Finite Group Databasebeta

← C61×#23412 #29526845

Subgroups — C61×#23412 #29526845

Order 15616.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#575C211yesmaximal, characteristic, complemented
2C2×C61×#575C211yesmaximal, characteristic, complemented
3C61×#3449C211yesmaximal, characteristic, complemented
4C2×C61×#421C211yesmaximal, characteristic, complemented
5C61×#2896C211yesmaximal, characteristic, complemented
6C2×C61×#410C211yesmaximal, characteristic, complemented
7C61×#2009C214yesmaximal, complemented
8C61×#2008C214yesmaximal, complemented
9C2×C61×#344C211yesmaximal, characteristic, complemented
10C22×#41×C61C2211yescharacteristic
11C22×#41×C61C2211yescharacteristic
12C22×#41×C61C2211yescharacteristic
13C61×#575—22no—
14C61×#575—22no—
15C61×#575—22no—
16C61×#575—22no—
17C61×#575—22no—
18C61×#575—22no—
19C61×#575—22no—
20C61×#575C2214yes—
21C2×#137×C61—21no—
22C2×#137×C61—21no—
23C2×#137×C61—21no—
24C2×#137×C61C2212yescomplemented
25C2×AGL(1,ℤ/8)×C61—21no—
26C2×AGL(1,ℤ/8)×C61—21no—
27C2×AGL(1,ℤ/8)×C61—21no—
28C2×AGL(1,ℤ/8)×C61C2212yescomplemented
29C2×#135×C61—22no—
30C2×#135×C61—22no—
31C22×M16×C61C2211yescharacteristic
32C22×M16×C61C2211yescharacteristic
33C61×#537—22no—
34C61×#536—21no—
35C61×#536C2212yescomplemented
36C61×#535—21no—
37C61×#535C2212yescomplemented
38C61×#534—22no—
39C61×#532—22no—
40C61×#525—22no—
41C61×#525—22no—
42C2×#117×C61C2211yescharacteristic
43C2×#117×C61C2211yescharacteristic
44C61×#421—22no—
45C61×#421C2214yescomplemented
46C2×#104×C61—22no—
47C61×#419C2212yescomplemented
48C61×#418C2212yescomplemented
49C61×#417—22no—
50C61×#416—22no—
51C61×#410—22no—
52C61×#410C2214yescomplemented
53C2×#99×C61—22no—
54C61×#344C2214yescomplemented
55C2×#41×C61—21no—
56C2×#41×C61—21no—
57C2×#41×C61—21no—
58C2×#41×C61—21no—
59C2×#41×C61—21no—
60C2×#41×C61—21no—
61C2×#41×C61—21no—
62C2×#41×C61—21no—
63C2×#41×C61—21no—
64C2×#41×C61—21no—
65C2×#41×C61—21no—
66C2×#41×C61—21no—
67C2×#41×C61—21no—
68C2×#41×C61—21no—
69C2×#41×C61—21no—
70C2×#41×C61—21no—
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61—21no—
74C2×#41×C61—21no—
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—21no—
84C2×#41×C61—21no—
85C2×#41×C61D412yes—
86C2×#41×C61D412yes—
87C2×#41×C61D412yes—
88C2×#41×C61D412yescomplemented
89C2×#41×C61C2312yes—
90C2×#41×C61C2312yes—
91C22×Q8×C61D411yescharacteristic
92C22×Q8×C61D411yescharacteristic, complemented
93C22×Q8×C61C2311yescharacteristic
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61D411yescharacteristic
98C22×D4×C61D411yescharacteristic, complemented
99C22×D4×C61C2311yescharacteristic
100C23×C4×C61—21no—
101C23×C4×C61—21no—
102C23×C4×C61—21no—
103C23×C4×C61C2311yescharacteristic
104#137×C61—24no—
105#137×C61—24no—
106#137×C61—24no—
107#137×C61—24no—
108#137×C61—24no—
109#137×C61—24no—
110#137×C61—24no—
111#137×C61—24no—
112AGL(1,ℤ/8)×C61—24no—
113AGL(1,ℤ/8)×C61—24no—
114AGL(1,ℤ/8)×C61—24no—
115AGL(1,ℤ/8)×C61—24no—
116AGL(1,ℤ/8)×C61—24no—
117AGL(1,ℤ/8)×C61—24no—
118AGL(1,ℤ/8)×C61—24no—
119AGL(1,ℤ/8)×C61—24no—
120#135×C61—28no—
