Finite Group Databasebeta

← C61×#18446 #29521879

Subgroups — C61×#18446 #29521879

Order 15616.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3534C211yesmaximal, characteristic, complemented
2C61×#3192C211yesmaximal, characteristic, complemented
3C61×#3188C211yesmaximal, characteristic, complemented
4C61×#2813C211yesmaximal, characteristic, complemented
5C61×#1618C211yesmaximal, characteristic, complemented
6C61×#1616C211yesmaximal, characteristic, complemented
7C61×#1615C211yesmaximal, characteristic, complemented
8C61×#1613C211yesmaximal, characteristic, complemented
9C61×#1600C211yesmaximal, characteristic, complemented
10C61×#1598C211yesmaximal, characteristic, complemented
11C61×#1597C211yesmaximal, characteristic, complemented
12C61×#1595C211yesmaximal, characteristic, complemented
13C61×#1519C211yesmaximal, characteristic, complemented
14C61×#1513C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16C61×#562—21no—
17C61×#560—21no—
18C61×#553—21no—
19C61×#551—21no—
20C61×#546—21no—
21C61×#546—21no—
22C61×#546—21no—
23D42×C61—21no—
24C61×#540—21no—
25C61×#539—21no—
26C61×#539C2211yescharacteristic
27C61×#538—21no—
28C61×#538C2211yescharacteristic
29C61×#537C2211yescharacteristic
30C61×#534—21no—
31C61×#534C2211yescharacteristic
32C61×#525C2211yescharacteristic
33C2×#123×C61C2211yescharacteristic
34C2×#121×C61C2211yescharacteristic
35C2×#121×C61C2211yescharacteristic, complemented
36C61×#484C2211yescharacteristic, complemented
37C61×#482—21no—
38C61×#481—21no—
39C61×#481C2211yescharacteristic
40C61×#481C2211yescharacteristic, complemented
41C61×#481C2211yescharacteristic, complemented
42C61×#469—21no—
43C61×#469—21no—
44C61×#466—21no—
45C61×#465—21no—
46C61×#450C2211yescharacteristic, complemented
47C61×#449—21no—
48C61×#447—21no—
49C61×#447C2211yescharacteristic
50C61×#447C2211yescharacteristic, complemented
51C61×#447C2211yescharacteristic, complemented
52C61×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#400C2211yescharacteristic, complemented
55C61×#399C2211yescharacteristic, complemented
56C61×#396—21no—
57C61×#394—21no—
58C61×#394—21no—
59C61×#394C2211yescharacteristic, complemented
60C61×#392—21no—
61C61×#392C2211yescharacteristic, complemented
62C61×#380C2211yescharacteristic, complemented
63C61×#328C2211yescharacteristic, complemented
64C61×#328C2211yescharacteristic, complemented
65C61×#327C2211yescharacteristic
66C61×#327C2211yescharacteristic
67C61×#327C2211yescharacteristic, complemented
68C61×#327C2211yescharacteristic, complemented
69C61×#327C2211yescharacteristic, complemented
70C61×#327C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic, complemented
74C61×#323C2211yescharacteristic, complemented
75C2×#41×C61—21no—
76C2×#41×C61D411yescharacteristic, complemented
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61D411yescharacteristic
83C22×D4×C61D411yescharacteristic, complemented
84C22×D4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C2×SD16×C61—21no—
87C2×D8×C61—21no—
88C2×D8×C61—21no—
89C2×D8×C61—21no—
90C2×M16×C61—21no—
91C22×C8×C61—21no—
92#127×C61—21no—
93#126×C61—21no—
94#126×C61—21no—
95#126×C61—21no—
96#126×C61—21no—
97#125×C61—21no—
98#125×C61—21no—
99#124×C61—21no—
100#124×C61—21no—
101#124×C61—21no—
102#123×C61—21no—
103#123×C61—21no—
104#123×C61—21no—
105#123×C61—21no—
106#123×C61—21no—
107#123×C61—21no—
