Finite Group Databasebeta

← C61×#18810 #29522243

Subgroups — C61×#18810 #29522243

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3519C211yesmaximal, characteristic, complemented
2C61×#3251C211yesmaximal, characteristic, complemented
3C61×#3207C211yesmaximal, characteristic, complemented
4C61×#3036C211yesmaximal, characteristic, complemented
5C61×#1646C211yesmaximal, characteristic, complemented
6C61×#1643C211yesmaximal, characteristic, complemented
7C61×#1642C211yesmaximal, characteristic, complemented
8C61×#1639C211yesmaximal, characteristic, complemented
9C61×#1624C211yesmaximal, characteristic, complemented
10C61×#1622C211yesmaximal, characteristic, complemented
11C61×#1621C211yesmaximal, characteristic, complemented
12C61×#1619C211yesmaximal, characteristic, complemented
13C61×#1560C211yesmaximal, characteristic, complemented
14C61×#1495C211yesmaximal, characteristic, complemented
15C61×#1486C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C61—21no—
17C61×#555C2211yescharacteristic
18C61×#554C2211yescharacteristic
19C61×#553—21no—
20C61×#553—21no—
21C61×#550C2211yescharacteristic
22C61×#546—22no—
23C61×#546—21no—
24D42×C61—21no—
25D42×C61C2211yescharacteristic
26C61×#540—21no—
27C61×#538—22no—
28C61×#532C2211yescharacteristic
29C61×#532C2211yescharacteristic, complemented
30C61×#529C2211yescharacteristic
31C61×#525—21no—
32C2×#121×C61—21no—
33C61×#518—21no—
34C2×C4×D4×C61C2211yescharacteristic
35C61×#493C2211yescharacteristic, complemented
36C61×#492C2211yescharacteristic, complemented
37C61×#487C2211yescharacteristic, complemented
38C61×#486C2211yescharacteristic, complemented
39C61×#478—21no—
40C61×#475C2211yescharacteristic, complemented
41C61×#474C2211yescharacteristic, complemented
42C61×#469—21no—
43C61×#468—21no—
44C61×#463—22no—
45C61×#463—21no—
46C61×#463—21no—
47C61×#463—21no—
48C61×#461C2211yescharacteristic
49C61×#461C2211yescharacteristic, complemented
50C61×#460C2211yescharacteristic, complemented
51C61×#459C2211yescharacteristic
52C61×#459C2211yescharacteristic, complemented
53C61×#459C2211yescharacteristic, complemented
54C61×#449—22no—
55C61×#431C2211yescharacteristic, complemented
56C61×#423C2211yescharacteristic, complemented
57C61×#423C2211yescharacteristic, complemented
58C61×#417—21no—
59C61×#333C2211yescharacteristic, complemented
60C61×#333C2211yescharacteristic, complemented
61C61×#331C2211yescharacteristic, complemented
62C61×#331C2211yescharacteristic, complemented
63C61×Q8⋊C8C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C61×D4⋊C8C2211yescharacteristic, complemented
68C61×D4⋊C8C2211yescharacteristic, complemented
69C61×D4⋊C8C2211yescharacteristic, complemented
70C61×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61D412yes—
74C22×D4×C61—22no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61D411yescharacteristic
78C23×C4×C61—21no—
79AGL(1,ℤ/8)×C61—44no—
80C2×SD16×C61—21no—
81C2×SD16×C61—21no—
82C2×SD16×C61—22no—
83C2×SD16×C61—21no—
84C2×D8×C61—21no—
85C2×D8×C61—21no—
86C2×D8×C61—22no—
87C2×D8×C61—21no—
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C4⋊Q8×C61C2311yescharacteristic
91C4⋊Q8×C61C2311yescharacteristic
92#127×C61—21no—
93#127×C61C2311yescharacteristic
94#127×C61C2311yescharacteristic
95#126×C61—22no—
96#126×C61—21no—
97#125×C61—21no—
