Finite Group Databasebeta

← C2×#21461820 #30615656

Subgroups — C2×#21461820 #30615656

Order 15616.

1794 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
1C2×#16840840C211yesmaximal, characteristic, complemented
2C2×#16840761C212yesmaximal, complemented
3C2×#16840742C211yesmaximal, characteristic, complemented
4#21461820C218yesmaximal, direct product factor
5C2×#16840633C212yesmaximal, complemented
6C2×#16840311C211yesmaximal, characteristic
7#16840840—24no—
8#16840840—22no—
9#16840840C2214yescomplemented
10C2×#14519864—24no—
11C2×D61⋊M16C2212yes—
12C22×#11758217—22no—
13C2×#14519856C2212yes—
14#16840761—24no—
15#16840761C2218yescomplemented
16C2×#14519842—24no—
17#16840742—22no—
18#16840742C2214yescomplemented
19C2×#14519835—22no—
20#16840633C2218yescomplemented
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—22no—
31C2×#14519737—22no—
32C2×C42×D61C2211yescharacteristic
33C2×#124×C61C411yescharacteristic, complemented
34#14519864—216no—
35#14519864—216no—
36C2×#11758213D414yescomplemented
37D61⋊M16—22no—
38D61⋊M16—22no—
39D61⋊M16D414yescomplemented
40D61⋊M16C2314yes—
41C2×#11758217—24no—
42C2×#11758217—28no—
43C2×#11758217—22no—
44C2×#11758217—28no—
45C2×D61⋊C8—22no—
46C22×#92420—24no—
47#14519856—22no—
48#14519856—22no—
49#14519856—22no—
50#14519856C2314yes—
51C2×C4⋊#6923—22no—
52C2×C22⋊#6923—22no—
53C2×C4×#6923—22no—
54#14519842—216no—
55#14519835—28no—
56C2×#11758226—21no—
57C2×#11758226—21no—
58C2×#11758226—22no—
59C2×#11758226—22no—
60C2×#11758226—22no—
61C2×#11758226—22no—
62C2×#11758226C2×C412yes—
63C2×#11758226C2312yes—
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224C2×C412yes—
69C2×#11758224D412yes—
70C2×#11758224D412yes—
71C2×#11758224C2312yes—
72C22×Dic122C2×C411yescharacteristic
73C22×D244—21no—
74C22×D244C2×C411yescharacteristic
75C22×C22⋊D61—22no—
76C22×C22⋊D61D412yes—
77C23×Dic61D412yes—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81#14519775—22no—
82#14519775C2×C414yescomplemented
83#14519773—22no—
84#14519773C2×C414yescomplemented
85#14519765—22no—
86#14519765C2×C414yescomplemented
87#14519750—28no—
88#14519750—28no—
89#14519737—28no—
90#14519737—28no—
91C2×#11758196—22no—
92C2×#11758198—22no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2×C411yescharacteristic
95C42×D61—21no—
96C42×D61—21no—
97C42×D61C2×C412yes—
98C42×D61C2312yes—
99C22×Q8×C61C2×C411yescharacteristic
100C22×D4×C61C2×C411yescharacteristic
101#124×C61—22no—
102#124×C61C2×C414yescomplemented
103C2×C22⋊C4×C61—22no—
104C2×C42×C61C2×C411yescharacteristic
105C24×C61C22⋊C412yes—
106C23×D61—21no—
107C23×D61C2×D411yescharacteristic
108C22×#6923—42no—
109C2×Q8×C61—21no—
110C2×Q8×C61—22no—
111C2×Q8×C61—22no—
112C2×Q8×C61C22×C412yes—
113C2×D4×C61—22no—
114C2×D4×C61—22no—
115C2×D4×C61C22⋊C412yes—
116C2×D4×C61C22×C412yes—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61C22×C411yescharacteristic
120C2×C22⋊D61—24no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61—28no—
123C2×C22⋊D61—48no—
124C2×C22⋊D61C22⋊C414yes—
125C2×C22⋊D61C2×D414yes—
126C22×Dic61—21no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61C22⋊C412yes—
132C22×Dic61C22⋊C414yes—
133C22×Dic61C2×D414yes—
134C22×Dic61C2×D411yescharacteristic
