Finite Group Databasebeta

← C61×#14761 #29518194

Subgroups — C61×#14761 #29518194

Order 15616.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C61C211yesmaximal, characteristic
2C2×C61×#394C211yesmaximal, characteristic
3C2×C61×#389C211yesmaximal, characteristic, complemented
4C2×C61×#388C211yesmaximal, characteristic, complemented
5C2×C61×#385C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C61×#1444C211yesmaximal, characteristic, complemented
8C61×#1442C211yesmaximal, characteristic, complemented
9C61×#1440C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C61×#1439C211yesmaximal, characteristic, complemented
13C61×#1438C211yesmaximal, characteristic
14C61×#1437C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C2×#123×C61—24no—
19C2×#123×C61—24no—
20C2×#123×C61—24no—
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C61×#394—24no—
41C61×#389—24no—
42C61×#388—24no—
43C61×#385—24no—
44C4×C22⋊C4×C61—24no—
45C2×#95×C61C2211yescharacteristic
46C2×#95×C61C2211yescharacteristic
47C2×#95×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C25×C61C2311yescharacteristic
60C25×C61C2311yescharacteristic
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—22no—
65C22×D4×C61—22no—
66C22×D4×C61—41no—
67C22×D4×C61—41no—
68C23×C4×C61—22no—
69C23×C4×C61—22no—
70C23×C4×C61—22no—
71C23×C4×C61—22no—
72C23×C4×C61—41no—
73C23×C4×C61—41no—
74C23×C4×C61D414yes—
75C23×C4×C61C2311yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88#123×C61—232no—
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61—41no—
104C2×C4⋊C4×C61—41no—
105C2×C4⋊C4×C61—41no—
106C2×C4⋊C4×C61D414yes—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—22no—
123C2×C22⋊C4×C61—22no—
124C2×C22⋊C4×C61—22no—
125C2×C22⋊C4×C61—22no—
126C2×C22⋊C4×C61—22no—
127C2×C22⋊C4×C61—22no—
128C2×C22⋊C4×C61—22no—
129C2×C22⋊C4×C61—22no—
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—22no—
132C2×C22⋊C4×C61—22no—
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61—22no—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—41no—
137C2×C22⋊C4×C61—41no—
138C2×C22⋊C4×C61D414yes—
139C2×C22⋊C4×C61D414yes—
140C2×C42×C61—22no—
141C2×C42×C61—22no—
142C2×C42×C61—22no—
143C2×C42×C61—22no—
144C2×C42×C61—41no—
145C2×C42×C61—41no—
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—22no—
149#95×C61—22no—
150#95×C61—22no—
151#95×C61—22no—
152#95×C61—22no—
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—22no—
158#95×C61—22no—
159#95×C61—41no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61C2×D412yes—
187C24×C61C2×D412yes—
188C24×C61C2×D412yes—
189C24×C61#4112yes—
190C24×C61C2411yescharacteristic
191C2×D4×C61—28no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—44no—
195C2×D4×C61—44no—
196C2×D4×C61—44no—
197C2×D4×C61—44no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—28no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—28no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—44no—
277C22×C4×C61—44no—
278C22×C4×C61—44no—
279C22×C4×C61—44no—
280C22×C4×C61—44no—
281C22×C4×C61C2×D412yes—
282C22×C4×C61C2×D412yes—
283C22×C4×C61C2×D412yes—
284C22×C4×C61C2×D412yes—
285C22×C4×C61C2×D412yes—
286C22×C4×C61C2×D412yes—
287C22×C4×C61C2×D412yes—
288C22×C4×C61C2×D412yes—
289C22×C4×C61C2×D412yes—
290C22×C4×C61#4112yes—
291C22×C4×C61#4112yes—
292C22×C4×C61#4112yes—
293C22×C4×C61#4112yes—
294C22×C4×C61#4112yes—
295C22×C4×C61#4112yes—
296C4⋊C4×C61—28no—
297C4⋊C4×C61—28no—
298C4⋊C4×C61—28no—
299C4⋊C4×C61—44no—
300C4⋊C4×C61—44no—
301C4⋊C4×C61—44no—
302C22⋊C4×C61—28no—
303C22⋊C4×C61—28no—
304C22⋊C4×C61—28no—
305C22⋊C4×C61—28no—
306C22⋊C4×C61—28no—
307C22⋊C4×C61—28no—
308C22⋊C4×C61—28no—
309C22⋊C4×C61—44no—
310C22⋊C4×C61—44no—
