Finite Group Databasebeta

← D61×#2001 #29706807

Subgroups — D61×#2001 #29706807

Order 15616.

2182 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D61C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×D61C212yesmaximal
3C2×#103×D61C212yesmaximal, complemented
4C2×C22⋊C8×D61C211yesmaximal, characteristic
5#21446830C211yesmaximal, characteristic, complemented
6#21446829C211yesmaximal, characteristic, complemented
7#21446828C212yesmaximal, complemented
8#21446827C212yesmaximal, complemented
9#21446826C211yesmaximal, characteristic, complemented
10#340×D61C211yesmaximal, characteristic, complemented
11C61×#2001C211yesmaximal, characteristic, complemented
12C22×Q8×D61C2212yes—
13C23×C4×D61C2211yescharacteristic
14C22×Dic244C2211yescharacteristic, complemented
15C22×#11758202C2212yescomplemented
16C2×Q16×D61—24no—
17C2×Q16×D61—28no—
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519757C2212yes—
21C2×#14519756C2212yes—
22C2×#14519755—22no—
23C2×#14519754—22no—
24C2×#14519753C2212yes—
25C22⋊Q8×D61—28no—
26C22⋊Q8×D61—28no—
27C2×C4⋊C4×D61—22no—
28C2×C4⋊C4×D61C2212yes—
29C2×C22⋊C4×D61—22no—
30C2×#14519702C2212yescomplemented
31C2×#14519701C2212yescomplemented
32C2×#14519700C2212yescomplemented
33#103×D61—28no—
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C22⋊C8×D61—24no—
38#16839525C2211yescharacteristic, complemented
39#16839524C2212yescomplemented
40C22×Q16×C61C2211yescharacteristic, complemented
41C2×C22⋊Q8×C61C2212yes—
42C2×#103×C61C2212yescomplemented
43C2×C22⋊C8×C61C2211yescharacteristic
44C61×#340C2211yescharacteristic, complemented
45C24×D61D411yescharacteristic
46C22×Dic122—22no—
47C22×Dic122C2312yes—
48C2×Q8×D61—24no—
49C2×Q8×D61—24no—
50C2×Q8×D61—24no—
51C2×Q8×D61—24no—
52C2×Q8×D61—24no—
53C2×Q8×D61D418yes—
54C23×Dic61D411yescharacteristic
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—24no—
59C22×C4×D61—24no—
60C22×C4×D61—22no—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C2×Dic244—24no—
66C2×Dic244—22no—
67C2×#11758202—24no—
68C2×#11758202—24no—
69C2×#11758202—24no—
70Q16×D61—232no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C2×C8×D61—24no—
74C2×C8×D61—22no—
75C2×C8×D61—24no—
76C2×C8×D61D414yes—
77#14519757—24no—
78#14519757—24no—
79#14519756—24no—
80#14519756—24no—
81#14519755—216no—
82#14519754—216no—
83#14519753—24no—
84#14519753—24no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61C2312yes—
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C4⋊C4×D61—216no—
91C4⋊C4×D61—24no—
92C4⋊C4×D61D418yes—
93C2×C22⋊Dic61—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C22⋊C4×D61—216no—
97#14519702—24no—
98#14519701—24no—
99#14519700—24no—
100C22⋊#92418—22no—
101#14519689—22no—
102#14519689—22no—
103C22×Q8×C61C2312yes—
104C23×C4×C61C2311yescharacteristic
105C2×Q16×C61—24no—
106C2×Q16×C61—22no—
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22⋊Q8×C61—24no—
110C22⋊Q8×C61—24no—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61C2312yes—
113C2×C22⋊C4×C61—22no—
114#103×C61—24no—
115C22⋊C8×C61—22no—
116C24×C61C2×D411yescharacteristic
117C23×D61—24no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—24no—
121C23×D61Q1614yescomplemented
122C23×D61C2×D411yescharacteristic
123C23×D61C2×D411yescharacteristic
124C2×Q8×C61—22no—
125C2×Q8×C61—22no—
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61—22no—
