Finite Group Databasebeta

← C61×#18448 #29521881

Subgroups — C61×#18448 #29521881

Order 15616.

968 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3535C211yesmaximal, characteristic, complemented
2C61×#3193C211yesmaximal, characteristic, complemented
3C61×#3188C211yesmaximal, characteristic, complemented
4C61×#2813C211yesmaximal, characteristic, complemented
5C61×#1618C211yesmaximal, characteristic, complemented
6C61×#1617C211yesmaximal, characteristic, complemented
7C61×#1615C211yesmaximal, characteristic, complemented
8C61×#1614C211yesmaximal, characteristic, complemented
9C61×#1600C211yesmaximal, characteristic, complemented
10C61×#1599C211yesmaximal, characteristic, complemented
11C61×#1597C211yesmaximal, characteristic, complemented
12C61×#1596C211yesmaximal, characteristic, complemented
13C61×#1520C211yesmaximal, characteristic, complemented
14C61×#1513C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16C61×#563—21no—
17C61×#562—21no—
18C61×#554—21no—
19C61×#552—21no—
20C61×#551—21no—
21C61×#551—21no—
22C61×#547—21no—
23C61×#546—21no—
24C61×#544C2211yescharacteristic
25C61×#543C2211yescharacteristic
26C61×#542—21no—
27C61×#539—21no—
28C61×#539—21no—
29C61×#539C2211yescharacteristic
30C61×#538C2211yescharacteristic
31C61×#536—21no—
32C61×#525C2211yescharacteristic
33C2×#123×C61C2211yescharacteristic
34C2×C22⋊Q8×C61C2211yescharacteristic
35C2×#121×C61C2211yescharacteristic
36C61×#484C2211yescharacteristic
37C61×#484C2211yescharacteristic
38C61×#484C2211yescharacteristic
39C61×#482—21no—
40C61×#481C2211yescharacteristic
41C61×#480—21no—
42C61×#468—21no—
43C61×#468—21no—
44C61×#466—21no—
45C61×#465—21no—
46C61×#450C2211yescharacteristic
47C61×#450C2211yescharacteristic
48C61×#450C2211yescharacteristic
49C61×#449—21no—
50C61×#448—21no—
51C61×#447C2211yescharacteristic
52C61×#407C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C61×#400C2211yescharacteristic
55C61×#399C2211yescharacteristic
56C61×#396—21no—
57C61×#394—21no—
58C61×#394—21no—
59C61×#394C2211yescharacteristic
60C61×#392—21no—
61C61×#392C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C61×#328C2211yescharacteristic
64C61×#328C2211yescharacteristic
65C61×#328C2211yescharacteristic
66C61×#328C2211yescharacteristic
67C61×#328C2211yescharacteristic
68C61×#328C2211yescharacteristic
69C61×#327C2211yescharacteristic
70C61×#327C2211yescharacteristic
71C61×#324C2211yescharacteristic
72C61×#324C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C2×#41×C61—21no—
76C2×#41×C61D411yescharacteristic, complemented
77C22×Q8×C61D411yescharacteristic, complemented
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61D411yescharacteristic
81C22×D4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C2×SD16×C61—21no—
84C2×SD16×C61—21no—
85C2×SD16×C61—21no—
86C2×D8×C61—21no—
87C2×M16×C61—21no—
88C22×C8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61—21no—
92#126×C61—21no—
93#126×C61—21no—
94#126×C61—21no—
95#126×C61—21no—
96#126×C61—21no—
97#126×C61—21no—
98#125×C61—21no—
99#125×C61—21no—
100#125×C61—21no—
101#125×C61—21no—
102#125×C61—21no—
103#124×C61—21no—
104#124×C61—21no—
105#124×C61—21no—
106#124×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—
116#123×C61—21no—
117#123×C61—21no—
118#123×C61—21no—
119#123×C61—21no—
120#123×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61D411yescharacteristic, complemented
136C22⋊Q8×C61D411yescharacteristic, complemented
137C22⋊Q8×C61D411yescharacteristic, complemented
138C22⋊Q8×C61C2311yescharacteristic
