Finite Group Databasebeta

← C61×#13080 #29516513

Subgroups — C61×#13080 #29516513

Order 15616.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C61C211yesmaximal, characteristic
2C61×#2405C211yesmaximal, characteristic
3C2×C61×#352C212yesmaximal, complemented
4C61×#1781C211yesmaximal, characteristic
5C61×#1390C212yesmaximal, complemented
6C23×D4×C61C2211yescharacteristic
7C22×M16×C61—21no—
8C2×#123×C61C411yescharacteristic, complemented
9C2×#123×C61C2211yescharacteristic
10C22×C22⋊C4×C61C411yescharacteristic, complemented
11C2×#100×C61—21no—
12C2×#100×C61—24no—
13C2×#100×C61C2212yes—
14C2×#99×C61—21no—
15C2×#99×C61C2212yes—
16C61×#394—21no—
17C61×#394—21no—
18C61×#386C411yescharacteristic, complemented
19C61×#386C2211yescharacteristic
20C61×#385—21no—
21C61×#379—21no—
22C61×#379—21no—
23C61×#379C411yescharacteristic, complemented
24C61×#352—24no—
25C25×C61C2×C411yescharacteristic
26C25×C61D411yescharacteristic
27C22×D4×C61—22no—
28C22×D4×C61—22no—
29C22×D4×C61—42no—
30C22×D4×C61—41no—
31C22×D4×C61—41no—
32C22×D4×C61C2×C411yescharacteristic
33C22×D4×C61D411yescharacteristic
34C22×D4×C61D411yescharacteristic
35C22×D4×C61C2311yescharacteristic
36C23×C4×C61C2×C411yescharacteristic
37C23×C4×C61C2×C411yescharacteristic
38C23×C4×C61D411yescharacteristic
39C2×M16×C61—24no—
40C2×M16×C61—22no—
41C2×M16×C61—41no—
42C2×M16×C61—42no—
43C22×C8×C61—41no—
44#123×C61—22no—
45#123×C61—22no—
46#123×C61—42no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—22no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—41no—
59C2×C22⋊C4×C61—41no—
60C2×C22⋊C4×C61—41no—
61C2×C22⋊C4×C61—41no—
62C2×C22⋊C4×C61C2×C411yescharacteristic
63C2×C22⋊C4×C61C2×C411yescharacteristic
64#100×C61—24no—
65#100×C61—22no—
66#100×C61D414yes—
67#99×C61—22no—
68#99×C61—22no—
69#99×C61—42no—
70#95×C61—21no—
71#95×C61—21no—
72C24×C61—21no—
73C24×C61—21no—
74C24×C61—21no—
75C24×C61—21no—
76C24×C61—22no—
77C24×C61—22no—
78C24×C61—41no—
79C24×C61—41no—
80C24×C61—42no—
81C24×C61—42no—
82C24×C61—81no—
83C24×C61—81no—
84C24×C61C22⋊C411yescharacteristic
85C24×C61C22⋊C411yescharacteristic
86C24×C61C22⋊C411yescharacteristic
87C24×C61C22×C411yescharacteristic
88C24×C61C2×D411yescharacteristic
89C2×D4×C61—22no—
90C2×D4×C61—22no—
91C2×D4×C61—22no—
92C2×D4×C61—22no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—44no—
102C2×D4×C61—44no—
103C2×D4×C61—44no—
104C2×D4×C61—44no—
105C2×D4×C61C2×D412yes—
106C2×D4×C61#4112yes—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61—42no—
121C22×C4×C61—81no—
122C22×C4×C61C22⋊C411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124M16×C61—24no—
125M16×C61—44no—
126M16×C61—42no—
127C2×C8×C61—44no—
128C2×C8×C61—42no—
129C4⋊C4×C61—42no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C22⋊C4×C61—22no—
133C22⋊C4×C61—42no—
134C22⋊C4×C61—42no—
135C22⋊C4×C61—42no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—42no—
139C22⋊C4×C61—41no—
140C22⋊C4×C61—42no—
141C22⋊C4×C61—42no—
142C22⋊C4×C61—81no—
143C22⋊C4×C61—81no—
144C22⋊C4×C61—81no—
145C22⋊C4×C61—82no—
146C22⋊C4×C61—82no—
147C23×C61—22no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—41no—
161C23×C61—42no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61—41no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—41no—
174C23×C61—41no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—81no—
178C23×C61—81no—
179C23×C61—81no—
180C23×C61—81no—
181C23×C61—84no—
182C23×C61—84no—
183C23×C61—84no—
184C23×C61—84no—
185C23×C61#9911yescharacteristic
186C23×C61#9911yescharacteristic
187C23×C61C2×C22⋊C411yescharacteristic
188C23×C61C4×D412yes—
189C23×C61#12112yes—
190D4×C61—42no—
191D4×C61—42no—
192D4×C61—44no—
193D4×C61—44no—
194D4×C61—42no—
195D4×C61—42no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—41no—
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—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—82no—
217C2×C4×C61—82no—
218C2×C4×C61—82no—
219C2×C4×C61—82no—
220C2×C4×C61—82no—
221C2×C4×C61#9912yes—
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61#12311yescharacteristic
224C8×C61—44no—
