Finite Group Databasebeta

← C61×#25080 #29528513

Subgroups — C61×#25080 #29528513

Order 15616.

1356 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#465C211yesmaximal, characteristic, complemented
2C2×C61×#460C211yesmaximal, characteristic, complemented
3C2×C61×#450C211yesmaximal, characteristic, complemented
4C22×#102×C61C211yesmaximal, characteristic, complemented
5C61×#2433C211yesmaximal, characteristic
6C61×#2360C211yesmaximal, characteristic, complemented
7C61×#2065C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#2041C211yesmaximal, characteristic, complemented
10C61×#2014C211yesmaximal, characteristic, complemented
11C61×#1982C211yesmaximal, characteristic, complemented
12C61×#1926C211yesmaximal, characteristic, complemented
13C61×#1880C211yesmaximal, characteristic, complemented
14C61×#1874C211yesmaximal, characteristic, complemented
15C61×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×SD16×C61C2211yescharacteristic, complemented
20C23×C8×C61C2211yescharacteristic
21C2×#127×C61C2211yescharacteristic
22C2×#127×C61C2211yescharacteristic
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#120×C61—21no—
26C2×#120×C61—21no—
27C2×C4×Q8×C61C2211yescharacteristic, complemented
28C22×C4⋊C4×C61C2211yescharacteristic
29C61×#465—24no—
30C61×#460—24no—
31C61×#450—24no—
32C2×#106×C61C2211yescharacteristic, complemented
33C2×C4⋊C8×C61C2211yescharacteristic, complemented
34C2×C4⋊C8×C61C2211yescharacteristic, complemented
35C2×#103×C61C2211yescharacteristic, complemented
36C2×#102×C61—24no—
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic, complemented
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#392—21no—
48C61×#392—21no—
49C61×#391C2211yescharacteristic, complemented
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#389—21no—
53C61×#389C2211yescharacteristic, complemented
54C61×#387—21no—
55C61×#385—21no—
56C4×C4⋊C4×C61C2211yescharacteristic, complemented
57C4×C22⋊C4×C61—21no—
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, complemented
63C25×C61—21no—
64C22×Q8×C61C2311yescharacteristic
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—21no—
68C22×D4×C61—22no—
69C22×D4×C61—21no—
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61—22no—
75C22×D4×C61—41no—
76C22×D4×C61—41no—
77C22×D4×C61C2311yescharacteristic
78C22×D4×C61C2311yescharacteristic
79C22×D4×C61C2311yescharacteristic
80C23×C4×C61—21no—
81C23×C4×C61C2311yescharacteristic
82C2×SD16×C61—22no—
83C2×SD16×C61—22no—
84C2×SD16×C61—22no—
85C2×SD16×C61—22no—
86C2×SD16×C61—22no—
87C2×SD16×C61—22no—
88C2×SD16×C61—41no—
89C2×SD16×C61—41no—
90C2×SD16×C61—41no—
91C22×C8×C61—22no—
92C22×C8×C61—22no—
93C22×C8×C61—41no—
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98#127×C61—22no—
99#127×C61—22no—
100#127×C61—41no—
101#127×C61—41no—
102C22⋊Q8×C61—22no—
103C22⋊Q8×C61D414yescomplemented
104#121×C61—22no—
105#121×C61—22no—
106#120×C61—44no—
107#120×C61—44no—
108C4×Q8×C61—22no—
109C4×Q8×C61—41no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—41no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
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—
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132#106×C61—22no—
133C4⋊C8×C61—22no—
134C4⋊C8×C61—41no—
135#103×C61—22no—
136#102×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—41no—
144#102×C61D414yescomplemented
145C22⋊C8×C61—22no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61—21no—
150#95×C61D411yescharacteristic
151#95×C61D411yescharacteristic
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—42no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—42no—
159C24×C61—42no—
160C24×C61—81no—
161C24×C61—81no—
162C24×C61C2×D411yescharacteristic
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61C2×D412yes—
169C2×D4×C61—28no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—44no—