139C22⋊Q8×C61C2311yescharacteristic
140C22⋊Q8×C61C2311yescharacteristic
141#121×C61—21no—
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61D411yescharacteristic, complemented
150#121×C61C2311yescharacteristic
151#120×C61—21no—
152#120×C61—21no—
153C4×Q8×C61—21no—
154C4×D4×C61—21no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161#117×C61—21no—
162#117×C61—21no—
163#117×C61—21no—
164#117×C61D411yescharacteristic, complemented
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61D411yescharacteristic, complemented
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
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#107×C61—21no—
186#107×C61—21no—
187#106×C61—21no—
188#103×C61—21no—
189#103×C61—21no—
190#103×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×C61C2×D411yescharacteristic
208C24×C61C2×D411yescharacteristic
209#41×C61—82no—
210#41×C61—81no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—81no—
215C2×Q8×C61C2×D411yescharacteristic
216C2×Q8×C61C2×D411yescharacteristic
217C2×Q8×C61C2×D411yescharacteristic
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—41no—
228C2×D4×C61—41no—
229C2×D4×C61—81no—
230C2×D4×C61—81no—
231C2×D4×C61—81no—
232C2×D4×C61—81no—
233C2×D4×C61—81no—
234C2×D4×C61—81no—
235C2×D4×C61—81no—
236C2×D4×C61C2×D411yescharacteristic
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—81no—
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2411yescharacteristic
257SD16×C61—81no—
258SD16×C61—81no—
259SD16×C61—81no—
260D8×C61—81no—
261M16×C61—81no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—81no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
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—81no—
293C4⋊C4×C61—81no—
294C4⋊C4×C61C2×D411yescharacteristic
295C4⋊C4×C61C2×D411yescharacteristic
296C4⋊C4×C61C2×D411yescharacteristic
297C4⋊C4×C61C2×D411yescharacteristic
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×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—41no—
322C22⋊C4×C61—41no—
323C22⋊C4×C61—81no—
324C22⋊C4×C61—81no—
325C22⋊C4×C61—81no—
326C22⋊C4×C61—81no—
327C22⋊C4×C61—81no—
328C42×C61—21no—
329C42×C61—21no—
330C42×C61—21no—
331C42×C61—21no—
332C42×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61#12011yescharacteristic
351C23×C61#12011yescharacteristic
352C23×C61C22×D411yescharacteristic
353Q8×C61—41no—
354Q8×C61—41no—
355Q8×C61—41no—
356Q8×C61—81no—
357Q8×C61—81no—
358Q8×C61—81no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—41no—
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—42no—
365D4×C61—42no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—81no—
369D4×C61—81no—
370D4×C61—81no—
371D4×C61—81no—
372D4×C61—82no—
373D4×C61—82no—
374D4×C61—84no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—42no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—81no—
406C2×C4×C61—81no—
407C2×C4×C61—81no—
408C2×C4×C61—81no—
409C2×C4×C61—81no—
410C2×C4×C61—81no—
411C2×C4×C61#12011yescharacteristic
412C2×C4×C61#12011yescharacteristic
413C2×C4×C61C22×D411yescharacteristic
414C2×C4×C61C22×D411yescharacteristic
415C8×C61—41no—
416C8×C61—41no—
417C8×C61—41no—
418C8×C61—41no—
419#18448C6111yesmaximal, characteristic, direct product factor, Sylow
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61C2×#12011yescharacteristic
446C22×C61#57711yescharacteristic
447C22×C61#57811yescharacteristic
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—41no—
453C4×C61—41no—
454C4×C61—41no—
455C4×C61—41no—
456C4×C61—41no—
457C4×C61—41no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—81no—
