Finite Group Databasebeta

← C61×#15269 #29518702

Subgroups — C61×#15269 #29518702

Order 15616.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C61C211yesmaximal, characteristic
2C2×C61×#397C211yesmaximal, characteristic, complemented
3C2×C61×#394C211yesmaximal, characteristic
4C2×C61×#386C211yesmaximal, characteristic
5C2×C61×#385C211yesmaximal, characteristic, complemented
6C2×C61×#380C211yesmaximal, characteristic, complemented
7C61×#1444C211yesmaximal, characteristic, complemented
8C61×#1444C211yesmaximal, characteristic, complemented
9C61×#1442C211yesmaximal, characteristic, complemented
10C61×#1441C211yesmaximal, characteristic, complemented
11C61×#1440C211yesmaximal, characteristic, complemented
12C61×#1440C211yesmaximal, characteristic, complemented
13C61×#1439C211yesmaximal, characteristic, complemented
14C61×C22⋊#95C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C24×C4×C61C2211yescharacteristic
19C2×#123×C61—24no—
20C2×#123×C61—24no—
21C2×#123×C61—24no—
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C4⋊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
38C61×#397—24no—
39C61×#394—24no—
40C61×#386—24no—
41C61×#385—24no—
42C61×#380—24no—
43C2×#95×C61C2211yescharacteristic
44C2×#95×C61C2211yescharacteristic
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—41no—
66C22×D4×C61—41no—
67C22×D4×C61D414yes—
68C23×C4×C61—22no—
69C23×C4×C61—22no—
70C23×C4×C61—22no—
71C23×C4×C61—22no—
72C23×C4×C61—22no—
73C23×C4×C61—22no—
74C23×C4×C61—22no—
75C23×C4×C61—22no—
76C23×C4×C61—22no—
77C23×C4×C61—22no—
78C23×C4×C61—41no—
79C23×C4×C61—41no—
80C23×C4×C61—41no—
81C23×C4×C61—41no—
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95#123×C61—232no—
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—22no—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—41no—
110C2×C4⋊C4×C61—41no—
111C2×C4⋊C4×C61—41no—
112C2×C4⋊C4×C61—41no—
113C2×C4⋊C4×C61—41no—
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—22no—
137C2×C22⋊C4×C61—41no—
138C2×C22⋊C4×C61—41no—
139C2×C22⋊C4×C61—41no—
140C2×C22⋊C4×C61—41no—
141C2×C22⋊C4×C61D414yes—
142C2×C22⋊C4×C61D414yes—
143C2×C22⋊C4×C61D414yes—
144#95×C61—22no—
145#95×C61—22no—
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—41no—
158#95×C61—41no—
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×C61C2×D412yes—
185C24×C61C2×D412yes—
186C24×C61C2×D412yes—
187C24×C61C2×D412yes—
188C24×C61C2×D412yes—
189C24×C61#4112yes—
190C24×C61C2411yescharacteristic
191C2×D4×C61—28no—
192C2×D4×C61—28no—
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—28no—
203C22×C4×C61—28no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
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—21no—
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—21no—
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—44no—
281C22×C4×C61—44no—
282C22×C4×C61—44no—
283C22×C4×C61—44no—
284C22×C4×C61—44no—
285C22×C4×C61—44no—
286C22×C4×C61—44no—
287C22×C4×C61—44no—
288C22×C4×C61—44no—
289C22×C4×C61—44no—
290C22×C4×C61—44no—
291C22×C4×C61—44no—
292C22×C4×C61C2×D412yes—
293C22×C4×C61C2×D412yes—
294C22×C4×C61C2×D412yes—
295C22×C4×C61C2×D412yes—
296C22×C4×C61C2×D412yes—
297C22×C4×C61C2×D412yes—
298C22×C4×C61C2×D412yes—
299C22×C4×C61#4112yes—
300C22×C4×C61#4112yes—
301C22×C4×C61#4112yes—
302C22×C4×C61#4112yes—
303C4⋊C4×C61—28no—
304C4⋊C4×C61—28no—
305C4⋊C4×C61—44no—
306C4⋊C4×C61—44no—
307C4⋊C4×C61—44no—
308C4⋊C4×C61—44no—
309C22⋊C4×C61—28no—
310C22⋊C4×C61—28no—
311C22⋊C4×C61—28no—
312C22⋊C4×C61—28no—
313C22⋊C4×C61—44no—
314C22⋊C4×C61—44no—
315C22⋊C4×C61—44no—
316C22⋊C4×C61—44no—
317C22⋊C4×C61—44no—
318C22⋊C4×C61—44no—
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—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
