Finite Group Databasebeta

← C61×#14100 #29517533

Subgroups — C61×#14100 #29517533

Order 15616.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C61C211yesmaximal, characteristic
2C2×C61×#390C211yesmaximal, characteristic, complemented
3C2×C61×#388C211yesmaximal, characteristic, complemented
4C2×C61×#386C211yesmaximal, characteristic, complemented
5C2×C61×#386C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
8C61×#1441C211yesmaximal, characteristic, complemented
9C61×#1438C211yesmaximal, characteristic, complemented
10C61×#1438C211yesmaximal, characteristic, complemented
11C61×#1438C211yesmaximal, characteristic, complemented
12C61×#1437C211yesmaximal, characteristic, complemented
13C61×#1437C211yesmaximal, characteristic, complemented
14C61×#1436C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C24×C4×C61C2211yescharacteristic
20C24×C4×C61C2211yescharacteristic
21C2×#121×C61—24no—
22C2×#121×C61—24no—
23C2×#121×C61C418yescomplemented
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C4⋊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×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C22×C42×C61C2211yescharacteristic
42C61×#390—24no—
43C61×#388—24no—
44C61×#386—24no—
45C61×#386—24no—
46C4×C22⋊C4×C61—24no—
47C4×C22⋊C4×C61—24no—
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
59C2×#95×C61C2211yescharacteristic
60C25×C61C2311yescharacteristic
61C25×C61C2311yescharacteristic
62C25×C61C2311yescharacteristic
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—22no—
70C22×D4×C61—22no—
71C22×D4×C61—22no—
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—41no—
76C22×D4×C61—41no—
77C22×D4×C61—41no—
78C22×D4×C61—41no—
79C22×D4×C61—41no—
80C22×D4×C61—41no—
81C22×D4×C61C2×C414yes—
82C22×D4×C61C2×C414yes—
83C22×D4×C61C2×C414yescomplemented
84C23×C4×C61—22no—
85C23×C4×C61—22no—
86C23×C4×C61—22no—
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—22no—
90C23×C4×C61—22no—
91C23×C4×C61—22no—
92C23×C4×C61—22no—
93C23×C4×C61—41no—
94C23×C4×C61—41no—
95C23×C4×C61—41no—
96C23×C4×C61—41no—
97C23×C4×C61C2×C414yescomplemented
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110#121×C61—232no—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—41no—
116C2×C4⋊C4×C61C2×C414yescomplemented
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—22no—
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—22no—
141C2×C22⋊C4×C61—22no—
142C2×C22⋊C4×C61—22no—
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×C61—41no—
149C2×C22⋊C4×C61—41no—
150C2×C22⋊C4×C61—41no—
151C2×C22⋊C4×C61C2×C414yes—
152C2×C22⋊C4×C61C2×C414yescomplemented
153C2×C22⋊C4×C61D414yes—
154C2×C22⋊C4×C61D414yes—
155C2×C22⋊C4×C61D414yescomplemented
156C2×C42×C61—22no—
157C2×C42×C61—22no—
158C2×C42×C61—22no—
159C2×C42×C61—22no—
160C2×C42×C61—22no—
161C2×C42×C61—22no—
162C2×C42×C61—41no—
163C2×C42×C61—41no—
164C2×C42×C61—41no—
165#95×C61—22no—
166#95×C61—22no—
167#95×C61—22no—
168#95×C61—22no—
169#95×C61—22no—
170#95×C61—22no—
171#95×C61—22no—
172#95×C61—22no—
173#95×C61—22no—
174#95×C61—41no—
175#95×C61—41no—
176#95×C61D414yescomplemented
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×C61—21no—
211C24×C61—21no—
