Finite Group Databasebeta

← C61×#23878 #29527311

Subgroups — C61×#23878 #29527311

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#575C211yesmaximal, characteristic, complemented
2C61×#3488C211yesmaximal, characteristic, complemented
3C2×C61×#455C211yesmaximal, characteristic, complemented
4C2×C61×#453C211yesmaximal, characteristic, complemented
5C61×#3005C211yesmaximal, characteristic, complemented
6C61×#2431C211yesmaximal, characteristic, complemented
7C61×#2007C211yesmaximal, characteristic, complemented
8C61×#2006C211yesmaximal, characteristic, complemented
9C61×#2004C211yesmaximal, characteristic, complemented
10C61×#2002C211yesmaximal, characteristic, complemented
11C61×#1900C211yesmaximal, characteristic, complemented
12C61×#1883C211yesmaximal, characteristic, complemented
13C61×#1882C211yesmaximal, characteristic, complemented
14C61×#1871C211yesmaximal, characteristic, complemented
15C61×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C22×#41×C61C2211yescharacteristic, complemented
19C61×#575—24no—
20C61×#575—24no—
21C2×#137×C61—21no—
22C2×#137×C61C2211yescharacteristic
23C2×#137×C61C2211yescharacteristic, complemented
24C2×#137×C61C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C61—21no—
26C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
29C2×#135×C61—21no—
30C2×#135×C61—21no—
31C22×M16×C61C2211yescharacteristic, complemented
32C61×#550—21no—
33C61×#548—21no—
34C61×#546—21no—
35C61×#546—22no—
36D42×C61—22no—
37D42×C61—21no—
38C61×#537—21no—
39C61×#537C2211yescharacteristic
40C61×#535—21no—
41C61×#535C2211yescharacteristic
42C2×#127×C61C2211yescharacteristic, complemented
43C2×#124×C61C2211yescharacteristic, complemented
44C61×#525—21no—
45C61×#525C2211yescharacteristic
46C2×#121×C61—21no—
47C2×#121×C61C2211yescharacteristic
48C61×#520C2211yescharacteristic
49C61×#455—24no—
50C61×#453—24no—
51C61×#452—21no—
52C61×#452—21no—
53C61×#449—21no—
54C61×#449—21no—
55C2×#104×C61C2211yescharacteristic
56C2×#104×C61C2211yescharacteristic
57C2×#104×C61C2211yescharacteristic, complemented
58C2×#104×C61C2211yescharacteristic, complemented
59C2×#104×C61C2211yescharacteristic, complemented
60C2×#104×C61C2211yescharacteristic, complemented
61C61×#419C2211yescharacteristic, complemented
62C61×#418C2211yescharacteristic, complemented
63C2×#100×C61C2211yescharacteristic, complemented
64C2×#100×C61C2211yescharacteristic, complemented
65C61×#407C2211yescharacteristic, complemented
66C61×#392—22no—
67C61×#391C2211yescharacteristic, complemented
68C61×#390C2211yescharacteristic, complemented
69C61×#386—22no—
70C4×C22⋊C4×C61C2211yescharacteristic, complemented
71C61×#343C2211yescharacteristic, complemented
72C61×#343C2211yescharacteristic, complemented
73C61×#339C2211yescharacteristic, complemented
74C61×#339C2211yescharacteristic, complemented
75H(5,𝔽2)×C61—22no—
76H(5,𝔽2)×C61—22no—
77H(5,𝔽2)×C61—41no—
78H(5,𝔽2)×C61—41no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—22no—
84C2×#41×C61—22no—
85C2×#41×C61—22no—
86C2×#41×C61—22no—
87C2×#41×C61—21no—
88C2×#41×C61—21no—
