Finite Group Databasebeta

← C61×#15913 #29519346

Subgroups — C61×#15913 #29519346

Order 15616.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C61C211yesmaximal, characteristic, complemented
2C2×C61×#397C211yesmaximal, characteristic, complemented
3C2×C61×#396C211yesmaximal, characteristic, complemented
4C2×C61×#390C211yesmaximal, characteristic
5C61×#1444C211yesmaximal, characteristic, complemented
6C61×#1440C211yesmaximal, characteristic, complemented
7C61×#1439C211yesmaximal, characteristic, complemented
8C61×#1439C211yesmaximal, characteristic, complemented
9C61×#1439C211yesmaximal, characteristic, complemented
10C61×#1438C211yesmaximal, characteristic
11C61×#1438C211yesmaximal, characteristic
12C61×#1437C211yesmaximal, characteristic, complemented
13C61×#1436C211yesmaximal, characteristic, complemented
14C61×#1436C211yesmaximal, characteristic, complemented
15C61×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C2×#126×C61—24no—
18C2×#126×C61—24no—
19C2×#126×C61—24no—
20C22×C4⋊C4×C61C2211yescharacteristic
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
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×C42×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C61×#397—24no—
41C61×#396—24no—
42C61×#390—24no—
43C2×#95×C61C2211yescharacteristic
44C2×#95×C61C2211yescharacteristic
45C2×#95×C61C2211yescharacteristic
46C2×#95×C61C2211yescharacteristic
47C2×#95×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C25×C61C2311yescharacteristic
58C25×C61C2311yescharacteristic
59C22×D4×C61—22no—
60C22×D4×C61—22no—
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—41no—
65C22×D4×C61—41no—
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C23×C4×C61C2311yescharacteristic
70C23×C4×C61C2311yescharacteristic
71C23×C4×C61C2311yescharacteristic
72C23×C4×C61C2311yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C23×C4×C61C2311yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79#126×C61—232no—
80C2×C4⋊C4×C61—22no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—41no—
93C2×C4⋊C4×C61—41no—
94C2×C4⋊C4×C61—41no—
95C2×C4⋊C4×C61—41no—
96C2×C4⋊C4×C61D414yescomplemented
97C2×C4⋊C4×C61D414yescomplemented
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—22no—
102C2×C22⋊C4×C61—22no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—22no—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—41no—
122C2×C22⋊C4×C61—41no—
123C2×C22⋊C4×C61—41no—
124C2×C22⋊C4×C61—41no—
125C2×C22⋊C4×C61—41no—
126C2×C22⋊C4×C61—41no—
127C2×C22⋊C4×C61—41no—
128C2×C22⋊C4×C61—41no—
129C2×C22⋊C4×C61—41no—
130C2×C22⋊C4×C61—41no—
131C2×C22⋊C4×C61—41no—
132C2×C22⋊C4×C61—41no—
133C2×C22⋊C4×C61D414yes—
134C2×C42×C61—22no—
135C2×C42×C61—22no—
136C2×C42×C61—22no—
137C2×C42×C61—22no—
138C2×C42×C61—22no—
139C2×C42×C61—41no—
140#95×C61—22no—
141#95×C61—22no—
142#95×C61—22no—
143#95×C61—22no—
144#95×C61—22no—
145#95×C61—22no—
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—22no—
149#95×C61—41no—
150#95×C61—41no—
151#95×C61—41no—
152#95×C61—41no—
153#95×C61—41no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61C2×D412yes—
183C24×C61#4112yes—
184C24×C61C2411yescharacteristic
185C2×D4×C61—28no—
186C2×D4×C61—44no—
187C2×D4×C61—44no—
188C2×D4×C61—44no—
189C2×D4×C61—44no—
190C2×D4×C61—44no—
191C2×D4×C61—44no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61C2×D412yes—
271C22×C4×C61C2×D412yes—
272C22×C4×C61C2×D412yes—
273C22×C4×C61C2×D412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61C2×D412yes—
278C22×C4×C61#4112yes—
279C22×C4×C61#4112yes—
280C22×C4×C61#4112yes—
281C22×C4×C61#4112yes—
282C22×C4×C61#4112yes—
283C4⋊C4×C61—28no—