98#125×C61D411yescharacteristic
99#124×C61—22no—
100#124×C61—21no—
101#124×C61D412yes—
102#124×C61D411yescharacteristic
103#123×C61—22no—
104#123×C61—22no—
105#123×C61—22no—
106#123×C61—21no—
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61—21no—
109C22⋊Q8×C61D411yescharacteristic
110#121×C61—22no—
111#121×C61—22no—
112#121×C61—22no—
113#121×C61—22no—
114#121×C61—22no—
115#121×C61—21no—
116#121×C61—21no—
117#121×C61—21no—
118#121×C61—21no—
119#121×C61—21no—
120#121×C61—21no—
121#121×C61—21no—
122#121×C61—21no—
123#121×C61—21no—
124#121×C61D411yescharacteristic
125#120×C61—22no—
126#120×C61—22no—
127#120×C61—22no—
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C4×D4×C61—21no—
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61—21no—
139C4×D4×C61—21no—
140C4×D4×C61—21no—
141C4×D4×C61D411yescharacteristic
142C4×D4×C61D411yescharacteristic
143C4×D4×C61C2311yescharacteristic
144C4×D4×C61C2311yescharacteristic
145C4×D4×C61C2311yescharacteristic
146#117×C61—21no—
147#117×C61—21no—
148#117×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61D411yescharacteristic
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—21no—
154C2×C42×C61C2311yescharacteristic
155#107×C61—21no—
156#106×C61—21no—
157C4⋊C8×C61—21no—
158C4⋊C8×C61—21no—
159C4⋊C8×C61—21no—
160C4⋊C8×C61C2311yescharacteristic
161C4⋊C8×C61C2311yescharacteristic
162C4⋊C8×C61C2311yescharacteristic
163C4⋊C8×C61C2311yescharacteristic
164#103×C61—22no—
165#103×C61—21no—
166#103×C61—21no—
167#103×C61—21no—
168#102×C61—22no—
169#102×C61—21no—
170#102×C61—21no—
171#102×C61—21no—
172#102×C61—21no—
173#102×C61—21no—
174C22⋊C8×C61—21no—
175C4×C8×C61C2311yescharacteristic
176C4×C8×C61C2311yescharacteristic
177C24×C61—22no—
178C24×C61—21no—
179#41×C61—42no—
180#41×C61—42no—
181#41×C61—81no—
182#41×C61—81no—
183#41×C61—82no—
184C2×Q8×C61—21no—
185C2×Q8×C61C2×D411yescharacteristic
186C2×Q8×C61C2×D412yes—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
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—41no—
202C2×D4×C61—42no—
203C2×D4×C61—42no—
204C2×D4×C61—41no—
205C2×D4×C61—81no—
206C2×D4×C61—81no—
207C2×D4×C61—84no—
208C2×D4×C61C2×D411yescharacteristic
209C2×D4×C61C2×D411yescharacteristic
210C2×D4×C61C2×D411yescharacteristic
211C2×D4×C61C2×D412yes—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—22no—
220C22×C4×C61—21no—
221C22×C4×C61—41no—
222C22×C4×C61—81no—
223C22×C4×C61—81no—
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227SD16×C61—42no—
228SD16×C61—42no—
229SD16×C61—81no—
230SD16×C61—82no—
231D8×C61—42no—
232D8×C61—42no—
233D8×C61—81no—
234D8×C61—82no—
235M16×C61—42no—
236M16×C61—81no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C4⋊C4×C61—22no—
244C4⋊C4×C61—22no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C2×D411yescharacteristic
255C4⋊C4×C61C2×D411yescharacteristic
256C4⋊C4×C61C2×D411yescharacteristic
257C4⋊C4×C61C2×D411yescharacteristic
258C22⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—41no—
275C22⋊C4×C61—41no—
276C42×C61—22no—
277C42×C61—21no—
278C42×C61C2×D411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2411yescharacteristic
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—44no—
289C23×C61—41no—
290C23×C61—81no—
291C23×C61—82no—
292C23×C61—82no—
293C23×C61#12011yescharacteristic
