Finite Group Databasebeta

← C61×#16526 #29519959

Subgroups — C61×#16526 #29519959

Order 15616.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#397C211yesmaximal, characteristic, complemented
2C2×C61×#394C211yesmaximal, characteristic, complemented
3C2×C61×#394C211yesmaximal, characteristic, complemented
4C2×C61×#394C211yesmaximal, characteristic, complemented
5C2×C61×#392C211yesmaximal, characteristic
6C2×C61×#390C211yesmaximal, characteristic, complemented
7C61×#1444C211yesmaximal, characteristic, complemented
8C61×#1440C211yesmaximal, characteristic, complemented
9C61×#1439C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C61×#1438C211yesmaximal, characteristic, complemented
13C61×#1438C211yesmaximal, characteristic, complemented
14C61×#1437C211yesmaximal, 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×C22⋊C4×C61C2211yescharacteristic
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C61×#397—24no—
40C61×#394—24no—
41C61×#394—24no—
42C61×#394—24no—
43C61×#392—24no—
44C61×#390—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
57C25×C61C2311yescharacteristic
58C25×C61C2311yescharacteristic
59C25×C61C2311yescharacteristic
60C22×D4×C61—22no—
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—22no—
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—41no—
69C22×D4×C61—41no—
70C22×D4×C61—41no—
71C22×D4×C61—41no—
72C22×D4×C61—41no—
73C22×D4×C61—41no—
74C22×D4×C61—41no—
75C22×D4×C61—41no—
76C22×D4×C61—41no—
77C22×D4×C61—41no—
78C22×D4×C61—41no—
79C22×D4×C61—41no—
80C22×D4×C61D414yes—
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
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
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—41no—
100C2×C4⋊C4×C61—41no—
101C2×C4⋊C4×C61—41no—
102C2×C4⋊C4×C61—41no—
103C2×C4⋊C4×C61—41no—
104C2×C4⋊C4×C61—41no—
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—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—41no—
132C2×C22⋊C4×C61—41no—
133C2×C22⋊C4×C61—41no—
134C2×C22⋊C4×C61—41no—
135C2×C22⋊C4×C61—41no—
136C2×C22⋊C4×C61—41no—
137C2×C22⋊C4×C61—41no—
138C2×C22⋊C4×C61—41no—
139C2×C22⋊C4×C61—41no—
140C2×C22⋊C4×C61—41no—
141C2×C22⋊C4×C61—41no—
142C2×C22⋊C4×C61—41no—
143C2×C22⋊C4×C61—41no—
144C2×C22⋊C4×C61—41no—
145C2×C22⋊C4×C61—41no—
146C2×C22⋊C4×C61—41no—
147C2×C22⋊C4×C61—41no—
148C2×C22⋊C4×C61—41no—
149C2×C22⋊C4×C61D414yescomplemented
150C2×C42×C61—22no—
151C2×C42×C61—41no—
152C2×C42×C61—41no—
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—22no—
158#95×C61—22no—
159#95×C61—22no—
160#95×C61—41no—
161#95×C61—41no—
162#95×C61—41no—
163#95×C61—41no—
164#95×C61D414yescomplemented
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×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×C61C2×D412yes—
208C24×C61C2×D412yes—
209C24×C61C2×D412yes—
210C24×C61C2411yescharacteristic
211C2×D4×C61—28no—
212C2×D4×C61—44no—
213C2×D4×C61—44no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—44no—
217C2×D4×C61—44no—
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—
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×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×C61C2×D412yes—
307C22×C4×C61C2×D412yes—
308C22×C4×C61C2×D412yes—
309C22×C4×C61C2×D412yes—
310C22×C4×C61C2×D412yes—
311C22×C4×C61C2×D412yes—
312C22×C4×C61#4112yes—
313C22×C4×C61#4112yes—
314C22×C4×C61#4112yes—
315C22×C4×C61#4112yes—
316C4⋊C4×C61—44no—
317C4⋊C4×C61—44no—
318C4⋊C4×C61—44no—
319C4⋊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×C61—44no—
326C22⋊C4×C61—44no—
327C22⋊C4×C61—44no—
328C22⋊C4×C61—44no—
329C22⋊C4×C61—44no—
330C22⋊C4×C61—44no—
331C22⋊C4×C61—44no—
332C22⋊C4×C61—44no—
