Finite Group Databasebeta

← C61×#24124 #29527557

Subgroups — C61×#24124 #29527557

Order 15616.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#553C211yesmaximal, characteristic, complemented
2C2×C61×#478C211yesmaximal, characteristic, complemented
3C2×C4×D8×C61C211yesmaximal, characteristic, complemented
4C61×#2535C211yesmaximal, characteristic, complemented
5C61×#2034C211yesmaximal, characteristic, complemented
6C61×#2033C211yesmaximal, characteristic, complemented
7C61×#1999C211yesmaximal, characteristic, complemented
8C61×#1999C211yesmaximal, characteristic, complemented
9C61×#1991C211yesmaximal, characteristic, complemented
10C61×#1954C211yesmaximal, characteristic, complemented
11C61×#1875C211yesmaximal, characteristic, complemented
12C61×#1874C211yesmaximal, characteristic, complemented
13C61×#1854C211yesmaximal, characteristic, complemented
14C61×#1852C211yesmaximal, characteristic, complemented
15C61×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C61C2211yescharacteristic
17C61×#553—24no—
18C61×#553—24no—
19C2×#126×C61—21no—
20C2×#125×C61C2211yescharacteristic
21C2×#123×C61—21no—
22C2×#121×C61—21no—
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#121×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C2×C4×D4×C61—21no—
28C2×C4×D4×C61C2211yescharacteristic
29C2×C4×D4×C61C2211yescharacteristic
30C2×C4×D4×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C61×#478—24no—
34C4×D8×C61—24no—
35C2×#107×C61C2211yescharacteristic
36C2×#107×C61C2211yescharacteristic
37C2×#106×C61C2211yescharacteristic
38C2×C4⋊C8×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×C4×C8×C61C2211yescharacteristic
50C61×#397—21no—
51C61×#392—21no—
52C61×#386—21no—
53C61×#386—21no—
54C61×#382C2211yescharacteristic
55C61×#380C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61D411yescharacteristic
68C22×D4×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C23×C4×C61—21no—
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C2×D8×C61—22no—
76C2×D8×C61—22no—
77C2×D8×C61—22no—
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C22×C8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82#126×C61—28no—
83#125×C61—22no—
84#125×C61D414yescomplemented
85#123×C61—28no—
86#121×C61—28no—
87#121×C61—22no—
88#121×C61—22no—
89#121×C61—22no—
90#121×C61—22no—
91#121×C61—22no—
92#121×C61—22no—
93#121×C61—41no—
94#121×C61—41no—
95C4×D4×C61—28no—
96C4×D4×C61—22no—
97C4×D4×C61—22no—
98C4×D4×C61—22no—
99C4×D4×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61D414yescomplemented
102#117×C61—22no—
103#117×C61—22no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61D411yescharacteristic
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129#107×C61—22no—
130#107×C61—22no—
131#106×C61—22no—
132C4⋊C8×C61—22no—
133#102×C61—22no—
134#102×C61—22no—
135#102×C61—22no—
136#102×C61—22no—
137#102×C61—41no—
138#102×C61—41no—
139C22⋊C8×C61—22no—
140C22⋊C8×C61—22no—
141C22⋊C8×C61—41no—
142C22⋊C8×C61—41no—
143C4×C8×C61—22no—
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61C2×D411yescharacteristic
151C24×C61C2×D411yescharacteristic
152C2×D4×C61—24no—
153C2×D4×C61—22no—
154C2×D4×C61—24no—
155C2×D4×C61—22no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—41no—
167C2×D4×C61—42no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61—81no—
177C2×D4×C61C2×D412yes—
178C2×D4×C61#4112yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—24no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—24no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—42no—
200C22×C4×C61—81no—
201C22×C4×C61—81no—
202C22×C4×C61—81no—
203C22×C4×C61—81no—
204C22×C4×C61—81no—
205C22×C4×C61—81no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2411yescharacteristic
211D8×C61—28no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61#4112yes—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2×D412yes—
238C4⋊C4×C61C2×D412yes—
239C4⋊C4×C61C2×D412yes—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—42no—
