Finite Group Databasebeta

← C2×#21461906 #30615942

Subgroups — C2×#21461906 #30615942

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840777C211yesmaximal, characteristic, complemented
2C2×#16840761C211yesmaximal, characteristic
3C22×#14519842C211yesmaximal, characteristic
4C2×M16×#6923C211yesmaximal, characteristic, complemented
5#21461906C218yesmaximal, direct product factor
6C2×#16840645C211yesmaximal, characteristic, complemented
7C2×#16840634C211yesmaximal, characteristic, complemented
8C2×#16839745C211yesmaximal, characteristic
9C22×#11758213C2211yescharacteristic
10C2×D61⋊M16C2211yescharacteristic
11C2×#14519856C2211yescharacteristic
12C22×C4×#6923C2211yescharacteristic
13#16840777—22no—
14#16840777C2214yescomplemented
15C2×#14519848—21no—
16C2×#14519847—21no—
17#16840761—22no—
18#16840761C2214yes—
19C2×#14519842—21no—
20C2×#14519842—21no—
21C2×#14519842—21no—
22C2×#14519842—21no—
23C2×#14519842—22no—
24C2×#14519842C2214yes—
25M16×#6923—22no—
26M16×#6923C2214yescomplemented
27C2×#14519831—21no—
28C2×C8×#6923—21no—
29#16840645C2214yescomplemented
30#16840634C2214yescomplemented
31C22×#11758226C2211yescharacteristic
32C2×M16×D61C2211yescharacteristic
33C2×M16×D61C2211yescharacteristic
34#16839745C414yescomplemented
35#16839745C2214yes—
36C2×#14519696C411yescharacteristic, complemented
37C2×#14519693C411yescharacteristic, complemented
38C2×#14519693C411yescharacteristic, complemented
39C2×#101×C61C411yescharacteristic, complemented
40C23×#6923—21no—
41C2×#11758213—21no—
42C2×#11758213—21no—
43C2×#11758213—21no—
44C2×#11758213—21no—
45C2×#11758213—21no—
46C2×#11758213D411yescharacteristic
47C2×#11758213D411yescharacteristic
48C2×#11758213C2312yes—
49D61⋊M16—21no—
50D61⋊M16—21no—
51D61⋊M16D412yes—
52D61⋊M16C2312yes—
53C2×#11758217—21no—
54C2×D61⋊C8—21no—
55C22×#92420—21no—
56#14519856—21no—
57#14519856—21no—
58#14519856—21no—
59#14519856C2312yes—
60C2×C4⋊#6923—21no—
61C2×C22⋊#6923—21no—
62C2×C4×#6923—21no—
63C2×C4×#6923—21no—
64C2×C4×#6923—21no—
65C2×C4×#6923—21no—
66C2×C4×#6923D411yescharacteristic
67C2×C4×#6923D411yescharacteristic
68C2×C4×#6923D412yes—
69C2×C4×#6923C2312yes—
70#14519848—24no—
71#14519847—24no—
72#14519842—24no—
73#14519842—24no—
74#14519842—24no—
75#14519842—24no—
76#14519831—24no—
77C8×#6923—24no—
78C2×#11758226—21no—
79C2×#11758226—21no—
80C2×#11758226—21no—
81C2×#11758226—21no—
82C2×#11758226—21no—
83C2×#11758226—21no—
84C2×#11758226—21no—
85C2×#11758226—21no—
86C2×#11758226—21no—
87C2×#11758226—21no—
88C2×#11758226C2×C412yes—
89C2×#11758226C2312yes—
90C22×D244—21no—
91C22×D244C2×C411yescharacteristic
92C22×C4×D61—21no—
93C22×C4×D61C2311yescharacteristic
94C2×#11758194C2×C411yescharacteristic
95C2×#11758194C2×C411yescharacteristic
96C2×#11758189—21no—
97C2×#11758189—21no—
98M16×D61—21no—
99M16×D61—21no—
100M16×D61—21no—
101M16×D61—21no—
102M16×D61C2×C412yes—
103M16×D61C2×C412yes—
104M16×D61C2312yes—
105M16×D61C2312yes—
106C2×C8×D61—21no—
107C2×C8×D61—21no—
