Finite Group Databasebeta

← C61×#14730 #29518163

Subgroups — C61×#14730 #29518163

Order 15616.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C61C211yesmaximal, characteristic, complemented
2C2×C61×#394C211yesmaximal, characteristic, complemented
3C2×C61×#392C211yesmaximal, characteristic
4C2×C61×#386C211yesmaximal, characteristic, complemented
5C2×C61×#386C211yesmaximal, characteristic, complemented
6C2×C61×#381C211yesmaximal, characteristic, complemented
7C61×#1442C211yesmaximal, 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×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C24×C4×C61C2211yescharacteristic
20C24×C4×C61C2211yescharacteristic
21C2×C4×D4×C61—24no—
22C2×C4×D4×C61—24no—
23C2×C4×D4×C61—24no—
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
40C61×#394—24no—
41C61×#392—24no—
42C61×#386—24no—
43C61×#386—24no—
44C61×#381—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
61C25×C61C2311yescharacteristic
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—22no—
70C22×D4×C61—22no—
71C22×D4×C61—22no—
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—22no—
77C22×D4×C61—22no—
78C22×D4×C61—41no—
79C22×D4×C61—41no—
80C22×D4×C61—41no—
81C22×D4×C61—41no—
82C22×D4×C61D414yes—
83C23×C4×C61—22no—
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—41no—
93C23×C4×C61—41no—
94C23×C4×C61—41no—
95C23×C4×C61—41no—
96C23×C4×C61D414yescomplemented
97C23×C4×C61C2311yescharacteristic
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
109C4×D4×C61—232no—
110C2×C4⋊C4×C61—22no—
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×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—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—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×C61—41no—
149C2×C22⋊C4×C61—41no—
150C2×C22⋊C4×C61—41no—
151C2×C22⋊C4×C61—41no—
152C2×C22⋊C4×C61—41no—
153C2×C22⋊C4×C61—41no—
154C2×C22⋊C4×C61D414yescomplemented
155C2×C42×C61—22no—
156C2×C42×C61—22no—
157C2×C42×C61—22no—
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—22no—
166#95×C61—22no—
167#95×C61—22no—
168#95×C61—41no—
169#95×C61—41no—
170#95×C61—41no—
171#95×C61D414yescomplemented
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×C61C2×D412yes—
211C24×C61C2×D412yes—
212C24×C61C2×D412yes—
213C24×C61C2×D412yes—
214C24×C61#4112yes—
215C24×C61#4112yes—
216C24×C61#4112yes—
217C24×C61C2411yescharacteristic
218C2×D4×C61—28no—
219C2×D4×C61—28no—
220C2×D4×C61—28no—
221C2×D4×C61—28no—
222C2×D4×C61—28no—
223C2×D4×C61—28no—
224C2×D4×C61—28no—
225C2×D4×C61—28no—
226C2×D4×C61—28no—
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—
237C2×D4×C61—44no—
238C2×D4×C61—44no—
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—28no—
248C22×C4×C61—28no—
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—28no—
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—21no—
308C22×C4×C61—21no—
309C22×C4×C61—21no—
310C22×C4×C61—21no—
311C22×C4×C61—21no—
312C22×C4×C61—21no—
313C22×C4×C61—21no—
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×C61—44no—
325C22×C4×C61C2×D412yes—
326C22×C4×C61C2×D412yes—
327C22×C4×C61C2×D412yes—
328C22×C4×C61C2×D412yes—
329C22×C4×C61C2×D412yes—
330C22×C4×C61C2×D412yes—
331C22×C4×C61C2×D412yes—
332C22×C4×C61C2×D412yes—
333C22×C4×C61#4112yes—
334C22×C4×C61#4112yes—
335C22×C4×C61#4112yes—
336C22×C4×C61#4112yes—
337C4⋊C4×C61—28no—
338C4⋊C4×C61—44no—
339C22⋊C4×C61—28no—
340C22⋊C4×C61—28no—
341C22⋊C4×C61—44no—
342C22⋊C4×C61—44no—
343C22⋊C4×C61—44no—
344C22⋊C4×C61—44no—
345C22⋊C4×C61—44no—
346C22⋊C4×C61—44no—
347C22⋊C4×C61—44no—
348C22⋊C4×C61—44no—
349C22⋊C4×C61—44no—
350C22⋊C4×C61—44no—
351C22⋊C4×C61—44no—
352C42×C61—28no—
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—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—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×C61—41no—
452C23×C61—41no—
453C23×C61—41no—
454C23×C61—41no—
455C23×C61—41no—
456C23×C61#12014yes—
457C23×C61#12314yes—
