Finite Group Databasebeta

← C2×#21461975 #30616296

Subgroups — C2×#21461975 #30616296

Order 15616.

1518 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519848C211yesmaximal, characteristic, complemented
2C22×#14519842C211yesmaximal, characteristic, complemented
3C22×#14519841C211yesmaximal, characteristic, complemented
4C2×#16840737C211yesmaximal, characteristic, complemented
5C2×#16840736C211yesmaximal, characteristic, complemented
6C22×#14519831C211yesmaximal, characteristic, complemented
7#21461975C218yesmaximal, direct product factor
8C22×#14519798C211yesmaximal, characteristic
9C22×#11758213C2211yescharacteristic
10C22×#11758213C2211yescharacteristic
11C22×D61⋊C8C2211yescharacteristic
12C22×C4×#6923C2211yescharacteristic
13C2×#14519848—24no—
14C2×#14519848C2214yescomplemented
15C2×#14519842—24no—
16C2×#14519842C2214yescomplemented
17C2×#14519841—24no—
18C2×#14519841C2214yescomplemented
19#16840737—22no—
20#16840737C2214yescomplemented
21#16840736—22no—
22#16840736C2214yescomplemented
23C2×#14519834—22no—
24C2×C22⋊#92420—22no—
25C2×#14519831—24no—
26C2×#14519831C2214yescomplemented
27C22×#11758226C2211yescharacteristic
28C22×#11758224C2211yescharacteristic
29C2×#14519798—24no—
30C2×#14519798—24no—
31C2×#14519798C414yescomplemented
32C2×#14519798C2214yes—
33C22×#11758202C411yescharacteristic, complemented
34C22×#11758190C411yescharacteristic, complemented
35C22×#11758199C411yescharacteristic, complemented
36C22×C8×D61C2211yescharacteristic
37C22×SD16×C61C411yescharacteristic, complemented
38C23×#6923—21no—
39C2×#11758213—22no—
40C2×#11758213—22no—
41C2×#11758213—22no—
42C2×#11758213—22no—
43C2×#11758213—21no—
44C2×#11758213—21no—
45C2×#11758213C2312yes—
46C2×#11758213C2312yes—
47C2×D61⋊C8—22no—
48C2×D61⋊C8—22no—
49C2×D61⋊C8D412yes—
50C2×D61⋊C8C2312yes—
51C22×#92420—21no—
52C22×#92420—21no—
53C22×#92420D412yes—
54C2×C4×#6923—22no—
55C2×C4×#6923—21no—
56C2×C4×#6923D414yes—
57C2×C4×#6923C2312yes—
58#14519848—28no—
59#14519842—28no—
60#14519841—28no—
61#14519834—28no—
62C22⋊#92420—28no—
63#14519831—28no—
64C2×#11758226—21no—
65C2×#11758226—21no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226C2×C412yes—
71C2×#11758226C2312yes—
72C2×#11758224—22no—
73C2×#11758224—22no—
74C2×#11758224—22no—
75C2×#11758224—21no—
76C2×#11758224—22no—
77C2×#11758224—21no—
78C2×#11758224C2×C412yes—
79C2×#11758224C2312yes—
80C22×Dic122C2×C411yescharacteristic
81C22×D244—21no—
82C22×D244C2×C411yescharacteristic
83C22×C22⋊D61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87#14519798—216no—
88#14519798—28no—
89#14519798—28no—
90C2×#11758202—24no—
91C2×#11758202C2×C414yescomplemented
92C2×#11758190—24no—
93C2×#11758190C2×C414yescomplemented
94C2×#11758199—24no—
95C2×#11758199C2×C414yescomplemented
96C22×#92418C2×C411yescharacteristic
97C2×C8×D61C2×C412yes—
98C2×C8×D61D414yes—
99C2×C8×D61D414yes—
100C2×C8×D61C2312yes—
101C22×Q8×C61C2×C411yescharacteristic
102C22×D4×C61C2×C411yescharacteristic
103C2×SD16×C61—24no—
104C2×SD16×C61C2×C414yescomplemented
105C22×C8×C61C2×C411yescharacteristic
106C24×C61—21no—
107C23×D61—21no—
108C23×D61#4111yescharacteristic
109C22×#6923—24no—
110C22×#6923—22no—
111C22×#6923—44no—
112C2×Q8×C61—21no—
113C2×Q8×C61—22no—
114C2×Q8×C61—22no—
115C2×Q8×C61C22×C412yes—
116C2×D4×C61—22no—
117C2×D4×C61—22no—
118C2×D4×C61—21no—
119C2×D4×C61C22×C412yes—
120C22×C4×C61—21no—
