Finite Group Databasebeta

← C61×#14728 #29518161

Subgroups — C61×#14728 #29518161

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C61C211yesmaximal, characteristic
2C2×C61×#398C212yesmaximal, complemented
3C2×C61×#385C211yesmaximal, characteristic
4C2×C61×#385C211yesmaximal, characteristic
5C2×C61×#380C211yesmaximal, characteristic
6C61×#1444C212yesmaximal, complemented
7C61×#1442C212yesmaximal, complemented
8C61×#1441C212yesmaximal, complemented
9C61×C22⋊#95C211yesmaximal, characteristic
10C61×C22⋊#95C211yesmaximal, characteristic
11C61×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C61C2211yescharacteristic
13C24×C4×C61C2211yescharacteristic
14C24×C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61—24no—
16C22×C4⋊C4×C61—28no—
17C22×C4⋊C4×C61C2211yescharacteristic
18C22×C4⋊C4×C61C2212yes—
19C22×C4⋊C4×C61C2212yes—
20C22×C4⋊C4×C61C2212yes—
21C22×C4⋊C4×C61C2212yes—
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C22⋊C4×C61C2211yescharacteristic
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C61×#398—28no—
28C61×#385—24no—
29C61×#385—24no—
30C61×#380—24no—
31C2×#95×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C2×#95×C61C2212yes—
41C25×C61C2311yescharacteristic
42C23×C4×C61—22no—
43C23×C4×C61—22no—
44C23×C4×C61—24no—
45C23×C4×C61—24no—
46C23×C4×C61—22no—
47C23×C4×C61—22no—
48C23×C4×C61—22no—
49C23×C4×C61—24no—
50C23×C4×C61—24no—
51C23×C4×C61—22no—
52C23×C4×C61—22no—
53C23×C4×C61—42no—
54C23×C4×C61—42no—
55C23×C4×C61D414yes—
56C23×C4×C61Q814yes—
57C23×C4×C61C2311yescharacteristic
58C23×C4×C61C2312yes—
59C23×C4×C61C2311yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C23×C4×C61C2312yes—
62C23×C4×C61C2312yes—
63C23×C4×C61C2311yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C23×C4×C61C2312yes—
67C2×C4⋊C4×C61—232no—
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61—24no—
70C2×C4⋊C4×C61—24no—
71C2×C4⋊C4×C61—24no—
72C2×C4⋊C4×C61—24no—
73C2×C4⋊C4×C61—24no—
74C2×C4⋊C4×C61—24no—
75C2×C4⋊C4×C61—22no—
76C2×C4⋊C4×C61—22no—
77C2×C4⋊C4×C61—24no—
78C2×C4⋊C4×C61—24no—
79C2×C4⋊C4×C61—24no—
80C2×C4⋊C4×C61—42no—
81C2×C4⋊C4×C61—42no—
82C2×C4⋊C4×C61—42no—
83C2×C4⋊C4×C61D418yes—
84C2×C22⋊C4×C61—22no—
85C2×C22⋊C4×C61—22no—
86C2×C22⋊C4×C61—22no—
87C2×C22⋊C4×C61—22no—
88C2×C22⋊C4×C61—22no—
89C2×C22⋊C4×C61—22no—
90C2×C22⋊C4×C61—22no—
91C2×C22⋊C4×C61—22no—
92C2×C22⋊C4×C61—22no—
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61D414yes—
95C2×C22⋊C4×C61Q814yes—
96#95×C61—24no—
97#95×C61—22no—
98#95×C61—22no—
99#95×C61—24no—
100#95×C61—24no—
101#95×C61—24no—
102#95×C61—24no—
103#95×C61—24no—
104#95×C61—24no—
105#95×C61—42no—
106C24×C61—22no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—22no—
110C24×C61C2×D412yes—
111C24×C61C2×D412yes—
112C24×C61C2×Q812yes—
113C24×C61C2×Q812yes—
114C24×C61#4112yes—
115C24×C61#4112yes—
116C24×C61#4112yes—
117C24×C61C2411yescharacteristic
118C22×C4×C61—28no—
119C22×C4×C61—216no—
120C22×C4×C61—28no—
121C22×C4×C61—28no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—216no—
130C22×C4×C61—28no—
