Finite Group Databasebeta

← C61×#15103 #29518536

Subgroups — C61×#15103 #29518536

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#400C211yesmaximal, characteristic, complemented
2C2×C61×#399C211yesmaximal, characteristic
3C2×C61×#388C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
5C61×#1441C212yesmaximal, complemented
6C61×#1441C211yesmaximal, characteristic, complemented
7C61×#1439C212yesmaximal
8C61×#1439C211yesmaximal, characteristic
9C61×#1437C212yesmaximal
10C61×#1436C212yesmaximal, complemented
11C61×C4⋊#95C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2212yes—
15C22×C4⋊C4×C61C2212yes—
16C22×C4⋊C4×C61C2211yescharacteristic
17C22×C22⋊C4×C61C2211yescharacteristic
18C22×C22⋊C4×C61C2211yescharacteristic
19C22×C22⋊C4×C61C2212yes—
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2212yes—
22C22×C42×C61C2211yescharacteristic
23C22×C42×C61C2212yes—
24C61×#400—24no—
25C61×#399—24no—
26C61×#388—24no—
27C4×C4⋊C4×C61—24no—
28C2×#95×C61C2212yes—
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C25×C61C2311yescharacteristic
40C23×C4×C61C2312yes—
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2311yescharacteristic
43C23×C4×C61C2312yes—
44C23×C4×C61C2311yescharacteristic
45C23×C4×C61C2312yes—
46C23×C4×C61C2312yes—
47C23×C4×C61C2311yescharacteristic
48C23×C4×C61C2311yescharacteristic
49C23×C4×C61C2311yescharacteristic
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—24no—
53C2×C4⋊C4×C61—22no—
54C2×C4⋊C4×C61—22no—
55C2×C4⋊C4×C61—24no—
56C2×C4⋊C4×C61—22no—
57C2×C4⋊C4×C61—24no—
58C2×C4⋊C4×C61—24no—
59C2×C4⋊C4×C61—24no—
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—42no—
62C2×C4⋊C4×C61—42no—
63C2×C4⋊C4×C61D414yes—
64C2×C22⋊C4×C61—22no—
65C2×C22⋊C4×C61—22no—
66C2×C22⋊C4×C61—22no—
67C2×C22⋊C4×C61—22no—
68C2×C22⋊C4×C61—24no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—24no—
71C2×C22⋊C4×C61—24no—
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61—24no—
74C2×C22⋊C4×C61—42no—
75C2×C22⋊C4×C61—42no—
76C2×C22⋊C4×C61—42no—
77C2×C22⋊C4×C61Q814yes—
78C2×C42×C61—24no—
79C2×C42×C61—24no—
80C2×C42×C61—42no—
81C2×C42×C61—42no—
82C2×C42×C61D414yes—
83#95×C61—24no—
84#95×C61—22no—
85#95×C61—22no—
86#95×C61—22no—
87#95×C61—24no—
88#95×C61—22no—
89#95×C61—24no—
90#95×C61—24no—
91#95×C61—24no—
92#95×C61—42no—
93#95×C61—42no—
94C24×C61—21no—
95C24×C61—21no—
96C24×C61—21no—
97C24×C61—22no—
98C24×C61—22no—
99C24×C61—21no—
100C24×C61—22no—
101C24×C61—22no—
102C24×C61—21no—
103C24×C61—21no—
104C24×C61C2×Q812yes—
105C24×C61C2411yescharacteristic
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61C2×D414yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2×Q812yes—
160C22×C4×C61C2×Q812yes—
161C22×C4×C61#4114yes—
162C22×C4×C61#4114yes—
163C22×C4×C61#4112yes—
164C22×C4×C61#4112yes—
165C22×C4×C61#4114yes—
166C4⋊C4×C61—28no—
167C4⋊C4×C61—28no—
168C4⋊C4×C61—48no—
169C4⋊C4×C61—48no—
170C4⋊C4×C61—44no—
171C22⋊C4×C61—28no—
172C22⋊C4×C61—48no—
173C22⋊C4×C61—48no—
174C22⋊C4×C61—44no—
175C22⋊C4×C61—44no—
176C42×C61—28no—
177C42×C61—48no—
178C23×C61—22no—
179C23×C61—24no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—24no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—41no—
189C23×C61—42no—
190C23×C61—41no—
191C23×C61—41no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—41no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61—42no—
199C23×C61—41no—
200C23×C61—42no—
201C23×C61C22×D411yescharacteristic
202C23×C61C22×D411yescharacteristic
203C23×C61C22×Q811yescharacteristic
204C23×C61C2×#4111yescharacteristic
205C23×C61C2×#4111yescharacteristic
