Finite Group Databasebeta

← C2×C61×#2008 #29526843

Subgroups — C2×C61×#2008 #29526843

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#575C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
3C2×C61×#535C211yesmaximal, characteristic, complemented
4C2×C61×#421C211yesmaximal, characteristic, complemented
5C2×C61×#418C211yesmaximal, characteristic, complemented
6C2×C61×#410C211yesmaximal, characteristic, complemented
7C61×#2008C218yesmaximal, direct product factor
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C22×#41×C61C2211yescharacteristic
10C22×#41×C61C2211yescharacteristic
11C23×D4×C61C2211yescharacteristic
12C61×#575—22no—
13C61×#575—22no—
14C61×#575—22no—
15C61×#575C2214yescomplemented
16C2×#137×C61—21no—
17C2×#137×C61—21no—
18C2×AGL(1,ℤ/8)×C61—22no—
19C2×AGL(1,ℤ/8)×C61—22no—
20C2×AGL(1,ℤ/8)×C61—22no—
21C2×AGL(1,ℤ/8)×C61—21no—
22C2×AGL(1,ℤ/8)×C61—21no—
23C2×AGL(1,ℤ/8)×C61—22no—
24C2×AGL(1,ℤ/8)×C61—22no—
25C2×AGL(1,ℤ/8)×C61C2214yescomplemented
26C2×#135×C61—22no—
27C22×SD16×C61—21no—
28C22×D8×C61—21no—
29C22×M16×C61C2211yescharacteristic
30C22×M16×C61C2211yescharacteristic
31C61×#535—22no—
32C61×#535—22no—
33C61×#535—22no—
34C61×#535C2214yescomplemented
35C2×#127×C61—21no—
36C2×#124×C61—21no—
37C2×#121×C61—22no—
38C2×#120×C61—22no—
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#421—22no—
42C61×#421C2214yescomplemented
43C2×#104×C61—22no—
44C61×#418—22no—
45C61×#418C2214yescomplemented
46C2×#102×C61—22no—
47C61×#410—22no—
48C61×#410C2214yescomplemented
49C2×#99×C61—22no—
50C61×#344C2214yescomplemented
51C25×C61—21no—
52C2×#41×C61—21no—
53C2×#41×C61—21no—
54C2×#41×C61—21no—
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×C61D412yes—
73C2×#41×C61D412yescomplemented
74C2×#41×C61C2312yes—
75C2×#41×C61C2312yes—
76C22×Q8×C61D411yescharacteristic
77C22×Q8×C61D411yescharacteristic, complemented
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—24no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C22×D4×C61—21no—
86C22×D4×C61—21no—
87C22×D4×C61—21no—
88C22×D4×C61—21no—
89C22×D4×C61—21no—
90C22×D4×C61—21no—
91C22×D4×C61—21no—
92C22×D4×C61D411yescharacteristic
93C22×D4×C61D412yes—
94C22×D4×C61D412yes—
95C22×D4×C61D411yescharacteristic, complemented
96C22×D4×C61C2312yes—
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100#137×C61—24no—
101#137×C61—24no—
102#137×C61—24no—
103#137×C61—24no—
104AGL(1,ℤ/8)×C61—28no—
105AGL(1,ℤ/8)×C61—28no—
106AGL(1,ℤ/8)×C61—24no—
107AGL(1,ℤ/8)×C61—24no—
108AGL(1,ℤ/8)×C61—28no—
109AGL(1,ℤ/8)×C61—24no—
110AGL(1,ℤ/8)×C61—24no—
111AGL(1,ℤ/8)×C61—28no—
112#135×C61—28no—
113#135×C61—28no—
114C2×Q16×C61—22no—
115C2×SD16×C61—24no—
116C2×SD16×C61—24no—
117C2×SD16×C61—22no—
118C2×SD16×C61—22no—
119C2×SD16×C61—24no—
120C2×D8×C61—24no—
121C2×D8×C61—24no—
122C2×D8×C61—22no—
123C2×D8×C61—24no—
124C2×M16×C61—21no—
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61—21no—
130C2×M16×C61—21no—
131C2×M16×C61D412yescomplemented
132C2×M16×C61D412yescomplemented
133C2×M16×C61D412yescomplemented
134C2×M16×C61C2312yes—
135C2×M16×C61C2312yes—
136C22×C8×C61—21no—
137C22×C8×C61D412yescomplemented
138#127×C61—24no—
139#127×C61—24no—