131C22×C4×C61—28no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—28no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—44no—
175C22×C4×C61—48no—
176C22×C4×C61—48no—
177C22×C4×C61—48no—
178C22×C4×C61—48no—
179C22×C4×C61—44no—
180C22×C4×C61—44no—
181C22×C4×C61C2×D414yes—
182C22×C4×C61C2×D412yes—
183C22×C4×C61C2×D414yes—
184C22×C4×C61C2×D412yes—
185C22×C4×C61C2×D414yes—
186C22×C4×C61C2×D414yes—
187C22×C4×C61C2×Q812yes—
188C22×C4×C61C2×Q812yes—
189C22×C4×C61C2×Q814yes—
190C22×C4×C61#4114yes—
191C4⋊C4×C61—216no—
192C4⋊C4×C61—216no—
193C4⋊C4×C61—48no—
194C4⋊C4×C61—48no—
195C4⋊C4×C61—44no—
196C4⋊C4×C61—44no—
197C22⋊C4×C61—28no—
198C22⋊C4×C61—28no—
199C22⋊C4×C61—44no—
200C22⋊C4×C61—44no—
201C23×C61—22no—
202C23×C61—24no—
203C23×C61—22no—
204C23×C61—24no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—24no—
208C23×C61—24no—
209C23×C61—24no—
210C23×C61—24no—
211C23×C61—24no—
212C23×C61—24no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—24no—
217C23×C61#12114yes—
218C23×C61C22⋊Q814yes—
219C23×C61C22⋊Q814yes—
220C23×C61#12314yes—
221C23×C61#12514yes—
222C23×C61#12514yes—
223C23×C61C4⋊Q814yes—
224C23×C61C22×D411yescharacteristic
225C23×C61C22×D412yes—
226C23×C61C22×D411yescharacteristic
227C23×C61C22×Q811yescharacteristic
228C23×C61C22×Q811yescharacteristic
229C23×C61C2×#4111yescharacteristic
230C23×C61C2×#4111yescharacteristic
231C23×C61C2×#4111yescharacteristic
232C23×C61C2×#4112yes—
233C23×C61H(5,𝔽2)12yes—
234C23×C612−1+412yes—
235C2×C4×C61—232no—
236C2×C4×C61—24no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—24no—
243C2×C4×C61—22no—
244C2×C4×C61—24no—
245C2×C4×C61—24no—
246C2×C4×C61—22no—
247C2×C4×C61—24no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—24no—
252C2×C4×C61—22no—
253C2×C4×C61—24no—
254C2×C4×C61—24no—
255C2×C4×C61—24no—
256C2×C4×C61—24no—
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—416no—
260C2×C4×C61—416no—
261C2×C4×C61—41no—
262C2×C4×C61—42no—
263C2×C4×C61—41no—
264C2×C4×C61—42no—
265C2×C4×C61—41no—
266C2×C4×C61—42no—
267C2×C4×C61—41no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—42no—
281C2×C4×C61—41no—
282C2×C4×C61—42no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61#12014yes—
295C2×C4×C61C22⋊Q818yes—
296#14728C6111yesmaximal, characteristic, direct product factor, Sylow
297C22×C61—24no—
298C22×C61—24no—
299C22×C61—24no—
300C22×C61—24no—
301C22×C61—24no—
302C22×C61—24no—
303C22×C61—28no—
304C22×C61—28no—
305C22×C61—28no—
306C22×C61—28no—
307C22×C61#39818yescomplemented
308C22×C61C2×#12011yescharacteristic
309C22×C61C2×#12111yescharacteristic
310C22×C61C2×C22⋊Q811yescharacteristic
311C22×C61C2×C22⋊Q811yescharacteristic
312C22×C61C2×C22⋊Q812yes—
313C22×C61C2×#12311yescharacteristic
314C22×C61#52511yescharacteristic
315C22×C61#52512yes—
316C22×C61C2×#12511yescharacteristic
317C22×C61C2×#12511yescharacteristic
318C22×C61C2×C4⋊Q811yescharacteristic
319C22×C61#53411yescharacteristic
320C22×C61#53611yescharacteristic
321C22×C61#53912yes—
322C22×C61#54412yes—
323C22×C61D4212yes—
324C22×C61#54612yes—
325C22×C61#54712yes—
