Finite Group Databasebeta

← C61×#24397 #29527830

Subgroups — C61×#24397 #29527830

Order 15616.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#537C211yesmaximal, characteristic, complemented
2C2×C61×#469C211yesmaximal, characteristic, complemented
3C2×C61×#465C211yesmaximal, characteristic, complemented
4C2×C61×#449C211yesmaximal, characteristic, complemented
5C2×C61×#408C211yesmaximal, characteristic, complemented
6C61×#2615C211yesmaximal, characteristic, complemented
7C61×#2035C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2000C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1894C211yesmaximal, characteristic, complemented
12C61×#1893C211yesmaximal, characteristic, complemented
13C61×#1874C211yesmaximal, characteristic, complemented
14C61×#1853C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic
21C23×C8×C61C2211yescharacteristic
22C61×#537—24no—
23C61×#537—24no—
24C2×C22⋊Q8×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×#121×C61—21no—
28C2×#121×C61—21no—
29C2×#121×C61—21no—
30C2×#121×C61C2211yescharacteristic
31C2×#121×C61C2211yescharacteristic
32C2×#121×C61C2211yescharacteristic
33C2×#121×C61C2211yescharacteristic
34C2×#121×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#469—24no—
37C61×#465—24no—
38C61×#449—24no—
39C2×#106×C61C2211yescharacteristic
40C2×#106×C61C2211yescharacteristic
41C2×#103×C61C2211yescharacteristic
42C2×#103×C61C2211yescharacteristic
43C2×#103×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C61×#408—24no—
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C61×#393—21no—
55C61×#392—21no—
56C61×#392—21no—
57C61×#392—21no—
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—22no—
71C2×#41×C61—22no—
72C2×#41×C61—22no—
73C2×#41×C61—41no—
74C2×#41×C61—41no—
75C2×#41×C61—41no—
76C2×#41×C61—41no—
77C22×Q8×C61D411yescharacteristic
78C22×Q8×C61C2311yescharacteristic
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C22×D4×C61D411yescharacteristic
86C22×D4×C61D411yescharacteristic
87C22×D4×C61D411yescharacteristic
88C22×D4×C61C2311yescharacteristic
89C22×D4×C61C2311yescharacteristic
90C23×C4×C61—21no—
91C23×C4×C61—21no—
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C2×SD16×C61—22no—
96C2×SD16×C61—22no—
97C2×SD16×C61—41no—
98C2×D8×C61—22no—
99C2×D8×C61—22no—
100C2×D8×C61—41no—
101C2×M16×C61—22no—
102C2×M16×C61—22no—
103C2×M16×C61—41no—
104C22×C8×C61—22no—
105C22×C8×C61—22no—
106C22×C8×C61—41no—
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22⋊Q8×C61—28no—
112C22⋊Q8×C61—22no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61D414yescomplemented
116#121×C61—28no—
117#121×C61—28no—
118#121×C61—28no—
119#121×C61—22no—
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61—22no—
124#121×C61—22no—
125#121×C61—22no—
126#121×C61—41no—
127#121×C61—41no—
128#121×C61D414yescomplemented
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149#106×C61—22no—
150#106×C61—22no—
151#103×C61—22no—
152#103×C61—22no—
153#103×C61—41no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61—41no—
159C22⋊C8×C61—22no—
160C22⋊C8×C61—22no—
161C22⋊C8×C61—22no—
162C22⋊C8×C61D414yescomplemented
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C24×C61C2×D411yescharacteristic
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178#41×C61—44no—
179C2×Q8×C61—22no—
180C2×Q8×C61—22no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—41no—
187C2×Q8×C61C2×D412yes—
188C2×D4×C61—24no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—41no—
209C2×D4×C61—41no—
210C2×D4×C61—41no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—42no—
216C2×D4×C61—81no—
217C2×D4×C61—81no—
218C2×D4×C61—81no—
219C2×D4×C61—81no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61—81no—
224C2×D4×C61—81no—
225C2×D4×C61—81no—
226C2×D4×C61C2×D412yes—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—24no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—24no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—42no—
250C22×C4×C61—42no—
251C22×C4×C61—81no—
252C22×C4×C61—81no—
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2×D412yes—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D412yes—
259C22×C4×C61#4112yes—
260C22×C4×C61C2411yescharacteristic
261SD16×C61—44no—
262D8×C61—44no—
263M16×C61—44no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—44no—
275C2×C8×C61C2×D412yes—
276C2×C8×C61C2×D412yes—
277C4⋊C4×C61—24no—