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—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61#12014yes—
388C23×C61#12114yes—
389C23×C61C22×D411yescharacteristic
390C23×C61C22×D411yescharacteristic
391C23×C61C22×D411yescharacteristic
392C23×C61C22×D411yescharacteristic
393C23×C61C2×#4111yescharacteristic
394C23×C61C2×#4111yescharacteristic
395C23×C61C2×#4111yescharacteristic
396C23×C61C2×#4111yescharacteristic
397C23×C61C2×#4111yescharacteristic
398C23×C61H(5,𝔽2)11yescharacteristic
399C23×C61H(5,𝔽2)11yescharacteristic
400C23×C61H(5,𝔽2)11yescharacteristic
401C23×C612−1+411yescharacteristic
402C23×C612−1+411yescharacteristic
403C23×C612−1+411yescharacteristic
404D4×C61—416no—
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—416no—
436C2×C4×C61—416no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
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—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61#12314yescomplemented
498#15269C6111yesmaximal, characteristic, direct product factor, Sylow
499C22×C61—24no—
500C22×C61—24no—
501C22×C61—24no—
502C22×C61—24no—
503C22×C61—24no—
504C22×C61—24no—
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—42no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61—42no—
521C22×C61—42no—
522C22×C61—42no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61—42no—
529C22×C61C2×#12011yescharacteristic
530C22×C61C2×#12111yescharacteristic
531C22×C61C2×#12311yescharacteristic
532C22×C61#52511yescharacteristic
533C22×C61#52911yescharacteristic
534C22×C61#53211yescharacteristic
535C22×C61#53411yescharacteristic
536C22×C61#53611yescharacteristic
537C22×C61#53611yescharacteristic
538C22×C61#53711yescharacteristic
539C22×C61#53811yescharacteristic
540C22×C61#53911yescharacteristic
541C22×C61#53911yescharacteristic
542C22×C61#54211yescharacteristic
543C22×C61#54211yescharacteristic
544C22×C61D4211yescharacteristic
545C22×C61D4211yescharacteristic
546C22×C61#54611yescharacteristic
547C22×C61#54611yescharacteristic
548C22×C61#54611yescharacteristic
549C22×C61#54611yescharacteristic
550C22×C61#54611yescharacteristic
551C22×C61#54711yescharacteristic
552C22×C61#54711yescharacteristic
553C22×C61#54711yescharacteristic
554C22×C61#54711yescharacteristic
555C22×C61#54711yescharacteristic
556C22×C61#54711yescharacteristic
557C22×C61#54711yescharacteristic
558C22×C61#55111yescharacteristic
559C22×C61#55211yescharacteristic
560C22×C61#55211yescharacteristic
561C22×C61#55311yescharacteristic
562C22×C61#56211yescharacteristic
563C22×C61#56311yescharacteristic
564C4×C61—24no—
565C4×C61—42no—
566C4×C61—42no—
567C4×C61—42no—
568C4×C61—42no—
569C4×C61—42no—
570C4×C61—42no—
571C4×C61—42no—
572C4×C61—42no—
573C4×C61—81no—
574C4×C61—81no—
575C4×C61—81no—
576C4×C61—81no—
577C22×#123C2×C6111yescharacteristic
578C2×#397C2×C6111yescharacteristic, complemented
579C2×#394C2×C6111yescharacteristic
580C2×#386C2×C6111yescharacteristic
581C2×#385C2×C6111yescharacteristic, complemented
582C2×#380C2×C6111yescharacteristic, complemented
583#1444C2×C6111yescharacteristic, complemented
584#1444C2×C6111yescharacteristic, complemented
585#1442C2×C6111yescharacteristic, complemented
586#1441C2×C6111yescharacteristic, complemented
587#1440C2×C6111yescharacteristic, complemented
588#1440C2×C6111yescharacteristic, complemented
589#1439C2×C6111yescharacteristic, complemented
590C22⋊#95C2×C6111yescharacteristic, complemented
591C22⋊#95C2×C6111yescharacteristic, complemented
592C2×C61—44no—
593C2×C61—44no—
594C2×C61#240611yescharacteristic
595C2×C61#241011yescharacteristic
596C2×C61#241811yescharacteristic
597C2×C61#242211yescharacteristic