294Q8×C61—21no—
295Q8×C61—21no—
296Q8×C61—42no—
297Q8×C61—41no—
298Q8×C61—41no—
299D4×C61—21no—
300D4×C61—21no—
301D4×C61—21no—
302D4×C61—21no—
303D4×C61—21no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—42no—
307D4×C61—44no—
308D4×C61—42no—
309D4×C61—44no—
310D4×C61—41no—
311D4×C61—41no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—82no—
319D4×C61—82no—
320D4×C61—82no—
321D4×C61—82no—
322D4×C61—82no—
323D4×C61AGL(1,ℤ/8)12yes—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—81no—
343C2×C4×C61—81no—
344C2×C4×C61—82no—
345C2×C4×C61—82no—
346C2×C4×C61—81no—
347C2×C4×C61—82no—
348C2×C4×C61—82no—
349C2×C4×C61#12011yescharacteristic
350C2×C4×C61#12011yescharacteristic
351C2×C4×C61#12011yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C8×C61—41no—
356C8×C61—41no—
357C8×C61—41no—
358C8×C61—41no—
359C8×C61—41no—
360C8×C61—41no—
361#18810C6111yesmaximal, characteristic, direct product factor, Sylow
362C22×C61—21no—
363C22×C61—22no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—42no—
371C22×C61—41no—
372C22×C61—42no—
373C22×C61—41no—
374C22×C61—42no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—84no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—164no—
382C22×C61C2×#12011yescharacteristic
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—42no—
393C4×C61—81no—
394C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
395C4×C61#57511yescharacteristic
396C4×C61#57611yescharacteristic
397C4×C61#57711yescharacteristic
398#3519C2×C6111yescharacteristic, complemented
399#3251C2×C6111yescharacteristic, complemented
400#3207C2×C6111yescharacteristic, complemented
401#3036C2×C6111yescharacteristic, complemented
402#1646C2×C6111yescharacteristic, complemented
403#1643C2×C6111yescharacteristic, complemented
404#1642C2×C6111yescharacteristic, complemented
405#1639C2×C6111yescharacteristic, complemented
406#1624C2×C6111yescharacteristic, complemented
407#1622C2×C6111yescharacteristic, complemented
408#1621C2×C6111yescharacteristic, complemented
409#1619C2×C6111yescharacteristic, complemented
410#1560C2×C6111yescharacteristic, complemented
411#1495C2×C6111yescharacteristic, complemented
412#1486C2×C6111yescharacteristic, complemented
413C2×C61—41no—
414C2×C61—42no—
415C2×C61—81no—
416C2×C61—82no—
417C2×C61—81no—
418C2×C61—161no—
419C2×C61#300611yescharacteristic
420C2×C61#301211yescharacteristic
421C2×C61#301911yescharacteristic
422C2×AGL(1,ℤ/8)—21no—
423#555C22×C6111yescharacteristic
424#554C22×C6111yescharacteristic
425#553—21no—
426#553—21no—
427#550C22×C6111yescharacteristic
428#546—22no—
429#546—21no—
430D42—21no—
431D42C22×C6111yescharacteristic
432#540—21no—
433#538—22no—
434#532C22×C6111yescharacteristic
435#532C22×C6111yescharacteristic, complemented
436#529C22×C6111yescharacteristic
437#525—21no—
438C2×#121—21no—
439#518—21no—
440C2×C4×D4C22×C6111yescharacteristic
441#493C22×C6111yescharacteristic, complemented
442#492C22×C6111yescharacteristic, complemented
443#487C22×C6111yescharacteristic, complemented
444#486C22×C6111yescharacteristic, complemented
445#478—21no—
446#475C22×C6111yescharacteristic, complemented
447#474C22×C6111yescharacteristic, complemented
448#469—21no—
449#468—21no—
450#463—22no—
451#463—21no—
452#463—21no—
453#463—21no—
454#461C22×C6111yescharacteristic
