Finite Group Databasebeta

← C2×#21461214 #30610925

Subgroups — C2×#21461214 #30610925

Order 15616.

1898 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
1C2×#16840734C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21461214C218yesmaximal, direct product factor
4C2×#16840614C212yesmaximal, complemented
5C2×#16840613C212yesmaximal, complemented
6C2×#121×D61C211yesmaximal, characteristic
7C22×#11758217—21no—
8C22×C22⋊#6923—21no—
9C22×C4×#6923—21no—
10#16840734—22no—
11#16840734C2214yescomplemented
12C2×#14519834—21no—
13C2×#14519834C2212yescomplemented
14C4×C22⋊#6923—22no—
15C4×C22⋊#6923C2214yescomplemented
16C2×(C2×#6923)⋊C4C2212yescomplemented
17#16840614C2218yescomplemented
18#16840613C2218yescomplemented
19C22×D4×D61—21no—
20C22×D4×D61C411yescharacteristic, complemented
21C23×C4×D61C2211yescharacteristic
22C2×#14519752C2211yescharacteristic
23C2×#14519751C411yescharacteristic, complemented
24C2×#14519750—21no—
25C2×#14519749—21no—
26C2×#14519748C2211yescharacteristic
27#121×D61—22no—
28#121×D61—22no—
29#121×D61C414yescomplemented
30#121×D61C2214yes—
31C2×C4⋊C4×D61C411yescharacteristic, complemented
32C2×C22⋊C4×D61—21no—
33C2×#121×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C2×#11758217—24no—
36C2×#11758217—44no—
37C22×#92420—22no—
38C2×C22⋊#6923—28no—
39C2×C22⋊#6923—24no—
40C2×C4×#6923—24no—
41C2×C4×#6923—44no—
42#14519834—24no—
43#14519834—22no—
44#14519834C2314yescomplemented
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4C2314yescomplemented
47C24×D61—21no—
48C24×D61D411yescharacteristic
49C22×D244—21no—
50C22×D244C2×C411yescharacteristic
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C22⋊D61—21no—
54C2×D4×D61—24no—
55C2×D4×D61—24no—
56C2×D4×D61—22no—
57C2×D4×D61—44no—
58C2×D4×D61—48no—
59C2×D4×D61C2×C414yescomplemented
60C23×Dic61D411yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—44no—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C412yes—
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D412yes—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D412yes—
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2312yes—
71#14519752—21no—
72#14519752—21no—
73#14519752C2×C412yes—
74#14519752C2312yes—
75#14519751—22no—
76#14519751C2×C414yescomplemented
77#14519750—24no—
78#14519750—24no—
79#14519749—24no—
80#14519749—24no—
81#14519748—21no—
82#14519748—21no—
83#14519748C2×C412yes—
84#14519748C2312yes—
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×#11758196—21no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61C2×C414yescomplemented
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C22⋊C4×D61—24no—
93C22⋊C4×D61—24no—
94C22×D4×C61—21no—
95C22×D4×C61C2×C411yescharacteristic
96C23×C4×C61C2×C411yescharacteristic
97#121×C61—22no—
98#121×C61C2×C414yescomplemented
99C2×C4⋊C4×C61C2×C411yescharacteristic
100C2×C22⋊C4×C61—21no—
101C24×C61—21no—
102C24×C61C22⋊C411yescharacteristic
103C23×D61—24no—
104C23×D61—24no—
105C23×D61—21no—
106C23×D61—24no—
107C23×D61—42no—
108C23×D61—44no—
109C23×D61—44no—
110C23×D61—44no—
111C23×D61C22⋊C412yes—
112C23×D61C22⋊C411yescharacteristic
113C23×D61C2×D412yes—
114C23×D61C2×D411yescharacteristic
115C22×#6923—28no—
116C22×#6923—24no—
117C22×#6923—44no—
118C22×#6923—44no—
119C2×D4×C61—24no—
120C2×D4×C61—21no—
121C2×D4×C61—42no—
122C2×D4×C61—44no—
123C2×D4×C61C22×C412yes—
124C22×C4×C61—21no—
125C22×C4×C61—42no—
