Finite Group Databasebeta

← C61×#24689 #29528122

Subgroups — C61×#24689 #29528122

Order 15616.

780 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#479C211yesmaximal, characteristic, complemented
2C2×C61×#440C211yesmaximal, characteristic
3C61×#2566C211yesmaximal, characteristic
4C61×#2355C211yesmaximal, characteristic, complemented
5C61×#2074C211yesmaximal, characteristic, complemented
6C61×#2072C211yesmaximal, characteristic, complemented
7C61×#2055C211yesmaximal, characteristic
8C61×#2055C211yesmaximal, characteristic
9C61×#1992C211yesmaximal, characteristic, complemented
10C61×#1949C211yesmaximal, characteristic, complemented
11C61×#1947C211yesmaximal, characteristic, complemented
12C61×#1940C211yesmaximal, characteristic, complemented
13C61×#1926C211yesmaximal, characteristic
14C61×#1925C211yesmaximal, characteristic
15C61×#1802C211yesmaximal, characteristic
16C22×SD16×C61C2211yescharacteristic
17C2×#125×C61C2211yescharacteristic
18C2×C4×Q8×C61C2211yescharacteristic
19C2×C4×D4×C61C2211yescharacteristic
20C61×#479—24no—
21C61×#440—24no—
22C2×#107×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C2×#106×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×#103×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#97×C61C2211yescharacteristic
35C61×#396—21no—
36C61×#396—21no—
37C61×#391C2211yescharacteristic
38C61×#391C2211yescharacteristic
39C61×#390C2211yescharacteristic
40C61×#390C2211yescharacteristic
41C61×#387—21no—
42C61×#387—21no—
43C61×#385—21no—
44C61×#385—21no—
45C61×#384C2211yescharacteristic
46C61×#384C2211yescharacteristic
47C61×#382—21no—
48C61×#382C2211yescharacteristic
49C4×C4⋊C4×C61—21no—
50C4×C4⋊C4×C61C2211yescharacteristic
51C4×C4⋊C4×C61C2211yescharacteristic
52C4×C4⋊C4×C61C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61C2311yescharacteristic
63C23×C4×C61—21no—
64C2×SD16×C61—22no—
65C2×SD16×C61—22no—
66C2×SD16×C61—22no—
67C22×C8×C61C2311yescharacteristic
68C22×C8×C61C2311yescharacteristic
69C22×C8×C61C2311yescharacteristic
70C22×C8×C61C2311yescharacteristic
71#125×C61—22no—
72#125×C61—22no—
73C4×Q8×C61—22no—
74C4×Q8×C61D414yes—
75C4×D4×C61—22no—
76C4×D4×C61—22no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61D411yescharacteristic
85C2×C4⋊C4×C61D411yescharacteristic
86C2×C4⋊C4×C61C2311yescharacteristic
87C2×C4⋊C4×C61C2311yescharacteristic
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C22⋊C4×C61—21no—
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61C2311yescharacteristic
101C2×C42×C61C2311yescharacteristic
102C2×C42×C61C2311yescharacteristic
103#107×C61—22no—
104#107×C61—22no—
105#106×C61—22no—
106C4⋊C8×C61—22no—
107C4⋊C8×C61—22no—
108C4⋊C8×C61—22no—
109#103×C61—22no—
110#103×C61—22no—
111#103×C61—22no—
112#102×C61—22no—
113#102×C61—22no—
114#102×C61—22no—
115#97×C61—22no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C24×C61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61C2×D412yes—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61#4112yes—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—42no—
147C22×C4×C61—81no—
148C22×C4×C61—81no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156SD16×C61—28no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61#4112yes—
169C4⋊C4×C61—24no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—41no—
183C4⋊C4×C61—42no—
184C4⋊C4×C61—42no—
185C4⋊C4×C61—42no—
186C4⋊C4×C61—81no—
187C4⋊C4×C61—81no—
188C4⋊C4×C61—81no—
189C4⋊C4×C61C2×D412yes—
190C22⋊C4×C61—42no—
191C22⋊C4×C61—42no—
192C22⋊C4×C61—42no—
193C22⋊C4×C61—81no—
194C22⋊C4×C61—81no—
195C42×C61—24no—
196C42×C61—21no—
197C42×C61—21no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—81no—
201C42×C61—81no—
202C42×C61C2×D412yes—
203C42×C61#4112yes—
204C23×C61—22no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61C22×D411yescharacteristic