284C4⋊C4×C61—28no—
285C4⋊C4×C61—28no—
286C4⋊C4×C61—44no—
287C4⋊C4×C61—44no—
288C4⋊C4×C61—44no—
289C22⋊C4×C61—28no—
290C22⋊C4×C61—28no—
291C22⋊C4×C61—28no—
292C22⋊C4×C61—44no—
293C22⋊C4×C61—44no—
294C22⋊C4×C61—44no—
295C22⋊C4×C61—44no—
296C22⋊C4×C61—44no—
297C22⋊C4×C61—44no—
298C22⋊C4×C61—44no—
299C22⋊C4×C61—44no—
300C22⋊C4×C61—44no—
301C42×C61—28no—
302C42×C61—44no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61C22×D411yescharacteristic
374C23×C61C22×D411yescharacteristic
375C23×C61C22×D411yescharacteristic
376C23×C61C2×#4111yescharacteristic
377C23×C61C2×#4111yescharacteristic
378C23×C61C2×#4111yescharacteristic
379C23×C61C2×#4111yescharacteristic
380C23×C61C2×#4111yescharacteristic
381C23×C61C2×#4111yescharacteristic
382C23×C61H(5,𝔽2)11yescharacteristic
383C23×C61H(5,𝔽2)11yescharacteristic
384C23×C61H(5,𝔽2)11yescharacteristic
385C23×C61H(5,𝔽2)11yescharacteristic
386C23×C612−1+411yescharacteristic
387C23×C612−1+411yescharacteristic
388D4×C61—416no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61#12014yes—
479C2×C4×C61#12614yescomplemented
480#15913C6111yesmaximal, characteristic, direct product factor, Sylow
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—42no—
484C22×C61—42no—
485C22×C61—42no—
486C22×C61—42no—
487C22×C61—42no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—81no—
496C22×C61—81no—
497C22×C61—81no—
498C22×C61—81no—
499C22×C61—81no—
500C22×C61—81no—
501C22×C61—81no—
502C22×C61—81no—
503C22×C61—81no—
504C22×C61—81no—
505C22×C61—81no—
506C22×C61—81no—
507C22×C61—81no—
508C22×C61—81no—
509C22×C61—81no—
510C22×C61—81no—
511C22×C61C2×#12011yescharacteristic
512C22×C61#52511yescharacteristic
513C22×C61C2×#12611yescharacteristic
514C22×C61#52911yescharacteristic
515C22×C61#53211yescharacteristic
516C22×C61#53211yescharacteristic
517C22×C61#53511yescharacteristic
518C22×C61#53711yescharacteristic
519C22×C61#53711yescharacteristic
520C22×C61#53811yescharacteristic
521C22×C61#53811yescharacteristic
522C22×C61#53911yescharacteristic
523C22×C61#53911yescharacteristic
524C22×C61#54211yescharacteristic
525C22×C61#54211yescharacteristic
526C22×C61#54611yescharacteristic
527C22×C61#54611yescharacteristic
528C22×C61#54611yescharacteristic
529C22×C61#54611yescharacteristic
530C22×C61#54611yescharacteristic
531C22×C61#54711yescharacteristic
532C22×C61#54711yescharacteristic
533C22×C61#54711yescharacteristic
534C22×C61#54811yescharacteristic
535C22×C61#55011yescharacteristic
536C22×C61#55011yescharacteristic
537C22×C61#55011yescharacteristic
538C22×C61#55111yescharacteristic
539C22×C61#55111yescharacteristic
540C22×C61#55311yescharacteristic
541C22×C61#55311yescharacteristic
542C22×C61#55611yescharacteristic
543C22×C61#55611yescharacteristic
544C22×C61#56011yescharacteristic
545C22×C61#56311yescharacteristic
546C4×C61—24no—
547C4×C61—24no—
548C4×C61—42no—
549C4×C61—42no—
550C4×C61—42no—
551C4×C61—42no—
552C4×C61—42no—
553C4×C61—42no—
554C4×C61—42no—
555C4×C61—81no—
556C4×C61—81no—
557C4×C61—81no—
558C4×C61—81no—
559C22×#126C2×C6111yescharacteristic, complemented
560C2×#397C2×C6111yescharacteristic, complemented
561C2×#396C2×C6111yescharacteristic, complemented
562C2×#390C2×C6111yescharacteristic
563#1444C2×C6111yescharacteristic, complemented
564#1440C2×C6111yescharacteristic, complemented
565#1439C2×C6111yescharacteristic, complemented
566#1439C2×C6111yescharacteristic, complemented
567#1439C2×C6111yescharacteristic, complemented
568#1438C2×C6111yescharacteristic
569#1438C2×C6111yescharacteristic
570#1437C2×C6111yescharacteristic, complemented
571#1436C2×C6111yescharacteristic, complemented