126C22×C4×C61C22⋊C411yescharacteristic
127C22×C4×C61C22⋊C412yes—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C412yes—
130C2×C22⋊D61—24no—
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—24no—
134C2×C22⋊D61—44no—
135C2×C22⋊D61—44no—
136C2×C22⋊D61—44no—
137C22×Dic61—24no—
138C22×Dic61—21no—
139C22×Dic61C22⋊C412yes—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D412yes—
143D4×D61—48no—
144D4×D61—48no—
145D4×D61—416no—
146D4×D61—416no—
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—21no—
150C2×D244—42no—
151C2×D244—44no—
152C2×D244C22×C412yes—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—24no—
156C2×C4×D61—44no—
157C2×C4×D61—44no—
158C2×C4×D61—44no—
159C2×C4×D61—44no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61—44no—
163C2×C4×D61C22⋊C412yes—
164C2×C4×D61C22⋊C412yes—
165C2×C4×D61C22⋊C412yes—
166C2×C4×D61C22×C412yes—
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C2×D412yes—
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D412yes—
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2411yescharacteristic
173C22⋊#6923—216no—
174#11758217—48no—
175C2×#92420—24no—
176C2×#92420—44no—
177C4×#6923—48no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61C22×C412yes—
180C22⋊C4×C61—24no—
181C22⋊Dic61—22no—
182C22⋊Dic61—22no—
183#11758198—24no—
184#11758198—22no—
185#11758198—22no—
186C4⋊Dic61—21no—
187C4⋊Dic61C22×C412yes—
188#11758196—24no—
189C23×C61—22no—
190C23×C61—22no—
191C23×C61—22no—
192C23×C61—22no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61C2×C22⋊C412yes—
197C23×C61C2×C22⋊C411yescharacteristic
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—22no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—416no—
210C22×D61—48no—
211C22×D61—48no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—48no—
216C22×D61—816no—
217C22×D61#10414yes—
218C22×D61C2×C22⋊C411yescharacteristic
219C22×D61C2×C22⋊C412yes—
220C22×D61AGL(1,ℤ/8)14yes—
221C22×D61C22×D411yescharacteristic
222C2×#6923—28no—
223C2×#6923—44no—
224C2×#6923—416no—
225C2×#6923—44no—
226D4×C61—42no—
227D4×C61—42no—
228D4×C61—48no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C412yes—
237C2×C4×C61C23×C411yescharacteristic
238C22⋊D61—48no—
239C22⋊D61—44no—
240C22⋊D61—44no—
241C22⋊D61—48no—
242C2×Dic61—22no—
243C2×Dic61—24no—
244C2×Dic61—24no—
245C2×Dic61—22no—
246C2×Dic61—42no—
247C2×Dic61#9914yes—
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C412yes—
250C2×Dic61C22×D411yescharacteristic
251D244—42no—
252D244—42no—
253D244—44no—
254D244—44no—
255C4×D61—24no—
256C4×D61—24no—
257C4×D61—24no—
258C4×D61—24no—
259C4×D61—42no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—42no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—48no—
266#92420—44no—
267C2×#1507—611nomaximal, Sylow
268C22×C61—22no—
269C22×C61—22no—
270C22×C61—22no—
271C22×C61—44no—
272C22×C61—42no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—84no—
276C22×C61C2×#9912yes—
277C22×C61#41812yes—
278C22×C61C2×#10412yes—
279C22×C61C22×C22⋊C411yescharacteristic
280C2×D61—21no—
281C2×D61—22no—
282C2×D61—21no—
283C2×D61—22no—
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—28no—
287C2×D61—28no—
288C2×D61—48no—
289C2×D61—48no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—816no—
294C2×D61—84no—
295C2×D61#41812yes—
296C2×D61C2×#10414yes—
297C2×D61C2×AGL(1,ℤ/8)12yes—
298#6923—48no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—22no—
