Finite Group Databasebeta

← C61×#25585 #29529018

Subgroups — C61×#25585 #29529018

Order 15616.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3505C211yesmaximal, characteristic, complemented
2C61×#2435C211yesmaximal, characteristic, complemented
3C61×#2433C211yesmaximal, characteristic, complemented
4C61×#2408C211yesmaximal, characteristic, complemented
5C61×#2021C214yesmaximal, complemented
6C61×#1996C211yesmaximal, characteristic, complemented
7C61×#1964C211yesmaximal, characteristic, complemented
8C61×#1889C214yesmaximal, complemented
9C4×#99×C61C211yesmaximal, characteristic, complemented
10C23×D4×C61C2211yescharacteristic
11C61×#553—21no—
12C61×#553—22no—
13C61×#552—21no—
14C61×#551—22no—
15C61×#548—21no—
16C61×#546—21no—
17C61×#539—21no—
18C61×#538—21no—
19C61×#534C2212yes—
20C2×#127×C61—21no—
21C61×#529—21no—
22C2×#124×C61—21no—
23C61×#525—21no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C2×#121×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C2×#120×C61C2214yes—
28C2×#120×C61C2212yes—
29C61×#518C2212yes—
30C2×C4×D4×C61C2211yescharacteristic
31C2×#99×C61C2212yes—
32C2×#99×C61C2214yes—
33C61×#394—21no—
34C61×#394—22no—
35C61×#392—21no—
36C61×#392—22no—
37C61×#390—21no—
38C61×#390—21no—
39C61×#390—21no—
40C61×#380C2211yescharacteristic
41C61×#379C2214yes—
42C61×#379C2212yes—
43C4×C22⋊C4×C61C2211yescharacteristic
44C4×C22⋊C4×C61C2211yescharacteristic
45C61×#342C2212yes—
46C61×#342C2214yes—
47C25×C61C2312yes—
48C2×#41×C61—21no—
49C22×Q8×C61D411yescharacteristic, complemented
50C22×D4×C61—24no—
51C22×D4×C61—22no—
52C22×D4×C61—21no—
53C22×D4×C61—21no—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C22×D4×C61—21no—
57C22×D4×C61—21no—
58C22×D4×C61—44no—
59C22×D4×C61D411yescharacteristic, complemented
60C22×D4×C61C2311yescharacteristic
61C22×D4×C61C2312yes—
62C23×C4×C61D411yescharacteristic, complemented
63C23×C4×C61C2311yescharacteristic
64#127×C61—44no—
65#126×C61—22no—
66#126×C61—22no—
67#126×C61—22no—
68#125×C61—22no—
69#125×C61—21no—
70#124×C61—22no—
71#124×C61—21no—
72#124×C61—44no—
73#123×C61—22no—
74#123×C61—22no—
75#123×C61—22no—
76#123×C61—22no—
77#123×C61—22no—
78C22⋊Q8×C61—22no—
79C22⋊Q8×C61—21no—
80C22⋊Q8×C61—21no—
81C22⋊Q8×C61—21no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—21no—
84#121×C61—22no—
85#121×C61—21no—
86#121×C61—22no—
87#121×C61—22no—
88#121×C61—21no—
89#121×C61—21no—
90#121×C61—21no—
91#121×C61—21no—
92#121×C61—44no—
93#120×C61—22no—
94#120×C61—22no—
95#120×C61—28no—
96#120×C61—44no—
97#120×C61—44no—
98C4×Q8×C61—21no—
99C4×D4×C61—21no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C4×D4×C61—21no—
104C4×D4×C61—21no—
105C4×D4×C61—22no—
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108C4×D4×C61—22no—
109#117×C61—22no—
110#117×C61—21no—
111#117×C61—22no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61D411yescharacteristic, complemented
114C2×C4⋊C4×C61D411yescharacteristic, complemented
115C2×C4⋊C4×C61D411yescharacteristic, complemented
116C2×C4⋊C4×C61D412yescomplemented
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—24no—
120C2×C22⋊C4×C61—24no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—22no—
123C2×C22⋊C4×C61—24no—
124C2×C22⋊C4×C61D411yescharacteristic, complemented
125C2×C22⋊C4×C61D412yescomplemented
126C2×C22⋊C4×C61C2312yes—
127C2×C22⋊C4×C61C2312yes—
128C2×C22⋊C4×C61C2312yes—
129C2×C22⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61C2312yes—
131C2×C42×C61—21no—
132C2×C42×C61—21no—
133C2×C42×C61D411yescharacteristic, complemented
134#99×C61—24no—
135#99×C61—44no—
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139C24×C61—22no—
140C24×C61—22no—
141C24×C61—22no—
142C24×C61—24no—
143C24×C61—24no—
144C24×C61—44no—
145C24×C61—82no—
146C24×C61C2×D412yes—
147C24×C61C2×D411yescharacteristic
148C24×C61C2411yescharacteristic
149#41×C61—82no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—42no—
153C2×D4×C61—24no—
154C2×D4×C61—24no—
155C2×D4×C61—24no—
156C2×D4×C61—21no—
157C2×D4×C61—22no—
158C2×D4×C61—21no—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—24no—