311C22⋊C4×C61—44no—
312C22⋊C4×C61—44no—
313C42×C61—44no—
314C42×C61—44no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61#12114yes—
385C23×C61C22×D411yescharacteristic
386C23×C61C22×D411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C23×C61C22×D411yescharacteristic
389C23×C61C2×#4111yescharacteristic
390C23×C61C2×#4111yescharacteristic
391C23×C61C2×#4111yescharacteristic
392C23×C61C2×#4111yescharacteristic
393C23×C61C2×#4111yescharacteristic
394C23×C61C2×#4111yescharacteristic
395C23×C61C2×#4111yescharacteristic
396C23×C61H(5,𝔽2)11yescharacteristic
397C23×C61H(5,𝔽2)11yescharacteristic
398C23×C612−1+411yescharacteristic
399C23×C612−1+411yescharacteristic
400D4×C61—416no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—416no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61—41no—
479C2×C4×C61—41no—
480C2×C4×C61—41no—
481C2×C4×C61—41no—
482C2×C4×C61—41no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61#12014yes—
492C2×C4×C61#12314yescomplemented
493#14761C6111yesmaximal, characteristic, direct product factor, Sylow
494C22×C61—24no—
495C22×C61—24no—
496C22×C61—24no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—42no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—42no—
516C22×C61—81no—
517C22×C61—81no—
518C22×C61—81no—
519C22×C61—81no—
520C22×C61—81no—
521C22×C61—81no—
522C22×C61—81no—
523C22×C61—81no—
524C22×C61C2×#12011yescharacteristic
525C22×C61C2×#12111yescharacteristic
526C22×C61C2×#12311yescharacteristic
527C22×C61#52511yescharacteristic
528C22×C61#52511yescharacteristic
529C22×C61#52511yescharacteristic
530C22×C61#52511yescharacteristic
531C22×C61#52911yescharacteristic
532C22×C61#52911yescharacteristic
533C22×C61#53211yescharacteristic
534C22×C61#53211yescharacteristic
535C22×C61#53211yescharacteristic
536C22×C61#53211yescharacteristic
537C22×C61#53411yescharacteristic
538C22×C61#53611yescharacteristic
539C22×C61#53911yescharacteristic
540C22×C61#53911yescharacteristic
541C22×C61#54211yescharacteristic
542C22×C61#54211yescharacteristic
543C22×C61D4211yescharacteristic
544C22×C61D4211yescharacteristic
545C22×C61#54611yescharacteristic
546C22×C61#54611yescharacteristic
547C22×C61#54711yescharacteristic
548C22×C61#54711yescharacteristic
549C22×C61#54711yescharacteristic
550C22×C61#54711yescharacteristic
551C22×C61#54811yescharacteristic
552C22×C61#54811yescharacteristic
553C22×C61#55111yescharacteristic
554C22×C61#55211yescharacteristic
555C22×C61#55211yescharacteristic
556C22×C61#55311yescharacteristic
557C22×C61#55311yescharacteristic
558C22×C61#55911yescharacteristic
559C4×C61—24no—
560C4×C61—24no—
561C4×C61—42no—
562C4×C61—42no—
563C4×C61—42no—
564C4×C61—42no—
565C4×C61—42no—
566C4×C61—42no—
567C4×C61—42no—
568C4×C61—42no—
569C4×C61—42no—
570C4×C61—81no—
571C4×C61—81no—
572C22×#123C2×C6111yescharacteristic
573C2×#394C2×C6111yescharacteristic
574C2×#389C2×C6111yescharacteristic, complemented
575C2×#388C2×C6111yescharacteristic, complemented
576C2×#385C2×C6111yescharacteristic, complemented
577C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
578#1444C2×C6111yescharacteristic, complemented
579#1442C2×C6111yescharacteristic, complemented
580#1440C2×C6111yescharacteristic, complemented
581#1439C2×C6111yescharacteristic, complemented
582#1439C2×C6111yescharacteristic, complemented
583#1439C2×C6111yescharacteristic, complemented
584#1438C2×C6111yescharacteristic
585#1437C2×C6111yescharacteristic, complemented
586#1436C2×C6111yescharacteristic, complemented
587C2×C61—44no—
588C2×C61—82no—
589C2×C61#238811yescharacteristic
590C2×C61#241011yescharacteristic
591C2×C61#241311yescharacteristic
592C2×C61#242211yescharacteristic