206C23×C61C2×#4112yes—
207C23×C61C2×#4112yes—
208C23×C61C2×#4112yes—
209C23×C61H(5,𝔽2)12yes—
210C23×C61H(5,𝔽2)11yescharacteristic
211C23×C612−1+411yescharacteristic
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—24no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—24no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—24no—
225C2×C4×C61—22no—
226C2×C4×C61—24no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—41no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—41no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—41no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—41no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—41no—
260C2×C4×C61—42no—
261C2×C4×C61—41no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61#12114yes—
270C2×C4×C61C22⋊Q814yes—
271C2×C4×C61#12314yes—
272#15103C6111yesmaximal, characteristic, direct product factor, Sylow
273C22×C61—44no—
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—44no—
278C22×C61—82no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—82no—
284C22×C61C2×#12111yescharacteristic
285C22×C61C2×C22⋊Q811yescharacteristic
286C22×C61C2×#12311yescharacteristic
287C22×C61#52511yescharacteristic
288C22×C61#52912yes—
289C22×C61#52912yes—
290C22×C61#53212yes—
291C22×C61#53211yescharacteristic
292C22×C61#53312yes—
293C22×C61#53511yescharacteristic
294C22×C61#53711yescharacteristic
295C22×C61#53812yes—
296C22×C61#53912yes—
297C22×C61#54612yes—
298C22×C61D4×Q811yescharacteristic
299C22×C61#55011yescharacteristic
300C22×C61#55112yes—
301C22×C61#55212yes—
302C22×C61#55312yes—
303C22×C61#55411yescharacteristic
304C22×C61#55412yes—
305C22×C61#55611yescharacteristic
306C22×C61#55912yes—
307C4×C61—24no—
308C4×C61—24no—
309C4×C61—24no—
310C4×C61—44no—
311C4×C61—42no—
312C4×C61—44no—
313C4×C61—44no—
314C4×C61—81no—
315C4×C61—81no—
316C4×C61—82no—
317C2×#400C2×C6111yescharacteristic, complemented
318C2×#399C2×C6111yescharacteristic
319C2×#388C2×C6111yescharacteristic
320C2×C4×C4⋊C4C2×C6111yescharacteristic, complemented
321#1441C2×C6111yescharacteristic, complemented
322#1441C2×C6112yescomplemented
323#1439C2×C6111yescharacteristic
324#1439C2×C6112yes—
325#1437C2×C6112yes—
326#1436C2×C6112yescomplemented
327C4⋊#95C2×C6111yescharacteristic, complemented
328C2×C61—82no—
329C2×C61#239611yescharacteristic
330C2×C61#248711yescharacteristic
331C2×C61#249811yescharacteristic
332C2×C61#253811yescharacteristic
333C2×C61#254411yescharacteristic
334C2×C61#255412yes—
335C2×C61#255612yes—
336C2×C61#258912yes—
337C2×C61#259612yes—
338C2×C61#263611yescharacteristic
339C2×C61#285411yescharacteristic
340C22×C4⋊C4C22×C6111yescharacteristic
341C22×C4⋊C4C22×C6111yescharacteristic
342C22×C4⋊C4C22×C6112yes—
343C22×C4⋊C4C22×C6112yes—
344C22×C4⋊C4C22×C6111yescharacteristic
345C22×C22⋊C4C22×C6111yescharacteristic
346C22×C22⋊C4C22×C6111yescharacteristic
347C22×C22⋊C4C22×C6112yes—
348C22×C22⋊C4C22×C6111yescharacteristic
349C22×C22⋊C4C22×C6112yes—
350C22×C42C22×C6111yescharacteristic
351C22×C42C22×C6112yes—
352#400—24no—
353#399—24no—
354#388—24no—
355C4×C4⋊C4—24no—
356C2×#95C22×C6111yescharacteristic
357C2×#95C22×C6111yescharacteristic
358C2×#95C22×C6112yes—
359C2×#95C22×C6112yes—
360C2×#95C22×C6112yes—
361C2×#95C22×C6111yescharacteristic
362C2×#95C22×C6112yes—
363C2×#95C22×C6112yes—
364C2×#95C22×C6111yescharacteristic
365C2×#95C22×C6112yes—
366C2×#95C22×C6112yes—
367C61#1510311yescharacteristic, direct product factor, Sylow
368C25C23×C6111yescharacteristic
369C23×C4C23×C6111yescharacteristic
370C23×C4C23×C6112yes—
371C23×C4C23×C6111yescharacteristic
