Finite Group Databasebeta

← C61×#29744 #29533177

Subgroups — C61×#29744 #29533177

Order 15616.

1168 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#468C211yesmaximal, characteristic, complemented
2C2×C61×#407C211yesmaximal, characteristic, complemented
3C61×#2848C211yesmaximal, characteristic, complemented
4C61×#2847C211yesmaximal, characteristic
5C61×#2076C211yesmaximal, characteristic, complemented
6C61×#2075C211yesmaximal, characteristic, complemented
7C61×#2036C211yesmaximal, characteristic, complemented
8C61×#2035C211yesmaximal, characteristic, complemented
9C61×#2034C211yesmaximal, characteristic, complemented
10C61×#2033C211yesmaximal, characteristic, complemented
11C61×#2000C211yesmaximal, characteristic, complemented
12C61×#2000C211yesmaximal, characteristic, complemented
13C61×#1895C211yesmaximal, characteristic, complemented
14C61×#1894C211yesmaximal, characteristic, complemented
15C61×#1809C211yesmaximal, characteristic, complemented
16C24×C4×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic, complemented
18C22×M16×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C2×C22⋊Q8×C61C2211yescharacteristic
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×C22⋊Q8×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#121×C61C2211yescharacteristic
26C2×#120×C61—21no—
27C61×#468—24no—
28C2×#107×C61C2211yescharacteristic, complemented
29C2×#107×C61C2211yescharacteristic, complemented
30C2×#106×C61C2211yescharacteristic, complemented
31C2×#103×C61C2211yescharacteristic, complemented
32C2×#103×C61C2211yescharacteristic, complemented
33C2×#103×C61C2211yescharacteristic, complemented
34C2×#102×C61C2211yescharacteristic, complemented
35C2×#102×C61C2211yescharacteristic, complemented
36C2×#102×C61C2211yescharacteristic, complemented
37C61×#407—24no—
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×C22⋊C8×C61C2211yescharacteristic
40C2×C22⋊C8×C61C2211yescharacteristic
41C2×C22⋊C8×C61C2211yescharacteristic
42C61×#386—21no—
43C61×#386—21no—
44C61×#386—21no—
45C61×#385—21no—
46C61×#385—21no—
47C61×#385—21no—
48C61×#380C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#380C2211yescharacteristic
54C61×#379—21no—
55C61×#340C2211yescharacteristic, complemented
56C61×#340C2211yescharacteristic, complemented
57C61×#340C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C25×C61D411yescharacteristic
62C22×Q8×C61C2311yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61C2311yescharacteristic
67C23×C4×C61—22no—
68C23×C4×C61—22no—
69C23×C4×C61—41no—
70C23×C4×C61—41no—
71C23×C4×C61—41no—
72C23×C4×C61—41no—
73C23×C4×C61D411yescharacteristic
74C23×C4×C61D411yescharacteristic
75C23×C4×C61D411yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C2×SD16×C61—22no—
80C2×SD16×C61—41no—
81C2×SD16×C61—41no—
82C2×M16×C61—22no—
83C2×M16×C61—41no—
84C2×M16×C61—41no—
85C2×M16×C61—41no—
86C2×M16×C61—41no—
87C2×M16×C61D414yescomplemented
88C22×C8×C61C2311yescharacteristic
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91C22×C8×C61C2311yescharacteristic
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61—22no—
94C22⋊Q8×C61—41no—
95C22⋊Q8×C61—41no—
96C22⋊Q8×C61—41no—
97C22⋊Q8×C61—41no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—41no—
101#121×C61—41no—
102#121×C61—41no—
103#121×C61—41no—
104#120×C61—44no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126#107×C61—22no—
127#107×C61—41no—
128#106×C61—41no—
129#103×C61—22no—
130#103×C61—41no—
131#103×C61—41no—
132#102×C61—22no—
133#102×C61—41no—
134#102×C61—41no—