278C4⋊C4×C61—24no—
279C4⋊C4×C61—24no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61C2×D412yes—
289C4⋊C4×C61C2×D412yes—
290C22⋊C4×C61—24no—
291C22⋊C4×C61—24no—
292C22⋊C4×C61—24no—
293C22⋊C4×C61—24no—
294C22⋊C4×C61—42no—
295C22⋊C4×C61—42no—
296C22⋊C4×C61—42no—
297C22⋊C4×C61—81no—
298C22⋊C4×C61—81no—
299C22⋊C4×C61—81no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—22no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61#12012yes—
334C23×C61#12112yes—
335C23×C61C22×D411yescharacteristic
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—44no—
339Q8×C61—41no—
340Q8×C61—41no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—44no—
344D4×C61—44no—
345D4×C61—44no—
346D4×C61—48no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—84no—
354D4×C61—84no—
355D4×C61—84no—
356D4×C61—84no—
357D4×C61—84no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—48no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—84no—
397C2×C4×C61#12012yes—
398C2×C4×C61#12112yes—
399C2×C4×C61C22×D411yescharacteristic
400C2×C4×C61C22×D411yescharacteristic
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C2×#4111yescharacteristic
403C2×C4×C61H(5,𝔽2)11yescharacteristic
404C2×C4×C61H(5,𝔽2)11yescharacteristic
405C8×C61—22no—
406C8×C61—22no—
407C8×C61—41no—
408C8×C61—41no—
409#24397C6111yesmaximal, characteristic, direct product factor, Sylow
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—42no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—42no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61C2×#12011yescharacteristic
446C22×C61C2×#12111yescharacteristic
447C22×C61#53411yescharacteristic
448C22×C61#57611yescharacteristic
449C22×C61#57711yescharacteristic
450C22×C61#57711yescharacteristic
451C22×C61#57711yescharacteristic
452C4×C61—22no—
453C4×C61—22no—
454C4×C61—41no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61—42no—
458C4×C61—81no—
459C4×C61—81no—
460C4×C61—81no—
461C4×C61D4211yescharacteristic
462C4×C61D4211yescharacteristic
463C4×C61#54611yescharacteristic
464C4×C61#54611yescharacteristic
465C2×#537C2×C6111yescharacteristic, complemented
466C2×#469C2×C6111yescharacteristic, complemented
467C2×#465C2×C6111yescharacteristic, complemented
468C2×#449C2×C6111yescharacteristic, complemented
469C2×#408C2×C6111yescharacteristic, complemented
470#2615C2×C6111yescharacteristic, complemented
471#2035C2×C6111yescharacteristic, complemented
472#2034C2×C6111yescharacteristic, complemented
473#2000C2×C6111yescharacteristic, complemented
474#1999C2×C6111yescharacteristic, complemented
475#1894C2×C6111yescharacteristic, complemented
476#1893C2×C6111yescharacteristic, complemented
477#1874C2×C6111yescharacteristic, complemented
478#1853C2×C6111yescharacteristic, complemented
479#1788C2×C6111yescharacteristic, complemented
480C2×C61—42no—
481C2×C61—42no—
482C2×C61—81no—
483C2×C61—82no—
484C2×C61—161no—
485C2×C61#241011yescharacteristic
486C2×C61#301011yescharacteristic
487C2×C61#301211yescharacteristic
488C2×C61#306011yescharacteristic
489C2×C61#306211yescharacteristic
490C2×C61#319811yescharacteristic
491C2×C61#320411yescharacteristic
492C22×#41C22×C6111yescharacteristic
493C22×#41C22×C6111yescharacteristic
494C22×SD16C22×C6111yescharacteristic
495C22×D8C22×C6111yescharacteristic
496C22×M16C22×C6111yescharacteristic
497C23×C8C22×C6111yescharacteristic
498#537—24no—
499#537—24no—
500C2×C22⋊Q8—21no—
501C2×C22⋊Q8C22×C6111yescharacteristic
502C2×C22⋊Q8C22×C6111yescharacteristic
503C2×#121—21no—
504C2×#121—21no—
505C2×#121—21no—
506C2×#121C22×C6111yescharacteristic
507C2×#121C22×C6111yescharacteristic
508C2×#121C22×C6111yescharacteristic
509C2×#121C22×C6111yescharacteristic
510C2×#121C22×C6111yescharacteristic
511C22×C4⋊C4C22×C6111yescharacteristic
512#469—24no—
513#465—24no—
514#449—24no—
515C2×#106C22×C6111yescharacteristic
516C2×#106C22×C6111yescharacteristic
517C2×#103C22×C6111yescharacteristic
518C2×#103C22×C6111yescharacteristic
519C2×#103C22×C6111yescharacteristic
520C2×#102C22×C6111yescharacteristic
521C2×#102C22×C6111yescharacteristic
522C2×#102C22×C6111yescharacteristic
523C2×#102C22×C6111yescharacteristic
524C2×#102C22×C6111yescharacteristic
525#408—24no—
526C2×C22⋊C8C22×C6111yescharacteristic
527C2×C22⋊C8C22×C6111yescharacteristic
528C2×C22⋊C8C22×C6111yescharacteristic
529C2×C22⋊C8C22×C6111yescharacteristic
530#393—21no—
531#392—21no—
532#392—21no—
533#392—21no—
