Finite Group Databasebeta

← C2×#21461958 #30616248

Subgroups — C2×#21461958 #30616248

Order 15616.

2218 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519835C214yesmaximal, complemented
2C2×#16840704C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
4#21461958C218yesmaximal, direct product factor
5C22×#14519748C211yesmaximal, characteristic
6C22×C4⋊#6923—21no—
7C22×C22⋊#6923C2212yes—
8C22×C22⋊#6923C2212yes—
9C22×C4×#6923—21no—
10C2×#14519835—216no—
11C2×#14519835C22116yescomplemented
12#16840704—22no—
13#16840704C2214yescomplemented
14C4×C22⋊#6923—22no—
15C4×C22⋊#6923C2214yescomplemented
16C2×(C2×#6923)⋊C4—21no—
17C2×(C2×#6923)⋊C4—21no—
18C23×C22⋊D61C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×#14519748—21no—
21C2×#14519748—21no—
22C2×#14519748—22no—
23C2×#14519748—21no—
24C2×#14519748—21no—
25C2×#14519748—22no—
26C2×#14519748C414yescomplemented
27C2×#14519748C2214yes—
28C22×C4⋊Dic61C411yescharacteristic, complemented
29C22×C22⋊Dic61C412yescomplemented
30C23×D4×C61C411yescharacteristic, complemented
31C23×#6923—22no—
32C23×#6923—22no—
33C2×C4⋊#6923—24no—
34C2×C4⋊#6923—44no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—24no—
37C2×C22⋊#6923—28no—
38C2×C22⋊#6923—22no—
39C2×C22⋊#6923D418yescomplemented
40C2×C22⋊#6923C2314yes—
41C2×C22⋊#6923C2314yes—
42C2×C4×#6923—24no—
43C2×C4×#6923—44no—
44#14519835—232no—
45(C2×#6923)⋊C4—24no—
46(C2×#6923)⋊C4—24no—
47C24×D61C2311yescharacteristic
48C22×C22⋊D61—28no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61—22no—
52C22×C22⋊D61—22no—
53C22×C22⋊D61—28no—
54C22×C22⋊D61C2×C414yes—
55C22×C22⋊D61C2314yes—
56C23×Dic61C2×C412yes—
57C23×Dic61C2×C411yescharacteristic
58C22×C4×D61—44no—
59C22×C4×D61C2×C412yes—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D412yes—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D412yes—
66C22×C4×D61C2312yes—
67#14519748—24no—
68#14519748—24no—
69#14519748—24no—
70#14519748—24no—
71#14519748—24no—
72#14519748—24no—
73#14519748—24no—
74#14519748—24no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2×C414yescomplemented
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—24no—
82C2×C22⋊Dic61C2×C418yescomplemented
83C25×C61C2×C412yes—
84C22×D4×C61—22no—
85C22×D4×C61—21no—
86C22×D4×C61—21no—
87C22×D4×C61—44no—
88C22×D4×C61C2×C414yescomplemented
89C23×C4×C61C2×C411yescharacteristic
90C24×C61—22no—
91C24×C61—22no—
92C24×C61—28no—
93C24×C61—44no—
94C24×C61—44no—
95C24×C61C22×C411yescharacteristic
96C24×C61C22×C414yes—
97C23×D61—42no—
98C23×D61—42no—
99C23×D61C22×C411yescharacteristic
100C23×D61C2×D411yescharacteristic
101C23×D61C2×D411yescharacteristic
102C23×D61C2×D411yescharacteristic
103C23×D61C2×D411yescharacteristic
104C23×D61C2×D414yes—
105C23×D61#4114yes—
106C23×D61C2411yescharacteristic
107C22×#6923—28no—
108C22×#6923—24no—
109C22×#6923—24no—
110C22×#6923—44no—
111C22×#6923—44no—
112C22×#6923—44no—
113C22×#6923—44no—
114C22×#6923—44no—
115C2×D4×C61—24no—
116C2×D4×C61—24no—
117C2×D4×C61—44no—
118C2×D4×C61—48no—
119C2×D4×C61—48no—
120C2×D4×C61—44no—
121C22×C4×C61—24no—
122C22×C4×C61C22⋊C411yescharacteristic
123C22×C4×C61C22⋊C412yes—
124C22×C4×C61C22⋊C411yescharacteristic
125C22×C4×C61C22×C412yes—
126C2×C22⋊D61—24no—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—216no—
129C2×C22⋊D61—28no—
130C2×C22⋊D61—24no—
131C2×C22⋊D61—24no—
132C2×C22⋊D61—28no—
