Finite Group Databasebeta

← C61×#23879 #29527312

Subgroups — C61×#23879 #29527312

Order 15616.

1840 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
2C61×#3489C211yesmaximal, characteristic, complemented
3C2×C61×#454C212yesmaximal, complemented
4C61×#3003C211yesmaximal, characteristic, complemented
5C61×#2435C211yesmaximal, characteristic, complemented
6C61×#2006C212yesmaximal, complemented
7C61×#2003C212yesmaximal, complemented
8C61×#1901C211yesmaximal, characteristic, complemented
9C61×#1883C212yesmaximal, complemented
10C61×#1871C211yesmaximal, characteristic, complemented
11C61×#1789C211yesmaximal, characteristic, complemented
12C2×2−1+4×C61C2211yescharacteristic, complemented
13C22×#41×C61C2211yescharacteristic
14C23×D4×C61C2211yescharacteristic
15C2×AGL(1,ℤ/8)×C61—21no—
16C2×AGL(1,ℤ/8)×C61—21no—
17C2×AGL(1,ℤ/8)×C61—28no—
18C2×AGL(1,ℤ/8)×C61C2212yes—
19C2×AGL(1,ℤ/8)×C61C2212yes—
20C2×AGL(1,ℤ/8)×C61C2212yescomplemented
21C22×SD16×C61—21no—
22C22×D8×C61—21no—
23C22×M16×C61C2211yescharacteristic
24D4×Q8×C61—21no—
25C61×#548—21no—
26C61×#547—21no—
27C61×#547—22no—
28C61×#546—21no—
29C61×#546—22no—
30C61×#537—21no—
31C61×#537C2211yescharacteristic, complemented
32C61×#536—21no—
33C61×#536C2211yescharacteristic, complemented
34C2×#124×C61C2212yescomplemented
35C61×#525—21no—
36C61×#525C2211yescharacteristic
37C2×C22⋊Q8×C61—21no—
38C2×C22⋊Q8×C61C2211yescharacteristic
39C61×#520C2211yescharacteristic, complemented
40C61×#454—28no—
41C61×#450—21no—
42C61×#450—21no—
43C61×#447—21no—
44C61×#447—21no—
45C2×#104×C61C2212yescomplemented
46C2×#104×C61C2212yescomplemented
47C2×#104×C61C2212yescomplemented
48C61×#418C2212yescomplemented
49C2×#101×C61C2212yescomplemented
50C61×#407C2211yescharacteristic
51C61×#394—22no—
52C61×#390C2212yescomplemented
53C61×#379—22no—
54C4×C22⋊C4×C61C2211yescharacteristic
55C61×#343C2212yescomplemented
56C61×#339C2212yescomplemented
57C25×C61—21no—
582−1+4×C61—24no—
592−1+4×C61—42no—
60C2×#41×C61—21no—
61C2×#41×C61—21no—
62C2×#41×C61—21no—
63C2×#41×C61—22no—
64C2×#41×C61—21no—
65C2×#41×C61—24no—
66C2×#41×C61—42no—
67C2×#41×C61D411yescharacteristic
68C2×#41×C61D411yescharacteristic
69C2×#41×C61C2311yescharacteristic
70C2×#41×C61C2311yescharacteristic
71C2×#41×C61C2311yescharacteristic
72C22×Q8×C61—21no—
73C22×Q8×C61—21no—
74C22×Q8×C61D411yescharacteristic
75C22×Q8×C61C2311yescharacteristic
76C22×D4×C61—24no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—42no—
84C22×D4×C61D411yescharacteristic
85C22×D4×C61C2312yes—
86C23×C4×C61—21no—
87C23×C4×C61C2311yescharacteristic
88AGL(1,ℤ/8)×C61—28no—
89AGL(1,ℤ/8)×C61—28no—
90AGL(1,ℤ/8)×C61—24no—
91AGL(1,ℤ/8)×C61—24no—
92AGL(1,ℤ/8)×C61—24no—
93AGL(1,ℤ/8)×C61—24no—
94AGL(1,ℤ/8)×C61—42no—
95AGL(1,ℤ/8)×C61D418yescomplemented
96C2×SD16×C61—28no—
97C2×SD16×C61—22no—
98C2×SD16×C61—22no—
99C2×SD16×C61—22no—
100C2×D8×C61—28no—
101C2×D8×C61—22no—
102C2×D8×C61—22no—
103C2×D8×C61—22no—
104C2×M16×C61—21no—
105C2×M16×C61—24no—
106C2×M16×C61C2312yes—
107C2×M16×C61C2312yes—
