Finite Group Databasebeta

← C61×#26947 #29530380

Subgroups — C61×#26947 #29530380

Order 15616.

992 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#480C211yesmaximal, characteristic, complemented
2C2×C61×#460C211yesmaximal, characteristic, complemented
3C61×#2428C211yesmaximal, characteristic
4C61×#2360C211yesmaximal, characteristic, complemented
5C61×#2087C211yesmaximal, characteristic, complemented
6C61×#2041C211yesmaximal, characteristic, complemented
7C61×#2000C211yesmaximal, characteristic, complemented
8C61×#2000C211yesmaximal, characteristic, complemented
9C61×#1973C211yesmaximal, characteristic, complemented
10C61×#1925C211yesmaximal, characteristic, complemented
11C61×#1924C211yesmaximal, characteristic, complemented
12C61×#1877C211yesmaximal, characteristic, complemented
13C61×#1874C211yesmaximal, characteristic, complemented
14C61×#1863C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C2×#127×C61C2211yescharacteristic
19C2×C22⋊Q8×C61C2211yescharacteristic
20C2×#121×C61—21no—
21C2×#121×C61C2211yescharacteristic
22C2×#121×C61C2211yescharacteristic
23C2×C4×Q8×C61C2211yescharacteristic
24C2×C4×D4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C61×#480—24no—
27C61×#460—24no—
28C2×#107×C61C2211yescharacteristic
29C2×#107×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×C22⋊C8×C61C2211yescharacteristic
40C2×C22⋊C8×C61C2211yescharacteristic
41C2×#97×C61C2211yescharacteristic
42C61×#394—21no—
43C61×#392—21no—
44C61×#391C2211yescharacteristic
45C61×#390C2211yescharacteristic
46C61×#389—21no—
47C61×#389C2211yescharacteristic
48C61×#389C2211yescharacteristic
49C61×#387—21no—
50C61×#386—21no—
51C61×#385—21no—
52C4×C4⋊C4×C61C2211yescharacteristic
53C4×C22⋊C4×C61—21no—
54C4×C22⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61C2311yescharacteristic
67C22×D4×C61C2311yescharacteristic
68C23×C4×C61—21no—
69C23×C4×C61—21no—
70C23×C4×C61C2311yescharacteristic
71C2×SD16×C61—22no—
72C2×SD16×C61—22no—
73C2×SD16×C61—22no—
74C2×SD16×C61—22no—
75C2×SD16×C61—41no—
76C2×SD16×C61—41no—
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C22×C8×C61C2311yescharacteristic
81#127×C61—22no—
82#127×C61—41no—
83C22⋊Q8×C61—22no—
84C22⋊Q8×C61—22no—
85#121×C61—22no—
86#121×C61—22no—
87#121×C61—44no—
88#121×C61—41no—
89#121×C61—41no—
90C4×Q8×C61—22no—
91C4×Q8×C61—41no—
92C4×D4×C61—22no—
93C4×D4×C61—41no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—41no—
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61D411yescharacteristic
113C2×C22⋊C4×C61D411yescharacteristic
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118#107×C61—22no—
119#107×C61—22no—
120C4⋊C8×C61—22no—
121#103×C61—22no—
122#103×C61—41no—
123#102×C61—22no—
124#102×C61—22no—
125#102×C61—22no—
126#102×C61—22no—
127#102×C61—41no—
128#102×C61D414yescomplemented
129C22⋊C8×C61—22no—
130C22⋊C8×C61—41no—
131#97×C61—41no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61—21no—
141C24×C61C2×D411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61#4112yes—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61—81no—
168C2×D4×C61—81no—
169C2×D4×C61—81no—
170C2×D4×C61—81no—
171C2×D4×C61C2×D412yes—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—42no—
185C22×C4×C61—42no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61—81no—
189C22×C4×C61—81no—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2411yescharacteristic
196SD16×C61—44no—
197SD16×C61—44no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61C2×D412yes—
210C4⋊C4×C61—24no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61—42no—
221C4⋊C4×C61—81no—
222C4⋊C4×C61C2×D412yes—
223C4⋊C4×C61#4112yes—
224C4⋊C4×C61#4112yes—
225C22⋊C4×C61—24no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C22⋊C4×C61—81no—
233C42×C61—21no—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—42no—
238C42×C61—81no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61AGL(1,ℤ/8)12yes—
260C23×C61C22×D411yescharacteristic
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61—41no—
264Q8×C61—41no—
265D4×C61—22no—
266D4×C61—22no—
