Finite Group Databasebeta

← C2×#21461909 #30615949

Subgroups — C2×#21461909 #30615949

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519839C211yesmaximal, characteristic
2C22×C8×#6923C211yesmaximal, characteristic, complemented
3C2×#16840714C211yesmaximal, characteristic
4C2×#16840713C211yesmaximal, characteristic, complemented
5#21461909C218yesmaximal, direct product factor
6C2×#16840636C211yesmaximal, characteristic, complemented
7C2×#16840635C211yesmaximal, characteristic, complemented
8C2×#102×D61C211yesmaximal, characteristic
9C22×D61⋊C8C2211yescharacteristic
10C22×C4⋊#6923—21no—
11C22×C4⋊#6923C2211yescharacteristic
12C22×C4⋊#6923C2211yescharacteristic
13C22×C22⋊#6923—21no—
14C22×C22⋊#6923—21no—
15C22×C4×#6923C2211yescharacteristic
16C2×#14519839—24no—
17C2×#14519839C2214yes—
18C2×C8×#6923—24no—
19C2×C8×#6923C2214yescomplemented
20#16840714—22no—
21#16840714C2214yes—
22#16840713—22no—
23#16840713C2214yescomplemented
24C2×(C2×#6923)⋊C4—21no—
25#16840636C2214yescomplemented
26#16840635C2214yescomplemented
27C22×D4×D61C2211yescharacteristic
28C22×C8×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×#14519699C411yescharacteristic, complemented
31C2×#14519698C411yescharacteristic, complemented
32C2×#14519697C411yescharacteristic, complemented
33#102×D61C414yescomplemented
34#102×D61C2214yes—
35C2×#102×C61C411yescharacteristic, complemented
36C23×#6923—21no—
37C23×#6923—21no—
38C23×#6923D411yescharacteristic
39C23×#6923D411yescharacteristic
40C2×D61⋊C8—21no—
41C2×D61⋊C8—22no—
42C2×D61⋊C8D414yes—
43C2×D61⋊C8C2312yes—
44C22×#92420—21no—
45C2×C4⋊#6923—22no—
46C2×C4⋊#6923—22no—
47C2×C4⋊#6923—22no—
48C2×C4⋊#6923—22no—
49C2×C4⋊#6923—24no—
50C2×C4⋊#6923—21no—
51C2×C4⋊#6923—21no—
52C2×C4⋊#6923—44no—
53C2×C4⋊#6923C2312yes—
54C2×C4⋊#6923C2312yes—
55C2×C22⋊#6923—24no—
56C2×C22⋊#6923—24no—
57C2×C22⋊#6923—44no—
58C2×C22⋊#6923—44no—
59C2×C4×#6923—22no—
60C2×C4×#6923—22no—
61C2×C4×#6923D412yes—
62C2×C4×#6923C2312yes—
63#14519839—28no—
64C8×#6923—28no—
65(C2×#6923)⋊C4—24no—
66C24×D61—21no—
67C22×D244C2×C411yescharacteristic
68C22×C22⋊D61—21no—
69C2×D4×D61—22no—
70C2×D4×D61—21no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61—22no—
74C2×D4×D61—21no—
75C2×D4×D61C2×C412yes—
76C2×D4×D61C2312yes—
77C22×C4×D61—21no—
78C22×C4×D61C2311yescharacteristic
79C22×#92418C2×C411yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61C2×C412yes—
83C2×C8×D61C2312yes—
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×#11758196—21no—
86C4⋊C4×D61—21no—
87C4⋊C4×D61—21no—
88C4⋊C4×D61C2×C412yes—
89C4⋊C4×D61C2312yes—
90#14519699C2×C414yescomplemented
91#14519698C2×C414yescomplemented
92#14519697C2×C414yescomplemented
93C22×D4×C61C2×C411yescharacteristic
94C22×C8×C61C2×C411yescharacteristic
95C2×C4⋊C4×C61C2×C411yescharacteristic
96#102×C61C2×C414yescomplemented
97C24×C61—21no—
98C23×D61—21no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61—42no—
102C23×D61—42no—
103C23×D61—42no—
104C23×D61—42no—
105C23×D61—42no—
106C23×D61—42no—
107C23×D61C2×D411yescharacteristic
108C22×#6923—22no—
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—22no—
112C22×#6923—22no—
113C22×#6923—22no—
114C22×#6923—42no—
115C22×#6923—42no—
116C22×#6923—42no—
117C22×#6923—42no—
118C22×#6923—42no—
119C22×#6923—42no—
120C22×#6923D814yes—
121C22×#6923SD1614yes—
122C22×#6923C2×D412yes—
123C22×#6923C2×D412yes—
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C2×D4×C61—21no—