89C2×#41×C61—21no—
90C2×#41×C61—21no—
91C2×#41×C61—41no—
92C2×#41×C61—41no—
93C2×#41×C61—41no—
94C2×#41×C61—41no—
95C2×#41×C61D411yescharacteristic, complemented
96C2×#41×C61D411yescharacteristic, complemented
97C2×#41×C61C2311yescharacteristic
98C2×#41×C61C2311yescharacteristic
99C2×#41×C61C2311yescharacteristic
100C22×Q8×C61D411yescharacteristic, complemented
101C22×Q8×C61C2311yescharacteristic
102C22×D4×C61—21no—
103C22×D4×C61—22no—
104C22×D4×C61—22no—
105C22×D4×C61—21no—
106C22×D4×C61—21no—
107C22×D4×C61—21no—
108C22×D4×C61—22no—
109C22×D4×C61D412yes—
110C22×D4×C61D411yescharacteristic, complemented
111C22×D4×C61C2311yescharacteristic
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61—21no—
115C23×C4×C61C2311yescharacteristic
116#137×C61—28no—
117#137×C61—22no—
118#137×C61—22no—
119#137×C61—22no—
120#137×C61—22no—
121#137×C61—41no—
122#137×C61D414yescomplemented
123AGL(1,ℤ/8)×C61—28no—
124AGL(1,ℤ/8)×C61—22no—
125AGL(1,ℤ/8)×C61—22no—
126AGL(1,ℤ/8)×C61—22no—
127AGL(1,ℤ/8)×C61—22no—
128AGL(1,ℤ/8)×C61—41no—
129AGL(1,ℤ/8)×C61D414yescomplemented
130#135×C61—28no—
131#135×C61—28no—
132C2×Q16×C61—21no—
133C2×Q16×C61—21no—
134C2×Q16×C61—21no—
135C2×SD16×C61—21no—
136C2×SD16×C61—21no—
137C2×SD16×C61—21no—
138C2×SD16×C61—21no—
139C2×SD16×C61—21no—
140C2×SD16×C61—21no—
141C2×D8×C61—21no—
142C2×D8×C61—21no—
143C2×D8×C61—21no—
144C2×M16×C61—21no—
145C2×M16×C61—22no—
146C2×M16×C61—22no—
147C2×M16×C61C2311yescharacteristic
148C2×M16×C61C2311yescharacteristic
149C2×M16×C61C2311yescharacteristic
150C2×M16×C61C2311yescharacteristic
151C22×C8×C61—21no—
152#127×C61—22no—
153#127×C61—21no—
154#127×C61—22no—
155#127×C61—41no—
156#124×C61—22no—
157#124×C61—21no—
158#124×C61—22no—
159#124×C61—41no—
160#123×C61—22no—
161#123×C61—21no—
162C22⋊Q8×C61—22no—
163C22⋊Q8×C61—21no—
164C22⋊Q8×C61—21no—
165C22⋊Q8×C61D411yescharacteristic, complemented
166C22⋊Q8×C61D411yescharacteristic, complemented
167#121×C61—22no—
168#121×C61—22no—
169#121×C61—22no—
170#121×C61—22no—
171#121×C61—22no—
172#121×C61—21no—
173#121×C61—21no—
174#121×C61—21no—
175#121×C61—22no—
176#121×C61—21no—
177#121×C61—21no—
178#121×C61—21no—
179#121×C61—21no—
180#121×C61—21no—
181#121×C61D411yescharacteristic, complemented
182#121×C61D411yescharacteristic, complemented
183#120×C61—22no—
184#120×C61—22no—
185#120×C61—22no—
186#120×C61—22no—
187#120×C61—21no—
188C4×Q8×C61—21no—
189C4×D4×C61—22no—
190C4×D4×C61—22no—
191C4×D4×C61—21no—
192C4×D4×C61—22no—
193C4×D4×C61—21no—
194C4×D4×C61—21no—
195#117×C61—21no—
196#117×C61C2311yescharacteristic
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61C2311yescharacteristic
199C2×C22⋊C4×C61—22no—
200C2×C22⋊C4×C61—21no—
201C2×C22⋊C4×C61—22no—
202C2×C22⋊C4×C61—22no—
203C2×C22⋊C4×C61D412yes—
204C2×C42×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206#104×C61—22no—
207#104×C61—22no—
208#104×C61—22no—
209#104×C61—22no—
210#104×C61—41no—
211#104×C61—41no—
212#103×C61—21no—
213#103×C61—21no—
214#102×C61—21no—
215#102×C61—21no—
216#100×C61—22no—
217#100×C61—22no—
218C22⋊C8×C61—21no—
219C22⋊C8×C61—21no—
