Finite Group Databasebeta

← C61×#14318 #29517751

Subgroups — C61×#14318 #29517751

Order 15616.

1254 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#400C211yesmaximal, characteristic
2C2×C61×#389C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C61C211yesmaximal, characteristic
4C61×#1445C211yesmaximal, characteristic
5C61×#1444C211yesmaximal, characteristic
6C61×#1444C212yesmaximal
7C61×#1442C212yesmaximal
8C61×#1441C211yesmaximal, characteristic
9C61×#1436C212yesmaximal
10C61×#1434C212yesmaximal
11C61×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2211yescharacteristic
16C22×C4⋊C4×C61C2212yes—
17C22×C4⋊C4×C61C2212yes—
18C22×C42×C61C2211yescharacteristic
19C22×C42×C61C2211yescharacteristic
20C22×C42×C61C2211yescharacteristic
21C61×#400C418yescomplemented
22C61×#389—24no—
23C4×C4⋊C4×C61—24no—
24C2×#95×C61C2211yescharacteristic
25C2×#95×C61C2211yescharacteristic
26C2×#95×C61C2212yes—
27C2×#95×C61C2212yes—
28C2×#95×C61C2212yes—
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C23×C4×C61C2312yes—
39C23×C4×C61C2312yes—
40C23×C4×C61C2312yes—
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2312yes—
43C23×C4×C61C2311yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C23×C4×C61C2311yescharacteristic
46C23×C4×C61C2311yescharacteristic
47C23×C4×C61C2311yescharacteristic
48C23×C4×C61C2311yescharacteristic
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—22no—
53C2×C4⋊C4×C61—22no—
54C2×C4⋊C4×C61—22no—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61—24no—
57C2×C4⋊C4×C61—22no—
58C2×C4⋊C4×C61—24no—
59C2×C4⋊C4×C61—42no—
60C2×C4⋊C4×C61—42no—
61C2×C4⋊C4×C61—42no—
62C2×C4⋊C4×C61—42no—
63C2×C4⋊C4×C61—42no—
64C2×C4⋊C4×C61C2×C414yes—
65C2×C4⋊C4×C61C2×C414yes—
66C2×C42×C61—22no—
67C2×C42×C61—22no—
68C2×C42×C61—22no—
69C2×C42×C61—42no—
70C2×C42×C61—42no—
71C2×C42×C61D414yes—
72C2×C42×C61Q814yes—
73#95×C61—22no—
74#95×C61—22no—
75#95×C61—24no—
76#95×C61—24no—
77#95×C61—22no—
78#95×C61—24no—
79#95×C61—42no—
80#95×C61—42no—
81#95×C61—42no—
82#95×C61—42no—
83#95×C61—42no—
84#95×C61C2×C414yes—
85#95×C61C2×C418yes—
86#95×C61C2×C418yes—
87C24×C61C2411yescharacteristic
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
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—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—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×C61C22×C414yes—
139C22×C4×C61C22×C412yes—
140C22×C4×C61C22×C414yes—
141C22×C4×C61C22×C412yes—
142C22×C4×C61C22×C412yes—
143C22×C4×C61C2×D412yes—
144C22×C4×C61C2×D412yes—
145C22×C4×C61C2×D412yes—
146C22×C4×C61C2×Q812yes—
147C22×C4×C61C2×Q812yes—
148C22×C4×C61C2×Q812yes—
149C22×C4×C61#4112yes—
150C22×C4×C61#4112yes—
151C22×C4×C61#4112yes—
152C22×C4×C61#4112yes—
153C4⋊C4×C61—28no—
154C4⋊C4×C61—28no—
155C4⋊C4×C61—28no—
156C4⋊C4×C61—44no—
157C4⋊C4×C61—48no—
158C4⋊C4×C61—48no—
159C42×C61—28no—
160C42×C61—44no—
161C42×C61—44no—
162C23×C61C23×C411yescharacteristic
163C23×C61C22×D411yescharacteristic
164C23×C61C22×Q811yescharacteristic
165C23×C61C2×#4111yescharacteristic
166C23×C61C2×#4111yescharacteristic
167C23×C61C2×#4111yescharacteristic
168C23×C61C2×#4111yescharacteristic
169C23×C61H(5,𝔽2)12yes—
170C23×C61H(5,𝔽2)12yes—
171C23×C612−1+412yes—