572#1436C2×C6111yescharacteristic, complemented
573C4⋊#95C2×C6111yescharacteristic, complemented
574C2×C61—82no—
575C2×C61—82no—
576C2×C61#240711yescharacteristic
577C2×C61#243011yescharacteristic
578C2×C61#243111yescharacteristic
579C2×C61#246611yescharacteristic
580C2×C61#248011yescharacteristic
581C2×C61#251211yescharacteristic
582C2×C61#251211yescharacteristic
583C2×C61#255411yescharacteristic
584C2×C61#256011yescharacteristic
585C2×C61#269111yescharacteristic
586C2×C61#270511yescharacteristic
587C2×C61#271411yescharacteristic
588C2×C61#271511yescharacteristic
589C2×C61#272311yescharacteristic
590C2×C61#272711yescharacteristic
591C23×D4C22×C6111yescharacteristic
592C2×#126—24no—
593C2×#126—24no—
594C2×#126—24no—
595C22×C4⋊C4C22×C6111yescharacteristic
596C22×C4⋊C4C22×C6111yescharacteristic
597C22×C4⋊C4C22×C6111yescharacteristic
598C22×C4⋊C4C22×C6111yescharacteristic
599C22×C4⋊C4C22×C6111yescharacteristic
600C22×C4⋊C4C22×C6111yescharacteristic
601C22×C22⋊C4C22×C6111yescharacteristic
602C22×C22⋊C4C22×C6111yescharacteristic
603C22×C22⋊C4C22×C6111yescharacteristic
604C22×C22⋊C4C22×C6111yescharacteristic
605C22×C22⋊C4C22×C6111yescharacteristic
606C22×C22⋊C4C22×C6111yescharacteristic
607C22×C22⋊C4C22×C6111yescharacteristic
608C22×C22⋊C4C22×C6111yescharacteristic
609C22×C22⋊C4C22×C6111yescharacteristic
610C22×C22⋊C4C22×C6111yescharacteristic
611C22×C22⋊C4C22×C6111yescharacteristic
612C22×C22⋊C4C22×C6111yescharacteristic
613C22×C42C22×C6111yescharacteristic
614C22×C42C22×C6111yescharacteristic
615#397—24no—
616#396—24no—
617#390—24no—
618C2×#95C22×C6111yescharacteristic
619C2×#95C22×C6111yescharacteristic
620C2×#95C22×C6111yescharacteristic
621C2×#95C22×C6111yescharacteristic
622C2×#95C22×C6111yescharacteristic
623C2×#95C22×C6111yescharacteristic
624C2×#95C22×C6111yescharacteristic
625C2×#95C22×C6111yescharacteristic
626C2×#95C22×C6111yescharacteristic
627C2×#95C22×C6111yescharacteristic
628C2×#95C22×C6111yescharacteristic
629C2×#95C22×C6111yescharacteristic
630C2×#95C22×C6111yescharacteristic
631C2×#95C22×C6111yescharacteristic
632C61#1591311yescharacteristic, direct product factor, Sylow
633C25C23×C6111yescharacteristic
634C25C23×C6111yescharacteristic
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C23×C4C23×C6111yescharacteristic
643C23×C4C23×C6111yescharacteristic
644C23×C4C23×C6111yescharacteristic
645C23×C4C23×C6111yescharacteristic
646C23×C4C23×C6111yescharacteristic
647C23×C4C23×C6111yescharacteristic
648C23×C4C23×C6111yescharacteristic
649C23×C4C23×C6111yescharacteristic
650C23×C4C23×C6111yescharacteristic
651C23×C4C23×C6111yescharacteristic
652C23×C4C23×C6111yescharacteristic
653C23×C4C23×C6111yescharacteristic
654C23×C4C23×C6111yescharacteristic
655#126—232no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4D4×C6114yescomplemented
673C2×C4⋊C4D4×C6114yescomplemented
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4D4×C6114yes—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—41no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24C2×D4×C6112yes—
759C24#41×C6112yes—
760C24C24×C6111yescharacteristic
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4C2×D4×C6112yes—
847C22×C4C2×D4×C6112yes—
848C22×C4C2×D4×C6112yes—
849C22×C4C2×D4×C6112yes—
850C22×C4C2×D4×C6112yes—
851C22×C4C2×D4×C6112yes—
852C22×C4C2×D4×C6112yes—
853C22×C4C2×D4×C6112yes—
854C22×C4#41×C6112yes—
855C22×C4#41×C6112yes—
856C22×C4#41×C6112yes—
857C22×C4#41×C6112yes—
858C22×C4#41×C6112yes—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C42—28no—
878C42—44no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C22×D4×C6111yescharacteristic
