Finite Group Databasebeta

← C61×#15131 #29518564

Subgroups — C61×#15131 #29518564

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#396C212yesmaximal
2C2×C61×#389C211yesmaximal, characteristic, complemented
3C2×C61×#389C211yesmaximal, characteristic, complemented
4C2×C61×#384C211yesmaximal, characteristic, complemented
5C2×C61×#380C211yesmaximal, characteristic
6C2×C61×#380C211yesmaximal, characteristic
7C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
8C61×#1441C212yesmaximal, complemented
9C61×#1441C212yesmaximal, complemented
10C61×#1439C212yesmaximal
11C61×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2212yes—
16C22×C4⋊C4×C61C2212yes—
17C22×C4⋊C4×C61C2212yes—
18C22×C4⋊C4×C61C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2212yes—
22C22×C22⋊C4×C61C2212yes—
23C22×C22⋊C4×C61C2211yescharacteristic
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C42×C61C2211yescharacteristic
26C22×C42×C61C2211yescharacteristic
27C61×#396—28no—
28C61×#389—24no—
29C61×#389—24no—
30C61×#384—24no—
31C61×#380—24no—
32C61×#380—24no—
33C4×C22⋊C4×C61—24no—
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C2×#95×C61C2212yes—
41C2×#95×C61C2212yes—
42C25×C61C2311yescharacteristic
43C23×C4×C61—22no—
44C23×C4×C61—22no—
45C23×C4×C61—22no—
46C23×C4×C61—22no—
47C23×C4×C61—22no—
48C23×C4×C61—22no—
49C23×C4×C61Q814yes—
50C23×C4×C61C2312yes—
51C23×C4×C61C2312yes—
52C23×C4×C61C2311yescharacteristic
53C23×C4×C61C2312yes—
54C23×C4×C61C2312yes—
55C23×C4×C61C2311yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C23×C4×C61C2311yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C23×C4×C61C2311yescharacteristic
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—22no—
62C2×C4⋊C4×C61—22no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—22no—
65C2×C4⋊C4×C61—22no—
66C2×C4⋊C4×C61—24no—
67C2×C4⋊C4×C61—24no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61—24no—
70C2×C4⋊C4×C61—24no—
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61—24no—
73C2×C4⋊C4×C61—24no—
74C2×C4⋊C4×C61—24no—
75C2×C4⋊C4×C61—24no—
76C2×C4⋊C4×C61—24no—
77C2×C4⋊C4×C61—22no—
78C2×C4⋊C4×C61—22no—
79C2×C4⋊C4×C61—42no—
80C2×C4⋊C4×C61—42no—
81C2×C4⋊C4×C61—42no—
82C2×C4⋊C4×C61D414yes—
83C2×C4⋊C4×C61D414yes—
84C2×C22⋊C4×C61—22no—
85C2×C22⋊C4×C61—22no—
86C2×C22⋊C4×C61—22no—
87C2×C22⋊C4×C61—22no—
88C2×C22⋊C4×C61—24no—
89C2×C22⋊C4×C61—24no—
90C2×C22⋊C4×C61—24no—
91C2×C22⋊C4×C61—24no—
92C2×C22⋊C4×C61—42no—
93C2×C22⋊C4×C61—42no—
94C2×C22⋊C4×C61D414yes—
95C2×C22⋊C4×C61Q814yes—
96C2×C42×C61—22no—
97C2×C42×C61—22no—
98C2×C42×C61—22no—
99C2×C42×C61—22no—
100C2×C42×C61—22no—
101C2×C42×C61D414yes—
102#95×C61—22no—
103#95×C61—22no—
104#95×C61—24no—
105#95×C61—24no—
106#95×C61—24no—
107#95×C61—24no—
108#95×C61—24no—
109#95×C61—42no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61—21no—
116C24×C61—21no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61—21no—
120C24×C61—21no—
121C24×C61—21no—
122C24×C61C2×D412yes—
123C24×C61C2×Q812yes—
124C24×C61C2×Q812yes—
125C24×C61C2411yescharacteristic
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—21no—
160C22×C4×C61—22no—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—21no—
164C22×C4×C61—28no—
165C22×C4×C61—28no—
166C22×C4×C61—28no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—44no—
182C22×C4×C61—44no—