140#124×C61—24no—
141#124×C61—24no—
142#121×C61—28no—
143#121×C61—28no—
144#120×C61—28no—
145#120×C61—28no—
146#117×C61—21no—
147#117×C61—21no—
148#117×C61—21no—
149#117×C61—21no—
150#117×C61—21no—
151#117×C61D412yes—
152#117×C61C2312yes—
153#117×C61C2312yes—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
156C2×C22⋊C4×C61—24no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61D412yes—
159C2×C42×C61—21no—
160C2×C42×C61—21no—
161#104×C61—28no—
162#102×C61—28no—
163#99×C61—28no—
164C24×C61—22no—
165C24×C61—21no—
166C24×C61—22no—
167C24×C61—21no—
168C24×C61—22no—
169C24×C61—41no—
170C24×C61—41no—
171C24×C61—41no—
172C24×C61—41no—
173C24×C61—84no—
174C24×C61C2×D411yescharacteristic
175#41×C61—22no—
176#41×C61—22no—
177#41×C61—22no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—22no—
181#41×C61—22no—
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—41no—
192#41×C61—41no—
193#41×C61—41no—
194#41×C61—41no—
195#41×C61—41no—
196#41×C61—41no—
197#41×C61—41no—
198#41×C61—41no—
199#41×C61—41no—
200#41×C61—41no—
201#41×C61—41no—
202#41×C61—41no—
203#41×C61—41no—
204#41×C61—41no—
205#41×C61—41no—
206#41×C61—41no—
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—21no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61C2×D412yes—
218C2×Q8×C61C2×D412yescomplemented
219C2×D4×C61—22no—
220C2×D4×C61—22no—
221C2×D4×C61—22no—
222C2×D4×C61—22no—
223C2×D4×C61—216no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—22no—
227C2×D4×C61—22no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—22no—
231C2×D4×C61—22no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—22no—
235C2×D4×C61—22no—
236C2×D4×C61—21no—
237C2×D4×C61—22no—
238C2×D4×C61—22no—
239C2×D4×C61—22no—
240C2×D4×C61—22no—
241C2×D4×C61—21no—
242C2×D4×C61—21no—
243C2×D4×C61—21no—
244C2×D4×C61—22no—
245C2×D4×C61—22no—
246C2×D4×C61—22no—
247C2×D4×C61—22no—
248C2×D4×C61—22no—
249C2×D4×C61—41no—
250C2×D4×C61—41no—
251C2×D4×C61—41no—
252C2×D4×C61—41no—
253C2×D4×C61—41no—
254C2×D4×C61—41no—
255C2×D4×C61—41no—
256C2×D4×C61—41no—
257C2×D4×C61—41no—
258C2×D4×C61—41no—
259C2×D4×C61—41no—
260C2×D4×C61—41no—
261C2×D4×C61—41no—
262C2×D4×C61—41no—
263C2×D4×C61—41no—
264C2×D4×C61—41no—
265C2×D4×C61—41no—
266C2×D4×C61—41no—
267C2×D4×C61—41no—
268C2×D4×C61—41no—
269C2×D4×C61—88no—
270C2×D4×C61C2×D414yes—
271C2×D4×C61C2×D412yes—
272C2×D4×C61C2×D412yescomplemented
273C22×C4×C61—22no—
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—22no—
277C22×C4×C61—22no—
278C22×C4×C61—22no—
279C22×C4×C61—22no—
280C22×C4×C61—41no—
281C22×C4×C61—41no—
282C22×C4×C61—41no—
283C22×C4×C61—41no—
284C22×C4×C61—41no—
285C22×C4×C61—41no—
286C22×C4×C61—41no—
287C22×C4×C61—41no—
288C22×C4×C61—41no—
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2×D411yescharacteristic
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2×D411yescharacteristic
295C22×C4×C61C2×D411yescharacteristic
296C22×C4×C61C2×D411yescharacteristic
297C22×C4×C61C2×D411yescharacteristic
298C22×C4×C61C2×D411yescharacteristic
299C22×C4×C61C2×D411yescharacteristic
300C22×C4×C61#4111yescharacteristic
301C22×C4×C61#4111yescharacteristic
302C22×C4×C61C2411yescharacteristic