455#461C22×C6111yescharacteristic, complemented
456#460C22×C6111yescharacteristic, complemented
457#459C22×C6111yescharacteristic
458#459C22×C6111yescharacteristic, complemented
459#459C22×C6111yescharacteristic, complemented
460#449—22no—
461#431C22×C6111yescharacteristic, complemented
462#423C22×C6111yescharacteristic, complemented
463#423C22×C6111yescharacteristic, complemented
464#417—21no—
465#333C22×C6111yescharacteristic, complemented
466#333C22×C6111yescharacteristic, complemented
467#331C22×C6111yescharacteristic, complemented
468#331C22×C6111yescharacteristic, complemented
469Q8⋊C8C22×C6111yescharacteristic, complemented
470Q8⋊C8C22×C6111yescharacteristic, complemented
471D4⋊C8C22×C6111yescharacteristic
472D4⋊C8C22×C6111yescharacteristic
473D4⋊C8C22×C6111yescharacteristic, complemented
474D4⋊C8C22×C6111yescharacteristic, complemented
475D4⋊C8C22×C6111yescharacteristic, complemented
476D4⋊C8C22×C6111yescharacteristic, complemented
477C61#1881011yescharacteristic, direct product factor, Sylow
478C2×#41—21no—
479C2×#41—21no—
480C2×#41D4×C6112yes—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C6111yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—44no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16—21no—
491C2×D8—21no—
492C2×D8—21no—
493C2×D8—22no—
494C2×D8—21no—
495C2×M16—21no—
496C2×M16—21no—
497C4⋊Q8C23×C6111yescharacteristic
498C4⋊Q8C23×C6111yescharacteristic
499#127—21no—
500#127C23×C6111yescharacteristic
501#127C23×C6111yescharacteristic
502#126—22no—
503#126—21no—
504#125—21no—
505#125D4×C6111yescharacteristic
506#124—22no—
507#124—21no—
508#124D4×C6111yescharacteristic
509#124D4×C6112yes—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—22no—
516C22⋊Q8D4×C6111yescharacteristic
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121D4×C6111yescharacteristic
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8C23×C6111yescharacteristic
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C6111yescharacteristic
549C4×D4D4×C6111yescharacteristic
550C4×D4C23×C6111yescharacteristic
551C4×D4C23×C6111yescharacteristic
552C4×D4C23×C6111yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C6111yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C42C23×C6111yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567C4⋊C8C23×C6111yescharacteristic
568C4⋊C8C23×C6111yescharacteristic
569C4⋊C8C23×C6111yescharacteristic
570C4⋊C8C23×C6111yescharacteristic
571#103—22no—
572#103—21no—
573#103—21no—
574#103—21no—
575#102—22no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581C22⋊C8—21no—
582C4×C8C23×C6111yescharacteristic
583C4×C8C23×C6111yescharacteristic
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C6111yescharacteristic
593C2×Q8C2×D4×C6112yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
615C2×D4C2×D4×C6111yescharacteristic
616C2×D4C2×D4×C6111yescharacteristic
617C2×D4C2×D4×C6111yescharacteristic
618C2×D4C2×D4×C6112yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C6111yescharacteristic
632C22×C4C2×D4×C6111yescharacteristic
633C22×C4C2×D4×C6111yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C2×D4×C6111yescharacteristic
662C4⋊C4C2×D4×C6111yescharacteristic
663C4⋊C4C2×D4×C6111yescharacteristic
664C4⋊C4C2×D4×C6111yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C6111yescharacteristic
