Finite Group Databasebeta

← C61×#10322 #29513755

Subgroups — C61×#10322 #29513755

Order 15616.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3187C211yesmaximal, characteristic, complemented
2C61×#2848C211yesmaximal, characteristic, complemented
3C61×#2847C211yesmaximal, characteristic
4C61×#1779C211yesmaximal, characteristic, complemented
5C61×#1520C211yesmaximal, characteristic, complemented
6C61×#1519C211yesmaximal, characteristic, complemented
7C61×#1289C211yesmaximal, characteristic, complemented
8C24×C4×C61C2211yescharacteristic
9C2×C22⋊Q8×C61—21no—
10C2×C22⋊Q8×C61C2211yescharacteristic
11C2×#121×C61—21no—
12C2×#121×C61C2211yescharacteristic
13C2×#120×C61—21no—
14C61×#483—21no—
15C61×#481—21no—
16C61×#465—22no—
17C61×#450—21no—
18C61×#448—21no—
19C2×C22⋊C8×C61—22no—
20C2×C22⋊C8×C61C2211yescharacteristic
21C2×C22⋊C8×C61C2211yescharacteristic
22C61×#386—21no—
23C61×#386—22no—
24C61×#385—21no—
25C61×#385—22no—
26C61×#380—21no—
27C61×#380—21no—
28C61×#380C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C61×#379—21no—
31C61×#328—22no—
32C61×#327—22no—
33C25×C61D411yescharacteristic
34C22×Q8×C61D411yescharacteristic, complemented
35C22×D4×C61—22no—
36C22×D4×C61—21no—
37C22×D4×C61D411yescharacteristic
38C23×C4×C61—21no—
39C23×C4×C61—21no—
40C23×C4×C61—21no—
41C23×C4×C61—21no—
42C23×C4×C61—21no—
43C23×C4×C61—21no—
44C23×C4×C61—44no—
45C23×C4×C61D411yescharacteristic
46C23×C4×C61C2311yescharacteristic
47C2×SD16×C61—22no—
48C22×C8×C61—21no—
49C22×C8×C61D412yescomplemented
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—44no—
55#121×C61—21no—
56#121×C61—21no—
57#121×C61—21no—
58#121×C61—21no—
59#121×C61—44no—
60#120×C61—42no—
61#120×C61—42no—
62C2×C4⋊C4×C61—22no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C4⋊C4×C61D411yescharacteristic, complemented
68C2×C22⋊C4×C61—22no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76#106×C61—22no—
77#103×C61—22no—
78#102×C61—22no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83C22⋊C8×C61—44no—
84#95×C61—22no—
85#95×C61—22no—
86#95×C61D412yes—
87#95×C61D412yescomplemented
88C24×C61—21no—
89C24×C61—21no—
90C24×C61—21no—
91C24×C61—21no—
92C24×C61—21no—
93C24×C61—21no—
94C24×C61—21no—
95C24×C61—42no—
96C24×C61—42no—
97C24×C61SD1612yescomplemented
98C24×C61C2×D411yescharacteristic
99C2×Q8×C61—21no—
100C2×Q8×C61—21no—
101C2×Q8×C61—42no—
102C2×D4×C61—21no—
103C2×D4×C61—21no—
104C2×D4×C61—42no—
105C2×D4×C61—44no—
106C2×D4×C61—44no—
107C2×D4×C61—44no—
108C2×D4×C61—41no—
109C2×D4×C61—41no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C2×D4×C61—41no—
113C2×D4×C61—41no—
114C22×C4×C61—24no—
115C22×C4×C61—24no—
116C22×C4×C61—24no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—21no—
125C22×C4×C61—42no—
126C22×C4×C61—42no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61—41no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61#4111yescharacteristic
146SD16×C61—82no—
147C2×C8×C61—22no—
148C2×C8×C61—42no—
149C2×C8×C61—42no—
150C2×C8×C61—41no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—42no—
156C4⋊C4×C61—42no—
157C4⋊C4×C61—44no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61—41no—
160C22⋊C4×C61—44no—
161C22⋊C4×C61—44no—
162C22⋊C4×C61—44no—
163C22⋊C4×C61—44no—
164C22⋊C4×C61—41no—
165C22⋊C4×C61—41no—
166C22⋊C4×C61—41no—
167C22⋊C4×C61—41no—
168C22⋊C4×C61—41no—
169C22⋊C4×C61—41no—
170C22⋊C4×C61—41no—
171C22⋊C4×C61—41no—
172C23×C61—22no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—41no—
182C23×C61—44no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61—44no—
191C23×C61—44no—
192C23×C61—44no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61#12011yescharacteristic
203C23×C61#12011yescharacteristic
204C23×C61#12111yescharacteristic
205C23×C61C2×SD1611yescharacteristic
206C23×C61#13511yescharacteristic
207C23×C61AGL(1,ℤ/8)11yescharacteristic
208C23×C61#13711yescharacteristic
209Q8×C61—42no—
210Q8×C61—81no—
211D4×C61—42no—
212D4×C61—81no—
213D4×C61—88no—
214D4×C61—81no—
215D4×C61—81no—
216D4×C61—81no—
217D4×C61—81no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—44no—
228C2×C4×C61—44no—
229C2×C4×C61—44no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—44no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61#12011yescharacteristic
249C2×C4×C61#12111yescharacteristic
250C2×C4×C61#12111yescharacteristic
251C2×C4×C61#12711yescharacteristic
252C8×C61—42no—
253C8×C61—81no—