303Q16×C61—28no—
304SD16×C61—216no—
305SD16×C61—28no—
306SD16×C61—28no—
307D8×C61—216no—
308D8×C61—28no—
309M16×C61—22no—
310M16×C61—22no—
311M16×C61—22no—
312M16×C61—22no—
313M16×C61—22no—
314M16×C61—22no—
315M16×C61—22no—
316M16×C61C2×D414yescomplemented
317C2×C8×C61—22no—
318C2×C8×C61—22no—
319C2×C8×C61—22no—
320C2×C8×C61—22no—
321C2×C8×C61—22no—
322C2×C8×C61C2×D414yescomplemented
323C4⋊C4×C61—22no—
324C4⋊C4×C61—22no—
325C4⋊C4×C61—22no—
326C4⋊C4×C61—41no—
327C22⋊C4×C61—216no—
328C22⋊C4×C61—22no—
329C22⋊C4×C61—22no—
330C22⋊C4×C61—41no—
331C22⋊C4×C61C2×D414yes—
332C42×C61—22no—
333C42×C61—22no—
334C42×C61—22no—
335C42×C61—41no—
336C23×C61—24no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—42no—
340C23×C61—44no—
341C23×C61—48no—
342C23×C61—42no—
343C23×C61—42no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—42no—
347C23×C61—42no—
348C23×C61—42no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—42no—
352C23×C61—84no—
353C23×C61—84no—
354C23×C61—82no—
355C23×C61—84no—
356C23×C61—84no—
357C23×C61—84no—
358C23×C61—84no—
359C23×C61#12011yescharacteristic
360C23×C61#12011yescharacteristic
361C23×C61#12111yescharacteristic
362C23×C61#12111yescharacteristic
363C23×C61#12711yescharacteristic
364C23×C61#12711yescharacteristic
365C23×C61C22×D411yescharacteristic
366Q8×C61—22no—
367Q8×C61—22no—
368Q8×C61—22no—
369Q8×C61—22no—
370Q8×C61—41no—
371Q8×C61—41no—
372Q8×C61—41no—
373Q8×C61—41no—
374D4×C61—22no—
375D4×C61—24no—
376D4×C61—22no—
377D4×C61—22no—
378D4×C61—24no—
379D4×C61—22no—
380D4×C61—42no—
381D4×C61—42no—
382D4×C61—42no—
383D4×C61—42no—
384D4×C61—42no—
385D4×C61—42no—
386D4×C61—42no—
387D4×C61—42no—
388D4×C61—42no—
389D4×C61—42no—
390D4×C61—42no—
391D4×C61—42no—
392D4×C61—42no—
393D4×C61—42no—
394D4×C61—41no—
395D4×C61—41no—
396D4×C61—41no—
397D4×C61—41no—
398D4×C61—816no—
399C2×C4×C61—24no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—44no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—42no—
408C2×C4×C61—42no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61—42no—
412C2×C4×C61—42no—
413C2×C4×C61—42no—
414C2×C4×C61—42no—
415C2×C4×C61—42no—
416C2×C4×C61—82no—
417C2×C4×C61#12011yescharacteristic
418C2×C4×C61#12011yescharacteristic
419C2×C4×C61#12011yescharacteristic
420C2×C4×C61#12011yescharacteristic
421C2×C4×C61#12011yescharacteristic
422C2×C4×C61#12011yescharacteristic
423C2×C4×C61#12011yescharacteristic
424C2×C4×C61#12011yescharacteristic
425C2×C4×C61#12011yescharacteristic
426C2×C4×C61#12011yescharacteristic
427C2×C4×C61#12111yescharacteristic
428C2×C4×C61#12111yescharacteristic
429C2×C4×C61#12111yescharacteristic
430C2×C4×C61#12111yescharacteristic
431C2×C4×C61#12111yescharacteristic
432C2×C4×C61#12111yescharacteristic
433C2×C4×C61#12111yescharacteristic
434C2×C4×C61#12111yescharacteristic
435C2×C4×C61#12111yescharacteristic
436C2×C4×C61#12111yescharacteristic
437C2×C4×C61#12711yescharacteristic
438C2×C4×C61#12711yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C22×D411yescharacteristic
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C2×#4111yescharacteristic
445C8×C61—24no—
446C8×C61—24no—