172C23×C612−1+412yes—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—24no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—24no—
185C2×C4×C61—24no—
186C2×C4×C61—24no—
187C2×C4×C61—22no—
188C2×C4×C61—24no—
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—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
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—42no—
209C2×C4×C61—41no—
210C2×C4×C61—42no—
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—42no—
218C2×C4×C61—42no—
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—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61C4×D414yes—
236C2×C4×C61C4×Q814yes—
237C2×C4×C61C22⋊Q814yes—
238#14318C6111yesmaximal, characteristic, direct product factor, Sylow
239C22×C61C2×C4×D411yescharacteristic
240C22×C61C2×C4×Q811yescharacteristic
241C22×C61C4×#4111yescharacteristic
242C22×C61#52012yes—
243C22×C61#52012yes—
244C22×C61C2×C22⋊Q811yescharacteristic
245C22×C61#52511yescharacteristic
246C22×C61#52911yescharacteristic
247C22×C61#53311yescharacteristic
248C22×C61#53411yescharacteristic
249C22×C61#53511yescharacteristic
250C22×C61#53611yescharacteristic
251C22×C61#53611yescharacteristic
252C22×C61#53812yes—
253C22×C61#53912yes—
254C22×C61#53912yes—
255C22×C61#54012yes—
256C22×C61#54112yes—
257C22×C61#54112yes—
258C22×C61#54212yes—
259C22×C61#54212yes—
260C22×C61#54412yes—
261C22×C61#54412yes—
262C4×C61—24no—
263C4×C61—24no—
264C4×C61—24no—
265C4×C61—42no—
266C4×C61—44no—
267C4×C61—44no—
268C4×C61—42no—
269C4×C61—42no—
270C4×C61—42no—
271C4×C61—82no—
272C4×C61—82no—
273C2×#400C2×C6111yescharacteristic
274C2×#389C2×C6111yescharacteristic
275C2×C4×C4⋊C4C2×C6111yescharacteristic
276#1445C2×C6111yescharacteristic
277#1444C2×C6112yes—
278#1444C2×C6111yescharacteristic
279#1442C2×C6112yes—
280#1441C2×C6111yescharacteristic
281#1436C2×C6112yes—
282#1434C2×C6111yescharacteristic
283#1434C2×C6112yes—
284C2×C61C4×C22⋊Q811yescharacteristic
285C2×C61#232211yescharacteristic
286C2×C61#232611yescharacteristic
287C2×C61#233012yes—
288C2×C61#233412yes—
289C2×C61#262711yescharacteristic
290C2×C61#262811yescharacteristic
291C2×C61#263411yescharacteristic
292C2×C61#263511yescharacteristic
293C2×C61#265412yes—
294C2×C61#266612yes—
295C22×C4⋊C4C22×C6111yescharacteristic
296C22×C4⋊C4C22×C6111yescharacteristic
297C22×C4⋊C4C22×C6111yescharacteristic
298C22×C4⋊C4C22×C6112yes—
299C22×C4⋊C4C22×C6111yescharacteristic
300C22×C4⋊C4C22×C6112yes—
301C22×C42C22×C6111yescharacteristic
302C22×C42C22×C6111yescharacteristic
303C22×C42C22×C6111yescharacteristic
304#400C4×C6118yescomplemented
305#389—24no—
306C4×C4⋊C4—24no—
307C2×#95C22×C6112yes—
308C2×#95C22×C6112yes—
309C2×#95C22×C6112yes—
310C2×#95C22×C6111yescharacteristic
311C2×#95C22×C6111yescharacteristic
312C2×#95C22×C6111yescharacteristic
313C2×#95C22×C6112yes—
314C2×#95C22×C6112yes—
315C2×#95C22×C6112yes—
316C2×#95C22×C6112yes—
317C2×#95C22×C6112yes—
318C2×#95C22×C6112yes—
319C2×#95C22×C6111yescharacteristic
320C2×#95C22×C6112yes—
321C61#1431811yescharacteristic, direct product factor, Sylow
322C23×C4C23×C6112yes—
323C23×C4C23×C6112yes—
324C23×C4C23×C6112yes—
325C23×C4C23×C6112yes—
326C23×C4C23×C6111yescharacteristic