121C22×C4×C61C22×C411yescharacteristic
122C2×C22⋊D61—22no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—42no—
125C2×C22⋊D61—42no—
126C22×Dic61—21no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—42no—
130C22×Dic61—42no—
131C22×Dic61C2×D411yescharacteristic
132#11758226—24no—
133#11758226—24no—
134#11758226—22no—
135#11758226—22no—
136#11758226—22no—
137#11758226—22no—
138#11758226—42no—
139#11758226—42no—
140#11758226—42no—
141#11758226—42no—
142#11758224—24no—
143#11758224—24no—
144#11758224—22no—
145#11758224—22no—
146#11758224—22no—
147#11758224—22no—
148#11758224—42no—
149#11758224—42no—
150#11758224—42no—
151#11758224—42no—
152C2×D244—22no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—22no—
156C2×D244—21no—
157C2×D244—42no—
158C2×D244—42no—
159C2×D244C22×C412yes—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×D412yes—
167C2×C4×D61C2×D412yes—
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61#4112yes—
170C2×C4×D61#4111yescharacteristic
171C2×C4×D61C2411yescharacteristic
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122—21no—
175C2×Dic122C22×C412yes—
176C2×#92420—24no—
177C2×#92420—22no—
178C2×#92420—22no—
179C2×#92420—42no—
180C2×#92420—42no—
181C2×#92420C2×D414yes—
182C4×#6923—24no—
183C4×#6923—22no—
184C4×#6923C2×D414yes—
185#11758213—22no—
186#11758213—22no—
187#11758213—22no—
188#11758213—22no—
189#11758213—42no—
190#11758213—42no—
191D61⋊C8—24no—
192D61⋊C8—22no—
193D61⋊C8—22no—
194SD16×C61—28no—
195C2×C8×C61C22⋊C414yes—
196C2×C8×C61C22×C412yes—
197#11758202—28no—
198#11758199—28no—
199C2×#92418C22⋊C414yes—
200C2×#92418C22×C412yes—
201#11758190—28no—
202C8×D61C22⋊C418yes—
203C8×D61C2×D414yes—
204C8×D61C2×D414yes—
205C23×C61—22no—
206C23×C61—42no—
207C23×C61—44no—
208C23×C61C4×D411yescharacteristic
209C22×D61—24no—
210C22×D61—22no—
211C22×D61—42no—
212C22×D61—44no—
213C22×D61C4×D411yescharacteristic
214C22×D61#12112yes—
215C22×D61#12412yes—
216C22×D61C2×#4111yescharacteristic
217C2×#6923—24no—
218C2×#6923—44no—
219C2×#6923—48no—
220Q8×C61—22no—
221Q8×C61—22no—
222Q8×C61—42no—
223D4×C61—22no—
224D4×C61—22no—
225D4×C61—42no—
226C2×C4×C61—22no—
227C2×C4×C61—42no—
228C2×C4×C61C2×C22⋊C412yes—
229C2×C4×C61C4×D412yes—
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—42no—
233C22⋊D61—42no—
234C22⋊D61—44no—
235C2×Dic61—22no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61—44no—
240C2×Dic61C4×D411yescharacteristic
241C2×Dic61#12112yes—
242C2×Dic61#12712yes—
243C2×Dic61C22×D411yescharacteristic
244D244—22no—
245D244—22no—
246D244—42no—
247D244—42no—
248D244—44no—
249D244—42no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—44no—
253C4×D61C2×C22⋊C412yes—
254C4×D61C4×D412yes—
255C4×D61#12112yes—
256C4×D61#12112yes—
257C4×D61#12412yes—
258C4×D61#12712yes—
259C4×D61C22×D411yescharacteristic
260C4×D61C22×D411yescharacteristic
261C4×D61C22×D411yescharacteristic
262C4×D61C2×#4111yescharacteristic
263Dic122—22no—
264Dic122—22no—
265Dic122—42no—
266#92420—24no—
267#92420—42no—
268#92420—42no—
269C8×C61C2×C22⋊C414yes—
270#92418C2×C22⋊C414yes—
271C2×#1975—611nomaximal, Sylow
272C22×C61—44no—
273C22×C61—42no—
274C22×C61—84no—
275C22×C61#39012yes—
276C22×C61#44414yes—
277C22×C61C2×C4×D411yescharacteristic
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—24no—
281C2×D61—24no—
282C2×D61—44no—
283C2×D61—42no—
284C2×D61—84no—