162C2×D4×C61—24no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—48no—
173C2×D4×C61—44no—
174C2×D4×C61—44no—
175C2×D4×C61—44no—
176C2×D4×C61—44no—
177C2×D4×C61—44no—
178C2×D4×C61—48no—
179C2×D4×C61—41no—
180C2×D4×C61—41no—
181C2×D4×C61—41no—
182C2×D4×C61—41no—
183C2×D4×C61—84no—
184C2×D4×C61—82no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—42no—
193C22×C4×C61—42no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C4⋊C4×C61—22no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—22no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—22no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—42no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—21no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—21no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—48no—
238C22⋊C4×C61—44no—
239C22⋊C4×C61—44no—
240C22⋊C4×C61—48no—
241C22⋊C4×C61—84no—
242C22⋊C4×C61—82no—
243C22⋊C4×C61#4114yescomplemented
244C42×C61—22no—
245C42×C61—22no—
246C42×C61—21no—
247C42×C61—21no—
248C42×C61—42no—
249C42×C61—42no—
250C23×C61—24no—
251C23×C61—24no—
252C23×C61—24no—
253C23×C61—21no—
254C23×C61—22no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—24no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—44no—
263C23×C61—42no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61—44no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61—42no—
272C23×C61—42no—
273C23×C61—42no—
274C23×C61—44no—
275C23×C61—44no—
276C23×C61—88no—
277C23×C61—88no—
278C23×C61C22×D411yescharacteristic
279C23×C61C22×D411yescharacteristic
280C23×C61C22×D411yescharacteristic
281C23×C61C2×#4112yes—
282C23×C61H(5,𝔽2)12yes—
283Q8×C61—42no—
284Q8×C61—81no—
285D4×C61—44no—
286D4×C61—44no—
287D4×C61—44no—
288D4×C61—42no—
289D4×C61—42no—
290D4×C61—42no—
291D4×C61—42no—
292D4×C61—44no—
293D4×C61—44no—
294D4×C61—42no—
295D4×C61—81no—
296D4×C61—82no—
297D4×C61—82no—
298D4×C61—816no—
299D4×C61—88no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—24no—
312C2×C4×C61—24no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—41no—
320C2×C4×C61—42no—
321C2×C4×C61—41no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—81no—
330C2×C4×C61—82no—
331C2×C4×C61—82no—
332C2×C4×C61#12011yescharacteristic
333C2×C4×C61#12011yescharacteristic
334C2×C4×C61#12011yescharacteristic
335C2×C4×C61#12011yescharacteristic
336#25585C6111yesmaximal, characteristic, direct product factor, Sylow
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—48no—
347C22×C61—44no—
348C22×C61—48no—
349C22×C61—44no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—42no—
354C22×C61—44no—
355C22×C61—42no—
356C22×C61—41no—
357C22×C61—84no—
358C22×C61—81no—
359C22×C61—84no—
360C22×C61—82no—
361C22×C61—84no—
362C22×C61—82no—
363C22×C61—82no—
364C22×C61—82no—
365C22×C61C2×#12011yescharacteristic
366C22×C61#53211yescharacteristic
367C22×C61#53511yescharacteristic
368C22×C61#54612yes—
369C22×C61#55012yes—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—44no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61—41no—
377C4×C61—42no—
378C4×C61—41no—
379C4×C61—42no—
380C4×C61—82no—
381C4×C61—82no—
382C4×C61B(4,𝔽2)12yes—
383#3505C2×C6111yescharacteristic, complemented
384#2435C2×C6111yescharacteristic, complemented
385#2433C2×C6111yescharacteristic, complemented
386#2408C2×C6111yescharacteristic, complemented
387#2021C2×C6114yescomplemented
388#1996C2×C6111yescharacteristic, complemented
389#1964C2×C6111yescharacteristic, complemented
390#1889C2×C6114yescomplemented
391C4×#99C2×C6111yescharacteristic, complemented
392C2×C61—22no—
393C2×C61—21no—
394C2×C61—22no—
395C2×C61—21no—
396C2×C61—84no—
397C2×C61—81no—
398C2×C61—82no—
399C2×C61#243111yescharacteristic
400C2×C61C2×B(4,𝔽2)11yescharacteristic
401C2×C61#302711yescharacteristic
402C23×D4C22×C6111yescharacteristic
403#553—21no—
404#553—22no—
405#552—21no—
406#551—22no—
407#548—21no—
408#546—21no—
409#539—21no—
410#538—21no—
411#534C22×C6112yes—
412C2×#127—21no—
413#529—21no—
414C2×#124—21no—
415#525—21no—
416C2×C22⋊Q8C22×C6111yescharacteristic
417C2×#121—21no—
418C2×#121C22×C6111yescharacteristic
419C2×#120C22×C6114yes—