135C22⋊C8×C61—22no—
136C22⋊C8×C61—22no—
137C22⋊C8×C61—22no—
138C22⋊C8×C61—22no—
139#95×C61—21no—
140#95×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143#95×C61—21no—
144#95×C61—21no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—21no—
149C24×C61—41no—
150C24×C61—41no—
151C24×C61—41no—
152C24×C61—41no—
153C24×C61C2×D411yescharacteristic
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61—42no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—41no—
204C22×C4×C61—41no—
205C22×C4×C61—41no—
206C22×C4×C61—41no—
207C22×C4×C61—41no—
208C22×C4×C61—41no—
209C22×C4×C61—44no—
210C22×C4×C61—44no—
211C22×C4×C61—44no—
212C22×C4×C61—44no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61#4112yes—
218C22×C4×C61C2411yescharacteristic
219SD16×C61—44no—
220M16×C61—44no—
221M16×C61—44no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61C2×D412yes—
233C2×C8×C61C2×D412yes—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—42no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—42no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—44no—
280C23×C61—44no—
281C23×C61—44no—
282C23×C61—44no—
283C23×C61—44no—
284C23×C61—44no—
285C23×C61—44no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61#12112yes—
294C23×C61AGL(1,ℤ/8)12yes—
295C23×C61#13712yes—
296C23×C61C22×D411yescharacteristic
297Q8×C61—41no—
298Q8×C61—41no—
299Q8×C61—41no—
300Q8×C61—41no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—84no—
306D4×C61—84no—
307D4×C61—84no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—44no—
321C2×C4×C61—44no—
322C2×C4×C61—44no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61#12112yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C2×C4×C61H(5,𝔽2)11yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C2×C4×C61H(5,𝔽2)11yescharacteristic
359C8×C61—22no—
360C8×C61—22no—
361C8×C61—41no—
362C8×C61—41no—
363#29744C6111yesmaximal, characteristic, direct product factor, Sylow
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—416no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61C2×#12111yescharacteristic
394C22×C61#53411yescharacteristic
395C22×C61#53411yescharacteristic
396C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C61C2×#13711yescharacteristic
398C22×C61#57511yescharacteristic
399C22×C61#57511yescharacteristic
400C4×C61—22no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—81no—
404C4×C61—81no—
405C4×C61—81no—
406C4×C61—81no—
407C4×C61—81no—
408C4×C61—81no—
409C4×C61—81no—
410C4×C61#53411yescharacteristic
411C4×C61#53511yescharacteristic
412C4×C61#53811yescharacteristic
413C4×C61#53811yescharacteristic
414C2×#468C2×C6111yescharacteristic, complemented
415C2×#407C2×C6111yescharacteristic, complemented
416#2848C2×C6111yescharacteristic, complemented
417#2847C2×C6111yescharacteristic
418#2076C2×C6111yescharacteristic, complemented
419#2075C2×C6111yescharacteristic, complemented
420#2036C2×C6111yescharacteristic, complemented
421#2035C2×C6111yescharacteristic, complemented
422#2034C2×C6111yescharacteristic, complemented
423#2033C2×C6111yescharacteristic, complemented
424#2000C2×C6111yescharacteristic, complemented
425#2000C2×C6111yescharacteristic, complemented
426#1895C2×C6111yescharacteristic, complemented
427#1894C2×C6111yescharacteristic, complemented
428#1809C2×C6111yescharacteristic, complemented
429C2×C61—42no—
430C2×C61—42no—
431C2×C61—42no—
432C2×C61—161no—
433C2×C61#261711yescharacteristic
434C2×C61#305511yescharacteristic
435C2×C61#305611yescharacteristic