121#135×C61—28no—
122#135×C61—28no—
123#135×C61—28no—
124C2×Q16×C61—22no—
125C2×Q16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61—22no—
128C2×SD16×C61—22no—
129C2×SD16×C61—22no—
130C2×D8×C61—22no—
131C2×D8×C61—22no—
132C2×M16×C61—21no—
133C2×M16×C61—21no—
134C2×M16×C61—21no—
135C2×M16×C61—21no—
136C2×M16×C61—21no—
137C2×M16×C61—21no—
138C2×M16×C61—21no—
139C2×M16×C61D412yescomplemented
140C2×M16×C61D412yescomplemented
141C2×M16×C61D412yescomplemented
142C2×M16×C61C2312yes—
143C2×M16×C61C2312yes—
144C22×C8×C61—21no—
145C22×C8×C61D412yescomplemented
146C4⋊Q8×C61—22no—
147#127×C61—22no—
148#124×C61—22no—
149#124×C61—22no—
150#123×C61—24no—
151#123×C61—24no—
152C22⋊Q8×C61—24no—
153C22⋊Q8×C61—24no—
154#121×C61—28no—
155#121×C61—24no—
156#121×C61—24no—
157#120×C61—24no—
158#120×C61—24no—
159C4×D4×C61—28no—
160#117×C61—21no—
161#117×C61—21no—
162#117×C61—21no—
163#117×C61—21no—
164#117×C61—21no—
165#117×C61D412yes—
166#117×C61C2312yes—
167#117×C61C2312yes—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C22⋊C4×C61—21no—
171C2×C22⋊C4×C61D412yes—
172C2×C42×C61—21no—
173C2×C42×C61—21no—
174#104×C61—28no—
175#103×C61—24no—
176#102×C61—24no—
177#99×C61—28no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61C2×D411yescharacteristic
182#41×C61—22no—
183#41×C61—22no—
184#41×C61—22no—
185#41×C61—22no—
186#41×C61—22no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—22no—
190#41×C61—22no—
191#41×C61—22no—
192#41×C61—22no—
193#41×C61—22no—
194#41×C61—22no—
195#41×C61—22no—
196#41×C61—22no—
197#41×C61—22no—
198#41×C61—22no—
199#41×C61—22no—
200#41×C61—22no—
201#41×C61—22no—
202#41×C61—22no—
203#41×C61—22no—
204#41×C61—22no—
205#41×C61—22no—
206#41×C61—41no—
207#41×C61—41no—
208#41×C61—41no—
209#41×C61—41no—
210#41×C61—41no—
211#41×C61—41no—
212#41×C61—41no—
213#41×C61—41no—
214#41×C61—41no—
215#41×C61—41no—
216#41×C61—41no—
217#41×C61—41no—
218#41×C61—41no—
219#41×C61—41no—
220#41×C61—41no—
221#41×C61—41no—
222#41×C61—41no—
223#41×C61—41no—
224#41×C61—41no—
225#41×C61—41no—
226#41×C61—41no—
227#41×C61—41no—
228#41×C61—41no—
229#41×C61—41no—
230C2×Q8×C61—21no—
231C2×Q8×C61—21no—
232C2×Q8×C61—21no—
233C2×Q8×C61—21no—
234C2×Q8×C61—21no—
235C2×Q8×C61—21no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—21no—
240C2×Q8×C61—21no—
241C2×Q8×C61—21no—
242C2×Q8×C61—21no—
243C2×Q8×C61—21no—
244C2×Q8×C61—21no—
245C2×Q8×C61C2×D412yes—
246C2×Q8×C61C2×D412yes—
247C2×Q8×C61C2×D412yes—
248C2×D4×C61—22no—
249C2×D4×C61—22no—
250C2×D4×C61—22no—
251C2×D4×C61—22no—
252C2×D4×C61—22no—
253C2×D4×C61—22no—
254C2×D4×C61—28no—
255C2×D4×C61—21no—
256C2×D4×C61—21no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61—21no—
270C2×D4×C61—41no—
271C2×D4×C61—41no—
272C2×D4×C61—41no—
273C2×D4×C61—41no—
274C2×D4×C61—41no—
275C2×D4×C61—41no—
276C2×D4×C61—41no—
277C2×D4×C61—41no—
278C2×D4×C61—41no—
279C2×D4×C61—41no—
280C2×D4×C61—41no—
281C2×D4×C61—41no—
282C2×D4×C61C2×D412yes—
283C2×D4×C61C2×D412yes—
284C2×D4×C61C2×D412yes—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—21no—
288C22×C4×C61—22no—
