Finite Group Databasebeta

← C61×#16290 #29519723

Subgroups — C61×#16290 #29519723

Order 15616.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#396C211yesmaximal, characteristic, complemented
2C2×C61×#396C211yesmaximal, characteristic, complemented
3C2×C61×#394C211yesmaximal, characteristic, complemented
4C2×C61×#394C211yesmaximal, characteristic, complemented
5C2×C61×#394C211yesmaximal, characteristic, complemented
6C2×C61×#392C211yesmaximal, characteristic
7C2×C61×#390C211yesmaximal, characteristic, complemented
8C2×C61×#388C211yesmaximal, characteristic, complemented
9C61×#1444C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C61×#1439C211yesmaximal, characteristic, complemented
13C61×#1438C211yesmaximal, characteristic, complemented
14C61×#1438C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C22×C4⋊C4×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2211yescharacteristic
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊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×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C61×#396—24no—
42C61×#396—24no—
43C61×#394—24no—
44C61×#394—24no—
45C61×#394—24no—
46C61×#392—24no—
47C61×#390—24no—
48C61×#388—24no—
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—41no—
74C22×D4×C61—41no—
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×C61—41no—
82C22×D4×C61—41no—
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—41no—
108C2×C4⋊C4×C61—41no—
109C2×C4⋊C4×C61—41no—
110C2×C4⋊C4×C61—41no—
111C2×C4⋊C4×C61—41no—
112C2×C4⋊C4×C61—41no—
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—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—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×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×C61—41no—
155C2×C22⋊C4×C61—41no—
156C2×C22⋊C4×C61D414yes—
157C2×C22⋊C4×C61D414yescomplemented
158C2×C42×C61—22no—
159C2×C42×C61—22no—
160C2×C42×C61—41no—
161#95×C61—22no—
162#95×C61—22no—
163#95×C61—22no—
164#95×C61—22no—
165#95×C61—22no—
166#95×C61—41no—
167#95×C61—41no—
168#95×C61—41no—
169#95×C61D414yescomplemented
170#95×C61D414yescomplemented
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×C61—21no—
211C24×C61—21no—
212C24×C61—21no—
213C24×C61C2×D412yes—
214C24×C61C2×D412yes—
215C24×C61#4112yes—
216C24×C61C2411yescharacteristic
217C2×D4×C61—28no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
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—
237C2×D4×C61—44no—
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—21no—
308C22×C4×C61—21no—
309C22×C4×C61—21no—
310C22×C4×C61C2×D412yes—
311C22×C4×C61C2×D412yes—
312C22×C4×C61C2×D412yes—
313C22×C4×C61C2×D412yes—
314C22×C4×C61C2×D412yes—
315C22×C4×C61C2×D412yes—
316C22×C4×C61C2×D412yes—
317C22×C4×C61C2×D412yes—
318C22×C4×C61C2×D412yes—
319C22×C4×C61C2×D412yes—
320C22×C4×C61#4112yes—
321C22×C4×C61#4112yes—
322C4⋊C4×C61—44no—
323C4⋊C4×C61—44no—
324C4⋊C4×C61—44no—
325C4⋊C4×C61—44no—
326C4⋊C4×C61—44no—
327C4⋊C4×C61—44no—
328C22⋊C4×C61—28no—
329C22⋊C4×C61—44no—
330C22⋊C4×C61—44no—
331C22⋊C4×C61—44no—
332C22⋊C4×C61—44no—
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—
343C42×C61—44no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—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—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—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×C61C22×D411yescharacteristic
450C23×C61C22×D411yescharacteristic
451C23×C61C22×D411yescharacteristic
452C23×C61C22×D411yescharacteristic
453C23×C61C2×#4111yescharacteristic
454C23×C61C2×#4111yescharacteristic