220#95×C61—21no—
221#95×C61—22no—
222C24×C61—22no—
223C24×C61—21no—
224C24×C61—21no—
225C24×C61C2×D412yes—
226C24×C61C2×D411yescharacteristic
227#41×C61—21no—
228#41×C61—21no—
229#41×C61—24no—
230#41×C61—24no—
231#41×C61—22no—
232#41×C61—22no—
233#41×C61—21no—
234#41×C61—21no—
235#41×C61—21no—
236#41×C61—21no—
237#41×C61—21no—
238#41×C61—21no—
239#41×C61—21no—
240#41×C61—21no—
241#41×C61—42no—
242#41×C61—42no—
243#41×C61—41no—
244#41×C61—41no—
245#41×C61—42no—
246#41×C61—42no—
247#41×C61—42no—
248#41×C61—42no—
249#41×C61—42no—
250#41×C61—42no—
251#41×C61—42no—
252#41×C61—42no—
253#41×C61—42no—
254#41×C61—42no—
255#41×C61—42no—
256#41×C61—42no—
257#41×C61C2×D412yes—
258#41×C61C2×D412yes—
259C2×Q8×C61—21no—
260C2×Q8×C61—21no—
261C2×Q8×C61—22no—
262C2×Q8×C61—21no—
263C2×Q8×C61—21no—
264C2×Q8×C61—21no—
265C2×Q8×C61—21no—
266C2×Q8×C61—41no—
267C2×Q8×C61C2×D411yescharacteristic
268C2×Q8×C61C2×D411yescharacteristic
269C2×Q8×C61C2×D411yescharacteristic
270C2×Q8×C61C2×D412yescomplemented
271C2×D4×C61—21no—
272C2×D4×C61—22no—
273C2×D4×C61—22no—
274C2×D4×C61—22no—
275C2×D4×C61—22no—
276C2×D4×C61—21no—
277C2×D4×C61—21no—
278C2×D4×C61—21no—
279C2×D4×C61—21no—
280C2×D4×C61—21no—
281C2×D4×C61—22no—
282C2×D4×C61—22no—
283C2×D4×C61—22no—
284C2×D4×C61—21no—
285C2×D4×C61—22no—
286C2×D4×C61—21no—
287C2×D4×C61—21no—
288C2×D4×C61—21no—
289C2×D4×C61—21no—
290C2×D4×C61—21no—
291C2×D4×C61—21no—
292C2×D4×C61—21no—
293C2×D4×C61—21no—
294C2×D4×C61—21no—
295C2×D4×C61—21no—
296C2×D4×C61—21no—
297C2×D4×C61—21no—
298C2×D4×C61—41no—
299C2×D4×C61—42no—
300C2×D4×C61—42no—
301C2×D4×C61—42no—
302C2×D4×C61—44no—
303C2×D4×C61—42no—
304C2×D4×C61—42no—
305C2×D4×C61—44no—
306C2×D4×C61—44no—
307C2×D4×C61—42no—
308C2×D4×C61—42no—
309C2×D4×C61—41no—
310C2×D4×C61—41no—
311C2×D4×C61—42no—
312C2×D4×C61—44no—
313C2×D4×C61—82no—
314C2×D4×C61—82no—
315C2×D4×C61—84no—
316C2×D4×C61C2×D411yescharacteristic
317C2×D4×C61C2×D411yescharacteristic
318C2×D4×C61C2×D411yescharacteristic
319C2×D4×C61C2×D412yescomplemented
320C22×C4×C61—21no—
321C22×C4×C61—21no—
322C22×C4×C61—21no—
323C22×C4×C61—21no—
324C22×C4×C61—21no—
325C22×C4×C61—22no—
326C22×C4×C61—21no—
327C22×C4×C61—21no—
328C22×C4×C61—21no—
329C22×C4×C61—22no—
330C22×C4×C61—21no—
331C22×C4×C61—21no—
332C22×C4×C61—21no—
333C22×C4×C61—21no—
334C22×C4×C61—21no—
335C22×C4×C61—42no—
336C22×C4×C61—42no—
337C22×C4×C61—42no—
338C22×C4×C61—42no—
339C22×C4×C61—41no—
340C22×C4×C61—41no—
341C22×C4×C61C2×D411yescharacteristic
342C22×C4×C61C2×D411yescharacteristic
343C22×C4×C61C2×D411yescharacteristic
344C22×C4×C61C2×D411yescharacteristic
345C22×C4×C61C2×D411yescharacteristic
346C22×C4×C61C2×D412yes—
347C22×C4×C61C2411yescharacteristic
348Q16×C61—24no—
349Q16×C61—24no—
350Q16×C61—42no—
351SD16×C61—24no—
352SD16×C61—24no—
353SD16×C61—24no—
354SD16×C61—24no—
355SD16×C61—42no—
356SD16×C61—42no—
357D8×C61—24no—
358D8×C61—24no—
359D8×C61—42no—
360M16×C61—24no—
361M16×C61—21no—
362M16×C61—21no—
363M16×C61—21no—
364M16×C61—21no—
365M16×C61—21no—
366M16×C61—21no—
367M16×C61C2×D412yescomplemented
