Finite Group Databasebeta

← C61×#14409 #29517842

Subgroups — C61×#14409 #29517842

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#387C212yesmaximal, complemented
2C2×C61×#385C211yesmaximal, characteristic
3C2×C61×#380C212yesmaximal
4C61×#1442C212yesmaximal, complemented
5C61×#1441C212yesmaximal, complemented
6C61×#1440C212yesmaximal
7C61×#1437C211yesmaximal, characteristic
8C61×#1437C211yesmaximal, characteristic
9C61×#1436C212yesmaximal, complemented
10C24×C4×C61C2211yescharacteristic
11C22×C4⋊C4×C61C2212yes—
12C22×C4⋊C4×C61C2212yes—
13C22×C4⋊C4×C61C2212yes—
14C22×C22⋊C4×C61C2212yes—
15C22×C22⋊C4×C61C2212yes—
16C22×C22⋊C4×C61C2211yescharacteristic
17C22×C22⋊C4×C61C2211yescharacteristic
18C22×C42×C61C2211yescharacteristic
19C22×C42×C61C2211yescharacteristic
20C61×#387—28no—
21C61×#385C418yescomplemented
22C61×#380—28no—
23C2×#95×C61C2212yes—
24C2×#95×C61C2212yes—
25C2×#95×C61C2212yes—
26C2×#95×C61C2212yes—
27C2×#95×C61C2212yes—
28C2×#95×C61C2212yes—
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C25×C61C2311yescharacteristic
35C23×C4×C61—24no—
36C23×C4×C61—24no—
37C23×C4×C61—41no—
38C23×C4×C61—41no—
39C23×C4×C61C2×C414yes—
40C23×C4×C61C2312yes—
41C23×C4×C61C2312yes—
42C23×C4×C61C2311yescharacteristic
43C23×C4×C61C2312yes—
44C23×C4×C61C2311yescharacteristic
45C23×C4×C61C2312yes—
46C23×C4×C61C2312yes—
47C23×C4×C61C2312yes—
48C2×C4⋊C4×C61—24no—
49C2×C4⋊C4×C61—24no—
50C2×C4⋊C4×C61—24no—
51C2×C4⋊C4×C61—24no—
52C2×C4⋊C4×C61—24no—
53C2×C4⋊C4×C61—24no—
54C2×C4⋊C4×C61—42no—
55C2×C4⋊C4×C61—42no—
56C2×C4⋊C4×C61C2×C418yes—
57C2×C22⋊C4×C61—24no—
58C2×C22⋊C4×C61—24no—
59C2×C22⋊C4×C61—24no—
60C2×C22⋊C4×C61—24no—
61C2×C22⋊C4×C61—24no—
62C2×C22⋊C4×C61—41no—
63C2×C22⋊C4×C61—41no—
64C2×C22⋊C4×C61—42no—
65C2×C22⋊C4×C61—42no—
66C2×C22⋊C4×C61C2×C414yes—
67C2×C22⋊C4×C61C2×C414yes—
68C2×C42×C61—24no—
69C2×C42×C61—41no—
70C2×C42×C61—42no—
71C2×C42×C61—41no—
72#95×C61—24no—
73#95×C61—24no—
74#95×C61—24no—
75#95×C61—24no—
76#95×C61—42no—
77#95×C61—42no—
78#95×C61—42no—
79#95×C61—41no—
80#95×C61—41no—
81#95×C61C2×C418yes—
82#95×C61D418yes—
83C24×C61—22no—
84C24×C61—22no—
85C24×C61—22no—
86C24×C61—21no—
87C24×C61—21no—
88C24×C61—22no—
89C24×C61—22no—
90C24×C61C22×C412yes—
91C24×C61#4114yes—
92C24×C61C2411yescharacteristic
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
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—216no—
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—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—44no—
139C22×C4×C61—44no—
140C22×C4×C61—48no—
141C22×C4×C61—44no—
142C22×C4×C61C22×C412yes—
143C22×C4×C61C22×C414yes—
144C22×C4×C61C22×C412yes—
145C22×C4×C61C22×C414yes—
146C22×C4×C61C2×D414yes—
147C22×C4×C61C2×D414yes—
148C22×C4×C61C2×D414yes—
149C22×C4×C61#4114yes—
150C4⋊C4×C61—216no—
151C4⋊C4×C61—48no—
152C4⋊C4×C61—48no—
153C22⋊C4×C61—28no—
154C22⋊C4×C61—44no—
155C22⋊C4×C61—48no—
156C22⋊C4×C61—48no—
157C42×C61—44no—
158C42×C61—44no—
159C23×C61—24no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61—24no—
163C23×C61—24no—
164C23×C61—24no—
165C23×C61—24no—
166C23×C61—24no—
167C23×C61—24no—
168C23×C61—24no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—41no—
174C23×C61—42no—