108#123×C61—21no—
109#123×C61—21no—
110#123×C61—21no—
111#123×C61—21no—
112#123×C61—21no—
113#123×C61—21no—
114#123×C61—21no—
115#123×C61—21no—
116C22⋊Q8×C61—21no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61D411yescharacteristic, complemented
122C22⋊Q8×C61C2311yescharacteristic
123#121×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61—21no—
137#121×C61—21no—
138#121×C61—21no—
139#121×C61—21no—
140#121×C61—21no—
141#121×C61—21no—
142#121×C61D411yescharacteristic, complemented
143#121×C61D411yescharacteristic, complemented
144#121×C61D411yescharacteristic, complemented
145#121×C61C2311yescharacteristic
146#121×C61C2311yescharacteristic
147#121×C61C2311yescharacteristic
148#120×C61—21no—
149#120×C61—21no—
150#120×C61—21no—
151#120×C61—21no—
152#120×C61—21no—
153#120×C61—21no—
154#120×C61—21no—
155#120×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61—21no—
164#117×C61—21no—
165#117×C61D411yescharacteristic, complemented
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61D411yescharacteristic, complemented
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C22⋊C4×C61C2311yescharacteristic
184#107×C61—21no—
185#106×C61—21no—
186#106×C61—21no—
187#106×C61—21no—
188#103×C61—21no—
189#102×C61—21no—
190#102×C61—21no—
191#102×C61—21no—
192#102×C61—21no—
193#102×C61—21no—
194#102×C61—21no—
195#102×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61C2311yescharacteristic
199C22⋊C8×C61C2311yescharacteristic
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202#95×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C24×C61—21no—
209C24×C61C2×D411yescharacteristic
210C24×C61C2×D411yescharacteristic
211#41×C61—81no—
212#41×C61—81no—
213#41×C61—81no—
214C2×Q8×C61—21no—
215C2×Q8×C61C2×D411yescharacteristic
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—41no—
236C2×D4×C61—41no—
237C2×D4×C61—81no—
238C2×D4×C61—81no—
239C2×D4×C61—81no—
240C2×D4×C61—81no—
241C2×D4×C61—81no—
242C2×D4×C61—81no—
243C2×D4×C61—81no—
244C2×D4×C61—81no—
245C2×D4×C61—81no—
246C2×D4×C61—81no—
247C2×D4×C61—81no—
248C2×D4×C61—81no—
249C2×D4×C61—82no—
250C2×D4×C61C2×D411yescharacteristic
251C2×D4×C61C2×D411yescharacteristic
252C2×D4×C61C2×D411yescharacteristic
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—81no—
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2411yescharacteristic
273SD16×C61—81no—
274D8×C61—81no—
275D8×C61—81no—
276D8×C61—81no—
277M16×C61—81no—
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C2×C8×C61—21no—
282C2×C8×C61—81no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61—81no—
299C4⋊C4×C61—81no—
300C4⋊C4×C61C2×D411yescharacteristic
301C4⋊C4×C61C2×D411yescharacteristic
302C4⋊C4×C61C2×D411yescharacteristic
303C4⋊C4×C61C2×D411yescharacteristic
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×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—41no—
330C22⋊C4×C61—41no—
331C22⋊C4×C61—81no—
332C22⋊C4×C61—81no—
333C22⋊C4×C61—81no—
334C22⋊C4×C61—81no—
335C22⋊C4×C61—81no—
336C42×C61—21no—
337C42×C61—21no—
338C42×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—42no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—81no—
360C23×C61—81no—
361C23×C61—81no—
362C23×C61—81no—
363C23×C61—81no—
364C23×C61#12011yescharacteristic
365C23×C61#12011yescharacteristic
366C23×C61C22×D411yescharacteristic
367Q8×C61—41no—
