Finite Group Databasebeta

← C61×#24405 #29527838

Subgroups — C61×#24405 #29527838

Order 15616.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3484C211yesmaximal, characteristic
2C2×C61×#458C211yesmaximal, characteristic, complemented
3C22×#99×C61C211yesmaximal, characteristic, complemented
4C61×#2412C212yesmaximal, complemented
5C61×#2405C211yesmaximal, characteristic, complemented
6C61×#2044C212yesmaximal, complemented
7C61×#2022C212yesmaximal, complemented
8C61×#1898C212yesmaximal, complemented
9C61×#1890C211yesmaximal, characteristic, complemented
10C61×#1867C211yesmaximal, characteristic, complemented
11C61×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C61C2211yescharacteristic
13C23×D4×C61C2211yescharacteristic
14C61×#546—22no—
15C61×#546—22no—
16D42×C61—22no—
17D42×C61—22no—
18C61×#535—21no—
19C61×#534—21no—
20C61×#534C2212yes—
21C61×#525—21no—
22C2×#123×C61C2211yescharacteristic
23C2×#123×C61C2212yescomplemented
24C2×#123×C61C2211yescharacteristic, complemented
25C2×#120×C61—21no—
26C2×#120×C61C2212yes—
27C61×#518C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic, complemented
29C22×C22⋊C4×C61C2212yescomplemented
30C61×#458—24no—
31C2×#99×C61—24no—
32C2×#99×C61C2211yescharacteristic
33C2×#99×C61C2211yescharacteristic
34C2×#99×C61C2212yescomplemented
35C2×#99×C61C2212yescomplemented
36C2×#99×C61C2212yescomplemented
37C61×#397—22no—
38C61×#394—21no—
39C61×#394—21no—
40C61×#394—22no—
41C61×#386—22no—
42C61×#386C2211yescharacteristic
43C61×#386C2211yescharacteristic, complemented
44C61×#386C2212yescomplemented
45C61×#385—21no—
46C61×#385C2212yescomplemented
47C61×#381C2212yescomplemented
48C61×#380—22no—
49C61×#379—21no—
50C61×#379C2211yescharacteristic, complemented
51C61×#342C2212yescomplemented
52C61×#342C2212yescomplemented
53C25×C61D411yescharacteristic
54C25×C61C2311yescharacteristic
55H(5,𝔽2)×C61—22no—
56H(5,𝔽2)×C61—22no—
57H(5,𝔽2)×C61—42no—
58C2×#41×C61—21no—
59C2×#41×C61—22no—
60C22×D4×C61—21no—
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—42no—
69C22×D4×C61D411yescharacteristic
70C22×D4×C61D411yescharacteristic
71C22×D4×C61D412yes—
72C22×D4×C61D412yes—
73C22×D4×C61C2311yescharacteristic
74C22×D4×C61C2312yes—
75C22×D4×C61C2311yescharacteristic
76C23×C4×C61—22no—
77C23×C4×C61D411yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C23×C4×C61C2311yescharacteristic
80#127×C61—22no—
81#124×C61—22no—
82#123×C61—22no—
83#123×C61—22no—
84#123×C61—22no—
85#123×C61—22no—
86#123×C61—22no—
87#123×C61—24no—
88#123×C61—42no—
89#123×C61—42no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—21no—
92#121×C61—22no—
93#121×C61—22no—
94#121×C61—22no—
95#121×C61—22no—
96#121×C61—21no—
97#121×C61—21no—
98#121×C61—22no—
99#121×C61—22no—
100#120×C61—22no—
101#120×C61—22no—
102#120×C61—22no—
103#120×C61—22no—
104#120×C61—22no—
105#120×C61—22no—
106#120×C61—22no—
107#120×C61—22no—
108#120×C61—22no—
109C4×D4×C61—22no—
110C4×D4×C61—22no—
111C4×D4×C61—22no—
112C4×D4×C61—22no—
113#117×C61—21no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—22no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—24no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—22no—
127C2×C22⋊C4×C61—22no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—22no—
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—22no—
135C2×C22⋊C4×C61—42no—
136C2×C22⋊C4×C61D412yes—
137C2×C22⋊C4×C61D412yes—
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61C2312yes—
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2312yes—