183C22×C4×C61—44no—
184C22×C4×C61—44no—
185C22×C4×C61C2×D414yes—
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D414yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2×D412yes—
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2×Q812yes—
195C22×C4×C61C2×Q812yes—
196C22×C4×C61C2×Q812yes—
197C22×C4×C61C2×Q812yes—
198C22×C4×C61#4112yes—
199C22×C4×C61#4112yes—
200C22×C4×C61#4112yes—
201C22×C4×C61#4112yes—
202C22×C4×C61#4112yes—
203C4⋊C4×C61—28no—
204C4⋊C4×C61—28no—
205C4⋊C4×C61—48no—
206C4⋊C4×C61—48no—
207C4⋊C4×C61—48no—
208C4⋊C4×C61—48no—
209C4⋊C4×C61—44no—
210C4⋊C4×C61—44no—
211C22⋊C4×C61—28no—
212C22⋊C4×C61—28no—
213C22⋊C4×C61—48no—
214C22⋊C4×C61—48no—
215C42×C61—28no—
216C42×C61—44no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61C4⋊Q814yes—
252C23×C61C22×D411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C22×D411yescharacteristic
256C23×C61C22×Q811yescharacteristic
257C23×C61C22×Q811yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61C2×#4111yescharacteristic
260C23×C61C2×#4111yescharacteristic
261C23×C61C2×#4111yescharacteristic
262C23×C61C2×#4111yescharacteristic
263C23×C61H(5,𝔽2)11yescharacteristic
264C23×C61H(5,𝔽2)11yescharacteristic
265C23×C612−1+411yescharacteristic
266C23×C612−1+411yescharacteristic
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—42no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—41no—
314C2×C4×C61—416no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61#12114yes—
330C2×C4×C61#12114yes—
331C2×C4×C61#12114yes—
332C2×C4×C61#12114yes—
333C2×C4×C61C22⋊Q814yes—
334C2×C4×C61C22⋊Q814yes—
335C2×C4×C61C22⋊Q814yes—
336C2×C4×C61C22⋊Q814yes—
337C2×C4×C61#12614yes—
338#15131C6111yesmaximal, characteristic, direct product factor, Sylow
339C22×C61—24no—
340C22×C61—24no—
341C22×C61—24no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61C2×#12111yescharacteristic
355C22×C61C2×#12111yescharacteristic
356C22×C61C2×#12111yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×C22⋊Q811yescharacteristic
359C22×C61C2×C22⋊Q811yescharacteristic
360C22×C61C2×C22⋊Q811yescharacteristic
361C22×C61C2×C22⋊Q811yescharacteristic
362C22×C61C2×#12611yescharacteristic
363C22×C61C2×C4⋊Q811yescharacteristic
364C22×C61#53211yescharacteristic
365C22×C61#53311yescharacteristic
366C22×C61#53311yescharacteristic
367C22×C61#53711yescharacteristic
368C22×C61#53711yescharacteristic
369C22×C61#54011yescharacteristic
370C22×C61#54111yescharacteristic
371C22×C61#54411yescharacteristic
372C22×C61#54411yescharacteristic
373C22×C61D4211yescharacteristic
374C22×C61D4211yescharacteristic
375C22×C61#54611yescharacteristic
376C22×C61#54711yescharacteristic
377C22×C61#54711yescharacteristic
378C22×C61#54711yescharacteristic
379C22×C61#54811yescharacteristic
380C22×C61D4×Q811yescharacteristic
381C22×C61D4×Q811yescharacteristic
382C22×C61#55011yescharacteristic
383C22×C61#55211yescharacteristic
384C22×C61#55311yescharacteristic
385C22×C61#55411yescharacteristic
386C22×C61#55411yescharacteristic
387C22×C61#55511yescharacteristic
388C22×C61#55611yescharacteristic
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—42no—
392C4×C61—44no—
393C4×C61—42no—
394C4×C61—44no—
395C4×C61—42no—
396C4×C61—82no—
397C4×C61—82no—
398C4×C61#39618yescomplemented
399C2×#396C2×C6112yes—
400C2×#389C2×C6111yescharacteristic, complemented