368M16×C61C2×D412yescomplemented
369C2×C8×C61—24no—
370C2×C8×C61—21no—
371C2×C8×C61—21no—
372C2×C8×C61—21no—
373C2×C8×C61—21no—
374C4⋊C4×C61—22no—
375C4⋊C4×C61—22no—
376C4⋊C4×C61—21no—
377C4⋊C4×C61—21no—
378C4⋊C4×C61—21no—
379C4⋊C4×C61—21no—
380C4⋊C4×C61C2×D411yescharacteristic
381C4⋊C4×C61C2×D411yescharacteristic
382C22⋊C4×C61—22no—
383C22⋊C4×C61—22no—
384C22⋊C4×C61—22no—
385C22⋊C4×C61—22no—
386C22⋊C4×C61—22no—
387C22⋊C4×C61—21no—
388C22⋊C4×C61—21no—
389C22⋊C4×C61—21no—
390C22⋊C4×C61—21no—
391C22⋊C4×C61—22no—
392C22⋊C4×C61—22no—
393C22⋊C4×C61—21no—
394C22⋊C4×C61—44no—
395C22⋊C4×C61—42no—
396C22⋊C4×C61—82no—
397C42×C61—22no—
398C42×C61—21no—
399C42×C61—21no—
400C42×C61—21no—
401C42×C61—21no—
402C42×C61—21no—
403C23×C61—21no—
404C23×C61—21no—
405C23×C61—21no—
406C23×C61—22no—
407C23×C61—21no—
408C23×C61—21no—
409C23×C61—22no—
410C23×C61—22no—
411C23×C61—22no—
412C23×C61—41no—
413C23×C61—41no—
414C23×C61—42no—
415C23×C61—42no—
416C23×C61—42no—
417C23×C61—42no—
418C23×C61—44no—
419C23×C61—42no—
420C23×C61—42no—
421C23×C61—41no—
422C23×C61—41no—
423C23×C61—81no—
424C23×C61—82no—
425C23×C61—82no—
426C23×C61#12011yescharacteristic
427C23×C61#12011yescharacteristic
428C23×C61C22×D411yescharacteristic
429Q8×C61—21no—
430Q8×C61—21no—
431Q8×C61—22no—
432Q8×C61—21no—
433Q8×C61—21no—
434Q8×C61—22no—
435Q8×C61—21no—
436Q8×C61—42no—
437Q8×C61—41no—
438Q8×C61—41no—
439Q8×C61#12012yes—
440D4×C61—22no—
441D4×C61—22no—
442D4×C61—21no—
443D4×C61—22no—
444D4×C61—21no—
445D4×C61—21no—
446D4×C61—21no—
447D4×C61—22no—
448D4×C61—21no—
449D4×C61—42no—
450D4×C61—42no—
451D4×C61—44no—
452D4×C61—42no—
453D4×C61—44no—
454D4×C61—44no—
455D4×C61—42no—
456D4×C61—44no—
457D4×C61—44no—
458D4×C61—41no—
459D4×C61—41no—
460D4×C61—41no—
461D4×C61—41no—
462D4×C61—41no—
463D4×C61—41no—
464D4×C61—41no—
465D4×C61—41no—
466D4×C61—41no—
467D4×C61—41no—
468D4×C61—81no—
469D4×C61—82no—
470D4×C61—82no—
471D4×C61—82no—
472D4×C61—82no—
473D4×C61—88no—
474D4×C61#12012yes—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—21no—
480C2×C4×C61—21no—
481C2×C4×C61—21no—
482C2×C4×C61—21no—
483C2×C4×C61—21no—
484C2×C4×C61—21no—
485C2×C4×C61—21no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—21no—
490C2×C4×C61—22no—
491C2×C4×C61—21no—
492C2×C4×C61—21no—
493C2×C4×C61—21no—
494C2×C4×C61—22no—
495C2×C4×C61—42no—
496C2×C4×C61—42no—
497C2×C4×C61—42no—
498C2×C4×C61—44no—
499C2×C4×C61—44no—
500C2×C4×C61—44no—
501C2×C4×C61—41no—
502C2×C4×C61—41no—
503C2×C4×C61—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61—41no—
509C2×C4×C61—42no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61—82no—
514C2×C4×C61#12011yescharacteristic
515C2×C4×C61#12011yescharacteristic
516C2×C4×C61C22×D411yescharacteristic
517C2×C4×C61C22×D411yescharacteristic
518C2×C4×C61C22×D411yescharacteristic
519C2×C4×C61C22×D411yescharacteristic
520C2×C4×C61H(5,𝔽2)11yescharacteristic
521C2×C4×C61H(5,𝔽2)11yescharacteristic
522C8×C61—22no—
523C8×C61—22no—
524C8×C61—41no—
525C8×C61—41no—
526#23878C6111yesmaximal, characteristic, direct product factor, Sylow
527C22×C61—21no—