247C22⋊C4×C61—42no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—81no—
250C22⋊C4×C61—81no—
251C42×C61—24no—
252C42×C61C2×D412yes—
253C42×C61C2×D412yes—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61#13512yes—
282C23×C61C22×D411yescharacteristic
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—44no—
288D4×C61—48no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—84no—
294D4×C61—84no—
295D4×C61—84no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—84no—
333C2×C4×C61—84no—
334C2×C4×C61—84no—
335C2×C4×C61#12012yes—
336C2×C4×C61#12012yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C612−1+411yescharacteristic
343C8×C61—22no—
344C8×C61—41no—
345C8×C61—41no—
346C8×C61—41no—
347#24124C6111yesmaximal, characteristic, direct product factor, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—41no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—42no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61C2×#12011yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61#54711yescharacteristic
379C22×C61C2×#13511yescharacteristic
380C22×C61#57511yescharacteristic
381C22×C61#57611yescharacteristic
382C22×C61#57611yescharacteristic
383C4×C61—22no—
384C4×C61—22no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—81no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61#52511yescharacteristic
394C4×C61#53711yescharacteristic
395C4×C61#54811yescharacteristic
396C4×C61#55011yescharacteristic
397C2×#553C2×C6111yescharacteristic, complemented
398C2×#478C2×C6111yescharacteristic, complemented
399C2×C4×D8C2×C6111yescharacteristic, complemented
400#2535C2×C6111yescharacteristic, complemented
401#2034C2×C6111yescharacteristic, complemented
402#2033C2×C6111yescharacteristic, complemented
403#1999C2×C6111yescharacteristic, complemented
404#1999C2×C6111yescharacteristic, complemented
405#1991C2×C6111yescharacteristic, complemented
406#1954C2×C6111yescharacteristic, complemented
407#1875C2×C6111yescharacteristic, complemented
408#1874C2×C6111yescharacteristic, complemented
409#1854C2×C6111yescharacteristic, complemented
410#1852C2×C6111yescharacteristic, complemented
411#1804C2×C6111yescharacteristic, complemented
412C2×C61—42no—
413C2×C61—81no—
414C2×C61—82no—
415C2×C61—82no—
416C2×C61#240711yescharacteristic
417C2×C61#300211yescharacteristic
418C2×C61#300811yescharacteristic
419C2×C61#329711yescharacteristic
420C2×C61#332211yescharacteristic
421C2×C61#333911yescharacteristic
422C2×C61#335511yescharacteristic
423C22×D8C22×C6111yescharacteristic
424#553—24no—
425#553—24no—
426C2×#126—21no—
427C2×#125C22×C6111yescharacteristic
428C2×#123—21no—
429C2×#121—21no—
430C2×#121C22×C6111yescharacteristic
431C2×#121C22×C6111yescharacteristic
432C2×#121C22×C6111yescharacteristic
433C2×#121C22×C6111yescharacteristic
434C2×C4×D4—21no—
435C2×C4×D4C22×C6111yescharacteristic
436C2×C4×D4C22×C6111yescharacteristic
437C2×C4×D4C22×C6111yescharacteristic
438C2×#117C22×C6111yescharacteristic
439C22×C4⋊C4C22×C6111yescharacteristic
440#478—24no—
441C4×D8—24no—
442C2×#107C22×C6111yescharacteristic
443C2×#107C22×C6111yescharacteristic
444C2×#106C22×C6111yescharacteristic
445C2×C4⋊C8C22×C6111yescharacteristic
446C2×#102C22×C6111yescharacteristic
447C2×#102C22×C6111yescharacteristic
448C2×#102C22×C6111yescharacteristic
449C2×#102C22×C6111yescharacteristic
450C2×#102C22×C6111yescharacteristic
451C2×#102C22×C6111yescharacteristic
452C2×C22⋊C8C22×C6111yescharacteristic
453C2×C22⋊C8C22×C6111yescharacteristic
454C2×C22⋊C8C22×C6111yescharacteristic
455C2×C22⋊C8C22×C6111yescharacteristic
456C2×C4×C8C22×C6111yescharacteristic
457#397—21no—
458#392—21no—
459#386—21no—
460#386—21no—
461#382C22×C6111yescharacteristic
462#380C22×C6111yescharacteristic
463#380C22×C6111yescharacteristic
464#340C22×C6111yescharacteristic
465#340C22×C6111yescharacteristic
466#340C22×C6111yescharacteristic
467#340C22×C6111yescharacteristic
468#340C22×C6111yescharacteristic
