Finite Group Databasebeta

← C61×#9520 #29512953

Subgroups — C61×#9520 #29512953

Order 15616.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3003C211yesmaximal, characteristic
2C61×#2976C211yesmaximal, characteristic, complemented
3C61×#1786C211yesmaximal, characteristic, complemented
4C61×#1783C211yesmaximal, characteristic, complemented
5C61×#1513C211yesmaximal, characteristic, complemented
6C61×#1305C211yesmaximal, characteristic, complemented
7C61×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C61C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C61—21no—
10C61×#525C2211yescharacteristic
11C61×#450—21no—
12C61×#450C412yescomplemented
13C61×#447—21no—
14C61×#447C412yescomplemented
15C61×#436—21no—
16C61×#435—21no—
17C61×#435—21no—
18C8×D4×C61—21no—
19C61×#433—21no—
20C61×#418—21no—
21C2×#102×C61—21no—
22C2×#102×C61—21no—
23C2×#100×C61—21no—
24C2×#100×C61—21no—
25C61×#408—21no—
26C61×#407C2211yescharacteristic
27C61×#407C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C61×#380C2211yescharacteristic
31C61×#328—21no—
32C61×#327—21no—
33C25×C61—21no—
34C2×#41×C61D411yescharacteristic
35C22×D4×C61—21no—
36C22×D4×C61—21no—
37C22×D4×C61—21no—
38C22×D4×C61—21no—
39C22×D4×C61—21no—
40C22×D4×C61—42no—
41C22×D4×C61—42no—
42C22×D4×C61C2×C412yes—
43C23×C4×C61C2311yescharacteristic
44AGL(1,ℤ/8)×C61—42no—
45AGL(1,ℤ/8)×C61—42no—
46C2×SD16×C61—22no—
47C2×D8×C61—22no—
48C2×M16×C61—21no—
49C2×M16×C61—21no—
50C2×M16×C61—21no—
51C2×M16×C61D411yescharacteristic
52C2×M16×C61D411yescharacteristic
53C22×C8×C61—21no—
54C22×C8×C61D411yescharacteristic
55C22×C8×C61D411yescharacteristic
56#123×C61—21no—
57C22⋊Q8×C61C2×C411yescharacteristic
58C22⋊Q8×C61D411yescharacteristic
59#121×C61C2×C411yescharacteristic
60#121×C61D411yescharacteristic
61#120×C61—21no—
62C4×D4×C61—21no—
63C4×D4×C61—21no—
64#117×C61D411yescharacteristic
65C2×C4⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69#102×C61—22no—
70#102×C61—22no—
71#102×C61—42no—
72#102×C61—42no—
73#100×C61—42no—
74#100×C61—42no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83C22⋊C8×C61—21no—
84C22⋊C8×C61C2×C412yes—
85#97×C61—21no—
86C4×C8×C61—21no—
87#95×C61—21no—
88C24×C61—22no—
89C24×C61—44no—
90C24×C61—41no—
91C24×C61—41no—
92C24×C61—81no—
93C24×C61—81no—
94C24×C61—82no—
95C24×C61#4111yescharacteristic
96#41×C61—41no—
97#41×C61—41no—
98C2×Q8×C61C22⋊C411yescharacteristic
99C2×D4×C61—22no—
100C2×D4×C61—22no—
101C2×D4×C61—22no—
102C2×D4×C61—22no—
103C2×D4×C61—22no—
104C2×D4×C61—22no—
105C2×D4×C61—21no—
106C2×D4×C61—21no—
107C2×D4×C61—21no—
108C2×D4×C61—22no—
109C2×D4×C61—22no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C2×D4×C61—41no—
113C2×D4×C61—41no—
114C2×D4×C61—41no—
115C2×D4×C61—41no—
116C2×D4×C61—44no—
117C2×D4×C61—44no—
118C2×D4×C61—44no—
119C2×D4×C61—41no—
120C2×D4×C61—41no—
121C2×D4×C61C22⋊C411yescharacteristic
122C22×C4×C61—21no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61#4111yescharacteristic
132SD16×C61—44no—
133D8×C61—44no—
134M16×C61—41no—
135M16×C61—41no—
136M16×C61—41no—
137M16×C61—41no—
138M16×C61—41no—
139M16×C61—41no—
140M16×C61—81no—
141C2×C8×C61—22no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—41no—
147C2×C8×C61—41no—
148C2×C8×C61—41no—
149C2×C8×C61—81no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61C22⋊C411yescharacteristic
155C4⋊C4×C61C22⋊C411yescharacteristic
156C22⋊C4×C61—21no—
157C22⋊C4×C61—21no—
158C22⋊C4×C61—21no—
159C22⋊C4×C61—21no—
160C22⋊C4×C61—21no—
161C22⋊C4×C61—81no—
162C42×C61—21no—
163C23×C61—21no—
164C23×C61—21no—
165C23×C61—24no—
166C23×C61—21no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—82no—
176C23×C61—81no—
177C23×C61—81no—
178C23×C61—82no—
179C23×C61—82no—
180C23×C61—82no—
181C23×C61—88no—
182C23×C61—88no—
183C23×C61—81no—
184C23×C61—81no—
185C23×C61C4×D411yescharacteristic
186C23×C61#12111yescharacteristic
187C23×C61#12311yescharacteristic
188Q8×C61—41no—
189D4×C61—24no—
190D4×C61—24no—
191D4×C61—41no—
192D4×C61—42no—
193D4×C61—42no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—41no—
197D4×C61—41no—
198D4×C61—42no—
199D4×C61—42no—
200D4×C61—81no—
201D4×C61—81no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—81no—
217C2×C4×C61—81no—
218C2×C4×C61—81no—
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C8×C61—42no—
224C8×C61—41no—
225C8×C61—41no—
226C8×C61—41no—
227C8×C61—41no—
228C8×C61—81no—