289C22×C4×C61—22no—
290C22×C4×C61—22no—
291C22×C4×C61—22no—
292C22×C4×C61—22no—
293C22×C4×C61—22no—
294C22×C4×C61—22no—
295C22×C4×C61—41no—
296C22×C4×C61—41no—
297C22×C4×C61—41no—
298C22×C4×C61—41no—
299C22×C4×C61—41no—
300C22×C4×C61—41no—
301C22×C4×C61—41no—
302C22×C4×C61—41no—
303C22×C4×C61—41no—
304C22×C4×C61—41no—
305C22×C4×C61—41no—
306C22×C4×C61—41no—
307C22×C4×C61—41no—
308C22×C4×C61C2×D411yescharacteristic
309C22×C4×C61C2×D411yescharacteristic
310C22×C4×C61C2×D411yescharacteristic
311C22×C4×C61C2×D411yescharacteristic
312C22×C4×C61C2×D411yescharacteristic
313C22×C4×C61C2×D411yescharacteristic
314C22×C4×C61C2×D411yescharacteristic
315C22×C4×C61C2×D411yescharacteristic
316C22×C4×C61C2×D411yescharacteristic
317C22×C4×C61C2×D411yescharacteristic
318C22×C4×C61C2×D411yescharacteristic
319C22×C4×C61#4111yescharacteristic
320C22×C4×C61#4111yescharacteristic
321C22×C4×C61C2411yescharacteristic
322Q16×C61—28no—
323Q16×C61—28no—
324SD16×C61—28no—
325SD16×C61—28no—
326SD16×C61—28no—
327SD16×C61—28no—
328D8×C61—28no—
329D8×C61—28no—
330M16×C61—22no—
331M16×C61—22no—
332M16×C61—22no—
333M16×C61—22no—
334M16×C61—22no—
335M16×C61—22no—
336M16×C61—22no—
337M16×C61C2×D414yes—
338C2×C8×C61—22no—
339C2×C8×C61—22no—
340C2×C8×C61—22no—
341C2×C8×C61—22no—
342C2×C8×C61—22no—
343C2×C8×C61C2×D414yes—
344C4⋊C4×C61—28no—
345C4⋊C4×C61—22no—
346C4⋊C4×C61—22no—
347C4⋊C4×C61—22no—
348C4⋊C4×C61—41no—
349C22⋊C4×C61—28no—
350C22⋊C4×C61—28no—
351C22⋊C4×C61—22no—
352C22⋊C4×C61—22no—
353C22⋊C4×C61—41no—
354C22⋊C4×C61C2×D414yes—
355C42×C61—22no—
356C42×C61—22no—
357C42×C61—22no—
358C42×C61—41no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—81no—
369C23×C61—82no—
370C23×C61—82no—
371C23×C61—82no—
372C23×C61#12011yescharacteristic
373C23×C61#12011yescharacteristic
374C23×C61#12111yescharacteristic
375C23×C61#12111yescharacteristic
376C23×C61#12711yescharacteristic
377C23×C61#12711yescharacteristic
378C23×C61C22×D411yescharacteristic
379Q8×C61—22no—
380Q8×C61—22no—
381Q8×C61—22no—
382Q8×C61—22no—
383Q8×C61—22no—
384Q8×C61—22no—
385Q8×C61—41no—
386Q8×C61—41no—
387Q8×C61—41no—
388Q8×C61—41no—
389Q8×C61—41no—
390Q8×C61—41no—
391D4×C61—22no—
392D4×C61—22no—
393D4×C61—22no—
394D4×C61—22no—
395D4×C61—22no—
396D4×C61—22no—
397D4×C61—42no—
398D4×C61—42no—
399D4×C61—42no—
400D4×C61—42no—
401D4×C61—42no—
402D4×C61—42no—
403D4×C61—42no—
404D4×C61—42no—
405D4×C61—42no—
406D4×C61—42no—
407D4×C61—42no—
408D4×C61—42no—
409D4×C61—41no—
410D4×C61—41no—
411D4×C61—41no—
412D4×C61—41no—
413D4×C61—41no—
414D4×C61—41no—
415D4×C61—88no—
416C2×C4×C61—24no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—42no—
427C2×C4×C61—42no—
428C2×C4×C61—42no—
429C2×C4×C61—42no—
430C2×C4×C61—42no—
431C2×C4×C61—42no—
432C2×C4×C61—42no—
433C2×C4×C61—42no—
434C2×C4×C61—42no—
435C2×C4×C61—42no—
436C2×C4×C61—42no—
437C2×C4×C61—42no—
438C2×C4×C61—42no—
439C2×C4×C61—82no—
440C2×C4×C61—82no—
441C2×C4×C61#12011yescharacteristic
442C2×C4×C61#12011yescharacteristic
443C2×C4×C61#12011yescharacteristic
444C2×C4×C61#12011yescharacteristic
445C2×C4×C61#12011yescharacteristic
