Finite Group Databasebeta

← C2×#21461904 #30615936

Subgroups — C2×#21461904 #30615936

Order 15616.

1026 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×#16840773C211yesmaximal, characteristic
2C2×#16840755C211yesmaximal, characteristic
3C22×#14519840C211yesmaximal, characteristic
4C2×#16840728C211yesmaximal, characteristic
5#21461904C218yesmaximal, direct product factor
6C2×#16840641C211yesmaximal, characteristic
7C2×#16840637C211yesmaximal, characteristic
8C2×#101×D61C211yesmaximal, characteristic
9C2×D61⋊M16C2211yescharacteristic
10C22×D61⋊C8C2211yescharacteristic
11C2×#14519856C2211yescharacteristic
12C22×C4⋊#6923C2211yescharacteristic
13#16840773—22no—
14#16840773C2214yes—
15C2×#14519846—21no—
16C2×#14519845—21no—
17#16840755—22no—
18#16840755C2214yes—
19C2×#14519840—21no—
20C2×#14519840—21no—
21C2×#14519840—22no—
22C2×#14519840—21no—
23C2×#14519840—21no—
24C2×#14519840C2214yes—
25#16840728—22no—
26#16840728C2214yes—
27C2×#14519831—21no—
28C2×C8×#6923—21no—
29#16840641C2214yes—
30#16840637C2214yes—
31C22×Q8×D61C2211yescharacteristic
32C2×M16×D61C2211yescharacteristic
33C2×M16×D61C2211yescharacteristic
34C2×#14519696C411yescharacteristic, complemented
35C2×#14519695C411yescharacteristic, complemented
36C2×#14519695C411yescharacteristic, complemented
37#101×D61C414yescomplemented
38#101×D61C2214yes—
39C2×#101×C61C411yescharacteristic, complemented
40C23×#6923—21no—
41C2×#11758213—21no—
42D61⋊M16—21no—
43D61⋊M16—21no—
44D61⋊M16—21no—
45D61⋊M16C2312yes—
46C2×#11758217—21no—
47C2×D61⋊C8—21no—
48C2×D61⋊C8—21no—
49C2×D61⋊C8—21no—
50C2×D61⋊C8—21no—
51C2×D61⋊C8D411yescharacteristic
52C2×D61⋊C8D411yescharacteristic
53C2×D61⋊C8D412yes—
54C2×D61⋊C8C2312yes—
55C22×#92420—21no—
56#14519856—21no—
57#14519856—21no—
58#14519856D412yes—
59#14519856C2312yes—
60C2×C4⋊#6923—21no—
61C2×C4⋊#6923—21no—
62C2×C4⋊#6923—21no—
63C2×C4⋊#6923—21no—
64C2×C4⋊#6923—21no—
65C2×C4⋊#6923D411yescharacteristic
66C2×C4⋊#6923D411yescharacteristic
67C2×C4⋊#6923C2312yes—
68C2×C22⋊#6923—21no—
69C2×C4×#6923—21no—
70#14519846—24no—
71#14519845—24no—
72#14519840—24no—
73#14519840—24no—
74#14519840—24no—
75#14519840—24no—
76#14519831—24no—
77C8×#6923—24no—
78C22×Dic122—21no—
79C22×Dic122C2×C411yescharacteristic
80C2×Q8×D61—21no—
81C2×Q8×D61—21no—
82C2×Q8×D61—21no—
83C2×Q8×D61—21no—
84C2×Q8×D61—21no—
85C2×Q8×D61—21no—
86C2×Q8×D61—21no—
87C2×Q8×D61—21no—
88C2×Q8×D61—21no—
89C2×Q8×D61—21no—
90C2×Q8×D61C2×C412yes—
91C2×Q8×D61C2312yes—
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#14519695C2×C414yescomplemented
110#14519695C2×C414yescomplemented
111C22×Q8×C61C2×C411yescharacteristic
112C2×M16×C61C2×C411yescharacteristic
113C2×M16×C61C2×C411yescharacteristic
114#101×C61C2×C414yescomplemented
115C23×D61#4111yescharacteristic
116C22×#6923—21no—
117C22×#6923—21no—
118C22×#6923—22no—
119C22×#6923—41no—
120C22×#6923—41no—
121C22×#6923—82no—
122C2×Q8×C61—21no—
123C2×Q8×C61—21no—
124C2×Q8×C61—21no—
125C2×Q8×C61—21no—
126C2×Q8×C61—21no—
127C2×Q8×C61C22×C412yes—
128C22×C4×C61—21no—
129C22×C4×C61C22×C411yescharacteristic
130C22×Dic61—21no—
131C22×Dic61#4111yescharacteristic
132Q8×D61—22no—
133Q8×D61—22no—
134Q8×D61—22no—
135Q8×D61—22no—
136Q8×D61—22no—
137Q8×D61—22no—
138Q8×D61—22no—
139Q8×D61—22no—
140Q8×D61—41no—
141Q8×D61—41no—
142Q8×D61—41no—
143Q8×D61—41no—
144Q8×D61—41no—
145Q8×D61—41no—
146Q8×D61—41no—