108C22×C8×C61—21no—
109C4⋊Q8×C61—22no—
110C4⋊Q8×C61—21no—
111#124×C61—22no—
112#124×C61—21no—
113#124×C61—24no—
114#124×C61—42no—
115#123×C61—22no—
116#123×C61—22no—
117#123×C61—22no—
118#123×C61—22no—
119#123×C61—21no—
120C22⋊Q8×C61—22no—
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61D411yescharacteristic
132C22⋊Q8×C61D411yescharacteristic
133#121×C61—22no—
134#121×C61—22no—
135#121×C61—22no—
136#121×C61—21no—
137#121×C61—21no—
138#121×C61—22no—
139#121×C61D411yescharacteristic
140#121×C61D411yescharacteristic
141#120×C61—22no—
142#120×C61—21no—
143C4×Q8×C61—21no—
144C4×D4×C61—22no—
145C4×D4×C61—22no—
146C4×D4×C61—21no—
147C4×D4×C61—22no—
148C4×D4×C61—21no—
149C4×D4×C61—21no—
150#117×C61—21no—
151#117×C61C2311yescharacteristic
152C2×C4⋊C4×C61—22no—
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61D412yes—
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—24no—
159C2×C22⋊C4×C61—24no—
160C2×C22⋊C4×C61D412yes—
161C2×C42×C61C2312yes—
162#104×C61—24no—
163#104×C61—24no—
164#104×C61—42no—
165#102×C61—22no—
166#102×C61—22no—
167#101×C61—24no—
168C22⋊C8×C61—21no—
169C22⋊C8×C61—21no—
170#95×C61—21no—
171C24×C61—22no—
172C24×C61—21no—
173C24×C61—44no—
174C24×C61—44no—
175C24×C61—41no—
176C24×C61—41no—
177C24×C61—82no—
178C24×C61C2×D411yescharacteristic
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—44no—
187#41×C61—41no—
188#41×C61—41no—
189#41×C61—44no—
190#41×C61—44no—
191#41×C61—48no—
192#41×C61—42no—
193#41×C61—42no—
194#41×C61C2×D414yes—
195C2×Q8×C61—22no—
196C2×Q8×C61—21no—
197C2×Q8×C61—22no—
198C2×Q8×C61—21no—
199C2×Q8×C61—21no—
200C2×Q8×C61—22no—
201C2×Q8×C61—22no—
202C2×Q8×C61—41no—
203C2×Q8×C61—44no—
204C2×Q8×C61—42no—
205C2×Q8×C61—42no—
206C2×Q8×C61C2×D411yescharacteristic
207C2×Q8×C61C2×D411yescharacteristic
208C2×Q8×C61C2×D411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61—24no—
211C2×D4×C61—24no—
212C2×D4×C61—22no—
213C2×D4×C61—22no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—22no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—22no—
223C2×D4×C61—22no—
224C2×D4×C61—22no—
225C2×D4×C61—22no—
226C2×D4×C61—22no—
227C2×D4×C61—41no—
228C2×D4×C61—44no—
229C2×D4×C61—44no—
230C2×D4×C61—44no—
231C2×D4×C61—42no—
232C2×D4×C61—42no—
233C2×D4×C61—44no—
234C2×D4×C61—41no—
235C2×D4×C61—41no—
236C2×D4×C61C2×D411yescharacteristic
237C2×D4×C61C2×D411yescharacteristic
238C2×D4×C61C2×D414yes—
239C2×D4×C61C2×D411yescharacteristic
240C22×C4×C61—21no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—22no—
245C22×C4×C61—21no—
246C22×C4×C61—22no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—22no—
252C22×C4×C61—44no—
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D412yes—
260C22×C4×C61C2411yescharacteristic
261SD16×C61—28no—
262SD16×C61—28no—
263SD16×C61—44no—
264D8×C61—28no—
265D8×C61—28no—
266D8×C61—44no—
267M16×C61—24no—
268M16×C61—22no—
269M16×C61—22no—
270M16×C61—22no—
271M16×C61C2×D414yes—
272C2×C8×C61—24no—
273C2×C8×C61—22no—
274C2×C8×C61—22no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—22no—