129C2×Q8×C61C2×D414yes—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—21no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—24no—
141C22×Dic61—22no—
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144Q8×D61—216no—
145Q8×D61—216no—
146Q8×D61—48no—
147Q8×D61—48no—
148C2×C4×D61—24no—
149C2×C4×D61—28no—
150C2×C4×D61—28no—
151C2×C4×D61—22no—
152C2×C4×D61—21no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—21no—
156C2×C4×D61—24no—
157C2×C4×D61—22no—
158C2×C4×D61—44no—
159C2×C4×D61—44no—
160C2×C4×D61—44no—
161C2×C4×D61—44no—
162C2×C4×D61—44no—
163C2×C4×D61—48no—
164C2×C4×D61—44no—
165C2×C4×D61C2×D414yes—
166C2×C4×D61C2×D412yes—
167C2×C4×D61C2×D414yes—
168C2×C4×D61#4112yes—
169C2×Dic122—22no—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122—28no—
175C2×Dic122—44no—
176C2×Dic122—44no—
177C2×Dic122C2×D414yes—
178Q16×C61—28no—
179C2×C8×C61—22no—
180C2×C8×C61—21no—
181C2×C8×C61—22no—
182C2×C8×C61C2×D412yes—
183C4⋊C4×C61—28no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61C2×D414yes—
186C22⋊C4×C61—28no—
187C22⋊Dic61—28no—
188#11758202—216no—
189#11758198—28no—
190#11758198—28no—
191C4⋊Dic61—28no—
192C4⋊Dic61—22no—
193C4⋊Dic61C2×D414yes—
194#11758196—28no—
195#11758196—28no—
196#11758196—28no—
197C2×#92418—22no—
198C2×#92418—21no—
199C2×#92418—22no—
200C2×#92418C2×D412yes—
201Dic244—28no—
202C8×D61—28no—
203C8×D61—44no—
204C23×C61—22no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—22no—
208C23×C61C2×Q1612yescomplemented
209C23×C61C22×D411yescharacteristic
210C22×D61—22no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—22no—
214C22×D61—216no—
215C22×D61—28no—
216C22×D61—44no—
217C22×D61—48no—
218C22×D61—44no—
219C22×D61#12014yes—
220C22×D61#12112yes—
221C22×D61C2×Q1612yes—
222C22×D61C2×Q1612yescomplemented
223C22×D61#13512yes—
224C22×D61#13714yes—
225Q8×C61—24no—
226Q8×C61—24no—
227Q8×C61—42no—
228Q8×C61—42no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—21no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—41no—
238C2×C4×C61—42no—
239C2×C4×C61—41no—
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D412yes—
243C2×C4×C61C2×#4111yescharacteristic
244C2×Dic61—24no—
245C2×Dic61—22no—
246C2×Dic61—24no—
247C2×Dic61—21no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—44no—
253C2×Dic61#12014yes—
254C2×Dic61#12112yes—
255C4×D61—44no—
256C4×D61—416no—
257C4×D61—416no—
258C4×D61—41no—
259C4×D61—42no—
260C4×D61—41no—
261C4×D61—44no—
262C4×D61#12014yes—
263C4×D61#12118yes—
264C4×D61#12714yes—
265Dic122—24no—
266Dic122—24no—
267Dic122—42no—
268Dic122—42no—
269Dic122—416no—
270C8×C61—22no—
271C8×C61—41no—
272#92418—22no—
273#92418—41no—
274C2×#2001—611nomaximal, Sylow
275C22×C61—24no—
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—42no—
279C22×C61—41no—
280C22×C61C2×#12012yes—
281C22×C61C2×#12111yescharacteristic
282C22×C61C22×Q1611yescharacteristic
283C22×C61C2×#13511yescharacteristic
284C22×C61C2×#13712yes—
285C2×D61—24no—
286C2×D61—22no—
287C2×D61—41no—
288C2×D61—42no—
289C2×D61—41no—
290C2×D61—416no—
291C2×D61#39214yes—
292C2×D61#45118yes—
293C2×D61#45218yes—
294C2×D61#46714yes—
295C2×D61#47014yes—
296C4×C61—44no—
297C4×C61—41no—
298C4×C61—44no—
299C4×C61C2×#12011yescharacteristic
300C4×C61C2×#12112yes—
301C4×C61C2×#12711yescharacteristic
302Dic61—44no—
303Dic61—41no—
304Dic61—44no—
305Dic61#39214yes—
306C23×Q16—611no—
307C22×C22⋊Q8—612no—
308C22×#103—612no—
309C22×C22⋊C8—611no—