212C24×C61—21no—
213C24×C61—21no—
214C24×C61—21no—
215C24×C61C22×C412yes—
216C24×C61C22×C412yes—
217C24×C61C22×C412yes—
218C24×C61C2×D412yes—
219C24×C61C2×D412yes—
220C24×C61C2×D412yes—
221C24×C61#4112yes—
222C24×C61C2411yescharacteristic
223C2×D4×C61—28no—
224C2×D4×C61—28no—
225C2×D4×C61—28no—
226C2×D4×C61—28no—
227C2×D4×C61—28no—
228C2×D4×C61—28no—
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—
237C2×D4×C61—44no—
238C2×D4×C61—44no—
239C2×D4×C61—44no—
240C2×D4×C61—44no—
241C2×D4×C61—44no—
242C2×D4×C61—44no—
243C2×D4×C61—44no—
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—28no—
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—28no—
298C22×C4×C61—28no—
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—21no—
308C22×C4×C61—21no—
309C22×C4×C61—21no—
310C22×C4×C61—21no—
311C22×C4×C61—21no—
312C22×C4×C61—21no—
313C22×C4×C61—44no—
314C22×C4×C61—44no—
315C22×C4×C61—44no—
316C22×C4×C61—44no—
317C22×C4×C61—44no—
318C22×C4×C61—44no—
319C22×C4×C61—44no—
320C22×C4×C61—44no—
321C22×C4×C61—44no—
322C22×C4×C61—44no—
323C22×C4×C61—44no—
324C22×C4×C61C22×C412yes—
325C22×C4×C61C22×C412yes—
326C22×C4×C61C22×C412yes—
327C22×C4×C61C22×C412yes—
328C22×C4×C61C2×D412yes—
329C22×C4×C61C2×D412yes—
330C22×C4×C61C2×D412yes—
331C22×C4×C61C2×D412yes—
332C22×C4×C61C2×D412yes—
333C22×C4×C61C2×D412yes—
334C22×C4×C61C2×D412yes—
335C22×C4×C61C2×D412yes—
336C22×C4×C61C2×D412yes—
337C22×C4×C61#4112yes—
338C22×C4×C61#4112yes—
339C22×C4×C61#4112yes—
340C22×C4×C61#4112yes—
341C22×C4×C61#4112yes—
342C4⋊C4×C61—28no—
343C4⋊C4×C61—44no—
344C22⋊C4×C61—28no—
345C22⋊C4×C61—28no—
346C22⋊C4×C61—28no—
347C22⋊C4×C61—28no—
348C22⋊C4×C61—44no—
349C22⋊C4×C61—44no—
350C22⋊C4×C61—44no—
351C22⋊C4×C61—44no—
352C22⋊C4×C61—44no—
353C22⋊C4×C61—44no—
354C22⋊C4×C61—44no—
355C22⋊C4×C61—44no—
356C22⋊C4×C61C22⋊C4116yescomplemented
357C42×C61—44no—
358C42×C61—44no—
359C42×C61—44no—
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—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
395C23×C61—22no—
396C23×C61—22no—
397C23×C61—22no—
398C23×C61—22no—
399C23×C61—22no—
400C23×C61—22no—
401C23×C61—22no—
402C23×C61—22no—
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×C61—41no—
452C23×C61—41no—
453C23×C61—41no—
454C23×C61—41no—
455C23×C61—41no—
456C23×C61—41no—
457C23×C61—41no—
458C23×C61—41no—
459C23×C61—41no—
460C23×C61—41no—
461C23×C61—41no—
462C23×C61—41no—
463C23×C61C2×C22⋊C414yes—
464C23×C61C4×D414yes—
465C23×C61C23×C411yescharacteristic
466C23×C61C22×D411yescharacteristic
467C23×C61C22×D411yescharacteristic
468C23×C61C22×D411yescharacteristic
469C23×C61C22×D411yescharacteristic
470C23×C61C2×#4111yescharacteristic
471C23×C61C2×#4111yescharacteristic
472C23×C61C2×#4111yescharacteristic
473C23×C61C2×#4111yescharacteristic
474C23×C61C2×#4111yescharacteristic
475C23×C61C2×#4111yescharacteristic
476C23×C61H(5,𝔽2)11yescharacteristic
477C23×C61H(5,𝔽2)11yescharacteristic
478C23×C61H(5,𝔽2)11yescharacteristic
479C23×C61H(5,𝔽2)11yescharacteristic
480D4×C61—416no—
481D4×C61—416no—
482D4×C61—416no—
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—22no—
507C2×C4×C61—22no—
508C2×C4×C61—22no—
509C2×C4×C61—22no—