108#14519696C2×C414yescomplemented
109#14519693C2×C414yescomplemented
110#14519693C2×C414yescomplemented
111C22×Q8×C61C2×C411yescharacteristic
112C2×M16×C61C2×C411yescharacteristic
113C2×M16×C61C2×C411yescharacteristic
114#101×C61C2×C414yescomplemented
115C23×D61—21no—
116C23×D61#4111yescharacteristic
117C22×#6923—21no—
118C22×#6923—22no—
119C22×#6923—21no—
120C22×#6923—22no—
121C22×#6923—44no—
122C22×#6923—41no—
123C2×Q8×C61—21no—
124C2×Q8×C61—21no—
125C2×Q8×C61—21no—
126C2×Q8×C61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61C22×C412yes—
129C22×C4×C61—21no—
130C22×C4×C61C22×C411yescharacteristic
131C22×Dic61#4111yescharacteristic
132#11758226—22no—
133#11758226—22no—
134#11758226—22no—
135#11758226—22no—
136#11758226—22no—
137#11758226—22no—
138#11758226—22no—
139#11758226—22no—
140#11758226—41no—
141#11758226—41no—
142#11758226—41no—
143#11758226—41no—
144#11758226—41no—
145#11758226—41no—
146#11758226—41no—
147#11758226—41no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—22no—
153C2×D244—22no—
154C2×D244—21no—
155C2×D244—41no—
156C2×D244—41no—
157C2×D244—41no—
158C2×D244—41no—
159C2×D244C22×C412yes—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—41no—
163C2×C4×D61—41no—
164C2×C4×D61—41no—
165C2×C4×D61—41no—
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61#4111yescharacteristic
172C2×C4×D61#4111yescharacteristic
173C2×C4×D61#4111yescharacteristic
174C2×C4×D61#4111yescharacteristic
175C2×C4×D61#4111yescharacteristic
176C2×C4×D61#4111yescharacteristic
177C2×C4×D61C2411yescharacteristic
178C22⋊#6923—22no—
179C22⋊#6923—41no—
180#11758217—22no—
181#11758217—22no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—22no—
185C2×#92420—41no—
186C2×#92420—41no—
187C4⋊#6923—22no—
188C4⋊#6923—41no—
189C4×#6923—21no—
190C4×#6923—22no—
191C4×#6923—21no—
192C4×#6923—22no—
193C4×#6923—22no—
194C4×#6923—41no—
195C4×#6923C2×D412yes—
196C4×#6923C2×D412yes—
197#11758213—21no—
198#11758213—21no—
199#11758213—22no—
200#11758213—22no—
201#11758213—41no—
202#11758213—41no—
203#11758213C2×D412yes—
204#11758213C2×D412yes—
205D61⋊C8—22no—
206D61⋊C8—22no—
207M16×C61—21no—
208M16×C61—21no—
209M16×C61C22×C412yes—
210M16×C61C22×C412yes—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213#11758194—21no—
214#11758194—21no—
215#11758194C22×C412yes—
216#11758194C22×C412yes—
217C2×#92418—21no—
218C2×#92418—21no—
219#11758189—22no—
220#11758189—22no—
221#11758189—22no—
222#11758189—22no—
223C8×D61—22no—
224C8×D61—22no—
225C8×D61—22no—
226C8×D61—22no—
227C23×C61#11711yescharacteristic
228C22×D61—22no—
229C22×D61—42no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—82no—
233C22×D61#11711yescharacteristic
234C22×D61#12311yescharacteristic
235C22×D61#12311yescharacteristic
236C22×D61#12411yescharacteristic
237C22×D61#12411yescharacteristic
238C22×D61C2×#4111yescharacteristic
239C2×#6923—24no—
240C2×#6923—22no—
241C2×#6923—22no—
242C2×#6923—44no—
243C2×#6923—44no—
244C2×#6923—42no—
