Finite Group Databasebeta

← C61×#14929 #29518362

Subgroups — C61×#14929 #29518362

Order 15616.

1506 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
1C22×#125×C61C211yesmaximal, characteristic
2C2×C61×#389C212yesmaximal
3C2×C61×#387C211yesmaximal, characteristic
4C61×#1444C211yesmaximal, characteristic
5C61×#1444C211yesmaximal, characteristic
6C61×#1444C212yesmaximal
7C61×#1442C211yesmaximal, characteristic
8C61×#1442C211yesmaximal, characteristic
9C61×#1441C212yesmaximal
10C61×#1436C212yesmaximal
11C4×#95×C61C211yesmaximal, characteristic
12C2×#125×C61—28no—
13C2×#125×C61—24no—
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2211yescharacteristic
16C22×C4⋊C4×C61C2212yes—
17C22×C4⋊C4×C61C2212yes—
18C22×C4⋊C4×C61C2211yescharacteristic
19C22×C4⋊C4×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2212yes—
21C22×C4⋊C4×C61C2212yes—
22C22×C42×C61C2212yes—
23C22×C42×C61C2211yescharacteristic
24C61×#389—28no—
25C61×#387—24no—
26C2×#95×C61C2211yescharacteristic
27C2×#95×C61C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C23×C4×C61C2311yescharacteristic
40C23×C4×C61C2311yescharacteristic
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2312yes—
43C23×C4×C61C2312yes—
44C23×C4×C61C2312yes—
45C23×C4×C61C2311yescharacteristic
46C23×C4×C61C2311yescharacteristic
47C23×C4×C61C2311yescharacteristic
48C23×C4×C61C2311yescharacteristic
49C23×C4×C61C2312yes—
50#125×C61—232no—
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—24no—
53C2×C4⋊C4×C61—24no—
54C2×C4⋊C4×C61—24no—
55C2×C4⋊C4×C61—24no—
56C2×C4⋊C4×C61—24no—
57C2×C4⋊C4×C61—24no—
58C2×C4⋊C4×C61—22no—
59C2×C4⋊C4×C61—22no—
60C2×C4⋊C4×C61—24no—
61C2×C4⋊C4×C61—24no—
62C2×C4⋊C4×C61—24no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—22no—
65C2×C4⋊C4×C61—24no—
66C2×C4⋊C4×C61—22no—
67C2×C4⋊C4×C61—24no—
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61—24no—
70C2×C4⋊C4×C61—42no—
71C2×C4⋊C4×C61D418yes—
72C2×C42×C61—24no—
73C2×C42×C61—24no—
74C2×C42×C61—24no—
75C2×C42×C61—42no—
76C2×C42×C61D414yes—
77#95×C61—22no—
78#95×C61—22no—
79#95×C61—22no—
80#95×C61—22no—
81#95×C61—24no—
82#95×C61—24no—
83#95×C61—24no—
84#95×C61—24no—
85#95×C61—24no—
86#95×C61—24no—
87#95×C61—42no—
88#95×C61Q814yes—
89#95×C61Q814yes—
90C24×C61C2411yescharacteristic
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
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—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
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—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
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—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61C2×D412yes—
141C22×C4×C61C2×D414yes—
142C22×C4×C61C2×D414yes—
143C22×C4×C61C2×D412yes—
144C22×C4×C61C2×D414yes—
145C22×C4×C61C2×D412yes—
146C22×C4×C61C2×Q814yes—
147C22×C4×C61C2×Q814yes—
148C22×C4×C61C2×Q812yes—
149C22×C4×C61C2×Q812yes—
150C22×C4×C61#4112yes—
151C22×C4×C61#4112yes—
152C22×C4×C61#4114yes—
153C22×C4×C61#4114yes—
154C4⋊C4×C61—216no—
155C4⋊C4×C61—28no—
156C4⋊C4×C61—28no—
157C4⋊C4×C61—28no—
158C4⋊C4×C61—216no—
159C4⋊C4×C61—216no—
160C4⋊C4×C61—48no—
161C4⋊C4×C61—44no—
162C42×C61—28no—
163C42×C61—48no—
164C23×C61C22×D411yescharacteristic
165C23×C61C22×D412yes—
166C23×C61C22×Q811yescharacteristic
167C23×C61C22×Q811yescharacteristic
168C23×C61C2×#4111yescharacteristic
