Finite Group Databasebeta

← C61×#14534 #29517967

Subgroups — C61×#14534 #29517967

Order 15616.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#392C211yesmaximal, characteristic
2C2×C61×#390C211yesmaximal, characteristic, complemented
3C2×C61×#390C211yesmaximal, characteristic, complemented
4C2×C61×#388C211yesmaximal, characteristic, complemented
5C2×C61×#386C211yesmaximal, characteristic, complemented
6C2×C61×#386C211yesmaximal, characteristic, complemented
7C2×C61×#385C211yesmaximal, characteristic, complemented
8C61×#1440C211yesmaximal, characteristic, complemented
9C61×#1439C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic, complemented
11C61×#1438C211yesmaximal, characteristic, complemented
12C61×#1438C211yesmaximal, characteristic, complemented
13C61×#1437C211yesmaximal, characteristic, complemented
14C61×#1436C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C24×C4×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2211yescharacteristic
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C22⋊C4×C61C2211yescharacteristic
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊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×C42×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C61×#392C418yescomplemented
40C61×#390—24no—
41C61×#390—24no—
42C61×#388—24no—
43C61×#386—24no—
44C61×#386—24no—
45C61×#385—24no—
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
58C25×C61C2311yescharacteristic
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—22no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—41no—
70C22×D4×C61—41no—
71C22×D4×C61—41no—
72C22×D4×C61—41no—
73C22×D4×C61—41no—
74C22×D4×C61—41no—
75C22×D4×C61—41no—
76C22×D4×C61—41no—
77C22×D4×C61—41no—
78C22×D4×C61—41no—
79C22×D4×C61C2×C414yes—
80C22×D4×C61C2×C414yes—
81C22×D4×C61C2×C414yescomplemented
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61—41no—
86C23×C4×C61—41no—
87C23×C4×C61—41no—
88C23×C4×C61—41no—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—41no—
106C2×C4⋊C4×C61—41no—
107C2×C4⋊C4×C61—41no—
108C2×C4⋊C4×C61—41no—
109C2×C4⋊C4×C61D414yescomplemented
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—41no—
131C2×C22⋊C4×C61—41no—
132C2×C22⋊C4×C61—41no—
133C2×C22⋊C4×C61—41no—
134C2×C22⋊C4×C61—41no—
135C2×C22⋊C4×C61—41no—
136C2×C22⋊C4×C61—41no—
137C2×C22⋊C4×C61—41no—
138C2×C22⋊C4×C61—41no—
139C2×C22⋊C4×C61—41no—
140C2×C22⋊C4×C61—41no—
141C2×C22⋊C4×C61—41no—
142C2×C22⋊C4×C61—41no—
143C2×C22⋊C4×C61—41no—
144C2×C22⋊C4×C61—41no—
145C2×C22⋊C4×C61—41no—
146C2×C22⋊C4×C61—41no—
147C2×C22⋊C4×C61—41no—
148C2×C22⋊C4×C61C2×C414yes—
149C2×C22⋊C4×C61C2×C414yescomplemented
150C2×C22⋊C4×C61C2×C414yescomplemented
151C2×C22⋊C4×C61D414yescomplemented
152C2×C42×C61—22no—
153C2×C42×C61—22no—
154C2×C42×C61—22no—
155C2×C42×C61—41no—
156C2×C42×C61—41no—
157C2×C42×C61—41no—
158#95×C61—22no—
159#95×C61—22no—
160#95×C61—22no—
161#95×C61—22no—
162#95×C61—22no—
163#95×C61—22no—
164#95×C61—22no—
165#95×C61—41no—
166#95×C61—41no—
167#95×C61—41no—
168#95×C61C2×C414yescomplemented
169#95×C61D414yescomplemented
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×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—21no—