135#11758226—24no—
136#11758226—24no—
137#11758226—24no—
138#11758226—24no—
139#11758226—42no—
140#11758226—42no—
141#11758226—42no—
142#11758226—42no—
143#11758224—24no—
144#11758224—24no—
145#11758224—24no—
146#11758224—24no—
147#11758224—24no—
148#11758224—24no—
149#11758224—24no—
150#11758224—24no—
151C2×D244—22no—
152C2×D244—22no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—21no—
156C2×D244—42no—
157C2×D244—42no—
158C2×D244C22×C412yes—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—44no—
164C2×C4×D61—41no—
165C2×C4×D61—41no—
166C2×C4×D61—41no—
167C2×C4×D61—41no—
168C2×C4×D61C22×C411yescharacteristic
169C2×C4×D61C2×D412yes—
170C2×C4×D61C2×D412yes—
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61#4112yes—
174C2×C4×D61#4112yes—
175C2×C4×D61C2411yescharacteristic
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122C22⋊C412yes—
179C2×Dic122C22×C412yes—
180C22⋊#6923—24no—
181C22⋊#6923—42no—
182#11758217—216no—
183#11758217—24no—
184#11758217—24no—
185C2×#92420—216no—
186C2×#92420—24no—
187C4⋊#6923—24no—
188C4⋊#6923—42no—
189C4×#6923—24no—
190C4×#6923—42no—
191#11758213—24no—
192#11758213C2×D418yescomplemented
193D61⋊C8—24no—
194D61⋊C8—24no—
195C22⋊C4×C61—28no—
196C42×C61—21no—
197C42×C61C22×C412yes—
198#11758198—28no—
199#11758196—28no—
200C4×Dic61—21no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61C22×C412yes—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—44no—
207C23×C61C2×C22⋊C411yescharacteristic
208C23×C61C2×C22⋊C414yes—
209C22×D61—22no—
210C22×D61—42no—
211C22×D61—44no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61C2×C22⋊C411yescharacteristic
215C22×D61#12112yes—
216C22×D61#12112yes—
217C22×D61C22×D411yescharacteristic
218C2×#6923—44no—
219C2×#6923—84no—
220Q8×C61—24no—
221Q8×C61—42no—
222D4×C61—24no—
223D4×C61—24no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C4×D412yes—
231C2×C4×C61C4×D412yes—
232C2×C4×C61C23×C411yescharacteristic
233C22⋊D61—28no—
234C22⋊D61—28no—
235C22⋊D61—416no—
236C2×Dic61—24no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—24no—
243C2×Dic61—24no—
244C2×Dic61C2×C22⋊C414yes—
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61#12011yescharacteristic
247C2×Dic61#12011yescharacteristic
248C2×Dic61#12311yescharacteristic
249C2×Dic61#12311yescharacteristic
250C2×Dic61C22×D411yescharacteristic
251D244—24no—
252D244—44no—
253D244—44no—
254D244—42no—
255C4×D61—44no—
256C4×D61—44no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61C4×D412yes—
262C4×D61C4×D412yes—
263C4×D61#12012yes—
264C4×D61#12112yes—
265C4×D61#12112yes—
266C4×D61#12312yes—
267C4×D61C22×D412yes—
268C4×D61C2×#4112yes—
269Dic122—24no—
270Dic122—24no—
271#92420—28no—
272C2×#1884—611nomaximal, Sylow
273C22×C61—22no—
274C22×C61—24no—
275C22×C61—44no—
276C22×C61—44no—
277C22×C61—82no—
278C22×C61#38611yescharacteristic
279C22×C61#38611yescharacteristic
280C22×C61C22×C22⋊C411yescharacteristic
281C2×D61—24no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—42no—
285C2×D61—44no—
286C2×D61—42no—
287C2×D61—82no—
288C2×D61—82no—
289C2×D61#38612yes—
290C2×D61C2×#12112yes—
291#6923—84no—
292C4×C61—42no—
293C4×C61—42no—
294C4×C61#38612yes—
295C4×C61C2×C4×D412yes—
296Dic61—24no—