285C2×D61#39012yes—
286C2×D61C2×#12111yescharacteristic
287C2×D61C2×#12411yescharacteristic
288#6923—44no—
289C4×C61—42no—
290C4×C61#39012yes—
291C4×C61C22×C22⋊C411yescharacteristic
292C4×C61C2×C4×D411yescharacteristic
293Dic61—42no—
294Dic61#39012yes—
295Dic61C2×#12111yescharacteristic
296Dic61C2×#12711yescharacteristic
297C22×#135—611no—
298C22×#108—611no—
299C22×#104—611no—
300C22×#104—611no—
301C2×#408—611no—
302C2×#408—611no—
303C22×#97—611no—
304#1975—618no—
305C2×C61—82no—
306C2×C61#197514yescomplemented
307C2×C61C2×#39011yescharacteristic
308C2×C61C2×#44412yes—
309D61—21no—
310D61—21no—
311D61—22no—
312D61—82no—
313C22×#41—611no—
314C22×#41—611no—
315C2×#135—614no—
316C2×#135—614no—
317C2×#135—1224no—
318C2×#135—1224no—
319C22×Q16—611no—
320C22×SD16—611no—
321C22×SD16#692311yescharacteristic, complemented
322C22×D8—611no—
323C22×M16—611no—
324C22×M16—611no—
325C23×C8—611no—
326C23×C8—611no—
327C22×C42—611no—
328C2×#108—614no—
329C2×#108—1224no—
330C2×#104—614no—
331C2×#104—614no—
332C2×#104—1224no—
333C2×#104—1224no—
334#408—614no—
335#408—614no—
336#408—1222no—
337#408—1222no—
338C2×C22⋊C8—1222no—
339C2×C22⋊C8—1222no—
340C2×#97—614no—
341C2×#97—1224no—
342C61C2×#197511yescharacteristic, complemented, Sylow
343C2×#41—612no—
344C2×#41—612no—
345C2×#41—612no—
346C2×#41—612no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1222no—
352C2×#41—1222no—
353C2×#41—1222no—
354C2×#41—1222no—
355C2×#41—1222no—
356C2×#41—1222no—
357C2×#41—1222no—
358C2×#41—1222no—
359C22×Q8—611no—
360C22×Q8C2×#692311yescharacteristic
361C22×D4—611no—
362C22×D4—1221no—
363C22×D4—1221no—
364C22×D4C2×#692311yescharacteristic
365C23×C4—611no—
366C23×C4—1221no—
367C23×C4—1221no—
368C23×C4—1221no—
369#135—1228no—
370#135—1228no—
371#135—12216no—
372C2×Q16—614no—
373C2×Q16—1224no—
374C2×SD16—24no—
375C2×SD16—614no—
376C2×SD16—1224no—
377C2×SD16C2×#692314yescomplemented
378C2×D8—614no—
379C2×D8—1224no—
380C2×M16—612no—
381C2×M16—612no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1222no—
385C2×M16—1222no—
386C2×M16—1222no—
387C2×M16—1222no—
388C22×C8—611no—
389C22×C8—614no—
390C22×C8—614no—
391C22×C8—612no—
392C22×C8—612no—
393C22×C8—612no—
394C22×C8—612no—
395C22×C8—612no—
396C22×C8—1222no—
397C22×C8—1222no—
398C22×C8—1221no—
399C22×C8—1221no—
400C22×C8C2×#692311yescharacteristic
401C2×C42—614no—
402C2×C42—612no—
403C2×C42—1222no—
404C2×C42—1221no—
405#108—1228no—
406#104—1228no—
407#104—1228no—
408C22⋊C8—1228no—
409C22⋊C8—1228no—
410#97—1228no—
411C24—21no—
412C24—611no—
413C24—1221no—
414#41—1222no—
415#41—1224no—
416#41—1222no—
417#41—1222no—
418#41—1224no—
419#41—1222no—
420#41—1222no—
421#41—1224no—
422#41—1222no—
423#41—1222no—
424#41—1224no—
425#41—1222no—
426#41—2442no—
427#41—2442no—
428#41—2442no—
429#41—2442no—
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—1221no—
439C2×Q8—1222no—
440C2×Q8—1222no—
441C2×Q8C22×#692312yes—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—612no—
446C2×D4—1222no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4—1221no—
453C2×D4—2442no—
454C2×D4—2442no—
455C2×D4—2442no—
456C2×D4—2442no—
457C2×D4C22×#692312yes—
458C22×C4—21no—
459C22×C4—611no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—612no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1224no—
473C22×C4—1222no—
474C22×C4—1221no—
475C22×C4—2442no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2444no—
