Finite Group Databasebeta

← C61×#25587 #29529020

Subgroups — C61×#25587 #29529020

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3505C211yesmaximal, characteristic, complemented
2C61×#2561C211yesmaximal, characteristic, complemented
3C61×#2539C211yesmaximal, characteristic, complemented
4C61×#2534C211yesmaximal, characteristic, complemented
5C61×#2022C212yesmaximal, complemented
6C61×#2021C212yesmaximal, complemented
7C61×#1996C211yesmaximal, characteristic, complemented
8C61×#1964C211yesmaximal, characteristic, complemented
9C61×#1890C212yesmaximal, complemented
10C61×#1889C212yesmaximal, complemented
11C4×#99×C61C211yesmaximal, characteristic, complemented
12C61×#553—22no—
13C61×#553—21no—
14C61×#552—21no—
15C61×#551—22no—
16C61×#548—21no—
17C61×#546—21no—
18C61×#539—21no—
19C61×#538—21no—
20C61×#534C2212yes—
21C61×#529—21no—
22C61×#525—21no—
23C2×#123×C61C2212yes—
24C2×#123×C61C2211yescharacteristic
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C2×#120×C61C2212yes—
28C2×#120×C61C2211yescharacteristic
29C61×#518C2212yes—
30C2×C4×D4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C2×#99×C61C2212yes—
33C2×#99×C61C2212yes—
34C2×#99×C61C2212yes—
35C61×#399—21no—
36C61×#397—21no—
37C61×#396—21no—
38C61×#394—21no—
39C61×#393—21no—
40C61×#392—21no—
41C61×#390—22no—
42C61×#388—22no—
43C61×#388—21no—
44C61×#386—21no—
45C61×#381C2212yes—
46C61×#381C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#379C2212yes—
49C61×#379C2211yescharacteristic
50C4×C22⋊C4×C61C2211yescharacteristic
51C4×C22⋊C4×C61C2211yescharacteristic
52C61×#342C2212yes—
53C61×#342C2212yes—
54C61×#342C2212yes—
55C25×C61C2311yescharacteristic
56C2×#41×C61—21no—
57C22×Q8×C61D411yescharacteristic, complemented
58C22×D4×C61—21no—
59C22×D4×C61—22no—
60C22×D4×C61D411yescharacteristic, complemented
61C22×D4×C61C2311yescharacteristic
62C22×D4×C61C2312yes—
63C23×C4×C61D411yescharacteristic, complemented
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66#126×C61—22no—
67#126×C61—22no—
68#126×C61—22no—
69#125×C61—22no—
70#125×C61—21no—
71#124×C61—22no—
72#124×C61—21no—
73#123×C61—22no—
74#123×C61—22no—
75#123×C61—22no—
76#123×C61—22no—
77#123×C61—22no—
78#123×C61—24no—
79#123×C61—42no—
80#123×C61—42no—
81C22⋊Q8×C61—22no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—21no—
84C22⋊Q8×C61—21no—
85C22⋊Q8×C61—21no—
86C22⋊Q8×C61—21no—
87#121×C61—22no—
88#121×C61—21no—
89#121×C61—22no—
90#121×C61—22no—
91#121×C61—21no—
92#121×C61—21no—
93#121×C61—21no—
94#121×C61—21no—
95#120×C61—22no—
96#120×C61—22no—
97#120×C61—24no—
98#120×C61—42no—
99#120×C61—42no—
100C4×Q8×C61—21no—
101C4×D4×C61—21no—
102C4×D4×C61—22no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—21no—
106C4×D4×C61—21no—
107C4×D4×C61—22no—
108C4×D4×C61—21no—
109C4×D4×C61—21no—
110C4×D4×C61—22no—
111#117×C61—22no—
112#117×C61—21no—
113#117×C61—22no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61D411yescharacteristic, complemented
118C2×C4⋊C4×C61D411yescharacteristic, complemented
119C2×C4⋊C4×C61D412yescomplemented
120C2×C4⋊C4×C61D411yescharacteristic, complemented
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—22no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—22no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61D411yescharacteristic, complemented
137C2×C22⋊C4×C61D412yescomplemented
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61C2312yes—
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61C2312yes—
144C2×C42×C61—21no—
145C2×C42×C61—21no—
146C2×C42×C61D411yescharacteristic, complemented
147#99×C61—24no—
148#99×C61—42no—
149#99×C61—42no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154#95×C61—22no—
155#95×C61—21no—
156#95×C61—22no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—42no—
163C24×C61—81no—
164C24×C61C2×D412yes—
165C24×C61C2×D411yescharacteristic
166C24×C61C2411yescharacteristic
167#41×C61—82no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—81no—
171C2×D4×C61—21no—
172C2×D4×C61—22no—