326C22×C61#54812yes—
327C22×C61D4×Q812yes—
328C22×C61#55212yes—
329C22×C61#55312yes—
330C22×C61#55412yes—
331C4×C61—28no—
332C4×C61—24no—
333C4×C61—42no—
334C4×C61—42no—
335C4×C61—42no—
336C4×C61—44no—
337C4×C61—44no—
338C4×C61—81no—
339C4×C61—81no—
340C4×C61—82no—
341C23×C4⋊C4C2×C6111yescharacteristic
342C2×#398C2×C6112yescomplemented
343C2×#385C2×C6111yescharacteristic
344C2×#385C2×C6111yescharacteristic
345C2×#380C2×C6111yescharacteristic
346#1444C2×C6112yescomplemented
347#1442C2×C6112yescomplemented
348#1441C2×C6112yescomplemented
349C22⋊#95C2×C6111yescharacteristic
350C22⋊#95C2×C6111yescharacteristic
351C22⋊#95C2×C6111yescharacteristic
352C2×C61—28no—
353C2×C61C2×#39811yescharacteristic
354C2×C61#240911yescharacteristic
355C2×C61#241011yescharacteristic
356C2×C61#241311yescharacteristic
357C2×C61#244012yes—
358C2×C61#244212yes—
359C2×C61#244312yes—
360C2×C61#247312yes—
361C2×C61#257911yescharacteristic
362C2×C61#262711yescharacteristic
363C2×C61#284811yescharacteristic
364C24×C4C22×C6111yescharacteristic
365C24×C4C22×C6111yescharacteristic
366C24×C4C22×C6111yescharacteristic
367C22×C4⋊C4—24no—
368C22×C4⋊C4—28no—
369C22×C4⋊C4C22×C6111yescharacteristic
370C22×C4⋊C4C22×C6112yes—
371C22×C4⋊C4C22×C6112yes—
372C22×C4⋊C4C22×C6112yes—
373C22×C4⋊C4C22×C6112yes—
374C22×C4⋊C4C22×C6111yescharacteristic
375C22×C22⋊C4C22×C6111yescharacteristic
376C22×C22⋊C4C22×C6111yescharacteristic
377C22×C22⋊C4C22×C6111yescharacteristic
378C22×C22⋊C4C22×C6111yescharacteristic
379#398—28no—
380#385—24no—
381#385—24no—
382#380—24no—
383C2×#95C22×C6112yes—
384C2×#95C22×C6112yes—
385C2×#95C22×C6112yes—
386C2×#95C22×C6112yes—
387C2×#95C22×C6112yes—
388C2×#95C22×C6111yescharacteristic
389C2×#95C22×C6112yes—
390C2×#95C22×C6111yescharacteristic
391C2×#95C22×C6112yes—
392C2×#95C22×C6112yes—
393C61#1472811yescharacteristic, direct product factor, Sylow
394C25C23×C6111yescharacteristic
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4D4×C6114yes—
409C23×C4Q8×C6114yes—
410C23×C4C23×C6111yescharacteristic
411C23×C4C23×C6112yes—
412C23×C4C23×C6111yescharacteristic
413C23×C4C23×C6112yes—
414C23×C4C23×C6111yescharacteristic
415C23×C4C23×C6112yes—
416C23×C4C23×C6111yescharacteristic
417C23×C4C23×C6111yescharacteristic
418C23×C4C23×C6111yescharacteristic
419C23×C4C23×C6112yes—
420C2×C4⋊C4—232no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4D4×C6118yes—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4D4×C6114yes—
448C2×C22⋊C4Q8×C6114yes—
449#95—24no—
450#95—22no—
451#95—22no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—42no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24C2×D4×C6112yes—
464C24C2×D4×C6112yes—
465C24C2×Q8×C6112yes—
466C24C2×Q8×C6112yes—
467C24#41×C6112yes—
468C24#41×C6112yes—
469C24#41×C6112yes—
470C24C24×C6111yescharacteristic
471C22×C4—28no—
472C22×C4—216no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—216no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—28no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—44no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4C2×D4×C6114yes—
