Finite Group Databasebeta

← C2×#21461984 #30616321

Subgroups — C2×#21461984 #30616321

Order 15616.

1746 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519842C212yesmaximal, complemented
2C22×#14519841C212yesmaximal, complemented
3C2×C4×#11758213C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
5#21461984C218yesmaximal, direct product factor
6C2×#16840311C211yesmaximal, characteristic
7C22×#11758213C2212yes—
8C22×C4⋊#6923—21no—
9C22×C4×#6923C2212yes—
10C2×#14519842—28no—
11C2×#14519842C2218yescomplemented
12C2×#14519841—28no—
13C2×#14519841C2218yescomplemented
14C4×#11758213—22no—
15C4×#11758213C2214yescomplemented
16C2×#14519832—21no—
17C2×C4×#92420—21no—
18C4×C4⋊#6923—22no—
19C4×C4⋊#6923C2214yescomplemented
20C2×(C2×#6923)⋊C4—21no—
21C22×#11758226C2211yescharacteristic
22C22×#11758224C2211yescharacteristic
23#16840311—22no—
24#16840311—22no—
25#16840311C414yescomplemented
26#16840311C2214yes—
27C2×#14519775C411yescharacteristic, complemented
28C2×#14519773C411yescharacteristic, complemented
29C2×#14519765C411yescharacteristic, complemented
30C2×#14519750—21no—
31C2×#14519750—21no—
32C2×#14519737—21no—
33C2×#14519737—21no—
34C2×C42×D61C2211yescharacteristic
35C2×#124×C61C411yescharacteristic, complemented
36C23×#6923—22no—
37C2×#11758213—22no—
38C2×#11758213—24no—
39C2×#11758213D418yescomplemented
40C2×#11758213C2314yes—
41C22×#92420—22no—
42C2×C4⋊#6923—28no—
43C2×C4⋊#6923—24no—
44C2×C4×#6923—24no—
45C2×C4×#6923—24no—
46C2×C4×#6923—22no—
47C2×C4×#6923C2314yes—
48#14519842—216no—
49#14519841—216no—
50#14519832—24no—
51C4×#92420—24no—
52(C2×#6923)⋊C4—24no—
53C2×#11758226—21no—
54C2×#11758226—21no—
55C2×#11758226—24no—
56C2×#11758226—24no—
57C2×#11758226C2×C412yes—
58C2×#11758226C2312yes—
59C2×#11758224—24no—
60C2×#11758224—21no—
61C2×#11758224—21no—
62C2×#11758224—24no—
63C2×#11758224C2×C412yes—
64C2×#11758224C2312yes—
65C22×Dic122C2×C411yescharacteristic
66C22×D244—21no—
67C22×D244C2×C411yescharacteristic
68C22×C22⋊D61—21no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76#14519775—22no—
77#14519775C2×C414yescomplemented
78#14519773—22no—
79#14519773C2×C414yescomplemented
80#14519765—22no—
81#14519765C2×C414yescomplemented
82#14519750—24no—
83#14519750—24no—
84#14519750—24no—
85#14519750—24no—
86#14519737—24no—
87#14519737—24no—
88#14519737—24no—
89#14519737—24no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61D411yescharacteristic
97C42×D61C2×C412yes—
98C42×D61D412yes—
99C42×D61D412yes—
100C42×D61C2312yes—
101C22×Q8×C61C2×C411yescharacteristic
102C22×D4×C61C2×C411yescharacteristic
103#124×C61—22no—
104#124×C61C2×C414yescomplemented
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C42×C61C2×C411yescharacteristic
108C24×C61—21no—
109C23×D61—21no—
110C23×D61C2×D411yescharacteristic
111C22×#6923—28no—
112C22×#6923—24no—
113C22×#6923—44no—
114C22×#6923—44no—
115C2×Q8×C61—21no—
116C2×Q8×C61—24no—
117C2×Q8×C61C22×C412yes—
118C2×D4×C61—21no—
119C2×D4×C61—24no—
120C2×D4×C61C22×C412yes—
121C22×C4×C61—21no—
122C22×C4×C61C22⋊C411yescharacteristic
123C22×C4×C61C22⋊C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—24no—
129C2×C22⋊D61—44no—
130C2×C22⋊D61—42no—
131C2×C22⋊D61—42no—
132C2×C22⋊D61—44no—
133C22×Dic61—21no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—44no—