173C2×D4×C61—21no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—22no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—44no—
186C2×D4×C61—42no—
187C2×D4×C61—44no—
188C2×D4×C61—42no—
189C2×D4×C61—81no—
190C2×D4×C61—82no—
191C2×D4×C61—81no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—81no—
206C22×C4×C61—81no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D412yes—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—44no—
232C4⋊C4×C61—42no—
233C4⋊C4×C61—81no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—44no—
254C22⋊C4×C61—44no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—44no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61—41no—
260C22⋊C4×C61—41no—
261C22⋊C4×C61—41no—
262C22⋊C4×C61—41no—
263C22⋊C4×C61—81no—
264C22⋊C4×C61—82no—
265C22⋊C4×C61#4114yescomplemented
266C42×C61—22no—
267C42×C61—22no—
268C42×C61—21no—
269C42×C61—21no—
270C42×C61—81no—
271C42×C61—81no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—42no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—42no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—84no—
300C23×C61—84no—
301C23×C61C22×D411yescharacteristic
302C23×C61C22×D411yescharacteristic
303C23×C61C22×D411yescharacteristic
304C23×C61C2×#4112yes—
305C23×C61H(5,𝔽2)12yes—
306Q8×C61—42no—
307Q8×C61—81no—
308D4×C61—42no—
309D4×C61—42no—
310D4×C61—42no—
311D4×C61—42no—
312D4×C61—42no—
313D4×C61—42no—
314D4×C61—42no—
315D4×C61—81no—
316D4×C61—82no—
317D4×C61—82no—
318D4×C61—88no—
319D4×C61—84no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—24no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61—42no—
340C2×C4×C61—41no—
341C2×C4×C61—42no—
342C2×C4×C61—41no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—42no—
358C2×C4×C61—81no—
359C2×C4×C61—82no—
360C2×C4×C61—82no—
361C2×C4×C61#12011yescharacteristic
362C2×C4×C61#12011yescharacteristic
363C2×C4×C61#12011yescharacteristic
364C2×C4×C61#12011yescharacteristic
365#25587C6111yesmaximal, characteristic, direct product factor, Sylow
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—44no—
376C22×C61—42no—
377C22×C61—44no—
378C22×C61—42no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—41no—
385C22×C61—42no—
386C22×C61—82no—
387C22×C61—82no—
388C22×C61—81no—
389C22×C61—82no—
390C22×C61—81no—
391C22×C61—82no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61C2×#12011yescharacteristic
396C22×C61#53211yescharacteristic
397C22×C61#53511yescharacteristic
398C22×C61#54612yes—
399C22×C61#55012yes—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—44no—
405C4×C61—41no—
406C4×C61—42no—
407C4×C61—41no—
408C4×C61—42no—
409C4×C61—41no—
410C4×C61—42no—
411C4×C61—81no—
412C4×C61—82no—
413C4×C61—81no—
414C4×C61—81no—
415#3505C2×C6111yescharacteristic, complemented
416#2561C2×C6111yescharacteristic, complemented
417#2539C2×C6111yescharacteristic, complemented
418#2534C2×C6111yescharacteristic, complemented
419#2022C2×C6112yescomplemented
420#2021C2×C6112yescomplemented
421#1996C2×C6111yescharacteristic, complemented
422#1964C2×C6111yescharacteristic, complemented
423#1890C2×C6112yescomplemented
424#1889C2×C6112yescomplemented
425C4×#99C2×C6111yescharacteristic, complemented
426C2×C61—22no—
427C2×C61—21no—
428C2×C61—22no—
429C2×C61—21no—
430C2×C61—82no—
431C2×C61—81no—
432C2×C61—82no—
433C2×C61#243111yescharacteristic
434C2×C61#302511yescharacteristic
435C2×C61#302611yescharacteristic
436#553—22no—
437#553—21no—
438#552—21no—
439#551—22no—
440#548—21no—
441#546—21no—
442#539—21no—
443#538—21no—
444#534C22×C6112yes—
445#529—21no—
446#525—21no—
447C2×#123C22×C6112yes—
448C2×#123C22×C6111yescharacteristic
449C2×C22⋊Q8C22×C6111yescharacteristic
450C2×#121C22×C6111yescharacteristic
451C2×#120C22×C6112yes—
452C2×#120C22×C6111yescharacteristic
453#518C22×C6112yes—
454C2×C4×D4C22×C6111yescharacteristic
455C22×C22⋊C4C22×C6111yescharacteristic
456C2×#99C22×C6112yes—
457C2×#99C22×C6112yes—
458C2×#99C22×C6112yes—
459#399—21no—
460#397—21no—
461#396—21no—
462#394—21no—
463#393—21no—
464#392—21no—
465#390—22no—
466#388—22no—
467#388—21no—
468#386—21no—
469#381C22×C6112yes—
470#381C22×C6111yescharacteristic