447C2×#2008C6111yesmaximal, characteristic, direct product factor, Sylow
448C22×C61—22no—
449C22×C61—22no—
450C22×C61—22no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—44no—
456C22×C61—48no—
457C22×C61—42no—
458C22×C61—42no—
459C22×C61—44no—
460C22×C61—82no—
461C22×C61—82no—
462C22×C61—84no—
463C22×C61—82no—
464C22×C61—84no—
465C22×C61—84no—
466C22×C61—84no—
467C22×C61—84no—
468C22×C61—82no—
469C22×C61—84no—
470C22×C61—82no—
471C22×C61#39211yescharacteristic
472C22×C61#39211yescharacteristic
473C22×C61#39211yescharacteristic
474C22×C61#39211yescharacteristic
475C22×C61C2×#12011yescharacteristic
476C22×C61C2×#12111yescharacteristic
477C22×C61C2×#12711yescharacteristic
478C4×C61—44no—
479C4×C61—42no—
480C4×C61—42no—
481C4×C61—82no—
482C4×C61#39211yescharacteristic
483C4×C61#39211yescharacteristic
484C4×C61#39211yescharacteristic
485C4×C61#39211yescharacteristic
486C4×C61C2×#12011yescharacteristic
487C4×C61C2×#12011yescharacteristic
488C4×C61C2×#12111yescharacteristic
489C4×C61C2×#12111yescharacteristic
490C2×#575C2×C6111yescharacteristic, complemented
491C22×AGL(1,ℤ/8)C2×C6111yescharacteristic, complemented
492C2×#535C2×C6111yescharacteristic, complemented
493C2×#421C2×C6111yescharacteristic, complemented
494C2×#418C2×C6111yescharacteristic, complemented
495C2×#410C2×C6111yescharacteristic, complemented
496#2008C2×C6118yesdirect product factor
497C2×#344C2×C6111yescharacteristic, complemented
498C2×C61—21no—
499C2×C61—21no—
500C2×C61—21no—
501C2×C61—21no—
502C2×C61—21no—
503C2×C61—21no—
504C2×C61—82no—
505C2×C61—84no—
506C2×C61—82no—
507C2×C61#200812yesdirect product factor
508C2×C61C2×#39211yescharacteristic
509C22×#41C22×C6111yescharacteristic
510C22×#41C22×C6111yescharacteristic
511C23×D4C22×C6111yescharacteristic
512#575—22no—
513#575—22no—
514#575—22no—
515#575C22×C6114yescomplemented
516C2×#137—21no—
517C2×#137—21no—
518C2×AGL(1,ℤ/8)—22no—
519C2×AGL(1,ℤ/8)—22no—
520C2×AGL(1,ℤ/8)—22no—
521C2×AGL(1,ℤ/8)—21no—
522C2×AGL(1,ℤ/8)—21no—
523C2×AGL(1,ℤ/8)—22no—
524C2×AGL(1,ℤ/8)—22no—
525C2×AGL(1,ℤ/8)C22×C6114yescomplemented
526C2×#135—22no—
527C22×SD16—21no—
528C22×D8—21no—
529C22×M16C22×C6111yescharacteristic
530C22×M16C22×C6111yescharacteristic
531#535—22no—
532#535—22no—
533#535—22no—
534#535C22×C6114yescomplemented
535C2×#127—21no—
536C2×#124—21no—
537C2×#121—22no—
538C2×#120—22no—
539C2×#117C22×C6111yescharacteristic
540C2×#117C22×C6111yescharacteristic
541#421—22no—
542#421C22×C6114yescomplemented
543C2×#104—22no—
544#418—22no—
545#418C22×C6114yescomplemented
546C2×#102—22no—
547#410—22no—
548#410C22×C6114yescomplemented
549C2×#99—22no—
550#344C22×C6114yescomplemented
551C61C2×#200811yescharacteristic, direct product factor, Sylow
552C25—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41D4×C6112yes—
574C2×#41D4×C6112yescomplemented
575C2×#41C23×C6112yes—
576C2×#41C23×C6112yes—
577C22×Q8D4×C6111yescharacteristic
578C22×Q8D4×C6111yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—24no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4D4×C6112yes—
594C22×D4D4×C6111yescharacteristic
595C22×D4D4×C6112yes—
596C22×D4D4×C6111yescharacteristic, complemented
597C22×D4C23×C6112yes—
