Finite Group Databasebeta

← C61×#18444 #29521877

Subgroups — C61×#18444 #29521877

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3560C211yesmaximal, characteristic
2C61×#3234C211yesmaximal, characteristic, complemented
3C61×#3232C211yesmaximal, characteristic, complemented
4C61×#2664C211yesmaximal, 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×#1509C211yesmaximal, characteristic, complemented
14C61×#1502C211yesmaximal, characteristic, complemented
15C61×#1473C211yesmaximal, characteristic, complemented
16C61×#563—21no—
17C61×#560—21no—
18C61×#553—21no—
19C61×#553—21no—
20C61×#551—21no—
21C61×#547—21no—
22C61×#546—21no—
23C61×#546—21no—
24C61×#542—21no—
25C61×#539—21no—
26C61×#539C2211yescharacteristic
27C61×#538—21no—
28C61×#538—21no—
29C61×#538C2211yescharacteristic
30C61×#537C2211yescharacteristic
31C61×#534C2211yescharacteristic
32C61×#532C2211yescharacteristic
33C61×#529C2211yescharacteristic
34C2×#126×C61C2211yescharacteristic
35C2×#125×C61C2211yescharacteristic, complemented
36C61×#501—21no—
37C61×#499—21no—
38C61×#490—21no—
39C61×#488—21no—
40C61×#484C2211yescharacteristic, complemented
41C61×#483C2211yescharacteristic, complemented
42C61×#481C2211yescharacteristic
43C61×#481C2211yescharacteristic
44C61×#481C2211yescharacteristic, complemented
45C61×#480C2211yescharacteristic
46C61×#480C2211yescharacteristic
47C61×#480C2211yescharacteristic, complemented
48C61×#479—21no—
49C61×#478—21no—
50C61×#478—21no—
51C61×#478—21no—
52C61×#432C2211yescharacteristic, complemented
53C61×#431C2211yescharacteristic, complemented
54C61×#400C2211yescharacteristic, complemented
55C61×#399C2211yescharacteristic
56C61×#398—21no—
57C61×#398C2211yescharacteristic, complemented
58C61×#397C2211yescharacteristic
59C61×#396—21no—
60C61×#389—21no—
61C61×#388—21no—
62C4×C4⋊C4×C61C2211yescharacteristic, complemented
63C61×#328C2211yescharacteristic, complemented
64C61×#328C2211yescharacteristic, complemented
65C61×#327C2211yescharacteristic
66C61×#327C2211yescharacteristic
67C61×#327C2211yescharacteristic
68C61×#327C2211yescharacteristic
69C61×#327C2211yescharacteristic, complemented
70C61×#327C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C22×D4×C61—21no—
78C4⋊Q8×C61—21no—
79C4⋊Q8×C61D411yescharacteristic
80#127×C61D411yescharacteristic
81#126×C61—21no—
82#126×C61—21no—
83#126×C61—21no—
84#126×C61—21no—
85#126×C61—21no—
86#126×C61—21no—
87#126×C61—21no—
88#126×C61—21no—
89#126×C61—21no—
90#125×C61—21no—
91#125×C61—21no—
92#125×C61—21no—
93#125×C61—21no—
94#125×C61—21no—
95#125×C61—21no—
96#125×C61D411yescharacteristic
97#124×C61—21no—
98#124×C61—21no—
99#124×C61—21no—
100#124×C61—21no—
101#124×C61D411yescharacteristic
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—
114C22⋊Q8×C61—21no—
115C22⋊Q8×C61—21no—
116C22⋊Q8×C61—21no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61C2311yescharacteristic
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×C61—21no—
133#121×C61—21no—
134#121×C61C2311yescharacteristic
135#121×C61C2311yescharacteristic
136#121×C61C2311yescharacteristic
137#120×C61—21no—
138#120×C61—21no—
139#120×C61—21no—
140#120×C61—21no—
141#120×C61—21no—
142C4×Q8×C61D411yescharacteristic
143C4×D4×C61—21no—
144C4×D4×C61—21no—
145C4×D4×C61—21no—
146C4×D4×C61—21no—
147C4×D4×C61—21no—
148C4×D4×C61—21no—
149C4×D4×C61—21no—
150C4×D4×C61—21no—
151C4×D4×C61D411yescharacteristic
152C4×D4×C61D411yescharacteristic
153C4×D4×C61D411yescharacteristic
154#117×C61—21no—
155#117×C61—21no—
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61—21no—
159C2×C4⋊C4×C61—21no—
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×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61C2311yescharacteristic
174C2×C42×C61—21no—
175C2×C42×C61C2311yescharacteristic
176#107×C61—21no—