528C22×C61—21no—
529C22×C61—21no—
530C22×C61—21no—
531C22×C61—22no—
532C22×C61—21no—
533C22×C61—21no—
534C22×C61—21no—
535C22×C61—21no—
536C22×C61—44no—
537C22×C61—41no—
538C22×C61—41no—
539C22×C61—41no—
540C22×C61—42no—
541C22×C61—41no—
542C22×C61—42no—
543C22×C61—41no—
544C22×C61—42no—
545C22×C61—41no—
546C22×C61—42no—
547C22×C61—41no—
548C22×C61—41no—
549C22×C61—81no—
550C22×C61—81no—
551C22×C61—82no—
552C22×C61—82no—
553C22×C61—82no—
554C22×C61—84no—
555C22×C61—81no—
556C22×C61—81no—
557C22×C61—164no—
558C22×C61C2×#12011yescharacteristic
559C22×C61D4211yescharacteristic
560C22×C61D4211yescharacteristic
561C4×C61—21no—
562C4×C61—21no—
563C4×C61—22no—
564C4×C61—42no—
565C4×C61—41no—
566C4×C61—41no—
567C4×C61—42no—
568C4×C61—41no—
569C4×C61—42no—
570C4×C61—41no—
571C4×C61—81no—
572C4×C61C2×#12011yescharacteristic
573C4×C61#53411yescharacteristic
574C4×C61D4211yescharacteristic
575C4×C61D4211yescharacteristic
576C2×#575C2×C6111yescharacteristic, complemented
577#3488C2×C6111yescharacteristic, complemented
578C2×#455C2×C6111yescharacteristic, complemented
579C2×#453C2×C6111yescharacteristic, complemented
580#3005C2×C6111yescharacteristic, complemented
581#2431C2×C6111yescharacteristic, complemented
582#2007C2×C6111yescharacteristic, complemented
583#2006C2×C6111yescharacteristic, complemented
584#2004C2×C6111yescharacteristic, complemented
585#2002C2×C6111yescharacteristic, complemented
586#1900C2×C6111yescharacteristic, complemented
587#1883C2×C6111yescharacteristic, complemented
588#1882C2×C6111yescharacteristic, complemented
589#1871C2×C6111yescharacteristic, complemented
590#1789C2×C6111yescharacteristic, complemented
591C2×C61—21no—
592C2×C61—21no—
593C2×C61—41no—
594C2×C61—41no—
595C2×C61—42no—
596C2×C61—82no—
597C2×C61—81no—
598C2×C61—82no—
599C2×C61—81no—
600C2×C61#240311yescharacteristic
601C2×C61#301811yescharacteristic
602C2×C61#301911yescharacteristic
603C2×H(5,𝔽2)C22×C6111yescharacteristic
604C22×#41C22×C6111yescharacteristic
605C22×#41C22×C6111yescharacteristic, complemented
606#575—24no—
607#575—24no—
608C2×#137—21no—
609C2×#137C22×C6111yescharacteristic
610C2×#137C22×C6111yescharacteristic, complemented
611C2×#137C22×C6111yescharacteristic, complemented
612C2×AGL(1,ℤ/8)—21no—
613C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
614C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
615C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
616C2×#135—21no—
617C2×#135—21no—
618C22×M16C22×C6111yescharacteristic, complemented
619#550—21no—
620#548—21no—
621#546—21no—
622#546—22no—
623D42—22no—
624D42—21no—
625#537—21no—
626#537C22×C6111yescharacteristic
627#535—21no—
628#535C22×C6111yescharacteristic
629C2×#127C22×C6111yescharacteristic, complemented
630C2×#124C22×C6111yescharacteristic, complemented
631#525—21no—
632#525C22×C6111yescharacteristic
633C2×#121—21no—
634C2×#121C22×C6111yescharacteristic
635#520C22×C6111yescharacteristic
636#455—24no—
637#453—24no—
638#452—21no—
639#452—21no—
640#449—21no—
641#449—21no—
642C2×#104C22×C6111yescharacteristic
