Finite Group Databasebeta

← C2×#21461847 #30615733

Subgroups — C2×#21461847 #30615733

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic
2C22×#14519838C212yesmaximal, complemented
3C2×#16840734C211yesmaximal, characteristic
4#21461847C218yesmaximal, direct product factor
5C2×#16840642C212yesmaximal, complemented
6C22×#14519755C211yesmaximal, characteristic
7C22×#11758213—21no—
8C2×D61⋊M16—28no—
9C2×D61⋊M16—22no—
10C2×D61⋊M16C2214yes—
11C22×#11758217C2212yes—
12C22×#11758217C2212yes—
13C22×D61⋊C8—21no—
14C2×#14519838—28no—
15C2×#14519838C2218yescomplemented
16#16840734—22no—
17#16840734C2214yes—
18C2×#14519834—21no—
19C2×#14519834—21no—
20#16840642C2218yescomplemented
21C23×Dic122C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C2×#14519755—21no—
24C2×#14519755—21no—
25C2×#14519755—22no—
26C2×#14519755—21no—
27C2×#14519755—22no—
28C2×#14519755—21no—
29C2×#14519755C414yes—
30C2×#14519755C2214yes—
31C22×#11758196C411yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758198C411yescharacteristic
34C22×#11758198C411yescharacteristic
35C22×C4⋊C4×C61C411yescharacteristic
36C2×#11758213—28no—
37C2×#11758213—24no—
38D61⋊M16—216no—
39D61⋊M16—216no—
40C2×#11758217—24no—
41C2×#11758217—22no—
42C2×#11758217—22no—
43C2×#11758217—24no—
44C2×#11758217—24no—
45C2×#11758217D418yes—
46C2×#11758217C2314yes—
47C2×#11758217C2314yes—
48C2×D61⋊C8—28no—
49C2×D61⋊C8—24no—
50C22×#92420—22no—
51C22×#92420—22no—
52#14519838—216no—
53#14519834—24no—
54#14519834—24no—
55C24×D61C2×C411yescharacteristic
56C22×Dic122—24no—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122—24no—
62C22×Dic122C2×C412yes—
63C22×Dic122C2312yes—
64C23×Dic61C2×C411yescharacteristic
65C23×Dic61C2×C411yescharacteristic
66C23×Dic61C2311yescharacteristic
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61C2×C412yes—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D412yes—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D412yes—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2312yes—
77#14519755—24no—
78#14519755—24no—
79#14519755—24no—
80#14519755—24no—
81#14519755—24no—
82#14519755—24no—
83#14519755—24no—
84#14519755—24no—
85C2×#11758196—22no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196C2×C414yes—
93C2×#11758196C2×C412yes—
94C2×#11758196C2312yes—
95C2×#11758198—21no—
96C2×#11758198—22no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—22no—
100C2×#11758198—21no—
101C2×#11758198C2×C414yes—
102C2×#11758198C2×C414yes—
103C23×C4×C61C2×C411yescharacteristic
104C23×C4×C61C2×C411yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61C2×C414yes—
110C24×C61C22×C411yescharacteristic
111C23×D61—24no—
112C23×D61—24no—
113C23×D61—42no—
114C23×D61C22⋊C411yescharacteristic
115C23×D61C22⋊C412yes—
116C23×D61C22⋊C411yescharacteristic
117C23×D61C22×C412yes—
118C22×C4×C61—24no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—24no—
124C22×C4×C61—42no—
125C22×C4×C61C22⋊C412yes—
126C22×C4×C61C22⋊C411yescharacteristic
127C22×C4×C61C22⋊C411yescharacteristic
128C22×C4×C61C22×C412yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C412yes—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—24no—
136C22×Dic61—42no—
137C22×Dic61C22×C412yes—
138C22×Dic61C22×C412yes—
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D414yes—
145C22×Dic61#4114yes—
146C22×Dic61C2411yescharacteristic
147C2×C4×D61—28no—
148C2×C4×D61—22no—
149C2×C4×D61—24no—
150C2×C4×D61—22no—
151C2×C4×D61—24no—
152C2×C4×D61—24no—
153C2×C4×D61—28no—
154C2×C4×D61—22no—
155C2×C4×D61—24no—
156C2×C4×D61—22no—
157C2×C4×D61—24no—
158C2×C4×D61—24no—
159C2×C4×D61C22⋊C412yes—
160C2×C4×D61C22⋊C412yes—
161C2×C4×D61C22⋊C412yes—
162C2×C4×D61C22⋊C412yes—
163C2×C4×D61C2×D412yes—
164C2×C4×D61C2×D412yes—
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×D412yes—
167C2×Dic122—22no—
168C2×Dic122—22no—
169C2×Dic122—28no—
170C2×Dic122—24no—
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122—24no—
174C2×Dic122—42no—
175C2×Dic122—42no—
176C2×Dic122—44no—
177C2×Dic122—44no—
178C2×Dic122—42no—
179C2×Dic122—42no—
180#11758217—28no—
181#11758217—24no—
