Finite Group Databasebeta

← C61×#25144 #29528577

Subgroups — C61×#25144 #29528577

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#471C211yesmaximal, characteristic, complemented
2C61×#3056C211yesmaximal, characteristic, complemented
3C61×#3003C211yesmaximal, characteristic
4C2×C61×#450C211yesmaximal, characteristic, complemented
5C61×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C61C211yesmaximal, characteristic, complemented
7C61×#2063C211yesmaximal, characteristic, complemented
8C61×#2051C211yesmaximal, characteristic, complemented
9C61×#2046C211yesmaximal, characteristic, complemented
10C61×#2019C211yesmaximal, characteristic, complemented
11C61×#1977C211yesmaximal, characteristic, complemented
12C61×#1931C211yesmaximal, characteristic, complemented
13C61×#1907C211yesmaximal, characteristic, complemented
14C61×#1901C211yesmaximal, characteristic, complemented
15C61×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C2×#137×C61C2211yescharacteristic, complemented
18C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
20C22×SD16×C61C2211yescharacteristic
21C22×SD16×C61C2211yescharacteristic
22C2×#131×C61C2211yescharacteristic, complemented
23C22×M16×C61C2211yescharacteristic
24C22×M16×C61C2211yescharacteristic
25C61×#525C2211yescharacteristic
26C2×C22⋊Q8×C61C2211yescharacteristic
27C61×#471—24no—
28C61×#470—21no—
29C61×#468—21no—
30C61×#467—21no—
31C61×#465—21no—
32C61×#450—21no—
33C61×#450—21no—
34C61×#450—21no—
35C61×#450—21no—
36C61×#450—21no—
37C61×#450—21no—
38C61×#447—21no—
39C61×#447—21no—
40C61×#436—21no—
41C61×#435—21no—
42C61×#435—21no—
43C8×D4×C61—21no—
44C2×#108×C61C2211yescharacteristic, complemented
45C2×#108×C61C2211yescharacteristic, complemented
46C61×#428C2211yescharacteristic, complemented
47C61×#424C2211yescharacteristic, complemented
48C61×#419C2211yescharacteristic, complemented
49C61×#418C2211yescharacteristic
50C61×#418C2211yescharacteristic
51C61×#417C2211yescharacteristic, complemented
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#101×C61C2211yescharacteristic, complemented
55C2×#101×C61C2211yescharacteristic, complemented
56C2×#100×C61—24no—
57C2×#100×C61C2211yescharacteristic
58C2×#100×C61C2211yescharacteristic
59C2×#100×C61C2211yescharacteristic
60C2×#100×C61C2211yescharacteristic
61C61×#408C2211yescharacteristic, complemented
62C61×#407C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C61×#405C2211yescharacteristic, complemented
65C61×#343C2211yescharacteristic, complemented
66C61×#343C2211yescharacteristic, complemented
67C61×#341C2211yescharacteristic, complemented
68C61×#341C2211yescharacteristic, complemented
69C25×C61—21no—
70C2×#41×C61C2311yescharacteristic
71C22×Q8×C61C2311yescharacteristic
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—41no—
80C22×D4×C61—41no—
81C22×D4×C61C2311yescharacteristic
82C22×D4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84#137×C61—22no—
85#137×C61—41no—
86AGL(1,ℤ/8)×C61—22no—
87AGL(1,ℤ/8)×C61—22no—
88AGL(1,ℤ/8)×C61—41no—
89AGL(1,ℤ/8)×C61—41no—
90C2×Q16×C61—21no—
91C2×SD16×C61—21no—
92C2×SD16×C61—21no—
93C2×SD16×C61—22no—
94C2×SD16×C61—21no—
95C2×SD16×C61—22no—
96C2×SD16×C61—21no—
97C2×SD16×C61—21no—
98C2×SD16×C61—21no—
99C2×SD16×C61—21no—
100C2×SD16×C61—41no—
101C2×SD16×C61—41no—
102C2×D8×C61—21no—
103C2×D8×C61—21no—
104#131×C61—22no—
105#131×C61—41no—
106C2×M16×C61—21no—
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C2×M16×C61—22no—