593C2×C61#243211yescharacteristic
594C2×C61#244311yescharacteristic
595C2×C61#245511yescharacteristic
596C2×C61#245811yescharacteristic
597C2×C61#246111yescharacteristic
598C2×C61#247011yescharacteristic
599C2×C61#255311yescharacteristic
600C2×C61#255811yescharacteristic
601C2×C61#260211yescharacteristic
602C2×C61#266311yescharacteristic
603C2×C61#285411yescharacteristic
604C23×D4C22×C6111yescharacteristic
605C24×C4C22×C6111yescharacteristic
606C2×#123—24no—
607C2×#123—24no—
608C2×#123—24no—
609C22×C4⋊C4C22×C6111yescharacteristic
610C22×C4⋊C4C22×C6111yescharacteristic
611C22×C4⋊C4C22×C6111yescharacteristic
612C22×C4⋊C4C22×C6111yescharacteristic
613C22×C4⋊C4C22×C6111yescharacteristic
614C22×C4⋊C4C22×C6111yescharacteristic
615C22×C22⋊C4C22×C6111yescharacteristic
616C22×C22⋊C4C22×C6111yescharacteristic
617C22×C22⋊C4C22×C6111yescharacteristic
618C22×C22⋊C4C22×C6111yescharacteristic
619C22×C22⋊C4C22×C6111yescharacteristic
620C22×C22⋊C4C22×C6111yescharacteristic
621C22×C22⋊C4C22×C6111yescharacteristic
622C22×C22⋊C4C22×C6111yescharacteristic
623C22×C22⋊C4C22×C6111yescharacteristic
624C22×C22⋊C4C22×C6111yescharacteristic
625C22×C22⋊C4C22×C6111yescharacteristic
626C22×C42C22×C6111yescharacteristic
627C22×C42C22×C6111yescharacteristic
628#394—24no—
629#389—24no—
630#388—24no—
631#385—24no—
632C4×C22⋊C4—24no—
633C2×#95C22×C6111yescharacteristic
634C2×#95C22×C6111yescharacteristic
635C2×#95C22×C6111yescharacteristic
636C2×#95C22×C6111yescharacteristic
637C2×#95C22×C6111yescharacteristic
638C2×#95C22×C6111yescharacteristic
639C2×#95C22×C6111yescharacteristic
640C2×#95C22×C6111yescharacteristic
641C2×#95C22×C6111yescharacteristic
642C2×#95C22×C6111yescharacteristic
643C2×#95C22×C6111yescharacteristic
644C2×#95C22×C6111yescharacteristic
645C2×#95C22×C6111yescharacteristic
646C2×#95C22×C6111yescharacteristic
647C61#1476111yescharacteristic, direct product factor, Sylow
648C25C23×C6111yescharacteristic
649C25C23×C6111yescharacteristic
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—41no—
656C22×D4—41no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—41no—
662C23×C4—41no—
663C23×C4D4×C6114yes—
664C23×C4C23×C6111yescharacteristic
665C23×C4C23×C6111yescharacteristic
666C23×C4C23×C6111yescharacteristic
667C23×C4C23×C6111yescharacteristic
668C23×C4C23×C6111yescharacteristic
669C23×C4C23×C6111yescharacteristic
670C23×C4C23×C6111yescharacteristic
671C23×C4C23×C6111yescharacteristic
672C23×C4C23×C6111yescharacteristic
673C23×C4C23×C6111yescharacteristic
674C23×C4C23×C6111yescharacteristic
675C23×C4C23×C6111yescharacteristic
676C23×C4C23×C6111yescharacteristic
677#123—232no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4D4×C6114yes—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4D4×C6114yes—
728C2×C22⋊C4D4×C6114yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—41no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—41no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C2×D4×C6112yes—
776C24C2×D4×C6112yes—
777C24C2×D4×C6112yes—
778C24#41×C6112yes—
779C24C24×C6111yescharacteristic
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—28no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—28no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4C2×D4×C6112yes—
871C22×C4C2×D4×C6112yes—
872C22×C4C2×D4×C6112yes—
873C22×C4C2×D4×C6112yes—
874C22×C4C2×D4×C6112yes—
875C22×C4C2×D4×C6112yes—
876C22×C4C2×D4×C6112yes—
877C22×C4C2×D4×C6112yes—
878C22×C4C2×D4×C6112yes—
879C22×C4#41×C6112yes—
880C22×C4#41×C6112yes—
881C22×C4#41×C6112yes—
882C22×C4#41×C6112yes—
883C22×C4#41×C6112yes—
884C22×C4#41×C6112yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C42—44no—