225#13080C6111yesmaximal, characteristic, direct product factor, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—22no—
234C22×C61—22no—
235C22×C61—42no—
236C22×C61—42no—
237C22×C61—42no—
238C22×C61—42no—
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—41no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61—41no—
245C22×C61—41no—
246C22×C61—41no—
247C22×C61—41no—
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—81no—
252C22×C61—84no—
253C22×C61—84no—
254C22×C61—81no—
255C22×C61—81no—
256C22×C61—81no—
257C22×C61—84no—
258C22×C61—84no—
259C22×C61#35212yescomplemented
260C22×C61#38611yescharacteristic
261C22×C61C2×#9911yescharacteristic
262C22×C61C2×#9911yescharacteristic
263C4×C61—21no—
264C4×C61—22no—
265C4×C61—21no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61—81no—
270C4×C61—162no—
271C22×#100C2×C6111yescharacteristic
272#2405C2×C6111yescharacteristic
273C2×#352C2×C6112yescomplemented
274#1781C2×C6111yescharacteristic
275#1390C2×C6112yescomplemented
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—22no—
279C2×C61—42no—
280C2×C61—41no—
281C2×C61—42no—
282C2×C61—81no—
283C2×C61—81no—
284C2×C61#189811yescharacteristic
285C2×C61C2×#35211yescharacteristic
286C2×C61#212111yescharacteristic
287C23×D4C22×C6111yescharacteristic
288C22×M16—21no—
289C2×#123C4×C6111yescharacteristic, complemented
290C2×#123C22×C6111yescharacteristic
291C22×C22⋊C4C4×C6111yescharacteristic, complemented
292C2×#100—21no—
293C2×#100—24no—
294C2×#100C22×C6112yes—
295C2×#99—21no—
296C2×#99C22×C6112yes—
297#394—21no—
298#394—21no—
299#386C4×C6111yescharacteristic, complemented
300#386C22×C6111yescharacteristic
301#385—21no—
302#379—21no—
303#379—21no—
304#379C4×C6111yescharacteristic, complemented
305#352—24no—
306C61#1308011yescharacteristic, direct product factor, Sylow
307C25C2×C4×C6111yescharacteristic
308C25D4×C6111yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C6111yescharacteristic
315C22×D4D4×C6111yescharacteristic
316C22×D4D4×C6111yescharacteristic
317C22×D4C23×C6111yescharacteristic
318C23×C4C2×C4×C6111yescharacteristic
319C23×C4C2×C4×C6111yescharacteristic
320C23×C4D4×C6111yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C6111yescharacteristic
345C2×C22⋊C4C2×C4×C6111yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C6114yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C6111yescharacteristic
367C24C22⋊C4×C6111yescharacteristic
368C24C22⋊C4×C6111yescharacteristic
369C24C22×C4×C6111yescharacteristic
370C24C2×D4×C6111yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C6112yes—
388C2×D4#41×C6112yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C6111yescharacteristic
405C22×C4C2×D4×C6111yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C6111yescharacteristic
468C23#99×C6111yescharacteristic
469C23C2×C22⋊C4×C6111yescharacteristic
470C23C4×D4×C6112yes—
471C23#121×C6112yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C6112yes—
504C2×C4#120×C6111yescharacteristic
505C2×C4#123×C6111yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22C61×#35212yescomplemented
541C22C61×#38611yescharacteristic
542C22C2×#99×C6111yescharacteristic
543C22C2×#99×C6111yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C61×#189811yescharacteristic
561C2C2×C61×#35211yescharacteristic
562C2C61×#212111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#99
commutatorC24C22×C4×C61
Frattini, cosocleC22×D4C23×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C24×C61 ◁ C23×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C61×#352C2semidirect
5. C61×#1390C2semidirect
8. C2×#123×C61C4semidirect
10. C22×C22⋊C4×C61C4semidirect
18. C61×#386C4semidirect
23. C61×#379C4semidirect
225. #13080C61direct (N × H)
259. C22×C61#352semidirect
273. C2×#352C2×C61semidirect
275. #1390C2×C61semidirect
289. C2×#123C4×C61semidirect
291. C22×C22⋊C4C4×C61semidirect
299. #386C4×C61semidirect
304. #379C4×C61semidirect
306. C61#13080direct (N × H)
540. C22C61×#352semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C612
C61×#24052
C2×C61×#3522
C61×#17812
C61×#13902
#1308061