177#107×C61—21no—
178#107×C61—21no—
179#107×C61—21no—
180#106×C61—21no—
181#106×C61—21no—
182#106×C61—21no—
183#106×C61—21no—
184C4⋊C8×C61—21no—
185C4⋊C8×C61—21no—
186#103×C61—21no—
187#103×C61—21no—
188#102×C61—21no—
189#102×C61—21no—
190#102×C61—21no—
191#102×C61—21no—
192#102×C61—21no—
193#102×C61—21no—
194C22⋊C8×C61C2311yescharacteristic
195C22⋊C8×C61C2311yescharacteristic
196C22⋊C8×C61C2311yescharacteristic
197C22⋊C8×C61C2311yescharacteristic
198#97×C61—21no—
199C4×C8×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×C61C2×D411yescharacteristic
208#41×C61—81no—
209#41×C61—81no—
210#41×C61—81no—
211#41×C61—81no—
212C2×Q8×C61—21no—
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—81no—
228C2×D4×C61—81no—
229C2×D4×C61C2×D411yescharacteristic
230C2×D4×C61C2×D411yescharacteristic
231C2×D4×C61C2×D411yescharacteristic
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2411yescharacteristic
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
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—42no—
276C4⋊C4×C61—42no—
277C4⋊C4×C61—41no—
278C4⋊C4×C61—41no—
279C4⋊C4×C61—41no—
280C4⋊C4×C61—41no—
281C4⋊C4×C61—81no—
282C4⋊C4×C61C2×D411yescharacteristic
283C4⋊C4×C61C2×D411yescharacteristic
284C4⋊C4×C61C2×D411yescharacteristic
285C4⋊C4×C61C2×D411yescharacteristic
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
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—42no—
312C22⋊C4×C61—81no—
313C42×C61—21no—
314C42×C61—21no—
315C42×C61—21no—
316C42×C61—81no—
317C42×C61C2×D411yescharacteristic
318C42×C61C2×D411yescharacteristic
319C42×C61C2×D411yescharacteristic
320C42×C61C2×D411yescharacteristic
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—81no—
330C23×C61—81no—
331C23×C61—81no—
332C23×C61C22×D411yescharacteristic
333Q8×C61—41no—
334Q8×C61—81no—
335Q8×C61—81no—
336D4×C61—41no—
337D4×C61—41no—
338D4×C61—41no—
339D4×C61—41no—
340D4×C61—41no—
341D4×C61—41no—
342D4×C61—41no—
343D4×C61—41no—
344D4×C61—41no—
345D4×C61—81no—
346D4×C61—81no—
347D4×C61—81no—
348D4×C61—81no—
349D4×C61—81no—
350D4×C61—81no—
351D4×C61—81no—
352D4×C61—81no—
353D4×C61—81no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—22no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—81no—
383C2×C4×C61—81no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
386C2×C4×C61—81no—
387C2×C4×C61—81no—
388C2×C4×C61—81no—
389C2×C4×C61—81no—
390C2×C4×C61#12011yescharacteristic
391C2×C4×C61#12011yescharacteristic
392C2×C4×C61#12011yescharacteristic
393C2×C4×C61#12011yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C8×C61—41no—
397C8×C61—41no—
398C8×C61—41no—
399C8×C61—41no—
400#18444C6111yesmaximal, characteristic, direct product factor, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—81no—
416C22×C61—81no—
417C22×C61—162no—
418C22×C61C2×#12011yescharacteristic
419C22×C61#57611yescharacteristic
420C22×C61#57711yescharacteristic
421C4×C61—21no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—42no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61—81no—
437C4×C61—81no—
438C4×C61—81no—
439#3560C2×C6111yescharacteristic
440#3234C2×C6111yescharacteristic, complemented
441#3232C2×C6111yescharacteristic, complemented
442#2664C2×C6111yescharacteristic, complemented
443#1618C2×C6111yescharacteristic, complemented
444#1616C2×C6111yescharacteristic, complemented
445#1615C2×C6111yescharacteristic, complemented
446#1613C2×C6111yescharacteristic, complemented
447#1612C2×C6111yescharacteristic, complemented
448#1610C2×C6111yescharacteristic, complemented
449#1609C2×C6111yescharacteristic, complemented
450#1607C2×C6111yescharacteristic, complemented
451#1509C2×C6111yescharacteristic, complemented
452#1502C2×C6111yescharacteristic, complemented
453#1473C2×C6111yescharacteristic, complemented
454C2×C61—21no—