143#99×C61—22no—
144#99×C61—24no—
145#99×C61—24no—
146#99×C61—42no—
147#99×C61D414yescomplemented
148#95×C61—22no—
149#95×C61—22no—
150#95×C61—22no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—22no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—22no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—41no—
162C24×C61—42no—
163C24×C61—42no—
164C24×C61—81no—
165C24×C61—81no—
166C24×C61C2×D411yescharacteristic
167C24×C61C2×D412yes—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D412yes—
170C24×C61C2×D412yes—
171C24×C61C2×D411yescharacteristic
172C24×C61C2×D411yescharacteristic
173C24×C61C2411yescharacteristic
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—42no—
177#41×C61—42no—
178C2×Q8×C61—21no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—21no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—41no—
204C2×D4×C61—41no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—44no—
214C2×D4×C61—82no—
215C2×D4×C61—82no—
216C2×D4×C61—82no—
217C2×D4×C61C2×D412yes—
218C2×D4×C61#4112yes—
219C22×C4×C61—21no—
220C22×C4×C61—22no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—22no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—22no—
227C22×C4×C61—22no—
228C22×C4×C61—21no—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—22no—
237C22×C4×C61—41no—
238C22×C4×C61—44no—
239C22×C4×C61—44no—
240C22×C4×C61—81no—
241C22×C4×C61—82no—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—44no—
252C4⋊C4×C61—42no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61—82no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—22no—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—22no—
272C22⋊C4×C61—44no—
273C22⋊C4×C61—44no—
274C22⋊C4×C61—42no—
275C22⋊C4×C61—42no—
276C22⋊C4×C61—41no—
277C22⋊C4×C61—42no—
278C22⋊C4×C61—41no—
279C22⋊C4×C61—42no—
280C22⋊C4×C61—81no—
281C22⋊C4×C61—81no—
282C22⋊C4×C61—81no—
283C22⋊C4×C61—82no—
284C22⋊C4×C61C2×D414yescomplemented
285C42×C61—22no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—24no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—42no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—41no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61—81no—
324C23×C61—81no—
325C23×C61—82no—
326C23×C61—82no—
327C23×C61—84no—
328C23×C61—81no—
329C23×C61—81no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61#12011yescharacteristic
333C23×C61#12012yes—
334C23×C61#12011yescharacteristic
335C23×C61#12112yes—
336C23×C61C22×D411yescharacteristic
337C23×C61C22×D412yes—
338C23×C61C22×D411yescharacteristic
339C23×C61C2×#4111yescharacteristic
340C23×C61H(5,𝔽2)12yes—
341Q8×C61—42no—
342D4×C61—24no—
343D4×C61—24no—
344D4×C61—44no—
345D4×C61—42no—
346D4×C61—44no—
347D4×C61—44no—
348D4×C61—44no—
349D4×C61—42no—
350D4×C61—42no—
351D4×C61—42no—
352D4×C61—42no—
353D4×C61—42no—
354D4×C61—42no—
355D4×C61—44no—
356D4×C61—82no—
357D4×C61—82no—
358D4×C61—82no—
359D4×C61—82no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—24no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61—44no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—42no—
388C2×C4×C61—42no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—42no—
396C2×C4×C61—42no—
397C2×C4×C61—42no—
398C2×C4×C61—81no—
399C2×C4×C61—81no—
400C2×C4×C61—88no—
401C2×C4×C61#12112yes—
402#24405C6111yesmaximal, characteristic, direct product factor, Sylow
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—21no—
406C22×C61—22no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—22no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—42no—