455C23×C61C2×#4111yescharacteristic
456C23×C61H(5,𝔽2)11yescharacteristic
457C23×C61H(5,𝔽2)11yescharacteristic
458C23×C61H(5,𝔽2)11yescharacteristic
459C23×C61H(5,𝔽2)11yescharacteristic
460C23×C61H(5,𝔽2)11yescharacteristic
461C23×C61H(5,𝔽2)11yescharacteristic
462C23×C612−1+411yescharacteristic
463C23×C612−1+411yescharacteristic
464D4×C61—416no—
465D4×C61—416no—
466D4×C61—416no—
467C2×C4×C61—22no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
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—41no—
501C2×C4×C61—41no—
502C2×C4×C61—41no—
503C2×C4×C61—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
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#12114yes—
551#16290C6111yesmaximal, characteristic, direct product factor, Sylow
552C22×C61—42no—
553C22×C61—42no—
554C22×C61—42no—
555C22×C61—42no—
556C22×C61—42no—
557C22×C61—42no—
558C22×C61—42no—
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—81no—
574C22×C61—81no—
575C22×C61—81no—
576C22×C61—81no—
577C22×C61—81no—
578C22×C61—81no—
579C22×C61—81no—
580C22×C61—81no—
581C22×C61—81no—
582C22×C61—81no—
583C22×C61—81no—
584C22×C61—81no—
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×C61C2×#12111yescharacteristic
598C22×C61#52511yescharacteristic
599C22×C61#53211yescharacteristic
600C22×C61#53411yescharacteristic
601C22×C61#53511yescharacteristic
602C22×C61#53511yescharacteristic
603C22×C61#53611yescharacteristic
604C22×C61#53711yescharacteristic
605C22×C61#53711yescharacteristic
606C22×C61#53711yescharacteristic
607C22×C61#53711yescharacteristic
608C22×C61#53811yescharacteristic
609C22×C61#53811yescharacteristic
610C22×C61#53811yescharacteristic
611C22×C61#53911yescharacteristic
612C22×C61#54011yescharacteristic
613C22×C61#54211yescharacteristic
614C22×C61#54211yescharacteristic
615C22×C61#54211yescharacteristic
616C22×C61D4211yescharacteristic
617C22×C61D4211yescharacteristic
618C22×C61D4211yescharacteristic
619C22×C61D4211yescharacteristic
620C22×C61D4211yescharacteristic
621C22×C61#54611yescharacteristic
622C22×C61#54611yescharacteristic
623C22×C61#54611yescharacteristic
624C22×C61#54711yescharacteristic
625C22×C61#54811yescharacteristic
626C22×C61#55011yescharacteristic
627C22×C61#55111yescharacteristic
628C22×C61#56011yescharacteristic
629C22×C61#56011yescharacteristic
630C22×C61#56211yescharacteristic
631C22×C61#56211yescharacteristic
632C4×C61—24no—
633C4×C61—42no—
634C4×C61—42no—
635C4×C61—42no—
636C4×C61—42no—
637C4×C61—42no—
638C4×C61—42no—
639C4×C61—42no—
640C4×C61—42no—
641C4×C61—42no—
642C4×C61—81no—
643C4×C61—81no—
644C2×#396C2×C6111yescharacteristic, complemented
645C2×#396C2×C6111yescharacteristic, complemented
646C2×#394C2×C6111yescharacteristic, complemented
647C2×#394C2×C6111yescharacteristic, complemented
648C2×#394C2×C6111yescharacteristic, complemented
649C2×#392C2×C6111yescharacteristic
650C2×#390C2×C6111yescharacteristic, complemented
651C2×#388C2×C6111yescharacteristic, complemented
652#1444C2×C6111yescharacteristic, complemented
653#1439C2×C6111yescharacteristic, complemented
654#1439C2×C6111yescharacteristic, complemented
655#1439C2×C6111yescharacteristic, complemented
656#1438C2×C6111yescharacteristic, complemented
657#1438C2×C6111yescharacteristic, complemented
658#1436C2×C6111yescharacteristic, complemented
659C2×C61—82no—
660C2×C61—82no—
661C2×C61—82no—
662C2×C61#242411yescharacteristic
663C2×C61#242811yescharacteristic
664C2×C61#246111yescharacteristic
665C2×C61#262011yescharacteristic
666C2×C61#263011yescharacteristic
667C2×C61#266211yescharacteristic
668C2×C61#266911yescharacteristic
