—42no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—42no—
272C22×C61—41no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—81no—
276C22×C61#38511yescharacteristic
277C22×C61#38511yescharacteristic
278C22×C61#38512yes—
279C22×C61C22×C4⋊C411yescharacteristic
280C22×C61C2×C4×D412yes—
281C2×D61—24no—
282C2×D61—22no—
283C2×D61—22no—
284C2×D61—24no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—41no—
299C2×D61—42no—
300C2×D61—44no—
301C2×D61—42no—
302C2×D61—44no—
303C2×D61—42no—
304C2×D61—82no—
305C2×D61—82no—
306C2×D61—81no—
307C2×D61#38511yescharacteristic
308C2×D61#38511yescharacteristic
309C2×D61#38512yes—
310C2×D61C2×#12011yescharacteristic
311C2×D61C2×C22⋊Q812yes—
312C2×D61C2×#12311yescharacteristic
313#6923—48no—
314#6923—82no—
315#6923—82no—
316C4×C61—22no—
317C4×C61—44no—
318Dic61—22no—
319Dic61—44no—
320C2×#518—611no—
321C22×#99—611no—
322#2315—612no—
323#2308—611no—
324#1867—618no—
325C2×#342—612no—
326C2×C61—22no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—21no—
330C2×C61—22no—
331C2×C61—42no—
332C2×C61C2×#38511yescharacteristic
333D61—21no—
334D61—21no—
335D61—21no—
336D61—22no—
337D61—22no—
338D61—42no—
339D61#302612yes—
340C23×D4—611no—
341#518—614no—
342#518—1224no—
343#518—1222no—
344C2×C4×D4—1224no—
345C2×#117—1221no—
346C22×C22⋊C4—612no—
347C22×C22⋊C4—612no—
348C22×C22⋊C4—611no—
349C22×C22⋊C4—611no—
350C22×C22⋊C4—1221no—
351C2×#99—611no—
352C2×#99—612no—
353C2×#99—614no—
354C2×#99—614no—
355C2×#99#692311yescharacteristic, complemented
356#386—614no—
357#386—1222no—
358#385—618no—
359#385—1224no—
360#381—1221no—
361#380—1224no—
362#379—1221no—
363#342—618no—
364C61#2088911yescharacteristic, complemented, Sylow
365C25—611no—
366C25—611no—
367C22×D4—611no—
368C22×D4—611no—
369C22×D4—612no—
370C22×D4—612no—
371C22×D4—612no—
372C22×D4—612no—
373C22×D4—611no—
374C22×D4—1222no—
375C22×D4—1222no—
376C22×D4—1222no—
377C22×D4—1222no—
378C22×D4C2×#692311yescharacteristic
379C23×C4—611no—
380C23×C4—614no—
381C23×C4—612no—
382C23×C4—1222no—
383C23×C4—1222no—
384C23×C4—1221no—
385C4×D4—12216no—
386C4×D4—12216no—
387#117—1224no—
388#117—1224no—
389C2×C4⋊C4—1222no—
390C2×C4⋊C4—1228no—
391C2×C22⋊C4—612no—
392C2×C22⋊C4—614no—
393C2×C22⋊C4—614no—
394C2×C22⋊C4—614no—
395C2×C22⋊C4—614no—
396C2×C22⋊C4—612no—
397C2×C22⋊C4—1222no—
398C2×C22⋊C4—1222no—
399C2×C22⋊C4—1222no—
400C2×C22⋊C4—1222no—
401C2×C22⋊C4—1222no—
402C2×C22⋊C4—1222no—
403C2×C22⋊C4—1222no—
404C2×C22⋊C4—1224no—
405C2×C22⋊C4—1222no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1224no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1222no—
413C2×C22⋊C4—1222no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4C2×#692312yescomplemented
416C2×C42—1222no—
417#99—614no—
418#99—618no—
419#99C2×#692314yescomplemented
420#95—1228no—
421#95—1224no—
422C24—611no—
423C24—611no—
424C24—612no—
425C24—612no—
426C24—611no—
427C24—611no—
428C24—611no—
429C24—612no—
430C24—612no—
431C24—611no—
432C24—612no—
433C24—611no—
434C24—612no—
435C24—1221no—
436C24—1221no—
437C24—1221no—
438C24—1221no—
439C24—4882no—
440C24—4882no—
441C24C4⋊#692311yescharacteristic, complemented
442C24C22×#692311yescharacteristic
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—612no—
446C2×D4—612no—
447C2×D4—612no—
448C2×D4—612no—
449C2×D4—612no—
450C2×D4—612no—
451C2×D4—1222no—
452C2×D4—1222no—
453C2×D4—1224no—
454C2×D4—1224no—
455C2×D4—1224no—
456C2×D4—1224no—
457C2×D4—1224no—
458C2×D4—1224no—
459C2×D4—1224no—
460C2×D4—1224no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—1222no—
465C2×D4C4⋊#692312yescomplemented
466C2×D4C22×#692312yes—
467C22×C4—22no—
468C22×C4—611no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—618no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1224no—
479C22×C4—1228no—
480C22×C4—1222no—
481C22×C4—1224no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1224no—
485C22×C4—4884no—
486C22×C4—4882no—
487C22×C4—4884no—
488C22×C4—4884no—
489C22×C4—4882no—
490C22×C4—2442no—
491C22×C4C4⋊#692311yescharacteristic, complemented
492C4⋊C4—1228no—
493C4⋊C4—4888no—
494C22⋊C4—22no—