278C4⋊C4×C61—22no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—22no—
281C4⋊C4×C61—22no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61C2×D411yescharacteristic
286C4⋊C4×C61C2×D411yescharacteristic
287C22⋊C4×C61—22no—
288C22⋊C4×C61—22no—
289C22⋊C4×C61—22no—
290C22⋊C4×C61—22no—
291C22⋊C4×C61—22no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—48no—
300C22⋊C4×C61—42no—
301C22⋊C4×C61—84no—
302C42×C61—22no—
303C42×C61—21no—
304C42×C61—22no—
305C42×C61—22no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—24no—
312C23×C61—41no—
313C23×C61—42no—
314C23×C61—44no—
315C23×C61—44no—
316C23×C61—44no—
317C23×C61—44no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—81no—
322C23×C61—82no—
323C23×C61—82no—
324C23×C61—82no—
325C23×C61—816no—
326C23×C61—82no—
327C23×C61#12011yescharacteristic
328C23×C61#12011yescharacteristic
329C23×C61C22×D411yescharacteristic
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—21no—
333Q8×C61—22no—
334Q8×C61—42no—
335Q8×C61—44no—
336Q8×C61—41no—
337Q8×C61—41no—
338Q8×C61—42no—
339Q8×C61#12012yes—
340D4×C61—24no—
341D4×C61—21no—
342D4×C61—24no—
343D4×C61—21no—
344D4×C61—21no—
345D4×C61—22no—
346D4×C61—24no—
347D4×C61—42no—
348D4×C61—42no—
349D4×C61—44no—
350D4×C61—44no—
351D4×C61—42no—
352D4×C61—44no—
353D4×C61—42no—
354D4×C61—42no—
355D4×C61—42no—
356D4×C61—42no—
357D4×C61—42no—
358D4×C61—81no—
359D4×C61—82no—
360D4×C61#12012yes—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—24no—
370C2×C4×C61—21no—
371C2×C4×C61—22no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—22no—
375C2×C4×C61—21no—
376C2×C4×C61—24no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61—44no—
381C2×C4×C61—44no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—42no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61—42no—
388C2×C4×C61—42no—
389C2×C4×C61—82no—
390C2×C4×C61#12011yescharacteristic
391C2×C4×C61#12011yescharacteristic
392C2×C4×C61C22×D411yescharacteristic
393C2×C4×C61C22×D412yes—
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61H(5,𝔽2)12yes—
396C8×C61—24no—
397C8×C61—42no—
398#23879C6111yesmaximal, characteristic, direct product factor, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—44no—
408C22×C61—48no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—44no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—84no—
419C22×C61—84no—
420C22×C61—88no—
421C22×C61—88no—
422C22×C61—82no—
423C22×C61—82no—
424C22×C61#45412yescomplemented
425C22×C61C2×#12011yescharacteristic
426C22×C61D4212yes—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—22no—
430C4×C61—42no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—42no—
435C4×C61—41no—
436C4×C61—82no—
437C4×C61C2×#12011yescharacteristic
438C4×C61#53411yescharacteristic
439C4×C61D4212yes—
440C22×AGL(1,ℤ/8)C2×C6111yescharacteristic, complemented
441#3489C2×C6111yescharacteristic, complemented
442C2×#454C2×C6112yescomplemented
443#3003C2×C6111yescharacteristic, complemented
444#2435C2×C6111yescharacteristic, complemented