455C2×C61—21no—
456C2×C61—81no—
457C2×C61—81no—
458C2×C61—81no—
459C2×C61—81no—
460C2×C61#301211yescharacteristic
461C2×C61#301811yescharacteristic
462C2×C61#302811yescharacteristic
463#563—21no—
464#560—21no—
465#553—21no—
466#553—21no—
467#551—21no—
468#547—21no—
469#546—21no—
470#546—21no—
471#542—21no—
472#539—21no—
473#539C22×C6111yescharacteristic
474#538—21no—
475#538—21no—
476#538C22×C6111yescharacteristic
477#537C22×C6111yescharacteristic
478#534C22×C6111yescharacteristic
479#532C22×C6111yescharacteristic
480#529C22×C6111yescharacteristic
481C2×#126C22×C6111yescharacteristic
482C2×#125C22×C6111yescharacteristic, complemented
483#501—21no—
484#499—21no—
485#490—21no—
486#488—21no—
487#484C22×C6111yescharacteristic, complemented
488#483C22×C6111yescharacteristic, complemented
489#481C22×C6111yescharacteristic
490#481C22×C6111yescharacteristic
491#481C22×C6111yescharacteristic, complemented
492#480C22×C6111yescharacteristic
493#480C22×C6111yescharacteristic
494#480C22×C6111yescharacteristic, complemented
495#479—21no—
496#478—21no—
497#478—21no—
498#478—21no—
499#432C22×C6111yescharacteristic, complemented
500#431C22×C6111yescharacteristic, complemented
501#400C22×C6111yescharacteristic, complemented
502#399C22×C6111yescharacteristic
503#398—21no—
504#398C22×C6111yescharacteristic, complemented
505#397C22×C6111yescharacteristic
506#396—21no—
507#389—21no—
508#388—21no—
509C4×C4⋊C4C22×C6111yescharacteristic, complemented
510#328C22×C6111yescharacteristic, complemented
511#328C22×C6111yescharacteristic, complemented
512#327C22×C6111yescharacteristic
513#327C22×C6111yescharacteristic
514#327C22×C6111yescharacteristic
515#327C22×C6111yescharacteristic
516#327C22×C6111yescharacteristic, complemented
517#327C22×C6111yescharacteristic, complemented
518#324C22×C6111yescharacteristic, complemented
519#324C22×C6111yescharacteristic, complemented
520#323C22×C6111yescharacteristic
521#323C22×C6111yescharacteristic
522C61#1844411yescharacteristic, direct product factor, Sylow
523C2×#41—21no—
524C2×#41—21no—
525C22×D4—21no—
526C4⋊Q8—21no—
527C4⋊Q8D4×C6111yescharacteristic
528#127D4×C6111yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#125—21no—
539#125—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125D4×C6111yescharacteristic
545#124—21no—
546#124—21no—
547#124—21no—
548#124—21no—
549#124D4×C6111yescharacteristic
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8C23×C6111yescharacteristic
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121C23×C6111yescharacteristic
583#121C23×C6111yescharacteristic
584#121C23×C6111yescharacteristic
585#120—21no—
586#120—21no—
587#120—21no—
588#120—21no—
589#120—21no—
590C4×Q8D4×C6111yescharacteristic
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4D4×C6111yescharacteristic
600C4×D4D4×C6111yescharacteristic
601C4×D4D4×C6111yescharacteristic
602#117—21no—
603#117—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C6111yescharacteristic
611C2×C4⋊C4D4×C6111yescharacteristic
612C2×C4⋊C4C23×C6111yescharacteristic
613C2×C4⋊C4C23×C6111yescharacteristic
614C2×C4⋊C4C23×C6111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4D4×C6111yescharacteristic
620C2×C22⋊C4D4×C6111yescharacteristic
621C2×C22⋊C4C23×C6111yescharacteristic
622C2×C42—21no—
623C2×C42C23×C6111yescharacteristic
624#107—21no—
625#107—21no—
626#107—21no—
627#107—21no—
628#106—21no—
629#106—21no—
630#106—21no—
631#106—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8C23×C6111yescharacteristic
643C22⋊C8C23×C6111yescharacteristic
644C22⋊C8C23×C6111yescharacteristic
645C22⋊C8C23×C6111yescharacteristic
646#97—21no—
647C4×C8—21no—
648#95—21no—
649#95—21no—
650#95—21no—
651#95—21no—
652#95C23×C6111yescharacteristic
653#95C23×C6111yescharacteristic
654C24—21no—