302C4×C61—42no—
303Dic61—21no—
304Dic61—21no—
305Dic61—42no—
306Dic61C2×#9914yes—
307C22×#121—611no—
308C2×#407—611no—
309C2×C4×C22⋊C4—611no—
310#1507—618no—
311C2×#327—612no—
312C2×#327—612no—
313C2×C61—42no—
314C2×C61—82no—
315C2×C61#150714yescomplemented
316C2×C61C22×#9911yescharacteristic
317C2×C61C2×#41811yescharacteristic
318C2×C61C22×#10411yescharacteristic
319D61—22no—
320D61—24no—
321D61—22no—
322D61—82no—
323C23×D4—611no—
324C23×D4—1221no—
325C24×C4—611no—
326C22×M16—1221no—
327C2×#121—611no—
328C2×#121—611no—
329C2×#121—614no—
330C2×#121—614no—
331C2×#121—611no—
332C2×#121—1221no—
333C2×#121—1222no—
334C2×#121—1222no—
335C2×#121—1221no—
336C2×#121#692311yescharacteristic, complemented
337C22×C4⋊C4—611no—
338C22×C22⋊C4—1221no—
339C22×C22⋊C4—1221no—
340C22×C42—1221no—
341#407—614no—
342#407—1222no—
343C2×C22⋊C8—612no—
344C2×C22⋊C8—1221no—
345C4×C22⋊C4—614no—
346C4×C22⋊C4—1222no—
347C2×#95—612no—
348#327—618no—
349#327—618no—
350C61C2×#150711yescharacteristic, complemented, Sylow
351C25—611no—
352C25—1221no—
353C22×D4—21no—
354C22×D4—614no—
355C22×D4—611no—
356C22×D4—1221no—
357C22×D4—1222no—
358C22×D4—1221no—
359C22×D4—1224no—
360C22×D4—1224no—
361C22×D4—1221no—
362C22×D4—1221no—
363C22×D4—2444no—
364C22×D4—2448no—
365C22×D4C2×#692311yescharacteristic
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—612no—
373C23×C4—611no—
374C23×C4—612no—
375C23×C4—1221no—
376C23×C4—1222no—
377C23×C4—2444no—
378C23×C4C2×#692311yescharacteristic
379C2×M16—1224no—
380C2×M16—2444no—
381C22×C8—1222no—
382#121—22no—
383#121—612no—
384#121—612no—
385#121—614no—
386#121—612no—
387#121—612no—
388#121—1224no—
389#121—1224no—
390#121—1221no—
391#121—1221no—
392#121—1221no—
393#121—1221no—
394#121—1224no—
395#121—1224no—
396#121—1222no—
397#121C2×#692314yescomplemented
398C2×C4⋊C4—611no—
399C2×C4⋊C4—614no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4C2×#692311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—1224no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1224no—
409C2×C22⋊C4—1228no—
410C2×C22⋊C4—1221no—
411C2×C42—1224no—
412C2×C42—2444no—
413C22⋊C8—614no—
414C22⋊C8—1222no—
415C22⋊C8—1224no—
416#95—614no—
417#95—1222no—
418C24—21no—
419C24—611no—
420C24—611no—
421C24—612no—
422C24—612no—
423C24—1224no—
424C24—1224no—
425C24—1224no—
426C24—1221no—
427C24—2442no—
428C24—2444no—
429C24—2444no—
430C24—2444no—
431C24C22⋊#692311yescharacteristic
432C2×D4—24no—
433C2×D4—21no—
434C2×D4—42no—
435C2×D4—44no—
436C2×D4—612no—
437C2×D4—1222no—
438C2×D4—1222no—
439C2×D4—1224no—
440C2×D4—1222no—
441C2×D4—1222no—
442C2×D4—1224no—
443C2×D4—1221no—
444C2×D4—2442no—
445C2×D4—2444no—
446C2×D4—2444no—
447C2×D4—2448no—
448C2×D4—2448no—
449C2×D4—24416no—
450C2×D4—24416no—
451C2×D4—2444no—
452C2×D4—2444no—
453C2×D4C22×#692312yes—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—611no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—611no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—611no—
465C22×C4—612no—
466C22×C4—611no—
467C22×C4—612no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—1224no—
471C22×C4—1224no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—1224no—
475C22×C4—1228no—
476C22×C4—1221no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2444no—
480C22×C4—2444no—
481C22×C4—2444no—
482C22×C4—2444no—
483C22×C4—2444no—
484C22×C4—2444no—
485C22×C4—2444no—
486C22×C4C22⋊#692311yescharacteristic