445#2006C2×C6112yescomplemented
446#2003C2×C6112yescomplemented
447#1901C2×C6111yescharacteristic, complemented
448#1883C2×C6112yescomplemented
449#1871C2×C6111yescharacteristic, complemented
450#1789C2×C6111yescharacteristic, complemented
451C2×C61—22no—
452C2×C61—22no—
453C2×C61—41no—
454C2×C61—42no—
455C2×C61—81no—
456C2×C61—81no—
457C2×C61—84no—
458C2×C61#240311yescharacteristic
459C2×C61C2×#45411yescharacteristic
460C2×C61#302111yescharacteristic
461C2×2−1+4C22×C6111yescharacteristic, complemented
462C22×#41C22×C6111yescharacteristic
463C23×D4C22×C6111yescharacteristic
464C2×AGL(1,ℤ/8)—21no—
465C2×AGL(1,ℤ/8)—21no—
466C2×AGL(1,ℤ/8)—28no—
467C2×AGL(1,ℤ/8)C22×C6112yes—
468C2×AGL(1,ℤ/8)C22×C6112yes—
469C2×AGL(1,ℤ/8)C22×C6112yescomplemented
470C22×SD16—21no—
471C22×D8—21no—
472C22×M16C22×C6111yescharacteristic
473D4×Q8—21no—
474#548—21no—
475#547—21no—
476#547—22no—
477#546—21no—
478#546—22no—
479#537—21no—
480#537C22×C6111yescharacteristic, complemented
481#536—21no—
482#536C22×C6111yescharacteristic, complemented
483C2×#124C22×C6112yescomplemented
484#525—21no—
485#525C22×C6111yescharacteristic
486C2×C22⋊Q8—21no—
487C2×C22⋊Q8C22×C6111yescharacteristic
488#520C22×C6111yescharacteristic, complemented
489#454—28no—
490#450—21no—
491#450—21no—
492#447—21no—
493#447—21no—
494C2×#104C22×C6112yescomplemented
495C2×#104C22×C6112yescomplemented
496C2×#104C22×C6112yescomplemented
497#418C22×C6112yescomplemented
498C2×#101C22×C6112yescomplemented
499#407C22×C6111yescharacteristic
500#394—22no—
501#390C22×C6112yescomplemented
502#379—22no—
503C4×C22⋊C4C22×C6111yescharacteristic
504#343C22×C6112yescomplemented
505#339C22×C6112yescomplemented
506C61#2387911yescharacteristic, direct product factor, Sylow
507C25—21no—
5082−1+4—24no—
5092−1+4—42no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—21no—
513C2×#41—22no—
514C2×#41—21no—
515C2×#41—24no—
516C2×#41—42no—
517C2×#41D4×C6111yescharacteristic
518C2×#41D4×C6111yescharacteristic
519C2×#41C23×C6111yescharacteristic
520C2×#41C23×C6111yescharacteristic
521C2×#41C23×C6111yescharacteristic
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8D4×C6111yescharacteristic
525C22×Q8C23×C6111yescharacteristic
526C22×D4—24no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—42no—
534C22×D4D4×C6111yescharacteristic
535C22×D4C23×C6112yes—
536C23×C4—21no—
537C23×C4C23×C6111yescharacteristic
538AGL(1,ℤ/8)—28no—
539AGL(1,ℤ/8)—28no—
540AGL(1,ℤ/8)—24no—
541AGL(1,ℤ/8)—24no—
542AGL(1,ℤ/8)—24no—
543AGL(1,ℤ/8)—24no—
544AGL(1,ℤ/8)—42no—
545AGL(1,ℤ/8)D4×C6118yescomplemented
546C2×SD16—28no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×D8—28no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×M16—21no—
555C2×M16—24no—
556C2×M16C23×C6112yes—
557C2×M16C23×C6112yes—
558C22×C8—21no—
559C4⋊Q8—22no—
560C4⋊Q8—21no—
561#124—22no—
562#124—21no—
563#124—24no—
564#124—42no—
565#123—22no—
566#123—22no—
567#123—22no—
568#123—21no—
569#123—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C6111yescharacteristic
