Finite Group Databasebeta

← C2×#21461866 #30615788

Subgroups — C2×#21461866 #30615788

Order 15616.

1694 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840830C211yesmaximal, characteristic, complemented
2C2×#16840761C212yesmaximal
3C2×D61⋊#101C211yesmaximal, characteristic, complemented
4#21461866C218yesmaximal, direct product factor
5C2×#16840629C212yesmaximal, complemented
6C2×#16840337C211yesmaximal, characteristic
7C2×D61⋊M16C2212yes—
8#16840830—24no—
9#16840830—22no—
10#16840830C2214yescomplemented
11C2×Q8×#6923—24no—
12C2×#14519856—22no—
13C2×#14519856C2212yes—
14#16840761—24no—
15#16840761C2218yes—
16C2×#14519842—24no—
17D61⋊#101—22no—
18D61⋊#101C2214yescomplemented
19C2×#14519838—22no—
20#16840629C2218yescomplemented
21C22×#11758226C2211yescharacteristic
22C22×Q8×D61C2211yescharacteristic
23#16840337—22no—
24#16840337—22no—
25#16840337C414yescomplemented
26#16840337C2214yes—
27C2×#14519775C411yescharacteristic, complemented
28C2×#14519766C411yescharacteristic, complemented
29C2×#14519765C411yescharacteristic, complemented
30C2×#14519762—22no—
31C2×#14519755—22no—
32C2×#14519734C2211yescharacteristic
33C2×C4⋊Q8×C61C411yescharacteristic, complemented
34C2×#11758213—22no—
35D61⋊M16—22no—
36D61⋊M16—22no—
37D61⋊M16—22no—
38D61⋊M16C2314yes—
39C2×#11758217—22no—
40C2×D61⋊C8—22no—
41Q8×#6923—216no—
42Q8×#6923—216no—
43#14519856—28no—
44#14519856—28no—
45#14519856—22no—
46#14519856—22no—
47#14519856D414yes—
48#14519856C2314yes—
49C2×C4⋊#6923—24no—
50C2×C4⋊#6923—22no—
51C2×C22⋊#6923—22no—
52C2×C4×#6923—24no—
53C2×C4×#6923D414yes—
54#14519842—216no—
55#14519838—28no—
56C2×#11758226—21no—
57C2×#11758226—21no—
58C2×#11758226—22no—
59C2×#11758226—22no—
60C2×#11758226—22no—
61C2×#11758226—22no—
62C2×#11758226C2×C412yes—
63C2×#11758226C2312yes—
64C22×Dic122C2×C411yescharacteristic
65C22×Dic122D412yes—
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61C2×C412yes—
71C2×Q8×D61D412yes—
72C2×Q8×D61D412yes—
73C2×Q8×D61C2312yes—
74C22×D244—21no—
75C22×D244C2×C411yescharacteristic
76C22×C4×D61—21no—
77C22×C4×D61D412yes—
78C22×C4×D61C2311yescharacteristic
79#14519775—22no—
80#14519775C2×C414yescomplemented
81#14519766—22no—
82#14519766C2×C414yescomplemented
83#14519765—22no—
84#14519765C2×C414yescomplemented
85#14519762—28no—
86#14519762—28no—
87#14519755—28no—
88#14519755—28no—
89#14519734—21no—
90#14519734—21no—
91#14519734C2×C412yes—
92#14519734C2312yes—
93C2×#11758196—22no—
94C2×#11758196—21no—
95C2×#11758198—21no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×C4×Dic61C2×C411yescharacteristic
99C22×Q8×C61C2×C411yescharacteristic
100C22×Q8×C61C2×C411yescharacteristic
101C4⋊Q8×C61—22no—
102C4⋊Q8×C61C2×C414yescomplemented
103C2×C4⋊C4×C61—22no—
104C2×C42×C61C2×C411yescharacteristic
105C23×D61—21no—
106C23×D61C2×D411yescharacteristic
107C22×#6923—24no—
108C2×Q8×C61—21no—
109C2×Q8×C61—22no—
110C2×Q8×C61—22no—
111C2×Q8×C61—22no—
112C2×Q8×C61—22no—
113C2×Q8×C61C22⋊C412yes—
114C2×Q8×C61C22×C412yes—
115C2×Q8×C61C22×C412yes—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61C22⋊C412yes—
119C22×C4×C61C22×C411yescharacteristic
120C22×Dic61—21no—
121C22×Dic61C22⋊C412yes—
