Finite Group Databasebeta

← C61×#13082 #29516515

Subgroups — C61×#13082 #29516515

Order 15616.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C61C211yesmaximal, characteristic, complemented
2C61×#2403C211yesmaximal, characteristic
3C2×C61×AΣL(1,𝔽16)C212yesmaximal, complemented
4C61×#1781C211yesmaximal, characteristic, complemented
5C61×#1390C212yesmaximal, complemented
6C23×D4×C61C411yescharacteristic, complemented
7C23×D4×C61C2211yescharacteristic
8C22×M16×C61—21no—
9C2×#120×C61—21no—
10C2×#120×C61C411yescharacteristic, complemented
11C2×#120×C61C2211yescharacteristic
12C2×#100×C61—21no—
13C2×#100×C61—24no—
14C2×#100×C61C2212yes—
15C2×#99×C61—21no—
16C2×#99×C61C2212yes—
17C61×#392—21no—
18C61×#392—21no—
19C61×#386—21no—
20C61×#386C411yescharacteristic, complemented
21C61×#386C2211yescharacteristic
22C61×#379—21no—
23C61×#379C411yescharacteristic, complemented
24C61×AΣL(1,𝔽16)—24no—
25C25×C61C2×C411yescharacteristic
26C25×C61C2×C411yescharacteristic
27C25×C61D411yescharacteristic
28C22×D4×C61—21no—
29C22×D4×C61—22no—
30C22×D4×C61—22no—
31C22×D4×C61—21no—
32C22×D4×C61—21no—
33C22×D4×C61—21no—
34C22×D4×C61—42no—
35C22×D4×C61—41no—
36C22×D4×C61—41no—
37C22×D4×C61—44no—
38C22×D4×C61—41no—
39C22×D4×C61—41no—
40C22×D4×C61C2×C411yescharacteristic
41C22×D4×C61D411yescharacteristic
42C22×D4×C61D411yescharacteristic
43C22×D4×C61C2311yescharacteristic
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C2×M16×C61—24no—
47C2×M16×C61—22no—
48C2×M16×C61—41no—
49C2×M16×C61—42no—
50C22×C8×C61—41no—
51#120×C61—22no—
52#120×C61—22no—
53#120×C61—44no—
54#120×C61—42no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—22no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—41no—
63C2×C22⋊C4×C61—41no—
64C2×C22⋊C4×C61C2×C411yescharacteristic
65C2×C22⋊C4×C61C2×C411yescharacteristic
66#100×C61—24no—
67#100×C61—22no—
68#100×C61D414yescomplemented
69#99×C61—22no—
70#99×C61—22no—
71#99×C61—42no—
72#95×C61—21no—
73#95×C61—21no—
74C24×C61—21no—
75C24×C61—21no—
76C24×C61—21no—
77C24×C61—21no—
78C24×C61—21no—
79C24×C61—22no—
80C24×C61—22no—
81C24×C61—22no—
82C24×C61—41no—
83C24×C61—41no—
84C24×C61—42no—
85C24×C61—41no—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61—41no—
89C24×C61—81no—
90C24×C61—81no—
91C24×C61—81no—
92C24×C61C22⋊C411yescharacteristic
93C24×C61C22⋊C411yescharacteristic
94C24×C61C22⋊C411yescharacteristic
95C24×C61C22×C411yescharacteristic
96C24×C61C2×D411yescharacteristic
97C2×D4×C61—24no—
98C2×D4×C61—22no—
99C2×D4×C61—22no—
100C2×D4×C61—22no—
101C2×D4×C61—22no—
102C2×D4×C61—21no—
103C2×D4×C61—21no—
104C2×D4×C61—41no—
105C2×D4×C61—41no—
106C2×D4×C61—41no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61—41no—
110C2×D4×C61—44no—
111C2×D4×C61—44no—
112C2×D4×C61—44no—
113C2×D4×C61—44no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C2×D4×C61—44no—
119C2×D4×C61—44no—
120C2×D4×C61—44no—
121C2×D4×C61—41no—
122C2×D4×C61—41no—
123C2×D4×C61—44no—
124C2×D4×C61—42no—
125C2×D4×C61—42no—
126C2×D4×C61—42no—
127C2×D4×C61—42no—
128C2×D4×C61—81no—
129C2×D4×C61—81no—
130C2×D4×C61C2×D412yes—
131C2×D4×C61#4112yes—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—42no—
141C22×C4×C61—41no—
142C22×C4×C61—42no—
143C22×C4×C61C22⋊C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145M16×C61—24no—
146M16×C61—44no—
147M16×C61—42no—