643C2×#104C22×C6111yescharacteristic
644C2×#104C22×C6111yescharacteristic, complemented
645C2×#104C22×C6111yescharacteristic, complemented
646C2×#104C22×C6111yescharacteristic, complemented
647C2×#104C22×C6111yescharacteristic, complemented
648#419C22×C6111yescharacteristic, complemented
649#418C22×C6111yescharacteristic, complemented
650C2×#100C22×C6111yescharacteristic, complemented
651C2×#100C22×C6111yescharacteristic, complemented
652#407C22×C6111yescharacteristic, complemented
653#392—22no—
654#391C22×C6111yescharacteristic, complemented
655#390C22×C6111yescharacteristic, complemented
656#386—22no—
657C4×C22⋊C4C22×C6111yescharacteristic, complemented
658#343C22×C6111yescharacteristic, complemented
659#343C22×C6111yescharacteristic, complemented
660#339C22×C6111yescharacteristic, complemented
661#339C22×C6111yescharacteristic, complemented
662C61#2387811yescharacteristic, direct product factor, Sylow
663H(5,𝔽2)—22no—
664H(5,𝔽2)—22no—
665H(5,𝔽2)—41no—
666H(5,𝔽2)—41no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—21no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—21no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41—41no—
683C2×#41D4×C6111yescharacteristic, complemented
684C2×#41D4×C6111yescharacteristic, complemented
685C2×#41C23×C6111yescharacteristic
686C2×#41C23×C6111yescharacteristic
687C2×#41C23×C6111yescharacteristic
688C22×Q8D4×C6111yescharacteristic, complemented
689C22×Q8C23×C6111yescharacteristic
690C22×D4—21no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—22no—
697C22×D4D4×C6112yes—
698C22×D4D4×C6111yescharacteristic, complemented
699C22×D4C23×C6111yescharacteristic
700C22×D4C23×C6111yescharacteristic
701C23×C4—21no—
702C23×C4—21no—
703C23×C4C23×C6111yescharacteristic
704#137—28no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—22no—
709#137—41no—
710#137D4×C6114yescomplemented
711AGL(1,ℤ/8)—28no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—22no—
716AGL(1,ℤ/8)—41no—
717AGL(1,ℤ/8)D4×C6114yescomplemented
718#135—28no—
719#135—28no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×Q16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×D8—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16C23×C6111yescharacteristic
736C2×M16C23×C6111yescharacteristic
737C2×M16C23×C6111yescharacteristic
738C2×M16C23×C6111yescharacteristic
739C22×C8—21no—
740#127—22no—
741#127—21no—
742#127—22no—
743#127—41no—
744#124—22no—
745#124—21no—
746#124—22no—
747#124—41no—
748#123—22no—
749#123—21no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8D4×C6111yescharacteristic, complemented
754C22⋊Q8D4×C6111yescharacteristic, complemented
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121D4×C6111yescharacteristic, complemented
770#121D4×C6111yescharacteristic, complemented
771#120—22no—
772#120—22no—
773#120—22no—
774#120—21no—
775#120—22no—
776C4×Q8—21no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783#117—21no—
784#117C23×C6111yescharacteristic
785C2×C4⋊C4—21no—
786C2×C4⋊C4C23×C6111yescharacteristic
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4D4×C6112yes—