582C22⋊Q8D4×C6111yescharacteristic
583#121—22no—
584#121—22no—
585#121—22no—
586#121—21no—
587#121—21no—
588#121—22no—
589#121D4×C6111yescharacteristic
590#121D4×C6111yescharacteristic
591#120—22no—
592#120—21no—
593C4×Q8—21no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—21no—
597C4×D4—22no—
598C4×D4—21no—
599C4×D4—21no—
600#117—21no—
601#117C23×C6111yescharacteristic
602C2×C4⋊C4—22no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4D4×C6112yes—
605C2×C4⋊C4C23×C6111yescharacteristic
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—24no—
610C2×C22⋊C4D4×C6112yes—
611C2×C42C23×C6112yes—
612#104—24no—
613#104—24no—
614#104—42no—
615#102—22no—
616#102—22no—
617#101—24no—
618C22⋊C8—21no—
619C22⋊C8—21no—
620#95—21no—
621C24—22no—
622C24—21no—
623C24—44no—
624C24—44no—
625C24—41no—
626C24—41no—
627C24—82no—
628C24C2×D4×C6111yescharacteristic
629#41—22no—
630#41—22no—
631#41—22no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—44no—
637#41—41no—
638#41—41no—
639#41—44no—
640#41—44no—
641#41—48no—
642#41—42no—
643#41—42no—
644#41C2×D4×C6114yes—
645C2×Q8—22no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—41no—
653C2×Q8—44no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8C2×D4×C6111yescharacteristic
657C2×Q8C2×D4×C6111yescharacteristic
658C2×Q8C2×D4×C6111yescharacteristic
659C2×D4—21no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—44no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4C2×D4×C6111yescharacteristic
687C2×D4C2×D4×C6111yescharacteristic
688C2×D4C2×D4×C6114yes—
689C2×D4C2×D4×C6111yescharacteristic
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—44no—
703C22×C4C2×D4×C6112yes—
704C22×C4C2×D4×C6111yescharacteristic
705C22×C4C2×D4×C6111yescharacteristic
706C22×C4C2×D4×C6111yescharacteristic
707C22×C4C2×D4×C6111yescharacteristic
708C22×C4C2×D4×C6111yescharacteristic
709C22×C4C2×D4×C6112yes—
710C22×C4C24×C6111yescharacteristic
711SD16—28no—
712SD16—28no—
713SD16—44no—
714D8—28no—
715D8—28no—
716D8—44no—
717M16—24no—
718M16—22no—
719M16—22no—
720M16—22no—
721M16C2×D4×C6114yes—
722C2×C8—24no—
723C2×C8—22no—
724C2×C8—22no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4C2×D4×C6111yescharacteristic
736C4⋊C4C2×D4×C6111yescharacteristic
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—48no—
750C22⋊C4—42no—
751C22⋊C4—84no—
752C42—22no—
753C42—21no—
754C42—22no—
755C42—22no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—24no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—42no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—81no—
772C23—82no—
773C23—82no—
774C23—82no—
775C23—816no—
776C23—82no—
777C23#120×C6111yescharacteristic
778C23#120×C6111yescharacteristic
779C23C22×D4×C6111yescharacteristic
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—21no—
784Q8—42no—
785Q8—44no—
786Q8—41no—
787Q8—42no—
788Q8—41no—
789Q8#120×C6112yes—
790D4—24no—
791D4—21no—
792D4—21no—
793D4—22no—
794D4—24no—
795D4—21no—
796D4—24no—
797D4—42no—
798D4—42no—
799D4—44no—
800D4—44no—
801D4—42no—
802D4—44no—