419C22×C61—44no—
420C22×C61—44no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—42no—
428C22×C61—41no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—42no—
432C22×C61—41no—
433C22×C61—82no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—82no—
438C22×C61—84no—
439C22×C61—82no—
440C22×C61—82no—
441C22×C61—81no—
442C22×C61—84no—
443C22×C61—162no—
444C22×C61#45812yescomplemented
445C22×C61C2×#12011yescharacteristic
446C22×C61C2×#12111yescharacteristic
447C22×C61#53411yescharacteristic
448C22×C61D4212yes—
449C22×C61#54612yes—
450C4×C61—22no—
451C4×C61—44no—
452C4×C61—41no—
453C4×C61—42no—
454C4×C61—42no—
455C4×C61—42no—
456C4×C61—81no—
457C4×C61—81no—
458C4×C61—82no—
459C4×C61—81no—
460C4×C61—81no—
461#3484C2×C6111yescharacteristic
462C2×#458C2×C6111yescharacteristic, complemented
463C22×#99C2×C6111yescharacteristic, complemented
464#2412C2×C6112yescomplemented
465#2405C2×C6111yescharacteristic, complemented
466#2044C2×C6112yescomplemented
467#2022C2×C6112yescomplemented
468#1898C2×C6112yescomplemented
469#1890C2×C6111yescharacteristic, complemented
470#1867C2×C6111yescharacteristic, complemented
471#1790C2×C6111yescharacteristic, complemented
472C2×C61—22no—
473C2×C61—21no—
474C2×C61—21no—
475C2×C61—22no—
476C2×C61—22no—
477C2×C61—42no—
478C2×C61—41no—
479C2×C61—42no—
480C2×C61—81no—
481C2×C61—82no—
482C2×C61#241011yescharacteristic
483C2×C61C2×#45811yescharacteristic
484C2×C61#302611yescharacteristic
485C2×H(5,𝔽2)C22×C6111yescharacteristic
486C23×D4C22×C6111yescharacteristic
487#546—22no—
488#546—22no—
489D42—22no—
490D42—22no—
491#535—21no—
492#534—21no—
493#534C22×C6112yes—
494#525—21no—
495C2×#123C22×C6111yescharacteristic
496C2×#123C22×C6112yescomplemented
497C2×#123C22×C6111yescharacteristic, complemented
498C2×#120—21no—
499C2×#120C22×C6112yes—
500#518C22×C6111yescharacteristic
501C22×C22⋊C4C22×C6111yescharacteristic, complemented
502C22×C22⋊C4C22×C6112yescomplemented
503#458—24no—
504C2×#99—24no—
505C2×#99C22×C6111yescharacteristic
506C2×#99C22×C6111yescharacteristic
507C2×#99C22×C6112yescomplemented
508C2×#99C22×C6112yescomplemented
509C2×#99C22×C6112yescomplemented
510#397—22no—
511#394—21no—
512#394—21no—
513#394—22no—
514#386—22no—
515#386C22×C6111yescharacteristic
516#386C22×C6111yescharacteristic, complemented
517#386C22×C6112yescomplemented
518#385—21no—
519#385C22×C6112yescomplemented
520#381C22×C6112yescomplemented
521#380—22no—
522#379—21no—
523#379C22×C6111yescharacteristic, complemented
524#342C22×C6112yescomplemented
525#342C22×C6112yescomplemented
526C61#2440511yescharacteristic, direct product factor, Sylow
527C25D4×C6111yescharacteristic
528C25C23×C6111yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C6111yescharacteristic
544C22×D4D4×C6111yescharacteristic
545C22×D4D4×C6112yes—
546C22×D4D4×C6112yes—
547C22×D4C23×C6112yes—
548C22×D4C23×C6111yescharacteristic
549C22×D4C23×C6111yescharacteristic
550C23×C4—22no—
551C23×C4D4×C6111yescharacteristic
552C23×C4C23×C6111yescharacteristic
553C23×C4C23×C6111yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C6112yes—
611C2×C22⋊C4D4×C6112yes—
612C2×C22⋊C4C23×C6112yes—
613C2×C22⋊C4C23×C6111yescharacteristic
614C2×C22⋊C4C23×C6111yescharacteristic
615C2×C22⋊C4C23×C6112yes—
616C2×C22⋊C4C23×C6112yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C6114yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C6111yescharacteristic
641C24C2×D4×C6112yes—
642C24C2×D4×C6111yescharacteristic
643C24C2×D4×C6112yes—