401C2×#389C2×C6111yescharacteristic, complemented
402C2×#384C2×C6111yescharacteristic, complemented
403C2×#380C2×C6111yescharacteristic
404C2×#380C2×C6111yescharacteristic
405C2×C4×C22⋊C4C2×C6111yescharacteristic
406#1441C2×C6112yescomplemented
407#1441C2×C6112yescomplemented
408#1439C2×C6112yes—
409C4⋊#95C2×C6111yescharacteristic, complemented
410C2×C61—44no—
411C2×C61C2×#39611yescharacteristic
412C2×C61#241611yescharacteristic
413C2×C61#241711yescharacteristic
414C2×C61#242811yescharacteristic
415C2×C61#242911yescharacteristic
416C2×C61#243911yescharacteristic
417C2×C61#244011yescharacteristic
418C2×C61#244011yescharacteristic
419C2×C61#244111yescharacteristic
420C2×C61#249611yescharacteristic
421C2×C61#249711yescharacteristic
422C2×C61#253711yescharacteristic
423C2×C61#253811yescharacteristic
424C2×C61#262911yescharacteristic
425C2×C61#285711yescharacteristic
426C24×C4C22×C6111yescharacteristic
427C22×C4⋊C4C22×C6112yes—
428C22×C4⋊C4C22×C6111yescharacteristic
429C22×C4⋊C4C22×C6111yescharacteristic
430C22×C4⋊C4C22×C6112yes—
431C22×C4⋊C4C22×C6112yes—
432C22×C4⋊C4C22×C6112yes—
433C22×C4⋊C4C22×C6111yescharacteristic
434C22×C4⋊C4C22×C6111yescharacteristic
435C22×C22⋊C4C22×C6112yes—
436C22×C22⋊C4C22×C6112yes—
437C22×C22⋊C4C22×C6111yescharacteristic
438C22×C22⋊C4C22×C6111yescharacteristic
439C22×C42C22×C6111yescharacteristic
440C22×C42C22×C6111yescharacteristic
441#396—28no—
442#389—24no—
443#389—24no—
444#384—24no—
445#380—24no—
446#380—24no—
447C4×C22⋊C4—24no—
448C2×#95C22×C6112yes—
449C2×#95C22×C6112yes—
450C2×#95C22×C6112yes—
451C2×#95C22×C6111yescharacteristic
452C2×#95C22×C6111yescharacteristic
453C2×#95C22×C6112yes—
454C2×#95C22×C6112yes—
455C2×#95C22×C6112yes—
456C61#1513111yescharacteristic, direct product factor, Sylow
457C25C23×C6111yescharacteristic
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4Q8×C6114yes—
465C23×C4C23×C6112yes—
466C23×C4C23×C6112yes—
467C23×C4C23×C6112yes—
468C23×C4C23×C6112yes—
469C23×C4C23×C6111yescharacteristic
470C23×C4C23×C6111yescharacteristic
471C23×C4C23×C6111yescharacteristic
472C23×C4C23×C6111yescharacteristic
473C23×C4C23×C6111yescharacteristic
474C23×C4C23×C6111yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4D4×C6114yes—
498C2×C4⋊C4D4×C6114yes—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4D4×C6114yes—
510C2×C22⋊C4Q8×C6114yes—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42D4×C6114yes—
517#95—22no—
518#95—22no—
519#95—24no—
520#95—24no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—42no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C6112yes—
538C24C2×Q8×C6112yes—
539C24C2×Q8×C6112yes—
540C24C24×C6111yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4C2×D4×C6114yes—
601C22×C4C2×D4×C6112yes—
602C22×C4C2×D4×C6114yes—
603C22×C4C2×D4×C6112yes—
604C22×C4C2×D4×C6112yes—
605C22×C4C2×D4×C6112yes—
606C22×C4C2×D4×C6112yes—
607C22×C4C2×D4×C6112yes—
608C22×C4C2×D4×C6112yes—
609C22×C4C2×Q8×C6112yes—
610C22×C4C2×Q8×C6112yes—
611C22×C4C2×Q8×C6112yes—
612C22×C4C2×Q8×C6112yes—
613C22×C4#41×C6112yes—
614C22×C4#41×C6112yes—
615C22×C4#41×C6112yes—
616C22×C4#41×C6112yes—
617C22×C4#41×C6112yes—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C42—28no—
631C42—44no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23C4⋊Q8×C6114yes—
667C23C22×D4×C6111yescharacteristic