792C2×C42C23×C6111yescharacteristic
793C2×C42C23×C6111yescharacteristic
794#104—22no—
795#104—22no—
796#104—22no—
797#104—22no—
798#104—41no—
799#104—41no—
800#103—21no—
801#103—21no—
802#102—21no—
803#102—21no—
804#100—22no—
805#100—22no—
806C22⋊C8—21no—
807C22⋊C8—21no—
808#95—21no—
809#95—22no—
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C6112yes—
814C24C2×D4×C6111yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C6112yes—
846#41C2×D4×C6112yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C6111yescharacteristic
856C2×Q8C2×D4×C6111yescharacteristic
857C2×Q8C2×D4×C6111yescharacteristic
858C2×Q8C2×D4×C6112yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C6111yescharacteristic
905C2×D4C2×D4×C6111yescharacteristic
906C2×D4C2×D4×C6111yescharacteristic
907C2×D4C2×D4×C6112yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C6111yescharacteristic
930C22×C4C2×D4×C6111yescharacteristic
931C22×C4C2×D4×C6111yescharacteristic
932C22×C4C2×D4×C6111yescharacteristic
933C22×C4C2×D4×C6111yescharacteristic
934C22×C4C2×D4×C6112yes—
935C22×C4C24×C6111yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C6112yescomplemented
956M16C2×D4×C6112yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C6111yescharacteristic
969C4⋊C4C2×D4×C6111yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—21no—
997C23—21no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23#120×C6111yescharacteristic
1015C23#120×C6111yescharacteristic
1016C23C22×D4×C6111yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—21no—
1020Q8—22no—
1021Q8—21no—
1022Q8—21no—
1023Q8—22no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8#120×C6112yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—21no—
1032D4—21no—
1033D4—22no—
1034D4—21no—
1035D4—21no—
1036D4—22no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—81no—
1057D4—82no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4#120×C6112yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4#120×C6111yescharacteristic
1103C2×C4#120×C6111yescharacteristic
1104C2×C4C22×D4×C6111yescharacteristic
1105C2×C4C22×D4×C6111yescharacteristic
1106C2×C4C22×D4×C6111yescharacteristic
1107C2×C4C22×D4×C6111yescharacteristic
1108C2×C4H(5,𝔽2)×C6111yescharacteristic
1109C2×C4H(5,𝔽2)×C6111yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—22no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×#120×C6111yescharacteristic
1146C22D42×C6111yescharacteristic
1147C22D42×C6111yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—81no—
1159C4C2×#120×C6111yescharacteristic
1160C4C61×#53411yescharacteristic
1161C4D42×C6111yescharacteristic
1162C4D42×C6111yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C61×#240311yescharacteristic
1173C2C61×#301811yescharacteristic
1174C2C61×#301911yescharacteristic
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. C2×C61×#575C2semidirect
2. C61×#3488C2semidirect
3. C2×C61×#455C2semidirect
4. C2×C61×#453C2semidirect
5. C61×#3005C2semidirect
6. C61×#2431C2semidirect
7. C61×#2007C2semidirect
8. C61×#2006C2semidirect