147Q8×D61—41no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61#4111yescharacteristic
160C2×C4×D61#4111yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×C4×D61#4111yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×C4×D61#4111yescharacteristic
165C2×C4×D61C2411yescharacteristic
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122—41no—
174C2×Dic122—41no—
175C2×Dic122—41no—
176C2×Dic122—41no—
177C2×Dic122C22×C412yes—
178C22⋊#6923—22no—
179C22⋊#6923—22no—
180#11758217—22no—
181#11758217—41no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—22no—
185C2×#92420—22no—
186C2×#92420—41no—
187C4⋊#6923—21no—
188C4⋊#6923—21no—
189C4⋊#6923—22no—
190C4⋊#6923—22no—
191C4⋊#6923—41no—
192C4⋊#6923—41no—
193C4⋊#6923C2×D412yes—
194C4⋊#6923C2×D412yes—
195C4×#6923—22no—
196C4×#6923—22no—
197#11758213—22no—
198#11758213—41no—
199D61⋊C8—21no—
200D61⋊C8—21no—
201D61⋊C8—22no—
202D61⋊C8—22no—
203D61⋊C8—22no—
204D61⋊C8—41no—
205D61⋊C8C2×D412yes—
206D61⋊C8C2×D412yes—
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—22no—
230C22×D61#11711yescharacteristic
231C22×D61#12111yescharacteristic
232C22×D61#12111yescharacteristic
233C22×D61#12611yescharacteristic
234C22×D61#12611yescharacteristic
235C22×D61C2×#4111yescharacteristic
236C2×#6923—22no—
237C2×#6923—22no—
238C2×#6923—42no—
239C2×#6923—42no—
240C2×#6923—42no—
241C2×#6923—82no—
242C2×#6923—82no—
243C2×#6923—82no—
244Q8×C61—22no—
245Q8×C61—22no—
246Q8×C61—41no—
247Q8×C61—41no—
248C2×C4×C61—22no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61#11711yescharacteristic
252C2×C4×C61C4×D411yescharacteristic
253C2×C4×C61C4×D411yescharacteristic
254C2×C4×C61C4×D411yescharacteristic
255C2×C4×C61C4×D411yescharacteristic
256C2×C4×C61C23×C411yescharacteristic
257C2×Dic61—22no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61#11711yescharacteristic
261C2×Dic61#12311yescharacteristic
262C2×Dic61#12311yescharacteristic
263C2×Dic61#12411yescharacteristic
264C2×Dic61#12411yescharacteristic
265C2×Dic61C2×#4111yescharacteristic
266C4×D61—42no—
267C4×D61—42no—
268C4×D61—42no—
269C4×D61—42no—
270C4×D61C4×D411yescharacteristic
271C4×D61C4×D411yescharacteristic
272C4×D61C4×D411yescharacteristic
273C4×D61C4×D411yescharacteristic
274C4×D61#12111yescharacteristic
275C4×D61#12111yescharacteristic
276C4×D61#12311yescharacteristic
277C4×D61#12311yescharacteristic
278C4×D61#12411yescharacteristic
279C4×D61#12411yescharacteristic
280C4×D61#12611yescharacteristic
281C4×D61#12611yescharacteristic
282C4×D61C22×D411yescharacteristic
283C4×D61C22×D411yescharacteristic
284C4×D61C2×#4111yescharacteristic
285C4×D61C2×#4111yescharacteristic
286Dic122—22no—
287Dic122—22no—
288Dic122—41no—
289Dic122—41no—
290Dic122—42no—
291Dic122—42no—
292Dic122—42no—
293Dic122—42no—
294#92420—22no—
295#92420—22no—
296#92420—42no—
297C8×C61—22no—
298C8×C61—22no—
299#92418—22no—
300#92418—22no—
301C2×#1930—611nomaximal, Sylow
302C22×C61—22no—
303C22×C61#38811yescharacteristic
304C22×C61#38811yescharacteristic
305C22×C61C2×#11711yescharacteristic
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—22no—
309C2×D61—21no—
310C2×D61—21no—
311C2×D61—21no—
312C2×D61—21no—
313C2×D61#38811yescharacteristic
314C2×D61#38811yescharacteristic
315C2×D61#47112yes—
316C2×D61#47312yes—
317C2×D61C2×#12111yescharacteristic
318C2×D61C2×#12611yescharacteristic
319#6923—42no—