436C2×C61#319311yescharacteristic
437C2×C61#319411yescharacteristic
438C2×C61#319611yescharacteristic
439C2×C61#319711yescharacteristic
440C24×C4C22×C6111yescharacteristic
441C22×SD16C22×C6111yescharacteristic, complemented
442C22×M16C22×C6111yescharacteristic
443C22×M16C22×C6111yescharacteristic
444C2×C22⋊Q8C22×C6111yescharacteristic
445C2×C22⋊Q8C22×C6111yescharacteristic
446C2×C22⋊Q8C22×C6111yescharacteristic
447C2×#121C22×C6111yescharacteristic
448C2×#121C22×C6111yescharacteristic
449C2×#121C22×C6111yescharacteristic
450C2×#120—21no—
451#468—24no—
452C2×#107C22×C6111yescharacteristic, complemented
453C2×#107C22×C6111yescharacteristic, complemented
454C2×#106C22×C6111yescharacteristic, complemented
455C2×#103C22×C6111yescharacteristic, complemented
456C2×#103C22×C6111yescharacteristic, complemented
457C2×#103C22×C6111yescharacteristic, complemented
458C2×#102C22×C6111yescharacteristic, complemented
459C2×#102C22×C6111yescharacteristic, complemented
460C2×#102C22×C6111yescharacteristic, complemented
461#407—24no—
462C2×C22⋊C8C22×C6111yescharacteristic
463C2×C22⋊C8C22×C6111yescharacteristic
464C2×C22⋊C8C22×C6111yescharacteristic
465C2×C22⋊C8C22×C6111yescharacteristic
466#386—21no—
467#386—21no—
468#386—21no—
469#385—21no—
470#385—21no—
471#385—21no—
472#380C22×C6111yescharacteristic
473#380C22×C6111yescharacteristic
474#380C22×C6111yescharacteristic
475#380C22×C6111yescharacteristic
476#380C22×C6111yescharacteristic
477#380C22×C6111yescharacteristic
478#379—21no—
479#340C22×C6111yescharacteristic, complemented
480#340C22×C6111yescharacteristic, complemented
481#340C22×C6111yescharacteristic, complemented
482#340C22×C6111yescharacteristic, complemented
483#340C22×C6111yescharacteristic, complemented
484#340C22×C6111yescharacteristic, complemented
485C61#2974411yescharacteristic, direct product factor, Sylow
486C25D4×C6111yescharacteristic
487C22×Q8C23×C6111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C23×C6111yescharacteristic
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4—41no—
497C23×C4—41no—
498C23×C4D4×C6111yescharacteristic
499C23×C4D4×C6111yescharacteristic
500C23×C4D4×C6111yescharacteristic
501C23×C4C23×C6111yescharacteristic
502C23×C4C23×C6111yescharacteristic
503C23×C4C23×C6111yescharacteristic
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×M16—22no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16D4×C6114yescomplemented
513C22×C8C23×C6111yescharacteristic
514C22×C8C23×C6111yescharacteristic
515C22×C8C23×C6111yescharacteristic
516C22×C8C23×C6111yescharacteristic
517C22⋊Q8—22no—
518C22⋊Q8—22no—
519C22⋊Q8—41no—
520C22⋊Q8—41no—
521C22⋊Q8—41no—
522C22⋊Q8—41no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—41no—
528#121—41no—
529#120—44no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4C23×C6111yescharacteristic
534C2×C4⋊C4C23×C6111yescharacteristic
535C2×C4⋊C4C23×C6111yescharacteristic
536C2×C4⋊C4C23×C6111yescharacteristic
537C2×C4⋊C4C23×C6111yescharacteristic
538C2×C4⋊C4C23×C6111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551#107—22no—
552#107—41no—
553#106—41no—
554#103—22no—
555#103—41no—
556#103—41no—
557#102—22no—
558#102—41no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95—21no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—21no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24—41no—
578C24C2×D4×C6111yescharacteristic
579C24C2×D4×C6111yescharacteristic
580C24C2×D4×C6111yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4C2×D4×C6111yescharacteristic