669C2×C61#267211yescharacteristic
670C2×C61#267511yescharacteristic
671C2×C61#267611yescharacteristic
672C2×C61#268111yescharacteristic
673C2×C61#268211yescharacteristic
674C2×C61#268511yescharacteristic
675C2×C61#270511yescharacteristic
676C2×C61#282911yescharacteristic
677C23×D4C22×C6111yescharacteristic
678C23×D4C22×C6111yescharacteristic
679C23×D4C22×C6111yescharacteristic
680C22×C4⋊C4C22×C6111yescharacteristic
681C22×C4⋊C4C22×C6111yescharacteristic
682C22×C4⋊C4C22×C6111yescharacteristic
683C22×C4⋊C4C22×C6111yescharacteristic
684C22×C4⋊C4C22×C6111yescharacteristic
685C22×C4⋊C4C22×C6111yescharacteristic
686C22×C22⋊C4C22×C6111yescharacteristic
687C22×C22⋊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×C42C22×C6111yescharacteristic
702#396—24no—
703#396—24no—
704#394—24no—
705#394—24no—
706#394—24no—
707#392—24no—
708#390—24no—
709#388—24no—
710C2×#95C22×C6111yescharacteristic
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
720C61#1629011yescharacteristic, direct product factor, Sylow
721C25C23×C6111yescharacteristic
722C25C23×C6111yescharacteristic
723C25C23×C6111yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
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—
745C23×C4C23×C6111yescharacteristic
746C23×C4C23×C6111yescharacteristic
747C23×C4C23×C6111yescharacteristic
748C23×C4C23×C6111yescharacteristic
749C23×C4C23×C6111yescharacteristic
750C23×C4C23×C6111yescharacteristic
751C23×C4C23×C6111yescharacteristic
752C23×C4C23×C6111yescharacteristic
753C23×C4C23×C6111yescharacteristic
754C23×C4C23×C6111yescharacteristic
755C23×C4C23×C6111yescharacteristic
756C23×C4C23×C6111yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C22⋊C4—22no—
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—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
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⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4D4×C6114yes—
819C2×C22⋊C4D4×C6114yescomplemented
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—41no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—41no—
829#95—41no—
830#95—41no—
831#95D4×C6114yescomplemented
832#95D4×C6114yescomplemented
833C24—21no—
834C24—21no—
835C24—21no—
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—
875C24C2×D4×C6112yes—
876C24C2×D4×C6112yes—
877C24#41×C6112yes—
878C24C24×C6111yescharacteristic
879C2×D4—28no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
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—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
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×C4C2×D4×C6112yes—
973C22×C4C2×D4×C6112yes—
974C22×C4C2×D4×C6112yes—
975C22×C4C2×D4×C6112yes—
976C22×C4C2×D4×C6112yes—
977C22×C4C2×D4×C6112yes—
978C22×C4C2×D4×C6112yes—
979C22×C4C2×D4×C6112yes—
980C22×C4C2×D4×C6112yes—
981C22×C4C2×D4×C6112yes—
982C22×C4#41×C6112yes—
983C22×C4#41×C6112yes—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C22⋊C4—28no—
991C22⋊C4—44no—
992C22⋊C4—44no—
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⋊C4—44no—
1005C42—44no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
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—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
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—
1111C23C22×D4×C6111yescharacteristic
1112C23C22×D4×C6111yescharacteristic
1113C23C22×D4×C6111yescharacteristic
1114C23C22×D4×C6111yescharacteristic
1115C23C2×#41×C6111yescharacteristic
1116C23C2×#41×C6111yescharacteristic
1117C23C2×#41×C6111yescharacteristic
1118C23H(5,𝔽2)×C6111yescharacteristic