122C22×Dic61C2×D411yescharacteristic
123#11758226—24no—
124#11758226—24no—
125#11758226—24no—
126#11758226—24no—
127#11758226—42no—
128#11758226—42no—
129#11758226—42no—
130#11758226—42no—
131Q8×D61—24no—
132Q8×D61—24no—
133Q8×D61—24no—
134Q8×D61—24no—
135Q8×D61—24no—
136Q8×D61—24no—
137Q8×D61—24no—
138Q8×D61—24no—
139C2×D244—22no—
140C2×D244—22no—
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—21no—
144C2×D244—41no—
145C2×D244—41no—
146C2×D244—41no—
147C2×D244—41no—
148C2×D244C22×C412yes—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61C22⋊C414yes—
158C2×C4×D61C22×C411yescharacteristic
159C2×C4×D61C2×D414yes—
160C2×C4×D61C2×D412yes—
161C2×C4×D61C2×D412yes—
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61#4112yes—
165C2×C4×D61#4112yes—
166C2×C4×D61C2411yescharacteristic
167C2×Dic122—22no—
168C2×Dic122—22no—
169C2×Dic122—24no—
170C2×Dic122—24no—
171C2×Dic122C22⋊C414yes—
172C2×Dic122C22⋊C412yes—
173C2×Dic122C22×C412yes—
174C2×Dic122C2×D414yes—
175C22⋊#6923—24no—
176C22⋊#6923—24no—
177#11758217—24no—
178#11758217—42no—
179C2×#92420—42no—
180C4⋊#6923—216no—
181C4⋊#6923—24no—
182C4⋊#6923—24no—
183C4×#6923—216no—
184C4×#6923—24no—
185C4×#6923C2×D418yes—
186#11758213—24no—
187#11758213—42no—
188D61⋊C8—24no—
189D61⋊C8—42no—
190C4⋊C4×C61—28no—
191C42×C61—21no—
192C42×C61C22×C412yes—
193#11758198—22no—
194#11758198—22no—
195#11758198—28no—
196#11758198—28no—
197#11758196—22no—
198#11758196—28no—
199#11758196—22no—
200C4×Dic61—21no—
201C4×Dic61C22×C412yes—
202C23×C61C2×C22⋊C411yescharacteristic
203C22×D61—22no—
204C22×D61—42no—
205C22×D61—44no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61C2×C22⋊C411yescharacteristic
209C22×D61#12011yescharacteristic
210C22×D61#12011yescharacteristic
211C22×D61#12311yescharacteristic
212C22×D61#12311yescharacteristic
213C22×D61C22×D411yescharacteristic
214C2×#6923—28no—
215C2×#6923—48no—
216Q8×C61—24no—
217Q8×C61—24no—
218Q8×C61—24no—
219Q8×C61—42no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—42no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61C2×C22⋊C414yes—
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C4×D412yes—
230C2×C4×C61C4×D412yes—
231C2×C4×C61C23×C411yescharacteristic
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—42no—
236C2×Dic61C2×C22⋊C414yes—
237C2×Dic61C2×C22⋊C411yescharacteristic
238C2×Dic61#12112yes—
239C2×Dic61#12112yes—
240C2×Dic61C22×D411yescharacteristic
241D244—24no—
242D244—42no—
243D244—42no—
244D244—42no—
245D244—42no—
246D244—42no—
247C4×D61—24no—
248C4×D61—24no—
249C4×D61—24no—
250C4×D61—24no—
251C4×D61—44no—
252C4×D61—44no—
253C4×D61C4×D412yes—
254C4×D61C4×D412yes—
255C4×D61#12012yes—
256C4×D61#12112yes—
257C4×D61#12112yes—
258C4×D61#12312yes—
259C4×D61C22×D412yes—
260C4×D61C2×#4112yes—
261Dic122—24no—
262Dic122—24no—
263Dic122—28no—
264Dic122—28no—
265#92420—44no—
266C2×#1912—611nomaximal, Sylow
267C22×C61—22no—
268C22×C61#38611yescharacteristic
269C22×C61#38611yescharacteristic
270C22×C61C22×C22⋊C411yescharacteristic
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—44no—
278C2×D61—42no—
279C2×D61—82no—
280C2×D61—82no—
281C2×D61#38611yescharacteristic
282C2×D61#38611yescharacteristic