368Q8×C61—81no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—41no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—42no—
377D4×C61—42no—
378D4×C61—41no—
379D4×C61—41no—
380D4×C61—41no—
381D4×C61—41no—
382D4×C61—41no—
383D4×C61—41no—
384D4×C61—81no—
385D4×C61—81no—
386D4×C61—81no—
387D4×C61—81no—
388D4×C61—81no—
389D4×C61—81no—
390D4×C61—81no—
391D4×C61—81no—
392D4×C61—81no—
393D4×C61—81no—
394D4×C61—81no—
395D4×C61—81no—
396D4×C61—82no—
397D4×C61—82no—
398D4×C61—84no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—81no—
427C2×C4×C61—81no—
428C2×C4×C61—81no—
429C2×C4×C61—81no—
430C2×C4×C61—81no—
431C2×C4×C61—81no—
432C2×C4×C61—81no—
433C2×C4×C61#12011yescharacteristic
434C2×C4×C61#12011yescharacteristic
435C2×C4×C61C22×D411yescharacteristic
436C2×C4×C61C22×D411yescharacteristic
437C8×C61—41no—
438C8×C61—41no—
439C8×C61—41no—
440C8×C61—41no—
441#18446C6111yesmaximal, characteristic, direct product factor, Sylow
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—81no—
463C22×C61—81no—
464C22×C61—81no—
465C22×C61—81no—
466C22×C61—81no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—81no—
470C22×C61—81no—
471C22×C61—81no—
472C22×C61—81no—
473C22×C61—162no—
474C22×C61—162no—
475C22×C61C2×#12011yescharacteristic
476C22×C61#57611yescharacteristic
477C22×C61#57711yescharacteristic
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487C4×C61—41no—
488C4×C61—41no—
489C4×C61—41no—
490C4×C61—81no—
491C4×C61—81no—
492C4×C61—81no—
493#3534C2×C6111yescharacteristic, complemented
494#3192C2×C6111yescharacteristic, complemented
495#3188C2×C6111yescharacteristic, complemented
496#2813C2×C6111yescharacteristic, complemented
497#1618C2×C6111yescharacteristic, complemented
498#1616C2×C6111yescharacteristic, complemented
499#1615C2×C6111yescharacteristic, complemented
500#1613C2×C6111yescharacteristic, complemented
501#1600C2×C6111yescharacteristic, complemented
502#1598C2×C6111yescharacteristic, complemented
503#1597C2×C6111yescharacteristic, complemented
504#1595C2×C6111yescharacteristic, complemented
505#1519C2×C6111yescharacteristic, complemented
506#1513C2×C6111yescharacteristic, complemented
507#1468C2×C6111yescharacteristic, complemented
508C2×C61—21no—
509C2×C61—21no—
510C2×C61—41no—
511C2×C61—41no—
512C2×C61—81no—
513C2×C61—81no—
514C2×C61—81no—
515C2×C61—81no—
516C2×C61—161no—
517C2×C61#301211yescharacteristic
518C2×C61#302111yescharacteristic
519C2×C61#302611yescharacteristic
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C22×C6111yescharacteristic
531#538—21no—
532#538C22×C6111yescharacteristic
533#537C22×C6111yescharacteristic
534#534—21no—
535#534C22×C6111yescharacteristic
536#525C22×C6111yescharacteristic
537C2×#123C22×C6111yescharacteristic
538C2×#121C22×C6111yescharacteristic
539C2×#121C22×C6111yescharacteristic, complemented
540#484C22×C6111yescharacteristic, complemented
541#482—21no—
542#481—21no—
543#481C22×C6111yescharacteristic
544#481C22×C6111yescharacteristic, complemented
545#481C22×C6111yescharacteristic, complemented
546#469—21no—
547#469—21no—
548#466—21no—
549#465—21no—
550#450C22×C6111yescharacteristic, complemented
551#449—21no—
552#447—21no—
553#447C22×C6111yescharacteristic
554#447C22×C6111yescharacteristic, complemented
555#447C22×C6111yescharacteristic, complemented
556#407C22×C6111yescharacteristic, complemented
557C2×C22⋊C8C22×C6111yescharacteristic, complemented