510C2×C4×C61—22no—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—22no—
516C2×C4×C61—22no—
517C2×C4×C61—22no—
518C2×C4×C61—22no—
519C2×C4×C61—22no—
520C2×C4×C61—22no—
521C2×C4×C61—22no—
522C2×C4×C61—22no—
523C2×C4×C61—22no—
524C2×C4×C61—22no—
525C2×C4×C61—416no—
526C2×C4×C61—416no—
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×C61—41no—
554C2×C4×C61—41no—
555C2×C4×C61—41no—
556C2×C4×C61—41no—
557C2×C4×C61—41no—
558C2×C4×C61—41no—
559C2×C4×C61—41no—
560C2×C4×C61—41no—
561C2×C4×C61—41no—
562C2×C4×C61—41no—
563C2×C4×C61—41no—
564C2×C4×C61—41no—
565C2×C4×C61C2×C22⋊C414yes—
566C2×C4×C61C2×C22⋊C414yes—
567C2×C4×C61C4×D414yes—
568C2×C4×C61#12114yescomplemented
569#14100C6111yesmaximal, characteristic, direct product factor, Sylow
570C22×C61—24no—
571C22×C61—24no—
572C22×C61—24no—
573C22×C61—24no—
574C22×C61—24no—
575C22×C61—24no—
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—42no—
586C22×C61—42no—
587C22×C61—42no—
588C22×C61—42no—
589C22×C61—42no—
590C22×C61—42no—
591C22×C61—42no—
592C22×C61—42no—
593C22×C61—42no—
594C22×C61—42no—
595C22×C61—42no—
596C22×C61—42no—
597C22×C61—42no—
598C22×C61—42no—
599C22×C61—42no—
600C22×C61—42no—
601C22×C61—42no—
602C22×C61—42no—
603C22×C61—42no—
604C22×C61—42no—
605C22×C61—42no—
606C22×C61—42no—
607C22×C61—81no—
608C22×C61—81no—
609C22×C61—81no—
610C22×C61—81no—
611C22×C61—81no—
612C22×C61—81no—
613C22×C61—81no—
614C22×C61—81no—
615C22×C61C22×C22⋊C411yescharacteristic
616C22×C61C2×C4×D411yescharacteristic
617C22×C61C2×C4×D411yescharacteristic
618C22×C61C4×#4111yescharacteristic
619C22×C61C4×#4111yescharacteristic
620C22×C61#51811yescharacteristic
621C22×C61#51811yescharacteristic
622C22×C61C2×#12111yescharacteristic
623C22×C61#52511yescharacteristic
624C22×C61#52511yescharacteristic
625C22×C61#52511yescharacteristic
626C22×C61#52911yescharacteristic
627C22×C61#53211yescharacteristic
628C22×C61#53211yescharacteristic
629C22×C61#53211yescharacteristic
630C22×C61#53811yescharacteristic
631C22×C61#53811yescharacteristic
632C22×C61#54011yescharacteristic
633C22×C61#54011yescharacteristic
634C22×C61D4211yescharacteristic
635C22×C61D4211yescharacteristic
636C22×C61D4211yescharacteristic
637C22×C61D4211yescharacteristic
638C22×C61#54611yescharacteristic
639C22×C61#54611yescharacteristic
640C22×C61#54611yescharacteristic
641C22×C61#54611yescharacteristic
642C22×C61#54611yescharacteristic
643C22×C61#54611yescharacteristic
644C22×C61#54611yescharacteristic
645C22×C61#55011yescharacteristic
646C22×C61#55311yescharacteristic
647C22×C61#55311yescharacteristic
648C22×C61#55311yescharacteristic
649C22×C61#55511yescharacteristic
650C4×C61—24no—
651C4×C61—24no—
652C4×C61—24no—
653C4×C61—24no—
654C4×C61—42no—
655C4×C61—42no—
656C4×C61—42no—
657C4×C61—42no—
658C4×C61—42no—
659C4×C61—42no—
660C4×C61—81no—
661C4×C61—81no—
662C22×#121C2×C6111yescharacteristic
663C2×#390C2×C6111yescharacteristic, complemented
664C2×#388C2×C6111yescharacteristic, complemented
665C2×#386C2×C6111yescharacteristic, complemented
666C2×#386C2×C6111yescharacteristic, complemented
667C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
668C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