310#2001—612no—
311#2001—611no—
312#2001—611no—
313#2001—611no—
314#2001—612no—
315#2001D6111yescharacteristic, direct product factor
316C2×#340—611no—
317C2×C61—42no—
318C2×C61C2×#39211yescharacteristic
319C2×C61C2×#45112yes—
320C2×C61C2×#45212yes—
321C2×C61C2×#46711yescharacteristic
322C2×C61C2×#47011yescharacteristic
323D61—42no—
324D61#200118yesdirect product factor
325C23×Q8—612no—
326C24×C4—611no—
327C22×Q16—612no—
328C22×Q16—611no—
329C22×Q16—1224no—
330C22×Q16—1228no—
331C22×Q16C2×D6111yescharacteristic, complemented
332C23×C8—611no—
333C23×C8—611no—
334C2×C22⋊Q8—612no—
335C2×C22⋊Q8—612no—
336C2×C22⋊Q8—612no—
337C2×C22⋊Q8—1222no—
338C2×C22⋊Q8—1222no—
339C2×C22⋊Q8—1228no—
340C2×C22⋊Q8—1228no—
341C2×C22⋊Q8C2×D6112yes—
342C22×C4⋊C4—612no—
343C22×C4⋊C4—1222no—
344C22×C22⋊C4—1222no—
345C2×#103—612no—
346C2×#103—612no—
347C2×#103—612no—
348C2×#103—1228no—
349C2×#103C2×D6112yescomplemented
350C2×C22⋊C8—611no—
351C2×C22⋊C8—611no—
352C2×C22⋊C8—611no—
353C2×C22⋊C8—1224no—
354C2×C22⋊C8C2×D6111yescharacteristic
355#340—611no—
356#340—612no—
357#340C2×D6111yescharacteristic, complemented
358C61C2×#200111yescharacteristic, complemented, Sylow
359C25—611no—
360C22×Q8—618no—
361C22×Q8—612no—
362C22×Q8—1222no—
363C22×Q8—1224no—
364C22×Q8—1224no—
365C22×Q8—1224no—
366C22×Q8—1224no—
367C22×Q8—1224no—
368C22×Q8C22×D6112yes—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—1224no—
375C23×C4—1224no—
376C23×C4—1222no—
377C23×C4—1222no—
378C23×C4—1222no—
379C23×C4—1222no—
380C23×C4C22×D6111yescharacteristic
381C2×Q16—24no—
382C2×Q16—22no—
383C2×Q16—1224no—
384C2×Q16—1224no—
385C2×Q16—12232no—
386C2×Q16—1224no—
387C2×Q16—1224no—
388C2×Q16—1222no—
389C22×C8—611no—
390C22×C8—614no—
391C22×C8—611no—
392C22×C8—1224no—
393C22×C8—1222no—
394C22×C8—1224no—
395C22×C8C22×D6111yescharacteristic
396C22×C8C22×D6111yescharacteristic
397C22⋊Q8—24no—
398C22⋊Q8—24no—
399C22⋊Q8—12216no—
400C22⋊Q8—1224no—
401C22⋊Q8—12216no—
402C22⋊Q8—1224no—
403C22⋊Q8—1224no—
404C22⋊Q8—1224no—
405C22⋊Q8—1224no—
406C22⋊Q8—1224no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—618no—
410C2×C4⋊C4—1224no—
411C2×C4⋊C4—12216no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1222no—
416C2×C4⋊C4C22×D6112yes—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—12216no—
419C2×C22⋊C4—1222no—
420C2×C22⋊C4—1222no—
421C2×C22⋊C4—1222no—
422#103—24no—
423#103—1224no—
424#103—1224no—
425#103—1224no—
426C22⋊C8—22no—
427C22⋊C8—1222no—
428C22⋊C8—1222no—
429C22⋊C8—1222no—
430C24—611no—
431C24—611no—
432C24—614no—
433C24—1224no—
434C24—1222no—
435C24—1222no—
436C24—1224no—
437C24D4×D6111yescharacteristic
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—614no—
444C2×Q8—1228no—
445C2×Q8—12216no—
446C2×Q8—12216no—
447C2×Q8—1222no—
448C2×Q8—1222no—
449C2×Q8—1222no—
450C2×Q8—1222no—
451C2×Q8—1222no—
452C2×Q8—2444no—
453C2×Q8—2444no—
454C2×Q8—2448no—
455C2×Q8—2448no—
456C2×Q8D4×D6114yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—611no—
464C22×C4—614no—
465C22×C4—614no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—611no—
469C22×C4—1224no—
470C22×C4—1222no—
471C22×C4—1228no—
472C22×C4—1228no—
473C22×C4—1224no—
474C22×C4—1222no—
475C22×C4—1224no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—2444no—
484C22×C4—2448no—
485C22×C4—2444no—
486C22×C4—2444no—
487C22×C4—2444no—
488C22×C4—2444no—
489C22×C4—2444no—
490C22×C4D4×D6111yescharacteristic