446C2×C4×C61#12011yescharacteristic
447C2×C4×C61#12011yescharacteristic
448C2×C4×C61#12011yescharacteristic
449C2×C4×C61#12011yescharacteristic
450C2×C4×C61#12011yescharacteristic
451C2×C4×C61#12111yescharacteristic
452C2×C4×C61#12111yescharacteristic
453C2×C4×C61#12111yescharacteristic
454C2×C4×C61#12111yescharacteristic
455C2×C4×C61#12111yescharacteristic
456C2×C4×C61#12111yescharacteristic
457C2×C4×C61#12111yescharacteristic
458C2×C4×C61#12111yescharacteristic
459C2×C4×C61#12111yescharacteristic
460C2×C4×C61#12111yescharacteristic
461C2×C4×C61#12711yescharacteristic
462C2×C4×C61#12711yescharacteristic
463C2×C4×C61C22×D411yescharacteristic
464C2×C4×C61C22×D411yescharacteristic
465C2×C4×C61C22×D411yescharacteristic
466C2×C4×C61C22×D411yescharacteristic
467C2×C4×C61C22×D411yescharacteristic
468C2×C4×C61C2×#4111yescharacteristic
469C8×C61—24no—
470C8×C61—24no—
471#23412C6111yesmaximal, characteristic, direct product factor, Sylow
472C22×C61—41no—
473C22×C61—41no—
474C22×C61—41no—
475C22×C61—41no—
476C22×C61—41no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—44no—
480C22×C61—44no—
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—42no—
484C22×C61—82no—
485C22×C61—82no—
486C22×C61—82no—
487C22×C61—82no—
488C22×C61—82no—
489C22×C61—82no—
490C22×C61—82no—
491C22×C61#39211yescharacteristic
492C22×C61#39211yescharacteristic
493C22×C61#39211yescharacteristic
494C22×C61#39211yescharacteristic
495C22×C61C2×#12011yescharacteristic
496C22×C61C2×#12111yescharacteristic
497C22×C61C2×#12711yescharacteristic
498C4×C61—44no—
499C4×C61—42no—
500C4×C61—42no—
501C4×C61—42no—
502C4×C61—82no—
503C4×C61#39211yescharacteristic
504C4×C61#39211yescharacteristic
505C4×C61#39211yescharacteristic
506C4×C61#39211yescharacteristic
507C4×C61C2×#12011yescharacteristic
508C4×C61C2×#12011yescharacteristic
509C4×C61C2×#12111yescharacteristic
510C4×C61C2×#12111yescharacteristic
511C2×#575C2×C6111yescharacteristic, complemented
512C2×#575C2×C6111yescharacteristic, complemented
513#3449C2×C6111yescharacteristic, complemented
514C2×#421C2×C6111yescharacteristic, complemented
515#2896C2×C6111yescharacteristic, complemented
516C2×#410C2×C6111yescharacteristic, complemented
517#2009C2×C6114yescomplemented
518#2008C2×C6114yescomplemented
519C2×#344C2×C6111yescharacteristic, complemented
520C2×C61—21no—
521C2×C61—21no—
522C2×C61—21no—
523C2×C61—21no—
524C2×C61—21no—
525C2×C61—21no—
526C2×C61—21no—
527C2×C61—82no—
528C2×C61—82no—
529C2×C61—82no—
530C2×C61C2×#39211yescharacteristic
531C22×#41C22×C6111yescharacteristic
532C22×#41C22×C6111yescharacteristic
533C22×#41C22×C6111yescharacteristic
534#575—22no—
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575C22×C6114yes—
542C2×#137—21no—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137C22×C6112yescomplemented
546C2×AGL(1,ℤ/8)—21no—
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)C22×C6112yescomplemented
550C2×#135—22no—
551C2×#135—22no—
552C22×M16C22×C6111yescharacteristic
553C22×M16C22×C6111yescharacteristic
554#537—22no—
555#536—21no—