245C2×#6923—42no—
246C2×#6923—82no—
247Q8×C61—22no—
248Q8×C61—22no—
249Q8×C61—41no—
250Q8×C61—41no—
251C2×C4×C61—22no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61#11711yescharacteristic
255C2×C4×C61C4×D411yescharacteristic
256C2×C4×C61C4×D411yescharacteristic
257C2×C4×C61C4×D411yescharacteristic
258C2×C4×C61C4×D411yescharacteristic
259C2×C4×C61C23×C411yescharacteristic
260C2×Dic61#11711yescharacteristic
261C2×Dic61#12111yescharacteristic
262C2×Dic61#12111yescharacteristic
263C2×Dic61#12611yescharacteristic
264C2×Dic61#12611yescharacteristic
265C2×Dic61C2×#4111yescharacteristic
266D244—22no—
267D244—22no—
268D244—42no—
269D244—42no—
270D244—42no—
271D244—42no—
272D244—41no—
273D244—41no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—42no—
277C4×D61—42no—
278C4×D61C4×D411yescharacteristic
279C4×D61C4×D411yescharacteristic
280C4×D61C4×D411yescharacteristic
281C4×D61C4×D411yescharacteristic
282C4×D61#12111yescharacteristic
283C4×D61#12111yescharacteristic
284C4×D61#12311yescharacteristic
285C4×D61#12311yescharacteristic
286C4×D61#12411yescharacteristic
287C4×D61#12411yescharacteristic
288C4×D61#12611yescharacteristic
289C4×D61#12611yescharacteristic
290C4×D61C22×D411yescharacteristic
291C4×D61C22×D411yescharacteristic
292C4×D61C2×#4111yescharacteristic
293C4×D61C2×#4111yescharacteristic
294#92420—22no—
295#92420—22no—
296#92420—42no—
297C8×C61—22no—
298C8×C61—22no—
299#92418—22no—
300#92418—22no—
301C2×#1932—611nomaximal, Sylow
302C22×C61—22no—
303C22×C61#38811yescharacteristic
304C22×C61#38811yescharacteristic
305C22×C61C2×#11711yescharacteristic
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—42no—
313C2×D61—82no—
314C2×D61—82no—
315C2×D61—82no—
316C2×D61#38811yescharacteristic
317C2×D61#38811yescharacteristic
318C2×D61C2×#12311yescharacteristic
319C2×D61C2×#12411yescharacteristic
320#6923—24no—
321#6923—42no—
322#6923—82no—
323C4×C61—42no—
324C4×C61#38811yescharacteristic
325C4×C61#38811yescharacteristic
326C4×C61C2×C4×D411yescharacteristic
327C4×C61C2×C4×D411yescharacteristic
328Dic61#38811yescharacteristic
329Dic61#38811yescharacteristic
330Dic61C2×#12111yescharacteristic
331Dic61C2×#12611yescharacteristic
332C2×#430—611no—
333C2×#421—611no—
334C22×#104—611no—
335C2×#413—611no—
336C2×C4×M16—611no—
337#1932—618no—
338C2×#344—611no—
339C2×#339—611no—
340C2×C61—21no—
341C2×C61—21no—
342C2×C61#193212yescomplemented
343C2×C61C2×#38811yescharacteristic
344D61—21no—
345D61—21no—
346D61—21no—
347D61—21no—
348D61—82no—
349C22×#41—611no—
350C22×M16—611no—
351C22×M16—611no—
352C22×M16—611no—
353C22×M16—611no—
354C2×#117—611no—
355C22×C42—611no—
356#430—614no—
357#430—1222no—
358C2×#108—1221no—
359C2×#108—1221no—
360#421—614no—
361#421—1222no—
362C2×#104—614no—
363C2×#104—1221no—
364C2×#104—1221no—
365C2×#104—1222no—
366C2×#104—1221no—
367C2×#104—1221no—
368#413—614no—
369#413—614no—
370C2×#101—611no—
371C2×#101#692311yescharacteristic, complemented
372C2×#100—611no—