127C2×D4×C61C22×C412yes—
128C22×C4×C61—21no—
129C22×C4×C61C22×C411yescharacteristic
130C2×C22⋊D61—22no—
131C2×C22⋊D61—22no—
132C2×C22⋊D61—42no—
133C2×C22⋊D61—42no—
134C22×Dic61—21no—
135C22×Dic61#4111yescharacteristic
136D4×D61—24no—
137D4×D61—24no—
138D4×D61—22no—
139D4×D61—22no—
140D4×D61—22no—
141D4×D61—22no—
142D4×D61—42no—
143D4×D61—42no—
144D4×D61—42no—
145D4×D61—42no—
146C2×D244—22no—
147C2×D244—22no—
148C2×D244—21no—
149C2×D244C22×C412yes—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C2×D412yes—
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4112yes—
158C2×C4×D61#4112yes—
159C2×C4×D61#4112yes—
160C2×C4×D61#4111yescharacteristic
161C2×C4×D61C2411yescharacteristic
162C22⋊#6923—48no—
163C22⋊#6923—48no—
164C2×#92420—24no—
165C2×#92420—22no—
166C4⋊#6923—22no—
167C4⋊#6923—22no—
168C4⋊#6923—22no—
169C4⋊#6923—22no—
170C4⋊#6923—48no—
171C4⋊#6923—42no—
172C4⋊#6923—42no—
173C4×#6923—24no—
174C4×#6923—22no—
175C4×#6923—22no—
176D61⋊C8—24no—
177D61⋊C8—22no—
178D61⋊C8C2×D414yes—
179C2×C8×C61—22no—
180C2×C8×C61C22×C412yes—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22×C412yes—
183C4⋊Dic61—21no—
184C4⋊Dic61C22×C412yes—
185#11758196—22no—
186#11758196—22no—
187C2×#92418—22no—
188C2×#92418C22×C412yes—
189C8×D61—24no—
190C8×D61—22no—
191C8×D61—22no—
192C23×C61—22no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61C4×D411yescharacteristic
197C22×D61—22no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—44no—
208C22×D61—44no—
209C22×D61—44no—
210C22×D61—84no—
211C22×D61—84no—
212C22×D61—84no—
213C22×D61—84no—
214C22×D61C4×D411yescharacteristic
215C22×D61#12112yes—
216C22×D61#12412yes—
217C22×D61C2×D812yes—
218C22×D61C2×SD1612yes—
219C22×D61#13512yes—
220C22×D61#13512yes—
221C22×D61C22×D411yescharacteristic
222C2×#6923—22no—
223C2×#6923—22no—
224C2×#6923—22no—
225C2×#6923—22no—
226C2×#6923—28no—
227C2×#6923—28no—
228C2×#6923—42no—
229C2×#6923—42no—
230C2×#6923—42no—
231C2×#6923—42no—
232C2×#6923—42no—
233C2×#6923—42no—
234C2×#6923—84no—
235C2×#6923—84no—
236C2×#6923C2×D814yes—
237C2×#6923C2×SD1614yes—
238D4×C61—22no—
239D4×C61—22no—
240D4×C61—42no—
241C2×C4×C61—22no—
242C2×C4×C61—42no—
243C2×C4×C61#11712yes—
244C2×C4×C61C4×D412yes—
245C2×C4×C61C4×D411yescharacteristic
246C2×C4×C61C23×C411yescharacteristic
247C22⋊D61—42no—
248C22⋊D61—42no—
249C22⋊D61—44no—
250C2×Dic61—22no—
251C2×Dic61—42no—
252C2×Dic61C4×D411yescharacteristic
253C2×Dic61#12312yes—
254C2×Dic61#12612yes—
255C2×Dic61C2×#4111yescharacteristic
256D244—22no—
257D244—22no—
258D244—42no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—44no—
262C4×D61#11712yes—
263C4×D61C4×D412yes—
264C4×D61#12112yes—
265C4×D61#12312yes—
266C4×D61#12412yes—
267C4×D61#12612yes—
268C4×D61C22×D411yescharacteristic
269C4×D61C2×#4111yescharacteristic
270C4×D61C2×#4111yescharacteristic
271C4×D61C2×#4111yescharacteristic
272#92420—24no—
273C8×C61—22no—
274#92418—22no—
275C2×#1934—611nomaximal, Sylow
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—84no—
280C22×C61#38812yes—
281C22×C61C4×D812yes—
282C22×C61C4×SD1612yes—
283C22×C61C2×C4×D411yescharacteristic
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—84no—
288C2×D61—82no—
289C2×D61—82no—
290C2×D61—88no—
291C2×D61—82no—
292C2×D61—82no—
293C2×D61#38812yes—
294C2×D61C4×D812yes—
295C2×D61C4×SD1612yes—
296C2×D61#46514yes—
297C2×D61#46614yes—
298C2×D61#48614yes—
299C2×D61#48814yes—
300C2×D61C2×#12111yescharacteristic
