Finite Group Databasebeta

← C61×#18262 #29521695

Subgroups — C61×#18262 #29521695

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3534C211yesmaximal, characteristic
2C61×#3094C211yesmaximal, characteristic, complemented
3C61×#3091C211yesmaximal, characteristic, complemented
4C61×#2498C211yesmaximal, characteristic, complemented
5C61×#1618C211yesmaximal, characteristic, complemented
6C61×#1616C211yesmaximal, characteristic, complemented
7C61×#1615C211yesmaximal, characteristic, complemented
8C61×#1613C211yesmaximal, characteristic, complemented
9C61×#1612C211yesmaximal, characteristic, complemented
10C61×#1610C211yesmaximal, characteristic, complemented
11C61×#1609C211yesmaximal, characteristic, complemented
12C61×#1607C211yesmaximal, characteristic, complemented
13C61×#1504C211yesmaximal, characteristic, complemented
14C2×C61×#327C211yesmaximal, 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×#117×C61C2211yescharacteristic, complemented
36C61×#485—21no—
37C61×#484C2211yescharacteristic, complemented
38C61×#483C2211yescharacteristic, complemented
39C61×#482—21no—
40C61×#482—21no—
41C61×#482—21no—
42C61×#481C2211yescharacteristic
43C61×#481C2211yescharacteristic, complemented
44C61×#481C2211yescharacteristic, complemented
45C61×#480C2211yescharacteristic
46C61×#480C2211yescharacteristic, complemented
47C61×#480C2211yescharacteristic, complemented
48C61×#428—21no—
49C61×#427—21no—
50C61×#418—21no—
51C61×#416—21no—
52C61×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#400C2211yescharacteristic, complemented
55C61×#399C2211yescharacteristic, complemented
56C61×#398C2211yescharacteristic, complemented
57C61×#397C2211yescharacteristic, complemented
58C61×#388—21no—
59C61×#387—21no—
60C61×#386—21no—
61C61×#380—21no—
62C2×#95×C61C2211yescharacteristic, 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
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61D411yescharacteristic
81C22×D4×C61D411yescharacteristic
82C23×C4×C61—21no—
83C23×C4×C61C2311yescharacteristic
84C2×M16×C61—21no—
85C22×C8×C61—21no—
86#127×C61—21no—
87#126×C61—21no—
88#126×C61—21no—
89#126×C61—21no—
90#126×C61—21no—
91#125×C61—21no—
92#125×C61—21no—
93#124×C61—21no—
94#124×C61—21no—
95#124×C61—21no—
96#123×C61—21no—
97#123×C61—21no—
98#123×C61—21no—
99#123×C61—21no—
100#123×C61—21no—
101#123×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—
110C22⋊Q8×C61—21no—
111C22⋊Q8×C61—21no—
112C22⋊Q8×C61—21no—
113C22⋊Q8×C61—21no—
114C22⋊Q8×C61—21no—
115C22⋊Q8×C61D411yescharacteristic
116C22⋊Q8×C61C2311yescharacteristic
117#121×C61—21no—
118#121×C61—21no—
119#121×C61—21no—
120#121×C61—21no—
121#121×C61—21no—
122#121×C61—21no—
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×C61D411yescharacteristic
133#121×C61D411yescharacteristic
134#121×C61D411yescharacteristic
135#121×C61C2311yescharacteristic
136#121×C61C2311yescharacteristic
137#121×C61C2311yescharacteristic
138#120×C61—21no—
139#120×C61—21no—
140#120×C61—21no—
141#120×C61—21no—
142#120×C61—21no—
143#120×C61—21no—
144#120×C61—21no—
145#120×C61—21no—
146C4×D4×C61—21no—
147C4×D4×C61—21no—
148C4×D4×C61—21no—
149C4×D4×C61—21no—
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154#117×C61—21no—
155#117×C61—21no—
156#117×C61—21no—
157#117×C61—21no—
158#117×C61—21no—
159#117×C61D411yescharacteristic
160C2×C4⋊C4×C61—21no—
161C2×C4⋊C4×C61—21no—
162C2×C4⋊C4×C61D411yescharacteristic
163C2×C4⋊C4×C61D411yescharacteristic
164C2×C4⋊C4×C61C2311yescharacteristic
165C2×C4⋊C4×C61C2311yescharacteristic
166C2×C4⋊C4×C61C2311yescharacteristic
167C2×C22⋊C4×C61—21no—
168C2×C22⋊C4×C61—21no—
169C2×C22⋊C4×C61—21no—
170C2×C22⋊C4×C61—21no—
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C22⋊C4×C61D411yescharacteristic