267D4×C61—41no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—41no—
273D4×C61—84no—
274D4×C61—84no—
275D4×C61—84no—
276D4×C61—84no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—84no—
314C2×C4×C61—84no—
315C2×C4×C61#13712yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C8×C61—22no—
323C8×C61—41no—
324C8×C61—41no—
325C8×C61—41no—
326#26947C6111yesmaximal, characteristic, direct product factor, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61#52511yescharacteristic
349C22×C61D4211yescharacteristic
350C22×C61#54611yescharacteristic
351C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C61C2×#13711yescharacteristic
353C22×C61#57611yescharacteristic
354C22×C61#57711yescharacteristic
355C4×C61—22no—
356C4×C61—41no—
357C4×C61—42no—
358C4×C61—41no—
359C4×C61—42no—
360C4×C61—41no—
361C4×C61—42no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—81no—
365C4×C61—81no—
366C4×C61#53211yescharacteristic
367C4×C61#54011yescharacteristic
368C4×C61#54611yescharacteristic
369C4×C61#55311yescharacteristic
370C2×#480C2×C6111yescharacteristic, complemented
371C2×#460C2×C6111yescharacteristic, complemented
372#2428C2×C6111yescharacteristic
373#2360C2×C6111yescharacteristic, complemented
374#2087C2×C6111yescharacteristic, complemented
375#2041C2×C6111yescharacteristic, complemented
376#2000C2×C6111yescharacteristic, complemented
377#2000C2×C6111yescharacteristic, complemented
378#1973C2×C6111yescharacteristic, complemented
379#1925C2×C6111yescharacteristic, complemented
380#1924C2×C6111yescharacteristic, complemented
381#1877C2×C6111yescharacteristic, complemented
382#1874C2×C6111yescharacteristic, complemented
383#1863C2×C6111yescharacteristic, complemented
384#1762C2×C6111yescharacteristic, complemented
385C2×C61—42no—
386C2×C61—82no—
387C2×C61—161no—
388C2×C61#246411yescharacteristic
389C2×C61#311211yescharacteristic
390C2×C61#311911yescharacteristic
391C2×C61#326411yescharacteristic
392C2×C61#326611yescharacteristic
393C2×C61#331011yescharacteristic
394C2×C61#333311yescharacteristic
395C22×SD16C22×C6111yescharacteristic
396C22×SD16C22×C6111yescharacteristic
397C2×#127C22×C6111yescharacteristic
398C2×C22⋊Q8C22×C6111yescharacteristic
399C2×#121—21no—
400C2×#121C22×C6111yescharacteristic
401C2×#121C22×C6111yescharacteristic
402C2×C4×Q8C22×C6111yescharacteristic
403C2×C4×D4C22×C6111yescharacteristic
404C22×C4⋊C4C22×C6111yescharacteristic
405#480—24no—
406#460—24no—
407C2×#107C22×C6111yescharacteristic
408C2×#107C22×C6111yescharacteristic
409C2×C4⋊C8C22×C6111yescharacteristic
410C2×#103C22×C6111yescharacteristic
411C2×#103C22×C6111yescharacteristic
412C2×#102C22×C6111yescharacteristic
413C2×#102C22×C6111yescharacteristic
414C2×#102C22×C6111yescharacteristic
415C2×#102C22×C6111yescharacteristic
416C2×#102C22×C6111yescharacteristic
417C2×#102C22×C6111yescharacteristic
418C2×C22⋊C8C22×C6111yescharacteristic
419C2×C22⋊C8C22×C6111yescharacteristic
420C2×#97C22×C6111yescharacteristic
421#394—21no—
422#392—21no—
423#391C22×C6111yescharacteristic
424#390C22×C6111yescharacteristic
425#389—21no—
426#389C22×C6111yescharacteristic
427#389C22×C6111yescharacteristic
428#387—21no—
429#386—21no—
430#385—21no—
431C4×C4⋊C4C22×C6111yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4C22×C6111yescharacteristic
434#340C22×C6111yescharacteristic
435#340C22×C6111yescharacteristic
436#340C22×C6111yescharacteristic
437#340C22×C6111yescharacteristic
438#336C22×C6111yescharacteristic
439#336C22×C6111yescharacteristic
440C61#2694711yescharacteristic, direct product factor, Sylow
441C22×Q8C23×C6111yescharacteristic
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C23×C6111yescharacteristic
447C22×D4C23×C6111yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4C23×C6111yescharacteristic
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—41no—
456C2×SD16—41no—
457C22×C8C23×C6111yescharacteristic
458C22×C8C23×C6111yescharacteristic
459C22×C8C23×C6111yescharacteristic
460C22×C8C23×C6111yescharacteristic
461#127—22no—
462#127—41no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465#121—22no—