558#400C22×C6111yescharacteristic, complemented
559#399C22×C6111yescharacteristic, complemented
560#396—21no—
561#394—21no—
562#394—21no—
563#394C22×C6111yescharacteristic, complemented
564#392—21no—
565#392C22×C6111yescharacteristic, complemented
566#380C22×C6111yescharacteristic, complemented
567#328C22×C6111yescharacteristic, complemented
568#328C22×C6111yescharacteristic, complemented
569#327C22×C6111yescharacteristic
570#327C22×C6111yescharacteristic
571#327C22×C6111yescharacteristic, complemented
572#327C22×C6111yescharacteristic, complemented
573#327C22×C6111yescharacteristic, complemented
574#327C22×C6111yescharacteristic, complemented
575#324C22×C6111yescharacteristic, complemented
576#324C22×C6111yescharacteristic, complemented
577#323C22×C6111yescharacteristic, complemented
578#323C22×C6111yescharacteristic, complemented
579C61#1844611yescharacteristic, direct product factor, Sylow
580C2×#41—21no—
581C2×#41D4×C6111yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C6111yescharacteristic
588C22×D4D4×C6111yescharacteristic, complemented
589C22×D4C23×C6111yescharacteristic
590C23×C4C23×C6111yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C6111yescharacteristic, complemented
627C22⋊Q8C23×C6111yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C6111yescharacteristic, complemented
648#121D4×C6111yescharacteristic, complemented
649#121D4×C6111yescharacteristic, complemented
650#121C23×C6111yescharacteristic
651#121C23×C6111yescharacteristic
652#121C23×C6111yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C6111yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4D4×C6111yescharacteristic
674C2×C4⋊C4D4×C6111yescharacteristic, complemented
675C2×C4⋊C4C23×C6111yescharacteristic
676C2×C4⋊C4C23×C6111yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C6111yescharacteristic
687C2×C22⋊C4D4×C6111yescharacteristic
688C2×C22⋊C4C23×C6111yescharacteristic
689#107—21no—
690#106—21no—
691#106—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C6111yescharacteristic
704C22⋊C8C23×C6111yescharacteristic
705C22⋊C8C23×C6111yescharacteristic
706C22⋊C8C23×C6111yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C6111yescharacteristic
710#95C23×C6111yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C6111yescharacteristic
715C24C2×D4×C6111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C6111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C6111yescharacteristic
756C2×D4C2×D4×C6111yescharacteristic
757C2×D4C2×D4×C6111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C6111yescharacteristic
770C22×C4C2×D4×C6111yescharacteristic
771C22×C4C2×D4×C6111yescharacteristic
772C22×C4C2×D4×C6111yescharacteristic
773C22×C4C2×D4×C6111yescharacteristic
774C22×C4C2×D4×C6111yescharacteristic
775C22×C4C2×D4×C6111yescharacteristic
776C22×C4C2×D4×C6111yescharacteristic
777C22×C4C24×C6111yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4—81no—
805C4⋊C4C2×D4×C6111yescharacteristic
806C4⋊C4C2×D4×C6111yescharacteristic
807C4⋊C4C2×D4×C6111yescharacteristic
808C4⋊C4C2×D4×C6111yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—81no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C22⋊C4—81no—
841C42—21no—
842C42—21no—
843C42—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C6111yescharacteristic
870C23#120×C6111yescharacteristic