110C2×M16×C61—22no—
111C2×M16×C61—41no—
112C2×M16×C61—41no—
113C2×M16×C61C2311yescharacteristic
114C2×M16×C61C2311yescharacteristic
115C2×M16×C61C2311yescharacteristic
116C2×M16×C61C2311yescharacteristic
117C2×M16×C61C2311yescharacteristic
118C2×M16×C61C2311yescharacteristic
119C22×C8×C61—21no—
120C22×C8×C61—21no—
121C22×C8×C61—21no—
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124#123×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61D411yescharacteristic
130C22⋊Q8×C61D411yescharacteristic
131#121×C61D411yescharacteristic
132#121×C61D411yescharacteristic
133#120×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136#117×C61C2311yescharacteristic
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140#108×C61—22no—
141#108×C61—41no—
142#107×C61—21no—
143#106×C61—21no—
144C4⋊C8×C61—21no—
145C4⋊C8×C61—21no—
146#103×C61—21no—
147#103×C61—21no—
148#103×C61—21no—
149#102×C61—21no—
150#102×C61—21no—
151#102×C61—21no—
152#102×C61—21no—
153#102×C61—21no—
154#102×C61—21no—
155#102×C61—21no—
156#102×C61—21no—
157#102×C61—21no—
158#101×C61—22no—
159#101×C61—41no—
160#100×C61—22no—
161#100×C61—22no—
162#100×C61—22no—
163#100×C61D414yescomplemented
164C22⋊C8×C61—21no—
165C22⋊C8×C61—21no—
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168C22⋊C8×C61D411yescharacteristic
169C22⋊C8×C61D411yescharacteristic
170C22⋊C8×C61D411yescharacteristic
171C22⋊C8×C61D411yescharacteristic
172#97×C61—21no—
173C4×C8×C61—21no—
174C24×C61—24no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—42no—
178C24×C61—41no—
179C24×C61—41no—
180C24×C61—82no—
181C24×C61—82no—
182C24×C61#4111yescharacteristic
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61C2×D411yescharacteristic
194C2×D4×C61—24no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—42no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—42no—
216C2×D4×C61—42no—
217C2×D4×C61—41no—
218C2×D4×C61—41no—
219C2×D4×C61C2×D412yes—
220C2×D4×C61C2×D411yescharacteristic
221C2×D4×C61#4112yes—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61#4111yescharacteristic
234C22×C4×C61C2411yescharacteristic
235Q16×C61—42no—
236SD16×C61—42no—
237SD16×C61—42no—
238SD16×C61—42no—
239SD16×C61—42no—
240SD16×C61—42no—
241SD16×C61—42no—
242SD16×C61—42no—
243D8×C61—42no—
244D8×C61—42no—
245M16×C61—21no—
246M16×C61—21no—
247M16×C61—21no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61—21no—
255M16×C61—42no—
256M16×C61—42no—
257M16×C61—42no—
258M16×C61C2×D412yes—
259M16×C61C2×D412yes—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—42no—
271C2×C8×C61—42no—
272C2×C8×C61—42no—
273C2×C8×C61C2×D411yescharacteristic
274C2×C8×C61C2×D411yescharacteristic
275C2×C8×C61C2×D411yescharacteristic
276C2×C8×C61C2×D411yescharacteristic
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—41no—
282C4⋊C4×C61—41no—
283C4⋊C4×C61C2×D411yescharacteristic
284C4⋊C4×C61C2×D411yescharacteristic
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—41no—
291C22⋊C4×C61—41no—
292C42×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—22no—
296C23×C61—21no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—44no—
301C23×C61—44no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—82no—
307C23×C61—82no—
308C23×C61—82no—
309C23×C61—81no—
310C23×C61—81no—
311C23×C61—81no—
312C23×C61—81no—
313C23×C61—88no—
314C23×C61—88no—
315C23×C61—82no—
316C23×C61#12111yescharacteristic