669#1441C2×C6111yescharacteristic, complemented
670#1438C2×C6111yescharacteristic, complemented
671#1438C2×C6111yescharacteristic, complemented
672#1438C2×C6111yescharacteristic, complemented
673#1437C2×C6111yescharacteristic, complemented
674#1437C2×C6111yescharacteristic, complemented
675#1436C2×C6111yescharacteristic, complemented
676C22⋊#95C2×C6111yescharacteristic, complemented
677C2×C61—44no—
678C2×C61—44no—
679C2×C61—82no—
680C2×C61#229711yescharacteristic
681C2×C61C4×#12111yescharacteristic
682C2×C61#233311yescharacteristic
683C2×C61D4×C22⋊C411yescharacteristic
684C2×C61D4×C22⋊C411yescharacteristic
685C2×C61#236311yescharacteristic
686C2×C61#236411yescharacteristic
687C2×C61#242411yescharacteristic
688C2×C61#242811yescharacteristic
689C2×C61#245611yescharacteristic
690C2×C61#246411yescharacteristic
691C2×C61#246411yescharacteristic
692C2×C61#247611yescharacteristic
693C2×C61#255511yescharacteristic
694C2×C61#255911yescharacteristic
695C23×D4C22×C6111yescharacteristic
696C23×D4C22×C6111yescharacteristic
697C23×D4C22×C6111yescharacteristic
698C24×C4C22×C6111yescharacteristic
699C24×C4C22×C6111yescharacteristic
700C2×#121—24no—
701C2×#121—24no—
702C2×#121C4×C6118yescomplemented
703C22×C4⋊C4C22×C6111yescharacteristic
704C22×C4⋊C4C22×C6111yescharacteristic
705C22×C22⋊C4C22×C6111yescharacteristic
706C22×C22⋊C4C22×C6111yescharacteristic
707C22×C22⋊C4C22×C6111yescharacteristic
708C22×C22⋊C4C22×C6111yescharacteristic
709C22×C22⋊C4C22×C6111yescharacteristic
710C22×C22⋊C4C22×C6111yescharacteristic
711C22×C22⋊C4C22×C6111yescharacteristic
712C22×C22⋊C4C22×C6111yescharacteristic
713C22×C22⋊C4C22×C6111yescharacteristic
714C22×C22⋊C4C22×C6111yescharacteristic
715C22×C22⋊C4C22×C6111yescharacteristic
716C22×C22⋊C4C22×C6111yescharacteristic
717C22×C22⋊C4C22×C6111yescharacteristic
718C22×C42C22×C6111yescharacteristic
719C22×C42C22×C6111yescharacteristic
720C22×C42C22×C6111yescharacteristic
721#390—24no—
722#388—24no—
723#386—24no—
724#386—24no—
725C4×C22⋊C4—24no—
726C4×C22⋊C4—24no—
727C2×#95C22×C6111yescharacteristic
728C2×#95C22×C6111yescharacteristic
729C2×#95C22×C6111yescharacteristic
730C2×#95C22×C6111yescharacteristic
731C2×#95C22×C6111yescharacteristic
732C2×#95C22×C6111yescharacteristic
733C2×#95C22×C6111yescharacteristic
734C2×#95C22×C6111yescharacteristic
735C2×#95C22×C6111yescharacteristic
736C2×#95C22×C6111yescharacteristic
737C2×#95C22×C6111yescharacteristic
738C2×#95C22×C6111yescharacteristic
739C61#1410011yescharacteristic, direct product factor, Sylow
740C25C23×C6111yescharacteristic
741C25C23×C6111yescharacteristic
742C25C23×C6111yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×C4×C6114yes—
762C22×D4C2×C4×C6114yes—
763C22×D4C2×C4×C6114yescomplemented
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—41no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4C2×C4×C6114yescomplemented
778C23×C4C23×C6111yescharacteristic
779C23×C4C23×C6111yescharacteristic
780C23×C4C23×C6111yescharacteristic
781C23×C4C23×C6111yescharacteristic
782C23×C4C23×C6111yescharacteristic
783C23×C4C23×C6111yescharacteristic
784C23×C4C23×C6111yescharacteristic
785C23×C4C23×C6111yescharacteristic
786C23×C4C23×C6111yescharacteristic