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140#11758226—28no—
141#11758226—24no—
142#11758226—24no—
143#11758226—44no—
144#11758226—42no—
145#11758226—42no—
146#11758224—28no—
147#11758224—24no—
148#11758224—24no—
149#11758224—44no—
150#11758224—42no—
151#11758224—42no—
152C2×D244—24no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—21no—
156C2×D244—42no—
157C2×D244—42no—
158C2×D244C22×C412yes—
159C2×C4×D61—24no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—42no—
163C2×C4×D61—44no—
164C2×C4×D61C22⋊C412yes—
165C2×C4×D61C22⋊C412yes—
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D412yes—
168C2×C4×D61C2×D412yes—
169C2×C4×D61C2×D414yes—
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61#4114yes—
173C2×C4×D61C2411yescharacteristic
174C2×Dic122—24no—
175C2×Dic122—21no—
176C2×Dic122C22×C412yes—
177C2×#92420—28no—
178C2×#92420—24no—
179C4⋊#6923—216no—
180C4×#6923—24no—
181C4×#6923—24no—
182C4×#6923—44no—
183#11758213—28no—
184#11758213—24no—
185#11758213C2×D418yescomplemented
186C22⋊C4×C61—24no—
187C22⋊C4×C61—24no—
188C42×C61C22⋊C412yes—
189C42×C61C22×C412yes—
190#11758198—24no—
191#11758198—24no—
192#11758196—24no—
193#11758196—24no—
194C4×Dic61C22⋊C412yes—
195C4×Dic61C22⋊C412yes—
196C4×Dic61C22⋊C412yes—
197C4×Dic61C22×C412yes—
198C4×Dic61C2×D412yes—
199C4×Dic61C2×D412yes—
200C23×C61—22no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61C2×C22⋊C411yescharacteristic
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—22no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61C2×C22⋊C411yescharacteristic
212C22×D61#12412yes—
213C22×D61#12712yes—
214C22×D61C22×D411yescharacteristic
215C2×#6923—28no—
216C2×#6923—44no—
217C2×#6923—416no—
218C2×#6923—44no—
219Q8×C61—24no—
220Q8×C61—42no—
221D4×C61—24no—
222D4×C61—42no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—42no—
227C2×C4×C61C2×C22⋊C412yes—
228C2×C4×C61C2×C22⋊C412yes—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C4×D414yes—
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—48no—
233C22⋊D61—42no—
234C22⋊D61—42no—
235C22⋊D61—44no—
236C22⋊D61—48no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—42no—
240C2×Dic61—44no—
241C2×Dic61—44no—
242C2×Dic61#10414yescomplemented
243C2×Dic61C2×C22⋊C412yes—
244C2×Dic61C2×C22⋊C411yescharacteristic
245C2×Dic61C2×C22⋊C412yes—
246C2×Dic61#12114yes—
247C2×Dic61C22×D411yescharacteristic
248D244—24no—
249D244—42no—
250D244—42no—
251D244—44no—
252D244—42no—
253C4×D61—24no—
254C4×D61—24no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—44no—
258C4×D61—44no—
259C4×D61C4×D414yes—
260C4×D61#12114yes—
261C4×D61#12412yes—
262C4×D61#12712yes—
263C4×D61C22×D412yes—
264C4×D61C2×#4112yes—
265Dic122—24no—
266Dic122—42no—
267#92420—28no—
268C2×#1980—611nomaximal, Sylow
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—84no—
273C22×C61#39012yes—
274C22×C61C2×#10412yes—
275C22×C61#42112yes—
276C22×C61C22×C22⋊C411yescharacteristic
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—24no—
282C2×D61—24no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—84no—
287C2×D61#39012yes—
288C2×D61C2×#12411yescharacteristic
289C2×D61C2×#12711yescharacteristic
290#6923—48no—
291C4×C61—22no—
292C4×C61—22no—
293C4×C61—42no—
294C4×C61#39012yes—
295C4×C61C2×C4×D412yes—
296Dic61—22no—
297Dic61—42no—
298Dic61#39012yes—
299Dic61C2×#10414yescomplemented