668C23C22×D4×C6111yescharacteristic
669C23C22×D4×C6111yescharacteristic
670C23C22×D4×C6111yescharacteristic
671C23C22×Q8×C6111yescharacteristic
672C23C22×Q8×C6111yescharacteristic
673C23C2×#41×C6111yescharacteristic
674C23C2×#41×C6111yescharacteristic
675C23C2×#41×C6111yescharacteristic
676C23C2×#41×C6111yescharacteristic
677C23C2×#41×C6111yescharacteristic
678C23H(5,𝔽2)×C6111yescharacteristic
679C23H(5,𝔽2)×C6111yescharacteristic
680C232−1+4×C6111yescharacteristic
681C232−1+4×C6111yescharacteristic
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4#121×C6114yes—
745C2×C4#121×C6114yes—
746C2×C4#121×C6114yes—
747C2×C4#121×C6114yes—
748C2×C4C22⋊Q8×C6114yes—
749C2×C4C22⋊Q8×C6114yes—
750C2×C4C22⋊Q8×C6114yes—
751C2×C4C22⋊Q8×C6114yes—
752C2×C4#126×C6114yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22C2×#121×C6111yescharacteristic
769C22C2×#121×C6111yescharacteristic
770C22C2×#121×C6111yescharacteristic
771C22C2×#121×C6111yescharacteristic
772C22C2×C22⋊Q8×C6111yescharacteristic
773C22C2×C22⋊Q8×C6111yescharacteristic
774C22C2×C22⋊Q8×C6111yescharacteristic
775C22C2×C22⋊Q8×C6111yescharacteristic
776C22C2×#126×C6111yescharacteristic
777C22C2×C4⋊Q8×C6111yescharacteristic
778C22C61×#53211yescharacteristic
779C22C61×#53311yescharacteristic
780C22C61×#53311yescharacteristic
781C22C61×#53711yescharacteristic
782C22C61×#53711yescharacteristic
783C22C61×#54011yescharacteristic
784C22C61×#54111yescharacteristic
785C22C61×#54411yescharacteristic
786C22C61×#54411yescharacteristic
787C22D42×C6111yescharacteristic
788C22D42×C6111yescharacteristic
789C22C61×#54611yescharacteristic
790C22C61×#54711yescharacteristic
791C22C61×#54711yescharacteristic
792C22C61×#54711yescharacteristic
793C22C61×#54811yescharacteristic
794C22D4×Q8×C6111yescharacteristic
795C22D4×Q8×C6111yescharacteristic
796C22C61×#55011yescharacteristic
797C22C61×#55211yescharacteristic
798C22C61×#55311yescharacteristic
799C22C61×#55411yescharacteristic
800C22C61×#55411yescharacteristic
801C22C61×#55511yescharacteristic
802C22C61×#55611yescharacteristic
803C4—24no—
804C4—24no—
805C4—44no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—82no—
811C4—82no—
812C4C61×#39618yescomplemented
813C2—44no—
814C2C2×C61×#39611yescharacteristic
815C2C61×#241611yescharacteristic
816C2C61×#241711yescharacteristic
817C2C61×#242811yescharacteristic
818C2C61×#242911yescharacteristic
819C2C61×#243911yescharacteristic
820C2C61×#244011yescharacteristic
821C2C61×#244011yescharacteristic
822C2C61×#244111yescharacteristic
823C2C61×#249611yescharacteristic
824C2C61×#249711yescharacteristic
825C2C61×#253711yescharacteristic
826C2C61×#253811yescharacteristic
827C2C61×#262911yescharacteristic
828C2C61×#285711yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#389C2semidirect
3. C2×C61×#389C2semidirect
4. C2×C61×#384C2semidirect
8. C61×#1441C2semidirect
9. C61×#1441C2semidirect
11. C61×C4⋊#95C2semidirect
338. #15131C61direct (N × H)
398. C4×C61#396semidirect
400. C2×#389C2×C61semidirect
401. C2×#389C2×C61semidirect
402. C2×#384C2×C61semidirect
406. #1441C2×C61semidirect
407. #1441C2×C61semidirect
409. C4⋊#95C2×C61semidirect
456. C61#15131direct (N × H)
812. C4C61×#396semidirect

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×#3892
C2×C61×#3842
C2×C61×#3802
C2×C4×C22⋊C4×C612
C61×#14412
C61×#14392
C61×C4⋊#952
#1513161