169C23×C61C2×#4112yes—
170C23×C61C2×#4111yescharacteristic
171C23×C61C2×#4112yes—
172C23×C61H(5,𝔽2)11yescharacteristic
173C23×C612−1+412yes—
174C23×C612−1+411yescharacteristic
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—24no—
181C2×C4×C61—24no—
182C2×C4×C61—24no—
183C2×C4×C61—24no—
184C2×C4×C61—24no—
185C2×C4×C61—24no—
186C2×C4×C61—24no—
187C2×C4×C61—24no—
188C2×C4×C61—24no—
189C2×C4×C61—22no—
190C2×C4×C61—24no—
191C2×C4×C61—24no—
192C2×C4×C61—22no—
193C2×C4×C61—24no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—24no—
197C2×C4×C61—22no—
198C2×C4×C61—24no—
199C2×C4×C61—24no—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
202C2×C4×C61—24no—
203C2×C4×C61—24no—
204C2×C4×C61—24no—
205C2×C4×C61—41no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
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—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—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61#12014yes—
236C2×C4×C61#12518yescomplemented
237C2×C4×C61C4⋊Q814yes—
238#14929C6111yesmaximal, characteristic, direct product factor, Sylow
239C22×C61C2×#12011yescharacteristic
240C22×C61#52511yescharacteristic
241C22×C61#52512yes—
242C22×C61C2×#12512yes—
243C22×C61C2×C4⋊Q811yescharacteristic
244C22×C61#53211yescharacteristic
245C22×C61#53211yescharacteristic
246C22×C61#53212yes—
247C22×C61#53312yes—
248C22×C61#53611yescharacteristic
249C22×C61#53711yescharacteristic
250C22×C61#53912yes—
251C22×C61#54112yes—
252C22×C61#54612yes—
253C22×C61#54712yes—
254C22×C61D4×Q812yes—
255C22×C61D4×Q812yes—
256C22×C61#55212yes—
257C22×C61#55212yes—
258C22×C61#55411yescharacteristic
259C22×C61#55411yescharacteristic
260C22×C61#55711yescharacteristic
261C22×C61#55711yescharacteristic
262C4×C61—24no—
263C4×C61—24no—
264C4×C61—28no—
265C4×C61—42no—
266C4×C61—42no—
267C4×C61—44no—
268C4×C61—42no—
269C4×C61—44no—
270C4×C61—44no—
271C4×C61—81no—
272C4×C61—81no—
273C22×#125C2×C6111yescharacteristic
274C2×#389C2×C6112yes—
275C2×#387C2×C6111yescharacteristic
276#1444C2×C6112yes—
277#1444C2×C6111yescharacteristic
278#1444C2×C6111yescharacteristic
279#1442C2×C6111yescharacteristic
280#1442C2×C6111yescharacteristic
281#1441C2×C6112yes—
282#1436C2×C6112yes—
283C4×#95C2×C6111yescharacteristic
284C2×C61#238811yescharacteristic
285C2×C61#243011yescharacteristic
286C2×C61#243411yescharacteristic
287C2×C61#246212yes—
288C2×C61#247312yes—
289C2×C61#250612yes—
290C2×C61#255612yes—
291C2×C61#258411yescharacteristic
292C2×C61#261111yescharacteristic
293C2×C61#266411yescharacteristic
294C2×C61#285911yescharacteristic
295C2×#125—28no—
296C2×#125—24no—
297C22×C4⋊C4C22×C6112yes—
298C22×C4⋊C4C22×C6111yescharacteristic
299C22×C4⋊C4C22×C6111yescharacteristic
300C22×C4⋊C4C22×C6111yescharacteristic
301C22×C4⋊C4C22×C6112yes—
302C22×C4⋊C4C22×C6111yescharacteristic
303C22×C4⋊C4C22×C6112yes—
304C22×C4⋊C4C22×C6112yes—
305C22×C42C22×C6112yes—
306C22×C42C22×C6111yescharacteristic
307#389—28no—
308#387—24no—
309C2×#95C22×C6112yes—
310C2×#95C22×C6111yescharacteristic
311C2×#95C22×C6112yes—
312C2×#95C22×C6112yes—
313C2×#95C22×C6112yes—
314C2×#95C22×C6111yescharacteristic
315C2×#95C22×C6112yes—
316C2×#95C22×C6111yescharacteristic
317C2×#95C22×C6111yescharacteristic
318C2×#95C22×C6112yes—
319C2×#95C22×C6112yes—
320C2×#95C22×C6111yescharacteristic