480C22×C4C22×#692311yescharacteristic
481Q16—1228no—
482SD16—28no—
483SD16—1228no—
484D8—1228no—
485M16—1222no—
486M16—1222no—
487M16—1222no—
488M16—1222no—
489M16—2442no—
490M16—2442no—
491C2×C8—614no—
492C2×C8—612no—
493C2×C8—614no—
494C2×C8—614no—
495C2×C8—618no—
496C2×C8—614no—
497C2×C8—1222no—
498C2×C8—1224no—
499C2×C8—1222no—
500C2×C8—1224no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2442no—
504C2×C8—2442no—
505C2×C8C22⋊#692314yes—
506C2×C8C22×#692312yes—
507C42—614no—
508C42—1222no—
509C42—1224no—
510C23—22no—
511C23—42no—
512C23—44no—
513C23—612no—
514C23—612no—
515C23—611no—
516C23—611no—
517C23—1224no—
518C23—1222no—
519C23—2442no—
520C23—2444no—
521C23D4×#692311yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—42no—
525Q8—1222no—
526Q8—1222no—
527Q8—2442no—
528D4—22no—
529D4—22no—
530D4—42no—
531D4—1222no—
532D4—1222no—
533D4—2442no—
534D4—2442no—
535D4—2444no—
536D4—2442no—
537D4—2442no—
538D4—2444no—
539D4—2442no—
540C2×C4—22no—
541C2×C4—42no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—612no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—1224no—
557C2×C4—1222no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2444no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2444no—
564C2×C4—2444no—
565C2×C4—2448no—
566C2×C4—2442no—
567C2×C4C2×C22⋊#692312yes—
568C2×C4D4×#692311yescharacteristic
569C2×C4D4×#692312yes—
570C2×C4C23×#692311yescharacteristic
571C8—614no—
572C8—1224no—
573C8—2442no—
574C8—2442no—
575C8C2×C22⋊#692314yes—
576C22—42no—
577C22—44no—
578C22—84no—
579C22—611no—
580C22—611no—
581C22—612no—
582C22—1222no—
583C22—1222no—
584C22—1224no—
585C22—1224no—
586C22—4884no—
587C22—2442no—
588C22—2444no—
589C22#1684071412yes—
590C22#1684080714yes—
591C22C2×D4×#692311yescharacteristic
592C4—42no—
593C4—611no—
594C4—611no—
595C4—612no—
596C4—2444no—
597C4—2442no—
598C4#1684071412yes—
599C4C22×C22⋊#692311yescharacteristic
600C4C2×D4×#692311yescharacteristic
601C2—82no—
602C2—1221no—
603C2—1221no—
604C2—1222no—
605C2—4882no—
606C2#2146197514yesdirect product factor
607C2C2×#1684071411yescharacteristic
608C2C2×#1684080712yes—
subgroupG/H
centerC23D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×SD16×C61C4
socleC23×C61C4×D4
prime radicalC22×#14519798C2
cosocleC2×C4×D61C24
hypercenterC22×SD16#6923
hypocenterC61C2×#1975
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#14519848C2semidirect
2. C22×#14519842C2semidirect
3. C22×#14519841C2semidirect
4. C2×#16840737C2semidirect
5. C2×#16840736C2semidirect
6. C22×#14519831C2semidirect
7. #21461975C2direct (N × H)
14. C2×#14519848C22semidirect
16. C2×#14519842C22semidirect
18. C2×#14519841C22semidirect
20. #16840737C22semidirect
22. #16840736C22semidirect
26. C2×#14519831C22semidirect
31. C2×#14519798C4semidirect
33. C22×#11758202C4semidirect
34. C22×#11758190C4semidirect
35. C22×#11758199C4semidirect
37. C22×SD16×C61C4semidirect
91. C2×#11758202C2×C4semidirect
93. C2×#11758190C2×C4semidirect
95. C2×#11758199C2×C4semidirect
104. C2×SD16×C61C2×C4semidirect
306. C2×C61#1975semidirect
321. C22×SD16#6923semidirect
342. C61C2×#1975semidirect
377. C2×SD16C2×#6923semidirect
606. C2#21461975direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198482
C22×#145198422
C22×#145198412
C2×#168407372
C2×#168407362
C22×#145198312
#214619752
C22×#145197982
C2×#197561