297Dic61—24no—
298Dic61#38611yescharacteristic
299Dic61#38611yescharacteristic
300Dic61C2×#12011yescharacteristic
301Dic61C2×#12311yescharacteristic
302C2×#568—611no—
303C2×#532—611no—
304C2×#421—612no—
305C2×#410—611no—
306#1884—618no—
307C2×#339—612no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—44no—
311C2×C61#188412yescomplemented
312C2×C61C2×#38611yescharacteristic
313D61—22no—
314D61—22no—
315D61—82no—
316C22×#41—611no—
317C22×#41—611no—
318#568—614no—
319#568—1224no—
320#568—1222no—
321C2×#131—1224no—
322C22×M16—612no—
323C22×M16—1222no—
324#532—614no—
325#532—614no—
326#532—1222no—
327#532—1222no—
328C2×C4⋊Q8—611no—
329C2×#127—611no—
330C2×#124—611no—
331C2×#124#692311yescharacteristic, complemented
332C2×#121—1222no—
333C2×C4×D4—1222no—
334C2×#117—612no—
335C22×C42—611no—
336#421—618no—
337#421—1224no—
338C2×#104—1224no—
339#410—614no—
340#410—1222no—
341C2×#99—1222no—
342#339—618no—
343C61C2×#188411yescharacteristic, complemented, Sylow
344C2×#41—612no—
345C2×#41—612no—
346C2×#41—612no—
347C2×#41—612no—
348C2×#41—612no—
349C2×#41—612no—
350C2×#41—1222no—
351C2×#41—1222no—
352C2×#41—1222no—
353C2×#41—1222no—
354C2×#41—1221no—
355C2×#41—1221no—
356C2×#41—1222no—
357C2×#41—1222no—
358C2×#41—1222no—
359C2×#41—1222no—
360C22×Q8—611no—
361C22×Q8C2×#692311yescharacteristic
362C22×D4—612no—
363C22×D4—611no—
364C22×D4—1221no—
365C22×D4—1222no—
366C22×D4C2×#692311yescharacteristic
367C23×C4—611no—
368C23×C4—612no—
369C23×C4—1221no—
370C23×C4—1221no—
371#131—12216no—
372#131—12216no—
373C2×M16—614no—
374C2×M16—614no—
375C2×M16—614no—
376C2×M16—1222no—
377C2×M16—1228no—
378C2×M16—1222no—
379C2×M16—1222no—
380C2×M16—1224no—
381C2×M16—1228no—
382C22×C8—1222no—
383C22×C8—1224no—
384C4⋊Q8—614no—
385C4⋊Q8—1222no—
386#127—614no—
387#127—1222no—
388#124—22no—
389#124—614no—
390#124—1222no—
391#124C2×#692314yescomplemented
392#121—1228no—
393#121—1228no—
394C4×D4—1228no—
395C4×D4—1228no—
396#117—614no—
397#117—1222no—
398#117—1222no—
399#117—1222no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1222no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—1222no—
404C2×C22⋊C4—1222no—
405C2×C42—611no—
406C2×C42—612no—
407C2×C42—612no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42—1221no—
411C2×C42—1222no—
412C2×C42C2×#692311yescharacteristic
413#104—12216no—
414#99—1228no—
415C24—611no—
416C24—1221no—
417C24C22⋊#692312yes—
418#41—1224no—
419#41—1224no—
420#41—1224no—
421#41—1224no—
422#41—1224no—
423#41—1224no—
424#41—1224no—
425#41—1224no—
426#41—1224no—
427#41—1224no—
428#41—1224no—
429#41—1224no—
430#41—2442no—
431#41—2442no—
432#41—2442no—
433#41—2442no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—612no—
438C2×Q8—612no—
439C2×Q8—1222no—
440C2×Q8—1222no—
441C2×Q8C22×#692312yes—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—614no—
445C2×D4—614no—
446C2×D4—612no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1224no—
450C2×D4—1224no—
451C2×D4—1228no—
452C2×D4—1221no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4—2442no—
456C2×D4—2442no—
457C2×D4—2448no—
458C2×D4C22⋊#692312yes—
459C2×D4C22×#692312yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—612no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—612no—