458C23×C61C22×D411yescharacteristic
459C23×C61C22×D411yescharacteristic
460C23×C61C22×D411yescharacteristic
461C23×C61C22×D411yescharacteristic
462C23×C61C2×#4111yescharacteristic
463C23×C61C2×#4111yescharacteristic
464C23×C61C2×#4111yescharacteristic
465C23×C61C2×#4111yescharacteristic
466C23×C61C2×#4111yescharacteristic
467C23×C61C2×#4111yescharacteristic
468C23×C61C2×#4111yescharacteristic
469C23×C61H(5,𝔽2)11yescharacteristic
470C23×C61H(5,𝔽2)11yescharacteristic
471C23×C61H(5,𝔽2)11yescharacteristic
472C23×C61H(5,𝔽2)11yescharacteristic
473D4×C61—232no—
474D4×C61—416no—
475D4×C61—416no—
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—416no—
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×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#12114yes—
561C2×C4×C61#12314yes—
562#14730C6111yesmaximal, characteristic, direct product factor, Sylow
563C22×C61—24no—
564C22×C61—24no—
565C22×C61—24no—
566C22×C61—24no—
567C22×C61—24no—
568C22×C61—24no—
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—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—81no—
601C22×C61—81no—
602C22×C61—81no—
603C22×C61—81no—
604C22×C61—81no—
605C22×C61—81no—
606C22×C61—81no—
607C22×C61—81no—
608C22×C61C2×#12011yescharacteristic
609C22×C61C2×#12111yescharacteristic
610C22×C61C2×#12311yescharacteristic
611C22×C61C2×#12311yescharacteristic
612C22×C61#52511yescharacteristic
613C22×C61#52511yescharacteristic
614C22×C61#52511yescharacteristic
615C22×C61#52511yescharacteristic
616C22×C61#52511yescharacteristic
617C22×C61#52511yescharacteristic
618C22×C61#52911yescharacteristic
619C22×C61#52911yescharacteristic
620C22×C61#53211yescharacteristic
621C22×C61#53411yescharacteristic
622C22×C61#53511yescharacteristic
623C22×C61#53811yescharacteristic
624C22×C61#53811yescharacteristic
625C22×C61#54011yescharacteristic
626C22×C61#54011yescharacteristic
627C22×C61D4211yescharacteristic
628C22×C61D4211yescharacteristic
629C22×C61#54611yescharacteristic
630C22×C61#54611yescharacteristic
631C22×C61#54611yescharacteristic
632C22×C61#54611yescharacteristic
633C22×C61#54611yescharacteristic
634C22×C61#54611yescharacteristic
635C22×C61#54611yescharacteristic
636C22×C61#55011yescharacteristic
637C22×C61#55111yescharacteristic
638C22×C61#55311yescharacteristic
639C22×C61#55311yescharacteristic
640C22×C61#55311yescharacteristic
641C22×C61#55511yescharacteristic
642C22×C61#55911yescharacteristic
643C4×C61—24no—
644C4×C61—24no—
645C4×C61—42no—
646C4×C61—42no—
647C4×C61—42no—
648C4×C61—42no—
649C4×C61—42no—
650C4×C61—42no—
651C4×C61—81no—
652C4×C61—81no—
653C4×C61—81no—
654C4×C61—81no—
655C22×C4×D4C2×C6111yescharacteristic, complemented
656C2×#394C2×C6111yescharacteristic, complemented
657C2×#392C2×C6111yescharacteristic
658C2×#386C2×C6111yescharacteristic, complemented
659C2×#386C2×C6111yescharacteristic, complemented
660C2×#381C2×C6111yescharacteristic, complemented
661#1442C2×C6111yescharacteristic, complemented
662#1440C2×C6111yescharacteristic, complemented
663#1439C2×C6111yescharacteristic, complemented
664#1439C2×C6111yescharacteristic, complemented
665#1438C2×C6111yescharacteristic, complemented
666#1438C2×C6111yescharacteristic, complemented
667#1437C2×C6111yescharacteristic, complemented
668#1436C2×C6111yescharacteristic, complemented
669C22⋊#95C2×C6111yescharacteristic, complemented
670C2×C61—44no—
671C2×C61—44no—
672C2×C61—82no—
673C2×C61#239211yescharacteristic
674C2×C61#240411yescharacteristic
675C2×C61#241011yescharacteristic
676C2×C61#241411yescharacteristic
677C2×C61#241811yescharacteristic
678C2×C61#242011yescharacteristic
679C2×C61#244411yescharacteristic
680C2×C61#244511yescharacteristic
681C2×C61#245611yescharacteristic
682C2×C61#245711yescharacteristic
683C2×C61#245911yescharacteristic
684C2×C61#246411yescharacteristic
685C2×C61#260011yescharacteristic
686C2×C61#263511yescharacteristic
687C2×C61#284911yescharacteristic
688C23×D4C22×C6111yescharacteristic