300Dic61C2×#12112yes—
301C2×#532—611no—
302C22×#104—612no—
303C22×#104—612no—
304C2×C4×M16—611no—
305C2×C4×C4⋊C4—611no—
306#1980—618no—
307C2×C61—82no—
308C2×C61#198014yescomplemented
309C2×C61C2×#39011yescharacteristic
310C2×C61C22×#10411yescharacteristic
311C2×C61C2×#42111yescharacteristic
312D61—21no—
313D61—21no—
314D61—22no—
315D61—82no—
316C22×#41—611no—
317C22×#41—611no—
318C22×M16—612no—
319#532—614no—
320#532—614no—
321#532—1222no—
322#532—1222no—
323C2×C4⋊Q8—611no—
324C2×#127—611no—
325C2×#124—611no—
326C2×#124#692311yescharacteristic, complemented
327C2×#121—1221no—
328C2×#121—1221no—
329C2×C4×D4—1221no—
330C2×C4×D4—1221no—
331C22×C4⋊C4—1221no—
332C22×C42—611no—
333C22×C42—612no—
334C2×#104—618no—
335C2×#104—618no—
336C2×#104—1228no—
337C2×#104—1228no—
338C4×M16—614no—
339C4×M16—1222no—
340C2×#97—1221no—
341C2×C4×C8—1221no—
342C4×C4⋊C4—614no—
343C4×C4⋊C4—1222no—
344C2×#95—1221no—
345C61C2×#198011yescharacteristic, complemented, Sylow
346C2×#41—612no—
347C2×#41—612no—
348C2×#41—612no—
349C2×#41—612no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1224no—
355C2×#41—1224no—
356C2×#41—1224no—
357C2×#41—1224no—
358C22×Q8—611no—
359C22×Q8C2×#692311yescharacteristic
360C22×D4—611no—
361C22×D4—1221no—
362C22×D4—1221no—
363C22×D4—1221no—
364C22×D4—1221no—
365C22×D4C2×#692311yescharacteristic
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—1221no—
370C23×C4—1221no—
371C23×C4—1222no—
372C2×M16—618no—
373C2×M16—614no—
374C2×M16—1224no—
375C2×M16—1222no—
376C22×C8—1222no—
377C4⋊Q8—614no—
378C4⋊Q8—1222no—
379#127—614no—
380#127—1222no—
381#124—22no—
382#124—614no—
383#124—1222no—
384#124C2×#692314yescomplemented
385#121—1224no—
386#121—1224no—
387#121—1224no—
388#121—1224no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1224no—
392C4×D4—1224no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1224no—
396C2×C4⋊C4—1228no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—612no—
405C2×C42—612no—
406C2×C42—612no—
407C2×C42—612no—
408C2×C42—614no—
409C2×C42—1224no—
410C2×C42—1224no—
411C2×C42—1222no—
412C2×C42C2×#692311yescharacteristic
413#104—12216no—
414#104—12216no—
415#97—1224no—
416C4×C8—1224no—
417#95—1224no—
418C24—21no—
419C24—611no—
420C24—1221no—
421#41—1224no—
422#41—1228no—
423#41—1224no—
424#41—1224no—
425#41—1228no—
426#41—1224no—
427#41—2444no—
428#41—2442no—
429#41—2442no—
430#41—2444no—
431#41—2442no—
432#41—2442no—
433C2×Q8—21no—
434C2×Q8—24no—
435C2×Q8—612no—
436C2×Q8—1221no—
437C2×Q8—1224no—
438C2×Q8C22×#692312yes—
439C2×D4—21no—
440C2×D4—24no—
441C2×D4—612no—
442C2×D4—1222no—
443C2×D4—1222no—
444C2×D4—1224no—
445C2×D4—1224no—
446C2×D4—1222no—
447C2×D4—1222no—
448C2×D4—1221no—
449C2×D4—1224no—
450C2×D4—2442no—
451C2×D4—2442no—
452C2×D4—2444no—
453C2×D4—2444no—
454C2×D4—2442no—
455C2×D4—2442no—
456C2×D4C22×#692312yes—
457C22×C4—21no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—614no—
463C22×C4—614no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—1224no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1224no—
477C22×C4—1228no—
478C22×C4—1221no—
479C22×C4—2442no—
480C22×C4—2444no—
481C22×C4—2444no—
482C22×C4—2444no—
483C22×C4—2444no—
484C22×C4C22⋊#692311yescharacteristic
485C22×C4C22⋊#692311yescharacteristic
486C22×C4C22×#692311yescharacteristic
487M16—618no—
488M16—1228no—