463C4×C61—81no—
464C4×C61—81no—
465#3535C2×C6111yescharacteristic, complemented
466#3193C2×C6111yescharacteristic, complemented
467#3188C2×C6111yescharacteristic, complemented
468#2813C2×C6111yescharacteristic, complemented
469#1618C2×C6111yescharacteristic, complemented
470#1617C2×C6111yescharacteristic, complemented
471#1615C2×C6111yescharacteristic, complemented
472#1614C2×C6111yescharacteristic, complemented
473#1600C2×C6111yescharacteristic, complemented
474#1599C2×C6111yescharacteristic, complemented
475#1597C2×C6111yescharacteristic, complemented
476#1596C2×C6111yescharacteristic, complemented
477#1520C2×C6111yescharacteristic, complemented
478#1513C2×C6111yescharacteristic, complemented
479#1468C2×C6111yescharacteristic, complemented
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—41no—
483C2×C61—41no—
484C2×C61—81no—
485C2×C61—81no—
486C2×C61—161no—
487C2×C61#301311yescharacteristic
488C2×C61#302111yescharacteristic
489C2×C61#302611yescharacteristic
490#563—21no—
491#562—21no—
492#554—21no—
493#552—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#544C22×C6111yescharacteristic
499#543C22×C6111yescharacteristic
500#542—21no—
501#539—21no—
502#539—21no—
503#539C22×C6111yescharacteristic
504#538C22×C6111yescharacteristic
505#536—21no—
506#525C22×C6111yescharacteristic
507C2×#123C22×C6111yescharacteristic
508C2×C22⋊Q8C22×C6111yescharacteristic
509C2×#121C22×C6111yescharacteristic
510#484C22×C6111yescharacteristic
511#484C22×C6111yescharacteristic
512#484C22×C6111yescharacteristic
513#482—21no—
514#481C22×C6111yescharacteristic
515#480—21no—
516#468—21no—
517#468—21no—
518#466—21no—
519#465—21no—
520#450C22×C6111yescharacteristic
521#450C22×C6111yescharacteristic
522#450C22×C6111yescharacteristic
523#449—21no—
524#448—21no—
525#447C22×C6111yescharacteristic
526#407C22×C6111yescharacteristic
527C2×C22⋊C8C22×C6111yescharacteristic
528#400C22×C6111yescharacteristic
529#399C22×C6111yescharacteristic
530#396—21no—
531#394—21no—
532#394—21no—
533#394C22×C6111yescharacteristic
534#392—21no—
535#392C22×C6111yescharacteristic
536#380C22×C6111yescharacteristic
537#328C22×C6111yescharacteristic
538#328C22×C6111yescharacteristic
539#328C22×C6111yescharacteristic
540#328C22×C6111yescharacteristic
541#328C22×C6111yescharacteristic
542#328C22×C6111yescharacteristic
543#327C22×C6111yescharacteristic
544#327C22×C6111yescharacteristic
545#324C22×C6111yescharacteristic
546#324C22×C6111yescharacteristic
547#323C22×C6111yescharacteristic
548#323C22×C6111yescharacteristic
549C61#1844811yescharacteristic, direct product factor, Sylow
550C2×#41—21no—
551C2×#41D4×C6111yescharacteristic, complemented
552C22×Q8D4×C6111yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C6111yescharacteristic
556C22×D4C23×C6111yescharacteristic
557C23×C4C23×C6111yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C6111yescharacteristic, complemented
611C22⋊Q8D4×C6111yescharacteristic, complemented
612C22⋊Q8D4×C6111yescharacteristic, complemented
613C22⋊Q8C23×C6111yescharacteristic
614C22⋊Q8C23×C6111yescharacteristic
615C22⋊Q8C23×C6111yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C6111yescharacteristic, complemented
625#121C23×C6111yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C6111yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4D4×C6111yescharacteristic
645C2×C4⋊C4D4×C6111yescharacteristic, complemented
646C2×C4⋊C4C23×C6111yescharacteristic
647C2×C4⋊C4C23×C6111yescharacteristic
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4D4×C6111yescharacteristic
