Finite Group Databasebeta

← C61×#15088 #29518521

Subgroups — C61×#15088 #29518521

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#387C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C61C211yesmaximal, characteristic
3C61×#1443C212yesmaximal
4C61×#1442C212yesmaximal
5C61×#1442C211yesmaximal, characteristic
6C61×#1442C211yesmaximal, characteristic
7C61×#1441C211yesmaximal, characteristic
8C61×#1441C211yesmaximal, characteristic
9C61×#1434C212yesmaximal
10C61×#1434C212yesmaximal
11C61×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2211yescharacteristic
16C22×C42×C61C2212yes—
17C22×C42×C61C2211yescharacteristic
18C61×#387—24no—
19C4×C4⋊C4×C61—24no—
20C2×#95×C61C2212yes—
21C2×#95×C61C2211yescharacteristic
22C2×#95×C61C2211yescharacteristic
23C2×#95×C61C2211yescharacteristic
24C2×#95×C61C2211yescharacteristic
25C2×#95×C61C2212yes—
26C2×#95×C61C2211yescharacteristic
27C2×#95×C61C2211yescharacteristic
28C2×#95×C61C2212yes—
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C23×C4×C61C2311yescharacteristic
38C23×C4×C61C2312yes—
39C23×C4×C61C2312yes—
40C23×C4×C61C2311yescharacteristic
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2311yescharacteristic
43C23×C4×C61C2312yes—
44C23×C4×C61C2312yes—
45C23×C4×C61C2311yescharacteristic
46C23×C4×C61C2311yescharacteristic
47C23×C4×C61C2311yescharacteristic
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61—24no—
52C2×C4⋊C4×C61—24no—
53C2×C4⋊C4×C61—22no—
54C2×C4⋊C4×C61—22no—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61—22no—
57C2×C4⋊C4×C61—22no—
58C2×C42×C61—22no—
59C2×C42×C61—22no—
60C2×C42×C61—24no—
61C2×C42×C61—24no—
62C2×C42×C61—24no—
63C2×C42×C61D414yes—
64#95×C61—24no—
65#95×C61—22no—
66#95×C61—22no—
67#95×C61—22no—
68#95×C61—22no—
69#95×C61—24no—
70#95×C61—24no—
71#95×C61—24no—
72#95×C61—24no—
73#95×C61—24no—
74#95×C61—24no—
75#95×C61—22no—
76#95×C61—22no—
77#95×C61—24no—
78#95×C61—42no—
79#95×C61—42no—
80#95×C61—42no—
81C24×C61C2411yescharacteristic
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—21no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2×D412yes—
141C22×C4×C61C2×D412yes—
142C22×C4×C61#4114yes—
143C22×C4×C61#4112yes—
144C22×C4×C61#4114yes—
145C22×C4×C61#4112yes—
146C22×C4×C61#4112yes—
147C22×C4×C61#4112yes—
148C22×C4×C61#4114yes—
149C4⋊C4×C61—28no—
150C4⋊C4×C61—28no—
151C4⋊C4×C61—28no—
152C4⋊C4×C61—44no—
153C42×C61—28no—
154C42×C61—48no—
155C23×C61C22×D411yescharacteristic
156C23×C61C2×#4111yescharacteristic
157C23×C61C2×#4111yescharacteristic
158C23×C61C2×#4112yes—
159C23×C61C2×#4112yes—
160C23×C61C2×#4111yescharacteristic
161C23×C61C2×#4111yescharacteristic
162C23×C61C2×#4112yes—
163C23×C61H(5,𝔽2)11yescharacteristic
164C23×C612−1+412yes—
165C23×C612−1+411yescharacteristic
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—24no—
170C2×C4×C61—24no—
171C2×C4×C61—22no—
172C2×C4×C61—24no—
173C2×C4×C61—24no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—24no—
179C2×C4×C61—22no—
180C2×C4×C61—24no—
181C2×C4×C61—24no—
182C2×C4×C61—22no—
183C2×C4×C61—24no—
184C2×C4×C61—24no—
185C2×C4×C61—22no—
186C2×C4×C61—24no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—41no—
196C2×C4×C61—42no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—41no—
200C2×C4×C61—42no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—42no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61#12314yes—
232C2×C4×C61#12414yes—
233#15088C6111yesmaximal, characteristic, direct product factor, Sylow
234C22×C61C2×#12311yescharacteristic
235C22×C61#52511yescharacteristic
236C22×C61#52511yescharacteristic
237C22×C61#52511yescharacteristic
238C22×C61C2×#12411yescharacteristic
239C22×C61#52912yes—
240C22×C61#52912yes—
241C22×C61#52912yes—
242C22×C61#52912yes—
243C22×C61#53611yescharacteristic
244C22×C61#53711yescharacteristic
245C22×C61#54112yes—
246C22×C61#54212yes—
247C22×C61#55212yes—
248C22×C61#55212yes—
249C22×C61#55211yescharacteristic
250C22×C61#55212yes—
251C22×C61#55212yes—
252C22×C61#55312yes—
253C22×C61#55311yescharacteristic
254C22×C61#55511yescharacteristic
255C22×C61#55612yes—
256C22×C61#55611yescharacteristic
257C4×C61—24no—
258C4×C61—24no—
259C4×C61—44no—
260C4×C61—42no—
261C4×C61—44no—
262C4×C61—42no—
263C4×C61—42no—
264C4×C61—81no—
265C4×C61—81no—