175C23×C61—41no—
176C23×C61—41no—
177C23×C61—42no—
178C23×C61—41no—
179C23×C61#11714yes—
180C23×C61C23×C411yescharacteristic
181C23×C61C22×D412yes—
182C23×C61C2×#4112yes—
183C23×C61C2×#4112yes—
184C23×C61H(5,𝔽2)11yescharacteristic
185C23×C61H(5,𝔽2)11yescharacteristic
186C23×C61H(5,𝔽2)12yes—
187C23×C612−1+412yes—
188C23×C612−1+412yes—
189C2×C4×C61—24no—
190C2×C4×C61—24no—
191C2×C4×C61—24no—
192C2×C4×C61—24no—
193C2×C4×C61—24no—
194C2×C4×C61—24no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—24no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
202C2×C4×C61—24no—
203C2×C4×C61—24no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—24no—
208C2×C4×C61—416no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—41no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—41no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—41no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—41no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
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×C61C4×D418yes—
242#14409C6111yesmaximal, characteristic, direct product factor, Sylow
243C22×C61—24no—
244C22×C61—28no—
245C22×C61—44no—
246C22×C61—42no—
247C22×C61—42no—
248C22×C61—44no—
249C22×C61—44no—
250C22×C61—44no—
251C22×C61—44no—
252C22×C61C2×#11711yescharacteristic
253C22×C61C2×C4×D412yes—
254C22×C61#51811yescharacteristic
255C22×C61#51911yescharacteristic
256C22×C61#52012yes—
257C22×C61#53612yes—
258C22×C61#53712yes—
259C22×C61#53912yes—
260C22×C61#53912yes—
261C22×C61#54112yes—
262C22×C61#54212yes—
263C22×C61D4211yescharacteristic
264C22×C61#54612yes—
265C22×C61#54612yes—
266C22×C61#54812yes—
267C22×C61#55111yescharacteristic
268C22×C61#55212yes—
269C22×C61#55312yes—
270C22×C61#56011yescharacteristic
271C22×C61#56212yes—
272C22×C61#56311yescharacteristic
273C4×C61—28no—
274C4×C61—44no—
275C4×C61—42no—
276C4×C61—42no—
277C4×C61—44no—
278C4×C61—44no—
279C4×C61—82no—
280C4×C61—82no—
281C2×#387C2×C6112yescomplemented
282C2×#385C2×C6111yescharacteristic
283C2×#380C2×C6112yes—
284#1442C2×C6112yescomplemented
285#1441C2×C6112yescomplemented
286#1440C2×C6112yes—
287#1437C2×C6111yescharacteristic
288#1437C2×C6111yescharacteristic
289#1436C2×C6112yescomplemented
290C2×C61—44no—
291C2×C61#231311yescharacteristic
292C2×C61#232312yes—
293C2×C61#235212yes—
294C2×C61#235811yescharacteristic
295C2×C61#237611yescharacteristic
296C2×C61#268112yes—
297C2×C61#269012yes—
298C2×C61#269112yes—
299C2×C61#274712yes—
300C24×C4C22×C6111yescharacteristic
301C22×C4⋊C4C22×C6112yes—
302C22×C4⋊C4C22×C6112yes—
303C22×C4⋊C4C22×C6112yes—
304C22×C22⋊C4C22×C6112yes—
305C22×C22⋊C4C22×C6112yes—
306C22×C22⋊C4C22×C6111yescharacteristic
307C22×C22⋊C4C22×C6111yescharacteristic
308C22×C42C22×C6111yescharacteristic
309C22×C42C22×C6111yescharacteristic
310#387—28no—
311#385C4×C6118yescomplemented
312#380—28no—
313C2×#95C22×C6112yes—
314C2×#95C22×C6112yes—
315C2×#95C22×C6112yes—
316C2×#95C22×C6112yes—
317C2×#95C22×C6112yes—
318C2×#95C22×C6112yes—
319C2×#95C22×C6111yescharacteristic
320C2×#95C22×C6111yescharacteristic
321C2×#95C22×C6112yes—
322C2×#95C22×C6112yes—
323C2×#95C22×C6112yes—
324C61#1440911yescharacteristic, direct product factor, Sylow