556#536C22×C6112yescomplemented
557#535—21no—
558#535C22×C6112yescomplemented
559#534—22no—
560#532—22no—
561#525—22no—
562#525—22no—
563C2×#117C22×C6111yescharacteristic
564C2×#117C22×C6111yescharacteristic
565#421—22no—
566#421C22×C6114yescomplemented
567C2×#104—22no—
568#419C22×C6112yescomplemented
569#418C22×C6112yescomplemented
570#417—22no—
571#416—22no—
572#410—22no—
573#410C22×C6114yescomplemented
574C2×#99—22no—
575#344C22×C6114yescomplemented
576C61#2341211yescharacteristic, direct product factor, Sylow
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C6112yes—
608C2×#41D4×C6112yes—
609C2×#41D4×C6112yes—
610C2×#41D4×C6112yescomplemented
611C2×#41C23×C6112yes—
612C2×#41C23×C6112yes—
613C22×Q8D4×C6111yescharacteristic
614C22×Q8D4×C6111yescharacteristic, complemented
615C22×Q8C23×C6111yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C6111yescharacteristic
620C22×D4D4×C6111yescharacteristic, complemented
621C22×D4C23×C6111yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C6111yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C6112yescomplemented
662C2×M16D4×C6112yescomplemented
663C2×M16D4×C6112yescomplemented
664C2×M16C23×C6112yes—
665C2×M16C23×C6112yes—
666C22×C8—21no—
667C22×C8D4×C6112yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C6112yes—
688#117C23×C6112yes—
689#117C23×C6112yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C6112yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C6111yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C6112yes—
768C2×Q8C2×D4×C6112yes—
769C2×Q8C2×D4×C6112yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C6112yes—
805C2×D4C2×D4×C6112yes—
806C2×D4C2×D4×C6112yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C6111yescharacteristic
831C22×C4C2×D4×C6111yescharacteristic
832C22×C4C2×D4×C6111yescharacteristic
833C22×C4C2×D4×C6111yescharacteristic
834C22×C4C2×D4×C6111yescharacteristic
835C22×C4C2×D4×C6111yescharacteristic
836C22×C4C2×D4×C6111yescharacteristic
837C22×C4C2×D4×C6111yescharacteristic
838C22×C4C2×D4×C6111yescharacteristic
839C22×C4C2×D4×C6111yescharacteristic
840C22×C4C2×D4×C6111yescharacteristic
841C22×C4#41×C6111yescharacteristic
842C22×C4#41×C6111yescharacteristic
843C22×C4C24×C6111yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C6114yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C6114yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C6114yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C6111yescharacteristic
895C23#120×C6111yescharacteristic
896C23#121×C6111yescharacteristic
897C23#121×C6111yescharacteristic
898C23#127×C6111yescharacteristic
899C23#127×C6111yescharacteristic
900C23C22×D4×C6111yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C6111yescharacteristic
964C2×C4#120×C6111yescharacteristic
965C2×C4#120×C6111yescharacteristic
966C2×C4#120×C6111yescharacteristic
967C2×C4#120×C6111yescharacteristic
968C2×C4#120×C6111yescharacteristic
969C2×C4#120×C6111yescharacteristic
970C2×C4#120×C6111yescharacteristic
971C2×C4#120×C6111yescharacteristic