598C2×C61#242511yescharacteristic
599C2×C61#243011yescharacteristic
600C2×C61#247011yescharacteristic
601C2×C61#248611yescharacteristic
602C2×C61#255311yescharacteristic
603C2×C61#267211yescharacteristic
604C2×C61#268011yescharacteristic
605C2×C61#268711yescharacteristic
606C2×C61#269511yescharacteristic
607C2×C61#270811yescharacteristic
608C2×C61#271711yescharacteristic
609C23×D4C22×C6111yescharacteristic
610C24×C4C22×C6111yescharacteristic
611C24×C4C22×C6111yescharacteristic
612C2×#123—24no—
613C2×#123—24no—
614C2×#123—24no—
615C22×C4⋊C4C22×C6111yescharacteristic
616C22×C4⋊C4C22×C6111yescharacteristic
617C22×C4⋊C4C22×C6111yescharacteristic
618C22×C4⋊C4C22×C6111yescharacteristic
619C22×C4⋊C4C22×C6111yescharacteristic
620C22×C4⋊C4C22×C6111yescharacteristic
621C22×C22⋊C4C22×C6111yescharacteristic
622C22×C22⋊C4C22×C6111yescharacteristic
623C22×C22⋊C4C22×C6111yescharacteristic
624C22×C22⋊C4C22×C6111yescharacteristic
625C22×C22⋊C4C22×C6111yescharacteristic
626C22×C22⋊C4C22×C6111yescharacteristic
627C22×C22⋊C4C22×C6111yescharacteristic
628C22×C22⋊C4C22×C6111yescharacteristic
629C22×C22⋊C4C22×C6111yescharacteristic
630C22×C22⋊C4C22×C6111yescharacteristic
631#397—24no—
632#394—24no—
633#386—24no—
634#385—24no—
635#380—24no—
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
647C2×#95C22×C6111yescharacteristic
648C2×#95C22×C6111yescharacteristic
649C2×#95C22×C6111yescharacteristic
650C2×#95C22×C6111yescharacteristic
651C2×#95C22×C6111yescharacteristic
652C61#1526911yescharacteristic, direct product factor, Sylow
653C25C23×C6111yescharacteristic
654C25C23×C6111yescharacteristic
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—41no—
660C22×D4—41no—
661C22×D4D4×C6114yes—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—41no—
675C23×C4—41no—
676C23×C4C23×C6111yescharacteristic
677C23×C4C23×C6111yescharacteristic
678C23×C4C23×C6111yescharacteristic
679C23×C4C23×C6111yescharacteristic
680C23×C4C23×C6111yescharacteristic
681C23×C4C23×C6111yescharacteristic
682C23×C4C23×C6111yescharacteristic
683C23×C4C23×C6111yescharacteristic
684C23×C4C23×C6111yescharacteristic
685C23×C4C23×C6111yescharacteristic
686C23×C4C23×C6111yescharacteristic
687C23×C4C23×C6111yescharacteristic
688C23×C4C23×C6111yescharacteristic
689#123—232no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—41no—
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—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4D4×C6114yes—
736C2×C22⋊C4D4×C6114yes—
737C2×C22⋊C4D4×C6114yes—
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—22no—
749#95—22no—
750#95—22no—
751#95—41no—
752#95—41no—
753#95—41no—
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—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C2×D4×C6112yes—
779C24C2×D4×C6112yes—
780C24C2×D4×C6112yes—
781C24C2×D4×C6112yes—
782C24C2×D4×C6112yes—
783C24#41×C6112yes—
784C24C24×C6111yescharacteristic
785C2×D4—28no—
786C2×D4—28no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—28no—
797C22×C4—28no—
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—21no—
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—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4C2×D4×C6112yes—
887C22×C4C2×D4×C6112yes—
888C22×C4C2×D4×C6112yes—
889C22×C4C2×D4×C6112yes—
890C22×C4C2×D4×C6112yes—
891C22×C4C2×D4×C6112yes—
892C22×C4C2×D4×C6112yes—
893C22×C4#41×C6112yes—
894C22×C4#41×C6112yes—
895C22×C4#41×C6112yes—
896C22×C4#41×C6112yes—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
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—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
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—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23#120×C6114yes—