320#6923—42no—
321#6923—82no—
322C4×C61—42no—
323C4×C61#38811yescharacteristic
324C4×C61#38811yescharacteristic
325C4×C61C2×C4×D411yescharacteristic
326C4×C61C2×C4×D411yescharacteristic
327Dic61—42no—
328Dic61#38811yescharacteristic
329Dic61#38811yescharacteristic
330Dic61C2×#12311yescharacteristic
331Dic61C2×#12411yescharacteristic
332C2×#428—611no—
333C2×#419—611no—
334C22×#103—611no—
335C22×#101—611no—
336C2×#405—611no—
337#1930—618no—
338C2×#343—611no—
339C2×#341—611no—
340C2×C61—21no—
341C2×C61—21no—
342C2×C61#193012yescomplemented
343C2×C61C2×#38811yescharacteristic
344D61—21no—
345D61—21no—
346D61#193012yescomplemented
347D61C2×#47111yescharacteristic
348D61C2×#47311yescharacteristic
349C23×Q8—611no—
350C22×M16—611no—
351C22×M16—611no—
352C22×M16—611no—
353C23×C8—611no—
354C2×#117—611no—
355C22×C4⋊C4—611no—
356#428—614no—
357#428—1222no—
358C2×#107—1221no—
359C2×#106—1221no—
360#419—614no—
361#419—1222no—
362C2×#103—614no—
363C2×#103—1221no—
364C2×#103—1221no—
365C2×#103—1221no—
366C2×#103—1221no—
367C2×#103—1222no—
368C2×#101—611no—
369C2×#101—611no—
370C2×#101—611no—
371C2×#101—614no—
372C2×#101—614no—
373C2×#101#692311yescharacteristic, complemented
374#405—614no—
375#405—1222no—
376C2×#97—1221no—
377C2×C4×C8—1221no—
378#343—614no—
379#341—614no—
380C61C2×#193011yescharacteristic, complemented, Sylow
381C22×Q8—612no—
382C22×Q8—612no—
383C22×Q8—611no—
384C22×Q8—1221no—
385C22×Q8—1221no—
386C22×Q8—1221no—
387C22×Q8—1221no—
388C22×Q8—1221no—
389C22×Q8—1221no—
390C22×Q8—1221no—
391C22×Q8—1221no—
392C22×Q8—1221no—
393C22×Q8—1221no—
394C22×Q8—1221no—
395C22×Q8C2×#692311yescharacteristic
396C23×C4—611no—
397C23×C4—1221no—
398C23×C4—1221no—
399C2×M16—611no—
400C2×M16—611no—
401C2×M16—612no—
402C2×M16—612no—
403C2×M16—612no—
404C2×M16—612no—
405C2×M16—612no—
406C2×M16—1221no—
407C2×M16—1221no—
408C2×M16—1221no—
409C2×M16—1221no—
410C2×M16—1221no—
411C2×M16—1221no—
412C2×M16—1221no—
413C2×M16—1221no—
414C2×M16—1221no—
415C2×M16—1221no—
416C2×M16—1221no—
417C2×M16C2×#692311yescharacteristic
418C2×M16C2×#692311yescharacteristic
419C22×C8—611no—
420C22×C8—611no—
421C22×C8—612no—
422C22×C8—612no—
423C22×C8—1221no—
424C22×C8—1221no—
425C22×C8—1221no—
426C22×C8—1221no—
427C22×C8—1221no—
428C22×C8—1221no—
429C22×C8—1221no—
430#117—612no—
431#117—612no—
432#117—1221no—
433#117—1221no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—612no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C42—1221no—
444#107—1224no—
445#106—1224no—
446#103—1224no—
447#103—1224no—
448#103—1224no—
449#103—1224no—
450#101—614no—
451#101—614no—
452#101—614no—
453#101C2×#692314yescomplemented
454#97—1224no—
455C4×C8—1224no—
456C24—611no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—612no—
463C2×Q8—1222no—
464C2×Q8—1222no—
465C2×Q8—1222no—
466C2×Q8—1222no—
467C2×Q8—1222no—
468C2×Q8—1222no—
469C2×Q8—1222no—
470C2×Q8—1222no—
471C2×Q8—1222no—
472C2×Q8—1222no—
473C2×Q8—1221no—
474C2×Q8—1221no—
475C2×Q8—1221no—
476C2×Q8—1221no—
477C2×Q8—1221no—
478C2×Q8—2441no—
479C2×Q8—2441no—
480C2×Q8—2441no—
481C2×Q8—2441no—
482C2×Q8—2441no—
483C2×Q8—2441no—
484C2×Q8—2441no—
485C2×Q8—2441no—
486C2×Q8—2441no—
487C2×Q8—2441no—
488C2×Q8—2441no—
489C2×Q8—2441no—
490C2×Q8C22×#692312yes—
491C22×C4—21no—
492C22×C4—611no—
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—1222no—