321C2×#95C22×C6111yescharacteristic
322C61#1492911yescharacteristic, direct product factor, Sylow
323C23×C4C23×C6111yescharacteristic
324C23×C4C23×C6111yescharacteristic
325C23×C4C23×C6112yes—
326C23×C4C23×C6112yes—
327C23×C4C23×C6111yescharacteristic
328C23×C4C23×C6112yes—
329C23×C4C23×C6111yescharacteristic
330C23×C4C23×C6111yescharacteristic
331C23×C4C23×C6111yescharacteristic
332C23×C4C23×C6111yescharacteristic
333C23×C4C23×C6112yes—
334#125—232no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4D4×C6118yes—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—42no—
360C2×C42D4×C6114yes—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—22no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—42no—
372#95Q8×C6114yes—
373#95Q8×C6114yes—
374C24C24×C6111yescharacteristic
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
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—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4C2×D4×C6112yes—
425C22×C4C2×D4×C6114yes—
426C22×C4C2×D4×C6114yes—
427C22×C4C2×D4×C6112yes—
428C22×C4C2×D4×C6114yes—
429C22×C4C2×D4×C6112yes—
430C22×C4C2×Q8×C6114yes—
431C22×C4C2×Q8×C6114yes—
432C22×C4C2×Q8×C6112yes—
433C22×C4C2×Q8×C6112yes—
434C22×C4#41×C6112yes—
435C22×C4#41×C6112yes—
436C22×C4#41×C6114yes—
437C22×C4#41×C6114yes—
438C4⋊C4—28no—
439C4⋊C4—28no—
440C4⋊C4—216no—
441C4⋊C4—216no—
442C4⋊C4—28no—
443C4⋊C4—216no—
444C4⋊C4—48no—
445C4⋊C4—44no—
446C42—28no—
447C42—48no—
448C23C22×D4×C6111yescharacteristic
449C23C22×D4×C6112yes—
450C23C22×Q8×C6111yescharacteristic
451C23C22×Q8×C6111yescharacteristic
452C23C2×#41×C6112yes—
453C23C2×#41×C6111yescharacteristic
454C23C2×#41×C6112yes—
455C23C2×#41×C6111yescharacteristic
456C23H(5,𝔽2)×C6111yescharacteristic
457C232−1+4×C6112yes—
458C232−1+4×C6111yescharacteristic
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4#120×C6114yes—
520C2×C4#125×C6118yescomplemented
521C2×C4C4⋊Q8×C6114yes—
522C22C2×#120×C6111yescharacteristic
523C22C61×#52511yescharacteristic
524C22C61×#52512yes—
525C22C2×#125×C6112yes—
526C22C2×C4⋊Q8×C6111yescharacteristic
527C22C61×#53212yes—
528C22C61×#53211yescharacteristic
529C22C61×#53211yescharacteristic
530C22C61×#53312yes—
531C22C61×#53611yescharacteristic
532C22C61×#53711yescharacteristic
533C22C61×#53912yes—
534C22C61×#54112yes—
535C22C61×#54612yes—
536C22C61×#54712yes—
537C22D4×Q8×C6112yes—
538C22D4×Q8×C6112yes—
539C22C61×#55212yes—
540C22C61×#55212yes—
541C22C61×#55411yescharacteristic
542C22C61×#55411yescharacteristic
543C22C61×#55711yescharacteristic
544C22C61×#55711yescharacteristic
545C4—24no—
546C4—24no—
547C4—28no—
548C4—44no—
549C4—42no—
550C4—42no—
551C4—44no—
552C4—42no—
553C4—44no—
554C4—81no—
555C4—81no—
556C2C61×#238811yescharacteristic
557C2C61×#243011yescharacteristic
558C2C61×#243411yescharacteristic
559C2C61×#246212yes—
560C2C61×#247312yes—
561C2C61×#250612yes—
562C2C61×#255612yes—
563C2C61×#258411yescharacteristic
564C2C61×#261111yescharacteristic
565C2C61×#266411yescharacteristic
566C2C61×#285911yescharacteristic
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
236. C2×C4×C61#125semidirect
238. #14929C61direct (N × H)
322. C61#14929direct (N × H)
520. C2×C4#125×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C612
C2×C61×#3892
C2×C61×#3872
C61×#14442
C61×#14422
C61×#14412
C61×#14362
C4×#95×C612
#1492961