182#11758217—24no—
183#11758217—24no—
184#11758217—44no—
185#11758217C2×D418yes—
186C2×#92420—28no—
187C2×#92420—24no—
188C2×#92420—24no—
189C2×#92420—44no—
190#11758213—216no—
191D61⋊C8—216no—
192C4⋊C4×C61—24no—
193C4⋊C4×C61—24no—
194#11758198—24no—
195#11758198—24no—
196#11758198—24no—
197#11758198—24no—
198#11758196—24no—
199#11758196—24no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61C2×C22⋊C411yescharacteristic
207C23×C61C2×C22⋊C411yescharacteristic
208C23×C61C4×D414yes—
209C23×C61C23×C411yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—24no—
213C22×D61—24no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—24no—
218C22×D61—24no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—416no—
222C22×D61#10114yescomplemented
223C22×D61C2×C22⋊C412yes—
224C22×D61C2×C22⋊C412yes—
225C2×C4×C61—24no—
226C2×C4×C61—24no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—24no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C22⋊C412yes—
238C2×C4×C61C2×C22⋊C412yes—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—24no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61C2×C22⋊C411yescharacteristic
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C4×D414yes—
250C2×Dic61#12012yes—
251C2×Dic61#12012yes—
252C2×Dic61#12114yes—
253C2×Dic61#12114yes—
254C2×Dic61#12312yes—
255C2×Dic61#12312yes—
256C2×Dic61C22×D412yes—
257C2×Dic61C22×D411yescharacteristic
258C2×Dic61C22×D411yescharacteristic
259C2×Dic61C2×#4112yes—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—24no—
263C4×D61—24no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—24no—
267C4×D61—24no—
268C4×D61—24no—
269C4×D61—24no—
270Dic122—42no—
271Dic122—44no—
272Dic122—42no—
273Dic122—44no—
274Dic122—44no—
275#92420—28no—
276#92420—44no—
277C2×#1901—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—28no—
283C22×C61#38612yes—
284C22×C61#38612yes—
285C22×C61C2×#10112yes—
286C22×C61#41312yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61C2×C4×D412yes—
289C2×D61—22no—
290C2×D61—28no—
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—48no—
296C2×D61—48no—
297C2×D61—44no—
298C2×D61C2×#10114yescomplemented
299C4×C61—22no—
300C4×C61—22no—
301C4×C61—42no—
302C4×C61—42no—
303Dic61—42no—
304Dic61—42no—
305Dic61#38612yes—
306Dic61#38612yes—
307Dic61C2×#12011yescharacteristic
308Dic61C2×#12112yes—
309Dic61C2×#12311yescharacteristic
310C23×M16—611no—
311C22×C22⋊Q8—611no—
312C22×#101—612no—
313C2×#407—611no—
314#1901—618no—
315C2×#343—612no—
316C2×C61—22no—
317C2×C61—22no—
318C2×C61#190114yescomplemented
319C2×C61C2×#38611yescharacteristic
320C2×C61C22×#10111yescharacteristic
321C2×C61C2×#41311yescharacteristic
322D61—24no—
323D61—42no—
324C23×Q8—611no—
325C24×C4—611no—
326C22×M16—612no—
327C22×M16—612no—
328C22×M16—614no—
329C22×M16—1228no—
330C22×M16—1222no—
331C22×M16—1221no—
332C23×C8—1221no—
333C2×C22⋊Q8—614no—
334C2×C22⋊Q8—614no—
335C2×C22⋊Q8—1221no—
336C2×C22⋊Q8—1222no—
337C2×C22⋊Q8—1221no—
338C2×C22⋊Q8—1221no—
339C2×C22⋊Q8—1221no—
340C2×C22⋊Q8—1222no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—611no—
343C22×C4⋊C4#692311yescharacteristic
344C22×C22⋊C4—611no—
345C22×C22⋊C4—611no—
346C2×#101—618no—
347C2×#101—1228no—
348#407—614no—
349#407—1222no—
350C2×C22⋊C8—1221no—
351C2×C22⋊C8—1221no—
352#343—618no—
353C61C2×#190111yescharacteristic, complemented, Sylow
354C25—611no—
355C22×Q8—612no—
356C22×Q8—612no—
357C22×Q8—1221no—
358C22×Q8—1221no—
359C22×Q8—1221no—
360C22×Q8—1221no—
361C22×Q8—1224no—
362C22×Q8—1224no—
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—612no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—612no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—1224no—
375C23×C4—1224no—
376C23×C4C2×#692311yescharacteristic
377C23×C4C2×#692311yescharacteristic
378C23×C4C2×#692311yescharacteristic
379C2×M16—618no—
380C2×M16—614no—
381C2×M16—614no—
382C2×M16—12216no—
383C2×M16—1222no—
384C2×M16—1224no—
385C2×M16—1224no—
386C2×M16—12216no—
387C2×M16—1228no—
388C2×M16—1222no—
389C2×M16—1224no—
390C2×M16—1224no—
391C22×C8—1222no—
392C22×C8—1224no—
393C22×C8—1228no—