175C2×C22⋊C4×C61C2311yescharacteristic
176C2×C42×C61—21no—
177#107×C61—21no—
178#107×C61—21no—
179#107×C61—21no—
180#107×C61—21no—
181#106×C61—21no—
182#106×C61—21no—
183#106×C61—21no—
184#106×C61—21no—
185#103×C61—21no—
186#103×C61—21no—
187#102×C61—21no—
188#102×C61—21no—
189#102×C61—21no—
190#102×C61—21no—
191#102×C61—21no—
192#102×C61—21no—
193C22⋊C8×C61—21no—
194C22⋊C8×C61—21no—
195C22⋊C8×C61C2311yescharacteristic
196C22⋊C8×C61C2311yescharacteristic
197C22⋊C8×C61C2311yescharacteristic
198C22⋊C8×C61C2311yescharacteristic
199#95×C61—21no—
200#95×C61—21no—
201#95×C61—21no—
202#95×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209C24×C61C2×D411yescharacteristic
210#41×C61—42no—
211#41×C61—81no—
212#41×C61—81no—
213C2×Q8×C61—21no—
214C2×Q8×C61C2×D411yescharacteristic
215C2×D4×C61—21no—
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—42no—
233C2×D4×C61—42no—
234C2×D4×C61—81no—
235C2×D4×C61—81no—
236C2×D4×C61—81no—
237C2×D4×C61—81no—
238C2×D4×C61—82no—
239C2×D4×C61C2×D411yescharacteristic
240C2×D4×C61C2×D411yescharacteristic
241C2×D4×C61C2×D411yescharacteristic
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—42no—
254C22×C4×C61—42no—
255C22×C4×C61—42no—
256C22×C4×C61—81no—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2411yescharacteristic
266M16×C61—42no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—42no—
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—42no—
290C4⋊C4×C61—81no—
291C4⋊C4×C61C2×D411yescharacteristic
292C4⋊C4×C61C2×D411yescharacteristic
293C4⋊C4×C61C2×D411yescharacteristic
294C4⋊C4×C61C2×D411yescharacteristic
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
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—42no—
321C22⋊C4×C61—41no—
322C22⋊C4×C61—41no—
323C22⋊C4×C61—81no—
324C42×C61—21no—
325C42×C61—21no—
326C42×C61—21no—
327C42×C61—41no—
328C42×C61—41no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—22no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—42no—
342C23×C61—81no—
343C23×C61—81no—
344C23×C61—81no—
345C23×C61—81no—
346C23×C61—81no—
347C23×C61#12011yescharacteristic
348C23×C61#12011yescharacteristic
349C23×C61C22×D411yescharacteristic
350Q8×C61—41no—
351Q8×C61—81no—
352D4×C61—41no—
353D4×C61—41no—
354D4×C61—41no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—42no—
362D4×C61—42no—
363D4×C61—81no—
364D4×C61—81no—
365D4×C61—81no—
366D4×C61—81no—
367D4×C61—81no—
368D4×C61—81no—
369D4×C61—81no—
370D4×C61—81no—
371D4×C61—81no—
372D4×C61—81no—
373D4×C61—81no—
374D4×C61—81no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
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—21no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
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—81no—
412C2×C4×C61—84no—
413C2×C4×C61#12011yescharacteristic
414C2×C4×C61#12011yescharacteristic
415C2×C4×C61C22×D411yescharacteristic
416C2×C4×C61C22×D411yescharacteristic
417C8×C61—41no—
418C8×C61—41no—
419C8×C61—41no—
420C8×C61—41no—
421#18262C6111yesmaximal, characteristic, direct product factor, Sylow
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—162no—
446C22×C61—162no—
447C22×C61#45812yes—
448C22×C61C2×#12011yescharacteristic
449C22×C61#57611yescharacteristic
450C22×C61#57711yescharacteristic
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—42no—
456C4×C61—41no—
457C4×C61—41no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—81no—
465C4×C61—81no—
466C4×C61—81no—
467#3534C2×C6111yescharacteristic
468#3094C2×C6111yescharacteristic, complemented
469#3091C2×C6111yescharacteristic, complemented
470#2498C2×C6111yescharacteristic, complemented
471#1618C2×C6111yescharacteristic, complemented
472#1616C2×C6111yescharacteristic, complemented
473#1615C2×C6111yescharacteristic, complemented