535C22×C4C2×D4×C6112yes—
536C22×C4C2×D4×C6114yes—
537C22×C4C2×D4×C6112yes—
538C22×C4C2×D4×C6114yes—
539C22×C4C2×D4×C6114yes—
540C22×C4C2×Q8×C6112yes—
541C22×C4C2×Q8×C6112yes—
542C22×C4C2×Q8×C6114yes—
543C22×C4#41×C6114yes—
544C4⋊C4—216no—
545C4⋊C4—216no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—44no—
549C4⋊C4—44no—
550C22⋊C4—28no—
551C22⋊C4—28no—
552C22⋊C4—44no—
553C22⋊C4—44no—
554C23—22no—
555C23—22no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—22no—
567C23—24no—
568C23—22no—
569C23—24no—
570C23#121×C6114yes—
571C23C22⋊Q8×C6114yes—
572C23C22⋊Q8×C6114yes—
573C23#123×C6114yes—
574C23#125×C6114yes—
575C23#125×C6114yes—
576C23C4⋊Q8×C6114yes—
577C23C22×D4×C6111yescharacteristic
578C23C22×D4×C6111yescharacteristic
579C23C22×D4×C6112yes—
580C23C22×Q8×C6111yescharacteristic
581C23C22×Q8×C6111yescharacteristic
582C23C2×#41×C6111yescharacteristic
583C23C2×#41×C6111yescharacteristic
584C23C2×#41×C6112yes—
585C23C2×#41×C6111yescharacteristic
586C23H(5,𝔽2)×C6112yes—
587C232−1+4×C6112yes—
588C2×C4—232no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—416no—
613C2×C4—416no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4#120×C6114yes—
648C2×C4C22⋊Q8×C6118yes—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—24no—
654C22—24no—
655C22—28no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22C61×#39818yescomplemented
660C22C2×#120×C6111yescharacteristic
661C22C2×#121×C6111yescharacteristic
662C22C2×C22⋊Q8×C6111yescharacteristic
663C22C2×C22⋊Q8×C6111yescharacteristic
664C22C2×C22⋊Q8×C6112yes—
665C22C2×#123×C6111yescharacteristic
666C22C61×#52511yescharacteristic
667C22C61×#52512yes—
668C22C2×#125×C6111yescharacteristic
669C22C2×#125×C6111yescharacteristic
670C22C2×C4⋊Q8×C6111yescharacteristic
671C22C61×#53411yescharacteristic
672C22C61×#53611yescharacteristic
673C22C61×#53912yes—
674C22C61×#54412yes—
675C22D42×C6112yes—
676C22C61×#54612yes—
677C22C61×#54712yes—
678C22C61×#54812yes—
679C22D4×Q8×C6112yes—
680C22C61×#55212yes—
681C22C61×#55312yes—
682C22C61×#55412yes—
683C4—28no—
684C4—24no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—44no—
689C4—44no—
690C4—81no—
691C4—81no—
692C4—82no—
693C2—28no—
694C2C2×C61×#39811yescharacteristic
695C2C61×#240911yescharacteristic
696C2C61×#241011yescharacteristic
697C2C61×#241311yescharacteristic
698C2C61×#244012yes—
699C2C61×#244212yes—
700C2C61×#244312yes—
701C2C61×#247312yes—
702C2C61×#257911yescharacteristic
703C2C61×#262711yescharacteristic
704C2C61×#284811yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#398C2semidirect
6. C61×#1444C2semidirect
7. C61×#1442C2semidirect
8. C61×#1441C2semidirect
296. #14728C61direct (N × H)
307. C22×C61#398semidirect
342. C2×#398C2×C61semidirect
346. #1444C2×C61semidirect
347. #1442C2×C61semidirect
348. #1441C2×C61semidirect
393. C61#14728direct (N × H)
659. C22C61×#398semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C612
C2×C61×#3982
C2×C61×#3852
C2×C61×#3802
C61×#14442
C61×#14422
C61×#14412
C61×C22⋊#952
#1472861