982C23#121×C6114yes—
983C23C22×D4×C6111yescharacteristic
984C23C22×D4×C6111yescharacteristic
985C23C22×D4×C6111yescharacteristic
986C23C22×D4×C6111yescharacteristic
987C23C2×#41×C6111yescharacteristic
988C23C2×#41×C6111yescharacteristic
989C23C2×#41×C6111yescharacteristic
990C23C2×#41×C6111yescharacteristic
991C23C2×#41×C6111yescharacteristic
992C23H(5,𝔽2)×C6111yescharacteristic
993C23H(5,𝔽2)×C6111yescharacteristic
994C23H(5,𝔽2)×C6111yescharacteristic
995C232−1+4×C6111yescharacteristic
996C232−1+4×C6111yescharacteristic
997C232−1+4×C6111yescharacteristic
998D4—416no—
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—416no—
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—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4#123×C6114yescomplemented
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22C2×#120×C6111yescharacteristic
1123C22C2×#121×C6111yescharacteristic
1124C22C2×#123×C6111yescharacteristic
1125C22C61×#52511yescharacteristic
1126C22C61×#52911yescharacteristic
1127C22C61×#53211yescharacteristic
1128C22C61×#53411yescharacteristic
1129C22C61×#53611yescharacteristic
1130C22C61×#53611yescharacteristic
1131C22C61×#53711yescharacteristic
1132C22C61×#53811yescharacteristic
1133C22C61×#53911yescharacteristic
1134C22C61×#53911yescharacteristic
1135C22C61×#54211yescharacteristic
1136C22C61×#54211yescharacteristic
1137C22D42×C6111yescharacteristic
1138C22D42×C6111yescharacteristic
1139C22C61×#54611yescharacteristic
1140C22C61×#54611yescharacteristic
1141C22C61×#54611yescharacteristic
1142C22C61×#54611yescharacteristic
1143C22C61×#54611yescharacteristic
1144C22C61×#54711yescharacteristic
1145C22C61×#54711yescharacteristic
1146C22C61×#54711yescharacteristic
1147C22C61×#54711yescharacteristic
1148C22C61×#54711yescharacteristic
1149C22C61×#54711yescharacteristic
1150C22C61×#54711yescharacteristic
1151C22C61×#55111yescharacteristic
1152C22C61×#55211yescharacteristic
1153C22C61×#55211yescharacteristic
1154C22C61×#55311yescharacteristic
1155C22C61×#56211yescharacteristic
1156C22C61×#56311yescharacteristic
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—44no—
1172C2C61×#240611yescharacteristic
1173C2C61×#241011yescharacteristic
1174C2C61×#241811yescharacteristic
1175C2C61×#242211yescharacteristic
1176C2C61×#242511yescharacteristic
1177C2C61×#243011yescharacteristic
1178C2C61×#247011yescharacteristic
1179C2C61×#248611yescharacteristic
1180C2C61×#255311yescharacteristic
1181C2C61×#267211yescharacteristic
1182C2C61×#268011yescharacteristic
1183C2C61×#268711yescharacteristic
1184C2C61×#269511yescharacteristic
1185C2C61×#270811yescharacteristic
1186C2C61×#271711yescharacteristic
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
2. C2×C61×#397C2semidirect
5. C2×C61×#385C2semidirect
6. C2×C61×#380C2semidirect
7. C61×#1444C2semidirect
8. C61×#1444C2semidirect
9. C61×#1442C2semidirect
10. C61×#1441C2semidirect
11. C61×#1440C2semidirect
12. C61×#1440C2semidirect
13. C61×#1439C2semidirect
14. C61×C22⋊#95C2semidirect
15. C61×C22⋊#95C2semidirect
497. C2×C4×C61#123semidirect
498. #15269C61direct (N × H)
578. C2×#397C2×C61semidirect
581. C2×#385C2×C61semidirect
582. C2×#380C2×C61semidirect
583. #1444C2×C61semidirect
584. #1444C2×C61semidirect
585. #1442C2×C61semidirect
586. #1441C2×C61semidirect
587. #1440C2×C61semidirect
588. #1440C2×C61semidirect
589. #1439C2×C61semidirect
590. C22⋊#95C2×C61semidirect
591. C22⋊#95C2×C61semidirect
652. C61#15269direct (N × H)
1091. 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×#3972
C2×C61×#3942
C2×C61×#3862
C2×C61×#3852
C2×C61×#3802
C61×#14442
C61×#14422
C61×#14412
C61×#14402
C61×#14392
C61×C22⋊#952
#1526961