466#121—22no—
467#121—44no—
468#121—41no—
469#121—41no—
470C4×Q8—22no—
471C4×Q8—41no—
472C4×D4—22no—
473C4×D4—41no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4C23×C6111yescharacteristic
482C2×C4⋊C4C23×C6111yescharacteristic
483C2×C4⋊C4C23×C6111yescharacteristic
484C2×C4⋊C4C23×C6111yescharacteristic
485C2×C4⋊C4C23×C6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C6111yescharacteristic
493C2×C22⋊C4D4×C6111yescharacteristic
494C2×C42—21no—
495C2×C42—21no—
496C2×C42C23×C6111yescharacteristic
497C2×C42C23×C6111yescharacteristic
498#107—22no—
499#107—22no—
500C4⋊C8—22no—
501#103—22no—
502#103—41no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—41no—
508#102D4×C6114yescomplemented
509C22⋊C8—22no—
510C22⋊C8—41no—
511#97—41no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95D4×C6111yescharacteristic
518#95D4×C6111yescharacteristic
519C24—21no—
520C24—21no—
521C24C2×D4×C6111yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#41×C6112yes—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4C2×D4×C6112yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4C2×D4×C6111yescharacteristic
571C22×C4C2×D4×C6111yescharacteristic
572C22×C4C2×D4×C6111yescharacteristic
573C22×C4C2×D4×C6111yescharacteristic
574C22×C4C2×D4×C6111yescharacteristic
575C22×C4C24×C6111yescharacteristic
576SD16—44no—
577SD16—44no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8C2×D4×C6112yes—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—81no—
602C4⋊C4C2×D4×C6112yes—
603C4⋊C4#41×C6112yes—
604C4⋊C4#41×C6112yes—
605C22⋊C4—24no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—42no—
618C42—81no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23AGL(1,ℤ/8)×C6112yes—
640C23C22×D4×C6111yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654D4—84no—
655D4—84no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4#137×C6112yes—
696C2×C4C22×D4×C6111yescharacteristic
697C2×C4C2×#41×C6111yescharacteristic
698C2×C4C2×#41×C6111yescharacteristic
699C2×C4C2×#41×C6111yescharacteristic
700C2×C4H(5,𝔽2)×C6111yescharacteristic
701C2×C4H(5,𝔽2)×C6111yescharacteristic
702C8—22no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C61×#52511yescharacteristic
728C22D42×C6111yescharacteristic
729C22C61×#54611yescharacteristic
730C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
731C22C2×#137×C6111yescharacteristic
732C22C61×#57611yescharacteristic
733C22C61×#57711yescharacteristic
734C4—22no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—41no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4C61×#53211yescharacteristic
746C4C61×#54011yescharacteristic
747C4C61×#54611yescharacteristic
748C4C61×#55311yescharacteristic
749C2—42no—
750C2—82no—
751C2—161no—
752C2C61×#246411yescharacteristic
753C2C61×#311211yescharacteristic
754C2C61×#311911yescharacteristic
755C2C61×#326411yescharacteristic
756C2C61×#326611yescharacteristic
757C2C61×#331011yescharacteristic
758C2C61×#333311yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#480C2semidirect
2. C2×C61×#460C2semidirect
4. C61×#2360C2semidirect
5. C61×#2087C2semidirect
6. C61×#2041C2semidirect
7. C61×#2000C2semidirect
8. C61×#2000C2semidirect
9. C61×#1973C2semidirect
10. C61×#1925C2semidirect
11. C61×#1924C2semidirect
12. C61×#1877C2semidirect
13. C61×#1874C2semidirect
14. C61×#1863C2semidirect
15. C61×#1762C2semidirect
128. #102×C61D4semidirect
326. #26947C61direct (N × H)
370. C2×#480C2×C61semidirect
371. C2×#460C2×C61semidirect
373. #2360C2×C61semidirect
374. #2087C2×C61semidirect
375. #2041C2×C61semidirect
376. #2000C2×C61semidirect
377. #2000C2×C61semidirect
378. #1973C2×C61semidirect
379. #1925C2×C61semidirect
380. #1924C2×C61semidirect
381. #1877C2×C61semidirect
382. #1874C2×C61semidirect
383. #1863C2×C61semidirect
384. #1762C2×C61semidirect
440. C61#26947direct (N × H)
508. #102D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4802
C2×C61×#4602
C61×#24282
C61×#23602
C61×#20872
C61×#20412
C61×#20002
C61×#19732
C61×#19252
C61×#19242
C61×#18772
C61×#18742
C61×#18632
C61×#17622
#2694761