471#380C22×C6111yescharacteristic
472#379C22×C6112yes—
473#379C22×C6111yescharacteristic
474C4×C22⋊C4C22×C6111yescharacteristic
475C4×C22⋊C4C22×C6111yescharacteristic
476#342C22×C6112yes—
477#342C22×C6112yes—
478#342C22×C6112yes—
479C61#2558711yescharacteristic, direct product factor, Sylow
480C25C23×C6111yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C6111yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C6111yescharacteristic, complemented
486C22×D4C23×C6111yescharacteristic
487C22×D4C23×C6112yes—
488C23×C4D4×C6111yescharacteristic, complemented
489C23×C4C23×C6111yescharacteristic
490C23×C4C23×C6111yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C6111yescharacteristic, complemented
543C2×C4⋊C4D4×C6111yescharacteristic, complemented
544C2×C4⋊C4D4×C6112yescomplemented
545C2×C4⋊C4D4×C6111yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C6111yescharacteristic, complemented
562C2×C22⋊C4D4×C6112yescomplemented
563C2×C22⋊C4C23×C6111yescharacteristic
564C2×C22⋊C4C23×C6111yescharacteristic
565C2×C22⋊C4C23×C6112yes—
566C2×C22⋊C4C23×C6111yescharacteristic
567C2×C22⋊C4C23×C6112yes—
568C2×C22⋊C4C23×C6112yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C6111yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C6112yes—
590C24C2×D4×C6111yescharacteristic
591C24C24×C6111yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C6111yescharacteristic
633C22×C4C2×D4×C6112yes—
634C22×C4C2×D4×C6111yescharacteristic
635C22×C4C2×D4×C6112yes—
636C22×C4C2×D4×C6111yescharacteristic
637C22×C4C2×D4×C6112yes—
638C22×C4C2×D4×C6111yescharacteristic
639C22×C4C2×D4×C6111yescharacteristic
640C22×C4C2×D4×C6111yescharacteristic
641C22×C4C2×D4×C6111yescharacteristic
642C22×C4C2×D4×C6111yescharacteristic
643C22×C4C2×D4×C6111yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C6114yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23C22×D4×C6111yescharacteristic
727C23C22×D4×C6111yescharacteristic
728C23C22×D4×C6111yescharacteristic
729C23C2×#41×C6112yes—
730C23H(5,𝔽2)×C6112yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C6111yescharacteristic
787C2×C4#120×C6111yescharacteristic
788C2×C4#120×C6111yescharacteristic
789C2×C4#120×C6111yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C6111yescharacteristic
820C22C61×#53211yescharacteristic
821C22C61×#53511yescharacteristic
822C22C61×#54612yes—
823C22C61×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—82no—
837C4—81no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C61×#243111yescharacteristic
847C2C61×#302511yescharacteristic
848C2C61×#302611yescharacteristic
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×#2561C2semidirect
3. C61×#2539C2semidirect
4. C61×#2534C2semidirect
5. C61×#2022C2semidirect
6. C61×#2021C2semidirect
7. C61×#1996C2semidirect
8. C61×#1964C2semidirect
9. C61×#1890C2semidirect
10. C61×#1889C2semidirect
11. C4×#99×C61C2semidirect
57. C22×Q8×C61D4semidirect
60. C22×D4×C61D4semidirect
63. C23×C4×C61D4semidirect
117. C2×C4⋊C4×C61D4semidirect
118. C2×C4⋊C4×C61D4semidirect
119. C2×C4⋊C4×C61D4semidirect
120. C2×C4⋊C4×C61D4semidirect
136. C2×C22⋊C4×C61D4semidirect
137. C2×C22⋊C4×C61D4semidirect
146. C2×C42×C61D4semidirect
265. C22⋊C4×C61#41semidirect
365. #25587C61direct (N × H)
415. #3505C2×C61semidirect
416. #2561C2×C61semidirect
417. #2539C2×C61semidirect
418. #2534C2×C61semidirect
419. #2022C2×C61semidirect
420. #2021C2×C61semidirect
421. #1996C2×C61semidirect
422. #1964C2×C61semidirect
423. #1890C2×C61semidirect
424. #1889C2×C61semidirect
425. C4×#99C2×C61semidirect
479. C61#25587direct (N × H)
482. C22×Q8D4×C61semidirect
485. C22×D4D4×C61semidirect
488. C23×C4D4×C61semidirect
542. C2×C4⋊C4D4×C61semidirect
543. C2×C4⋊C4D4×C61semidirect
544. C2×C4⋊C4D4×C61semidirect
545. C2×C4⋊C4D4×C61semidirect
561. C2×C22⋊C4D4×C61semidirect
562. C2×C22⋊C4D4×C61semidirect
571. C2×C42D4×C61semidirect
690. 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×#25612
C61×#25392
C61×#25342
C61×#20222
C61×#20212
C61×#19962
C61×#19642
C61×#18902
C61×#18892
C4×#99×C612
#2558761