202C24×C61—21no—
203C24×C61—21no—
204C24×C61—21no—
205C24×C61—21no—
206C24×C61—21no—
207C24×C61—21no—
208C24×C61—21no—
209C24×C61—21no—
210C24×C61C22×C412yes—
211C24×C61C22×C412yes—
212C24×C61C22×C412yes—
213C24×C61C2×D412yes—
214C24×C61#4112yes—
215C24×C61C2411yescharacteristic
216C2×D4×C61—28no—
217C2×D4×C61—28no—
218C2×D4×C61—28no—
219C2×D4×C61—28no—
220C2×D4×C61—44no—
221C2×D4×C61—44no—
222C2×D4×C61—44no—
223C2×D4×C61—44no—
224C2×D4×C61—44no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
227C2×D4×C61—44no—
228C2×D4×C61—44no—
229C2×D4×C61—44no—
230C2×D4×C61—44no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
236C2×D4×C61—44no—
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—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—21no—
284C22×C4×C61—21no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—21no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61—21no—
291C22×C4×C61—21no—
292C22×C4×C61—21no—
293C22×C4×C61—21no—
294C22×C4×C61—21no—
295C22×C4×C61—21no—
296C22×C4×C61—21no—
297C22×C4×C61—21no—
298C22×C4×C61—21no—
299C22×C4×C61—21no—
300C22×C4×C61—21no—
301C22×C4×C61—21no—
302C22×C4×C61—21no—
303C22×C4×C61—21no—
304C22×C4×C61—21no—
305C22×C4×C61—21no—
306C22×C4×C61—21no—
307C22×C4×C61—44no—
308C22×C4×C61—44no—
309C22×C4×C61—44no—
310C22×C4×C61—44no—
311C22×C4×C61—44no—
312C22×C4×C61—44no—
313C22×C4×C61—44no—
314C22×C4×C61C22×C412yes—
315C22×C4×C61C22×C412yes—
316C22×C4×C61C22×C412yes—
317C22×C4×C61C22×C412yes—
318C22×C4×C61C2×D412yes—
319C22×C4×C61C2×D412yes—
320C22×C4×C61C2×D412yes—
321C22×C4×C61C2×D412yes—
322C22×C4×C61C2×D412yes—
323C22×C4×C61C2×D412yes—
324C22×C4×C61C2×D412yes—
325C22×C4×C61C2×D412yes—
326C22×C4×C61#4112yes—
327C22×C4×C61#4112yes—
328C4⋊C4×C61—44no—
329C4⋊C4×C61—44no—
330C4⋊C4×C61—44no—
331C22⋊C4×C61—28no—
332C22⋊C4×C61—28no—
333C22⋊C4×C61—44no—
334C22⋊C4×C61—44no—
335C22⋊C4×C61—44no—
336C22⋊C4×C61—44no—
337C22⋊C4×C61—44no—
338C22⋊C4×C61—44no—
339C22⋊C4×C61—44no—
340C22⋊C4×C61—44no—
341C22⋊C4×C61—44no—
342C22⋊C4×C61—44no—
343C22⋊C4×C61—44no—
344C22⋊C4×C61—44no—
345C42×C61—44no—
346C42×C61—44no—
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—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—22no—
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—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—41no—
414C23×C61—41no—
415C23×C61—41no—
416C23×C61—41no—
417C23×C61—41no—
418C23×C61—41no—
419C23×C61—41no—
420C23×C61—41no—
421C23×C61—41no—
422C23×C61—41no—
423C23×C61—41no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—41no—
438C23×C61—41no—
439C23×C61—41no—
440C23×C61—41no—
441C23×C61—41no—
442C23×C61—41no—
443C23×C61—41no—
444C23×C61—41no—
445C23×C61—41no—
446C23×C61—41no—
447C23×C61—41no—
448C23×C61—41no—
449C23×C61—41no—
450C23×C61—41no—
451C23×C61C4×D414yes—
452C23×C61C23×C411yescharacteristic
453C23×C61C22×D411yescharacteristic
454C23×C61C22×D411yescharacteristic
455C23×C61C22×D411yescharacteristic
456C23×C61C2×#4111yescharacteristic
457C23×C61C2×#4111yescharacteristic
458C23×C61C2×#4111yescharacteristic
459C23×C61H(5,𝔽2)11yescharacteristic
460C23×C61H(5,𝔽2)11yescharacteristic
461C23×C61H(5,𝔽2)11yescharacteristic