506C22×C4—1222no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1222no—
511C22×C4—4882no—
512C22×C4—2441no—
513C22×C4—2441no—
514C22×C4—2441no—
515C22×C4—2441no—
516C22×C4—2441no—
517C22×C4—2441no—
518C22×C4C22×#692311yescharacteristic
519M16—21no—
520M16—21no—
521M16—612no—
522M16—612no—
523M16—1222no—
524M16—1222no—
525M16—1222no—
526M16—1222no—
527M16—1221no—
528M16—1221no—
529M16—1222no—
530M16—1222no—
531M16—2441no—
532M16—2441no—
533M16C22×#692312yes—
534M16C22×#692312yes—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—612no—
538C2×C8—612no—
539C2×C8—1222no—
540C2×C8—1222no—
541C2×C8—1222no—
542C2×C8—1222no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1222no—
546C2×C8—1222no—
547C2×C8—1222no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1222no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1222no—
554C2×C8—2441no—
555C2×C8—2441no—
556C4⋊C4—612no—
557C4⋊C4—612no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1222no—
561C4⋊C4—1222no—
562C4⋊C4—2441no—
563C4⋊C4—2441no—
564C22⋊C4—1222no—
565C22⋊C4—1222no—
566C42—1222no—
567C42—1222no—
568C23—611no—
569C23—611no—
570C23—611no—
571C23—611no—
572C23—611no—
573C23—611no—
574C23—1222no—
575C23—1222no—
576C23#1451985611yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581Q8—1222no—
582Q8—1222no—
583Q8—2442no—
584Q8—2442no—
585Q8—2442no—
586Q8—2442no—
587Q8—2441no—
588Q8—2441no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—611no—
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—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—4882no—
618C2×C4—4882no—
619C2×C4—4882no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4—2442no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2442no—
627C2×C4—2441no—
628C2×C4—2441no—
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—612no—
646C22—612no—
647C22—611no—
648C22—611no—
649C22—1221no—
650C22—1221no—
651C22—1221no—
652C22—1222no—
653C22—1221no—
654C22—1222no—
655C22—1222no—
656C22#1684071211yescharacteristic
657C22#1684071211yescharacteristic
658C22C2×#1451985611yescharacteristic
659C4—42no—
660C4—611no—
661C4—611no—
662C4—611no—
663C4—611no—
664C4—4882no—
665C4—2442no—
666C4—2442no—
667C4—2442no—
668C4#1684071211yescharacteristic
669C4#1684071211yescharacteristic
670C4C2×D4×#692311yescharacteristic
671C4C2×D4×#692311yescharacteristic
672C2—21no—
673C2—21no—
674C2—611no—
675C2—611no—
676C2—612no—
677C2—1221no—
678C2—1221no—
679C2#2146190412yesdirect product factor
680C2C2×#1684071211yescharacteristic
subgroupG/H
centerC22#16840712
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#101×C61C4
socleC22×C61#388
prime radicalC23×D61#41
cosocleC2×C4×D61C24
hypercenterC2×#101#6923
hypocenterC61C2×#1930
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
5. #21461904C2direct (N × H)
34. C2×#14519696C4semidirect
35. C2×#14519695C4semidirect
36. C2×#14519695C4semidirect
37. #101×D61C4semidirect
39. C2×#101×C61C4semidirect
108. #14519696C2×C4semidirect
109. #14519695C2×C4semidirect
110. #14519695C2×C4semidirect
114. #101×C61C2×C4semidirect
342. C2×C61#1930semidirect
346. D61#1930semidirect
373. C2×#101#6923semidirect
380. C61C2×#1930semidirect
453. #101C2×#6923semidirect
679. C2#21461904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407732
C2×#168407552
C22×#145198402
C2×#168407282
#214619042
C2×#168406412
C2×#168406372
C2×#101×D612
C2×#193061