871C23C22×D4×C6111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—82no—
902D4—82no—
903D4—84no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C6111yescharacteristic
939C2×C4#120×C6111yescharacteristic
940C2×C4C22×D4×C6111yescharacteristic
941C2×C4C22×D4×C6111yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C6111yescharacteristic
980C22C61×#57611yescharacteristic
981C22C61×#57711yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C61×#301211yescharacteristic
1007C2C61×#302111yescharacteristic
1008C2C61×#302611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3534C2semidirect
2. C61×#3192C2semidirect
3. C61×#3188C2semidirect
4. C61×#2813C2semidirect
5. C61×#1618C2semidirect
6. C61×#1616C2semidirect
7. C61×#1615C2semidirect
8. C61×#1613C2semidirect
9. C61×#1600C2semidirect
10. C61×#1598C2semidirect
11. C61×#1597C2semidirect
12. C61×#1595C2semidirect
13. C61×#1519C2semidirect
14. C61×#1513C2semidirect
15. C61×#1468C2semidirect
35. C2×#121×C61C22semidirect
36. C61×#484C22semidirect
40. C61×#481C22semidirect
41. C61×#481C22semidirect
46. C61×#450C22semidirect
50. C61×#447C22semidirect
51. C61×#447C22semidirect
52. C61×#407C22semidirect
53. C2×C22⋊C8×C61C22semidirect
54. C61×#400C22semidirect
55. C61×#399C22semidirect
59. C61×#394C22semidirect
61. C61×#392C22semidirect
62. C61×#380C22semidirect
63. C61×#328C22semidirect
64. C61×#328C22semidirect
67. C61×#327C22semidirect
68. C61×#327C22semidirect
69. C61×#327C22semidirect
70. C61×#327C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
73. C61×#323C22semidirect
74. C61×#323C22semidirect
76. C2×#41×C61D4semidirect
83. C22×D4×C61D4semidirect
121. C22⋊Q8×C61D4semidirect
142. #121×C61D4semidirect
143. #121×C61D4semidirect
144. #121×C61D4semidirect
165. #117×C61D4semidirect
169. C2×C4⋊C4×C61D4semidirect
441. #18446C61direct (N × H)
493. #3534C2×C61semidirect
494. #3192C2×C61semidirect
495. #3188C2×C61semidirect
496. #2813C2×C61semidirect
497. #1618C2×C61semidirect
498. #1616C2×C61semidirect
499. #1615C2×C61semidirect
500. #1613C2×C61semidirect
501. #1600C2×C61semidirect
502. #1598C2×C61semidirect
503. #1597C2×C61semidirect
504. #1595C2×C61semidirect
505. #1519C2×C61semidirect
506. #1513C2×C61semidirect
507. #1468C2×C61semidirect
539. C2×#121C22×C61semidirect
540. #484C22×C61semidirect
544. #481C22×C61semidirect
545. #481C22×C61semidirect
550. #450C22×C61semidirect
554. #447C22×C61semidirect
555. #447C22×C61semidirect
556. #407C22×C61semidirect
557. C2×C22⋊C8C22×C61semidirect
558. #400C22×C61semidirect
559. #399C22×C61semidirect
563. #394C22×C61semidirect
565. #392C22×C61semidirect
566. #380C22×C61semidirect
567. #328C22×C61semidirect
568. #328C22×C61semidirect
571. #327C22×C61semidirect
572. #327C22×C61semidirect
573. #327C22×C61semidirect
574. #327C22×C61semidirect
575. #324C22×C61semidirect
576. #324C22×C61semidirect
577. #323C22×C61semidirect
578. #323C22×C61semidirect
579. C61#18446direct (N × H)
581. C2×#41D4×C61semidirect
588. C22×D4D4×C61semidirect
626. C22⋊Q8D4×C61semidirect
647. #121D4×C61semidirect
648. #121D4×C61semidirect
649. #121D4×C61semidirect
670. #117D4×C61semidirect
674. C2×C4⋊C4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35342
C61×#31922
C61×#31882
C61×#28132
C61×#16182
C61×#16162
C61×#16152
C61×#16132
C61×#16002
C61×#15982
C61×#15972
C61×#15952
C61×#15192
C61×#15132
C61×#14682
#1844661