689C23×D4C22×C6111yescharacteristic
690C23×D4C22×C6111yescharacteristic
691C24×C4C22×C6111yescharacteristic
692C24×C4C22×C6111yescharacteristic
693C2×C4×D4—24no—
694C2×C4×D4—24no—
695C2×C4×D4—24no—
696C22×C4⋊C4C22×C6111yescharacteristic
697C22×C4⋊C4C22×C6111yescharacteristic
698C22×C22⋊C4C22×C6111yescharacteristic
699C22×C22⋊C4C22×C6111yescharacteristic
700C22×C22⋊C4C22×C6111yescharacteristic
701C22×C22⋊C4C22×C6111yescharacteristic
702C22×C22⋊C4C22×C6111yescharacteristic
703C22×C22⋊C4C22×C6111yescharacteristic
704C22×C22⋊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×C42C22×C6111yescharacteristic
712#394—24no—
713#392—24no—
714#386—24no—
715#386—24no—
716#381—24no—
717C2×#95C22×C6111yescharacteristic
718C2×#95C22×C6111yescharacteristic
719C2×#95C22×C6111yescharacteristic
720C2×#95C22×C6111yescharacteristic
721C2×#95C22×C6111yescharacteristic
722C2×#95C22×C6111yescharacteristic
723C2×#95C22×C6111yescharacteristic
724C2×#95C22×C6111yescharacteristic
725C2×#95C22×C6111yescharacteristic
726C2×#95C22×C6111yescharacteristic
727C2×#95C22×C6111yescharacteristic
728C2×#95C22×C6111yescharacteristic
729C2×#95C22×C6111yescharacteristic
730C2×#95C22×C6111yescharacteristic
731C61#1473011yescharacteristic, direct product factor, Sylow
732C25C23×C6111yescharacteristic
733C25C23×C6111yescharacteristic
734C25C23×C6111yescharacteristic
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
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—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—41no—
755C22×D4D4×C6114yes—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4D4×C6114yescomplemented
770C23×C4C23×C6111yescharacteristic
771C23×C4C23×C6111yescharacteristic
772C23×C4C23×C6111yescharacteristic
773C23×C4C23×C6111yescharacteristic
774C23×C4C23×C6111yescharacteristic
775C23×C4C23×C6111yescharacteristic
776C23×C4C23×C6111yescharacteristic
777C23×C4C23×C6111yescharacteristic
778C23×C4C23×C6111yescharacteristic
779C23×C4C23×C6111yescharacteristic
780C23×C4C23×C6111yescharacteristic
781C23×C4C23×C6111yescharacteristic
782C4×D4—232no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—41no—
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—22no—
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—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4D4×C6114yescomplemented
828C2×C42—22no—
829C2×C42—22no—
830C2×C42—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—41no—
842#95—41no—
843#95—41no—
844#95D4×C6114yescomplemented
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—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24C2×D4×C6112yes—
884C24C2×D4×C6112yes—
885C24C2×D4×C6112yes—
886C24C2×D4×C6112yes—
887C24#41×C6112yes—
888C24#41×C6112yes—
889C24#41×C6112yes—
890C24C24×C6111yescharacteristic
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
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—28no—
921C22×C4—28no—
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—28no—
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—21no—
978C22×C4—21no—
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—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C6112yes—
999C22×C4C2×D4×C6112yes—
1000C22×C4C2×D4×C6112yes—
1001C22×C4C2×D4×C6112yes—
1002C22×C4C2×D4×C6112yes—
1003C22×C4C2×D4×C6112yes—
1004C22×C4C2×D4×C6112yes—
1005C22×C4C2×D4×C6112yes—
1006C22×C4#41×C6112yes—
1007C22×C4#41×C6112yes—
1008C22×C4#41×C6112yes—
1009C22×C4#41×C6112yes—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C42—28no—
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—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—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—
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#120×C6114yes—
1130C23#123×C6114yes—
1131C23C22×D4×C6111yescharacteristic
1132C23C22×D4×C6111yescharacteristic
1133C23C22×D4×C6111yescharacteristic
1134C23C22×D4×C6111yescharacteristic
1135C23C2×#41×C6111yescharacteristic