187C2×D4×C61—44no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—44no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61—42no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61—42no—
203C2×D4×C61—81no—
204C2×D4×C61—81no—
205C2×D4×C61—81no—
206C2×D4×C61—81no—
207C2×D4×C61C2×D412yes—
208C2×D4×C61#4112yes—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—42no—
219C22×C4×C61—42no—
220C22×C4×C61—81no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61#4112yes—
228C22×C4×C61C2411yescharacteristic
229SD16×C61—44no—
230SD16×C61—44no—
231SD16×C61—44no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—44no—
244C2×C8×C61C2×D412yes—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—42no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61—81no—
255C4⋊C4×C61C2×D412yes—
256C4⋊C4×C61C2×D412yes—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—42no—
261C22⋊C4×C61—42no—
262C22⋊C4×C61—42no—
263C22⋊C4×C61—42no—
264C22⋊C4×C61SD1614yescomplemented
265C42×C61—21no—
266C42×C61—21no—
267C42×C61—21no—
268C42×C61—21no—
269C42×C61—42no—
270C42×C61—81no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—48no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—84no—
298C23×C61—84no—
299C23×C61—84no—
300C23×C61—84no—
301C23×C61—84no—
302C23×C61—84no—
303C23×C61#12112yes—
304C23×C61C2×SD1612yes—
305C23×C61AGL(1,ℤ/8)12yes—
306C23×C61C22×D411yescharacteristic
307Q8×C61—22no—
308Q8×C61—22no—
309Q8×C61—41no—
310Q8×C61—41no—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—48no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—41no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—41no—
324D4×C61—84no—
325D4×C61—84no—
326D4×C61—84no—
327D4×C61—84no—
328D4×C61—84no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—84no—
361C2×C4×C61#12112yes—
362C2×C4×C61C2×SD1612yes—
363C2×C4×C61C2×SD1612yes—
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C2×#4111yescharacteristic
367C2×C4×C61C2×#4111yescharacteristic
368C2×C4×C61H(5,𝔽2)11yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C8×C61—22no—
371C8×C61—41no—
372C8×C61—41no—
373C8×C61—41no—
374#25080C6111yesmaximal, characteristic, direct product factor, Sylow
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—816no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61#46014yescomplemented
404C22×C61C2×#12111yescharacteristic
405C22×C61D4211yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61C22×SD1611yescharacteristic
408C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C61#57611yescharacteristic
410C22×C61#57711yescharacteristic
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—42no—
415C4×C61—41no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61—41no—
419C4×C61—81no—
420C4×C61—81no—
421C4×C61#52511yescharacteristic
422C4×C61#53811yescharacteristic
423C4×C61D4211yescharacteristic
424C4×C61#54611yescharacteristic
425C2×#465C2×C6111yescharacteristic, complemented
426C2×#460C2×C6111yescharacteristic, complemented
427C2×#450C2×C6111yescharacteristic, complemented
428C22×#102C2×C6111yescharacteristic, complemented
429#2433C2×C6111yescharacteristic
430#2360C2×C6111yescharacteristic, complemented
431#2065C2×C6111yescharacteristic, complemented
432#2055C2×C6111yescharacteristic, complemented
433#2041C2×C6111yescharacteristic, complemented
434#2014C2×C6111yescharacteristic, complemented
435#1982C2×C6111yescharacteristic, complemented
436#1926C2×C6111yescharacteristic, complemented
437#1880C2×C6111yescharacteristic, complemented
438#1874C2×C6111yescharacteristic, complemented
439#1850C2×C6111yescharacteristic, complemented
440C2×C61—24no—
441C2×C61—82no—
442C2×C61—82no—
443C2×C61—161no—
444C2×C61#242411yescharacteristic
445C2×C61C2×#46011yescharacteristic
446C2×C61#304511yescharacteristic
447C2×C61#326411yescharacteristic