487C22×C4C22⋊#692312yes—
488C22×C4C22×#692311yescharacteristic
489C22×C4C22×#692312yes—
490M16—2448no—
491C2×C8—1224no—
492C2×C8—2444no—
493C4⋊C4—21no—
494C4⋊C4—612no—
495C4⋊C4—1224no—
496C4⋊C4—1221no—
497C4⋊C4C22×#692312yes—
498C22⋊C4—24no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—12216no—
504C22⋊C4—1224no—
505C42—2448no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—614no—
514C23—614no—
515C23—612no—
516C23—611no—
517C23—611no—
518C23—1224no—
519C23—1224no—
520C23—1224no—
521C23—1224no—
522C23—1222no—
523C23—1222no—
524C23—1222no—
525C23—1222no—
526C23—1222no—
527C23—48816no—
528C23—2442no—
529C23—2442no—
530C23—2448no—
531C23—24416no—
532C23—2448no—
533C23—2448no—
534C23—2442no—
535C23—2442no—
536C23—2442no—
537C23C2×C22⋊#692312yes—
538C23C2×C22⋊#692311yescharacteristic
539D4—42no—
540D4—42no—
541D4—48no—
542D4—2442no—
543D4—2442no—
544D4—2444no—
545D4—2444no—
546D4—2448no—
547D4—2448no—
548D4—2444no—
549D4—2444no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—614no—
557C2×C4—612no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—1224no—
561C2×C4—1224no—
562C2×C4—1224no—
563C2×C4—1224no—
564C2×C4—1224no—
565C2×C4—1224no—
566C2×C4—1222no—
567C2×C4—1228no—
568C2×C4—1222no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2448no—
576C2×C4—2444no—
577C2×C4—2444no—
578C2×C4—24416no—
579C2×C4—2442no—
580C2×C4C2×C22⋊#692312yes—
581C2×C4C2×C22⋊#692311yescharacteristic
582C2×C4C23×#692311yescharacteristic
583C8—2444no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—84no—
592C22—612no—
593C22—612no—
594C22—614no—
595C22—1221no—
596C22—1221no—
597C22—1222no—
598C22—1222no—
599C22—1221no—
600C22—1221no—
601C22—1228no—
602C22—1228no—
603C22—48816no—
604C22—4884no—
605C22—2448no—
606C22—2448no—
607C22—2442no—
608C22—2442no—
609C22—2442no—
610C22D61⋊#9912yes—
611C22#1684075412yes—
612C22D61⋊#10412yes—
613C22C22×C22⋊#692311yescharacteristic
614C4—22no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—614no—
619C4—1221no—
620C4—1221no—
621C4—2448no—
622C4—2442no—
623C2—42no—
624C2—82no—
625C2—1222no—
626C2—1224no—
627C2—1222no—
628C2—4882no—
629C2#2146121414yesdirect product factor
630C2C2×D61⋊#9911yescharacteristic
631C2C2×#1684075411yescharacteristic
632C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#121×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#121×D61C2
cosocleC2×C4×D61C24
hypercenterC2×#121#6923
hypocenterC61C2×#1507
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840734C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21461214C2direct (N × H)
4. C2×#16840614C2semidirect
5. C2×#16840613C2semidirect
11. #16840734C22semidirect
13. C2×#14519834C22semidirect
15. C4×C22⋊#6923C22semidirect
16. C2×(C2×#6923)⋊C4C22semidirect
17. #16840614C22semidirect
18. #16840613C22semidirect
20. C22×D4×D61C4semidirect
23. C2×#14519751C4semidirect
29. #121×D61C4semidirect
31. C2×C4⋊C4×D61C4semidirect
33. C2×#121×C61C4semidirect
44. #14519834C23semidirect
46. (C2×#6923)⋊C4C23semidirect
59. C2×D4×D61C2×C4semidirect
76. #14519751C2×C4semidirect
88. C4⋊C4×D61C2×C4semidirect
98. #121×C61C2×C4semidirect
315. C2×C61#1507semidirect
336. C2×#121#6923semidirect
350. C61C2×#1507semidirect
397. #121C2×#6923semidirect
629. C2#21461214direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407342
C2×C4×C22⋊#69232
#214612142
C2×#168406142
C2×#168406132
C2×#121×D612
C2×#150761