372C23×C4C23×C6112yes—
373C23×C4C23×C6111yescharacteristic
374C23×C4C23×C6112yes—
375C23×C4C23×C6112yes—
376C23×C4C23×C6111yescharacteristic
377C23×C4C23×C6111yescharacteristic
378C23×C4C23×C6111yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4D4×C6114yes—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4Q8×C6114yes—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42D4×C6114yes—
412#95—24no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—24no—
417#95—22no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—42no—
422#95—42no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24C2×Q8×C6112yes—
434C24C24×C6111yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4C2×D4×C6114yes—
484C22×C4C2×D4×C6112yes—
485C22×C4C2×D4×C6112yes—
486C22×C4C2×D4×C6112yes—
487C22×C4C2×D4×C6112yes—
488C22×C4C2×Q8×C6112yes—
489C22×C4C2×Q8×C6112yes—
490C22×C4#41×C6114yes—
491C22×C4#41×C6114yes—
492C22×C4#41×C6112yes—
493C22×C4#41×C6112yes—
494C22×C4#41×C6114yes—
495C4⋊C4—28no—
496C4⋊C4—28no—
497C4⋊C4—48no—
498C4⋊C4—48no—
499C4⋊C4—44no—
500C22⋊C4—28no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C22⋊C4—44no—
504C22⋊C4—44no—
505C42—28no—
506C42—48no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—22no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23C22×D4×C6111yescharacteristic
531C23C22×D4×C6111yescharacteristic
532C23C22×Q8×C6111yescharacteristic
533C23C2×#41×C6112yes—
534C23C2×#41×C6112yes—
535C23C2×#41×C6112yes—
536C23C2×#41×C6111yescharacteristic
537C23C2×#41×C6111yescharacteristic
538C23H(5,𝔽2)×C6112yes—
539C23H(5,𝔽2)×C6111yescharacteristic
540C232−1+4×C6111yescharacteristic
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4#121×C6114yes—
599C2×C4C22⋊Q8×C6114yes—
600C2×C4#123×C6114yes—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—81no—
607C22—82no—
608C22—82no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22C2×#121×C6111yescharacteristic
613C22C2×C22⋊Q8×C6111yescharacteristic
614C22C2×#123×C6111yescharacteristic
615C22C61×#52511yescharacteristic
616C22C61×#52912yes—
617C22C61×#52912yes—
618C22C61×#53211yescharacteristic
619C22C61×#53212yes—
620C22C61×#53312yes—
621C22C61×#53511yescharacteristic
622C22C61×#53711yescharacteristic
623C22C61×#53812yes—
624C22C61×#53912yes—
625C22C61×#54612yes—
626C22D4×Q8×C6111yescharacteristic
627C22C61×#55011yescharacteristic
628C22C61×#55112yes—
629C22C61×#55212yes—
630C22C61×#55312yes—
631C22C61×#55411yescharacteristic
632C22C61×#55412yes—
633C22C61×#55611yescharacteristic
634C22C61×#55912yes—
635C4—24no—
636C4—24no—
637C4—24no—
638C4—42no—
639C4—44no—
640C4—44no—
641C4—44no—
642C4—81no—
643C4—82no—
644C4—81no—
645C2—82no—
646C2C61×#239611yescharacteristic
647C2C61×#248711yescharacteristic
648C2C61×#249811yescharacteristic
649C2C61×#253811yescharacteristic
650C2C61×#254411yescharacteristic
651C2C61×#255412yes—
652C2C61×#255612yes—
653C2C61×#258912yes—
654C2C61×#259612yes—
655C2C61×#263611yescharacteristic
656C2C61×#285411yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#400C2semidirect
4. C2×C4×C4⋊C4×C61C2semidirect
5. C61×#1441C2semidirect
6. C61×#1441C2semidirect
10. C61×#1436C2semidirect
11. C61×C4⋊#95C2semidirect
272. #15103C61direct (N × H)
317. C2×#400C2×C61semidirect
320. C2×C4×C4⋊C4C2×C61semidirect
321. #1441C2×C61semidirect
322. #1441C2×C61semidirect
326. #1436C2×C61semidirect
327. C4⋊#95C2×C61semidirect
367. C61#15103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4002
C2×C61×#3992
C2×C61×#3882
C2×C4×C4⋊C4×C612
C61×#14412
C61×#14392
C61×#14372
C61×#14362
C61×C4⋊#952
#1510361