491C22×C4C23×D6111yescharacteristic
492Q16—28no—
493Q16—1228no—
494Q16—12216no—
495C2×C8—22no—
496C2×C8—21no—
497C2×C8—22no—
498C2×C8—612no—
499C2×C8—1228no—
500C2×C8—1222no—
501C2×C8—1221no—
502C2×C8—1222no—
503C2×C8—2444no—
504C2×C8D4×D6112yes—
505C4⋊C4—28no—
506C4⋊C4—22no—
507C4⋊C4—614no—
508C4⋊C4—1228no—
509C4⋊C4—1228no—
510C4⋊C4—1228no—
511C4⋊C4—1228no—
512C4⋊C4—1222no—
513C4⋊C4D4×D6114yes—
514C22⋊C4—28no—
515C22⋊C4—1228no—
516C22⋊C4—1228no—
517C22⋊C4—1228no—
518C23—22no—
519C23—21no—
520C23—21no—
521C23—22no—
522C23—614no—
523C23—612no—
524C23—612no—
525C23—612no—
526C23—614no—
527C23—612no—
528C23—1228no—
529C23—12216no—
530C23—1222no—
531C23—1221no—
532C23—1221no—
533C23—1222no—
534C23—2444no—
535C23—2444no—
536C23—2448no—
537C23Q16×D6112yescomplemented
538C23C2×D4×D6111yescharacteristic
539Q8—24no—
540Q8—24no—
541Q8—42no—
542Q8—42no—
543Q8—1224no—
544Q8—1224no—
545Q8—24416no—
546Q8—2442no—
547Q8—2442no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—614no—
560C2×C4—612no—
561C2×C4—614no—
562C2×C4—618no—
563C2×C4—614no—
564C2×C4—1224no—
565C2×C4—1224no—
566C2×C4—1222no—
567C2×C4—1221no—
568C2×C4—2444no—
569C2×C4—2444no—
570C2×C4—24416no—
571C2×C4—24416no—
572C2×C4—2444no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2441no—
578C2×C4—2442no—
579C2×C4—2441no—
580C2×C4C2×D4×D6112yes—
581C2×C4C2×D4×D6111yescharacteristic
582C2×C4C2×D4×D6112yes—
583C2×C4#41×D6111yescharacteristic
584C8—22no—
585C8—41no—
586C8—1222no—
587C8—2441no—
588C22—22no—
589C22—24no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—614no—
594C22—614no—
595C22—614no—
596C22—618no—
597C22—618no—
598C22—1222no—
599C22—1224no—
600C22—24416no—
601C22—2441no—
602C22—2441no—
603C22—2442no—
604C22#120×D6112yes—
605C22#121×D6111yescharacteristic
606C22C2×Q16×D6111yescharacteristic
607C22#135×D6111yescharacteristic
608C22#137×D6112yes—
609C4—41no—
610C4—44no—
611C4—44no—
612C4—614no—
613C4—2441no—
614C4—2444no—
615C4—2444no—
616C4#120×D6111yescharacteristic
617C4#121×D6112yes—
618C4#127×D6111yescharacteristic
619C2—42no—
620C2—618no—
621C2—2442no—
622C2#392×D6111yescharacteristic
623C2#451×D6112yes—
624C2#452×D6112yes—
625C2#467×D6111yescharacteristic
626C2#470×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2001C2
socleC23×C61C22×D4
prime radicalC24×D61D4
hypercenter#2001D61
hypocenterC61C2×#2001
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
1. C22×Q16×D61C2semidirect
3. C2×#103×D61C2semidirect
5. #21446830C2semidirect
6. #21446829C2semidirect
7. #21446828C2semidirect
8. #21446827C2semidirect
9. #21446826C2semidirect
10. #340×D61C2semidirect
11. C61×#2001C2semidirect
14. C22×Dic244C22semidirect
15. C22×#11758202C22semidirect
30. C2×#14519702C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519700C22semidirect
38. #16839525C22semidirect
39. #16839524C22semidirect
40. C22×Q16×C61C22semidirect
42. C2×#103×C61C22semidirect
44. C61×#340C22semidirect
121. C23×D61Q16semidirect
208. C23×C61C2×Q16semidirect
222. C22×D61C2×Q16semidirect
315. #2001D61direct (N × H)
324. D61#2001direct (N × H)
331. C22×Q16C2×D61semidirect
349. C2×#103C2×D61semidirect
357. #340C2×D61semidirect
358. C61C2×#2001semidirect
537. C23Q16×D61semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D612
C2×C22⋊Q8×D612
C2×#103×D612
C2×C22⋊C8×D612
#214468302
#214468292
#214468282
#214468272
#214468262
#340×D612
C61×#20012
C2×#200161