317C23×C61#12111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319Q8×C61—21no—
320Q8×C61—21no—
321Q8×C61—41no—
322Q8×C61—41no—
323Q8×C61—41no—
324Q8×C61—41no—
325D4×C61—21no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—21no—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—44no—
332D4×C61—44no—
333D4×C61—41no—
334D4×C61—41no—
335D4×C61—42no—
336D4×C61—41no—
337D4×C61—41no—
338D4×C61—41no—
339D4×C61—41no—
340D4×C61—81no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—81no—
361C2×C4×C61#12111yescharacteristic
362C2×C4×C61#12111yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C2×#4111yescharacteristic
367C2×C4×C61H(5,𝔽2)11yescharacteristic
368C2×C4×C61H(5,𝔽2)11yescharacteristic
369C8×C61—21no—
370C8×C61—21no—
371C8×C61—22no—
372C8×C61—22no—
373C8×C61—21no—
374C8×C61—21no—
375C8×C61—41no—
376C8×C61—41no—
377C8×C61—41no—
378C8×C61—41no—
379#25144C6111yesmaximal, characteristic, direct product factor, Sylow
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—82no—
395C22×C61—82no—
396C22×C61—88no—
397C22×C61—82no—
398C22×C61—82no—
399C22×C61—88no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61#47112yescomplemented
405C22×C61C2×#12111yescharacteristic
406C22×C61#52511yescharacteristic
407C22×C61#53811yescharacteristic
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61—81no—
414C4×C61—81no—
415C4×C61D4211yescharacteristic
416C4×C61D4211yescharacteristic
417C4×C61#54611yescharacteristic
418C4×C61#54611yescharacteristic
419C2×#471C2×C6111yescharacteristic, complemented
420#3056C2×C6111yescharacteristic, complemented
421#3003C2×C6111yescharacteristic
422C2×#450C2×C6111yescharacteristic, complemented
423#2933C2×C6111yescharacteristic, complemented
424C22×#100C2×C6111yescharacteristic, complemented
425#2063C2×C6111yescharacteristic, complemented
426#2051C2×C6111yescharacteristic, complemented
427#2046C2×C6111yescharacteristic, complemented
428#2019C2×C6111yescharacteristic, complemented
429#1977C2×C6111yescharacteristic, complemented
430#1931C2×C6111yescharacteristic, complemented
431#1907C2×C6111yescharacteristic, complemented
432#1901C2×C6111yescharacteristic, complemented
433#1855C2×C6111yescharacteristic, complemented
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—22no—
437C2×C61—41no—
438C2×C61—81no—
439C2×C61—82no—
440C2×C61—82no—
441C2×C61#242411yescharacteristic
442C2×C61C2×#47111yescharacteristic
443C2×C61#306811yescharacteristic
444C23×D4C22×C6111yescharacteristic
445C2×#137C22×C6111yescharacteristic, complemented
446C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
447C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
448C22×SD16C22×C6111yescharacteristic
449C22×SD16C22×C6111yescharacteristic
450C2×#131C22×C6111yescharacteristic, complemented
451C22×M16C22×C6111yescharacteristic
452C22×M16C22×C6111yescharacteristic
453#525C22×C6111yescharacteristic
454C2×C22⋊Q8C22×C6111yescharacteristic
455#471—24no—
456#470—21no—
457#468—21no—
458#467—21no—
459#465—21no—
460#450—21no—
461#450—21no—
462#450—21no—
463#450—21no—
464#450—21no—
465#450—21no—
466#447—21no—
467#447—21no—
468#436—21no—
469#435—21no—
470#435—21no—
471C8×D4—21no—
472C2×#108C22×C6111yescharacteristic, complemented
473C2×#108C22×C6111yescharacteristic, complemented
474#428C22×C6111yescharacteristic, complemented
475#424C22×C6111yescharacteristic, complemented
476#419C22×C6111yescharacteristic, complemented