254#10322C6111yesmaximal, characteristic, direct product factor, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—24no—
262C22×C61—24no—
263C22×C61—24no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—82no—
281C22×C61—82no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61#39211yescharacteristic
286C22×C61#44811yescharacteristic
287C22×C61#44911yescharacteristic
288C22×C61#45011yescharacteristic
289C22×C61#45211yescharacteristic
290C22×C61#46511yescharacteristic
291C22×C61#46811yescharacteristic
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—42no—
296C4×C61—82no—
297C4×C61—82no—
298C4×C61—81no—
299C4×C61—81no—
300C4×C61—81no—
301C4×C61B(4,𝔽2)12yes—
302#3187C2×C6111yescharacteristic, complemented
303#2848C2×C6111yescharacteristic, complemented
304#2847C2×C6111yescharacteristic
305#1779C2×C6111yescharacteristic, complemented
306#1520C2×C6111yescharacteristic, complemented
307#1519C2×C6111yescharacteristic, complemented
308#1289C2×C6111yescharacteristic, complemented
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—44no—
316C2×C61—161no—
317C2×C61#200011yescharacteristic
318C2×C61#201011yescharacteristic
319C2×C61#202111yescharacteristic
320C24×C4C22×C6111yescharacteristic
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8C22×C6111yescharacteristic
323C2×#121—21no—
324C2×#121C22×C6111yescharacteristic
325C2×#120—21no—
326#483—21no—
327#481—21no—
328#465—22no—
329#450—21no—
330#448—21no—
331C2×C22⋊C8—22no—
332C2×C22⋊C8C22×C6111yescharacteristic
333C2×C22⋊C8C22×C6111yescharacteristic
334#386—21no—
335#386—22no—
336#385—21no—
337#385—22no—
338#380—21no—
339#380—21no—
340#380C22×C6111yescharacteristic
341#380C22×C6111yescharacteristic
342#379—21no—
343#328—22no—
344#327—22no—
345C61#1032211yescharacteristic, direct product factor, Sylow
346C25D4×C6111yescharacteristic
347C22×Q8D4×C6111yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C6111yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C6111yescharacteristic
359C23×C4C23×C6111yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C6112yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C6111yescharacteristic
380C2×C4⋊C4D4×C6111yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C6112yes—
400#95D4×C6112yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C6112yescomplemented
411C24C2×D4×C6111yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C6111yescharacteristic
454C22×C4C2×D4×C6111yescharacteristic
455C22×C4C2×D4×C6111yescharacteristic
456C22×C4C2×D4×C6111yescharacteristic
457C22×C4C2×D4×C6111yescharacteristic
458C22×C4#41×C6111yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C6111yescharacteristic
516C23#120×C6111yescharacteristic
517C23#121×C6111yescharacteristic
518C23C2×SD16×C6111yescharacteristic
519C23#135×C6111yescharacteristic
520C23AGL(1,ℤ/8)×C6111yescharacteristic
521C23#137×C6111yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C6111yescharacteristic
562C2×C4#121×C6111yescharacteristic
563C2×C4#121×C6111yescharacteristic
564C2×C4#127×C6111yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C61×#39211yescharacteristic
598C22C61×#44811yescharacteristic
599C22C61×#44911yescharacteristic
600C22C61×#45011yescharacteristic
601C22C61×#45211yescharacteristic
602C22C61×#46511yescharacteristic
603C22C61×#46811yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C61×B(4,𝔽2)12yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2C61×#200011yescharacteristic
623C2C61×#201011yescharacteristic
624C2C61×#202111yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC23×C4C23×C61
prime radicalC61×#2847C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3187C2semidirect
2. C61×#2848C2semidirect
4. C61×#1779C2semidirect
5. C61×#1520C2semidirect
6. C61×#1519C2semidirect
7. C61×#1289C2semidirect
34. C22×Q8×C61D4semidirect
49. C22×C8×C61D4semidirect
67. C2×C4⋊C4×C61D4semidirect
87. #95×C61D4semidirect
97. C24×C61SD16semidirect
254. #10322C61direct (N × H)
302. #3187C2×C61semidirect
303. #2848C2×C61semidirect
305. #1779C2×C61semidirect
306. #1520C2×C61semidirect
307. #1519C2×C61semidirect
308. #1289C2×C61semidirect
345. C61#10322direct (N × H)
347. C22×Q8D4×C61semidirect
362. C22×C8D4×C61semidirect
380. C2×C4⋊C4D4×C61semidirect
400. #95D4×C61semidirect
410. C24SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31872
C61×#28482
C61×#28472
C61×#17792
C61×#15202
C61×#15192
C61×#12892
#1032261