495C22⋊C4—614no—
496C22⋊C4—1224no—
497C22⋊C4—1224no—
498C22⋊C4—1224no—
499C22⋊C4—1224no—
500C22⋊C4—1224no—
501C22⋊C4—1224no—
502C22⋊C4—1228no—
503C22⋊C4—1222no—
504C22⋊C4—1224no—
505C22⋊C4—4884no—
506C22⋊C4—2441no—
507C22⋊C4—2441no—
508C22⋊C4—2441no—
509C22⋊C4—2442no—
510C22⋊C4—2441no—
511C22⋊C4C22×#692314yescomplemented
512C42—1228no—
513C23—21no—
514C23—21no—
515C23—81no—
516C23—81no—
517C23—611no—
518C23—612no—
519C23—611no—
520C23—611no—
521C23—612no—
522C23—612no—
523C23—612no—
524C23—612no—
525C23—612no—
526C23—611no—
527C23—611no—
528C23—612no—
529C23—611no—
530C23—611no—
531C23—611no—
532C23—612no—
533C23—612no—
534C23—612no—
535C23—612no—
536C23—1222no—
537C23—1222no—
538C23—1222no—
539C23—1222no—
540C23—1221no—
541C23—1221no—
542C23—4882no—
543C23—4881no—
544C23—4882no—
545C23—4882no—
546C23—4881no—
547C23—4881no—
548C23—4882no—
549C23—4881no—
550C23—4882no—
551C23—4882no—
552C23—2444no—
553C23—2442no—
554C23—2444no—
555C23—2442no—
556C23—2442no—
557C23—2444no—
558C23—2444no—
559C23C2×C4⋊#692312yes—
560C23C2×C4⋊#692311yescharacteristic
561C23C2×C4⋊#692311yescharacteristic
562C23D4×#692312yes—
563C23D4×#692312yes—
564C23C23×#692311yescharacteristic
565D4—24no—
566D4—24no—
567D4—1224no—
568D4—1224no—
569D4—1224no—
570D4—1224no—
571D4—1224no—
572D4—1224no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—24no—
576C2×C4—82no—
577C2×C4—612no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1228no—
585C2×C4—1224no—
586C2×C4—4884no—
587C2×C4—4884no—
588C2×C4—4882no—
589C2×C4—4884no—
590C2×C4—4888no—
591C2×C4—2448no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2448no—
597C2×C4—2448no—
598C2×C4—2448no—
599C2×C4C2×C4⋊#692312yes—
600C22—22no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—611no—
610C22—611no—
611C22—611no—
612C22—611no—
613C22—612no—
614C22—612no—
615C22—1224no—
616C22—1224no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—1222no—
621C22—4881no—
622C22—4882no—
623C22—4882no—
624C22—2442no—
625C22—2442no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22—2442no—
630C22—2442no—
631C22—2442no—
632C22—2441no—
633C22—2441no—
634C22—2442no—
635C22—2442no—
636C22—2442no—
637C22—2442no—
638C22—2442no—
639C22—2444no—
640C22—2444no—
641C22#1684070911yescharacteristic
642C22#1684070911yescharacteristic
643C22#1684070912yes—
644C22C22×C4⋊#692311yescharacteristic
645C22C2×D4×#692312yes—
646C4—22no—
647C4—44no—
648C4—1222no—
649C4—4882no—
650C4—4882no—
651C4—2444no—
652C4—2448no—
653C2—22no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—22no—
658C2—42no—
659C2—612no—
660C2—1221no—
661C2—1221no—
662C2—1221no—
663C2—1222no—
664C2—1222no—
665C2—2442no—
666C2C2×#1684070911yescharacteristic
subgroupG/H
centerC2C2×#16840709
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#99×C61C4
socleC2×C61C2×#385
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenterC2×#99#6923
hypocenterC61#20889
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #21462298C2semidirect
4. #21461790C2semidirect
5. C2×#16840639C2semidirect
19. #16840709C22semidirect
23. #16840639C22semidirect
26. C2×#14519692C4semidirect
27. C2×#14519691C4semidirect
28. #99×D61C4semidirect
30. C2×#99×C61C4semidirect
77. C2×C22⋊Dic61C2×C4semidirect
81. C22⋊C4×D61C2×C4semidirect
83. #14519692C2×C4semidirect
84. #14519691C2×C4semidirect
86. C2×C22⋊C4×C61C2×C4semidirect
87. #99×C61C2×C4semidirect
88. C24×C61C4⋊C4semidirect
96. C23×D61C4⋊C4semidirect
97. C23×D61C4⋊C4semidirect
123. C2×D4×C61C4⋊C4semidirect
126. C22×C4×C61C4⋊C4semidirect
131. C2×C22⋊D61C4⋊C4semidirect
132. C2×C22⋊D61C4⋊C4semidirect
136. C22×Dic61C4⋊C4semidirect
147. C2×D244C4⋊C4semidirect
156. C2×C4×D61C4⋊C4semidirect
174. C22⋊C4×C61C22×C4semidirect
176. C22⋊Dic61C22×C4semidirect
355. C2×#99#6923semidirect
364. C61#20889semidirect
415. C2×C22⋊C4C2×#6923semidirect
419. #99C2×#6923semidirect
441. C24C4⋊#6923semidirect
465. C2×D4C4⋊#6923semidirect
491. C22×C4C4⋊#6923semidirect
511. C22⋊C4C22×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408292
#214622982
#214622912
#214617902
C2×#168406392
C2×#99×D612
#2088961