1119C23H(5,𝔽2)×C6111yescharacteristic
1120C23H(5,𝔽2)×C6111yescharacteristic
1121C23H(5,𝔽2)×C6111yescharacteristic
1122C23H(5,𝔽2)×C6111yescharacteristic
1123C23H(5,𝔽2)×C6111yescharacteristic
1124C232−1+4×C6111yescharacteristic
1125C232−1+4×C6111yescharacteristic
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
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—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
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#121×C6114yes—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×#121×C6111yescharacteristic
1259C22C61×#52511yescharacteristic
1260C22C61×#53211yescharacteristic
1261C22C61×#53411yescharacteristic
1262C22C61×#53511yescharacteristic
1263C22C61×#53511yescharacteristic
1264C22C61×#53611yescharacteristic
1265C22C61×#53711yescharacteristic
1266C22C61×#53711yescharacteristic
1267C22C61×#53711yescharacteristic
1268C22C61×#53711yescharacteristic
1269C22C61×#53811yescharacteristic
1270C22C61×#53811yescharacteristic
1271C22C61×#53811yescharacteristic
1272C22C61×#53911yescharacteristic
1273C22C61×#54011yescharacteristic
1274C22C61×#54211yescharacteristic
1275C22C61×#54211yescharacteristic
1276C22C61×#54211yescharacteristic
1277C22D42×C6111yescharacteristic
1278C22D42×C6111yescharacteristic
1279C22D42×C6111yescharacteristic
1280C22D42×C6111yescharacteristic
1281C22D42×C6111yescharacteristic
1282C22C61×#54611yescharacteristic
1283C22C61×#54611yescharacteristic
1284C22C61×#54611yescharacteristic
1285C22C61×#54711yescharacteristic
1286C22C61×#54811yescharacteristic
1287C22C61×#55011yescharacteristic
1288C22C61×#55111yescharacteristic
1289C22C61×#56011yescharacteristic
1290C22C61×#56011yescharacteristic
1291C22C61×#56211yescharacteristic
1292C22C61×#56211yescharacteristic
1293C4—24no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2C61×#242411yescharacteristic
1309C2C61×#242811yescharacteristic
1310C2C61×#246111yescharacteristic
1311C2C61×#262011yescharacteristic
1312C2C61×#263011yescharacteristic
1313C2C61×#266211yescharacteristic
1314C2C61×#266911yescharacteristic
1315C2C61×#267211yescharacteristic
1316C2C61×#267511yescharacteristic
1317C2C61×#267611yescharacteristic
1318C2C61×#268111yescharacteristic
1319C2C61×#268211yescharacteristic
1320C2C61×#268511yescharacteristic
1321C2C61×#270511yescharacteristic
1322C2C61×#282911yescharacteristic
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. C2×C61×#396C2semidirect
2. C2×C61×#396C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#394C2semidirect
5. C2×C61×#394C2semidirect
7. C2×C61×#390C2semidirect
8. C2×C61×#388C2semidirect
9. C61×#1444C2semidirect
10. C61×#1439C2semidirect
11. C61×#1439C2semidirect
12. C61×#1439C2semidirect
13. C61×#1438C2semidirect
14. C61×#1438C2semidirect
15. C61×#1436C2semidirect
157. C2×C22⋊C4×C61D4semidirect
169. #95×C61D4semidirect
170. #95×C61D4semidirect
551. #16290C61direct (N × H)
644. C2×#396C2×C61semidirect
645. C2×#396C2×C61semidirect
646. C2×#394C2×C61semidirect
647. C2×#394C2×C61semidirect
648. C2×#394C2×C61semidirect
650. C2×#390C2×C61semidirect
651. C2×#388C2×C61semidirect
652. #1444C2×C61semidirect
653. #1439C2×C61semidirect
654. #1439C2×C61semidirect
655. #1439C2×C61semidirect
656. #1438C2×C61semidirect
657. #1438C2×C61semidirect
658. #1436C2×C61semidirect
720. C61#16290direct (N × H)
819. C2×C22⋊C4D4×C61semidirect
831. #95D4×C61semidirect
832. #95D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3962
C2×C61×#3942
C2×C61×#3922
C2×C61×#3902
C2×C61×#3882
C61×#14442
C61×#14392
C61×#14382
C61×#14362
#1629061