803D4—42no—
804D4—42no—
805D4—42no—
806D4—42no—
807D4—42no—
808D4—81no—
809D4—82no—
810D4#120×C6112yes—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—24no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—82no—
840C2×C4#120×C6111yescharacteristic
841C2×C4#120×C6111yescharacteristic
842C2×C4C22×D4×C6111yescharacteristic
843C2×C4C22×D4×C6111yescharacteristic
844C2×C4C22×D4×C6112yes—
845C2×C4H(5,𝔽2)×C6112yes—
846C8—24no—
847C8—42no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—21no—
855C22—21no—
856C22—44no—
857C22—48no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—44no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—84no—
868C22—84no—
869C22—88no—
870C22—88no—
871C22—82no—
872C22—82no—
873C22C61×#45412yescomplemented
874C22C2×#120×C6111yescharacteristic
875C22D42×C6112yes—
876C4—21no—
877C4—21no—
878C4—22no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—82no—
886C4C2×#120×C6111yescharacteristic
887C4C61×#53411yescharacteristic
888C4D42×C6112yes—
889C2—22no—
890C2—22no—
891C2—41no—
892C2—42no—
893C2—84no—
894C2—81no—
895C2—81no—
896C2C61×#240311yescharacteristic
897C2C2×C61×#45411yescharacteristic
898C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
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. C22×AGL(1,ℤ/8)×C61C2semidirect
2. C61×#3489C2semidirect
3. C2×C61×#454C2semidirect
4. C61×#3003C2semidirect
5. C61×#2435C2semidirect
6. C61×#2006C2semidirect
7. C61×#2003C2semidirect
8. C61×#1901C2semidirect
9. C61×#1883C2semidirect
10. C61×#1871C2semidirect
11. C61×#1789C2semidirect
12. C2×2−1+4×C61C22semidirect
20. C2×AGL(1,ℤ/8)×C61C22semidirect
31. C61×#537C22semidirect
33. C61×#536C22semidirect
34. C2×#124×C61C22semidirect
39. C61×#520C22semidirect
45. C2×#104×C61C22semidirect
46. C2×#104×C61C22semidirect
47. C2×#104×C61C22semidirect
48. C61×#418C22semidirect
49. C2×#101×C61C22semidirect
52. C61×#390C22semidirect
55. C61×#343C22semidirect
56. C61×#339C22semidirect
95. AGL(1,ℤ/8)×C61D4semidirect
398. #23879C61direct (N × H)
424. C22×C61#454semidirect
440. C22×AGL(1,ℤ/8)C2×C61semidirect
441. #3489C2×C61semidirect
442. C2×#454C2×C61semidirect
443. #3003C2×C61semidirect
444. #2435C2×C61semidirect
445. #2006C2×C61semidirect
446. #2003C2×C61semidirect
447. #1901C2×C61semidirect
448. #1883C2×C61semidirect
449. #1871C2×C61semidirect
450. #1789C2×C61semidirect
461. C2×2−1+4C22×C61semidirect
469. C2×AGL(1,ℤ/8)C22×C61semidirect
480. #537C22×C61semidirect
482. #536C22×C61semidirect
483. C2×#124C22×C61semidirect
488. #520C22×C61semidirect
494. C2×#104C22×C61semidirect
495. C2×#104C22×C61semidirect
496. C2×#104C22×C61semidirect
497. #418C22×C61semidirect
498. C2×#101C22×C61semidirect
501. #390C22×C61semidirect
504. #343C22×C61semidirect
505. #339C22×C61semidirect
506. C61#23879direct (N × H)
545. AGL(1,ℤ/8)D4×C61semidirect
873. C22C61×#454semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C612
C61×#34892
C2×C61×#4542
C61×#30032
C61×#24352
C61×#20062
C61×#20032
C61×#19012
C61×#18832
C61×#18712
C61×#17892
#2387961