229#9520C6111yesmaximal, characteristic, direct product factor, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—42no—
239C22×C61—42no—
240C22×C61—41no—
241C22×C61—44no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61—82no—
245C22×C61—82no—
246C22×C61—82no—
247C22×C61—82no—
248C22×C61—84no—
249C22×C61—84no—
250C22×C61—84no—
251C22×C61—84no—
252C22×C61—82no—
253C22×C61—82no—
254C22×C61#38611yescharacteristic
255C22×C61#47111yescharacteristic
256C22×C61#47211yescharacteristic
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—161no—
264C4×C61B(4,𝔽2)11yescharacteristic
265C4×C61B(4,𝔽2)11yescharacteristic
266#3003C2×C6111yescharacteristic
267#2976C2×C6111yescharacteristic, complemented
268#1786C2×C6111yescharacteristic, complemented
269#1783C2×C6111yescharacteristic, complemented
270#1513C2×C6111yescharacteristic, complemented
271#1305C2×C6111yescharacteristic, complemented
272#1293C2×C6111yescharacteristic, complemented
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—41no—
276C2×C61—41no—
277C2×C61—81no—
278C2×C61—84no—
279C2×C61#188911yescharacteristic
280C2×C61#190311yescharacteristic
281C2×C61#190711yescharacteristic
282C23×D4C22×C6111yescharacteristic
283C2×AGL(1,ℤ/8)—21no—
284#525C22×C6111yescharacteristic
285#450—21no—
286#450C4×C6112yescomplemented
287#447—21no—
288#447C4×C6112yescomplemented
289#436—21no—
290#435—21no—
291#435—21no—
292C8×D4—21no—
293#433—21no—
294#418—21no—
295C2×#102—21no—
296C2×#102—21no—
297C2×#100—21no—
298C2×#100—21no—
299#408—21no—
300#407C22×C6111yescharacteristic
301#407C22×C6111yescharacteristic
302#407C22×C6111yescharacteristic
303C2×C22⋊C8C22×C6111yescharacteristic
304#380C22×C6111yescharacteristic
305#328—21no—
306#327—21no—
307C61#952011yescharacteristic, direct product factor, Sylow
308C25—21no—
309C2×#41D4×C6111yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C6112yes—
318C23×C4C23×C6111yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C6111yescharacteristic
327C2×M16D4×C6111yescharacteristic
328C22×C8—21no—
329C22×C8D4×C6111yescharacteristic
330C22×C8D4×C6111yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C6111yescharacteristic
333C22⋊Q8D4×C6111yescharacteristic
334#121C2×C4×C6111yescharacteristic
335#121D4×C6111yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C6111yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C6112yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C6111yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C6111yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C6111yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C6111yescharacteristic
402C22×C4C2×D4×C6111yescharacteristic
403C22×C4C2×D4×C6111yescharacteristic
404C22×C4C2×D4×C6111yescharacteristic
405C22×C4C2×D4×C6111yescharacteristic
406C22×C4#41×C6111yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C6111yescharacteristic
430C4⋊C4C22⋊C4×C6111yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—82no—
453C23—81no—
454C23—81no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C6111yescharacteristic
461C23#121×C6111yescharacteristic
462C23#123×C6111yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
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—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C6111yescharacteristic
495C2×C4C4×D4×C6111yescharacteristic
496C2×C4#120×C6111yescharacteristic
497C2×C4#121×C6111yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C61×#38611yescharacteristic
529C22C61×#47111yescharacteristic
530C22C61×#47211yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4C61×B(4,𝔽2)11yescharacteristic
539C4C61×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C61×#188911yescharacteristic
547C2C61×#190311yescharacteristic
548C2C61×#190711yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC61×#3003C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2976C2semidirect
3. C61×#1786C2semidirect
4. C61×#1783C2semidirect
5. C61×#1513C2semidirect
6. C61×#1305C2semidirect
7. C61×#1293C2semidirect
12. C61×#450C4semidirect
14. C61×#447C4semidirect
229. #9520C61direct (N × H)
267. #2976C2×C61semidirect
268. #1786C2×C61semidirect
269. #1783C2×C61semidirect
270. #1513C2×C61semidirect
271. #1305C2×C61semidirect
272. #1293C2×C61semidirect
286. #450C4×C61semidirect
288. #447C4×C61semidirect
307. C61#9520direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30032
C61×#29762
C61×#17862
C61×#17832
C61×#15132
C61×#13052
C61×#12932
#952061