477#418C22×C6111yescharacteristic
478#418C22×C6111yescharacteristic
479#417C22×C6111yescharacteristic, complemented
480C2×#102C22×C6111yescharacteristic
481C2×#102C22×C6111yescharacteristic
482C2×#101C22×C6111yescharacteristic, complemented
483C2×#101C22×C6111yescharacteristic, complemented
484C2×#100—24no—
485C2×#100C22×C6111yescharacteristic
486C2×#100C22×C6111yescharacteristic
487C2×#100C22×C6111yescharacteristic
488C2×#100C22×C6111yescharacteristic
489#408C22×C6111yescharacteristic, complemented
490#407C22×C6111yescharacteristic
491C2×C22⋊C8C22×C6111yescharacteristic
492#405C22×C6111yescharacteristic, complemented
493#343C22×C6111yescharacteristic, complemented
494#343C22×C6111yescharacteristic, complemented
495#341C22×C6111yescharacteristic, complemented
496#341C22×C6111yescharacteristic, complemented
497C61#2514411yescharacteristic, direct product factor, Sylow
498C25—21no—
499C2×#41C23×C6111yescharacteristic
500C22×Q8C23×C6111yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C6111yescharacteristic
511C22×D4C23×C6111yescharacteristic
512C23×C4C23×C6111yescharacteristic
513#137—22no—
514#137—41no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—22no—
523C2×SD16—21no—
524C2×SD16—22no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—21no—
532C2×D8—21no—
533#131—22no—
534#131—41no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16C23×C6111yescharacteristic
543C2×M16C23×C6111yescharacteristic
544C2×M16C23×C6111yescharacteristic
545C2×M16C23×C6111yescharacteristic
546C2×M16C23×C6111yescharacteristic
547C2×M16C23×C6111yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C6111yescharacteristic
552C22×C8C23×C6111yescharacteristic
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8D4×C6111yescharacteristic
559C22⋊Q8D4×C6111yescharacteristic
560#121D4×C6111yescharacteristic
561#121D4×C6111yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C23×C6111yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C6111yescharacteristic
568C2×C22⋊C4—21no—
569#108—22no—
570#108—41no—
571#107—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#101—22no—
588#101—41no—
589#100—22no—
590#100—22no—
591#100—22no—
592#100D4×C6114yescomplemented
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8D4×C6111yescharacteristic
598C22⋊C8D4×C6111yescharacteristic
599C22⋊C8D4×C6111yescharacteristic
600C22⋊C8D4×C6111yescharacteristic
601#97—21no—
602C4×C8—21no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#41×C6111yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×D4×C6111yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4C2×D4×C6112yes—
649C2×D4C2×D4×C6111yescharacteristic
650C2×D4#41×C6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4C2×D4×C6111yescharacteristic
659C22×C4C2×D4×C6111yescharacteristic
660C22×C4C2×D4×C6111yescharacteristic
661C22×C4C2×D4×C6111yescharacteristic
662C22×C4#41×C6111yescharacteristic
663C22×C4C24×C6111yescharacteristic
664Q16—42no—
665SD16—42no—
666SD16—42no—
667SD16—42no—
668SD16—42no—
669SD16—42no—
670SD16—42no—
671SD16—42no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C6112yes—
688M16C2×D4×C6112yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8C2×D4×C6111yescharacteristic
703C2×C8C2×D4×C6111yescharacteristic
704C2×C8C2×D4×C6111yescharacteristic
705C2×C8C2×D4×C6111yescharacteristic
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C6111yescharacteristic