301C2×D61C2×#12411yescharacteristic
302C2×D61C22×D811yescharacteristic
303C2×D61C22×SD1611yescharacteristic
304C2×D61C2×#13511yescharacteristic
305C2×D61C2×#13511yescharacteristic
306#6923—24no—
307#6923—24no—
308#6923—82no—
309#6923—82no—
310C4×C61—42no—
311C4×C61#38812yes—
312C4×C61C2×#11711yescharacteristic
313C4×C61C2×C4×D411yescharacteristic
314Dic61—42no—
315Dic61#38812yes—
316Dic61C2×#12311yescharacteristic
317Dic61C2×#12611yescharacteristic
318C22×#102—611no—
319C22×#102—611no—
320C22×C4×C8—611no—
321C2×#390—611no—
322C2×#389—611no—
323#1934—618no—
324C2×#340—611no—
325C2×#340—611no—
326C2×C61—82no—
327C2×C61#193414yescomplemented
328C2×C61C2×#38811yescharacteristic
329C2×C61C2×C4×D811yescharacteristic
330C2×C61C2×C4×SD1611yescharacteristic
331D61—82no—
332D61#193414yescomplemented
333D61C2×#46511yescharacteristic
334D61C2×#46611yescharacteristic
335D61C2×#48611yescharacteristic
336D61C2×#48811yescharacteristic
337C23×D4—611no—
338C23×C8—611no—
339C23×C8—611no—
340C22×C4⋊C4—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—611no—
343C22×C4⋊C4—1221no—
344C22×C22⋊C4—1221no—
345C22×C22⋊C4—1221no—
346C22×C42—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—614no—
351C2×#102—614no—
352C2×#102—614no—
353C2×#102—1224no—
354C2×#102#692311yescharacteristic, complemented
355C2×C4×C8—614no—
356C2×C4×C8—1224no—
357#390—614no—
358#390—1222no—
359#389—614no—
360#389—1222no—
361C2×#95—1221no—
362#340—614no—
363#340—614no—
364C61C2×#193411yescharacteristic, complemented, Sylow
365C25—1221no—
366C22×D4—612no—
367C22×D4—612no—
368C22×D4—611no—
369C22×D4—1222no—
370C22×D4—1222no—
371C22×D4—1222no—
372C22×D4—1222no—
373C22×D4—1221no—
374C22×D4—1221no—
375C22×D4—1221no—
376C22×D4C2×#692311yescharacteristic
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—1221no—
381C23×C4—1221no—
382C23×C4—1221no—
383C22×C8—614no—
384C22×C8—612no—
385C22×C8—611no—
386C22×C8—612no—
387C22×C8—612no—
388C22×C8—1222no—
389C22×C8—1222no—
390C22×C8—1221no—
391C22×C8—1222no—
392C22×C8—1221no—
393C22×C8C2×#692311yescharacteristic
394C2×C4⋊C4—611no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1224no—
409C2×C4⋊C4—2444no—
410C2×C4⋊C4C2×#692311yescharacteristic
411C2×C22⋊C4—1224no—
412C2×C22⋊C4—1224no—
413C2×C22⋊C4—2444no—
414C2×C22⋊C4—2444no—
415C2×C42—612no—
416C2×C42—612no—
417C2×C42—1222no—
418C2×C42—1222no—
419#102—614no—
420#102—614no—
421#102—614no—
422#102—1228no—
423#102C2×#692314yescomplemented
424C4×C8—1228no—
425#95—1224no—
426C24—21no—
427C24—611no—
428C24—1222no—
429C24—1222no—
430C24—1221no—
431C24—2442no—
432C24—2442no—
433C24—2442no—
434C24—2442no—
435C24—2442no—
436C24—2442no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—612no—
441C2×D4—1222no—
442C2×D4—1224no—
443C2×D4—1222no—
444C2×D4—1222no—
445C2×D4—1224no—
446C2×D4—1222no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1222no—
451C2×D4—1221no—
452C2×D4—2442no—
453C2×D4—2442no—
454C2×D4—2442no—
455C2×D4—2442no—
456C2×D4—2442no—
457C2×D4—2442no—
458C2×D4C22×#692312yes—
459C22×C4—21no—
460C22×C4—611no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—611no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—614no—
472C22×C4—614no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4C22×#692311yescharacteristic
491C2×C8—22no—
492C2×C8—614no—
493C2×C8—612no—
494C2×C8—1222no—
495C2×C8—1224no—
496C2×C8—1222no—
497C2×C8—1224no—
498C2×C8—1222no—