325C25C23×C6111yescharacteristic
326C23×C4—24no—
327C23×C4—24no—
328C23×C4—41no—
329C23×C4—41no—
330C23×C4C2×C4×C6114yes—
331C23×C4C23×C6112yes—
332C23×C4C23×C6112yes—
333C23×C4C23×C6111yescharacteristic
334C23×C4C23×C6112yes—
335C23×C4C23×C6111yescharacteristic
336C23×C4C23×C6112yes—
337C23×C4C23×C6112yes—
338C23×C4C23×C6112yes—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4C2×C4×C6118yes—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4C2×C4×C6114yes—
358C2×C22⋊C4C2×C4×C6114yes—
359C2×C42—24no—
360C2×C42—41no—
361C2×C42—42no—
362C2×C42—41no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—41no—
371#95—41no—
372#95C2×C4×C6118yes—
373#95D4×C6118yes—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—22no—
381C24C22×C4×C6112yes—
382C24#41×C6114yes—
383C24C24×C6111yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—216no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4C22×C4×C6112yes—
434C22×C4C22×C4×C6114yes—
435C22×C4C22×C4×C6112yes—
436C22×C4C22×C4×C6114yes—
437C22×C4C2×D4×C6114yes—
438C22×C4C2×D4×C6114yes—
439C22×C4C2×D4×C6114yes—
440C22×C4#41×C6114yes—
441C4⋊C4—216no—
442C4⋊C4—48no—
443C4⋊C4—48no—
444C22⋊C4—28no—
445C22⋊C4—44no—
446C22⋊C4—48no—
447C22⋊C4—48no—
448C42—44no—
449C42—44no—
450C23—24no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—22no—
458C23—22no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—41no—
470C23#117×C6114yes—
471C23C23×C4×C6111yescharacteristic
472C23C22×D4×C6112yes—
473C23C2×#41×C6112yes—
474C23C2×#41×C6112yes—
475C23H(5,𝔽2)×C6112yes—
476C23H(5,𝔽2)×C6111yescharacteristic
477C23H(5,𝔽2)×C6111yescharacteristic
478C232−1+4×C6112yes—
479C232−1+4×C6112yes—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4C4×D4×C6118yes—
533C22—24no—
534C22—28no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22C2×#117×C6111yescharacteristic
543C22C2×C4×D4×C6112yes—
544C22C61×#51811yescharacteristic
545C22C61×#51911yescharacteristic
546C22C61×#52012yes—
547C22C61×#53612yes—
548C22C61×#53712yes—
549C22C61×#53912yes—
550C22C61×#53912yes—
551C22C61×#54112yes—
552C22C61×#54212yes—
553C22D42×C6111yescharacteristic
554C22C61×#54612yes—
555C22C61×#54612yes—
556C22C61×#54812yes—
557C22C61×#55111yescharacteristic
558C22C61×#55212yes—
559C22C61×#55312yes—
560C22C61×#56011yescharacteristic
561C22C61×#56212yes—
562C22C61×#56311yescharacteristic
563C4—28no—
564C4—44no—
565C4—42no—
566C4—42no—
567C4—44no—
568C4—44no—
569C4—82no—
570C4—82no—
571C2—44no—
572C2C61×#231311yescharacteristic
573C2C61×#232312yes—
574C2C61×#235212yes—
575C2C61×#235811yescharacteristic
576C2C61×#237611yescharacteristic
577C2C61×#268112yes—
578C2C61×#269012yes—
579C2C61×#269112yes—
580C2C61×#274712yes—
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#387C2semidirect
4. C61×#1442C2semidirect
5. C61×#1441C2semidirect
9. C61×#1436C2semidirect
21. C61×#385C4semidirect
242. #14409C61direct (N × H)
281. C2×#387C2×C61semidirect
284. #1442C2×C61semidirect
285. #1441C2×C61semidirect
289. #1436C2×C61semidirect
311. #385C4×C61semidirect
324. C61#14409direct (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×C61×#3852
C2×C61×#3802
C61×#14422
C61×#14412
C61×#14402
C61×#14372
C61×#14362
#1440961