462C23×C61H(5,𝔽2)11yescharacteristic
463C23×C61H(5,𝔽2)11yescharacteristic
464C23×C61H(5,𝔽2)11yescharacteristic
465C23×C61H(5,𝔽2)11yescharacteristic
466C23×C612−1+411yescharacteristic
467D4×C61—416no—
468D4×C61—416no—
469D4×C61—416no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—22no—
477C2×C4×C61—22no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—22no—
490C2×C4×C61—22no—
491C2×C4×C61—22no—
492C2×C4×C61—22no—
493C2×C4×C61—22no—
494C2×C4×C61—22no—
495C2×C4×C61—22no—
496C2×C4×C61—22no—
497C2×C4×C61—22no—
498C2×C4×C61—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—22no—
505C2×C4×C61—22no—
506C2×C4×C61—416no—
507C2×C4×C61—41no—
508C2×C4×C61—41no—
509C2×C4×C61—41no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61—41no—
514C2×C4×C61—41no—
515C2×C4×C61—41no—
516C2×C4×C61—41no—
517C2×C4×C61—41no—
518C2×C4×C61—41no—
519C2×C4×C61—41no—
520C2×C4×C61—41no—
521C2×C4×C61—41no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
524C2×C4×C61—41no—
525C2×C4×C61—41no—
526C2×C4×C61—41no—
527C2×C4×C61—41no—
528C2×C4×C61—41no—
529C2×C4×C61—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61—41no—
533C2×C4×C61—41no—
534C2×C4×C61—41no—
535C2×C4×C61—41no—
536C2×C4×C61—41no—
537C2×C4×C61—41no—
538C2×C4×C61—41no—
539C2×C4×C61—41no—
540C2×C4×C61—41no—
541C2×C4×C61—41no—
542C2×C4×C61—41no—
543C2×C4×C61—41no—
544C2×C4×C61—41no—
545C2×C4×C61—41no—
546C2×C4×C61—41no—
547C2×C4×C61—41no—
548C2×C4×C61—41no—
549C2×C4×C61—41no—
550C2×C4×C61—41no—
551C2×C4×C61—41no—
552C2×C4×C61—41no—
553C2×C4×C61C4×D414yes—
554C2×C4×C61C4×D414yes—
555#14534C6111yesmaximal, characteristic, direct product factor, Sylow
556C22×C61—24no—
557C22×C61—24no—
558C22×C61—24no—
559C22×C61—42no—
560C22×C61—42no—
561C22×C61—42no—
562C22×C61—42no—
563C22×C61—42no—
564C22×C61—42no—
565C22×C61—42no—
566C22×C61—42no—
567C22×C61—42no—
568C22×C61—42no—
569C22×C61—42no—
570C22×C61—42no—
571C22×C61—42no—
572C22×C61—42no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—42no—
580C22×C61—42no—
581C22×C61—42no—
582C22×C61—42no—
583C22×C61—42no—
584C22×C61—42no—
585C22×C61—81no—
586C22×C61—81no—
587C22×C61—81no—
588C22×C61—81no—
589C22×C61—81no—
590C22×C61—81no—
591C22×C61—81no—
592C22×C61—81no—
593C22×C61—81no—
594C22×C61—81no—
595C22×C61—81no—
596C22×C61—81no—
597C22×C61—81no—
598C22×C61—81no—
599C22×C61—81no—
600C22×C61—81no—
601C22×C61C2×C4×D411yescharacteristic
602C22×C61C2×C4×D411yescharacteristic
603C22×C61C2×C4×D411yescharacteristic
604C22×C61#51811yescharacteristic
605C22×C61#51811yescharacteristic
606C22×C61#51811yescharacteristic
607C22×C61#52011yescharacteristic
608C22×C61#53411yescharacteristic
609C22×C61#53411yescharacteristic
610C22×C61#53511yescharacteristic
611C22×C61#53511yescharacteristic
612C22×C61#53511yescharacteristic
613C22×C61#53711yescharacteristic
614C22×C61#53811yescharacteristic
615C22×C61#53811yescharacteristic
616C22×C61#53811yescharacteristic
617C22×C61#53811yescharacteristic
618C22×C61#54011yescharacteristic
619C22×C61#54211yescharacteristic
620C22×C61D4211yescharacteristic
621C22×C61D4211yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61#54611yescharacteristic
624C22×C61#54611yescharacteristic