499C2×C8—1224no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8C22×#692312yes—
503C4⋊C4—21no—
504C4⋊C4—612no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1221no—
512C4⋊C4—2442no—
513C4⋊C4—2442no—
514C4⋊C4—2448no—
515C4⋊C4C22×#692312yes—
516C22⋊C4—2448no—
517C22⋊C4—2448no—
518C42—1222no—
519C42—1224no—
520C42—1222no—
521C23—22no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—612no—
526C23—612no—
527C23—612no—
528C23—612no—
529C23—612no—
530C23—612no—
531C23—611no—
532C23—611no—
533C23—1222no—
534C23—4884no—
535C23—4884no—
536C23—4884no—
537C23—4884no—
538C23—2442no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23—2444no—
543C23—2442no—
544C23—2444no—
545C23—2442no—
546C23—2444no—
547C23—2442no—
548C23—2442no—
549C23—2442no—
550C23D4×#692311yescharacteristic
551D4—22no—
552D4—22no—
553D4—42no—
554D4—1222no—
555D4—1222no—
556D4—2442no—
557D4—2442no—
558D4—2444no—
559D4—2442no—
560C2×C4—22no—
561C2×C4—42no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—612no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—614no—
577C2×C4—614no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1228no—
583C2×C4—1228no—
584C2×C4—1222no—
585C2×C4—4884no—
586C2×C4—4884no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2444no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4#1451985612yes—
598C2×C4D4×#692311yescharacteristic
599C2×C4D4×#692312yes—
600C2×C4C23×#692311yescharacteristic
601C8—22no—
602C8—1224no—
603C8—1222no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—84no—
608C22—611no—
609C22—611no—
610C22—612no—
611C22—611no—
612C22—611no—
613C22—612no—
614C22—611no—
615C22—611no—
616C22—612no—
617C22—614no—
618C22—614no—
619C22—614no—
620C22—614no—
621C22—4882no—
622C22—4882no—
623C22—4882no—
624C22—4882no—
625C22—4888no—
626C22—4884no—
627C22—2442no—
628C22—2442no—
629C22—2442no—
630C22#1684071212yes—
631C22D8×#692312yes—
632C22SD16×#692312yes—
633C22C2×D4×#692311yescharacteristic
634C4—42no—
635C4—611no—
636C4—611no—
637C4—612no—
638C4—1224no—
639C4—1224no—
640C4—4882no—
641C4—4882no—
642C4—2442no—
643C4#1684071212yes—
644C4C2×#1451985611yescharacteristic
645C4C2×D4×#692311yescharacteristic
646C2—82no—
647C2—611no—
648C2—611no—
649C2—611no—
650C2—611no—
651C2—614no—
652C2—4882no—
653C2#2146190914yesdirect product factor
654C2C2×#1684071211yescharacteristic
655C2C2×D8×#692311yescharacteristic
656C2C2×SD16×#692311yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#102×C61C4
socleC23×C61C4×D4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#102#6923
hypocenterC61C2×#1934
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×C8×#6923C2semidirect
4. C2×#16840713C2semidirect
5. #21461909C2direct (N × H)
6. C2×#16840636C2semidirect
7. C2×#16840635C2semidirect
19. C2×C8×#6923C22semidirect
23. #16840713C22semidirect
25. #16840636C22semidirect
26. #16840635C22semidirect
30. C2×#14519699C4semidirect
31. C2×#14519698C4semidirect
32. C2×#14519697C4semidirect
33. #102×D61C4semidirect
35. C2×#102×C61C4semidirect
90. #14519699C2×C4semidirect
91. #14519698C2×C4semidirect
92. #14519697C2×C4semidirect
96. #102×C61C2×C4semidirect
327. C2×C61#1934semidirect
332. D61#1934semidirect
354. C2×#102#6923semidirect
364. C61C2×#1934semidirect
423. #102C2×#6923semidirect
653. C2#21461909direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198392
C22×C8×#69232
C2×#168407142
C2×#168407132
#214619092
C2×#168406362
C2×#168406352
C2×#102×D612
C2×#193461