394C22×C8—1222no—
395C22⋊Q8—1224no—
396C22⋊Q8—1224no—
397C22⋊Q8—1224no—
398C22⋊Q8—1224no—
399C22⋊Q8—1224no—
400C22⋊Q8—1224no—
401C22⋊Q8—1224no—
402C22⋊Q8—1224no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—612no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4—614no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4C2×#692314yes—
417C2×C22⋊C4—614no—
418C2×C22⋊C4—614no—
419C2×C22⋊C4—1222no—
420C2×C22⋊C4—1222no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425#101—12216no—
426C22⋊C8—1224no—
427C22⋊C8—1224no—
428C24—611no—
429C24—611no—
430C24—612no—
431C24—612no—
432C24—1224no—
433C24—1224no—
434C24—2442no—
435C24C22×#692311yescharacteristic
436C2×Q8—1224no—
437C2×Q8—1222no—
438C2×Q8—1222no—
439C2×Q8—1222no—
440C2×Q8—1222no—
441C2×Q8—1228no—
442C2×Q8—1224no—
443C2×Q8—2442no—
444C2×Q8—2442no—
445C2×Q8—2444no—
446C2×Q8—2444no—
447C2×Q8—2442no—
448C2×Q8—2442no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—24no—
455C22×C4—42no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—614no—
461C22×C4—614no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—612no—
472C22×C4—612no—
473C22×C4—612no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1224no—
479C22×C4—1224no—
480C22×C4—1228no—
481C22×C4—1222no—
482C22×C4—1224no—
483C22×C4—1222no—
484C22×C4—1228no—
485C22×C4—1224no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1224no—
491C22×C4—2442no—
492C22×C4C22⋊#692312yes—
493C22×C4C22⋊#692311yescharacteristic
494C22×C4C22⋊#692311yescharacteristic
495C22×C4C22×#692312yes—
496C22×C4C22×#692312yes—
497C22×C4C22×#692312yes—
498M16—618no—
499M16—1228no—
500M16—1224no—
501M16—12216no—
502M16—1224no—
503M16—1224no—
504M16—2444no—
505C2×C8—1228no—
506C2×C8—1224no—
507C2×C8—12216no—
508C2×C8—1224no—
509C2×C8—2444no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1224no—
517C4⋊C4—1224no—
518C22⋊C4—1224no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C23—22no—
523C23—22no—
524C23—614no—
525C23—612no—
526C23—612no—
527C23—1224no—
528C23—1224no—
529C23—1222no—
530C23—1222no—
531C23—1224no—
532C23—1222no—
533C23—1222no—
534C23—1222no—
535C23—1224no—
536C23—2442no—
537C23—2442no—
538C23—24416no—
539C23C2×C22⋊#692311yescharacteristic
540C23C2×C22⋊#692311yescharacteristic
541C23D4×#692314yes—
542C23C23×#692311yescharacteristic
543Q8—2442no—
544Q8—2444no—
545Q8—2442no—
546Q8—2444no—
547Q8—2444no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—614no—
563C2×C4—614no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—614no—
571C2×C4—612no—
572C2×C4—612no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1224no—
576C2×C4—1224no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1224no—
580C2×C4—1224no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1224no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4C2×C22⋊#692312yes—
592C2×C4C2×C22⋊#692312yes—
593C8—1228no—
594C8—2444no—
595C22—28no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—614no—
601C22—1228no—
602C22—1222no—
603C22—1222no—
604C22—1222no—
605C22—1222no—
606C22—1222no—
607C22—2448no—
608C22—2448no—
609C22—2444no—
610C22#1684071012yes—
611C22#1684071012yes—
612C22D61⋊#10112yes—
613C22#1684074812yes—
614C22C22×C22⋊#692311yescharacteristic
615C22C2×D4×#692312yes—
616C4—22no—
617C4—22no—
618C4—42no—
619C4—42no—
620C4—611no—
621C4—612no—
622C4—611no—
623C4—612no—
624C4—612no—
625C4—2442no—
626C4—2442no—
627C2—22no—
628C2—22no—
629C2—1224no—
630C2—2442no—
631C2#2146184714yesdirect product factor
632C2C2×#1684071011yescharacteristic
633C2C2×D61⋊#10111yescharacteristic
634C2C2×#1684074811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1901
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#14519838C2semidirect
4. #21461847C2direct (N × H)
5. C2×#16840642C2semidirect
15. C2×#14519838C22semidirect
20. #16840642C22semidirect
222. C22×D61#101semidirect
298. C2×D61C2×#101semidirect
318. C2×C61#1901semidirect
353. C61C2×#1901semidirect
631. C2#21461847direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C22×#145198382
C2×#168407342
#214618472
C2×#168406422
C22×#145197552
C2×#190161