448C2×C61D4×SD1611yescharacteristic
449C2×C61#329511yescharacteristic
450C2×C61#331011yescharacteristic
451C23×D4C22×C6111yescharacteristic
452C22×SD16C22×C6111yescharacteristic
453C22×SD16C22×C6111yescharacteristic
454C22×SD16C22×C6111yescharacteristic, complemented
455C23×C8C22×C6111yescharacteristic
456C2×#127C22×C6111yescharacteristic
457C2×#127C22×C6111yescharacteristic
458C2×C22⋊Q8C22×C6111yescharacteristic
459C2×#121C22×C6111yescharacteristic
460C2×#120—21no—
461C2×#120—21no—
462C2×C4×Q8C22×C6111yescharacteristic, complemented
463C22×C4⋊C4C22×C6111yescharacteristic
464#465—24no—
465#460—24no—
466#450—24no—
467C2×#106C22×C6111yescharacteristic, complemented
468C2×C4⋊C8C22×C6111yescharacteristic, complemented
469C2×C4⋊C8C22×C6111yescharacteristic, complemented
470C2×#103C22×C6111yescharacteristic, complemented
471C2×#102—24no—
472C2×#102C22×C6111yescharacteristic
473C2×#102C22×C6111yescharacteristic
474C2×#102C22×C6111yescharacteristic
475C2×#102C22×C6111yescharacteristic
476C2×#102C22×C6111yescharacteristic
477C2×#102C22×C6111yescharacteristic
478C2×#102C22×C6111yescharacteristic, complemented
479C2×#102C22×C6111yescharacteristic, complemented
480C2×#102C22×C6111yescharacteristic, complemented
481C2×C22⋊C8C22×C6111yescharacteristic
482#392—21no—
483#392—21no—
484#391C22×C6111yescharacteristic, complemented
485#390C22×C6111yescharacteristic
486#390C22×C6111yescharacteristic
487#389—21no—
488#389C22×C6111yescharacteristic, complemented
489#387—21no—
490#385—21no—
491C4×C4⋊C4C22×C6111yescharacteristic, complemented
492C4×C22⋊C4—21no—
493C4×C22⋊C4C22×C6111yescharacteristic
494#340C22×C6111yescharacteristic, complemented
495#340C22×C6111yescharacteristic, complemented
496#336C22×C6111yescharacteristic, complemented
497#336C22×C6111yescharacteristic, complemented
498C61#2508011yescharacteristic, direct product factor, Sylow
499C25—21no—
500C22×Q8C23×C6111yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C23×C6111yescharacteristic
514C22×D4C23×C6111yescharacteristic
515C22×D4C23×C6111yescharacteristic
516C23×C4—21no—
517C23×C4C23×C6111yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8C23×C6111yescharacteristic
531C22×C8C23×C6111yescharacteristic
532C22×C8C23×C6111yescharacteristic
533C22×C8C23×C6111yescharacteristic
534#127—22no—
535#127—22no—
536#127—41no—
537#127—41no—
538C22⋊Q8—22no—
539C22⋊Q8D4×C6114yescomplemented
540#121—22no—
541#121—22no—
542#120—44no—
543#120—44no—
544C4×Q8—22no—
545C4×Q8—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4C23×C6111yescharacteristic
553C2×C4⋊C4C23×C6111yescharacteristic
554C2×C4⋊C4C23×C6111yescharacteristic
555C2×C4⋊C4C23×C6111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4D4×C6111yescharacteristic
563C2×C22⋊C4D4×C6111yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C23×C6111yescharacteristic
567C2×C42C23×C6111yescharacteristic
568#106—22no—
569C4⋊C8—22no—
570C4⋊C8—41no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—41no—
580#102D4×C6114yescomplemented
581C22⋊C8—22no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586#95D4×C6111yescharacteristic
587#95D4×C6111yescharacteristic
588C24—21no—
589C24—21no—
590C24—21no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×D4×C6111yescharacteristic
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C2×D4×C6112yes—
605C2×D4—28no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4C2×D4×C6112yes—
644C2×D4#41×C6112yes—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4C2×D4×C6111yescharacteristic
658C22×C4C2×D4×C6111yescharacteristic
659C22×C4C2×D4×C6111yescharacteristic
660C22×C4C2×D4×C6112yes—
661C22×C4C2×D4×C6111yescharacteristic
662C22×C4C2×D4×C6111yescharacteristic
663C22×C4#41×C6112yes—
664C22×C4C24×C6111yescharacteristic
665SD16—44no—
666SD16—44no—
667SD16—44no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—44no—