644C24C2×D4×C6112yes—
645C24C2×D4×C6111yescharacteristic
646C24C2×D4×C6111yescharacteristic
647C24C24×C6111yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C6112yes—
692C2×D4#41×C6112yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C6112yes—
717C22×C4C2×D4×C6111yescharacteristic
718C22×C4C2×D4×C6111yescharacteristic
719C22×C4C2×D4×C6112yes—
720C22×C4C2×D4×C6112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C6114yescomplemented
759C42—22no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—24no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—22no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—21no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C6111yescharacteristic
807C23#120×C6112yes—
808C23#120×C6111yescharacteristic
809C23#121×C6112yes—
810C23C22×D4×C6111yescharacteristic
811C23C22×D4×C6112yes—
812C23C22×D4×C6111yescharacteristic
813C23C2×#41×C6111yescharacteristic
814C23H(5,𝔽2)×C6112yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—44no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C6112yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—44no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—82no—
913C22—82no—
914C22—81no—
915C22—84no—
916C22—162no—
917C22C61×#45812yescomplemented
918C22C2×#120×C6111yescharacteristic
919C22C2×#121×C6111yescharacteristic
920C22C61×#53411yescharacteristic
921C22D42×C6112yes—
922C22C61×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—81no—
930C4—81no—
931C4—82no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C61×#241011yescharacteristic
945C2C2×C61×#45811yescharacteristic
946C2C61×#302611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
prime radicalC61×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#458C2semidirect
3. C22×#99×C61C2semidirect
4. C61×#2412C2semidirect
5. C61×#2405C2semidirect
6. C61×#2044C2semidirect
7. C61×#2022C2semidirect
8. C61×#1898C2semidirect
9. C61×#1890C2semidirect
10. C61×#1867C2semidirect
11. C61×#1790C2semidirect
23. C2×#123×C61C22semidirect
24. C2×#123×C61C22semidirect
28. C22×C22⋊C4×C61C22semidirect
29. C22×C22⋊C4×C61C22semidirect
34. C2×#99×C61C22semidirect
35. C2×#99×C61C22semidirect
36. C2×#99×C61C22semidirect
43. C61×#386C22semidirect
44. C61×#386C22semidirect
46. C61×#385C22semidirect
47. C61×#381C22semidirect
50. C61×#379C22semidirect
51. C61×#342C22semidirect
52. C61×#342C22semidirect
147. #99×C61D4semidirect
284. C22⋊C4×C61C2×D4semidirect
402. #24405C61direct (N × H)
444. C22×C61#458semidirect
462. C2×#458C2×C61semidirect
463. C22×#99C2×C61semidirect
464. #2412C2×C61semidirect
465. #2405C2×C61semidirect
466. #2044C2×C61semidirect
467. #2022C2×C61semidirect
468. #1898C2×C61semidirect
469. #1890C2×C61semidirect
470. #1867C2×C61semidirect
471. #1790C2×C61semidirect
496. C2×#123C22×C61semidirect
497. C2×#123C22×C61semidirect
501. C22×C22⋊C4C22×C61semidirect
502. C22×C22⋊C4C22×C61semidirect
507. C2×#99C22×C61semidirect
508. C2×#99C22×C61semidirect
509. C2×#99C22×C61semidirect
516. #386C22×C61semidirect
517. #386C22×C61semidirect
519. #385C22×C61semidirect
520. #381C22×C61semidirect
523. #379C22×C61semidirect
524. #342C22×C61semidirect
525. #342C22×C61semidirect
526. C61#24405direct (N × H)
621. #99D4×C61semidirect
758. C22⋊C4C2×D4×C61semidirect
917. C22C61×#458semidirect

Maximal subgroups

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

subgroupindex
C61×#34842
C2×C61×#4582
C22×#99×C612
C61×#24122
C61×#24052
C61×#20442
C61×#20222
C61×#18982
C61×#18902
C61×#18672
C61×#17902
#2440561