950C23C22×D4×C6111yescharacteristic
951C23C22×D4×C6111yescharacteristic
952C23C2×#41×C6111yescharacteristic
953C23C2×#41×C6111yescharacteristic
954C23C2×#41×C6111yescharacteristic
955C23C2×#41×C6111yescharacteristic
956C23C2×#41×C6111yescharacteristic
957C23C2×#41×C6111yescharacteristic
958C23H(5,𝔽2)×C6111yescharacteristic
959C23H(5,𝔽2)×C6111yescharacteristic
960C23H(5,𝔽2)×C6111yescharacteristic
961C23H(5,𝔽2)×C6111yescharacteristic
962C232−1+4×C6111yescharacteristic
963C232−1+4×C6111yescharacteristic
964D4—416no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4#120×C6114yes—
1055C2×C4#126×C6114yescomplemented
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22C2×#120×C6111yescharacteristic
1087C22C61×#52511yescharacteristic
1088C22C2×#126×C6111yescharacteristic
1089C22C61×#52911yescharacteristic
1090C22C61×#53211yescharacteristic
1091C22C61×#53211yescharacteristic
1092C22C61×#53511yescharacteristic
1093C22C61×#53711yescharacteristic
1094C22C61×#53711yescharacteristic
1095C22C61×#53811yescharacteristic
1096C22C61×#53811yescharacteristic
1097C22C61×#53911yescharacteristic
1098C22C61×#53911yescharacteristic
1099C22C61×#54211yescharacteristic
1100C22C61×#54211yescharacteristic
1101C22C61×#54611yescharacteristic
1102C22C61×#54611yescharacteristic
1103C22C61×#54611yescharacteristic
1104C22C61×#54611yescharacteristic
1105C22C61×#54611yescharacteristic
1106C22C61×#54711yescharacteristic
1107C22C61×#54711yescharacteristic
1108C22C61×#54711yescharacteristic
1109C22C61×#54811yescharacteristic
1110C22C61×#55011yescharacteristic
1111C22C61×#55011yescharacteristic
1112C22C61×#55011yescharacteristic
1113C22C61×#55111yescharacteristic
1114C22C61×#55111yescharacteristic
1115C22C61×#55311yescharacteristic
1116C22C61×#55311yescharacteristic
1117C22C61×#55611yescharacteristic
1118C22C61×#55611yescharacteristic
1119C22C61×#56011yescharacteristic
1120C22C61×#56311yescharacteristic
1121C4—24no—
1122C4—24no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C2—82no—
1135C2—82no—
1136C2C61×#240711yescharacteristic
1137C2C61×#243011yescharacteristic
1138C2C61×#243111yescharacteristic
1139C2C61×#246611yescharacteristic
1140C2C61×#248011yescharacteristic
1141C2C61×#251211yescharacteristic
1142C2C61×#251211yescharacteristic
1143C2C61×#255411yescharacteristic
1144C2C61×#256011yescharacteristic
1145C2C61×#269111yescharacteristic
1146C2C61×#270511yescharacteristic
1147C2C61×#271411yescharacteristic
1148C2C61×#271511yescharacteristic
1149C2C61×#272311yescharacteristic
1150C2C61×#272711yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#126×C61C2semidirect
2. C2×C61×#397C2semidirect
3. C2×C61×#396C2semidirect
5. C61×#1444C2semidirect
6. C61×#1440C2semidirect
7. C61×#1439C2semidirect
8. C61×#1439C2semidirect
9. C61×#1439C2semidirect
12. C61×#1437C2semidirect
13. C61×#1436C2semidirect
14. C61×#1436C2semidirect
15. C61×C4⋊#95C2semidirect
96. C2×C4⋊C4×C61D4semidirect
97. C2×C4⋊C4×C61D4semidirect
479. C2×C4×C61#126semidirect
480. #15913C61direct (N × H)
559. C22×#126C2×C61semidirect
560. C2×#397C2×C61semidirect
561. C2×#396C2×C61semidirect
563. #1444C2×C61semidirect
564. #1440C2×C61semidirect
565. #1439C2×C61semidirect
566. #1439C2×C61semidirect
567. #1439C2×C61semidirect
570. #1437C2×C61semidirect
571. #1436C2×C61semidirect
572. #1436C2×C61semidirect
573. C4⋊#95C2×C61semidirect
632. C61#15913direct (N × H)
672. C2×C4⋊C4D4×C61semidirect
673. C2×C4⋊C4D4×C61semidirect
1055. C2×C4#126×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C612
C2×C61×#3972
C2×C61×#3962
C2×C61×#3902
C61×#14442
C61×#14402
C61×#14392
C61×#14382
C61×#14372
C61×#14362
C61×C4⋊#952
#1591361