680C2×C8C2×D4×C6112yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—81no—
691C4⋊C4C2×D4×C6112yes—
692C4⋊C4C2×D4×C6112yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4SD16×C6114yescomplemented
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—81no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#121×C6112yes—
740C23C2×SD16×C6112yes—
741C23AGL(1,ℤ/8)×C6112yes—
742C23C22×D4×C6111yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4#121×C6112yes—
798C2×C4C2×SD16×C6112yes—
799C2×C4C2×SD16×C6112yes—
800C2×C4C22×D4×C6111yescharacteristic
801C2×C4C22×D4×C6111yescharacteristic
802C2×C4C2×#41×C6111yescharacteristic
803C2×C4C2×#41×C6111yescharacteristic
804C2×C4H(5,𝔽2)×C6111yescharacteristic
805C2×C4H(5,𝔽2)×C6111yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22C61×#46014yescomplemented
839C22C2×#121×C6111yescharacteristic
840C22D42×C6111yescharacteristic
841C22C61×#54611yescharacteristic
842C22C22×SD16×C6111yescharacteristic
843C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
844C22C61×#57611yescharacteristic
845C22C61×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4C61×#52511yescharacteristic
857C4C61×#53811yescharacteristic
858C4D42×C6111yescharacteristic
859C4C61×#54611yescharacteristic
860C2—24no—
861C2—82no—
862C2—82no—
863C2—161no—
864C2C61×#242411yescharacteristic
865C2C2×C61×#46011yescharacteristic
866C2C61×#304511yescharacteristic
867C2C61×#326411yescharacteristic
868C2D4×SD16×C6111yescharacteristic
869C2C61×#329511yescharacteristic
870C2C61×#331011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2433C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#465C2semidirect
2. C2×C61×#460C2semidirect
3. C2×C61×#450C2semidirect
4. C22×#102×C61C2semidirect
6. C61×#2360C2semidirect
7. C61×#2065C2semidirect
8. C61×#2055C2semidirect
9. C61×#2041C2semidirect
10. C61×#2014C2semidirect
11. C61×#1982C2semidirect
12. C61×#1926C2semidirect
13. C61×#1880C2semidirect
14. C61×#1874C2semidirect
15. C61×#1850C2semidirect
19. C22×SD16×C61C22semidirect
27. C2×C4×Q8×C61C22semidirect
32. C2×#106×C61C22semidirect
33. C2×C4⋊C8×C61C22semidirect
34. C2×C4⋊C8×C61C22semidirect
35. C2×#103×C61C22semidirect
43. C2×#102×C61C22semidirect
44. C2×#102×C61C22semidirect
45. C2×#102×C61C22semidirect
49. C61×#391C22semidirect
53. C61×#389C22semidirect
56. C4×C4⋊C4×C61C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#336C22semidirect
62. C61×#336C22semidirect
103. C22⋊Q8×C61D4semidirect
144. #102×C61D4semidirect
264. C22⋊C4×C61SD16semidirect
374. #25080C61direct (N × H)
403. C22×C61#460semidirect
425. C2×#465C2×C61semidirect
426. C2×#460C2×C61semidirect
427. C2×#450C2×C61semidirect
428. C22×#102C2×C61semidirect
430. #2360C2×C61semidirect
431. #2065C2×C61semidirect
432. #2055C2×C61semidirect
433. #2041C2×C61semidirect
434. #2014C2×C61semidirect
435. #1982C2×C61semidirect
436. #1926C2×C61semidirect
437. #1880C2×C61semidirect
438. #1874C2×C61semidirect
439. #1850C2×C61semidirect
454. C22×SD16C22×C61semidirect
462. C2×C4×Q8C22×C61semidirect
467. C2×#106C22×C61semidirect
468. C2×C4⋊C8C22×C61semidirect
469. C2×C4⋊C8C22×C61semidirect
470. C2×#103C22×C61semidirect
478. C2×#102C22×C61semidirect
479. C2×#102C22×C61semidirect
480. C2×#102C22×C61semidirect
484. #391C22×C61semidirect
488. #389C22×C61semidirect
491. C4×C4⋊C4C22×C61semidirect
494. #340C22×C61semidirect
495. #340C22×C61semidirect
496. #336C22×C61semidirect
497. #336C22×C61semidirect
498. C61#25080direct (N × H)
539. C22⋊Q8D4×C61semidirect
580. #102D4×C61semidirect
700. C22⋊C4SD16×C61semidirect
838. C22C61×#460semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4652
C2×C61×#4602
C2×C61×#4502
C22×#102×C612
C61×#24332
C61×#23602
C61×#20652
C61×#20552
C61×#20412
C61×#20142
C61×#19822
C61×#19262
C61×#18802
C61×#18742
C61×#18502
#2508061