212Q8×C61—22no—
213Q8×C61—22no—
214Q8×C61—41no—
215Q8×C61—41no—
216D4×C61—22no—
217D4×C61—22no—
218D4×C61—41no—
219D4×C61—41no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
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—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—84no—
257C2×C4×C61#12112yes—
258C2×C4×C61#12112yes—
259C2×C4×C61#13712yes—
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C2×C4×C612−1+411yescharacteristic
266C8×C61—22no—
267C8×C61—41no—
268C8×C61—41no—
269C8×C61—41no—
270#24689C6111yesmaximal, characteristic, direct product factor, Sylow
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—42no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61C2×#12111yescharacteristic
279C22×C61#54711yescharacteristic
280C22×C61#54811yescharacteristic
281C22×C61C2×#13711yescharacteristic
282C22×C61#57511yescharacteristic
283C22×C61#57611yescharacteristic
284C22×C61#57711yescharacteristic
285C4×C61—22no—
286C4×C61—22no—
287C4×C61—22no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—42no—
292C4×C61—42no—
293C4×C61—81no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61—81no—
297C4×C61—81no—
298C4×C61#52511yescharacteristic
299C4×C61#53611yescharacteristic
300C4×C61#55211yescharacteristic
301C4×C61#55611yescharacteristic
302C2×#479C2×C6111yescharacteristic, complemented
303C2×#440C2×C6111yescharacteristic
304#2566C2×C6111yescharacteristic
305#2355C2×C6111yescharacteristic, complemented
306#2074C2×C6111yescharacteristic, complemented
307#2072C2×C6111yescharacteristic, complemented
308#2055C2×C6111yescharacteristic
309#2055C2×C6111yescharacteristic
310#1992C2×C6111yescharacteristic, complemented
311#1949C2×C6111yescharacteristic, complemented
312#1947C2×C6111yescharacteristic, complemented
313#1940C2×C6111yescharacteristic, complemented
314#1926C2×C6111yescharacteristic
315#1925C2×C6111yescharacteristic
316#1802C2×C6111yescharacteristic
317C2×C61—82no—
318C2×C61#241511yescharacteristic
319C2×C61#303711yescharacteristic
320C2×C61#304511yescharacteristic
321C2×C61#334611yescharacteristic
322C2×C61#335011yescharacteristic
323C2×C61#337011yescharacteristic
324C2×C61#337211yescharacteristic
325C22×SD16C22×C6111yescharacteristic
326C2×#125C22×C6111yescharacteristic
327C2×C4×Q8C22×C6111yescharacteristic
328C2×C4×D4C22×C6111yescharacteristic
329#479—24no—
330#440—24no—
331C2×#107C22×C6111yescharacteristic
332C2×#107C22×C6111yescharacteristic
333C2×#106C22×C6111yescharacteristic
334C2×C4⋊C8C22×C6111yescharacteristic
335C2×C4⋊C8C22×C6111yescharacteristic
336C2×C4⋊C8C22×C6111yescharacteristic
337C2×#103C22×C6111yescharacteristic
338C2×#103C22×C6111yescharacteristic
339C2×#103C22×C6111yescharacteristic
340C2×#102C22×C6111yescharacteristic
341C2×#102C22×C6111yescharacteristic
342C2×#102C22×C6111yescharacteristic
343C2×#97C22×C6111yescharacteristic
344#396—21no—
345#396—21no—
346#391C22×C6111yescharacteristic
347#391C22×C6111yescharacteristic
348#390C22×C6111yescharacteristic
349#390C22×C6111yescharacteristic
350#387—21no—
351#387—21no—
352#385—21no—
353#385—21no—
354#384C22×C6111yescharacteristic
355#384C22×C6111yescharacteristic
356#382—21no—
357#382C22×C6111yescharacteristic
358C4×C4⋊C4—21no—
359C4×C4⋊C4C22×C6111yescharacteristic
360C4×C4⋊C4C22×C6111yescharacteristic
361C4×C4⋊C4C22×C6111yescharacteristic
362#340C22×C6111yescharacteristic
363#340C22×C6111yescharacteristic
364#340C22×C6111yescharacteristic
365#340C22×C6111yescharacteristic
366#340C22×C6111yescharacteristic
367#340C22×C6111yescharacteristic
368#336C22×C6111yescharacteristic
369#336C22×C6111yescharacteristic
370C61#2468911yescharacteristic, direct product factor, Sylow
371C22×Q8C23×C6111yescharacteristic
372C22×D4C23×C6111yescharacteristic
373C23×C4—21no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C22×C8C23×C6111yescharacteristic