148C2×C8×C61—44no—
149C2×C8×C61—42no—
150C22⋊C4×C61—22no—
151C22⋊C4×C61—42no—
152C22⋊C4×C61—42no—
153C22⋊C4×C61—42no—
154C22⋊C4×C61—42no—
155C22⋊C4×C61—41no—
156C22⋊C4×C61—41no—
157C22⋊C4×C61—41no—
158C22⋊C4×C61—42no—
159C22⋊C4×C61—42no—
160C22⋊C4×C61—81no—
161C22⋊C4×C61—82no—
162C22⋊C4×C61—82no—
163C23×C61—22no—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61—21no—
167C23×C61—21no—
168C23×C61—21no—
169C23×C61—21no—
170C23×C61—22no—
171C23×C61—21no—
172C23×C61—21no—
173C23×C61—21no—
174C23×C61—21no—
175C23×C61—21no—
176C23×C61—21no—
177C23×C61—41no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61—41no—
188C23×C61—42no—
189C23×C61—41no—
190C23×C61—42no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—42no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—42no—
202C23×C61—81no—
203C23×C61—81no—
204C23×C61—81no—
205C23×C61—81no—
206C23×C61—82no—
207C23×C61—84no—
208C23×C61—84no—
209C23×C61—84no—
210C23×C61—84no—
211C23×C61—84no—
212C23×C61—84no—
213C23×C61—82no—
214C23×C61#9911yescharacteristic
215C23×C61#9911yescharacteristic
216C23×C61C2×C22⋊C411yescharacteristic
217C23×C61C4×D412yes—
218C23×C61#12112yes—
219D4×C61—42no—
220D4×C61—42no—
221D4×C61—44no—
222D4×C61—44no—
223D4×C61—42no—
224D4×C61—42no—
225D4×C61—44no—
226D4×C61—48no—
227D4×C61—44no—
228D4×C61—84no—
229D4×C61—84no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—22no—
239C2×C4×C61—41no—
240C2×C4×C61—42no—
241C2×C4×C61—41no—
242C2×C4×C61—42no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—82no—
250C2×C4×C61—82no—
251C2×C4×C61—82no—
252C2×C4×C61#9912yes—
253C2×C4×C61#12011yescharacteristic
254C2×C4×C61#12311yescharacteristic
255C8×C61—44no—
256#13082C6111yesmaximal, characteristic, direct product factor, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—22no—
265C22×C61—22no—
266C22×C61—42no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—42no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—42no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—81no—
286C22×C61—84no—
287C22×C61—84no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61—81no—
293C22×C61—84no—
294C22×C61—84no—
295C22×C61—84no—
296C22×C61—84no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61AΣL(1,𝔽16)12yescomplemented
300C22×C61#38611yescharacteristic
301C22×C61C2×#9911yescharacteristic
302C22×C61C2×#9911yescharacteristic
303C4×C61—21no—
304C4×C61—22no—
305C4×C61—21no—
306C4×C61—42no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61—162no—
310C22×#100C2×C6111yescharacteristic, complemented
311#2403C2×C6111yescharacteristic
312C2×AΣL(1,𝔽16)C2×C6112yescomplemented
313#1781C2×C6111yescharacteristic, complemented
314#1390C2×C6112yescomplemented
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—22no—
318C2×C61—42no—
319C2×C61—41no—
320C2×C61—42no—
321C2×C61—81no—
322C2×C61—82no—
323C2×C61—81no—
324C2×C61#189811yescharacteristic
325C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
326C2×C61#212111yescharacteristic
327C23×D4C4×C6111yescharacteristic, complemented
328C23×D4C22×C6111yescharacteristic
329C22×M16—21no—
330C2×#120—21no—
331C2×#120C4×C6111yescharacteristic, complemented
332C2×#120C22×C6111yescharacteristic
333C2×#100—21no—
334C2×#100—24no—
335C2×#100C22×C6112yes—
336C2×#99—21no—
337C2×#99C22×C6112yes—
338#392—21no—