333C22⋊C4×C61—44no—
334C22⋊C4×C61—44no—
335C42×C61—44no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
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—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×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×C61C22×D411yescharacteristic
442C23×C61C22×D411yescharacteristic
443C23×C61C22×D411yescharacteristic
444C23×C61C2×#4111yescharacteristic
445C23×C61C2×#4111yescharacteristic
446C23×C61C2×#4111yescharacteristic
447C23×C61C2×#4111yescharacteristic
448C23×C61H(5,𝔽2)11yescharacteristic
449C23×C61H(5,𝔽2)11yescharacteristic
450C23×C61H(5,𝔽2)11yescharacteristic
451C23×C61H(5,𝔽2)11yescharacteristic
452C23×C61H(5,𝔽2)11yescharacteristic
453C23×C61H(5,𝔽2)11yescharacteristic
454C23×C61H(5,𝔽2)11yescharacteristic
455C23×C612−1+411yescharacteristic
456D4×C61—416no—
457D4×C61—416no—
458D4×C61—416no—
459C2×C4×C61—22no—
460C2×C4×C61—22no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—22no—
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—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
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#12314yes—
543#16526C6111yesmaximal, characteristic, direct product factor, Sylow
544C22×C61—42no—
545C22×C61—42no—
546C22×C61—42no—
547C22×C61—42no—
548C22×C61—42no—
549C22×C61—42no—
550C22×C61—42no—
551C22×C61—42no—
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—81no—
566C22×C61—81no—
567C22×C61—81no—
568C22×C61—81no—
569C22×C61—81no—
570C22×C61—81no—
571C22×C61—81no—
572C22×C61—81no—
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×C61C2×#12311yescharacteristic
590C22×C61#53211yescharacteristic
591C22×C61#53211yescharacteristic
592C22×C61#53411yescharacteristic
593C22×C61#53411yescharacteristic
594C22×C61#53411yescharacteristic
595C22×C61#53511yescharacteristic
596C22×C61#53511yescharacteristic
597C22×C61#53711yescharacteristic
598C22×C61#53811yescharacteristic
599C22×C61#53811yescharacteristic
600C22×C61#53811yescharacteristic
601C22×C61#53811yescharacteristic
602C22×C61#53811yescharacteristic
603C22×C61#53811yescharacteristic
604C22×C61#54011yescharacteristic
605C22×C61#54011yescharacteristic
606C22×C61#54211yescharacteristic
607C22×C61#54211yescharacteristic
608C22×C61D4211yescharacteristic
609C22×C61D4211yescharacteristic
610C22×C61D4211yescharacteristic
611C22×C61#54611yescharacteristic
612C22×C61#54611yescharacteristic
613C22×C61#54611yescharacteristic
614C22×C61#54711yescharacteristic
615C22×C61#54711yescharacteristic
616C22×C61#55011yescharacteristic
617C22×C61#55311yescharacteristic
618C22×C61#55511yescharacteristic
619C22×C61#55911yescharacteristic
620C22×C61#56011yescharacteristic
621C22×C61#56011yescharacteristic
622C22×C61#56211yescharacteristic
623C22×C61#56211yescharacteristic
624C4×C61—24no—
625C4×C61—42no—
626C4×C61—42no—
627C4×C61—42no—
628C4×C61—42no—
629C4×C61—42no—
630C4×C61—42no—
631C4×C61—42no—
632C4×C61—81no—
633C4×C61—81no—
634C4×C61—81no—
635C4×C61—81no—
636C2×#397C2×C6111yescharacteristic, complemented
637C2×#394C2×C6111yescharacteristic, complemented
638C2×#394C2×C6111yescharacteristic, complemented
639C2×#394C2×C6111yescharacteristic, complemented
640C2×#392C2×C6111yescharacteristic
641C2×#390C2×C6111yescharacteristic, complemented
642#1444C2×C6111yescharacteristic, complemented
643#1440C2×C6111yescharacteristic, complemented
644#1439C2×C6111yescharacteristic, complemented
645#1439C2×C6111yescharacteristic, complemented
646#1439C2×C6111yescharacteristic, complemented
647#1438C2×C6111yescharacteristic, complemented
648#1438C2×C6111yescharacteristic, complemented
649#1437C2×C6111yescharacteristic, complemented