534#380C22×C6111yescharacteristic
535#380C22×C6111yescharacteristic
536#380C22×C6111yescharacteristic
537#340C22×C6111yescharacteristic
538#340C22×C6111yescharacteristic
539#340C22×C6111yescharacteristic
540#340C22×C6111yescharacteristic
541C61#2439711yescharacteristic, direct product factor, Sylow
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C6111yescharacteristic
555C22×Q8C23×C6111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C6111yescharacteristic
563C22×D4D4×C6111yescharacteristic
564C22×D4D4×C6111yescharacteristic
565C22×D4C23×C6111yescharacteristic
566C22×D4C23×C6111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C6111yescharacteristic
570C23×C4C23×C6111yescharacteristic
571C23×C4C23×C6111yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C6111yescharacteristic
585C22×C8C23×C6111yescharacteristic
586C22×C8C23×C6111yescharacteristic
587C22×C8C23×C6111yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C6114yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C6114yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C6111yescharacteristic
612C2×C4⋊C4C23×C6111yescharacteristic
613C2×C4⋊C4C23×C6111yescharacteristic
614C2×C4⋊C4C23×C6111yescharacteristic
615C2×C4⋊C4C23×C6111yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C6114yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C6111yescharacteristic
646C24C2×D4×C6111yescharacteristic
647C24C2×D4×C6111yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C6112yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C6112yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C6111yescharacteristic
731C22×C4C2×D4×C6111yescharacteristic
732C22×C4C2×D4×C6112yes—
733C22×C4C2×D4×C6112yes—
734C22×C4C2×D4×C6111yescharacteristic
735C22×C4C2×D4×C6112yes—
736C22×C4#41×C6112yes—
737C22×C4C24×C6111yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C6112yes—
753C2×C8C2×D4×C6112yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C6112yes—
766C4⋊C4C2×D4×C6112yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#120×C6112yes—
811C23#121×C6112yes—
812C23C22×D4×C6111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4#120×C6112yes—
875C2×C4#121×C6112yes—
876C2×C4C22×D4×C6111yescharacteristic
877C2×C4C22×D4×C6111yescharacteristic
878C2×C4C22×D4×C6111yescharacteristic
879C2×C4C2×#41×C6111yescharacteristic
880C2×C4H(5,𝔽2)×C6111yescharacteristic
881C2×C4H(5,𝔽2)×C6111yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C6111yescharacteristic
922C22C2×#121×C6111yescharacteristic
923C22C61×#53411yescharacteristic
924C22C61×#57611yescharacteristic
925C22C61×#57711yescharacteristic
926C22C61×#57711yescharacteristic
927C22C61×#57711yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C6111yescharacteristic
938C4D42×C6111yescharacteristic
939C4C61×#54611yescharacteristic
940C4C61×#54611yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C61×#241011yescharacteristic
947C2C61×#301011yescharacteristic
948C2C61×#301211yescharacteristic
949C2C61×#306011yescharacteristic
950C2C61×#306211yescharacteristic
951C2C61×#319811yescharacteristic
952C2C61×#320411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#537C2semidirect
2. C2×C61×#469C2semidirect
3. C2×C61×#465C2semidirect
4. C2×C61×#449C2semidirect
5. C2×C61×#408C2semidirect
6. C61×#2615C2semidirect
7. C61×#2035C2semidirect
8. C61×#2034C2semidirect
9. C61×#2000C2semidirect
10. C61×#1999C2semidirect
11. C61×#1894C2semidirect
12. C61×#1893C2semidirect
13. C61×#1874C2semidirect
14. C61×#1853C2semidirect
15. C61×#1788C2semidirect
115. C22⋊Q8×C61D4semidirect
128. #121×C61D4semidirect
162. C22⋊C8×C61D4semidirect
409. #24397C61direct (N × H)
465. C2×#537C2×C61semidirect
466. C2×#469C2×C61semidirect
467. C2×#465C2×C61semidirect
468. C2×#449C2×C61semidirect
469. C2×#408C2×C61semidirect
470. #2615C2×C61semidirect
471. #2035C2×C61semidirect
472. #2034C2×C61semidirect
473. #2000C2×C61semidirect
474. #1999C2×C61semidirect
475. #1894C2×C61semidirect
476. #1893C2×C61semidirect
477. #1874C2×C61semidirect
478. #1853C2×C61semidirect
479. #1788C2×C61semidirect
541. C61#24397direct (N × H)
592. C22⋊Q8D4×C61semidirect
605. #121D4×C61semidirect
639. 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×#5372
C2×C61×#4692
C2×C61×#4652
C2×C61×#4492
C2×C61×#4082
C61×#26152
C61×#20352
C61×#20342
C61×#20002
C61×#19992
C61×#18942
C61×#18932
C61×#18742
C61×#18532
C61×#17882
#2439761