133C2×C22⋊D61—48no—
134C2×C22⋊D61—48no—
135C2×C22⋊D61—44no—
136C2×C22⋊D61—44no—
137C2×C22⋊D61—44no—
138C2×C22⋊D61—44no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—28no—
142C22×Dic61—42no—
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C22⋊C411yescharacteristic
145C22×Dic61C22⋊C412yes—
146C22×Dic61C22×C414yes—
147C22×Dic61C22×C412yes—
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—44no—
151C2×C4×D61—44no—
152C2×C4×D61—44no—
153C2×C4×D61—44no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61C22⋊C412yes—
157C2×C4×D61C22⋊C412yes—
158C2×C4×D61C22⋊C412yes—
159C2×C4×D61C22⋊C412yes—
160C2×C4×D61C2×D412yes—
161C2×C4×D61C2×D412yes—
162C2×C4×D61C2×D412yes—
163C2×C4×D61C2×D412yes—
164C22⋊#6923—28no—
165C22⋊#6923—24no—
166C22⋊#6923—28no—
167C22⋊#6923—44no—
168C22⋊#6923C2×D418yescomplemented
169C4⋊#6923—48no—
170C4×#6923—48no—
171C22⋊Dic61—28no—
172C22⋊Dic61—28no—
173C4⋊Dic61—24no—
174C4⋊Dic61—24no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—24no—
178C23×C61—28no—
179C23×C61—44no—
180C23×C61—44no—
181C23×C61—44no—
182C23×C61—44no—
183C23×C61—44no—
184C23×C61—44no—
185C23×C61—44no—
186C23×C61—44no—
187C23×C61—816no—
188C23×C61C2×C22⋊C411yescharacteristic
189C23×C61C2×C22⋊C411yescharacteristic
190C23×C61C4×D414yes—
191C23×C61C23×C411yescharacteristic
192C22×D61—22no—
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—22no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—48no—
204C22×D61—48no—
205C22×D61—41no—
206C22×D61C2×C22⋊C411yescharacteristic
207C22×D61C2×C22⋊C411yescharacteristic
208C22×D61C4×D414yes—
209C22×D61#12114yes—
210C22×D61#12114yes—
211C22×D61#12412yes—
212C22×D61#12412yes—
213C22×D61#12712yes—
214C22×D61#12712yes—
215C22×D61C22×D411yescharacteristic
216C22×D61C22×D411yescharacteristic
217C22×D61C22×D412yes—
218C22×D61C2×#4112yes—
219C2×#6923—28no—
220C2×#6923—44no—
221C2×#6923—44no—
222C2×#6923—416no—
223C2×#6923—44no—
224C2×#6923—44no—
225C2×#6923—44no—
226C2×#6923—88no—
227D4×C61—48no—
228D4×C61—48no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61#9914yescomplemented
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C2×C22⋊C412yes—
235C22⋊D61—48no—
236C22⋊D61—44no—
237C22⋊D61—44no—
238C22⋊D61—48no—
239C22⋊D61—48no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—24no—
243C2×Dic61—28no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—44no—
247C2×Dic61—44no—
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C412yes—
250C4×D61—24no—
251C4×D61—24no—
252C4×D61—24no—
253C4×D61—24no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258C2×#1964—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—28no—
264C22×C61—44no—
265C22×C61—44no—
266C22×C61—44no—
267C22×C61—88no—
268C22×C61—88no—
269C22×C61—88no—
270C22×C61#39012yes—
271C22×C61#39012yes—
272C22×C61C2×#9912yes—
273C22×C61#41012yes—
274C22×C61C22×C22⋊C411yescharacteristic
275C22×C61C2×C4×D412yes—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—28no—
285C2×D61—24no—
286C2×D61—24no—
287C2×D61—44no—
288C2×D61—44no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61#39012yes—
294C2×D61#39012yes—
295C2×D61C2×#12112yes—
296C2×D61C2×#12411yescharacteristic
297C2×D61C2×#12711yescharacteristic
298#6923—48no—
299#6923—84no—
300C4×C61—22no—
301C4×C61C2×#9914yescomplemented
302Dic61—22no—
303Dic61—22no—
304Dic61—44no—
305C22×#121—611no—
306C22×#99—614no—