625C22×C61#54711yescharacteristic
626C22×C61#54811yescharacteristic
627C22×C61#55011yescharacteristic
628C22×C61#55011yescharacteristic
629C22×C61#55111yescharacteristic
630C22×C61#55311yescharacteristic
631C22×C61#55911yescharacteristic
632C22×C61#56011yescharacteristic
633C22×C61#56011yescharacteristic
634C22×C61#56211yescharacteristic
635C22×C61#56211yescharacteristic
636C4×C61—24no—
637C4×C61—24no—
638C4×C61—42no—
639C4×C61—42no—
640C4×C61—42no—
641C4×C61—42no—
642C4×C61—42no—
643C4×C61—42no—
644C4×C61—42no—
645C4×C61—42no—
646C4×C61—81no—
647C4×C61—81no—
648C2×#392C2×C6111yescharacteristic
649C2×#390C2×C6111yescharacteristic, complemented
650C2×#390C2×C6111yescharacteristic, complemented
651C2×#388C2×C6111yescharacteristic, complemented
652C2×#386C2×C6111yescharacteristic, complemented
653C2×#386C2×C6111yescharacteristic, complemented
654C2×#385C2×C6111yescharacteristic, complemented
655#1440C2×C6111yescharacteristic, complemented
656#1439C2×C6111yescharacteristic, complemented
657#1439C2×C6111yescharacteristic, complemented
658#1438C2×C6111yescharacteristic, complemented
659#1438C2×C6111yescharacteristic, complemented
660#1437C2×C6111yescharacteristic, complemented
661#1436C2×C6111yescharacteristic, complemented
662#1436C2×C6111yescharacteristic, complemented
663C2×C61—44no—
664C2×C61—82no—
665C2×C61—82no—
666C2×C61#232111yescharacteristic
667C2×C61#232111yescharacteristic
668C2×C61#232411yescharacteristic
669C2×C61#235811yescharacteristic
670C2×C61#236111yescharacteristic
671C2×C61#236611yescharacteristic
672C2×C61#237711yescharacteristic
673C2×C61#266911yescharacteristic
674C2×C61#267311yescharacteristic
675C2×C61#267611yescharacteristic
676C2×C61#268211yescharacteristic
677C2×C61#271011yescharacteristic
678C2×C61#271411yescharacteristic
679C2×C61#273011yescharacteristic
680C2×C61#279711yescharacteristic
681C23×D4C22×C6111yescharacteristic
682C23×D4C22×C6111yescharacteristic
683C23×D4C22×C6111yescharacteristic
684C24×C4C22×C6111yescharacteristic
685C22×C4⋊C4C22×C6111yescharacteristic
686C22×C4⋊C4C22×C6111yescharacteristic
687C22×C4⋊C4C22×C6111yescharacteristic
688C22×C22⋊C4C22×C6111yescharacteristic
689C22×C22⋊C4C22×C6111yescharacteristic
690C22×C22⋊C4C22×C6111yescharacteristic
691C22×C22⋊C4C22×C6111yescharacteristic
692C22×C22⋊C4C22×C6111yescharacteristic
693C22×C22⋊C4C22×C6111yescharacteristic
694C22×C22⋊C4C22×C6111yescharacteristic
695C22×C22⋊C4C22×C6111yescharacteristic
696C22×C22⋊C4C22×C6111yescharacteristic
697C22×C22⋊C4C22×C6111yescharacteristic
698C22×C22⋊C4C22×C6111yescharacteristic
699C22×C22⋊C4C22×C6111yescharacteristic
700C22×C22⋊C4C22×C6111yescharacteristic
701C22×C22⋊C4C22×C6111yescharacteristic
702C22×C42C22×C6111yescharacteristic
703C22×C42C22×C6111yescharacteristic
704#392C4×C6118yescomplemented
705#390—24no—
706#390—24no—
707#388—24no—
708#386—24no—
709#386—24no—
710#385—24no—
711C2×#95C22×C6111yescharacteristic
712C2×#95C22×C6111yescharacteristic
713C2×#95C22×C6111yescharacteristic
714C2×#95C22×C6111yescharacteristic
715C2×#95C22×C6111yescharacteristic
716C2×#95C22×C6111yescharacteristic
717C2×#95C22×C6111yescharacteristic
718C2×#95C22×C6111yescharacteristic