474#1613C2×C6111yescharacteristic, complemented
475#1612C2×C6111yescharacteristic, complemented
476#1610C2×C6111yescharacteristic, complemented
477#1609C2×C6111yescharacteristic, complemented
478#1607C2×C6111yescharacteristic, complemented
479#1504C2×C6111yescharacteristic, complemented
480C2×#327C2×C6111yescharacteristic, complemented
481#1468C2×C6111yescharacteristic, complemented
482C2×C61—21no—
483C2×C61—21no—
484C2×C61—22no—
485C2×C61—41no—
486C2×C61—81no—
487C2×C61—81no—
488C2×C61—81no—
489C2×C61—81no—
490C2×C61#301211yescharacteristic
491C2×C61#301811yescharacteristic
492C2×C61C2×#45811yescharacteristic
493#562—21no—
494#560—21no—
495#553—21no—
496#551—21no—
497#546—21no—
498#546—21no—
499#546—21no—
500D42—21no—
501#540—21no—
502#539—21no—
503#539C22×C6111yescharacteristic
504#538—21no—
505#538C22×C6111yescharacteristic
506#537C22×C6111yescharacteristic
507#534—21no—
508#534C22×C6111yescharacteristic
509#525C22×C6111yescharacteristic
510C2×#123C22×C6111yescharacteristic
511C2×#121C22×C6111yescharacteristic
512C2×#117C22×C6111yescharacteristic, complemented
513#485—21no—
514#484C22×C6111yescharacteristic, complemented
515#483C22×C6111yescharacteristic, complemented
516#482—21no—
517#482—21no—
518#482—21no—
519#481C22×C6111yescharacteristic
520#481C22×C6111yescharacteristic, complemented
521#481C22×C6111yescharacteristic, complemented
522#480C22×C6111yescharacteristic
523#480C22×C6111yescharacteristic, complemented
524#480C22×C6111yescharacteristic, complemented
525#428—21no—
526#427—21no—
527#418—21no—
528#416—21no—
529#407C22×C6111yescharacteristic, complemented
530C2×C22⋊C8C22×C6111yescharacteristic, complemented
531#400C22×C6111yescharacteristic, complemented
532#399C22×C6111yescharacteristic, complemented
533#398C22×C6111yescharacteristic, complemented
534#397C22×C6111yescharacteristic, complemented
535#388—21no—
536#387—21no—
537#386—21no—
538#380—21no—
539C2×#95C22×C6111yescharacteristic, complemented
540#328C22×C6111yescharacteristic, complemented
541#328C22×C6111yescharacteristic, complemented
542#327C22×C6111yescharacteristic
543#327C22×C6111yescharacteristic
544#327C22×C6111yescharacteristic, complemented
545#327C22×C6111yescharacteristic, complemented
546#327C22×C6111yescharacteristic, complemented
547#327C22×C6111yescharacteristic, complemented
548#324C22×C6111yescharacteristic, complemented
549#324C22×C6111yescharacteristic, complemented
550#323C22×C6111yescharacteristic, complemented
551#323C22×C6111yescharacteristic, complemented
552C61#1826211yescharacteristic, direct product factor, Sylow
553C2×#41—21no—
554C2×#41D4×C6111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C6111yescharacteristic
559C22×D4D4×C6111yescharacteristic
560C23×C4—21no—
561C23×C4C23×C6111yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C6111yescharacteristic
594C22⋊Q8C23×C6111yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C6111yescharacteristic
611#121D4×C6111yescharacteristic
612#121D4×C6111yescharacteristic
613#121C23×C6111yescharacteristic
614#121C23×C6111yescharacteristic
615#121C23×C6111yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C6111yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C6111yescharacteristic
641C2×C4⋊C4D4×C6111yescharacteristic
642C2×C4⋊C4C23×C6111yescharacteristic
643C2×C4⋊C4C23×C6111yescharacteristic
644C2×C4⋊C4C23×C6111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C6111yescharacteristic
652C2×C22⋊C4D4×C6111yescharacteristic
653C2×C22⋊C4C23×C6111yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—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#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C6111yescharacteristic
683#95C23×C6111yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C6111yescharacteristic
