Finite Group Databasebeta

← C61×#9117 #29512550

Subgroups — C61×#9117 #29512550

Order 15616.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#407C211yesmaximal, characteristic, complemented
2C61×#2847C211yesmaximal, characteristic
3C2×C61×#327C212yesmaximal, complemented
4C61×C22⋊#95C211yesmaximal, characteristic, complemented
5C61×#1294C212yesmaximal, complemented
6C24×C4×C61C2211yescharacteristic
7C22×M16×C61—21no—
8C2×#121×C61C411yescharacteristic, complemented
9C2×#121×C61C411yescharacteristic, complemented
10C2×#121×C61C2211yescharacteristic
11C2×#120×C61—21no—
12C22×C22⋊C4×C61—21no—
13C61×#407—24no—
14C2×C22⋊C8×C61—21no—
15C2×C22⋊C8×C61C2212yes—
16C61×#386—21no—
17C61×#386—21no—
18C61×#386—21no—
19C61×#380C411yescharacteristic, complemented
20C61×#380C411yescharacteristic, complemented
21C61×#380C2211yescharacteristic
22C2×#95×C61—21no—
23C2×#95×C61C2212yes—
24C61×#327—24no—
25C25×C61D411yescharacteristic
26C22×D4×C61—21no—
27C22×D4×C61—21no—
28C22×D4×C61—21no—
29C22×D4×C61C2×C411yescharacteristic
30C23×C4×C61—22no—
31C23×C4×C61—22no—
32C23×C4×C61—22no—
33C23×C4×C61—42no—
34C23×C4×C61—42no—
35C23×C4×C61C2×C411yescharacteristic
36C23×C4×C61C2×C411yescharacteristic
37C23×C4×C61D411yescharacteristic
38C23×C4×C61D411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C23×C4×C61C2311yescharacteristic
41C2×M16×C61—24no—
42C2×M16×C61—42no—
43C2×M16×C61—42no—
44C22×C8×C61—22no—
45#121×C61—22no—
46#121×C61—22no—
47#121×C61—42no—
48#121×C61—42no—
49#120×C61—44no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—24no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—42no—
61C2×C22⋊C4×C61—42no—
62C22⋊C8×C61—24no—
63C22⋊C8×C61—22no—
64C22⋊C8×C61D414yescomplemented
65#95×C61—21no—
66#95×C61—21no—
67#95×C61—21no—
68#95×C61—22no—
69#95×C61—22no—
70#95×C61—42no—
71C24×C61—22no—
72C24×C61—22no—
73C24×C61—21no—
74C24×C61—21no—
75C24×C61—22no—
76C24×C61—22no—
77C24×C61—21no—
78C24×C61—41no—
79C24×C61—41no—
80C24×C61C22⋊C411yescharacteristic
81C24×C61C22⋊C411yescharacteristic
82C24×C61C2×D411yescharacteristic
83C2×D4×C61—22no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—42no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C2×D4×C61—42no—
90C2×D4×C61—42no—
91C2×D4×C61—42no—
92C2×D4×C61—42no—
93C2×D4×C61—42no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
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—21no—
107C22×C4×C61—21no—
108C22×C4×C61—24no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—41no—
113C22×C4×C61—41no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61—48no—
120C22×C4×C61—48no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61—42no—
127C22×C4×C61C22⋊C411yescharacteristic
128C22×C4×C61C22⋊C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D412yes—
132C22×C4×C61#4112yes—
133M16×C61—48no—
134C2×C8×C61—24no—
135C2×C8×C61—42no—
136C2×C8×C61—42no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C22⋊C4×C61—42no—
141C22⋊C4×C61—48no—
142C22⋊C4×C61—42no—
143C22⋊C4×C61—42no—
144C22⋊C4×C61—42no—
145C22⋊C4×C61—42no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—24no—
153C23×C61—24no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61—44no—
167C23×C61—44no—
168C23×C61—44no—
169C23×C61—44no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61#9912yes—
182C23×C61#10412yes—
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61#12112yes—
185C23×C61AGL(1,ℤ/8)11yescharacteristic
186C23×C61AGL(1,ℤ/8)12yes—
187C23×C61#13711yescharacteristic
188D4×C61—82no—
189D4×C61—84no—
190D4×C61—84no—
191D4×C61—82no—
192D4×C61—82no—
193C2×C4×C61—24no—
194C2×C4×C61—24no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—44no—
207C2×C4×C61—44no—
208C2×C4×C61—44no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—44no—
212C2×C4×C61—44no—
213C2×C4×C61—44no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—82no—
224C2×C4×C61—82no—
225C2×C4×C61—82no—
226C2×C4×C61—82no—
227C2×C4×C61#9912yes—
228C2×C4×C61C4×D412yes—
229C2×C4×C61#12011yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C8×C61—44no—
232#9117C6111yesmaximal, characteristic, direct product factor, Sylow
233C22×C61—22no—
234C22×C61—22no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—22no—
238C22×C61—22no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—22no—
242C22×C61—22no—
243C22×C61—22no—
244C22×C61—22no—
245C22×C61—22no—
246C22×C61—22no—
247C22×C61—48no—
248C22×C61—48no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61#38611yescharacteristic
265C22×C61C2×#9911yescharacteristic
266C22×C61C2×#9911yescharacteristic
267C22×C61#41711yescharacteristic
268C22×C61#41811yescharacteristic
269C22×C61C2×#10411yescharacteristic
270C22×C61#42111yescharacteristic
271C22×C61#46812yes—
272C22×C61#46912yes—
273C4×C61—21no—