719C2×#95C22×C6111yescharacteristic
720C2×#95C22×C6111yescharacteristic
721C2×#95C22×C6111yescharacteristic
722C2×#95C22×C6111yescharacteristic
723C61#1453411yescharacteristic, direct product factor, Sylow
724C25C23×C6111yescharacteristic
725C25C23×C6111yescharacteristic
726C25C23×C6111yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4C2×C4×C6114yes—
746C22×D4C2×C4×C6114yes—
747C22×D4C2×C4×C6114yescomplemented
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—41no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4C23×C6111yescharacteristic
756C23×C4C23×C6111yescharacteristic
757C23×C4C23×C6111yescharacteristic
758C23×C4C23×C6111yescharacteristic
759C23×C4C23×C6111yescharacteristic
760C23×C4C23×C6111yescharacteristic
761C23×C4C23×C6111yescharacteristic
762C23×C4C23×C6111yescharacteristic
763C23×C4C23×C6111yescharacteristic
764C23×C4C23×C6111yescharacteristic
765C23×C4C23×C6111yescharacteristic
766C23×C4C23×C6111yescharacteristic
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4D4×C6114yescomplemented
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4C2×C4×C6114yes—
815C2×C22⋊C4C2×C4×C6114yescomplemented
816C2×C22⋊C4C2×C4×C6114yescomplemented
817C2×C22⋊C4D4×C6114yescomplemented
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822C2×C42—41no—
823C2×C42—41no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—41no—
832#95—41no—
833#95—41no—
834#95C2×C4×C6114yescomplemented
835#95D4×C6114yescomplemented
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24C22×C4×C6112yes—
877C24C22×C4×C6112yes—
878C24C22×C4×C6112yes—
879C24C2×D4×C6112yes—
880C24#41×C6112yes—
881C24C24×C6111yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4C22×C4×C6112yes—
981C22×C4C22×C4×C6112yes—
982C22×C4C22×C4×C6112yes—
983C22×C4C22×C4×C6112yes—
984C22×C4C2×D4×C6112yes—
985C22×C4C2×D4×C6112yes—
986C22×C4C2×D4×C6112yes—
987C22×C4C2×D4×C6112yes—
988C22×C4C2×D4×C6112yes—
989C22×C4C2×D4×C6112yes—
990C22×C4C2×D4×C6112yes—
991C22×C4C2×D4×C6112yes—
992C22×C4#41×C6112yes—
993C22×C4#41×C6112yes—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C42—44no—
1012C42—44no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23C4×D4×C6114yes—
1118C23C23×C4×C6111yescharacteristic
1119C23C22×D4×C6111yescharacteristic
1120C23C22×D4×C6111yescharacteristic
1121C23C22×D4×C6111yescharacteristic
1122C23C2×#41×C6111yescharacteristic
1123C23C2×#41×C6111yescharacteristic
1124C23C2×#41×C6111yescharacteristic
1125C23H(5,𝔽2)×C6111yescharacteristic
1126C23H(5,𝔽2)×C6111yescharacteristic
1127C23H(5,𝔽2)×C6111yescharacteristic
1128C23H(5,𝔽2)×C6111yescharacteristic
1129C23H(5,𝔽2)×C6111yescharacteristic
1130C23H(5,𝔽2)×C6111yescharacteristic
1131C23H(5,𝔽2)×C6111yescharacteristic
1132C232−1+4×C6111yescharacteristic
1133D4—416no—
1134D4—416no—
1135D4—416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—416no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4C4×D4×C6114yes—
1220C2×C4C4×D4×C6114yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22C2×C4×D4×C6111yescharacteristic
1267C22C2×C4×D4×C6111yescharacteristic
1268C22C2×C4×D4×C6111yescharacteristic
1269C22C61×#51811yescharacteristic
1270C22C61×#51811yescharacteristic