9. C61×#2004C2semidirect
10. C61×#2002C2semidirect
11. C61×#1900C2semidirect
12. C61×#1883C2semidirect
13. C61×#1882C2semidirect
14. C61×#1871C2semidirect
15. C61×#1789C2semidirect
18. C22×#41×C61C22semidirect
23. C2×#137×C61C22semidirect
24. C2×#137×C61C22semidirect
27. C2×AGL(1,ℤ/8)×C61C22semidirect
28. C2×AGL(1,ℤ/8)×C61C22semidirect
31. C22×M16×C61C22semidirect
42. C2×#127×C61C22semidirect
43. C2×#124×C61C22semidirect
57. C2×#104×C61C22semidirect
58. C2×#104×C61C22semidirect
59. C2×#104×C61C22semidirect
60. C2×#104×C61C22semidirect
61. C61×#419C22semidirect
62. C61×#418C22semidirect
63. C2×#100×C61C22semidirect
64. C2×#100×C61C22semidirect
65. C61×#407C22semidirect
67. C61×#391C22semidirect
68. C61×#390C22semidirect
70. C4×C22⋊C4×C61C22semidirect
71. C61×#343C22semidirect
72. C61×#343C22semidirect
73. C61×#339C22semidirect
74. C61×#339C22semidirect
95. C2×#41×C61D4semidirect
96. C2×#41×C61D4semidirect
100. C22×Q8×C61D4semidirect
110. C22×D4×C61D4semidirect
122. #137×C61D4semidirect
129. AGL(1,ℤ/8)×C61D4semidirect
165. C22⋊Q8×C61D4semidirect
166. C22⋊Q8×C61D4semidirect
181. #121×C61D4semidirect
182. #121×C61D4semidirect
270. C2×Q8×C61C2×D4semidirect
319. C2×D4×C61C2×D4semidirect
367. M16×C61C2×D4semidirect
368. M16×C61C2×D4semidirect
526. #23878C61direct (N × H)
576. C2×#575C2×C61semidirect
577. #3488C2×C61semidirect
578. C2×#455C2×C61semidirect
579. C2×#453C2×C61semidirect
580. #3005C2×C61semidirect
581. #2431C2×C61semidirect
582. #2007C2×C61semidirect
583. #2006C2×C61semidirect
584. #2004C2×C61semidirect
585. #2002C2×C61semidirect
586. #1900C2×C61semidirect
587. #1883C2×C61semidirect
588. #1882C2×C61semidirect
589. #1871C2×C61semidirect
590. #1789C2×C61semidirect
605. C22×#41C22×C61semidirect
610. C2×#137C22×C61semidirect
611. C2×#137C22×C61semidirect
614. C2×AGL(1,ℤ/8)C22×C61semidirect
615. C2×AGL(1,ℤ/8)C22×C61semidirect
618. C22×M16C22×C61semidirect
629. C2×#127C22×C61semidirect
630. C2×#124C22×C61semidirect
644. C2×#104C22×C61semidirect
645. C2×#104C22×C61semidirect
646. C2×#104C22×C61semidirect
647. C2×#104C22×C61semidirect
648. #419C22×C61semidirect
649. #418C22×C61semidirect
650. C2×#100C22×C61semidirect
651. C2×#100C22×C61semidirect
652. #407C22×C61semidirect
654. #391C22×C61semidirect
655. #390C22×C61semidirect
657. C4×C22⋊C4C22×C61semidirect
658. #343C22×C61semidirect
659. #343C22×C61semidirect
660. #339C22×C61semidirect
661. #339C22×C61semidirect
662. C61#23878direct (N × H)
683. C2×#41D4×C61semidirect
684. C2×#41D4×C61semidirect
688. C22×Q8D4×C61semidirect
698. C22×D4D4×C61semidirect
710. #137D4×C61semidirect
717. AGL(1,ℤ/8)D4×C61semidirect
753. C22⋊Q8D4×C61semidirect
754. C22⋊Q8D4×C61semidirect
769. #121D4×C61semidirect
770. #121D4×C61semidirect
858. C2×Q8C2×D4×C61semidirect
907. C2×D4C2×D4×C61semidirect
955. M16C2×D4×C61semidirect
956. M16C2×D4×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×#34882
C2×C61×#4552
C2×C61×#4532
C61×#30052
C61×#24312
C61×#20072
C61×#20062
C61×#20042
C61×#20022
C61×#19002
C61×#18832
C61×#18822
C61×#18712
C61×#17892
#2387861