469#340C22×C6111yescharacteristic
470C61#2412411yescharacteristic, direct product factor, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C6111yescharacteristic
476C22×D4C23×C6111yescharacteristic
477C22×D4C23×C6111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C6111yescharacteristic
482C23×C4C23×C6111yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C6111yescharacteristic
487C22×C8C23×C6111yescharacteristic
488C22×C8C23×C6111yescharacteristic
489C22×C8C23×C6111yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C6114yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C6114yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C6111yescharacteristic
518C2×C4⋊C4C23×C6111yescharacteristic
519C2×C4⋊C4C23×C6111yescharacteristic
520C2×C4⋊C4C23×C6111yescharacteristic
521C2×C4⋊C4C23×C6111yescharacteristic
522C2×C4⋊C4C23×C6111yescharacteristic
523C2×C4⋊C4C23×C6111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C6111yescharacteristic
534C2×C22⋊C4D4×C6111yescharacteristic
535C2×C42—21no—
536C2×C42C23×C6111yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C6111yescharacteristic
559C24C2×D4×C6111yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C6112yes—
586C2×D4#41×C6112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C6111yescharacteristic
615C22×C4C2×D4×C6111yescharacteristic
616C22×C4C2×D4×C6111yescharacteristic
617C22×C4C2×D4×C6111yescharacteristic
618C22×C4C24×C6111yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C6112yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C6112yes—
646C4⋊C4C2×D4×C6112yes—
647C4⋊C4C2×D4×C6112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C6112yes—
661C42C2×D4×C6112yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C6112yes—
690C23C22×D4×C6111yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C6112yes—
744C2×C4#120×C6112yes—
745C2×C4C22×D4×C6111yescharacteristic
746C2×C4C22×D4×C6111yescharacteristic
747C2×C4C2×#41×C6111yescharacteristic
748C2×C4C2×#41×C6111yescharacteristic
749C2×C4H(5,𝔽2)×C6111yescharacteristic
750C2×C42−1+4×C6111yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C6111yescharacteristic
784C22C61×#54611yescharacteristic
785C22C61×#54711yescharacteristic
786C22C2×#135×C6111yescharacteristic
787C22C61×#57511yescharacteristic
788C22C61×#57611yescharacteristic
789C22C61×#57611yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4C61×#52511yescharacteristic
801C4C61×#53711yescharacteristic
802C4C61×#54811yescharacteristic
803C4C61×#55011yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C61×#240711yescharacteristic
809C2C61×#300211yescharacteristic
810C2C61×#300811yescharacteristic
811C2C61×#329711yescharacteristic
812C2C61×#332211yescharacteristic
813C2C61×#333911yescharacteristic
814C2C61×#335511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#553C2semidirect
2. C2×C61×#478C2semidirect
3. C2×C4×D8×C61C2semidirect
4. C61×#2535C2semidirect
5. C61×#2034C2semidirect
6. C61×#2033C2semidirect
7. C61×#1999C2semidirect
8. C61×#1999C2semidirect
9. C61×#1991C2semidirect
10. C61×#1954C2semidirect
11. C61×#1875C2semidirect
12. C61×#1874C2semidirect
13. C61×#1854C2semidirect
14. C61×#1852C2semidirect
15. C61×#1804C2semidirect
84. #125×C61D4semidirect
101. C4×D4×C61D4semidirect
347. #24124C61direct (N × H)
397. C2×#553C2×C61semidirect
398. C2×#478C2×C61semidirect
399. C2×C4×D8C2×C61semidirect
400. #2535C2×C61semidirect
401. #2034C2×C61semidirect
402. #2033C2×C61semidirect
403. #1999C2×C61semidirect
404. #1999C2×C61semidirect
405. #1991C2×C61semidirect
406. #1954C2×C61semidirect
407. #1875C2×C61semidirect
408. #1874C2×C61semidirect
409. #1854C2×C61semidirect
410. #1852C2×C61semidirect
411. #1804C2×C61semidirect
470. C61#24124direct (N × H)
492. #125D4×C61semidirect
509. C4×D4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5532
C2×C61×#4782
C2×C4×D8×C612
C61×#25352
C61×#20342
C61×#20332
C61×#19992
C61×#19912
C61×#19542
C61×#18752
C61×#18742
C61×#18542
C61×#18522
C61×#18042
#2412461