639C22×C4C2×D4×C6111yescharacteristic
640C22×C4C2×D4×C6111yescharacteristic
641C22×C4C2×D4×C6112yes—
642C22×C4#41×C6112yes—
643C22×C4C24×C6111yescharacteristic
644SD16—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8C2×D4×C6112yes—
658C2×C8C2×D4×C6112yes—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23#121×C6112yes—
719C23AGL(1,ℤ/8)×C6112yes—
720C23#137×C6112yes—
721C23C22×D4×C6111yescharacteristic
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4#121×C6112yes—
778C2×C4C22×D4×C6111yescharacteristic
779C2×C4C2×#41×C6111yescharacteristic
780C2×C4H(5,𝔽2)×C6111yescharacteristic
781C2×C4H(5,𝔽2)×C6111yescharacteristic
782C2×C4H(5,𝔽2)×C6111yescharacteristic
783C2×C4H(5,𝔽2)×C6111yescharacteristic
784C8—22no—
785C8—22no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C2×#121×C6111yescharacteristic
818C22C61×#53411yescharacteristic
819C22C61×#53411yescharacteristic
820C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
821C22C2×#137×C6111yescharacteristic
822C22C61×#57511yescharacteristic
823C22C61×#57511yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C61×#53411yescharacteristic
835C4C61×#53511yescharacteristic
836C4C61×#53811yescharacteristic
837C4C61×#53811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—161no—
842C2C61×#261711yescharacteristic
843C2C61×#305511yescharacteristic
844C2C61×#305611yescharacteristic
845C2C61×#319311yescharacteristic
846C2C61×#319411yescharacteristic
847C2C61×#319611yescharacteristic
848C2C61×#319711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ 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×#468C2semidirect
2. C2×C61×#407C2semidirect
3. C61×#2848C2semidirect
5. C61×#2076C2semidirect
6. C61×#2075C2semidirect
7. C61×#2036C2semidirect
8. C61×#2035C2semidirect
9. C61×#2034C2semidirect
10. C61×#2033C2semidirect
11. C61×#2000C2semidirect
12. C61×#2000C2semidirect
13. C61×#1895C2semidirect
14. C61×#1894C2semidirect
15. C61×#1809C2semidirect
17. C22×SD16×C61C22semidirect
28. C2×#107×C61C22semidirect
29. C2×#107×C61C22semidirect
30. C2×#106×C61C22semidirect
31. C2×#103×C61C22semidirect
32. C2×#103×C61C22semidirect
33. C2×#103×C61C22semidirect
34. C2×#102×C61C22semidirect
35. C2×#102×C61C22semidirect
36. C2×#102×C61C22semidirect
55. C61×#340C22semidirect
56. C61×#340C22semidirect
57. C61×#340C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
87. C2×M16×C61D4semidirect
363. #29744C61direct (N × H)
414. C2×#468C2×C61semidirect
415. C2×#407C2×C61semidirect
416. #2848C2×C61semidirect
418. #2076C2×C61semidirect
419. #2075C2×C61semidirect
420. #2036C2×C61semidirect
421. #2035C2×C61semidirect
422. #2034C2×C61semidirect
423. #2033C2×C61semidirect
424. #2000C2×C61semidirect
425. #2000C2×C61semidirect
426. #1895C2×C61semidirect
427. #1894C2×C61semidirect
428. #1809C2×C61semidirect
441. C22×SD16C22×C61semidirect
452. C2×#107C22×C61semidirect
453. C2×#107C22×C61semidirect
454. C2×#106C22×C61semidirect
455. C2×#103C22×C61semidirect
456. C2×#103C22×C61semidirect
457. C2×#103C22×C61semidirect
458. C2×#102C22×C61semidirect
459. C2×#102C22×C61semidirect
460. C2×#102C22×C61semidirect
479. #340C22×C61semidirect
480. #340C22×C61semidirect
481. #340C22×C61semidirect
482. #340C22×C61semidirect
483. #340C22×C61semidirect
484. #340C22×C61semidirect
485. C61#29744direct (N × H)
512. C2×M16D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4682
C2×C61×#4072
C61×#28482
C61×#28472
C61×#20762
C61×#20752
C61×#20362
C61×#20352
C61×#20342
C61×#20332
C61×#20002
C61×#18952
C61×#18942
C61×#18092
#2974461