307C2×#380—611no—
308C2×C4×C22⋊C4—611no—
309#1964—618no—
310C2×C61—22no—
311C2×C61—22no—
312C2×C61—84no—
313C2×C61#196414yescomplemented
314C2×C61C2×#39011yescharacteristic
315C2×C61C22×#9911yescharacteristic
316C2×C61C2×#41011yescharacteristic
317D61—22no—
318D61—21no—
319D61—21no—
320D61—22no—
321D61—22no—
322C23×D4—612no—
323C23×D4#692311yescharacteristic, complemented
324C24×C4—611no—
325C2×#121—614no—
326C2×#121—614no—
327C2×#121—1221no—
328C2×#121—1221no—
329C2×#121—1221no—
330C2×#121—1221no—
331C2×#121—1222no—
332C2×#121—1222no—
333C22×C4⋊C4—611no—
334C22×C4⋊C4—1221no—
335C22×C22⋊C4—612no—
336C22×C22⋊C4—612no—
337C22×C22⋊C4—612no—
338C22×C42—1221no—
339C2×#99—6116no—
340C2×#99—12216no—
341#380—614no—
342#380—1222no—
343C4×C22⋊C4—614no—
344C4×C22⋊C4—1222no—
345C2×#95—1221no—
346C2×#95—1221no—
347C61C2×#196411yescharacteristic, complemented, Sylow
348C25—611no—
349C25C2×#692312yes—
350C22×D4—22no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—44no—
354C22×D4—614no—
355C22×D4—614no—
356C22×D4—1222no—
357C22×D4—1222no—
358C22×D4—1222no—
359C22×D4—1222no—
360C22×D4—1228no—
361C22×D4—1228no—
362C22×D4C2×#692314yescomplemented
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—612no—
369C23×C4—612no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—612no—
373C23×C4—1222no—
374C23×C4—1222no—
375C23×C4—2444no—
376C23×C4C2×#692311yescharacteristic
377#121—1224no—
378#121—1224no—
379#121—1224no—
380#121—1224no—
381#121—1224no—
382#121—1224no—
383#121—1224no—
384#121—1224no—
385C2×C4⋊C4—614no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1224no—
390C2×C4⋊C4—2444no—
391C2×C22⋊C4—618no—
392C2×C22⋊C4—614no—
393C2×C22⋊C4—618no—
394C2×C22⋊C4—614no—
395C2×C22⋊C4—1222no—
396C2×C22⋊C4—1222no—
397C2×C22⋊C4—1224no—
398C2×C22⋊C4—1224no—
399C2×C22⋊C4—1222no—
400C2×C22⋊C4—1228no—
401C2×C22⋊C4—1222no—
402C2×C42—1224no—
403C2×C42—2444no—
404#99—12232no—
405#95—1224no—
406#95—1224no—
407C24—22no—
408C24—22no—
409C24—28no—
410C24—44no—
411C24—44no—
412C24—611no—
413C24—611no—
414C24—611no—
415C24—611no—
416C24—614no—
417C24—614no—
418C24—611no—
419C24—611no—
420C24—2442no—
421C24—2442no—
422C24C22×#692311yescharacteristic
423C24C22×#692314yes—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—44no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—44no—
430C2×D4—1228no—
431C2×D4—1224no—
432C2×D4—1224no—
433C2×D4—1224no—
434C2×D4—1224no—
435C2×D4—12216no—
436C2×D4—1228no—
437C2×D4—2448no—
438C2×D4—2444no—
439C2×D4—2444no—
440C2×D4—2448no—
441C2×D4—2444no—
442C2×D4—2444no—
443C22×C4—24no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—612no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—612no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—614no—
457C22×C4—1224no—
458C22×C4—1224no—
459C22×C4—1224no—
460C22×C4—1228no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1228no—
464C22×C4—1224no—
465C22×C4—2444no—
466C22×C4—2444no—
467C22×C4—2444no—
468C22×C4—2444no—
469C22×C4—2442no—
470C22×C4—2442no—
471C22×C4—2442no—
472C22×C4—2444no—
473C22×C4—2444no—
474C22×C4—2444no—
475C22×C4—2444no—
476C22×C4—2444no—
477C22×C4C22⋊#692312yes—
478C22×C4C22⋊#692311yescharacteristic
479C22×C4C22⋊#692311yescharacteristic
480C22×C4C22×#692312yes—
481C4⋊C4—1224no—
482C4⋊C4—1224no—
483C4⋊C4—2448no—
484C22⋊C4—618no—
485C22⋊C4—1228no—
486C22⋊C4—1228no—
487C22⋊C4—1228no—