972C2×C4#120×C6111yescharacteristic
973C2×C4#121×C6111yescharacteristic
974C2×C4#121×C6111yescharacteristic
975C2×C4#121×C6111yescharacteristic
976C2×C4#121×C6111yescharacteristic
977C2×C4#121×C6111yescharacteristic
978C2×C4#121×C6111yescharacteristic
979C2×C4#121×C6111yescharacteristic
980C2×C4#121×C6111yescharacteristic
981C2×C4#121×C6111yescharacteristic
982C2×C4#121×C6111yescharacteristic
983C2×C4#127×C6111yescharacteristic
984C2×C4#127×C6111yescharacteristic
985C2×C4C22×D4×C6111yescharacteristic
986C2×C4C22×D4×C6111yescharacteristic
987C2×C4C22×D4×C6111yescharacteristic
988C2×C4C22×D4×C6111yescharacteristic
989C2×C4C22×D4×C6111yescharacteristic
990C2×C4C2×#41×C6111yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22C61×#39211yescharacteristic
1013C22C61×#39211yescharacteristic
1014C22C61×#39211yescharacteristic
1015C22C61×#39211yescharacteristic
1016C22C2×#120×C6111yescharacteristic
1017C22C2×#121×C6111yescharacteristic
1018C22C2×#127×C6111yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4C61×#39211yescharacteristic
1025C4C61×#39211yescharacteristic
1026C4C61×#39211yescharacteristic
1027C4C61×#39211yescharacteristic
1028C4C2×#120×C6111yescharacteristic
1029C4C2×#120×C6111yescharacteristic
1030C4C2×#121×C6111yescharacteristic
1031C4C2×#121×C6111yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×C61×#39211yescharacteristic
subgroupG/H
centerC4×C61#392
commutator, Frattini, cosocleC22×C4C24×C61
socleC2×C61C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#575C2semidirect
2. C2×C61×#575C2semidirect
3. C61×#3449C2semidirect
4. C2×C61×#421C2semidirect
5. C61×#2896C2semidirect
6. C2×C61×#410C2semidirect
7. C61×#2009C2semidirect
8. C61×#2008C2semidirect
9. C2×C61×#344C2semidirect
24. C2×#137×C61C22semidirect
28. C2×AGL(1,ℤ/8)×C61C22semidirect
35. C61×#536C22semidirect
37. C61×#535C22semidirect
45. C61×#421C22semidirect
47. C61×#419C22semidirect
48. C61×#418C22semidirect
52. C61×#410C22semidirect
54. C61×#344C22semidirect
88. C2×#41×C61D4semidirect
92. C22×Q8×C61D4semidirect
98. C22×D4×C61D4semidirect
139. C2×M16×C61D4semidirect
140. C2×M16×C61D4semidirect
141. C2×M16×C61D4semidirect
145. C22×C8×C61D4semidirect
471. #23412C61direct (N × H)
511. C2×#575C2×C61semidirect
512. C2×#575C2×C61semidirect
513. #3449C2×C61semidirect
514. C2×#421C2×C61semidirect
515. #2896C2×C61semidirect
516. C2×#410C2×C61semidirect
517. #2009C2×C61semidirect
518. #2008C2×C61semidirect
519. C2×#344C2×C61semidirect
545. C2×#137C22×C61semidirect
549. C2×AGL(1,ℤ/8)C22×C61semidirect
556. #536C22×C61semidirect
558. #535C22×C61semidirect
566. #421C22×C61semidirect
568. #419C22×C61semidirect
569. #418C22×C61semidirect
573. #410C22×C61semidirect
575. #344C22×C61semidirect
576. C61#23412direct (N × H)
610. C2×#41D4×C61semidirect
614. C22×Q8D4×C61semidirect
620. C22×D4D4×C61semidirect
661. C2×M16D4×C61semidirect
662. C2×M16D4×C61semidirect
663. C2×M16D4×C61semidirect
667. 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×#5752
C61×#34492
C2×C61×#4212
C61×#28962
C2×C61×#4102
C61×#20092
C61×#20082
C2×C61×#3442
#2341261