339#392—21no—
340#386—21no—
341#386C4×C6111yescharacteristic, complemented
342#386C22×C6111yescharacteristic
343#379—21no—
344#379C4×C6111yescharacteristic, complemented
345AΣL(1,𝔽16)—24no—
346C61#1308211yescharacteristic, direct product factor, Sylow
347C25C2×C4×C6111yescharacteristic
348C25C2×C4×C6111yescharacteristic
349C25D4×C6111yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—44no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C6111yescharacteristic
363C22×D4D4×C6111yescharacteristic
364C22×D4D4×C6111yescharacteristic
365C22×D4C23×C6111yescharacteristic
366C23×C4C2×C4×C6111yescharacteristic
367C23×C4D4×C6111yescharacteristic
368C2×M16—24no—
369C2×M16—22no—
370C2×M16—41no—
371C2×M16—42no—
372C22×C8—41no—
373#120—22no—
374#120—22no—
375#120—44no—
376#120—42no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4C2×C4×C6111yescharacteristic
387C2×C22⋊C4C2×C4×C6111yescharacteristic
388#100—24no—
389#100—22no—
390#100D4×C6114yescomplemented
391#99—22no—
392#99—22no—
393#99—42no—
394#95—21no—
395#95—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—41no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C6111yescharacteristic
415C24C22⋊C4×C6111yescharacteristic
416C24C22⋊C4×C6111yescharacteristic
417C24C22×C4×C6111yescharacteristic
418C24C2×D4×C6111yescharacteristic
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C6112yes—
453C2×D4#41×C6112yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4C22⋊C4×C6111yescharacteristic
466C22×C4C2×D4×C6111yescharacteristic
467M16—24no—
468M16—44no—
469M16—42no—
470C2×C8—44no—
471C2×C8—42no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—82no—
484C22⋊C4—82no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23#99×C6111yescharacteristic
537C23#99×C6111yescharacteristic
538C23C2×C22⋊C4×C6111yescharacteristic
539C23C4×D4×C6112yes—
540C23#121×C6112yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#99×C6112yes—
575C2×C4#120×C6111yescharacteristic
576C2×C4#123×C6111yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22C61×AΣL(1,𝔽16)12yescomplemented
621C22C61×#38611yescharacteristic
622C22C2×#99×C6111yescharacteristic
623C22C2×#99×C6111yescharacteristic
624C4—21no—
625C4—22no—
626C4—21no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2C61×#189811yescharacteristic
641C2C2×C61×AΣL(1,𝔽16)11yescharacteristic
642C2C61×#212111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#99
commutatorC24C22×C4×C61
Frattini, cosocleC22×D4C23×C61
prime radicalC61×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C24×C61 ◁ C23×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#100×C61C2semidirect
3. C2×C61×AΣL(1,𝔽16)C2semidirect
4. C61×#1781C2semidirect
5. C61×#1390C2semidirect
6. C23×D4×C61C4semidirect
10. C2×#120×C61C4semidirect
20. C61×#386C4semidirect
23. C61×#379C4semidirect
68. #100×C61D4semidirect
256. #13082C61direct (N × H)
299. C22×C61AΣL(1,𝔽16)semidirect
310. C22×#100C2×C61semidirect
312. C2×AΣL(1,𝔽16)C2×C61semidirect
313. #1781C2×C61semidirect
314. #1390C2×C61semidirect
327. C23×D4C4×C61semidirect
331. C2×#120C4×C61semidirect
341. #386C4×C61semidirect
344. #379C4×C61semidirect
346. C61#13082direct (N × H)
390. #100D4×C61semidirect
620. C22C61×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C612
C61×#24032
C2×C61×AΣL(1,𝔽16)2
C61×#17812
C61×#13902
#1308261