1136C23C2×#41×C6111yescharacteristic
1137C23C2×#41×C6111yescharacteristic
1138C23C2×#41×C6111yescharacteristic
1139C23C2×#41×C6111yescharacteristic
1140C23C2×#41×C6111yescharacteristic
1141C23C2×#41×C6111yescharacteristic
1142C23H(5,𝔽2)×C6111yescharacteristic
1143C23H(5,𝔽2)×C6111yescharacteristic
1144C23H(5,𝔽2)×C6111yescharacteristic
1145C23H(5,𝔽2)×C6111yescharacteristic
1146D4—232no—
1147D4—416no—
1148D4—416no—
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—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—416no—
1180C2×C4—416no—
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×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#121×C6114yes—
1234C2×C4#123×C6114yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
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—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×#120×C6111yescharacteristic
1281C22C2×#121×C6111yescharacteristic
1282C22C2×#123×C6111yescharacteristic
1283C22C2×#123×C6111yescharacteristic
1284C22C61×#52511yescharacteristic
1285C22C61×#52511yescharacteristic
1286C22C61×#52511yescharacteristic
1287C22C61×#52511yescharacteristic
1288C22C61×#52511yescharacteristic
1289C22C61×#52511yescharacteristic
1290C22C61×#52911yescharacteristic
1291C22C61×#52911yescharacteristic
1292C22C61×#53211yescharacteristic
1293C22C61×#53411yescharacteristic
1294C22C61×#53511yescharacteristic
1295C22C61×#53811yescharacteristic
1296C22C61×#53811yescharacteristic
1297C22C61×#54011yescharacteristic
1298C22C61×#54011yescharacteristic
1299C22D42×C6111yescharacteristic
1300C22D42×C6111yescharacteristic
1301C22C61×#54611yescharacteristic
1302C22C61×#54611yescharacteristic
1303C22C61×#54611yescharacteristic
1304C22C61×#54611yescharacteristic
1305C22C61×#54611yescharacteristic
1306C22C61×#54611yescharacteristic
1307C22C61×#54611yescharacteristic
1308C22C61×#55011yescharacteristic
1309C22C61×#55111yescharacteristic
1310C22C61×#55311yescharacteristic
1311C22C61×#55311yescharacteristic
1312C22C61×#55311yescharacteristic
1313C22C61×#55511yescharacteristic
1314C22C61×#55911yescharacteristic
1315C4—24no—
1316C4—24no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2C61×#239211yescharacteristic
1331C2C61×#240411yescharacteristic
1332C2C61×#241011yescharacteristic
1333C2C61×#241411yescharacteristic
1334C2C61×#241811yescharacteristic
1335C2C61×#242011yescharacteristic
1336C2C61×#244411yescharacteristic
1337C2C61×#244511yescharacteristic
1338C2C61×#245611yescharacteristic
1339C2C61×#245711yescharacteristic
1340C2C61×#245911yescharacteristic
1341C2C61×#246411yescharacteristic
1342C2C61×#260011yescharacteristic
1343C2C61×#263511yescharacteristic
1344C2C61×#284911yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC2×C61×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C61C2semidirect
2. C2×C61×#394C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C61×#381C2semidirect
7. C61×#1442C2semidirect
8. C61×#1440C2semidirect
9. C61×#1439C2semidirect
10. C61×#1439C2semidirect
11. C61×#1438C2semidirect
12. C61×#1438C2semidirect
13. C61×#1437C2semidirect
14. C61×#1436C2semidirect
15. C61×C22⋊#95C2semidirect
96. C23×C4×C61D4semidirect
154. C2×C22⋊C4×C61D4semidirect
171. #95×C61D4semidirect
562. #14730C61direct (N × H)
655. C22×C4×D4C2×C61semidirect
656. C2×#394C2×C61semidirect
658. C2×#386C2×C61semidirect
659. C2×#386C2×C61semidirect
660. C2×#381C2×C61semidirect
661. #1442C2×C61semidirect
662. #1440C2×C61semidirect
663. #1439C2×C61semidirect
664. #1439C2×C61semidirect
665. #1438C2×C61semidirect
666. #1438C2×C61semidirect
667. #1437C2×C61semidirect
668. #1436C2×C61semidirect
669. C22⋊#95C2×C61semidirect
731. C61#14730direct (N × H)
769. C23×C4D4×C61semidirect
827. C2×C22⋊C4D4×C61semidirect
844. #95D4×C61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C612
C2×C61×#3942
C2×C61×#3922
C2×C61×#3862
C2×C61×#3812
C61×#14422
C61×#14402
C61×#14392
C61×#14382
C61×#14372
C61×#14362
C61×C22⋊#952
#1473061