650#1436C2×C6111yescharacteristic, complemented
651C2×C61—82no—
652C2×C61—82no—
653C2×C61—82no—
654C2×C61#242211yescharacteristic
655C2×C61#244511yescharacteristic
656C2×C61#255511yescharacteristic
657C2×C61#262211yescharacteristic
658C2×C61#266111yescharacteristic
659C2×C61#266211yescharacteristic
660C2×C61#266811yescharacteristic
661C2×C61#266911yescharacteristic
662C2×C61#267111yescharacteristic
663C2×C61#268211yescharacteristic
664C2×C61#268611yescharacteristic
665C2×C61#271011yescharacteristic
666C2×C61#271411yescharacteristic
667C2×C61#280311yescharacteristic
668C2×C61#282911yescharacteristic
669C23×D4C22×C6111yescharacteristic
670C23×D4C22×C6111yescharacteristic
671C23×D4C22×C6111yescharacteristic
672C22×C4⋊C4C22×C6111yescharacteristic
673C22×C4⋊C4C22×C6111yescharacteristic
674C22×C4⋊C4C22×C6111yescharacteristic
675C22×C4⋊C4C22×C6111yescharacteristic
676C22×C22⋊C4C22×C6111yescharacteristic
677C22×C22⋊C4C22×C6111yescharacteristic
678C22×C22⋊C4C22×C6111yescharacteristic
679C22×C22⋊C4C22×C6111yescharacteristic
680C22×C22⋊C4C22×C6111yescharacteristic
681C22×C22⋊C4C22×C6111yescharacteristic
682C22×C22⋊C4C22×C6111yescharacteristic
683C22×C22⋊C4C22×C6111yescharacteristic
684C22×C22⋊C4C22×C6111yescharacteristic
685C22×C22⋊C4C22×C6111yescharacteristic
686C22×C22⋊C4C22×C6111yescharacteristic
687C22×C22⋊C4C22×C6111yescharacteristic
688C22×C22⋊C4C22×C6111yescharacteristic
689C22×C22⋊C4C22×C6111yescharacteristic
690C22×C22⋊C4C22×C6111yescharacteristic
691C22×C42C22×C6111yescharacteristic
692#397—24no—
693#394—24no—
694#394—24no—
695#394—24no—
696#392—24no—
697#390—24no—
698C2×#95C22×C6111yescharacteristic
699C2×#95C22×C6111yescharacteristic
700C2×#95C22×C6111yescharacteristic
701C2×#95C22×C6111yescharacteristic
702C2×#95C22×C6111yescharacteristic
703C2×#95C22×C6111yescharacteristic
704C2×#95C22×C6111yescharacteristic
705C2×#95C22×C6111yescharacteristic
706C2×#95C22×C6111yescharacteristic
707C2×#95C22×C6111yescharacteristic
708C2×#95C22×C6111yescharacteristic
709C2×#95C22×C6111yescharacteristic
710C61#1652611yescharacteristic, direct product factor, Sylow
711C25C23×C6111yescharacteristic
712C25C23×C6111yescharacteristic
713C25C23×C6111yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4D4×C6114yes—
735C23×C4C23×C6111yescharacteristic
736C23×C4C23×C6111yescharacteristic
737C23×C4C23×C6111yescharacteristic
738C23×C4C23×C6111yescharacteristic
739C23×C4C23×C6111yescharacteristic
740C23×C4C23×C6111yescharacteristic
741C23×C4C23×C6111yescharacteristic
742C23×C4C23×C6111yescharacteristic
743C23×C4C23×C6111yescharacteristic
744C23×C4C23×C6111yescharacteristic
745C23×C4C23×C6111yescharacteristic
746C23×C4C23×C6111yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
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—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4D4×C6114yescomplemented
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C6114yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
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—
861C24C2×D4×C6112yes—
862C24C2×D4×C6112yes—
863C24C2×D4×C6112yes—
864C24C24×C6111yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
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×C4C2×D4×C6112yes—
961C22×C4C2×D4×C6112yes—
962C22×C4C2×D4×C6112yes—
963C22×C4C2×D4×C6112yes—
964C22×C4C2×D4×C6112yes—
965C22×C4C2×D4×C6112yes—
966C22×C4#41×C6112yes—
967C22×C4#41×C6112yes—
968C22×C4#41×C6112yes—
969C22×C4#41×C6112yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
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—
1095C23C22×D4×C6111yescharacteristic
1096C23C22×D4×C6111yescharacteristic