655C24C2×D4×C6111yescharacteristic
656#41—81no—
657#41—81no—
658#41—81no—
659#41—81no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C6111yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C6111yescharacteristic
678C2×D4C2×D4×C6111yescharacteristic
679C2×D4C2×D4×C6111yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C2×D4×C6111yescharacteristic
693C22×C4C2×D4×C6111yescharacteristic
694C22×C4C2×D4×C6111yescharacteristic
695C22×C4C2×D4×C6111yescharacteristic
696C22×C4C2×D4×C6111yescharacteristic
697C22×C4C24×C6111yescharacteristic
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—41no—
729C4⋊C4—81no—
730C4⋊C4C2×D4×C6111yescharacteristic
731C4⋊C4C2×D4×C6111yescharacteristic
732C4⋊C4C2×D4×C6111yescharacteristic
733C4⋊C4C2×D4×C6111yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—42no—
760C22⋊C4—81no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—81no—
765C42C2×D4×C6111yescharacteristic
766C42C2×D4×C6111yescharacteristic
767C42C2×D4×C6111yescharacteristic
768C42C2×D4×C6111yescharacteristic
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—41no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23C22×D4×C6111yescharacteristic
781Q8—41no—
782Q8—81no—
783Q8—81no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—81no—
794D4—81no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4#120×C6111yescharacteristic
839C2×C4#120×C6111yescharacteristic
840C2×C4#120×C6111yescharacteristic
841C2×C4#120×C6111yescharacteristic
842C2×C4C22×D4×C6111yescharacteristic
843C2×C4C22×D4×C6111yescharacteristic
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C22—21no—
849C22—21no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22C2×#120×C6111yescharacteristic
866C22C61×#57611yescharacteristic
867C22C61×#57711yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—21no—
887C2—21no—
888C2—81no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2C61×#301211yescharacteristic
893C2C61×#301811yescharacteristic
894C2C61×#302811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3560C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3234C2semidirect
3. C61×#3232C2semidirect
4. C61×#2664C2semidirect
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×#1509C2semidirect
14. C61×#1502C2semidirect
15. C61×#1473C2semidirect
35. C2×#125×C61C22semidirect
40. C61×#484C22semidirect
41. C61×#483C22semidirect
44. C61×#481C22semidirect
47. C61×#480C22semidirect
52. C61×#432C22semidirect
53. C61×#431C22semidirect
54. C61×#400C22semidirect
57. C61×#398C22semidirect
62. C4×C4⋊C4×C61C22semidirect
63. C61×#328C22semidirect
64. C61×#328C22semidirect
69. C61×#327C22semidirect
70. C61×#327C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
400. #18444C61direct (N × H)
440. #3234C2×C61semidirect
441. #3232C2×C61semidirect
442. #2664C2×C61semidirect
443. #1618C2×C61semidirect
444. #1616C2×C61semidirect
445. #1615C2×C61semidirect
446. #1613C2×C61semidirect
447. #1612C2×C61semidirect
448. #1610C2×C61semidirect
449. #1609C2×C61semidirect
450. #1607C2×C61semidirect
451. #1509C2×C61semidirect
452. #1502C2×C61semidirect
453. #1473C2×C61semidirect
482. C2×#125C22×C61semidirect
487. #484C22×C61semidirect
488. #483C22×C61semidirect
491. #481C22×C61semidirect
494. #480C22×C61semidirect
499. #432C22×C61semidirect
500. #431C22×C61semidirect
501. #400C22×C61semidirect
504. #398C22×C61semidirect
509. C4×C4⋊C4C22×C61semidirect
510. #328C22×C61semidirect
511. #328C22×C61semidirect
516. #327C22×C61semidirect
517. #327C22×C61semidirect
518. #324C22×C61semidirect
519. #324C22×C61semidirect
522. C61#18444direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35602
C61×#32342
C61×#32322
C61×#26642
C61×#16182
C61×#16162
C61×#16152
C61×#16132
C61×#16122
C61×#16102
C61×#16092
C61×#16072
C61×#15092
C61×#15022
C61×#14732
#1844461