598C23×C4—21no—
599C23×C4—21no—
600C23×C4C23×C6111yescharacteristic
601#137—24no—
602#137—24no—
603#137—24no—
604#137—24no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—28no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—24no—
609AGL(1,ℤ/8)—28no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—24no—
612AGL(1,ℤ/8)—28no—
613#135—28no—
614#135—28no—
615C2×Q16—22no—
616C2×SD16—24no—
617C2×SD16—24no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—24no—
621C2×D8—24no—
622C2×D8—24no—
623C2×D8—22no—
624C2×D8—24no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16—21no—
632C2×M16D4×C6112yescomplemented
633C2×M16D4×C6112yescomplemented
634C2×M16D4×C6112yescomplemented
635C2×M16C23×C6112yes—
636C2×M16C23×C6112yes—
637C22×C8—21no—
638C22×C8D4×C6112yescomplemented
639#127—24no—
640#127—24no—
641#124—24no—
642#124—24no—
643#121—28no—
644#121—28no—
645#120—28no—
646#120—28no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117—21no—
652#117D4×C6112yes—
653#117C23×C6112yes—
654#117C23×C6112yes—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4D4×C6112yes—
660C2×C42—21no—
661C2×C42—21no—
662#104—28no—
663#102—28no—
664#99—28no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C6111yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C6112yes—
719C2×Q8C2×D4×C6112yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C6114yes—
772C2×D4C2×D4×C6112yes—
773C2×D4C2×D4×C6112yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C6111yescharacteristic
791C22×C4C2×D4×C6111yescharacteristic
792C22×C4C2×D4×C6111yescharacteristic
793C22×C4C2×D4×C6111yescharacteristic
794C22×C4C2×D4×C6111yescharacteristic
795C22×C4C2×D4×C6111yescharacteristic
796C22×C4C2×D4×C6111yescharacteristic
797C22×C4C2×D4×C6111yescharacteristic
798C22×C4C2×D4×C6111yescharacteristic
799C22×C4C2×D4×C6111yescharacteristic
800C22×C4C2×D4×C6111yescharacteristic
801C22×C4#41×C6111yescharacteristic
802C22×C4#41×C6111yescharacteristic
803C22×C4C24×C6111yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C6114yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C6114yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C6114yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—42no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23#120×C6111yescharacteristic
861C23#120×C6111yescharacteristic
862C23#121×C6111yescharacteristic
863C23#121×C6111yescharacteristic
864C23#127×C6111yescharacteristic
865C23#127×C6111yescharacteristic
866C23C22×D4×C6111yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—41no—
894D4—41no—
895D4—41no—
896D4—41no—
897D4—42no—
898D4—42no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4#120×C6111yescharacteristic
919C2×C4#120×C6111yescharacteristic
920C2×C4#120×C6111yescharacteristic
921C2×C4#120×C6111yescharacteristic
922C2×C4#120×C6111yescharacteristic
923C2×C4#120×C6111yescharacteristic
924C2×C4#120×C6111yescharacteristic
925C2×C4#120×C6111yescharacteristic
926C2×C4#120×C6111yescharacteristic
927C2×C4#120×C6111yescharacteristic
928C2×C4#121×C6111yescharacteristic
929C2×C4#121×C6111yescharacteristic
930C2×C4#121×C6111yescharacteristic
931C2×C4#121×C6111yescharacteristic