1097C23C22×D4×C6111yescharacteristic
1098C23C2×#41×C6111yescharacteristic
1099C23C2×#41×C6111yescharacteristic
1100C23C2×#41×C6111yescharacteristic
1101C23C2×#41×C6111yescharacteristic
1102C23H(5,𝔽2)×C6111yescharacteristic
1103C23H(5,𝔽2)×C6111yescharacteristic
1104C23H(5,𝔽2)×C6111yescharacteristic
1105C23H(5,𝔽2)×C6111yescharacteristic
1106C23H(5,𝔽2)×C6111yescharacteristic
1107C23H(5,𝔽2)×C6111yescharacteristic
1108C23H(5,𝔽2)×C6111yescharacteristic
1109C232−1+4×C6111yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
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—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
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#123×C6114yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#123×C6111yescharacteristic
1243C22C61×#53211yescharacteristic
1244C22C61×#53211yescharacteristic
1245C22C61×#53411yescharacteristic
1246C22C61×#53411yescharacteristic
1247C22C61×#53411yescharacteristic
1248C22C61×#53511yescharacteristic
1249C22C61×#53511yescharacteristic
1250C22C61×#53711yescharacteristic
1251C22C61×#53811yescharacteristic
1252C22C61×#53811yescharacteristic
1253C22C61×#53811yescharacteristic
1254C22C61×#53811yescharacteristic
1255C22C61×#53811yescharacteristic
1256C22C61×#53811yescharacteristic
1257C22C61×#54011yescharacteristic
1258C22C61×#54011yescharacteristic
1259C22C61×#54211yescharacteristic
1260C22C61×#54211yescharacteristic
1261C22D42×C6111yescharacteristic
1262C22D42×C6111yescharacteristic
1263C22D42×C6111yescharacteristic
1264C22C61×#54611yescharacteristic
1265C22C61×#54611yescharacteristic
1266C22C61×#54611yescharacteristic
1267C22C61×#54711yescharacteristic
1268C22C61×#54711yescharacteristic
1269C22C61×#55011yescharacteristic
1270C22C61×#55311yescharacteristic
1271C22C61×#55511yescharacteristic
1272C22C61×#55911yescharacteristic
1273C22C61×#56011yescharacteristic
1274C22C61×#56011yescharacteristic
1275C22C61×#56211yescharacteristic
1276C22C61×#56211yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C61×#242211yescharacteristic
1293C2C61×#244511yescharacteristic
1294C2C61×#255511yescharacteristic
1295C2C61×#262211yescharacteristic
1296C2C61×#266111yescharacteristic
1297C2C61×#266211yescharacteristic
1298C2C61×#266811yescharacteristic
1299C2C61×#266911yescharacteristic
1300C2C61×#267111yescharacteristic
1301C2C61×#268211yescharacteristic
1302C2C61×#268611yescharacteristic
1303C2C61×#271011yescharacteristic
1304C2C61×#271411yescharacteristic
1305C2C61×#280311yescharacteristic
1306C2C61×#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×#397C2semidirect
2. C2×C61×#394C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#394C2semidirect
6. C2×C61×#390C2semidirect
7. C61×#1444C2semidirect
8. C61×#1440C2semidirect
9. C61×#1439C2semidirect
10. C61×#1439C2semidirect
11. C61×#1439C2semidirect
12. C61×#1438C2semidirect
13. C61×#1438C2semidirect
14. C61×#1437C2semidirect
15. C61×#1436C2semidirect
149. C2×C22⋊C4×C61D4semidirect
164. #95×C61D4semidirect
543. #16526C61direct (N × H)
636. C2×#397C2×C61semidirect
637. C2×#394C2×C61semidirect
638. C2×#394C2×C61semidirect
639. C2×#394C2×C61semidirect
641. C2×#390C2×C61semidirect
642. #1444C2×C61semidirect
643. #1440C2×C61semidirect
644. #1439C2×C61semidirect
645. #1439C2×C61semidirect
646. #1439C2×C61semidirect
647. #1438C2×C61semidirect
648. #1438C2×C61semidirect
649. #1437C2×C61semidirect
650. #1436C2×C61semidirect
710. C61#16526direct (N × H)
803. C2×C22⋊C4D4×C61semidirect
818. #95D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3972
C2×C61×#3942
C2×C61×#3922
C2×C61×#3902
C61×#14442
C61×#14402
C61×#14392
C61×#14382
C61×#14372
C61×#14362
#1652661