488C22⋊C4—1224no—
489C22⋊C4—1228no—
490C22⋊C4—2444no—
491C42—2448no—
492C23—22no—
493C23—22no—
494C23—24no—
495C23—28no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—44no—
502C23—44no—
503C23—44no—
504C23—816no—
505C23—614no—
506C23—612no—
507C23—612no—
508C23—611no—
509C23—611no—
510C23—611no—
511C23—611no—
512C23—614no—
513C23—612no—
514C23—612no—
515C23—614no—
516C23—612no—
517C23—612no—
518C23—1222no—
519C23—1222no—
520C23—1222no—
521C23—1222no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2441no—
527C23—2441no—
528C23—2441no—
529C23—2441no—
530C23—2448no—
531C23—2448no—
532C23C2×C22⋊#692311yescharacteristic
533C23C2×C22⋊#692311yescharacteristic
534C23D4×#692314yes—
535C23C23×#692311yescharacteristic
536D4—48no—
537D4—48no—
538D4—2448no—
539D4—2444no—
540D4—2444no—
541D4—2448no—
542D4—2448no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1224no—
551C2×C4—1224no—
552C2×C4—1224no—
553C2×C4—1224no—
554C2×C4—1228no—
555C2×C4—1224no—
556C2×C4—1228no—
557C2×C4—4888no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2444no—
565C2×C4—2444no—
566C2×C4—2444no—
567C2×C4—2444no—
568C2×C4—2444no—
569C2×C4—24416no—
570C2×C4—2444no—
571C2×C4—2444no—
572C2×C4#1451983514yescomplemented
573C2×C4C2×C22⋊#692312yes—
574C2×C4C2×C22⋊#692312yes—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—28no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—88no—
584C22—88no—
585C22—88no—
586C22—612no—
587C22—611no—
588C22—611no—
589C22—612no—
590C22—612no—
591C22—1221no—
592C22—1221no—
593C22—1221no—
594C22—1221no—
595C22—1221no—
596C22—1221no—
597C22—1221no—
598C22—1221no—
599C22—1224no—
600C22—1228no—
601C22—1224no—
602C22—2442no—
603C22—2444no—
604C22—2442no—
605C22—2442no—
606C22—2442no—
607C22—2444no—
608C22#1684071412yes—
609C22#1684071412yes—
610C22C2×#1451983512yes—
611C22#1684074212yes—
612C22C22×C22⋊#692311yescharacteristic
613C22C2×D4×#692312yes—
614C4—22no—
615C4—1222no—
616C4—1222no—
617C4—4884no—
618C4—2448no—
619C4—2444no—
620C4C2×#1451983514yescomplemented
621C2—22no—
622C2—22no—
623C2—84no—
624C2—1221no—
625C2—1222no—
626C2—1221no—
627C2—1222no—
628C2—1222no—
629C2#2146195814yesdirect product factor
630C2C2×#1684071411yescharacteristic
631C2C22×#1451983511yescharacteristic
632C2C2×#1684074211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC23×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#14519748C2
cosocleC23×D61C24
hypercenterC23×D4#6923
hypocenterC61C2×#1964
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14519835C2semidirect
2. C2×#16840704C2semidirect
3. C2×C4×C22⋊#6923C2semidirect
4. #21461958C2direct (N × H)
11. C2×#14519835C22semidirect
13. #16840704C22semidirect
15. C4×C22⋊#6923C22semidirect
26. C2×#14519748C4semidirect
28. C22×C4⋊Dic61C4semidirect
29. C22×C22⋊Dic61C4semidirect
30. C23×D4×C61C4semidirect
39. C2×C22⋊#6923D4semidirect
78. C2×C4⋊Dic61C2×C4semidirect
82. C2×C22⋊Dic61C2×C4semidirect
88. C22×D4×C61C2×C4semidirect
168. C22⋊#6923C2×D4semidirect
232. C2×C4×C61#99semidirect
301. C4×C61C2×#99semidirect
313. C2×C61#1964semidirect
323. C23×D4#6923semidirect
347. C61C2×#1964semidirect
362. C22×D4C2×#6923semidirect
572. C2×C4#14519835semidirect
620. C4C2×#14519835semidirect
629. C2#21461958direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198352
C2×#168407042
C2×C4×C22⋊#69232
#214619582
C22×#145197482
C2×#196461