489M16—1224no—
490C2×C8—1224no—
491C2×C8—1228no—
492C4⋊C4—1224no—
493C4⋊C4—1224no—
494C4⋊C4—12216no—
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—1224no—
498C22⋊C4—1224no—
499C42—612no—
500C42—612no—
501C42—612no—
502C42—612no—
503C42—612no—
504C42—612no—
505C42—1224no—
506C42—1224no—
507C42—2444no—
508C42C22⋊#692312yes—
509C42C22×#692312yes—
510C23—22no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—612no—
515C23—612no—
516C23—611no—
517C23—611no—
518C23—1222no—
519C23—1222no—
520C23—1222no—
521C23—2442no—
522C23—2442no—
523C23—2442no—
524C23C2×C22⋊#692311yescharacteristic
525Q8—24no—
526Q8—42no—
527Q8—1224no—
528Q8—2442no—
529D4—24no—
530D4—42no—
531D4—1224no—
532D4—2442no—
533D4—2442no—
534D4—2444no—
535D4—2448no—
536D4—2448no—
537D4—2442no—
538D4—2442no—
539D4—2444no—
540D4—2442no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—614no—
546C2×C4—614no—
547C2×C4—612no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—614no—
551C2×C4—612no—
552C2×C4—612no—
553C2×C4—614no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—1224no—
558C2×C4—1224no—
559C2×C4—1222no—
560C2×C4—1228no—
561C2×C4—1222no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2444no—
565C2×C4—2444no—
566C2×C4—2444no—
567C2×C4—2444no—
568C2×C4—2444no—
569C2×C4—2444no—
570C2×C4—24416no—
571C2×C4—2442no—
572C2×C4C2×C22⋊#692312yes—
573C2×C4C2×C22⋊#692312yes—
574C2×C4C2×C22⋊#692311yescharacteristic
575C2×C4D4×#692314yes—
576C2×C4C23×#692311yescharacteristic
577C8—1228no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—84no—
582C22—611no—
583C22—611no—
584C22—612no—
585C22—1221no—
586C22—1221no—
587C22—1221no—
588C22—1221no—
589C22—1224no—
590C22—1224no—
591C22—4884no—
592C22—2442no—
593C22—2442no—
594C22—2442no—
595C22#1684071412yes—
596C22D61⋊#10412yes—
597C22#1684075912yes—
598C22C22×C22⋊#692311yescharacteristic
599C4—22no—
600C4—22no—
601C4—42no—
602C4—612no—
603C4—612no—
604C4—614no—
605C4—1222no—
606C4—2448no—
607C4—2442no—
608C4#1684071412yes—
609C4C2×D4×#692312yes—
610C2—82no—
611C2—1221no—
612C2—1221no—
613C2—1222no—
614C2—4882no—
615C2#2146198414yesdirect product factor
616C2C2×#1684071411yescharacteristic
617C2C2×D61⋊#10411yescharacteristic
618C2C2×#1684075911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840311C2
cosocleC2×C4×D61C24
hypercenterC2×#124#6923
hypocenterC61C2×#1980
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×#14519842C2semidirect
2. C22×#14519841C2semidirect
3. C2×C4×#11758213C2semidirect
4. C2×C4×C4⋊#6923C2semidirect
5. #21461984C2direct (N × H)
11. C2×#14519842C22semidirect
13. C2×#14519841C22semidirect
15. C4×#11758213C22semidirect
19. C4×C4⋊#6923C22semidirect
25. #16840311C4semidirect
27. C2×#14519775C4semidirect
28. C2×#14519773C4semidirect
29. C2×#14519765C4semidirect
35. C2×#124×C61C4semidirect
39. C2×#11758213D4semidirect
77. #14519775C2×C4semidirect
79. #14519773C2×C4semidirect
81. #14519765C2×C4semidirect
104. #124×C61C2×C4semidirect
185. #11758213C2×D4semidirect
242. C2×Dic61#104semidirect
299. Dic61C2×#104semidirect
308. C2×C61#1980semidirect
326. C2×#124#6923semidirect
345. C61C2×#1980semidirect
384. #124C2×#6923semidirect
615. C2#21461984direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198422
C22×#145198412
C2×C4×#117582132
C2×C4×C4⋊#69232
#214619842
C2×#168403112
C2×#198061