373C2×#100—611no—
374C4×M16—614no—
375C4×M16—1222no—
376C2×#97—1221no—
377C2×C4×C8—1221no—
378#344—614no—
379#339—614no—
380C61C2×#193211yescharacteristic, complemented, Sylow
381C2×#41—612no—
382C2×#41—612no—
383C2×#41—1221no—
384C2×#41—1221no—
385C2×#41—1221no—
386C2×#41—1221no—
387C2×#41—1221no—
388C2×#41—1221no—
389C2×#41—1221no—
390C2×#41—1221no—
391C2×#41—1221no—
392C2×#41—1221no—
393C22×Q8C2×#692311yescharacteristic
394C22×D4—611no—
395C22×D4—1221no—
396C23×C4—611no—
397C23×C4—1221no—
398C23×C4—1221no—
399C2×M16—612no—
400C2×M16—612no—
401C2×M16—611no—
402C2×M16—611no—
403C2×M16—611no—
404C2×M16—611no—
405C2×M16—612no—
406C2×M16—612no—
407C2×M16—612no—
408C2×M16—612no—
409C2×M16—612no—
410C2×M16—1221no—
411C2×M16—1221no—
412C2×M16—1221no—
413C2×M16—1221no—
414C2×M16—1221no—
415C2×M16—1221no—
416C2×M16—1221no—
417C2×M16—1221no—
418C2×M16—1221no—
419C2×M16—1221no—
420C2×M16—1221no—
421C2×M16—1221no—
422C2×M16—1221no—
423C2×M16—1221no—
424C2×M16C2×#692311yescharacteristic
425C2×M16C2×#692311yescharacteristic
426C22×C8—1221no—
427C22×C8—1221no—
428C22×C8—1221no—
429C22×C8—1221no—
430#117—612no—
431#117—1221no—
432#117—1221no—
433#117—1221no—
434C2×C4⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—612no—
439C2×C42—612no—
440C2×C42—1221no—
441C2×C42—1221no—
442C2×C42—1221no—
443C2×C42—1221no—
444#108—1224no—
445#108—1224no—
446#104—1224no—
447#104—1224no—
448#104—1224no—
449#104—1224no—
450#101—614no—
451#101C2×#692314yescomplemented
452#100—614no—
453#100—614no—
454#97—1224no—
455C4×C8—1224no—
456C24—611no—
457C24—1221no—
458#41—1222no—
459#41—1222no—
460#41—1222no—
461#41—1222no—
462#41—1222no—
463#41—1222no—
464#41—1222no—
465#41—1222no—
466#41—2441no—
467#41—2441no—
468#41—2441no—
469#41—2441no—
470#41—2441no—
471#41—2441no—
472#41—2441no—
473#41—2441no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×#692312yes—
480C2×D4—612no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—1221no—
487C2×D4—1221no—
488C2×D4—2441no—
489C2×D4—2441no—
490C2×D4—2441no—
491C2×D4—2441no—
492C22×C4—21no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1221no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1221no—
512C22×C4—2441no—
513C22×C4—2441no—
514C22×C4—2441no—
515C22×C4—2441no—
516C22×C4—2444no—
517C22×C4—2441no—
518C22×C4C22×#692311yescharacteristic
519M16—21no—
520M16—21no—
521M16—612no—
522M16—612no—
523M16—612no—
524M16—612no—
525M16—1222no—
526M16—1222no—
527M16—1222no—
528M16—1222no—
529M16—1221no—
530M16—1221no—
531M16—1222no—
532M16—1222no—
533M16—1221no—
534M16—1221no—
535M16—1222no—
536M16—1222no—
537M16—2441no—
538M16—2441no—
539M16C22×#692312yes—
540M16C22×#692312yes—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—1222no—
544C2×C8—1222no—
545C2×C8—1222no—
546C2×C8—1222no—
547C2×C8—1222no—
548C2×C8—1222no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1222no—
554C2×C8—2441no—
555C2×C8—2441no—
556C4⋊C4—1222no—
557C4⋊C4—2441no—
558C22⋊C4—1222no—
559C22⋊C4—2441no—