1271C22C61×#51811yescharacteristic
1272C22C61×#52011yescharacteristic
1273C22C61×#53411yescharacteristic
1274C22C61×#53411yescharacteristic
1275C22C61×#53511yescharacteristic
1276C22C61×#53511yescharacteristic
1277C22C61×#53511yescharacteristic
1278C22C61×#53711yescharacteristic
1279C22C61×#53811yescharacteristic
1280C22C61×#53811yescharacteristic
1281C22C61×#53811yescharacteristic
1282C22C61×#53811yescharacteristic
1283C22C61×#54011yescharacteristic
1284C22C61×#54211yescharacteristic
1285C22D42×C6111yescharacteristic
1286C22D42×C6111yescharacteristic
1287C22D42×C6111yescharacteristic
1288C22C61×#54611yescharacteristic
1289C22C61×#54611yescharacteristic
1290C22C61×#54711yescharacteristic
1291C22C61×#54811yescharacteristic
1292C22C61×#55011yescharacteristic
1293C22C61×#55011yescharacteristic
1294C22C61×#55111yescharacteristic
1295C22C61×#55311yescharacteristic
1296C22C61×#55911yescharacteristic
1297C22C61×#56011yescharacteristic
1298C22C61×#56011yescharacteristic
1299C22C61×#56211yescharacteristic
1300C22C61×#56211yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2C61×#232111yescharacteristic
1317C2C61×#232111yescharacteristic
1318C2C61×#232411yescharacteristic
1319C2C61×#235811yescharacteristic
1320C2C61×#236111yescharacteristic
1321C2C61×#236611yescharacteristic
1322C2C61×#237711yescharacteristic
1323C2C61×#266911yescharacteristic
1324C2C61×#267311yescharacteristic
1325C2C61×#267611yescharacteristic
1326C2C61×#268211yescharacteristic
1327C2C61×#271011yescharacteristic
1328C2C61×#271411yescharacteristic
1329C2C61×#273011yescharacteristic
1330C2C61×#279711yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC2×C61×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#390C2semidirect
3. C2×C61×#390C2semidirect
4. C2×C61×#388C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C61×#386C2semidirect
7. C2×C61×#385C2semidirect
8. C61×#1440C2semidirect
9. C61×#1439C2semidirect
10. C61×#1439C2semidirect
11. C61×#1438C2semidirect
12. C61×#1438C2semidirect
13. C61×#1437C2semidirect
14. C61×#1436C2semidirect
15. C61×#1436C2semidirect
39. C61×#392C4semidirect
81. C22×D4×C61C2×C4semidirect
109. C2×C4⋊C4×C61D4semidirect
149. C2×C22⋊C4×C61C2×C4semidirect
150. C2×C22⋊C4×C61C2×C4semidirect
151. C2×C22⋊C4×C61D4semidirect
168. #95×C61C2×C4semidirect
169. #95×C61D4semidirect
555. #14534C61direct (N × H)
649. C2×#390C2×C61semidirect
650. C2×#390C2×C61semidirect
651. C2×#388C2×C61semidirect
652. C2×#386C2×C61semidirect
653. C2×#386C2×C61semidirect
654. C2×#385C2×C61semidirect
655. #1440C2×C61semidirect
656. #1439C2×C61semidirect
657. #1439C2×C61semidirect
658. #1438C2×C61semidirect
659. #1438C2×C61semidirect
660. #1437C2×C61semidirect
661. #1436C2×C61semidirect
662. #1436C2×C61semidirect
704. #392C4×C61semidirect
723. C61#14534direct (N × H)
747. C22×D4C2×C4×C61semidirect
775. C2×C4⋊C4D4×C61semidirect
815. C2×C22⋊C4C2×C4×C61semidirect
816. C2×C22⋊C4C2×C4×C61semidirect
817. C2×C22⋊C4D4×C61semidirect
834. #95C2×C4×C61semidirect
835. #95D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3922
C2×C61×#3902
C2×C61×#3882
C2×C61×#3862
C2×C61×#3852
C61×#14402
C61×#14392
C61×#14382
C61×#14372
C61×#14362
#1453461