657C2×C22⋊C4D4×C6111yescharacteristic
658C2×C22⋊C4C23×C6111yescharacteristic
659#107—21no—
660#107—21no—
661#107—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C6111yescharacteristic
674C22⋊C8C23×C6111yescharacteristic
675C22⋊C8C23×C6111yescharacteristic
676C22⋊C8C23×C6111yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C6111yescharacteristic
680#95C23×C6111yescharacteristic
681C24—21no—
682C24C2×D4×C6111yescharacteristic
683C24C2×D4×C6111yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C6111yescharacteristic
691C2×Q8C2×D4×C6111yescharacteristic
692C2×Q8C2×D4×C6111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C6111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C6111yescharacteristic
724C22×C4C2×D4×C6111yescharacteristic
725C22×C4C2×D4×C6111yescharacteristic
726C22×C4C2×D4×C6111yescharacteristic
727C22×C4C2×D4×C6111yescharacteristic
728C22×C4C2×D4×C6111yescharacteristic
729C22×C4C2×D4×C6111yescharacteristic
730C22×C4C2×D4×C6111yescharacteristic
731C22×C4C24×C6111yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C6111yescharacteristic
770C4⋊C4C2×D4×C6111yescharacteristic
771C4⋊C4C2×D4×C6111yescharacteristic
772C4⋊C4C2×D4×C6111yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—41no—
797C22⋊C4—41no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C22⋊C4—81no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C6111yescharacteristic
826C23#120×C6111yescharacteristic
827C23C22×D4×C6111yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—82no—
848D4—82no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C6111yescharacteristic
887C2×C4#120×C6111yescharacteristic
888C2×C4C22×D4×C6111yescharacteristic
889C2×C4C22×D4×C6111yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C6111yescharacteristic
920C22C61×#57711yescharacteristic
921C22C61×#57811yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C61×#301311yescharacteristic
947C2C61×#302111yescharacteristic
948C2C61×#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×#3535C2semidirect
2. C61×#3193C2semidirect
3. C61×#3188C2semidirect
4. C61×#2813C2semidirect
5. C61×#1618C2semidirect
6. C61×#1617C2semidirect
7. C61×#1615C2semidirect
8. C61×#1614C2semidirect
9. C61×#1600C2semidirect
10. C61×#1599C2semidirect
11. C61×#1597C2semidirect
12. C61×#1596C2semidirect
13. C61×#1520C2semidirect
14. C61×#1513C2semidirect
15. C61×#1468C2semidirect
76. C2×#41×C61D4semidirect
77. C22×Q8×C61D4semidirect
135. C22⋊Q8×C61D4semidirect
136. C22⋊Q8×C61D4semidirect
137. C22⋊Q8×C61D4semidirect
149. #121×C61D4semidirect
164. #117×C61D4semidirect
170. C2×C4⋊C4×C61D4semidirect
419. #18448C61direct (N × H)
465. #3535C2×C61semidirect
466. #3193C2×C61semidirect
467. #3188C2×C61semidirect
468. #2813C2×C61semidirect
469. #1618C2×C61semidirect
470. #1617C2×C61semidirect
471. #1615C2×C61semidirect
472. #1614C2×C61semidirect
473. #1600C2×C61semidirect
474. #1599C2×C61semidirect
475. #1597C2×C61semidirect
476. #1596C2×C61semidirect
477. #1520C2×C61semidirect
478. #1513C2×C61semidirect
479. #1468C2×C61semidirect
549. C61#18448direct (N × H)
551. C2×#41D4×C61semidirect
552. C22×Q8D4×C61semidirect
610. C22⋊Q8D4×C61semidirect
611. C22⋊Q8D4×C61semidirect
612. C22⋊Q8D4×C61semidirect
624. #121D4×C61semidirect
639. #117D4×C61semidirect
645. 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×#35352
C61×#31932
C61×#31882
C61×#28132
C61×#16182
C61×#16172
C61×#16152
C61×#16142
C61×#16002
C61×#15992
C61×#15972
C61×#15962
C61×#15202
C61×#15132
C61×#14682
#1844861