787C23×C4C23×C6111yescharacteristic
788C23×C4C23×C6111yescharacteristic
789C23×C4C23×C6111yescharacteristic
790#121—232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4C2×C4×C6114yescomplemented
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4C2×C4×C6114yes—
832C2×C22⋊C4C2×C4×C6114yescomplemented
833C2×C22⋊C4D4×C6114yes—
834C2×C22⋊C4D4×C6114yes—
835C2×C22⋊C4D4×C6114yescomplemented
836C2×C42—22no—
837C2×C42—22no—
838C2×C42—22no—
839C2×C42—22no—
840C2×C42—22no—
841C2×C42—22no—
842C2×C42—41no—
843C2×C42—41no—
844C2×C42—41no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—41no—
855#95—41no—
856#95D4×C6114yescomplemented
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—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24C22×C4×C6112yes—
896C24C22×C4×C6112yes—
897C24C22×C4×C6112yes—
898C24C2×D4×C6112yes—
899C24C2×D4×C6112yes—
900C24C2×D4×C6112yes—
901C24#41×C6112yes—
902C24C24×C6111yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
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—28no—
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—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4C22×C4×C6112yes—
1005C22×C4C22×C4×C6112yes—
1006C22×C4C22×C4×C6112yes—
1007C22×C4C22×C4×C6112yes—
1008C22×C4C2×D4×C6112yes—
1009C22×C4C2×D4×C6112yes—
1010C22×C4C2×D4×C6112yes—
1011C22×C4C2×D4×C6112yes—
1012C22×C4C2×D4×C6112yes—
1013C22×C4C2×D4×C6112yes—
1014C22×C4C2×D4×C6112yes—
1015C22×C4C2×D4×C6112yes—
1016C22×C4C2×D4×C6112yes—
1017C22×C4#41×C6112yes—
1018C22×C4#41×C6112yes—
1019C22×C4#41×C6112yes—
1020C22×C4#41×C6112yes—
1021C22×C4#41×C6112yes—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4C22⋊C4×C61116yescomplemented
1037C42—44no—
1038C42—44no—
1039C42—44no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
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—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊C4×C6114yes—
1144C23C4×D4×C6114yes—
1145C23C23×C4×C6111yescharacteristic
1146C23C22×D4×C6111yescharacteristic
1147C23C22×D4×C6111yescharacteristic
1148C23C22×D4×C6111yescharacteristic
1149C23C22×D4×C6111yescharacteristic
1150C23C2×#41×C6111yescharacteristic
1151C23C2×#41×C6111yescharacteristic
1152C23C2×#41×C6111yescharacteristic
1153C23C2×#41×C6111yescharacteristic
1154C23C2×#41×C6111yescharacteristic
1155C23C2×#41×C6111yescharacteristic
1156C23H(5,𝔽2)×C6111yescharacteristic
1157C23H(5,𝔽2)×C6111yescharacteristic
1158C23H(5,𝔽2)×C6111yescharacteristic
1159C23H(5,𝔽2)×C6111yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
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—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—416no—
1206C2×C4—416no—
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×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4C2×C22⋊C4×C6114yes—
1246C2×C4C2×C22⋊C4×C6114yes—
1247C2×C4C4×D4×C6114yes—
1248C2×C4#121×C6114yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊C4×C6111yescharacteristic
1295C22C2×C4×D4×C6111yescharacteristic
1296C22C2×C4×D4×C6111yescharacteristic
1297C22C4×#41×C6111yescharacteristic
1298C22C4×#41×C6111yescharacteristic
1299C22C61×#51811yescharacteristic
1300C22C61×#51811yescharacteristic