686C42C2×D4×C6111yescharacteristic
687C42C2×D4×C6111yescharacteristic
688C42C24×C6111yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C6111yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4AGL(1,ℤ/8)×C6112yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4#120×C6111yescharacteristic
757C2×C4#120×C6111yescharacteristic
758C2×C4#120×C6111yescharacteristic
759C2×C4C22×D4×C6111yescharacteristic
760C2×C4C22×D4×C6111yescharacteristic
761C2×C4C22×D4×C6111yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×#120×C6111yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4C2×AGL(1,ℤ/8)×C6111yescharacteristic
801C4C61×#57511yescharacteristic
802C4C61×#57611yescharacteristic
803C4C61×#57711yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2C61×#300611yescharacteristic
811C2C61×#301211yescharacteristic
812C2C61×#301911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3519C2semidirect
2. C61×#3251C2semidirect
3. C61×#3207C2semidirect
4. C61×#3036C2semidirect
5. C61×#1646C2semidirect
6. C61×#1643C2semidirect
7. C61×#1642C2semidirect
8. C61×#1639C2semidirect
9. C61×#1624C2semidirect
10. C61×#1622C2semidirect
11. C61×#1621C2semidirect
12. C61×#1619C2semidirect
13. C61×#1560C2semidirect
14. C61×#1495C2semidirect
15. C61×#1486C2semidirect
29. C61×#532C22semidirect
35. C61×#493C22semidirect
36. C61×#492C22semidirect
37. C61×#487C22semidirect
38. C61×#486C22semidirect
40. C61×#475C22semidirect
41. C61×#474C22semidirect
49. C61×#461C22semidirect
50. C61×#460C22semidirect
52. C61×#459C22semidirect
53. C61×#459C22semidirect
55. C61×#431C22semidirect
56. C61×#423C22semidirect
57. C61×#423C22semidirect
59. C61×#333C22semidirect
60. C61×#333C22semidirect
61. C61×#331C22semidirect
62. C61×#331C22semidirect
63. C61×Q8⋊C8C22semidirect
64. C61×Q8⋊C8C22semidirect
67. C61×D4⋊C8C22semidirect
68. C61×D4⋊C8C22semidirect
69. C61×D4⋊C8C22semidirect
70. C61×D4⋊C8C22semidirect
361. #18810C61direct (N × H)
398. #3519C2×C61semidirect
399. #3251C2×C61semidirect
400. #3207C2×C61semidirect
401. #3036C2×C61semidirect
402. #1646C2×C61semidirect
403. #1643C2×C61semidirect
404. #1642C2×C61semidirect
405. #1639C2×C61semidirect
406. #1624C2×C61semidirect
407. #1622C2×C61semidirect
408. #1621C2×C61semidirect
409. #1619C2×C61semidirect
410. #1560C2×C61semidirect
411. #1495C2×C61semidirect
412. #1486C2×C61semidirect
435. #532C22×C61semidirect
441. #493C22×C61semidirect
442. #492C22×C61semidirect
443. #487C22×C61semidirect
444. #486C22×C61semidirect
446. #475C22×C61semidirect
447. #474C22×C61semidirect
455. #461C22×C61semidirect
456. #460C22×C61semidirect
458. #459C22×C61semidirect
459. #459C22×C61semidirect
461. #431C22×C61semidirect
462. #423C22×C61semidirect
463. #423C22×C61semidirect
465. #333C22×C61semidirect
466. #333C22×C61semidirect
467. #331C22×C61semidirect
468. #331C22×C61semidirect
469. Q8⋊C8C22×C61semidirect
470. Q8⋊C8C22×C61semidirect
473. D4⋊C8C22×C61semidirect
474. D4⋊C8C22×C61semidirect
475. D4⋊C8C22×C61semidirect
476. D4⋊C8C22×C61semidirect
477. C61#18810direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35192
C61×#32512
C61×#32072
C61×#30362
C61×#16462
C61×#16432
C61×#16422
C61×#16392
C61×#16242
C61×#16222
C61×#16212
C61×#16192
C61×#15602
C61×#14952
C61×#14862
#1881061