903C42—44no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23#121×C6114yes—
974C23C22×D4×C6111yescharacteristic
975C23C22×D4×C6111yescharacteristic
976C23C22×D4×C6111yescharacteristic
977C23C22×D4×C6111yescharacteristic
978C23C2×#41×C6111yescharacteristic
979C23C2×#41×C6111yescharacteristic
980C23C2×#41×C6111yescharacteristic
981C23C2×#41×C6111yescharacteristic
982C23C2×#41×C6111yescharacteristic
983C23C2×#41×C6111yescharacteristic
984C23C2×#41×C6111yescharacteristic
985C23H(5,𝔽2)×C6111yescharacteristic
986C23H(5,𝔽2)×C6111yescharacteristic
987C232−1+4×C6111yescharacteristic
988C232−1+4×C6111yescharacteristic
989D4—416no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—416no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4#120×C6114yes—
1081C2×C4#123×C6114yescomplemented
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×#120×C6111yescharacteristic
1113C22C2×#121×C6111yescharacteristic
1114C22C2×#123×C6111yescharacteristic
1115C22C61×#52511yescharacteristic
1116C22C61×#52511yescharacteristic
1117C22C61×#52511yescharacteristic
1118C22C61×#52511yescharacteristic
1119C22C61×#52911yescharacteristic
1120C22C61×#52911yescharacteristic
1121C22C61×#53211yescharacteristic
1122C22C61×#53211yescharacteristic
1123C22C61×#53211yescharacteristic
1124C22C61×#53211yescharacteristic
1125C22C61×#53411yescharacteristic
1126C22C61×#53611yescharacteristic
1127C22C61×#53911yescharacteristic
1128C22C61×#53911yescharacteristic
1129C22C61×#54211yescharacteristic
1130C22C61×#54211yescharacteristic
1131C22D42×C6111yescharacteristic
1132C22D42×C6111yescharacteristic
1133C22C61×#54611yescharacteristic
1134C22C61×#54611yescharacteristic
1135C22C61×#54711yescharacteristic
1136C22C61×#54711yescharacteristic
1137C22C61×#54711yescharacteristic
1138C22C61×#54711yescharacteristic
1139C22C61×#54811yescharacteristic
1140C22C61×#54811yescharacteristic
1141C22C61×#55111yescharacteristic
1142C22C61×#55211yescharacteristic
1143C22C61×#55211yescharacteristic
1144C22C61×#55311yescharacteristic
1145C22C61×#55311yescharacteristic
1146C22C61×#55911yescharacteristic
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C2—44no—
1161C2—82no—
1162C2C61×#238811yescharacteristic
1163C2C61×#241011yescharacteristic
1164C2C61×#241311yescharacteristic
1165C2C61×#242211yescharacteristic
1166C2C61×#243211yescharacteristic
1167C2C61×#244311yescharacteristic
1168C2C61×#245511yescharacteristic
1169C2C61×#245811yescharacteristic
1170C2C61×#246111yescharacteristic
1171C2C61×#247011yescharacteristic
1172C2C61×#255311yescharacteristic
1173C2C61×#255811yescharacteristic
1174C2C61×#260211yescharacteristic
1175C2C61×#266311yescharacteristic
1176C2C61×#285411yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C61×#389C2semidirect
4. C2×C61×#388C2semidirect
5. C2×C61×#385C2semidirect
6. C2×C4×C22⋊C4×C61C2semidirect
7. C61×#1444C2semidirect
8. C61×#1442C2semidirect
9. C61×#1440C2semidirect
10. C61×#1439C2semidirect
11. C61×#1439C2semidirect
12. C61×#1439C2semidirect
14. C61×#1437C2semidirect
15. C61×#1436C2semidirect
492. C2×C4×C61#123semidirect
493. #14761C61direct (N × H)
574. C2×#389C2×C61semidirect
575. C2×#388C2×C61semidirect
576. C2×#385C2×C61semidirect
577. C2×C4×C22⋊C4C2×C61semidirect
578. #1444C2×C61semidirect
579. #1442C2×C61semidirect
580. #1440C2×C61semidirect
581. #1439C2×C61semidirect
582. #1439C2×C61semidirect
583. #1439C2×C61semidirect
585. #1437C2×C61semidirect
586. #1436C2×C61semidirect
647. C61#14761direct (N × H)
1081. C2×C4#123×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C612
C2×C61×#3942
C2×C61×#3892
C2×C61×#3882
C2×C61×#3852
C2×C4×C22⋊C4×C612
C61×#14442
C61×#14422
C61×#14402
C61×#14392
C61×#14382
C61×#14372
C61×#14362
#1476161