560C42—612no—
561C42—612no—
562C42—1221no—
563C42—1222no—
564C42—1221no—
565C42—1222no—
566C42—1222no—
567C42—2441no—
568C23—611no—
569C23—611no—
570C23—611no—
571C23—611no—
572C23—611no—
573C23—611no—
574C23—1222no—
575C23—4882no—
576C23—2442no—
577C23—2441no—
578C23—2441no—
579C23#1451985611yescharacteristic
580Q8—22no—
581Q8—22no—
582Q8—41no—
583Q8—41no—
584D4—1222no—
585D4—1222no—
586D4—2442no—
587D4—2442no—
588D4—2442no—
589D4—2442no—
590D4—2441no—
591D4—2441no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—611no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—611no—
616C2×C4—611no—
617C2×C4—1222no—
618C2×C4—1224no—
619C2×C4—1222no—
620C2×C4—4882no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4—2442no—
624C2×C4—2442no—
625C2×C4—2444no—
626C2×C4—2444no—
627C2×C4—2442no—
628C2×C4—2442no—
629C2×C4#1451985611yescharacteristic
630C2×C4D4×#692311yescharacteristic
631C2×C4D4×#692311yescharacteristic
632C2×C4D4×#692311yescharacteristic
633C2×C4D4×#692311yescharacteristic
634C2×C4C23×#692311yescharacteristic
635C8—22no—
636C8—22no—
637C8—1222no—
638C8—1222no—
639C8—1222no—
640C8—1222no—
641C8—2442no—
642C22—22no—
643C22—611no—
644C22—611no—
645C22—611no—
646C22—611no—
647C22—1222no—
648C22—1222no—
649C22—4882no—
650C22—4882no—
651C22—4882no—
652C22—2441no—
653C22—2441no—
654C22—2441no—
655C22—2441no—
656C22—2442no—
657C22#1684071211yescharacteristic
658C22#1684071211yescharacteristic
659C22C2×#1451985611yescharacteristic
660C4—42no—
661C4—611no—
662C4—611no—
663C4—611no—
664C4—611no—
665C4—1224no—
666C4—4882no—
667C4—2442no—
668C4#1684071211yescharacteristic
669C4#1684071211yescharacteristic
670C4C2×D4×#692311yescharacteristic
671C4C2×D4×#692311yescharacteristic
672C2—21no—
673C2—21no—
674C2—1221no—
675C2—1221no—
676C2—1221no—
677C2—1221no—
678C2—4882no—
679C2#2146190612yesdirect product factor
680C2C2×#1684071211yescharacteristic
subgroupG/H
centerC22#16840712
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#101×C61C4
socleC22×C61#388
prime radicalC22×#11758226C22
cosocleC2×C4×D61C24
hypercenterC2×#101#6923
hypocenterC61C2×#1932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#16840777C2semidirect
4. C2×M16×#6923C2semidirect
5. #21461906C2direct (N × H)
6. C2×#16840645C2semidirect
7. C2×#16840634C2semidirect
14. #16840777C22semidirect
26. M16×#6923C22semidirect
29. #16840645C22semidirect
30. #16840634C22semidirect
34. #16839745C4semidirect
36. C2×#14519696C4semidirect
37. C2×#14519693C4semidirect
38. C2×#14519693C4semidirect
39. C2×#101×C61C4semidirect
108. #14519696C2×C4semidirect
109. #14519693C2×C4semidirect
110. #14519693C2×C4semidirect
114. #101×C61C2×C4semidirect
342. C2×C61#1932semidirect
371. C2×#101#6923semidirect
380. C61C2×#1932semidirect
451. #101C2×#6923semidirect
679. C2#21461906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407772
C2×#168407612
C22×#145198422
C2×M16×#69232
#214619062
C2×#168406452
C2×#168406342
C2×#168397452
C2×#193261