283C2×D61C2×#12011yescharacteristic
284C2×D61C2×#12311yescharacteristic
285#6923—48no—
286C4×C61—24no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61#38612yes—
290C4×C61C2×C4×D412yes—
291Dic61—24no—
292Dic61—42no—
293Dic61#38612yes—
294Dic61C2×#12112yes—
295C2×#536—611no—
296C2×#519—611no—
297C2×#421—612no—
298C22×#101—611no—
299#1912—618no—
300C2×H(3,ℤ/4)—612no—
301C2×C61—21no—
302C2×C61—21no—
303C2×C61#191212yescomplemented
304C2×C61C2×#38611yescharacteristic
305D61—21no—
306D61—21no—
307D61—21no—
308D61—21no—
309D61—82no—
310C22×#41—611no—
311C23×Q8—611no—
312C22×M16—612no—
313#536—614no—
314#536—614no—
315#536—1222no—
316#536—1222no—
317C2×C4⋊Q8—611no—
318C2×C4⋊Q8#692311yescharacteristic, complemented
319C2×#124—611no—
320C2×#124—611no—
321C2×#123—1222no—
322C2×C22⋊Q8—1222no—
323#519—614no—
324#519—1224no—
325#519—1222no—
326C2×C4×Q8—1224no—
327C2×#117—612no—
328C2×#117—611no—
329C2×#117—1222no—
330#421—618no—
331#421—1224no—
332C2×#104—1224no—
333C2×#101—614no—
334C2×#101—1222no—
335C2×#101—1222no—
336H(3,ℤ/4)—618no—
337C61C2×#191211yescharacteristic, complemented, Sylow
338C2×#41—612no—
339C2×#41—612no—
340C2×#41—1221no—
341C2×#41—1221no—
342C2×#41—1222no—
343C2×#41—1222no—
344C2×#41—1222no—
345C2×#41—1222no—
346C22×Q8—612no—
347C22×Q8—612no—
348C22×Q8—612no—
349C22×Q8—612no—
350C22×Q8—612no—
351C22×Q8—611no—
352C22×Q8—1222no—
353C22×Q8—1222no—
354C22×Q8—1222no—
355C22×Q8—1222no—
356C22×Q8C2×#692311yescharacteristic
357C22×Q8C2×#692311yescharacteristic
358C22×D4—611no—
359C22×D4—1221no—
360C23×C4—611no—
361C23×C4—612no—
362C23×C4—1221no—
363C2×M16—614no—
364C2×M16—1222no—
365C2×M16—1222no—
366C2×M16—1222no—
367C2×M16—1222no—
368C2×M16—1222no—
369C22×C8—1222no—
370C4⋊Q8—22no—
371C4⋊Q8—614no—
372C4⋊Q8—1222no—
373C4⋊Q8C2×#692314yescomplemented
374#124—614no—
375#124—614no—
376#124—1222no—
377#124—1222no—
378#123—1228no—
379#123—1228no—
380C22⋊Q8—1228no—
381C22⋊Q8—1228no—
382C4×Q8—12216no—
383C4×Q8—12216no—
384#117—614no—
385#117—614no—
386#117—612no—
387#117—612no—
388#117—1221no—
389#117—1221no—
390#117—1222no—
391#117—1222no—
392#117—1228no—
393#117—1228no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1224no—
399C2×C22⋊C4—1222no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1222no—
402C2×C22⋊C4—1222no—
403C2×C42—614no—
404C2×C42—611no—
405C2×C42—1224no—
406C2×C42C2×#692311yescharacteristic
407#104—12216no—
408#101—1228no—
409C24—611no—
410C24—1221no—
411#41—1224no—
412#41—1224no—
413#41—1224no—
414#41—1224no—
415#41—2442no—
416#41—2442no—
417#41—2442no—
418#41—2442no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—614no—
425C2×Q8—614no—
426C2×Q8—612no—
427C2×Q8—612no—
428C2×Q8—1224no—
429C2×Q8—1224no—
430C2×Q8—1224no—
431C2×Q8—1224no—
432C2×Q8—1224no—
433C2×Q8—1224no—
434C2×Q8—1224no—
435C2×Q8—1224no—
436C2×Q8—1224no—
437C2×Q8—1224no—
438C2×Q8—1222no—
439C2×Q8—1222no—
440C2×Q8C22⋊#692312yes—
441C2×Q8C22×#692312yes—
442C2×Q8C22×#692312yes—
443C2×D4—612no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—1221no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—2441no—
450C2×D4—2441no—
451C2×D4—2441no—