266C4×C61—82no—
267C4×C61—82no—
268C2×#387C2×C6111yescharacteristic
269C2×C4×C4⋊C4C2×C6111yescharacteristic
270#1443C2×C6112yes—
271#1442C2×C6111yescharacteristic
272#1442C2×C6111yescharacteristic
273#1442C2×C6112yes—
274#1441C2×C6111yescharacteristic
275#1441C2×C6111yescharacteristic
276#1434C2×C6111yescharacteristic
277#1434C2×C6112yes—
278#1434C2×C6112yes—
279C2×C61#239811yescharacteristic
280C2×C61#248511yescharacteristic
281C2×C61#250311yescharacteristic
282C2×C61#252412yes—
283C2×C61#252512yes—
284C2×C61#252812yes—
285C2×C61#252912yes—
286C2×C61#256211yescharacteristic
287C2×C61#259911yescharacteristic
288C2×C61#263711yescharacteristic
289C2×C61#285311yescharacteristic
290C22×C4⋊C4C22×C6111yescharacteristic
291C22×C4⋊C4C22×C6111yescharacteristic
292C22×C4⋊C4C22×C6111yescharacteristic
293C22×C4⋊C4C22×C6111yescharacteristic
294C22×C42C22×C6112yes—
295C22×C42C22×C6111yescharacteristic
296#387—24no—
297C4×C4⋊C4—24no—
298C2×#95C22×C6112yes—
299C2×#95C22×C6111yescharacteristic
300C2×#95C22×C6111yescharacteristic
301C2×#95C22×C6111yescharacteristic
302C2×#95C22×C6111yescharacteristic
303C2×#95C22×C6112yes—
304C2×#95C22×C6112yes—
305C2×#95C22×C6112yes—
306C2×#95C22×C6112yes—
307C2×#95C22×C6112yes—
308C2×#95C22×C6112yes—
309C2×#95C22×C6111yescharacteristic
310C2×#95C22×C6112yes—
311C2×#95C22×C6111yescharacteristic
312C2×#95C22×C6112yes—
313C2×#95C22×C6112yes—
314C2×#95C22×C6112yes—
315C61#1508811yescharacteristic, direct product factor, Sylow
316C23×C4C23×C6111yescharacteristic
317C23×C4C23×C6111yescharacteristic
318C23×C4C23×C6112yes—
319C23×C4C23×C6112yes—
320C23×C4C23×C6111yescharacteristic
321C23×C4C23×C6111yescharacteristic
322C23×C4C23×C6111yescharacteristic
323C23×C4C23×C6112yes—
324C23×C4C23×C6112yes—
325C23×C4C23×C6111yescharacteristic
326C23×C4C23×C6111yescharacteristic
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42D4×C6114yes—
343#95—24no—
344#95—22no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—22no—
355#95—22no—
356#95—24no—
357#95—42no—
358#95—42no—
359#95—42no—
360C24C24×C6111yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4C2×D4×C6112yes—
419C22×C4C2×D4×C6112yes—
420C22×C4C2×D4×C6112yes—
421C22×C4#41×C6112yes—
422C22×C4#41×C6114yes—
423C22×C4#41×C6112yes—
424C22×C4#41×C6114yes—
425C22×C4#41×C6112yes—
426C22×C4#41×C6112yes—
427C22×C4#41×C6114yes—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—28no—
431C4⋊C4—44no—
432C42—28no—
433C42—48no—
434C23C22×D4×C6111yescharacteristic
435C23C2×#41×C6112yes—
436C23C2×#41×C6112yes—
437C23C2×#41×C6111yescharacteristic
438C23C2×#41×C6111yescharacteristic
439C23C2×#41×C6112yes—
440C23C2×#41×C6111yescharacteristic
441C23C2×#41×C6111yescharacteristic
442C23H(5,𝔽2)×C6111yescharacteristic
443C232−1+4×C6112yes—
444C232−1+4×C6111yescharacteristic
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4#123×C6114yes—
511C2×C4#124×C6114yes—
512C22C2×#123×C6111yescharacteristic
513C22C61×#52511yescharacteristic
514C22C61×#52511yescharacteristic
515C22C61×#52511yescharacteristic
516C22C2×#124×C6111yescharacteristic
517C22C61×#52912yes—
518C22C61×#52912yes—
519C22C61×#52912yes—
520C22C61×#52912yes—
521C22C61×#53611yescharacteristic
522C22C61×#53711yescharacteristic
523C22C61×#54112yes—
524C22C61×#54212yes—
525C22C61×#55212yes—
526C22C61×#55212yes—
527C22C61×#55212yes—
528C22C61×#55211yescharacteristic
529C22C61×#55212yes—
530C22C61×#55311yescharacteristic
531C22C61×#55312yes—
532C22C61×#55511yescharacteristic
533C22C61×#55611yescharacteristic
534C22C61×#55612yes—
535C4—24no—
536C4—24no—
537C4—44no—
538C4—42no—
539C4—44no—
540C4—42no—
541C4—42no—
542C4—82no—
543C4—82no—
544C4—81no—
545C4—81no—
546C2C61×#239811yescharacteristic
547C2C61×#248511yescharacteristic
548C2C61×#250311yescharacteristic
549C2C61×#252412yes—
550C2C61×#252512yes—
551C2C61×#252812yes—
552C2C61×#252912yes—
553C2C61×#256211yescharacteristic
554C2C61×#259911yescharacteristic
555C2C61×#263711yescharacteristic
556C2C61×#285311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C61C24
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
233. #15088C61direct (N × H)
315. C61#15088direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#3872
C2×C4×C4⋊C4×C612
C61×#14432
C61×#14422
C61×#14412
C61×#14342
#1508861