713C4⋊C4C2×D4×C6111yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#121×C6111yescharacteristic
746C23#121×C6111yescharacteristic
747C23C2×#41×C6111yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—21no—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—41no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4#121×C6111yescharacteristic
791C2×C4#121×C6111yescharacteristic
792C2×C4C22×D4×C6111yescharacteristic
793C2×C4C22×D4×C6111yescharacteristic
794C2×C4C22×D4×C6111yescharacteristic
795C2×C4C2×#41×C6111yescharacteristic
796C2×C4H(5,𝔽2)×C6111yescharacteristic
797C2×C4H(5,𝔽2)×C6111yescharacteristic
798C8—21no—
799C8—21no—
800C8—22no—
801C8—22no—
802C8—21no—
803C8—21no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—88no—
825C22—82no—
826C22—82no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22C61×#47112yescomplemented
833C22C2×#121×C6111yescharacteristic
834C22C61×#52511yescharacteristic
835C22C61×#53811yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4D42×C6111yescharacteristic
844C4D42×C6111yescharacteristic
845C4C61×#54611yescharacteristic
846C4C61×#54611yescharacteristic
847C2—21no—
848C2—22no—
849C2—21no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2C61×#242411yescharacteristic
855C2C2×C61×#47111yescharacteristic
856C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3003C2
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×#471C2semidirect
2. C61×#3056C2semidirect
4. C2×C61×#450C2semidirect
5. C61×#2933C2semidirect
6. C22×#100×C61C2semidirect
7. C61×#2063C2semidirect
8. C61×#2051C2semidirect
9. C61×#2046C2semidirect
10. C61×#2019C2semidirect
11. C61×#1977C2semidirect
12. C61×#1931C2semidirect
13. C61×#1907C2semidirect
14. C61×#1901C2semidirect
15. C61×#1855C2semidirect
17. C2×#137×C61C22semidirect
22. C2×#131×C61C22semidirect
44. C2×#108×C61C22semidirect
45. C2×#108×C61C22semidirect
46. C61×#428C22semidirect
47. C61×#424C22semidirect
48. C61×#419C22semidirect
51. C61×#417C22semidirect
54. C2×#101×C61C22semidirect
55. C2×#101×C61C22semidirect
61. C61×#408C22semidirect
64. C61×#405C22semidirect
65. C61×#343C22semidirect
66. C61×#343C22semidirect
67. C61×#341C22semidirect
68. C61×#341C22semidirect
163. #100×C61D4semidirect
379. #25144C61direct (N × H)
404. C22×C61#471semidirect
419. C2×#471C2×C61semidirect
420. #3056C2×C61semidirect
422. C2×#450C2×C61semidirect
423. #2933C2×C61semidirect
424. C22×#100C2×C61semidirect
425. #2063C2×C61semidirect
426. #2051C2×C61semidirect
427. #2046C2×C61semidirect
428. #2019C2×C61semidirect
429. #1977C2×C61semidirect
430. #1931C2×C61semidirect
431. #1907C2×C61semidirect
432. #1901C2×C61semidirect
433. #1855C2×C61semidirect
445. C2×#137C22×C61semidirect
450. C2×#131C22×C61semidirect
472. C2×#108C22×C61semidirect
473. C2×#108C22×C61semidirect
474. #428C22×C61semidirect
475. #424C22×C61semidirect
476. #419C22×C61semidirect
479. #417C22×C61semidirect
482. C2×#101C22×C61semidirect
483. C2×#101C22×C61semidirect
489. #408C22×C61semidirect
492. #405C22×C61semidirect
493. #343C22×C61semidirect
494. #343C22×C61semidirect
495. #341C22×C61semidirect
496. #341C22×C61semidirect
497. C61#25144direct (N × H)
592. #100D4×C61semidirect
832. C22C61×#471semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4712
C61×#30562
C61×#30032
C2×C61×#4502
C61×#29332
C22×#100×C612
C61×#20632
C61×#20512
C61×#20462
C61×#20192
C61×#19772
C61×#19312
C61×#19072
C61×#19012
C61×#18552
#2514461