420C2×#120C22×C6112yes—
421#518C22×C6112yes—
422C2×C4×D4C22×C6111yescharacteristic
423C2×#99C22×C6112yes—
424C2×#99C22×C6114yes—
425#394—21no—
426#394—22no—
427#392—21no—
428#392—22no—
429#390—21no—
430#390—21no—
431#390—21no—
432#380C22×C6111yescharacteristic
433#379C22×C6112yes—
434#379C22×C6114yes—
435C4×C22⋊C4C22×C6111yescharacteristic
436C4×C22⋊C4C22×C6111yescharacteristic
437#342C22×C6112yes—
438#342C22×C6114yes—
439C61#2558511yescharacteristic, direct product factor, Sylow
440C25C23×C6112yes—
441C2×#41—21no—
442C22×Q8D4×C6111yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C6111yescharacteristic, complemented
453C22×D4C23×C6111yescharacteristic
454C22×D4C23×C6112yes—
455C23×C4D4×C6111yescharacteristic, complemented
456C23×C4C23×C6111yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C6111yescharacteristic, complemented
507C2×C4⋊C4D4×C6111yescharacteristic, complemented
508C2×C4⋊C4D4×C6111yescharacteristic, complemented
509C2×C4⋊C4D4×C6112yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C6111yescharacteristic, complemented
518C2×C22⋊C4D4×C6112yescomplemented
519C2×C22⋊C4C23×C6112yes—
520C2×C22⋊C4C23×C6112yes—
521C2×C22⋊C4C23×C6111yescharacteristic
522C2×C22⋊C4C23×C6112yes—
523C2×C22⋊C4C23×C6112yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C6111yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C6112yes—
540C24C2×D4×C6111yescharacteristic
541C24C24×C6111yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C6111yescharacteristic
588C22×C4C2×D4×C6112yes—
589C22×C4C2×D4×C6111yescharacteristic
590C22×C4C2×D4×C6111yescharacteristic
591C22×C4C2×D4×C6111yescharacteristic
592C22×C4C2×D4×C6111yescharacteristic
593C22×C4C2×D4×C6112yes—
594C22×C4C2×D4×C6111yescharacteristic
595C22×C4C2×D4×C6112yes—
596C22×C4C2×D4×C6111yescharacteristic
597C22×C4C2×D4×C6111yescharacteristic
598C22×C4C2×D4×C6111yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C6114yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—44no—
667C23—44no—
668C23—42no—
669C23—88no—
670C23—88no—
671C23C22×D4×C6111yescharacteristic
672C23C22×D4×C6111yescharacteristic
673C23C22×D4×C6111yescharacteristic
674C23C2×#41×C6112yes—
675C23H(5,𝔽2)×C6112yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C6111yescharacteristic
726C2×C4#120×C6111yescharacteristic
727C2×C4#120×C6111yescharacteristic
728C2×C4#120×C6111yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C6111yescharacteristic
758C22C61×#53211yescharacteristic
759C22C61×#53511yescharacteristic
760C22C61×#54612yes—
761C22C61×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C61×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C61×#243111yescharacteristic
783C2C2×C61×B(4,𝔽2)11yescharacteristic
784C2C61×#302711yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3505C2semidirect
2. C61×#2435C2semidirect
3. C61×#2433C2semidirect
4. C61×#2408C2semidirect
5. C61×#2021C2semidirect
6. C61×#1996C2semidirect
7. C61×#1964C2semidirect
8. C61×#1889C2semidirect
9. C4×#99×C61C2semidirect
49. C22×Q8×C61D4semidirect
59. C22×D4×C61D4semidirect
62. C23×C4×C61D4semidirect
113. C2×C4⋊C4×C61D4semidirect
114. C2×C4⋊C4×C61D4semidirect
115. C2×C4⋊C4×C61D4semidirect
116. C2×C4⋊C4×C61D4semidirect
124. C2×C22⋊C4×C61D4semidirect
125. C2×C22⋊C4×C61D4semidirect
133. C2×C42×C61D4semidirect
243. C22⋊C4×C61#41semidirect
336. #25585C61direct (N × H)
383. #3505C2×C61semidirect
384. #2435C2×C61semidirect
385. #2433C2×C61semidirect
386. #2408C2×C61semidirect
387. #2021C2×C61semidirect
388. #1996C2×C61semidirect
389. #1964C2×C61semidirect
390. #1889C2×C61semidirect
391. C4×#99C2×C61semidirect
439. C61#25585direct (N × H)
442. C22×Q8D4×C61semidirect
452. C22×D4D4×C61semidirect
455. C23×C4D4×C61semidirect
506. C2×C4⋊C4D4×C61semidirect
507. C2×C4⋊C4D4×C61semidirect
508. C2×C4⋊C4D4×C61semidirect
509. C2×C4⋊C4D4×C61semidirect
517. C2×C22⋊C4D4×C61semidirect
518. C2×C22⋊C4D4×C61semidirect
526. C2×C42D4×C61semidirect
636. C22⋊C4#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35052
C61×#24352
C61×#24332
C61×#24082
C61×#20212
C61×#19962
C61×#19642
C61×#18892
C4×#99×C612
#2558561