274C4×C61—22no—
275C4×C61—21no—
276C4×C61—22no—
277C4×C61—41no—
278C4×C61—84no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61—81no—
282C2×#407C2×C6111yescharacteristic, complemented
283#2847C2×C6111yescharacteristic
284C2×#327C2×C6112yescomplemented
285C22⋊#95C2×C6111yescharacteristic, complemented
286#1294C2×C6112yescomplemented
287C2×C61—22no—
288C2×C61—22no—
289C2×C61—42no—
290C2×C61—42no—
291C2×C61—161no—
292C2×C61#150411yescharacteristic
293C2×C61#150711yescharacteristic
294C2×C61#151011yescharacteristic
295C2×C61#151311yescharacteristic
296C2×C61#187111yescharacteristic
297C2×C61#189511yescharacteristic
298C2×C61#189811yescharacteristic
299C24×C4C22×C6111yescharacteristic
300C22×M16—21no—
301C2×#121C4×C6111yescharacteristic, complemented
302C2×#121C4×C6111yescharacteristic, complemented
303C2×#121C22×C6111yescharacteristic
304C2×#120—21no—
305C22×C22⋊C4—21no—
306#407—24no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8C22×C6112yes—
309#386—21no—
310#386—21no—
311#386—21no—
312#380C4×C6111yescharacteristic, complemented
313#380C4×C6111yescharacteristic, complemented
314#380C22×C6111yescharacteristic
315C2×#95—21no—
316C2×#95C22×C6112yes—
317#327—24no—
318C61#911711yescharacteristic, direct product factor, Sylow
319C25D4×C6111yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C2×C4×C6111yescharacteristic
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—42no—
328C23×C4—42no—
329C23×C4C2×C4×C6111yescharacteristic
330C23×C4C2×C4×C6111yescharacteristic
331C23×C4D4×C6111yescharacteristic
332C23×C4D4×C6111yescharacteristic
333C23×C4D4×C6111yescharacteristic
334C23×C4C23×C6111yescharacteristic
335C2×M16—24no—
336C2×M16—42no—
337C2×M16—42no—
338C22×C8—22no—
339#121—22no—
340#121—22no—
341#121—42no—
342#121—42no—
343#120—44no—
344C2×C4⋊C4C2×C4×C6111yescharacteristic
345C2×C4⋊C4C2×C4×C6111yescharacteristic
346C2×C4⋊C4C2×C4×C6111yescharacteristic
347C2×C22⋊C4—24no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C22⋊C8—24no—
357C22⋊C8—22no—
358C22⋊C8D4×C6114yescomplemented
359#95—21no—
360#95—21no—
361#95—21no—
362#95—22no—
363#95—22no—
364#95—42no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—41no—
373C24—41no—
374C24C22⋊C4×C6111yescharacteristic
375C24C22⋊C4×C6111yescharacteristic
376C24C2×D4×C6111yescharacteristic
377C2×D4—22no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—41no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—48no—
414C22×C4—48no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4C22⋊C4×C6111yescharacteristic
422C22×C4C22⋊C4×C6111yescharacteristic
423C22×C4C22×C4×C6111yescharacteristic
424C22×C4C2×D4×C6111yescharacteristic
425C22×C4C2×D4×C6112yes—
426C22×C4#41×C6112yes—
427M16—48no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C22⋊C4—42no—
435C22⋊C4—48no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23#99×C6112yes—
476C23#104×C6112yes—
477C23C2×C22⋊C4×C6111yescharacteristic
478C23#121×C6112yes—
479C23AGL(1,ℤ/8)×C6111yescharacteristic
480C23AGL(1,ℤ/8)×C6112yes—
481C23#137×C6111yescharacteristic
482D4—82no—
483D4—84no—
484D4—84no—
485D4—82no—
486D4—82no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4#99×C6112yes—
522C2×C4C4×D4×C6112yes—
523C2×C4#120×C6111yescharacteristic
524C2×C4#123×C6111yescharacteristic
525C8—44no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C61×#38611yescharacteristic
558C22C2×#99×C6111yescharacteristic
559C22C2×#99×C6111yescharacteristic
560C22C61×#41711yescharacteristic
561C22C61×#41811yescharacteristic
562C22C2×#104×C6111yescharacteristic
563C22C61×#42111yescharacteristic
564C22C61×#46812yes—
565C22C61×#46912yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—84no—
572C4—81no—
573C4—81no—
574C4—81no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—161no—
580C2C61×#150411yescharacteristic
581C2C61×#150711yescharacteristic
582C2C61×#151011yescharacteristic
583C2C61×#151311yescharacteristic
584C2C61×#187111yescharacteristic
585C2C61×#189511yescharacteristic
586C2C61×#189811yescharacteristic
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC61×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#407C2semidirect
3. C2×C61×#327C2semidirect
4. C61×C22⋊#95C2semidirect
5. C61×#1294C2semidirect
8. C2×#121×C61C4semidirect
9. C2×#121×C61C4semidirect
19. C61×#380C4semidirect
20. C61×#380C4semidirect
64. C22⋊C8×C61D4semidirect
232. #9117C61direct (N × H)
282. C2×#407C2×C61semidirect
284. C2×#327C2×C61semidirect
285. C22⋊#95C2×C61semidirect
286. #1294C2×C61semidirect
301. C2×#121C4×C61semidirect
302. C2×#121C4×C61semidirect
312. #380C4×C61semidirect
313. #380C4×C61semidirect
318. C61#9117direct (N × H)
358. C22⋊C8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4072
C61×#28472
C2×C61×#3272
C61×C22⋊#952
C61×#12942
#911761