1301C22C2×#121×C6111yescharacteristic
1302C22C61×#52511yescharacteristic
1303C22C61×#52511yescharacteristic
1304C22C61×#52511yescharacteristic
1305C22C61×#52911yescharacteristic
1306C22C61×#53211yescharacteristic
1307C22C61×#53211yescharacteristic
1308C22C61×#53211yescharacteristic
1309C22C61×#53811yescharacteristic
1310C22C61×#53811yescharacteristic
1311C22C61×#54011yescharacteristic
1312C22C61×#54011yescharacteristic
1313C22D42×C6111yescharacteristic
1314C22D42×C6111yescharacteristic
1315C22D42×C6111yescharacteristic
1316C22D42×C6111yescharacteristic
1317C22C61×#54611yescharacteristic
1318C22C61×#54611yescharacteristic
1319C22C61×#54611yescharacteristic
1320C22C61×#54611yescharacteristic
1321C22C61×#54611yescharacteristic
1322C22C61×#54611yescharacteristic
1323C22C61×#54611yescharacteristic
1324C22C61×#55011yescharacteristic
1325C22C61×#55311yescharacteristic
1326C22C61×#55311yescharacteristic
1327C22C61×#55311yescharacteristic
1328C22C61×#55511yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C61×#229711yescharacteristic
1345C2C4×#121×C6111yescharacteristic
1346C2C61×#233311yescharacteristic
1347C2D4×C22⋊C4×C6111yescharacteristic
1348C2D4×C22⋊C4×C6111yescharacteristic
1349C2C61×#236311yescharacteristic
1350C2C61×#236411yescharacteristic
1351C2C61×#242411yescharacteristic
1352C2C61×#242811yescharacteristic
1353C2C61×#245611yescharacteristic
1354C2C61×#246411yescharacteristic
1355C2C61×#246411yescharacteristic
1356C2C61×#247611yescharacteristic
1357C2C61×#255511yescharacteristic
1358C2C61×#255911yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC22×#121×C61C2
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×#388C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C4×C22⋊C4×C61C2semidirect
7. C2×C4×C22⋊C4×C61C2semidirect
8. C61×#1441C2semidirect
9. C61×#1438C2semidirect
10. C61×#1438C2semidirect
11. C61×#1438C2semidirect
12. C61×#1437C2semidirect
13. C61×#1437C2semidirect
14. C61×#1436C2semidirect
15. C61×C22⋊#95C2semidirect
23. C2×#121×C61C4semidirect
83. C22×D4×C61C2×C4semidirect
97. C23×C4×C61C2×C4semidirect
116. C2×C4⋊C4×C61C2×C4semidirect
152. C2×C22⋊C4×C61C2×C4semidirect
155. C2×C22⋊C4×C61D4semidirect
176. #95×C61D4semidirect
356. C22⋊C4×C61C22⋊C4semidirect
568. C2×C4×C61#121semidirect
569. #14100C61direct (N × H)
663. C2×#390C2×C61semidirect
664. C2×#388C2×C61semidirect
665. C2×#386C2×C61semidirect
666. C2×#386C2×C61semidirect
667. C2×C4×C22⋊C4C2×C61semidirect
668. C2×C4×C22⋊C4C2×C61semidirect
669. #1441C2×C61semidirect
670. #1438C2×C61semidirect
671. #1438C2×C61semidirect
672. #1438C2×C61semidirect
673. #1437C2×C61semidirect
674. #1437C2×C61semidirect
675. #1436C2×C61semidirect
676. C22⋊#95C2×C61semidirect
702. C2×#121C4×C61semidirect
739. C61#14100direct (N × H)
763. C22×D4C2×C4×C61semidirect
777. C23×C4C2×C4×C61semidirect
796. C2×C4⋊C4C2×C4×C61semidirect
832. C2×C22⋊C4C2×C4×C61semidirect
835. C2×C22⋊C4D4×C61semidirect
856. #95D4×C61semidirect
1036. C22⋊C4C22⋊C4×C61semidirect
1248. C2×C4#121×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C612
C2×C61×#3902
C2×C61×#3882
C2×C61×#3862
C2×C4×C22⋊C4×C612
C61×#14412
C61×#14382
C61×#14372
C61×#14362
C61×C22⋊#952
#1410061