687C24C2×D4×C6111yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
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—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C6111yescharacteristic
718C2×D4C2×D4×C6111yescharacteristic
719C2×D4C2×D4×C6111yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C6111yescharacteristic
736C22×C4C2×D4×C6111yescharacteristic
737C22×C4C2×D4×C6111yescharacteristic
738C22×C4C2×D4×C6111yescharacteristic
739C22×C4C2×D4×C6111yescharacteristic
740C22×C4C2×D4×C6111yescharacteristic
741C22×C4C2×D4×C6111yescharacteristic
742C22×C4C2×D4×C6111yescharacteristic
743C22×C4C24×C6111yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
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—42no—
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—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C6111yescharacteristic
826C23#120×C6111yescharacteristic
827C23C22×D4×C6111yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
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—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C6111yescharacteristic
892C2×C4#120×C6111yescharacteristic
893C2×C4C22×D4×C6111yescharacteristic
894C2×C4C22×D4×C6111yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C61×#45812yes—
925C22C2×#120×C6111yescharacteristic
926C22C61×#57611yescharacteristic
927C22C61×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C61×#301211yescharacteristic
953C2C61×#301811yescharacteristic
954C2C2×C61×#45811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3534C2
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
2. C61×#3094C2semidirect
3. C61×#3091C2semidirect
4. C61×#2498C2semidirect
5. C61×#1618C2semidirect
6. C61×#1616C2semidirect
7. C61×#1615C2semidirect
8. C61×#1613C2semidirect
9. C61×#1612C2semidirect
10. C61×#1610C2semidirect
11. C61×#1609C2semidirect
12. C61×#1607C2semidirect
13. C61×#1504C2semidirect
14. C2×C61×#327C2semidirect
15. C61×#1468C2semidirect
35. C2×#117×C61C22semidirect
37. C61×#484C22semidirect
38. C61×#483C22semidirect
43. C61×#481C22semidirect
44. C61×#481C22semidirect
46. C61×#480C22semidirect
47. C61×#480C22semidirect
52. C61×#407C22semidirect
53. C2×C22⋊C8×C61C22semidirect
54. C61×#400C22semidirect
55. C61×#399C22semidirect
56. C61×#398C22semidirect
57. C61×#397C22semidirect
62. C2×#95×C61C22semidirect
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
421. #18262C61direct (N × H)
468. #3094C2×C61semidirect
469. #3091C2×C61semidirect
470. #2498C2×C61semidirect
471. #1618C2×C61semidirect
472. #1616C2×C61semidirect
473. #1615C2×C61semidirect
474. #1613C2×C61semidirect
475. #1612C2×C61semidirect
476. #1610C2×C61semidirect
477. #1609C2×C61semidirect
478. #1607C2×C61semidirect
479. #1504C2×C61semidirect
480. C2×#327C2×C61semidirect
481. #1468C2×C61semidirect
512. C2×#117C22×C61semidirect
514. #484C22×C61semidirect
515. #483C22×C61semidirect
520. #481C22×C61semidirect
521. #481C22×C61semidirect
523. #480C22×C61semidirect
524. #480C22×C61semidirect
529. #407C22×C61semidirect
530. C2×C22⋊C8C22×C61semidirect
531. #400C22×C61semidirect
532. #399C22×C61semidirect
533. #398C22×C61semidirect
534. #397C22×C61semidirect
539. C2×#95C22×C61semidirect
540. #328C22×C61semidirect
541. #328C22×C61semidirect
544. #327C22×C61semidirect
545. #327C22×C61semidirect
546. #327C22×C61semidirect
547. #327C22×C61semidirect
548. #324C22×C61semidirect
549. #324C22×C61semidirect
550. #323C22×C61semidirect
551. #323C22×C61semidirect
552. C61#18262direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35342
C61×#30942
C61×#30912
C61×#24982
C61×#16182
C61×#16162
C61×#16152
C61×#16132
C61×#16122
C61×#16102
C61×#16092
C61×#16072
C61×#15042
C2×C61×#3272
C61×#14682
#1826261