932C2×C4#121×C6111yescharacteristic
933C2×C4#121×C6111yescharacteristic
934C2×C4#121×C6111yescharacteristic
935C2×C4#121×C6111yescharacteristic
936C2×C4#121×C6111yescharacteristic
937C2×C4#121×C6111yescharacteristic
938C2×C4#127×C6111yescharacteristic
939C2×C4#127×C6111yescharacteristic
940C2×C4C22×D4×C6111yescharacteristic
941C2×C4C22×D4×C6111yescharacteristic
942C2×C4C22×D4×C6111yescharacteristic
943C2×C4C22×D4×C6111yescharacteristic
944C2×C4C22×D4×C6111yescharacteristic
945C2×C4C2×#41×C6111yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—82no—
962C22—84no—
963C22—82no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—84no—
968C22—82no—
969C22—84no—
970C22—82no—
971C22C61×#39211yescharacteristic
972C22C61×#39211yescharacteristic
973C22C61×#39211yescharacteristic
974C22C61×#39211yescharacteristic
975C22C2×#120×C6111yescharacteristic
976C22C2×#121×C6111yescharacteristic
977C22C2×#127×C6111yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4C61×#39211yescharacteristic
983C4C61×#39211yescharacteristic
984C4C61×#39211yescharacteristic
985C4C61×#39211yescharacteristic
986C4C2×#120×C6111yescharacteristic
987C4C2×#120×C6111yescharacteristic
988C4C2×#121×C6111yescharacteristic
989C4C2×#121×C6111yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C61×#200812yesdirect product factor
1000C2C2×C61×#39211yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#575C2semidirect
2. C22×AGL(1,ℤ/8)×C61C2semidirect
3. C2×C61×#535C2semidirect
4. C2×C61×#421C2semidirect
5. C2×C61×#418C2semidirect
6. C2×C61×#410C2semidirect
7. C61×#2008C2direct (N × H)
8. C2×C61×#344C2semidirect
15. C61×#575C22semidirect
25. C2×AGL(1,ℤ/8)×C61C22semidirect
34. C61×#535C22semidirect
42. C61×#421C22semidirect
45. C61×#418C22semidirect
48. C61×#410C22semidirect
50. C61×#344C22semidirect
73. C2×#41×C61D4semidirect
77. C22×Q8×C61D4semidirect
95. C22×D4×C61D4semidirect
131. C2×M16×C61D4semidirect
132. C2×M16×C61D4semidirect
133. C2×M16×C61D4semidirect
137. C22×C8×C61D4semidirect
218. C2×Q8×C61C2×D4semidirect
272. C2×D4×C61C2×D4semidirect
316. M16×C61C2×D4semidirect
322. C2×C8×C61C2×D4semidirect
447. C2×#2008C61direct (N × H)
490. C2×#575C2×C61semidirect
491. C22×AGL(1,ℤ/8)C2×C61semidirect
492. C2×#535C2×C61semidirect
493. C2×#421C2×C61semidirect
494. C2×#418C2×C61semidirect
495. C2×#410C2×C61semidirect
496. #2008C2×C61direct (N × H)
497. C2×#344C2×C61semidirect
507. C2×C61#2008direct (N × H)
515. #575C22×C61semidirect
525. C2×AGL(1,ℤ/8)C22×C61semidirect
534. #535C22×C61semidirect
542. #421C22×C61semidirect
545. #418C22×C61semidirect
548. #410C22×C61semidirect
550. #344C22×C61semidirect
551. C61C2×#2008direct (N × H)
574. C2×#41D4×C61semidirect
578. C22×Q8D4×C61semidirect
596. C22×D4D4×C61semidirect
632. C2×M16D4×C61semidirect
633. C2×M16D4×C61semidirect
634. C2×M16D4×C61semidirect
638. C22×C8D4×C61semidirect
719. C2×Q8C2×D4×C61semidirect
773. C2×D4C2×D4×C61semidirect
817. M16C2×D4×C61semidirect
823. C2×C8C2×D4×C61semidirect
999. C2C61×#2008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5752
C22×AGL(1,ℤ/8)×C612
C2×C61×#5352
C2×C61×#4212
C2×C61×#4182
C2×C61×#4102
C61×#20082
C2×C61×#3442
C2×#200861