472C22×C4—614no—
473C22×C4—614no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—2441no—
484C22×C4—2441no—
485C22×C4—2441no—
486C22×C4—2441no—
487C22×C4—2444no—
488C22×C4—2442no—
489C22×C4C22×#692311yescharacteristic
490M16—618no—
491M16—1224no—
492M16—1224no—
493M16—1224no—
494M16—12216no—
495C2×C8—1224no—
496C2×C8—1224no—
497C2×C8—1224no—
498C2×C8—12216no—
499C4⋊C4—1228no—
500C4⋊C4—1224no—
501C4⋊C4—2442no—
502C22⋊C4—28no—
503C22⋊C4—1228no—
504C22⋊C4—1224no—
505C22⋊C4—2442no—
506C42—21no—
507C42—612no—
508C42—1222no—
509C42—1222no—
510C42—1224no—
511C42—1221no—
512C42—2442no—
513C42C22×#692312yes—
514C23—22no—
515C23—22no—
516C23—44no—
517C23—612no—
518C23—612no—
519C23—611no—
520C23—611no—
521C23—1222no—
522C23—2442no—
523C23—2444no—
524C23—2441no—
525C23—2441no—
526C23C2×C22⋊#692311yescharacteristic
527C23C2×C22⋊#692314yes—
528Q8—24no—
529Q8—42no—
530Q8—1224no—
531Q8—1224no—
532D4—24no—
533D4—24no—
534D4—1228no—
535D4—1228no—
536D4—1224no—
537D4—2444no—
538D4—2444no—
539D4—24416no—
540D4—2442no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—612no—
560C2×C4—614no—
561C2×C4—1224no—
562C2×C4—1224no—
563C2×C4—1224no—
564C2×C4—1224no—
565C2×C4—1224no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—4884no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2444no—
575C2×C4—2444no—
576C2×C4—2444no—
577C2×C4C2×C22⋊#692311yescharacteristic
578C2×C4D4×#692312yes—
579C2×C4D4×#692312yes—
580C2×C4C23×#692311yescharacteristic
581C8—1228no—
582C22—22no—
583C22—24no—
584C22—44no—
585C22—44no—
586C22—82no—
587C22—612no—
588C22—612no—
589C22—1224no—
590C22—4882no—
591C22—4882no—
592C22—2441no—
593C22—2441no—
594C22—2442no—
595C22—2444no—
596C22—2442no—
597C22#1684071011yescharacteristic
598C22#1684071011yescharacteristic
599C22C22×C22⋊#692311yescharacteristic
600C4—42no—
601C4—42no—
602C4—611no—
603C4—611no—
604C4—611no—
605C4—611no—
606C4—1224no—
607C4—1224no—
608C4—4884no—
609C4#1684071012yes—
610C4C2×D4×#692312yes—
611C2—21no—
612C2—21no—
613C2—44no—
614C2—1222no—
615C2—1222no—
616C2—4882no—
617C2#2146182012yesdirect product factor
618C2C2×#1684071011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61#386
prime radicalC2×#16840311C2
cosocleC2×C4×D61C24
hypercenterC2×#124#6923
hypocenterC61C2×#1884
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16840840C2semidirect
2. C2×#16840761C2semidirect
3. C2×#16840742C2semidirect
4. #21461820C2direct (N × H)
5. C2×#16840633C2semidirect
9. #16840840C22semidirect
15. #16840761C22semidirect
18. #16840742C22semidirect
20. #16840633C22semidirect
25. #16840311C4semidirect
27. C2×#14519775C4semidirect
28. C2×#14519773C4semidirect
29. C2×#14519765C4semidirect
33. C2×#124×C61C4semidirect
36. C2×#11758213D4semidirect
39. D61⋊M16D4semidirect
82. #14519775C2×C4semidirect
84. #14519773C2×C4semidirect
86. #14519765C2×C4semidirect
102. #124×C61C2×C4semidirect
192. #11758213C2×D4semidirect
311. C2×C61#1884semidirect
331. C2×#124#6923semidirect
343. C61C2×#1884semidirect
391. #124C2×#6923semidirect
617. C2#21461820direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168408402
C2×#168407612
C2×#168407422
#214618202
C2×#168406332
C2×#168403112
C2×#188461