327C23×C4C23×C6111yescharacteristic
328C23×C4C23×C6111yescharacteristic
329C23×C4C23×C6111yescharacteristic
330C23×C4C23×C6111yescharacteristic
331C23×C4C23×C6111yescharacteristic
332C23×C4C23×C6111yescharacteristic
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4C2×C4×C6114yes—
349C2×C4⋊C4C2×C4×C6114yes—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42D4×C6114yes—
356C2×C42Q8×C6114yes—
357#95—22no—
358#95—22no—
359#95—24no—
360#95—24no—
361#95—22no—
362#95—24no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95C2×C4×C6114yes—
369#95C2×C4×C6118yes—
370#95C2×C4×C6118yes—
371C24C24×C6111yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
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—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4C22×C4×C6114yes—
423C22×C4C22×C4×C6114yes—
424C22×C4C22×C4×C6112yes—
425C22×C4C22×C4×C6112yes—
426C22×C4C22×C4×C6112yes—
427C22×C4C2×D4×C6112yes—
428C22×C4C2×D4×C6112yes—
429C22×C4C2×D4×C6112yes—
430C22×C4C2×Q8×C6112yes—
431C22×C4C2×Q8×C6112yes—
432C22×C4C2×Q8×C6112yes—
433C22×C4#41×C6112yes—
434C22×C4#41×C6112yes—
435C22×C4#41×C6112yes—
436C22×C4#41×C6112yes—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—28no—
440C4⋊C4—44no—
441C4⋊C4—48no—
442C4⋊C4—48no—
443C42—28no—
444C42—44no—
445C42—44no—
446C23C23×C4×C6111yescharacteristic
447C23C22×D4×C6111yescharacteristic
448C23C22×Q8×C6111yescharacteristic
449C23C2×#41×C6111yescharacteristic
450C23C2×#41×C6111yescharacteristic
451C23C2×#41×C6111yescharacteristic
452C23C2×#41×C6111yescharacteristic
453C23H(5,𝔽2)×C6112yes—
454C23H(5,𝔽2)×C6112yes—
455C232−1+4×C6112yes—
456C232−1+4×C6112yes—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4C4×D4×C6114yes—
520C2×C4C4×Q8×C6114yes—
521C2×C4C22⋊Q8×C6114yes—
522C22C2×C4×D4×C6111yescharacteristic
523C22C2×C4×Q8×C6111yescharacteristic
524C22C4×#41×C6111yescharacteristic
525C22C61×#52012yes—
526C22C61×#52012yes—
527C22C2×C22⋊Q8×C6111yescharacteristic
528C22C61×#52511yescharacteristic
529C22C61×#52911yescharacteristic
530C22C61×#53311yescharacteristic
531C22C61×#53411yescharacteristic
532C22C61×#53511yescharacteristic
533C22C61×#53611yescharacteristic
534C22C61×#53611yescharacteristic
535C22C61×#53812yes—
536C22C61×#53912yes—
537C22C61×#53912yes—
538C22C61×#54012yes—
539C22C61×#54112yes—
540C22C61×#54112yes—
541C22C61×#54212yes—
542C22C61×#54212yes—
543C22C61×#54412yes—
544C22C61×#54412yes—
545C4—24no—
546C4—24no—
547C4—24no—
548C4—42no—
549C4—44no—
550C4—44no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—82no—
555C4—82no—
556C2C4×C22⋊Q8×C6111yescharacteristic
557C2C61×#232211yescharacteristic
558C2C61×#232611yescharacteristic
559C2C61×#233012yes—
560C2C61×#233412yes—
561C2C61×#262711yescharacteristic
562C2C61×#262811yescharacteristic
563C2C61×#263411yescharacteristic
564C2C61×#263511yescharacteristic
565C2C61×#265412yes—
566C2C61×#266612yes—
subgroupG/H
center, socle, prime radicalC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
21. C61×#400C4semidirect
238. #14318C61direct (N × H)
304. #400C4×C61semidirect
321. C61#14318direct (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×#3892
C2×C4×C4⋊C4×C612
C61×#14452
C61×#14442
C61×#14422
C61×#14412
C61×#14362
C61×#14342
#1431861