452C2×D4—2441no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—612no—
465C22×C4—614no—
466C22×C4—614no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1224no—
474C22×C4—1221no—
475C22×C4—2442no—
476C22×C4—2442no—
477C22×C4C22⋊#692312yes—
478C22×C4C22×#692311yescharacteristic
479M16—1224no—
480M16—1224no—
481M16—2442no—
482M16—2442no—
483C2×C8—1224no—
484C2×C8—2442no—
485C2×C8—2442no—
486C4⋊C4—28no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1228no—
490C4⋊C4—1224no—
491C4⋊C4—1224no—
492C4⋊C4—12216no—
493C22⋊C4—1228no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—1224no—
497C22⋊C4—1224no—
498C22⋊C4—1228no—
499C42—21no—
500C42—618no—
501C42—612no—
502C42—1224no—
503C42—12216no—
504C42—1221no—
505C42C22×#692312yes—
506C23—611no—
507C23—611no—
508C23—611no—
509C23—611no—
510C23—611no—
511C23—611no—
512C23—1222no—
513C23—2442no—
514C23—2444no—
515C23—2441no—
516C23—2441no—
517C23C2×C22⋊#692311yescharacteristic
518Q8—24no—
519Q8—24no—
520Q8—24no—
521Q8—42no—
522Q8—1228no—
523Q8—1228no—
524Q8—1224no—
525Q8—1224no—
526D4—1224no—
527D4—2442no—
528D4—2442no—
529D4—2442no—
530D4—2442no—
531D4—2442no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—612no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—614no—
552C2×C4—1224no—
553C2×C4—1224no—
554C2×C4—1224no—
555C2×C4—1224no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1228no—
559C2×C4—1222no—
560C2×C4—2444no—
561C2×C4—2444no—
562C2×C4—2442no—
563C2×C4—2448no—
564C2×C4C2×C22⋊#692314yes—
565C2×C4C2×C22⋊#692311yescharacteristic
566C2×C4D4×#692312yes—
567C2×C4D4×#692312yes—
568C2×C4C23×#692311yescharacteristic
569C8—2444no—
570C22—22no—
571C22—611no—
572C22—611no—
573C22—611no—
574C22—611no—
575C22—1222no—
576C22—1222no—
577C22—4882no—
578C22—4882no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2444no—
584C22—2442no—
585C22#1684071011yescharacteristic
586C22#1684071011yescharacteristic
587C22C22×C22⋊#692311yescharacteristic
588C4—24no—
589C4—42no—
590C4—42no—
591C4—612no—
592C4—612no—
593C4—1224no—
594C4—2442no—
595C4—2448no—
596C4#1684071012yes—
597C4C2×D4×#692312yes—
598C2—21no—
599C2—21no—
600C2—1221no—
601C2—1221no—
602C2—1221no—
603C2—1221no—
604C2—4882no—
605C2#2146186612yesdirect product factor
606C2C2×#1684071011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61#386
prime radicalC22×#11758226C22
cosocleC2×C4×D61C24
hypercenterC2×C4⋊Q8#6923
hypocenterC61C2×#1912
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840830C2semidirect
3. C2×D61⋊#101C2semidirect
4. #21461866C2direct (N × H)
5. C2×#16840629C2semidirect
10. #16840830C22semidirect
18. D61⋊#101C22semidirect
20. #16840629C22semidirect
25. #16840337C4semidirect
27. C2×#14519775C4semidirect
28. C2×#14519766C4semidirect
29. C2×#14519765C4semidirect
33. C2×C4⋊Q8×C61C4semidirect
80. #14519775C2×C4semidirect
82. #14519766C2×C4semidirect
84. #14519765C2×C4semidirect
102. C4⋊Q8×C61C2×C4semidirect
303. C2×C61#1912semidirect
318. C2×C4⋊Q8#6923semidirect
337. C61C2×#1912semidirect
373. C4⋊Q8C2×#6923semidirect
605. C2#21461866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168408302
C2×#168407612
C2×D61⋊#1012
#214618662
C2×#168406292
C2×#168403372
C2×#191261