378C22×C8C23×C6111yescharacteristic
379C22×C8C23×C6111yescharacteristic
380C22×C8C23×C6111yescharacteristic
381#125—22no—
382#125—22no—
383C4×Q8—22no—
384C4×Q8D4×C6114yes—
385C4×D4—22no—
386C4×D4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C6111yescharacteristic
395C2×C4⋊C4D4×C6111yescharacteristic
396C2×C4⋊C4C23×C6111yescharacteristic
397C2×C4⋊C4C23×C6111yescharacteristic
398C2×C4⋊C4C23×C6111yescharacteristic
399C2×C4⋊C4C23×C6111yescharacteristic
400C2×C4⋊C4C23×C6111yescharacteristic
401C2×C4⋊C4C23×C6111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42C23×C6111yescharacteristic
411C2×C42C23×C6111yescharacteristic
412C2×C42C23×C6111yescharacteristic
413#107—22no—
414#107—22no—
415#106—22no—
416C4⋊C8—22no—
417C4⋊C8—22no—
418C4⋊C8—22no—
419#103—22no—
420#103—22no—
421#103—22no—
422#102—22no—
423#102—22no—
424#102—22no—
425#97—22no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95D4×C6111yescharacteristic
435#95D4×C6111yescharacteristic
436C24—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C6112yes—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4#41×C6112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—42no—
457C22×C4—81no—
458C22×C4—81no—
459C22×C4C2×D4×C6111yescharacteristic
460C22×C4C2×D4×C6111yescharacteristic
461C22×C4C2×D4×C6111yescharacteristic
462C22×C4C2×D4×C6111yescharacteristic
463C22×C4C2×D4×C6111yescharacteristic
464C22×C4C2×D4×C6111yescharacteristic
465C22×C4C24×C6111yescharacteristic
466SD16—28no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8#41×C6112yes—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4—81no—
499C4⋊C4C2×D4×C6112yes—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C42—24no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—81no—
511C42—81no—
512C42C2×D4×C6112yes—
513C42#41×C6112yes—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×D4×C6111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—84no—
567C2×C4#121×C6112yes—
568C2×C4#121×C6112yes—
569C2×C4#137×C6112yes—
570C2×C4C22×D4×C6111yescharacteristic
571C2×C4C2×#41×C6111yescharacteristic
572C2×C4C2×#41×C6111yescharacteristic
573C2×C4C2×#41×C6111yescharacteristic
574C2×C42−1+4×C6111yescharacteristic
575C2×C42−1+4×C6111yescharacteristic
576C8—22no—
577C8—41no—
578C8—41no—
579C8—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×#121×C6111yescharacteristic
588C22C61×#54711yescharacteristic
589C22C61×#54811yescharacteristic
590C22C2×#137×C6111yescharacteristic
591C22C61×#57511yescharacteristic
592C22C61×#57611yescharacteristic
593C22C61×#57711yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C61×#52511yescharacteristic
608C4C61×#53611yescharacteristic
609C4C61×#55211yescharacteristic
610C4C61×#55611yescharacteristic
611C2—82no—
612C2C61×#241511yescharacteristic
613C2C61×#303711yescharacteristic
614C2C61×#304511yescharacteristic
615C2C61×#334611yescharacteristic
616C2C61×#335011yescharacteristic
617C2C61×#337011yescharacteristic
618C2C61×#337211yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×D4×C61C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C4⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#479C2semidirect
4. C61×#2355C2semidirect
5. C61×#2074C2semidirect
6. C61×#2072C2semidirect
9. C61×#1992C2semidirect
10. C61×#1949C2semidirect
11. C61×#1947C2semidirect
12. C61×#1940C2semidirect
270. #24689C61direct (N × H)
302. C2×#479C2×C61semidirect
305. #2355C2×C61semidirect
306. #2074C2×C61semidirect
307. #2072C2×C61semidirect
310. #1992C2×C61semidirect
311. #1949C2×C61semidirect
312. #1947C2×C61semidirect
313. #1940C2×C61semidirect
370. C61#24689direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4792
C2×C61×#4402
C61×#25662
C61×#23552
C61×#20742
C61×#20722
C61×#20552
C61×#19922
C61×#19492
C61×#19472
C61×#19402
C61×#19262
C61×#19252
C61×#18022
#2468961